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Directed cell growth and alignment on protein-patterned 3D hydrogels with stereolithography

Directed cell growth and alignment on protein-patterned3D hydrogels with stereolithographyVincent Chan a,d $,Mitchell B.Collens a,d $,Jae Hyun Jeong b ,Kidong Park c,d ,Hyunjoon Kong b and Rashid Bashir a,c,d *aDepartment of Bioengineering,University of Illinois at Urbana-Champaign,Urbana,Illinois,61801,USA bDepartment of Chemical and Biomolecular Engineering,University of Illinois at Urbana-Champaign,Urbana,Illinois,61801,USAcDepartment of Electrical and Computer Engineering,University of Illinois at Urbana-Champaign,Urbana,Illinois,61801,USAdMicro and Nanotechnology Laboratory,University of Illinois at Urbana-Champaign,Urbana,Illinois,61801,USA(Received 2July 2012;ﬁnal version received 3July 2012)The stereolithography apparatus (SLA)is a computer-assisted,three-dimensional (3D)printing system that is gaining attention in the medical field for the fabrication of patient-specific prosthetics and implants.An attractive class of implantable biomaterials for the SLA is photopolymerisable hydrogels because of their resemblance to soft tissues and intrinsic support of living cells.However,most laser-based SLA machines lack the minimum feature size required to imitate cell growth and alignment patterns in complex tissue architecture.In this study,we demonstrate a simple method for aligning cells on 3D hydrogels by combining the micro-contact printing (m CP)technique with the stereolitho-graphic process.Fibronectin modified with acrylate groups was printed on glass coverslips with unpatterned,10,50,and 100m m wide line patterns,which were then transferred to hydrogels through chemical linkages during photopolymerisation.Fibroblasts cultured on protein-printed 3D hydrogels aligned in the direction of the patterns,as confirmed by fast Fourier transform and cell morphometrics.Keywords:stereolithography;micro-contact printing;hydrogels;cell alignment1.IntroductionThe stereolithography apparatus (SLA)is a computer-assisted,three-dimensional (3D)printing system used for creating complex structures from photopolymerisable resins (Jacobs 1992).Traditionally,it is a manufacturing technique intended to produce 3D models and prototypes,but practi-tioners in the medical field have embraced it as a way to develop custom end-use parts and preoperative surgical plans (Barker et al .1994,Winder and Bibb 2005).The SLA and other 3D printing platforms have greatly improved theperformance and fit of prosthetics and implants in combina-tion with computed tomography (CT)or magnetic reso-nance imaging (MRI)technologies (Melchels et al .2012).Fabricated parts from the SLA have been implanted as scaffolding for bone ingrowth (Cooke et al.2003,Seitz et al.2005),moulds for breast reconstruction (Melchels et al .2011),replicas for aortic heart valves (Sodian et al.2002),and shells for ‘in-the-ear’hearing aids.In the past few years,photopolymerisable hydrogels have been explored in the SLA as a potential class of implantable,*Corresponding author.Email:rbashir@ $Both authors contributed equally for this study.Virtual and Physical Prototyping 2012,1Á10,iFirstarticleVirtual and Physical PrototypingISSN 1745-2759print/ISSN 1745-2767online #2012Taylor &Francis/10.1080/17452759.2012.709423soft materials(Melchels et al.2010).Hydrogels,which are networks of cross-linked polymers that imbibe large amounts of water,can be used directly with living cells as a synthetic extracellular matrix(ECM)analog for providing a variety of physical,chemical,and biological cues(Nguyen and West2002,Ifkovits and Burdick2007,Tibbitt and Anseth2009,Jabbari2011).In contrast to stiff2D substrates made of polystyrene or glass,hydrogels possess3D archi-tecture and have tunable elasticity similar to tissues and organs.Cell attachment(Nguyen and West2002,Hadjipa-nayi et al.2009,Guillame-Gentil et al.2010),spreading (Wong et al.2004,Discher et al.2005,Bott et al.2010), communication(Reinhart-King et al.2008,Geiger et al. 2009,Buxboim et al.2010),and differentiation of stem cells (Discher et al.2005,Engler et al.2006,Vogel and Sheetz 2006)are a few of the physical effects of matrix elasticity. Poly(ethylene glycol)diacrylate(PEGDA)is the most commonly used photopolymerisable hydrogel in the SLA. Using the working curve equation(Jacobs1992),PEGDA with varying molecular weights was characterised for building complex3D structures(Arcaute et al.2006).Living cells encapsulated in PEGDA(]M W1,000g×mol(1) survived the stereolithographic process and remained viable within the hydrogel for up to two weeks(Chan et al.2010). Integrating living cells with PEGDA hydrogels patterned in the SLA offers exciting new possibilities for tissue engineer-ing and the development of cellular systems.For example, the SLA was used to examine cell interactions of co-cultures, such as neurons and muscle cells,encapsulated in discrete spatial locales in the same3D construct(Zorlutuna et al. 2011).In another example,geometric patterns of hydrogels defined in the SLA were used to localise gradients of angiogenic growth factors secreted by encapsulated fibro-blasts.When implanted in vivo on a vascular membrane,new blood vessels sprouted on the membrane in the same pattern as the hydrogel(Jeong et al.2012).Furthermore,the SLA was modified for applications using multiple materials,such as hydrogel cantilevers and actuators that mimic the elasticity of the native myocardium for contractile muscle cells(Chan et al.2012).Despite recent progress,the SLA is limited to minimum feature sizes that are dependent on the diameter of the laser mercial SLA systems utilise gas or solid-state lasers that have a spot size between75and250m m.This limits the ability of researchers interested in creating patterns that control cell growth and alignment to imitate the in vivo tissue architecture.Distinct patterns are seen throughout the body,such as complex neural networks in the brain and linear arrangement of muscle cells around the myocardium(McDevitt et al.2002).Protein immobilisation for patterning has been shown on and in hydrogels(Khetan and Burdick2011)using thiol chemistry and two-photon irradiation(Lee et al.2008,West2011),and photolitho-graphy.Additionally,cell patterning has been shown mechanically by creating grooves(Charest et al.2006, Park et al.2006,Kim et al.2007,Aubin et al.2010), microchannels(Sarig-Nadir et al.2009),and geometric restrictions(Parker et al.2002,Aubin et al.2010);however, these methods can alter material properties and mechanics which are important to maintain for specific applications. In this current study,we exploited the cells’dependence on ECM molecules to control their growth,organisation, and distribution.Specifically,we have developed a simple method to align cells on structures fabricated using the SLA by first stamping polydimethylsiloxane(PDMS)patterns of acryl-fibronectin with micro-contact printing(m CP)and transferring the patterns to hydrogels fabricated in the SLA. This technique can then be used to align living cells on3D hydrogel geometries,including neurons,muscle cells,and endothelial cells.From a biological perspective,the elastic properties of hydrogels combined with the ability to align cells allows for realistic in vitro models for understanding the biology of cell development,organisation,and disease. From an engineering perspective,using the SLA to create geometrically-defined,biohybrid constructs generates ex-emplary new applications in tissue engineering,regenerative medicine,synthetic biology,and cellular machines.2.Materials and methods2.1Preparation of PDMS stampMaster moulds for the PDMS stamps were fabricated on a silicon wafer with SU-8negative photoresist following a standard procedure(Chen et al.1998,Kane et al.1999).The master moulds contained patterns of10,50,and100m m wide lines with equal spacing.The height of each pattern was 5m m.The patterned master moulds were silanised with (tridecafluoro-1,1,2,2-tetrahydrooctyl)-1-trichlorosilane in vacuum for1hour.PDMS(Dow Corning Sylgard184 Silicone Elastomer Kit)was weighed out at a10:1ratio of polymer-to-curing agent(heat activated).The materials were thoroughly mixed for3minutes to ensure even distribution of the curing agent and poured onto the patterned master moulds.Samples were placed in a desiccator,pulled under vacuum,and baked at808C overnight.2.2Preparation of fibronectin and acryl-fibronectin ink Fibronectin from bovine plasma solution(Sigma Aldrich, St.Louis,MO,USA)was diluted in phosphate buffer solution(PBS)to a concentration of50m g mL(1.For acryl-fibronectin ink,monoacrylated poly(ethylene glycol)-N-hydroxysuccinimide(acryl-PEG-NHS,M W3500 g×mol(1,JenKem Technology,Allen,TX,USA)was dissolved in PBS at a concentration of30mg mL(1.A working solution of acryl-fibronectin ink was prepared by mixing acryl-PEG-NHS with fibronectin at a2:1molar ratio2V.Chan et al.of acrylate-to-lysine.Acryl-PEG-NHS reacts spontaneously with primary amines on the fibronectin and releases N-hydroxysuccinimide to form a covalent bond.The reaction was allowed to proceed for30minutes at48C.2.3Micro-contact printing ink on glass coverslipsGlass coverslips were patterned by m CP(Chen et al.1998, Kane et al.1999)using clean PDMS stamps.Fibronectin and acryl-fibronectin ink(50m g mL(1)were coated onto PDMS stamps for one hour at378C.After incubation, excess ink was aspirated and dried under a stream of N2. Stamps were placed pattern-side down onto18mm2glass coverslips.Pressure was applied for30s to allow adsorption of ink to the glass,and the coverslips were incubated for 45minutes.Stamps were removed,and the coverslips were used within one hour.2.4Preparation of hydrogel pre-polymer solution Hydrogel pre-polymer solutions were prepared by dissol-ving20%poly(ethylene glycol)diacrylate(PEGDA,M W 3400g×mol(1,Laysan Bio,Arab,AL USA)in PBS. The photoinitiator,1-[4-(2-hydroxyethoxy)-phenyl]-2-hy-droxy-2-methyl-1-propane-1-one(Irgacure2959,Ciba, Basel,Switzerland),was diluted to a50%(w/v)stock solution in dimethyl sulfoxide(DMSO,Fisher Scientific).A final concentration of0.5%(w/v)was added to the pre-polymer solution.All materials were prepared immediately before photopolymerisation in the SLA.2.5Fabrication of photopolymerisable hydrogelsHydrogel constructs were fabricated with a modified stereolithography apparatus(SLA250/50,3D Systems, Rock Hill,SC)(Chan et al.2010).Cylindrical disks (5mm radius)were designed in AutoCAD2012(Autodesk, San Rafael,CA USA)and prepared in3D Lightyear v1.4 software(3D Systems,Rock Hill,SC)for cross-sectional slicing into2D layers.Parameters were specified based on desired layer thickness.An18mm2glass coverslip with unpatterned and patterned lines of fibronectin or acryl-fibronectin ink10,50,or100m m wide was fixed to a35mm polystyrene dish with double-sided tape.Surfaces with no patterns were always used as controls.The dish was coated with hydrogel pre-polymer solution at a characterised volume determined by desired layer thickness.It was positioned at the centre of the SLA platform and photo-polymerised with a characterised energy dose of150mJ cm(2.After photopolymerisation,disks were rinsed in PBS and allowed to swell overnight before cell seeding.2.6Cell cultureNIH/3T3mouse embryonic fibroblasts(ATCC,Manassas, V A USA)were cultured at378C and5%CO2in Dulbecco’s modified Eagle medium(DMEM,Cellgro,Manassas,V A USA)supplemented with10%foetal bovine serum(FBS, Sigma-Aldrich,St.Louis,MO USA),100IU penicillin,and 100m g ml(1streptomycin(Gibco,Carlsbad,CA USA). Cells were passaged no more than10times using0.25% trypsin and0.04%ethylenediaminetetraacetic acid(EDTA) in Hank’s balanced salt solution(HBSS)(Gibco,Carlsbad, CA USA).Prior to cell seeding,hydrogel constructs were positioned in12-well plates with fibronectin and acryl-fibronectin patterns facing up.Cells were then seeded at a density of90,000cells cm(2over the hydrogels.2.7Fluorescence immunostainingTo verify fibronectin transfer from patterned glass slides to hydrogels,monoclonal anti-fibronectin produced in mouse (Sigma-Aldrich,St.Louis,MO USA)was diluted at1:300in PBS and added to the samples overnight at48C.The solution was then aspirated and rinsed three times with PBS. Alexa Fluor488goat anti-mouse IgG(Life Technologies, Grand Island,NY USA)was diluted at1:1000in PBS and added for2hours at378C.After rinsing three times with PBS,the samples were imaged with an inverted fluorescence microscope(IX81,Olympus,Center Valley,PA USA).To visualise the morphology of fibroblasts on hydrogel constructs,the cells were fixed and labelled at different time points.For fixation,samples were rinsed with PBS and incubated in4%paraformaldehyde(PFA,Sigma-Aldrich, St.Louis,MO USA)for30minutes.After rinsing three times with PBS,a solution of3,3?-dihexyloxacarbocyanine iodide(DiOC6,Life Technologies)was added at1:1000 dilution in PBS to stain for a cell’s endoplasmic reticulum, vesicle membranes,and mitochondria.Samples were then permeabilised with0.1%Triton X-100(Sigma Aldrich)for 10minutes and blocked with2.5%bovine serum albumin (BSA)in PBS to prevent non-specific binding.Cell nuclei were stained with a1:1000dilution of2-(4-amidinophenyl)-1H-indole-6-carboxamidine(DAPI,Life Technologies), and actin was stained with a1:1000dilution of rhodamine phalloidin(BD Biosciences).Fluorescent images were taken with the inverted fluorescence microscope.2.8Fibronectin and acryl-fibronectin transfer to hydrogels Image J software(Abramoff et al.2004)was used for analysis of fibronectin,acryl-fibronectin,and cell alignment patterns.Transfer of fibronectin and acryl-fibronectin from glass coverslips to hydrogels were confirmed quantitatively by measuring the pixel intensity of fluorescent images. To calculate pixel intensity values,a line profile was drawn3Virtual and Physical Prototypingacross the image and grey values were extracted at each point on the line.To determine the integrity and resolution of patterns,line width measurements of m CP glass cover-slips and patterned hydrogels were taken.The line profile tool was used to draw horizontal lines perpendicular to patterned lines on40x images,and the measured line widths were recorded.2.9Fast Fourier transform analysisFast Fourier transform(FFT)image processing analysis was previously demonstrated for cell patterning on hydro-gels(Millet et al.2011).Briefly,Image J software was used to enhance image contrast,subtract the background,and filter noise from the image.Images were converted to the frequency domain by FFT transformation and rotated908 to account for the inherent rotation that occurs during transformation.A circle was drawn over the FFT image, and the oval profile plugin was used to radially sum pixel intensities around the circle.A power spectrum was generated based on radially summated values,with 08correlating to frequencies at3o’clock,908at12o’clock, 1808at9o’clock,and2708at6o’clock.2.10Cell morphometrics analysisThe effect of patterning at the cellular level was analysed by observing changes in cell shape,direction of cell elongation, and orientation of nuclei.Post-image processing,a thresh-old was applied to make a binary image and individual cells were identified.Image J software object tools were used to measure and compare the cell circularity and nuclear orientation.Ten circularity bins of0.1intervals were set up,and circularity values between0and1were placed in each bin(0being a line and1being a circle).Significance was verified with a Student’s t-test statistical analysis. Nuclear orientation was measured by using the‘analyse particles’tool to fit an ellipse to threshold images of DAPI-stained nuclei and measuring the angle of the ellipse. Direction and length of cell elongation was determined by measuring the angle and distance from the nucleus to the furthest edge of the actin stained cell.3.Results3.1Fibronectin transfer and pattern retentionTo create patterns of proteins on3D hydrogel constructs, we modified fibronectin molecules with chemically linkable acrylate groups for crosslinking to the backbone of PEGDA hydrogels during photopolymerisation.This sim-ple concept allowed us to utilise the m CP technique to pattern acryl-fibronectin onto hydrogels prepared with the SLA(Figure1).We confirmed the transfer of acryl-fibronectin from glass coverslips to hydrogels by quantita-tive analysis of immunofluorescence parison of hydrogels built on glass coverslips with fibronectin (Figure2A)and acryl-fibronectin(Figure2B)showed that acryl-fibronectin successfully transferred from the glass coverslip to PEGDA(M W3400g×mol(1)hydrogels. The average pixel intensity of acryl-fibronectin on hydrogels was measured at129910.9,while fibronectin on hydrogels had an average pixel intensity of2.690.5(Figure2C). Patterned line widths of10,50,and100m m on glass coverslips and hydrogels were measured to verify pattern integrity after acryl-fibronectin transfer.Figure3shows fluorescent images of patterned lines on glass coverslips and hydrogels.The actual line widths were11.590.4m m, 49.191.8m m,and98.790.60m m,respectively,after PDMS stamping on glass coverslips(Figure3A),and 13.490.5m m,57.390.6m m,110.595.8m m,respectively, after acryl-fibronectin transfer to the3D hydrogel con-structs(Figure3B).Fibronectin transfer did not occur without acrylate groups(Figure3C).It is well-known that PEGDA(M W3400g×mol(1)swells after photopolymerisa-tion and subsequent washing in PBS.This phenomenon caused the measured line widths on the hydrogels to be greater than those on the glass coverslip(Figure3D). However,the average pixel intensity of fluorescently-labelled acryl-fibronectin patterns on hydrogels did not appear to decrease significantly to the extent that it would affect cell alignment.3.2Cell growth and alignment on hydrogelsNIH/3T3mouse embryonic fibroblasts were cultured on3D hydrogel constructs with acryl-fibronectin patterns of un-patterned,10,50,and100m m wide lines to demonstrate feasibility of cell alignment.The cells rapidly adhered to and began to spread on the line patterns after one hour in culture.Within24hours,the cells were activated to proliferate along the line patterns.Figure4A shows that the cells recognised the acryl-fibronectin patterns and aligned parallel to the lines.As the line spacing decrea-sed from100to10m m,the number of cells that bridged patterned lines increased.Regardless of cell bridging,the cells continued to align parallel to the lines.It was evident from the fluorescent images that as line width patterns decreased,alignment of individual cells increased.This was confirmed quantitatively with fast Fourier transform analysis(Figure4B).Conversion of images to the frequency domain revealed directed fibroblast growth and linear pattern formation.Distinct peaks were seen in the power spectrum of fibroblasts grown on patterned lines of all widths at08and1808.Fibroblasts grown on unpatterned hydrogels lacked these peaks and had more uniformly-scattered spectrums.Furthermore,as4V.Chan et al.the line widths increased,the peaks also decreased,and the spectrums were more scattered.Cell morphometrics were used to examine the individual shape of cells on patterned and unpatterned 3D hydrogel constructs.Growth of cells along the patterned lines altered their shape,making them more linear.Figure 4C shows the decreasing shift of cell circularity measurements between patterned and unpatterned cells.Average circularity was significantly different (Student ’s t-test,P -values 01.97E-25and 4.83E-25for 10and 50m m lines,respectively)between unpatterned fibroblasts (0.4190.22)and fibroblasts re-stricted to growth on 10m m (0.1590.10)and 50m m (0.1590.11)lines.Cell shape was altered on 100m m lines but was not statistically significant.Figure 5shows further analysis of the effect of acryl-fibronectin patterns on cell shape and growth.Fibroblastelongation,which was measured from the furthest edge of stained actin on each side of the cell to the nucleus,was parallel to line direction.Average angles were 90.98,88.98,and 89.98for 10,50,and 100m m lines,respectively.Unpatterned fibroblasts had an average angle of 95.48which was significantly different than patterned fibroblasts (Student ’s t-test,P -values 04.6E-2, 4.9E-3,and 8.6E-4,respectively).Standard deviations of the average angles were 13.08,27.38,and 48.08for 10,50,and 100m m lines,respectively.Length of elongation caused by patterning showed a significantly greater difference.The average length of extended actin in the cell was 44.33m m for unpatterned fibroblasts.Patterned cells had average lengths of 78.8,54.9,and 40.6m m for 10,50,and 100m m lines,respec-tively (Student ’s t-test,P -values 09.16E-18,6.78E-08,and 2.05E-4).The scatter plot in Figure 5AdemonstratesFigure 1.Patterning acryl-ﬁbronectin hydrogels.(1)Silicon wafers were coated with 5m m of SU-8photoresist.(2)Line patterns were formed after exposure of photoresist and silicon with UV light through a chrome mask.(3)PDMS was poured over the silicon master and polymerised by baking.A negative of the pattern from the silicon master was imprinted on the surface of the PDMS making a stamp.(4)An ink solution containing acryl-ﬁbronectin was pipetted onto the PDMS stamp.Acrylic ﬁbronectin was made by mixing acryl-PEG-NHS and ﬁbronectin in PBS and allowing the PEGDA cross-linker to attach to free lysine groups in ﬁbronectin.(5)After stamps were incubated with ink,line patterns were transferred to glass slides by stamping.(6)Pre-polymer solution of PEGDA (M W 3400)and a photoactivator is poured into a dish over patterned glass slides.(7)The dish containing pre-polymer and patterned glass is put into the stereolithography apparatus (SLA)and polymerised to form a hydrogel.(8)3D structures were built layer-by-layer adding additional pre-polymer before cross-linking.(9)Hydrogels were inverted and seeded with cells.During building of the ﬁrst layer,acryl-ﬁbronectin was transferred to the surface of the hydrogel allowing for cell attachment.5Virtual and Physical Prototypingclustering of the cell elongation around 908for cells grown on patterns,while the standard deviation plot in Figure 5B shows that the spread of those angles is much smaller with narrower line widths.4.DiscussionApplications for the SLA and other 3D printing platforms using living cells and cell-instructive 3D microenvironments are expanding rapidly.However,none of these enabling technologies are without their drawbacks,and continual development is needed to accommodate the growing number of applications.One of the current limitations ofcommercial laser-based stereolithographic systems is the minimum feature size required to imitate cell growth and alignment patterns in complex tissue architecture.While photopolymerisable hydrogels can be functionalised with proteins and peptides to enhance cell attachment,it is difficult to pattern them with the SLA at length scales comparable to the cell size.Grooves,microchannels,and other geometrically-restrictive techniques that affect the topology of the hydrogels can alter mechanical properties,which are important in many of these applications.There-fore,micro-contact printing (m CP)offers the capability of directing cell alignment on hydrogel structures without compromising the benefit of creating complex 3D architec-tures with the SLA.For example,3D hydrogelcantileversFigure 2.Measuring the transfer of ﬁbronectin and acryl-ﬁbronectin on hydrogels.Hydrogels were fabricated on glass slides with ﬂuorescently-labelled ﬁbronectin and acryl-ﬁbronectin.(A)Fluorescent image of a hydrogel fabricated on a glass slide with ﬁbronectin.(B)Fluorescent image of a hydrogel built on a slide with acryl-ﬁbronectin.(C)Using Image J software,ﬂuorescent intensity of ﬁbronectin and acryl-ﬁbronectin images were extracted and compared.Hydrogels with ﬁbronectin had an average intensity of 2.6,while those with acryl-ﬁbronectin had an average intensity of 129.9.This con ﬁrmed that acryl-ﬁbronectin chemically cross-linked ﬁbronectin to the hydrogels.6V .Chan et al .fabricated with the SLA can be protein-patterned using our m CP method to align cardiomyocytes for improved actua-tion force (Chan et al.2012).Micro-contact printing (m CP)is a well-established tech-nique that does not affect the mechanical properties of hydrogels.It was chosen to pattern acryl-fibronectin in combination with the SLA based on its ease of use,compatible setup,and unrestricted variation in shapes and sizes.Modification of fibronectin with acrylate groups (acryl-fibronectin)was the key component to this method.Without tethered ECM proteins or peptides,PEGDA hydrogels are intrinsically resistant to protein adsorption and cell adhesion.Based on low measured fluorescent intensity,unmodified fibronectin did not transfer to the PEGDA hydrogels (Figure 2A).In contrast,acryl-fibronectin had uniform and high fluorescent intensity throughout the surface of the hydrogels (Figure 2B).This method is not restricted to fibronectin;other proteins or peptides with free lysine (-NH 3)groups,such as laminin,collagen,and gelatin,can also be modified with acrylate groups using the same method described.PEGDA was chosen as the hydrogel material based on its tunable swelling ratio,elastic modulus,and mesh size.It can also be modified for cell-specific adhesion,enzyme-sensitive or hydrolytic degradation,and growth factor-binding signals (Zhu 2010).The swelling ratio and mesh size should be large enough to allow for an adequate supply of oxygen and nutrients,while the elastic modulus and patterning resolution should be high enough for the specific applica-tion.Figure 3,which compared the measured line widths on glass coverslips and hydrogels,shows a decrease in the patterning resolution on the PEGDA (M W 3400g ×mol (1)hydrogels.By decreasing the M W of PEGDA,the patterning resolution can be improved because of the reduced swelling,but this can also affect the organisation and function of cells on the hydrogels.Although a variety of other configurations are possible,we used line patterns to demonstrate directed cell growth and alignment on the hydrogels.The widths of those line patterns were varied to determine the length scale at which cells would align on the hydrogels.If widths are too thin,cell bodies may be larger than the lines,preventing appropriate cell attachment;if widths are too wide,cells may not recognise the patterns and align to them (Dike et al.1999).Previous findings show that individual cells can recognise lines measuring 5Á100m m wide (Kaji et al.2003).Trends in our data support these findings,with single cells patterning to 10Á50m m wide lines and multiple cells patterning to 100m m wide lines.In addition,a reduction in circularity can be seen,length of cell elongation,and angle of cell elongation differs between cells grown on patterned lines opposed to unpatterned cells.Line spacing was also varied to determine length scales at which ‘bridging ’of cells between patterns occurred.This could prove useful for applications that require cell-cell connections between patterns or formation of cell sheets,without disturbing their alignment.For example,it is known that the complex organisation of cardiac muscle cells and fibroblasts is critical to electrical and mechanical properties in the heart.Because of this,biological canti-levers and actuators cultured with aligned sheets of contractile muscle cells could generate more force than unaligned sheets.Cell bridging would synchronise contrac-tion of the aligned muscle cells and increase density of cells on the devices.However,an optimum line width and spacing would need to be characterised to maximise the performance of the muscle cell sheet.If line spacing wastooFigure 3.Transferring ﬁbronectin patterns from glass coverslips to hydrogels.(A)Glass coverslips with ﬂuorescently-labelled acryl-ﬁbronectin lines 10,50,and 100m m wide.(B)Hydrogels with ﬂuorescently-labelled acryl-ﬁbronectin lines 10,50,and 100m m wide transferred from glass coverslips.(C)Hydrogels with ﬂuorescently-labelled ﬁbronectin lines 10,50,and 100m m wide (control).(D)Comparison of measured line widths on glass coverslips and hydrogels.Scale bars represent 50m m wide.7Virtual and Physical Prototyping。

Computers & Electrical Engineering样文

Adaptive control of dynamic mobile robots withnonholonomic constraintsFarzad Pourboghrat *,Mattias P.KarlssonDepartment of Electrical and Computer Engineering,Southern Illinois University,Carbondale,IL 62901-6603,USAReceived 16November 1999;accepted 22August 2000AbstractThis paper presents adaptive control rules,at the dynamics level,for the nonholonomic mobile robots with unknown dynamic parameters.Adaptive controls are derived for mobile robots,using backstepping technique,for tracking of a reference trajectory and stabilization to a ﬁxed posture.For the tracking problem,the controller guarantees the asymptotic convergence of the tracking error to zero.For stabili-zation,the problem is converted to an equivalent tracking problem,using a time varying error feedback,before the tracking control is applied.The designed controller ensures the asymptotic zeroing of the sta-bilization error.The proposed control laws include a velocity/acceleration limiter that prevents the robot Õs wheels from slipping.Ó2002Elsevier Science Ltd.All rights reserved.Keywords:Mobile robot;Nonholonomic constraint;Dynamics level motion control;Stabilization and tracking;Adaptive control;Backstepping technique;Asymptotic stability1.IntroductionMotion control of mobile robots has found considerable attention over the past few years.Most of these reports have focused on the steering or trajectory generation problem at the ki-nematics level i.e.,considering the system velocities as control inputs and ignoring the mechanical system dynamics [1–3].Very few reports have been published on control design in the presence of uncertainties in the dynamic model [4].Some preliminary results on control of nonholonomic systems with uncertainties are given in Refs.[4–6].Two of the most important control problems concerning mobile robots are tracking of a refer-ence trajectory and stabilization to a ﬁxed posture.The tracking problem has received solutions *Corresponding author.Tel.:+1-618-453-7026.E-mail address:pour@ (F.Pourboghrat).0045-7906/02/$-see front matter Ó2002Elsevier Science Ltd.All rights reserved.PII:S0045-7906(00)00053-7242 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253including classical nonlinear control techniques[1,2,7].The basic idea is to have a reference car that generates a trajectory for the mobile robot to follow.In Refs.[1,2],nonlinear velocity control inputs were deﬁned that made the tracking error go to zero as long as the reference car was moving.In Ref.[7],they used input–output linearization to make a mobile platform follow a desired trajec-tory.The problem of stabilization about aﬁxed posture has been shown to be rather complicated. This is due to violating the BrockettÕs condition[8],which states that for nonholonomic systems a single equilibrium solution cannot be asymptotically stabilized using continuous static state feedback[9,10].The BrockettÕs condition essentially states that for nonholonomic systems an equilibrium solution can be asymptotically stabilized only by either a time varying,a discontin-uous,or a dynamic state feedback.In addressing the above problem,in Ref.[10]a smooth feedback control was presented for the kinematics control problem resulting in a globally marginally stable closed loop system.They also designed a smooth feedback control for a dynamical state-space model resulting in a Lagrange stable closed loop system,as deﬁned in their paper.A two dimensional Lyapunov function was utilized in Ref.[3]to prescribe a set of desired trajectories to navigate a mobile robot to a speciﬁed conﬁguration.The desired trajectory was then tracked using sliding mode control,resulting in discontinuous control signals.The mobile robot was shown to be exponentially stable for a class of quadratic Lyapunov functions.In Ref.[9],they formulated a reduced order state equation for a class of nonholonomic systems.Several other researchers have later used this reduced order state equation in their studies.In Ref.[4],the problem of controlling nonholonomic mechanical sys-tems with uncertainties,at the dynamics level,was ing the reduced state equation in Ref.[9],they proposed an adaptive controller for a number of important nonholonomic control problems,including stabilization of general systems to an equilibrium manifold and stabilization of diﬀerentiallyﬂat and Caplygin systems to an equilibrium point.In Ref.[2],they gave several examples on how the stabilization problem can be solved for a mobile robot at the kinematics level.Their solutions included time-varying control,piecewise continuous control,and time-varying piecewise continuous control.They also showed how a solution to the tracking problem could be extended to work even for the stabilization problem.Here,we present adaptive control schemes for the tracking problem and for the problem of stabilization to aﬁxed posture when the dynamic model of the mobile robot contains unknown parameters.Our work is based on,and can be seen as an extension of,the work presented in Refs. [1,2].Using backstepping technique we derive adaptive control laws that work even when the model of the dynamical system contains uncertainties in the form of unknown constants.The assumption for the uncertainty in robotÕs parameters,particularly the mass,and hence the inertia, can be justiﬁed in real applications such as in automotive manufacturing industry and warehouses, where the robots are to move a variety of parts with diﬀerent shapes and masses.In these cases,the robotÕs mass and inertia may vary up to10%or20%,justifying an adaptive control approach.2.Dynamic model of mobile robotHere,we consider a three-wheeled mobile robot moving on a horizontal plane(Fig.1).The mobile robot features two diﬀerentially driven rear wheels and a castor front wheel.The radius ofthe wheels is denoted r and the length of the rear wheel axis is 2l .Inputs to the system are two torques T 1and T 2,provided by two motors attached to the rear wheels.The dynamic model for the above wheeled-mobile robot is given by Refs.[10,11].€x ¼k m sin /þb 1u 1cos /€y ¼Àk cos /þb 1u 1sin /€/¼b 2u 28><>:ð1Þ_x sin /À_y cos /¼0ð2Þwhere b 1¼1=ðrm Þ,b 2¼l =ðrI Þ,and that m and I denote the mass and the moment of inertia of the mobile robot,respectively.Also,u 1¼T 1þT 2and u 2¼T 1ÀT 2are the control inputs,and k is the Lagrange multiplier,given by k ¼Àm _/_x cos /þ_y sin /ðÞ.Here,it is assumed that b 1and b 2are unknown constants with known signs.The assumption that the signs of b 1and b 2are known is practical since b 1and b 2represent combinations of the robot Õs mass,moment of inertia,wheel radius,and distance between the rear wheels.Eq.(2)is the nonholonomic constraint,coming from the assumption that the wheels do not slip.The triplet vector function q t ðÞ¼x t ðÞ;y t ðÞ;/t ðÞ½ T denotes the trajectory (position and orientation)of the robot with respect to a ﬁxed workspace frame.That is,at any given time,q ¼½x ;y ;/ T describes the robot Õs conﬁguration (posture)at that time.We assume that,at any time,the robot Õs posture,q ¼½x ;y ;/ T ,as well as its derivative,_q¼½_x ;_y ;_/ T ,are available for feedback.3.Tracking problem deﬁnitionThe tracking problem consists of making the trajectory q of the mobile robot follow a reference trajectory q r .The reference trajectory q r t ðÞ¼x r t ðÞ;y r t ðÞ;/r t ðÞ½ T is generated by a reference ve-hicle/robot whose equations are_xr ¼v r cos /r _y r¼v r sin /_/r ¼x r8<:ð3ÞThe subscript ‘‘r’’stands for reference,and v r and x r are the reference translational (linear)velocity and the reference rotational (angular)velocity,respectively.We assume that v r and x r ,as well as their derivatives are available and that they all are bounded.Assumption A 1.For the tracking problem it is assumed that the reference velocities v r and x r do not both go to zero simultaneously.That is,it is assumed that at any time either lim t !1v r t ðÞ90and/or lim t !1x r t ðÞ90.The tracking problem,under the Assumption A 1,is to ﬁnd a feedback control law u 1u 2 ¼u q ;_q ;q r ;v r ;x r ;_v r ;_x r ðÞsuch that lim t !1~q t ðÞ¼0,where ~q t ðÞ¼q r t ðÞÀq t ðÞis deﬁned as the trajectory tracking error.As in Ref.[1],we deﬁne the equivalent trajectory tracking error ase ¼T ~qð4Þwhere e ¼½e 1;e 2;e 3 T ,and T ¼cos /sin /0Àsin /cos /00010@1A .Note that since T matrix is nonsingular,e is nonzero as long as ~q¼0.Assuming that the angles /r and /are given in the range ½Àp ;p ,we have the equivalent trajectory tracking error e ¼0only if q ¼q r .The purpose of the tracking controller is to force the equivalent trajectory tracking error e to 0.In the sequel we refer to e as the trajectory tracking error.Using the nonholonomic constraint (2),the derivative of the trajectory tracking error given in Eq.(4)can be written as,[1],_e1¼e 2x Àv þv r cos e 3_e 2¼Àe 1x þv r sin e 3_e3¼x r Àx 8<:ð5Þwhere v and x are the translational and rotational velocities of the mobile robot,respectively,and are expressed asv ¼_xcos /þ_y sin /x ¼_/ð6Þ4.Tracking controller designHere,the goal is to design a controller to force the tracking error e ¼½e 1;e 2;e 3 T to ing backstepping technique,since the actual control variables u 1and u 2do not appear in Eq.(5),we consider variables v and x as virtual controls.Let v d and x d denote the desired virtual controls for the mobile robot.That is,with v d and x d the trajectory tracking error e converges tozero asymptotically.Also let us deﬁne ~vand ~x as virtual control errors.Then,v and x can be written asv ¼v d þ~vx ¼x d þ~x ð7Þ244 F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253Let us choose the virtual controls v d and x d ,asv d v r ;x r ;e 1;e 3ðÞ¼v r cos e 3þk 1v r ;x r ðÞe 1x d v r ;x r ;e 2;e 3ðÞ¼x r þk 2v r e 2þk 3v r ;x r ðÞsin e 3ð8Þwhere k 2is a positive constant and k 1ðÁÞand k 3ðÁÞare bounded continuous functions with bounded ﬁrst derivatives,strictly positive on R ÂR -ð0;0Þ.Observe that our approach from here on is general for any v d and x d (with well deﬁned ﬁrst derivatives),i.e.any diﬀerentiable control law that makes the kinematics model of the mobile robot track a desired trajectory can be used instead of Eq.(8).Eq.(8)is similar to the control law proposed by Ref.[1],but with the advantage,as we are going to prove later,that it can be used to track any reference trajectory as long as As-sumption A 1holds.Now,consider the following adaptive control scheme:u 1¼^b 1ðÀc 1~v þe 1þ_v d Þu 2¼^b 2 Àc 2~x þ1k 2sin e 3þ_x d _^b 1¼Àc 1sign b 1ðÞ~v ðÀc 1~v þe 1þ_v d Þ_^b 2¼Àc 2sign b 2ðÞ~x Àc 2~x þ1k 2sin e 3þ_x d ð9Þwhere c 1,c 2,c 1,and c 2are positive constants and ^b 1is an estimate of b 1¼1=b 1and ^b 2is an estimate of b 2¼1=b 2.Result 1.If Assumption A 1holds ,then the adaptive control scheme (9)makes the origin e ¼0uniformly asymptotically stable.Proof .Consider the following Lyapunov function candidateV 1¼12e 21Àþe 22Áþ1k 21ðÀcos e 3Þð10Þwhere k 2is a positive constant.Clearly V 1is positive deﬁnite and V 1¼0only if e ¼0.Taking the time derivative of V 1,we obtain_V 1¼e 1ðÀv þv r cos e 3Þþe 2v r sin e 3þ1k 2sin e 3x r ðÀx Þð11ÞFurthermore,using Eqs.(7)and (8),we have_V 1¼Àk 1e 21Àk 3k 2sin 2e 3À~v e 1À~x 1k 2sin e 3ð12ÞIn view of Eqs.(1),(2)and (6),we ﬁnd the time derivatives of ~vand ~x ,as _~v¼_v À_v d ¼€x cos /À_x sin /_/þ€y sin /þ_y cos /_/À_v d ¼b 1u 1À_v d _~x ¼_x À_x d ¼€/À_x d ¼b 2u 2À_x d ð13ÞF.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253245Consider the Lyapunov function candidateV2¼V1þ12ð~v2þ~x2Þþb1j j2c1~b21þb2j j2c2~b22ð14Þwhere~b1¼b1À^b1¼1=b1À^b1and~b2¼b2À^b2¼1=b2À^b2.Considering Eq.(9)we get:_V 2¼Àk1e21Àk3k2sin2e3Àc1~v2Àc2~x260ð15ÞSince V2is bounded from below and_V2is negative semi-deﬁnite,V2converges to aﬁnite limit. Also,V2,as well as,e1,e2,e3,~v,~x,^b1,and^b2are all bounded.Furthermore,using Eqs.(5),(7)–(9)and(13),the second derivative of V2can be written as€V 2¼À2k1e1e2ðx rþk2v r e2þk3sin e3þ~xÞþ2k1e1ðk1e1þ~vÞÀ_k1e21þ2k3k2cos e3sin e3ðk2v r e2þk3sin e3þ~xÞÀ_k3k2sin2e3À2c1~vðb1^b1ðÀc1~vþe1þ_v dÞÀ_v dÞÀ2c2~x b2^b2Àc2~xþ1k2sin e3þ_x dÀ_x dð16Þwhich from the properties of k1,k2,and k3,the assumption that v r and x r and their derivatives are bounded,and from the above results,can be shown to be bounded,i.e.,_V2is uniformly contin-uous.Since V2ðtÞis diﬀerentiable and converges to some constant value and that€V2is bounded,by BarbalatÕs lemma,_V2tðÞ!0as t!1.This in turn implies that e1,e3,~v,and~x converge to zero [12,13].To show that e2also goes to zero,note that,using the above results,theﬁrst error equation can be written as_e1¼e2x rÀk1e1ð17ÞThe second derivative of e1is€e1¼_x r e2þx rðÀe1xþv r sin e3ÞÀk1e2x rðÀk1e1ÞÀ_k1e1ð18Þwhich can be shown to be bounded by once again using the properties of k1,the assumptions on v r and x r,and Eqs.(7)and(8).Since e1is diﬀerentiable and converges to zero and€e1is bounded,by BarbalatÕs lemma,_e1,and hence,e2x r tend to zero.Proceeding in the same manner,the third error equation can be written as_e3¼Àk2v r e2Àk3sin e3ð19Þand its second derivative can be shown to be bounded.Since e3is diﬀerentiable and converges to zero and€e3is bounded,again by BarbalatÕs lemma,_e3!0as t!1.Hence,k2v r e2and thus v r e2 tend to zero as t!1.Clearly,both v r e2and x r e2converge to zero.However,since v r and x r do not both tend to zero(by Assumption A1),e2must converge to zero.That is,e1,e2,e3,~v,and~x must all converge to zero.hIn Section3,we demonstrated that the system is stable if k2is a positive constant,and that k1ðÁÞand k3ðÁÞare bounded continuous functions with boundedﬁrst derivatives and are strictly positive on RÂR-ð0;0Þ.To get a better understanding on how the control gains aﬀect the response of the system,we write the equations for the closed loop system when~v and~x are equal to zero as[1] 246 F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253_e¼Àk 1e 1þx r þk 2v r e 2þk 3sin e 3ðÞe 2Àx r þk 2v r e 2þk 3sin e 3ðÞe 1þv r sin e 3Àk 2v r e 2Àk 3sin e 30@1A ð20ÞBy linearizing the diﬀerential equation (20)around e ¼0,we get_e¼Ae ð21Þwhere A ¼Àk 1x r 0Àx r 0v r 0Àk 2v r Àk 30@1A ð22ÞTo simplify the analysis,we assume that v r and x r are constants.The system Õs closed loop poles are now equal to the roots of the following characteristic polynomial equation:s ðþ2nx 0Þs 2Àþ2nx 0s þx 20Áð23Þwhere n and x 0are positive real numbers.The corresponding control gains arek 1¼2nx 0k 2¼x 20Àx 2r v 2r k 3¼2nx 0ð24ÞWith a ﬁxed pole placement strategy (n and x 0are constant),the control gain k 2increaseswithout bound when v r tends to zero.One way to avoid this is by letting the closed loop polesdepend on the values of v r and x r .As in Ref.[2],we choose x 0¼x 2r þbv 2r ÀÁð1=2Þwith b >0.The control gains then becomek 1¼2n x 2r Àþbv 2rÁ1=2k 2¼b k 3¼2n x 2r Àþbv 2r Á1=2ð25Þand the resulting control is now deﬁned for any values of v r and x r .In the above,it is shown that the proposed algorithm works for any desired velocities,ðv d ;x d Þ.However,in practice,if the tracking errors initially are large or if the reference trajectory does not have a continuous curvature (e.g.,if the reference trajectory is a straight line connected to a circle segment),either or both of the virtual reference velocities in Eq.(8)might become too large for a real robot to attain in practice.Hence,the translational/rotational acceleration might become too large causing the robot to slip [1].In order to prevent the mobile robot from slipping,in a real application,a simple velocity/acceleration limiter may be implemented [1],as shown in Fig.2.This limits the virtual reference velocities ðv d ;x d Þby constants ðv max ;x max Þand the virtual referenceaccelerations ða ;a Þby constants ða max ;a max Þ,where a ¼_vd and a ¼_x d are the virtual reference accelerations.In practice,these parameters must be determined experimentally as the largest values with which the mobile robot never slips.F.Pourboghrat,M.P.Karlsson /Computers and Electrical Engineering 28(2002)241–253247An important advantage of adding the limiter is that it lowers the control gains indirectly only when the tracking errors are large,i.e.,when too high a gain could cause the robot to slip,while for small tracking errors it does not aﬀect the performance at all.Thus,by using the limiter one can have higher control gains for small tracking errors to allow for better tracking,while letting the limiter to‘‘scale down’’the gains,indirectly,for large tracking errors,to prevent the robot from slipping.5.Simulation results for tracking control problemHere,the results of computer simulation,using MATLAB/SIMULINK,are presented for a mobile robot with the proposed tracking control and with the velocity/acceleration limiter.The computer simulations for the above controller without the limiter,although not shown here,produce similar results,but with somewhat diﬀerent transient characteristics.All simulations have the common parameters of c1¼c2¼100,c1¼c2¼10and b¼250.Also selected are,the damping factor n¼1,v max¼1:5m/s,x max¼3rad/s,a max¼5m/s2and a max¼25rad/s2.Moreover,the robotÕs dy-namic parameters are chosen as b1¼b2¼0:5,which are assumed to be unknown to the con-troller,but with known signs.Simulation results for the case where the reference trajectory is a straight line are shown in Figs. 3and4for t2½0;10 .The reference trajectory is given by x rðtÞ¼0:5t,y rðtÞ¼0:5t and/rðtÞ¼p=4, deﬁning a straight line,starting from q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½0;0;p=4 T.The mobile robot, however,is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½1;0;0 T,where/¼0indicates that the robot is heading toward positive direction of x.As it can be seen from theseﬁgures,ﬁrst the robot backs up and then heads toward the virtual reference robot moving on the straight line.Figs.5and6show the simulation results for tracking a circular trajectory.The reference trajectory is a point moving counter clockwise on a circle of radius1,starting at q rð0Þ¼½x rð0Þ;y rð0Þ;/rð0Þ T¼½1;0;p=2 T.The reference velocity is kept constant at v rðtÞ¼0:5m/s.The initial conditions for the mobile robot,however,is taken as qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;0;0 T.Again,as it is seen from theseﬁgures,the robot immediately heads toward the reference robot,which is moving on the circle.It then reaches it quickly and continues to track it.6.Stabilization problem deﬁnitionThe stabilization problem,given an arbitrary desired posture q d ,is to ﬁnd a feedback control law,u 1u 2¼u q Àq d ;_q ;t ðÞ,such that lim t !1q t ðÞÀq d ðÞ¼0,for any arbitrary initial robot posture q ð0Þ.Without loss of generality,we may take q d ¼½0;0;0 T.6.1.Stabilization controller designRecall that there is no continuous static state feedback that can asymptotically stabilize a nonholonomic system about a ﬁxed posture [8–10].The approach to the problem taken here is the dynamic extension of that in Ref.[2]where a kinematics model of the mobile robot is used.In-stead of designing a new controller for the stabilization problem the same controller as for the tracking problem is used.The idea is to let the reference vehicle move along a path that passes through the point ðx d ;y d Þwith heading angle /d .The stabilization to a ﬁxed posture problem isnow equivalent to,and can be treated as,a tracking problem(convergence of the tracking errors to zero)with the additional requirement that the reference vehicle should itself be asymptotically stabilized about the desired posture.As in Ref.[2],we let the reference vehicle move along the x-axis,i.e.y rðtÞ¼0and/rðtÞ¼0,for all values on t.The design method is the same as derived for the tracking case.However,in this casev r¼_x r¼Àk4x rþgðe;tÞ;ð26Þwithgðe;tÞ¼k e k sin tð27Þwhere k4>0.Diﬀerent time-varying functions gðe;tÞhave also been suggested in the literature,see Refs.[2,11]and the references therein.Since,from the Section5,the tracking errors e1,e2,and e3are bounded,the time-varying function gðe;tÞis bounded.Therefore v r and the state x r also remain bounded.By taking the time derivative of Eq.(26),it can be shown in the same way that_v r is bounded.Since v r and_v r are bounded,the assumptions made in Section3concerning the reference velocity are fulﬁlled.If v r is not equal to zero,then e must converge to zero.When e tends to zero,gðe;tÞalso tends to zero. Therefore,the robotÕs position x must track x r,which converges to zero and hence lead the mobile robot to the desired posture.6.2.Simulation results for stabilization control problemHere,the simulation results for the stabilization problem are shown in Figs.7and8.The control parameters and system parameters are the same as for the simulations shown for the tracking problem and k4¼1.The mobile robot is initially at qð0Þ¼½xð0Þ;yð0Þ;/ð0Þ T¼½0;1;0 T.As it is seen from theﬁgures,the stabilization about theﬁnal posture at the origin is achieved quite satisfactorily.Note,in this case,that the robot actually turns around and backs up into the ﬁnal posture.7.ConclusionsTwo important control problems concerning mobile robots with unknown dynamic parameters have been considered,namely,tracking of a reference trajectory and stabilization to aﬁxed posture.An adaptive control law has been proposed for the tracking problem and has been ex-tended for the stabilization problem.A simple velocity/acceleration limiter was added to the controller,for practical applications,to avoid any slippage of the robotÕs wheels,and to improve the tracking performance.Several simulation results have been included to demonstrate the performance of the proposed adaptive control law.References[1]Kanayama Y,Kimura Y,Miyazaki F,Noguchi T.A stable tracking control method for an autonomous mobilerobot.vol.1.Proceedings of IEEE International Conference on Robotics and Automation,Cincinnati,Ohio,1990, p.384–9.[2]Canudas de Wit C,Khennouf H,Samson C,Sordalen OJ.Nonlinear control design for mobile robots.In:ZhengYF,editor.Recent trends in Mobile robots,World Scientiﬁc,1993.p.121–56.[3]Guldner J,Utkin VI.Stabilization of nonholonomic mobile robot using Lyapunov functions for navigation andsliding mode control.Control-Theory Adv Technol1994;10(4):635–47.[4]Colbaugh R,Barany E,Glass K.Adaptive Control of Nonholonomic Mechanical Systems.Proceedings of35thConference on Decision and Control,Kobe,Japan,1996.p.1428–34.[5]Fierro R,Lewis FL.Control of nonholonomic mobile robot:backstepping kinematics into dynamics.J Robot Sys1997;14(3)149-163.[6]Jiang ZP,Pomet bining backstepping and time-varying techniques for a new set of adaptive controllers.Proceedings of33rd IEEE Conf on Decision and Control,Lake Buena Vista,FL,1994.p.2207–12.[7]Sarkar N,Yun X,Kumar V.Control of mechanical systems with rolling constraints:application to dynamiccontrol of mobile robots.Int J Robot Res1994;13(1):55–69.[8]Brockett RW.Asymptotic stability and feedback stabilization.In:Brockett RW,Millman RS,Sussmann HJ,editors.Diﬀerential Geometric Control Theory,Boston,MA:Birkhauser;1983.p.181–91.[9]Bloch AM,Reyhanoglu MR,McClamroch NH.Control and stabilization of nonholonomic dynamic systems.IEEE Trans Automat Contr1992;37(11):1746–56.[10]Campion G,d’Andrea-Novel B,Bastin G.Controllability and state feedback stabilization of nonholonomicmechanical systems.Canudas de Wit C,editor.Advanced Robot Control,Berlin:Springer;1991.p.106–24. [11]Kolmanovsky I,McClamroch NH.Developments in nonholonomic control problems.IEEE Contr Sys Magaz1995;15(6):20–36.[12]Krstic M,Kanellakopoulos I,Kokotovic P.Nonlinear and Adaptive Control Design,New York:Wiley;1995.[13]Karlsson MP.Control of nonholonomic systems with applications to mobile robots.Master Thesis,SouthernIllinois University,Carbondale,IL62901,USA,1997.Farzad Pourboghrat received his Ph.D.degree in Electrical Engineering from the University of Iowa in1984. He is now with the Department of Electrical and Computer Engineering at Southern Illinois University at Carbondale(SIU-C)where he is an Associate Professor.His research interests are in adaptive and slidingcontrol with applications to DSP embedded systems,mechatronics,ﬂexible structures andMEMS.Mattias Karlsson received the B.S.E.E.degree from the University of Bor a s,Sweden and the M.S.E.E.degree from Southern Illinois University,Carbondale,IL,in1995and1997,respectively.He has been employed at Orian Technology since1997.He is currently an on-site consultant at Caterpillar Inc.Õs Technical Center, Mossville,IL.His current interests include control algorithm development for mechanical and electrical systems and software development for embedded systems.F.Pourboghrat,M.P.Karlsson/Computers and Electrical Engineering28(2002)241–253253。

莱欧斯利冻绽放原理

莱欧斯利冻绽放原理The principle of cryogenic freezing, also known as cryopreservation, involves slowing biological and chemical processes to extremely low temperatures, typically below -130 degrees Celsius. 莱欧斯利的冷冻绽放原理，也被称为低温保存，涉及到将生物和化学过程减缓到极低的温度，通常低于摄氏零下130度。

This process is often used in the preservation of biological samples, embryos, and even whole organs for transplantation, to prolong their viability and increase the likelihood of successful preservation. 这一过程通常用于生物样本、胚胎甚至整个器官的保存，以延长其存活期并增加成功保存的可能性。

One of the key challenges in cryogenic freezing is the formation ofice crystals, which can damage the cellular structure and reduce the quality of the preserved material. 低温冷冻的一个关键挑战是冰晶的形成，这会损害细胞结构并降低保存材料的质量。

To address this issue, cryoprotectants are often added to the samples prior to freezing, to minimize ice crystal formation andmaintain the integrity of the cells and tissues. 为了解决这个问题，在冷冻之前通常会向样本中加入冷冻保护剂，以最小化冰晶的形成并保持细胞和组织的完整性。

美国正在开发用于生物分离的活性纳米表面

美国正在开发用于生物分离的活性纳米表面
佚名
【期刊名称】《纳米科技》
【年(卷),期】2006(3)6
【摘要】美国国家科学基金会（NSF）资助了一个研究团队100万美元，用于研究生物分离的改进方法。

在Rensselaer Polytechnic研究所的化学和生物工程学副教授Ravi Kane的领导下，该团队计划开发在DNA存在的情况下重组的活性纳米表面，并最终开发出能更有效地分离基因组和蛋白质组的工具。

【总页数】2页(P73-74)
【关键词】美国国家科学基金会;生物分离;开发;表面;纳米;活性;生物工程学;蛋白质组
【正文语种】中文
【中图分类】Q503
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因版权原因，仅展示原文概要，查看原文内容请购买。

非厄米谐振薄膜

非厄米谐振薄膜【中英文版】Title: Non-Hermitian Resonance in Thin Films中文标题：非厄米谐振薄膜---In the realm of optics, non-Hermitian resonance in thin films has garnered significant attention due to its unique properties and potential applications.在光学领域，非厄米谐振薄膜因其独特的性质和潜在的应用而受到了广泛关注。

---When light interacts with a thin film, the propagation constant can become complex, leading to a resonance that is not purely real.This non-Hermitian resonance is characterized by a complex frequency and a corresponding complex propagation constant.当光与薄膜相互作用时，传播常数可能变得复杂，导致谐振不是纯实数的。

这种非厄米谐振由复频率和相应的复传播常数特征。

---The emergence of this resonance phenomenon can lead to interesting optical phenomena such as enhanced absorption, modified refractive index, and unique dispersion characteristics.These properties make thin films with non-Hermitian resonance promising candidates forvarious optical devices, including sensors, filters, and optical modulators.这种谐振现象的出现可以导致诸如增强吸收、改变折射率和独特的色散特性等有趣的光学现象。

Lamellarins的抗癌特性

附录Ⅱ文献翻译Lamellarins的抗癌特性Christian Bailly摘要:1985年，lamellarins第一次成功从一个小海洋海螺中提取。

今天,超过50种lamellarins衍生物已经清晰，众多其衍生品参与合成抗病毒和抗癌药物测试。

lamellarin D铅化合物也属于lamellarin家族,被描述为一种核和线粒体拓扑异构酶的有效抑制剂，能够直接干扰线粒体触发癌细胞死亡。

这里详细讨论lamellarin D的药理学和化学性质以及其机械的构象。

Lamellarins经常作为设计抗癌化合物的出发点。

我们一直致力于改进lamellarin的结构和合成方法,使lamellarins成为和pyrrole-derived有关的海洋生物碱。

关键词:lamellarins;海洋天然产物；癌；拓扑异构酶I；线粒体；药物合成Lamellarin类海洋生物碱海洋prosobranch软体动物物种丰富,通常使用双壳类软体动物采取其中毒素和用于食品采购。

例如,红色海螺Neptunea安迪瓜(家庭蛾螺科)近岸的物种出现在大西洋东部的冷温带水域，北方区域使用其唾腺神经毒素毒鼠强用于狩猎和喂养[1]。

这些软体动物依靠生物活性化合物对喂养也是防守的元素来逃避捕食。

由于他们非凡的生产能力，能产生各种复杂的化学物质,海洋生物,软体动物具体来说,已经成为一个热点的研究。

在过去的20年[2]吲哚和吡咯生物碱,如topsentin[3,4],tambjamine D[5],spongiacidin C[6]的discorhabdines[7],具有治疗潜力,经常被视为一种抗癌药物(8、9)。

化学自然产品的修改可能创造出具有强大的抗肿瘤效果的药物。

是这样的两个合成iminoquinones衍生品BA-TPQ 及其氟导数FBA-TPQ,类似物的生物碱makaluvamines,显示显著的抗肿瘤活动在体外和体内不同的异种移植模型(10 - 14)。

单分子综述-NATURE NANOTECHNOLOGY-Single-molecule junctions beyond electronic transport-2013

Stimulated by the initial proposal that molecules could be used as the functional building blocks in electronic devices 1, researchers around the world have been probing transport phenomena at the single-molecule level both experimentally and theoretically 2–11. Recent experimental advances include the demonstration of conductance switching 12–16, rectification 17–21, and illustrations on how quantum interference effects 22–26 play a critical role in the electronic properties of single metal–molecule–metal junctions. The focus of these experiments has been to both provide a fundamental understanding of transport phenomena in nanoscale devices as well as to demonstrate the engineering of functionality from rational chemical design in single-molecule junctions. Although so far there are no ‘molecular electronics’ devices manufactured commercially, basic research in this area has advanced significantly. Specifically, the drive to create functional molecular devices has pushed the frontiers of both measurement capabilities and our fundamental understanding of varied physi-cal phenomena at the single-molecule level, including mechan-ics, thermoelectrics, optoelectronics and spintronics in addition to electronic transport characterizations. Metal–molecule–metal junctions thus represent a powerful template for understanding and controlling these physical and chemical properties at the atomic- and molecular-length scales. I n this realm, molecular devices have atomically defined precision that is beyond what is achievable at present with quantum dots. Combined with the vast toolkit afforded by rational molecular design 27, these techniques hold a significant promise towards the development of actual devices that can transduce a variety of physical stimuli, beyond their proposed utility as electronic elements 28.n this Review we discuss recent measurements of physi-cal properties of single metal–molecule–metal junctions that go beyond electronic transport characterizations (Fig. 1). We present insights into experimental investigations of single-molecule junc-tions under different stimuli: mechanical force, optical illumina-tion and thermal gradients. We then review recent progress in spin- and quantum interference-based phenomena in molecular devices. I n what follows, we discuss the emerging experimentalSingle-molecule junctions beyond electronic transportSriharsha V. Aradhya and Latha Venkataraman*The id ea of using ind ivid ual molecules as active electronic components provid ed the impetus to d evelop a variety of experimental platforms to probe their electronic transport properties. Among these, single-molecule junctions in a metal–molecule–metal motif have contributed significantly to our fundamental understanding of the principles required to realize molecular-scale electronic components from resistive wires to reversible switches. The success of these techniques and the growing interest of other disciplines in single-molecule-level characterization are prompting new approaches to investigate metal–molecule–metal junctions with multiple probes. Going beyond electronic transport characterization, these new studies are highlighting both the fundamental and applied aspects of mechanical, optical and thermoelectric properties at the atomic and molecular scales. Furthermore, experimental demonstrations of quantum interference and manipulation of electronic and nuclear spins in single-molecule circuits are heralding new device concepts with no classical analogues. In this Review, we present the emerging methods being used to interrogate multiple properties in single molecule-based devices, detail how these measurements have advanced our understanding of the structure–function relationships in molecular junctions, and discuss the potential for future research and applications.methods, focusing on the scientific significance of investigations enabled by these methods, and their potential for future scientific and technological progress. The details and comparisons of the dif-ferent experimental platforms used for electronic transport char-acterization of single-molecule junctions can be found in ref. 29. Together, these varied investigations underscore the importance of single-molecule junctions in current and future research aimed at understanding and controlling a variety of physical interactions at the atomic- and molecular-length scale.Structure–function correlations using mechanicsMeasurements of electronic properties of nanoscale and molecu-lar junctions do not, in general, provide direct structural informa-tion about the junction. Direct imaging with atomic resolution as demonstrated by Ohnishi et al.30 for monoatomic Au wires can be used to correlate structure with electronic properties, however this has not proved feasible for investigating metal–molecule–metal junctions in which carbon-based organic molecules are used. Simultaneous mechanical and electronic measurements provide an alternate method to address questions relating to the struc-ture of atomic-size junctions 31. Specifically, the measurements of forces across single metal–molecule–metal junctions and of metal point contacts provide independent mechanical information, which can be used to: (1) relate junction structure to conduct-ance, (2) quantify bonding at the molecular scale, and (3) provide a mechanical ‘knob’ that can be used to control transport through nanoscale devices. The first simultaneous measurements of force and conductance in nanoscale junctions were carried out for Au point contacts by Rubio et al.32, where it was shown that the force data was unambiguously correlated to the quantized changes in conductance. Using a conducting atomic force microscope (AFM) set-up, Tao and coworkers 33 demonstrated simultaneous force and conductance measurements on Au metal–molecule–metal junc-tions; these experiments were performed at room temperature in a solution of molecules, analogous to the scanning tunnelling microscope (STM)-based break-junction scheme 8 that has now been widely adopted to perform conductance measurements.Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA. *e-mail: lv2117@DOI: 10.1038/NNANO.2013.91These initial experiments relied on the so-called static mode of AFM-based force spectroscopy, where the force on the canti-lever is monitored as a function of junction elongation. I n this method the deflection of the AFM cantilever is directly related to the force on the junction by Hooke’s law (force = cantilever stiff-ness × cantilever deflection). Concurrently, advances in dynamic force spectroscopy — particularly the introduction of the ‘q-Plus’ configuration 34 that utilizes a very stiff tuning fork as a force sen-sor — are enabling high-resolution measurements of atomic-size junctions. In this technique, the frequency shift of an AFM cantilever under forced near-resonance oscillation is measuredas a function of junction elongation. This frequency shift can be related to the gradient of the tip–sample force. The underlying advantage of this approach is that frequency-domain measure-ments of high-Q resonators is significantly easier to carry out with high precision. However, in contrast to the static mode, recover-ing the junction force from frequency shifts — especially in the presence of dissipation and dynamic structural changes during junction elongation experiments — is non-trivial and a detailed understanding remains to be developed 35.The most basic information that can be determined throughsimultaneous measurement of force and conductance in metalThermoelectricsSpintronics andMechanicsOptoelectronicsHotColdFigure 1 | Probing multiple properties of single-molecule junctions. phenomena in addition to demonstrations of quantum mechanical spin- and interference-dependent transport concepts for which there are no analogues in conventional electronics.contacts is the relation between the measured current and force. An experimental study by Ternes et al.36 attempted to resolve a long-standing theoretical prediction 37 that indicated that both the tunnelling current and force between two atomic-scale metal contacts scale similarly with distance (recently revisited by Jelinek et al.38). Using the dynamic force microscopy technique, Ternes et al. effectively probed the interplay between short-range forces and conductance under ultrahigh-vacuum conditions at liquid helium temperatures. As illustrated in Fig. 2a, the tunnel-ling current through the gap between the metallic AFM probe and the substrate, and the force on the cantilever were recorded, and both were found to decay exponentially with increasing distance with nearly the same decay constant. Although an exponential decay in current with distance is easily explained by considering an orbital overlap of the tip and sample wavefunctions through a tunnel barrier using Simmons’ model 39, the exponential decay in the short-range forces indicated that perhaps the same orbital controlled the interatomic short-range forces (Fig. 2b).Using such dynamic force microscopy techniques, research-ers have also studied, under ultrahigh-vacuum conditions, forces and conductance across junctions with diatomic adsorbates such as CO (refs 40,41) and more recently with fullerenes 42, address-ing the interplay between electronic transport, binding ener-getics and structural evolution. I n one such experiment, Tautz and coworkers 43 have demonstrated simultaneous conduct-ance and stiffness measurements during the lifting of a PTCDA (3,4,9,10-perylene-tetracarboxylicacid-dianhydride) molecule from a Ag(111) substrate using the dynamic mode method with an Ag-covered tungsten AFM tip. The authors were able to follow the lifting process (Fig. 2c,d) monitoring the junction stiffness as the molecule was peeled off the surface to yield a vertically bound molecule, which could also be characterized electronically to determine the conductance through the vertical metal–molecule–metal junction with an idealized geometry. These measurements were supported by force field-based model calculations (Fig. 2c and dashed black line in Fig. 2d), presenting a way to correlate local geometry to the electronic transport.Extending the work from metal point contacts, ambient meas-urements of force and conductance across single-molecule junc-tions have been carried out using the static AFM mode 33. These measurements allow correlation of the bond rupture forces with the chemistry of the linker group and molecular backbone. Single-molecule junctions are formed between a Au-metal sub-strate and a Au-coated cantilever in an environment of molecules. Measurements of current through the junction under an applied bias determine conductance, while simultaneous measurements of cantilever deflection relate to the force applied across the junction as shown in Fig. 2e. Although measurements of current throughzF zyxCantileverIVabConductance G (G 0)1 2 3Tip–sample distance d (Å)S h o r t -r a n g e f o r c e F z (n N )10−310−210−11110−110−210−3e10−410−210C o n d u c t a n c e (G 0)Displacement86420Force (nN)0.5 nm420−2F o r c e (n N )−0.4−0.200.20.4Displacement (nm)SSfIncreasing rupture forcegc(iv)(i)(iii)(ii)Low HighCounts d9630−3d F /d z (n N n m −1)(i)(iv)(iii)(ii)A p p r o a chL i ft i n g110−210−4G (2e 2/h )2051510z (Å)H 2NNH 2H 2NNH 2NNFigure 2 | Simultaneous measurements of electronic transport and mechanics. a , A conducting AFM set-up with a stiff probe (shown schematically) enabled the atomic-resolution imaging of a Pt adsorbate on a Pt(111) surface (tan colour topography), before the simultaneous measurement of interatomic forces and currents. F z , short-range force. b , Semilogarithmic plot of tunnelling conductance and F z measured over the Pt atom. A similar decay constant for current and force as a function of interatomic distance is seen. The blue dashed lines are exponential fits to the data. c , Structural snapshots showing a molecular mechanics simulation of a PTCDA molecule held between a Ag substrate and tip (read right to left). It shows the evolution of the Ag–PTCDA–Ag molecular junction as a function of tip–surface distance. d , Upper panel shows experimental stiffness (d F /d z ) measurements during the lifting process performed with a conducting AFM. The calculated values from the simulation are overlaid (dashed black line). Lower panel shows simultaneously measured conductance (G ). e , Simultaneously measured conductance (red) and force (blue) measurements showing evolution of a molecular junction as a function of junction elongation. A Au point contact is first formed, followed by the formation of a single-molecule junction, which then ruptures on further elongation. f , A two-dimensional histogram of thousands of single-molecule junctionrupture events (for 1,4-bis(methyl sulphide) butane; inset), constructed by redefining the rupture location as the zero displacement point. The most frequently measured rupture force is the drop in force (shown by the double-headed arrow) at the rupture location in the statistically averaged force trace (overlaid black curve). g , Beyond the expected dependence on the terminal group, the rupture force is also sensitive to the molecular backbone, highlighting the interplay between chemical structure and mechanics. In the case of nitrogen-terminated molecules, rupture force increases fromaromatic amines to aliphatic amines and the highest rupture force is for molecules with pyridyl moieties. Figure reproduced with permission from: a ,b , ref. 36, © 2011 APS; c ,d , ref. 43, © 2011 APS.DOI: 10.1038/NNANO.2013.91such junctions are easily accomplished using standard instru-mentation, measurements of forces with high resolution are not straightforward. This is because a rather stiff cantilever (with a typical spring constant of ~50 N m−1) is typically required to break the Au point contact that is first formed between the tip and sub-strate, before the molecular junctions are created. The force reso-lution is then limited by the smallest deflection of the cantilever that can be measured. With a custom-designed system24 our group has achieved a cantilever displacement resolution of ~2 pm (com-pare with Au atomic diameter of ~280 pm) using an optical detec-tion scheme, allowing the force noise floor of the AFM set-up to be as low as 0.1 nN even with these stiff cantilevers (Fig. 2e). With this system, and a novel analysis technique using two-dimensional force–displacement histograms as illustrated in Fig. 2f, we have been able to systematically probe the influence of the chemical linker group44,45 and the molecular backbone46 on single-molecule junction rupture force as illustrated in Fig. 2g.Significant future opportunities with force measurements exist for investigations that go beyond characterizations of the junc-tion rupture force. In two independent reports, one by our group47 and another by Wagner et al.48, force measurements were used to quantitatively measure the contribution of van der Waals interac-tions at the single-molecule level. Wagner et al. used the stiffness data from the lifting of PTCDA molecules on a Au(111) surface, and fitted it to the stiffness calculated from model potentials to estimate the contribution of the various interactions between the molecule and the surface48. By measuring force and conductance across single 4,4’-bipyridine molecules attached to Au electrodes, we were able to directly quantify the contribution of van der Waals interactions to single-molecule-junction stiffness and rupture force47. These experimental measurements can help benchmark the several theoretical frameworks currently under development aiming to reliably capture van der Waals interactions at metal/ organic interfaces due to their importance in diverse areas includ-ing catalysis, electronic devices and self-assembly.In most of the experiments mentioned thus far, the measured forces were typically used as a secondary probe of junction prop-erties, instead relying on the junction conductance as the primary signature for the formation of the junction. However, as is the case in large biological molecules49, forces measured across single-mol-ecule junctions can also provide the primary signature, thereby making it possible to characterize non-conducting molecules that nonetheless do form junctions. Furthermore, molecules pos-sess many internal degrees of motion (including vibrations and rotations) that can directly influence the electronic transport50, and the measurement of forces with such molecules can open up new avenues for mechanochemistry51. This potential of using force measurements to elucidate the fundamentals of electronic transport and binding interactions at the single-molecule level is prompting new activity in this area of research52–54. Optoelectronics and optical spectroscopyAddressing optical properties and understanding their influence on electronic transport in individual molecular-scale devices, col-lectively referred to as ‘molecular optoelectronics’, is an area with potentially important applications55. However, the fundamental mismatch between the optical (typically, approximately at the micrometre scale) and molecular-length scales has historically presented a barrier to experimental investigations. The motiva-tions for single-molecule optoelectronic studies are twofold: first, optical spectroscopies (especially Raman spectroscopy) could lead to a significantly better characterization of the local junction structure. The nanostructured metallic electrodes used to real-ize single-molecule junctions are coincidentally some of the best candidates for local field enhancement due to plasmons (coupled excitations of surface electrons and incident photons). This there-fore provides an excellent opportunity for understanding the interaction of plasmons with molecules at the nanoscale. Second, controlling the electronic transport properties using light as an external stimulus has long been sought as an attractive alternative to a molecular-scale field-effect transistor.Two independent groups have recently demonstrated simulta-neous optical and electrical measurements on molecular junctions with the aim of providing structural information using an optical probe. First, Ward et al.56 used Au nanogaps formed by electromi-gration57 to create molecular junctions with a few molecules. They then irradiated these junctions with a laser operating at a wavelength that is close to the plasmon resonance of these Au nanogaps to observe a Raman signal attributable to the molecules58 (Fig. 3a). As shown in Fig. 3b, they observed correlations between the intensity of the Raman features and magnitude of the junction conductance, providing direct evidence that Raman signatures could be used to identify junction structures. They later extended this experimental approach to estimate vibrational and electronic heating in molecu-lar junctions59. For this work, they measured the ratio of the Raman Stokes and anti-Stokes intensities, which were then related to the junction temperature as a function of the applied bias voltage. They found that the anti-Stokes intensity changed with bias voltage while the Stokes intensity remained constant, indicating that the effective temperature of the Raman-active mode was affected by passing cur-rent through the junction60. Interestingly, Ward et al. found that the vibrational mode temperatures exceeded several hundred kelvin, whereas earlier work by Tao and co-workers, who used models for junction rupture derived from biomolecule research, had indicated a much smaller value (~10 K) for electronic heating61. Whether this high temperature determined from the ratio of the anti-Stokes to Stokes intensities indicates that the electronic temperature is also similarly elevated is still being debated55, however, one can definitely conclude that such measurements under a high bias (few hundred millivolts) are clearly in a non-equilibrium transport regime, and much more research needs to be performed to understand the details of electronic heating.Concurrently, Liu et al.62 used the STM-based break-junction technique8 and combined this with Raman spectroscopy to per-form simultaneous conductance and Raman measurements on single-molecule junctions formed between a Au STM tip and a Au(111) substrate. They coupled a laser to a molecular junction as shown in Fig. 3c with a 4,4’-bipyridine molecule bridging the STM tip (top) and the substrate (bottom). Pyridines show clear surface-enhanced Raman signatures on metal58, and 4,4’-bipy-ridine is known to form single-molecule junctions in the STM break-junction set-up8,15. Similar to the study of Ward et al.56, Liu et al.62 found that conducting molecular junctions had a Raman signature that was distinct from the broken molecu-lar junctions. Furthermore, the authors studied the spectra of 4,4’-bipyridine at different bias voltages, ranging from 10 to 800 mV, and reported a reversible splitting of the 1,609 cm–1 peak (Fig. 3d). Because this Raman signature is due to a ring-stretching mode, they interpreted this splitting as arising from the break-ing of the degeneracy between the rings connected to the source and drain electrodes at high biases (Fig. 3c). Innovative experi-ments such as these have demonstrated that there is new physics to be learned through optical probing of molecular junctions, and are initiating further interest in understanding the effect of local structure and vibrational effects on electronic transport63. Experiments that probe electroluminescence — photon emis-sion induced by a tunnelling current — in these types of molec-ular junction can also offer insight into structure–conductance correlations. Ho and co-workers have demonstrated simultaneous measurement of differential conductance and photon emissionDOI: 10.1038/NNANO.2013.91from individual molecules at a submolecular-length scale using an STM 64,65. Instead of depositing molecules directly on a metal sur-face, they used an insulating layer to decouple the molecule from the metal 64,65 (Fig. 3e). This critical factor, combined with the vac-uum gap with the STM tip, ensures that the metal electrodes do not quench the radiated photons, and therefore the emitted photons carry molecular fingerprints. Indeed, the experimental observation of molecular electroluminescence of C 60 monolayers on Au(110) by Berndt et al.66 was later attributed to plasmon-mediated emission of the metallic electrodes, indirectly modulated by the molecule 67. The challenge of finding the correct insulator–molecule combination and performing the experiments at low temperature makes electro-luminescence relatively uncommon compared with the numerous Raman studies; however, progress is being made on both theoretical and experimental fronts to understand and exploit emission pro-cesses in single-molecule junctions 68.Beyond measurements of the Raman spectra of molecular junctions, light could be used to control transport in junctions formed with photochromic molecular backbones that occur in two (or more) stable and optically accessible states. Some common examples include azobenzene derivatives, which occur in a cis or trans form, as well as diarylene compounds that can be switched between a conducting conjugated form and a non-conducting cross-conjugated form 69. Experiments probing the conductance changes in molecular devices formed with such compounds have been reviewed in depth elsewhere 70,71. However, in the single-mol-ecule context, there are relatively few examples of optical modula-tion of conductance. To a large extent, this is due to the fact that although many molecular systems are known to switch reliably in solution, contact to metallic electrodes can dramatically alter switching properties, presenting a significant challenge to experi-ments at the single-molecule level.Two recent experiments have attempted to overcome this chal-lenge and have probed conductance changes in single-molecule junctions while simultaneously illuminating the junctions with visible light 72,73. Battacharyya et al.72 used a porphyrin-C 60 ‘dyad’ molecule deposited on an indium tin oxide (I TO) substrate to demonstrate the light-induced creation of an excited-state mol-ecule with a different conductance. The unconventional transpar-ent ITO electrode was chosen to provide optical access while also acting as a conducting electrode. The porphyrin segment of the molecule was the chromophore, whereas the C 60 segment served as the electron acceptor. The authors found, surprisingly, that the charge-separated molecule had a much longer lifetime on ITO than in solution. I n the break-junction experiments, the illuminated junctions showed a conductance feature that was absent without1 μm Raman shift (cm –1)1,609 cm –1(–)Source 1,609 cm–1Drain (+)Low voltage High voltageMgPNiAl(110)STM tip (Ag)VacuumThin alumina 1.4 1.5 1.6 1.701020 3040200400Photon energy (eV)3.00 V 2.90 V 2.80 V 2.70 V 2.60 V2.55 V 2.50 VP h o t o n c o u n t s (a .u .)888 829 777731Wavelength (nm)Oxideacebd f Raman intensity (CCD counts)1,5001,00050000.40.30.20.10.01,590 cm −11,498 cm −1d I /d V (μA V –1)1,609 cm –11,631 cm–11 μm1 μmTime (s)Figure 3 | Simultaneous studies of optical effects and transport. a , A scanning electron micrograph (left) of an electromigrated Au junction (light contrast) lithographically defined on a Si substrate (darker contrast). The nanoscale gap results in a ‘hot spot’ where Raman signals are enhanced, as seen in the optical image (right). b , Simultaneously measured differential conductance (black, bottom) and amplitudes of two molecular Raman features (blue traces, middle and top) as a function of time in a p-mercaptoaniline junction. c , Schematic representation of a bipyridine junction formed between a Au STM tip and a Au(111) substrate, where the tip enhancement from the atomically sharp STM tip results in a large enhancement of the Raman signal. d , The measured Raman spectra as a function of applied bias indicate breaking of symmetry in the bound molecule. e , Schematic representation of a Mg-porphyrin (MgP) molecule sandwiched between a Ag STM tip and a NiAl(110) substrate. A subnanometre alumina insulating layer is a key factor in measuring the molecular electroluminescence, which would otherwise be overshadowed by the metallic substrate. f , Emission spectra of a single Mg-porphyrin molecule as a function of bias voltage (data is vertically offset for clarity). At high biases, individual vibronic peaks become apparent. The spectra from a bare oxide layer (grey) is shown for reference. Figure reproduced with permission from: a ,b , ref. 56, © 2008 ACS; c ,d , ref. 62, © 2011 NPG; e ,f , ref. 65, © 2008 APS.DOI: 10.1038/NNANO.2013.91light, which the authors assigned to the charge-separated state. In another approach, Lara-Avila et al.73 have reported investigations of a dihydroazulene (DHA)/vinylheptafulvene (VHF) molecule switch, utilizing nanofabricated gaps to perform measurements of Au–DHA–Au single-molecule junctions. Based on the early work by Daub et al.74, DHA was known to switch to VHF under illumina-tion by 353-nm light and switch back to DHA thermally. In three of four devices, the authors observed a conductance increase after irradiating for a period of 10–20 min. In one of those three devices, they also reported reversible switching after a few hours. Although much more detailed studies are needed to establish the reliability of optical single-molecule switches, these experiments provide new platforms to perform in situ investigations of single-molecule con-ductance under illumination.We conclude this section by briefly pointing to the rapid pro-gress occurring in the development of optical probes at the single-molecule scale, which is also motivated by the tremendous interest in plasmonics and nano-optics. As mentioned previously, light can be coupled into nanoscale gaps, overcoming experimental chal-lenges such as local heating. Banerjee et al.75 have exploited these concepts to demonstrate plasmon-induced electrical conduction in a network of Au nanoparticles that form metal–molecule–metal junctions between them (Fig. 3f). Although not a single-molecule measurement, the control of molecular conductance through plas-monic coupling can benefit tremendously from the diverse set of new concepts under development in this area, such as nanofabri-cated transmission lines 76, adiabatic focusing of surface plasmons, electrical excitation of surface plasmons and nanoparticle optical antennas. The convergence of plasmonics and electronics at the fundamental atomic- and molecular-length scales can be expected to provide significant opportunities for new studies of light–mat-ter interaction 77–79.Thermoelectric characterization of single-molecule junctions Understanding the electronic response to heating in a single-mole-cule junction is not only of basic scientific interest; it can have a tech-nological impact by improving our ability to convert wasted heat into usable electricity through the thermoelectric effect, where a temper-ature difference between two sides of a device induces a voltage drop across it. The efficiency of such a device depends on its thermopower (S ; also known as the Seebeck coefficient), its electric and thermal conductivity 80. Strategies for increasing the efficiency of thermoelec-tric devices turned to nanoscale devices a decade ago 81, where one could, in principle, increase the electronic conductivity and ther-mopower while independently minimizing the thermal conductiv-ity 82. This has motivated the need for a fundamental understandingof thermoelectrics at the single-molecule level 83, and in particular, the measurement of the Seebeck coefficient in such junctions. The Seebeck coefficient, S = −(ΔV /ΔT )|I = 0, determines the magnitude of the voltage developed across the junction when a temperature dif-ference ΔT is applied, as illustrated in Fig. 4a; this definition holds both for bulk devices and for single-molecule junctions. If an addi-tional external voltage ΔV exists across the junction, then the cur-rent I through the junction is given by I = G ΔV + GS ΔT where G is the junction conductance 83. Transport through molecular junctions is typically in the coherent regime where conductance, which is pro-portional to the electronic transmission probability, is given by the Landauer formula 84. The Seebeck coefficient at zero applied voltage is then related to the derivative of the transmission probability at the metal Fermi energy (in the off-resonance limit), with, S = −∂E ∂ln( (E ))π2k 2B T E 3ewhere k B is the Boltzmann constant, e is the charge of the electron, T (E ) is the energy-dependent transmission function and E F is the Fermi energy. When the transmission function for the junction takes on a simple Lorentzian form 85, and transport is in the off-resonance limit, the sign of S can be used to deduce the nature of charge carriers in molecular junctions. In such cases, a positive S results from hole transport through the highest occupied molecu-lar orbital (HOMO) whereas a negative S indicates electron trans-port through the lowest unoccupied molecular orbital (LUMO). Much work has been performed on investigating the low-bias con-ductance of molecular junctions using a variety of chemical linker groups 86–89, which, in principle, can change the nature of charge carriers through the junction. Molecular junction thermopower measurements can thus be used to determine the nature of charge carriers, correlating the backbone and linker chemistry with elec-tronic aspects of conduction.Experimental measurements of S and conductance were first reported by Ludoph and Ruitenbeek 90 in Au point contacts at liquid helium temperatures. This work provided a method to carry out thermoelectric measurements on molecular junctions. Reddy et al.91 implemented a similar technique in the STM geome-try to measure S of molecular junctions, although due to electronic limitations, they could not simultaneously measure conductance. They used thiol-terminated oligophenyls with 1-3-benzene units and found a positive S that increased with increasing molecular length (Fig. 4b). These pioneering experiments allowed the iden-tification of hole transport through thiol-terminated molecular junctions, while also introducing a method to quantify S from statistically significant datasets. Following this work, our group measured the thermoelectric current through a molecular junction held under zero external bias voltage to determine S and the con-ductance through the same junction at a finite bias to determine G (ref. 92). Our measurements showed that amine-terminated mol-ecules conduct through the HOMO whereas pyridine-terminatedmolecules conduct through the LUMO (Fig. 4b) in good agree-ment with calculations.S has now been measured on a variety of molecular junctionsdemonstrating both hole and electron transport 91–95. Although the magnitude of S measured for molecular junctions is small, the fact that it can be tuned by changing the molecule makes these experiments interesting from a scientific perspective. Future work on the measurements of the thermal conductance at the molecu-lar level can be expected to establish a relation between chemical structure and the figure of merit, which defines the thermoelec-tric efficiencies of such devices and determines their viability for practical applications.SpintronicsWhereas most of the explorations of metal–molecule–metal junc-tions have been motivated by the quest for the ultimate minia-turization of electronic components, the quantum-mechanical aspects that are inherent to single-molecule junctions are inspir-ing entirely new device concepts with no classical analogues. In this section, we review recent experiments that demonstrate the capability of controlling spin (both electronic and nuclear) in single-molecule devices 96. The early experiments by the groups of McEuen and Ralph 97, and Park 98 in 2002 explored spin-depend-ent transport and the Kondo effect in single-molecule devices, and this topic has recently been reviewed in detail by Scott and Natelson 99. Here, we focus on new types of experiment that are attempting to control the spin state of a molecule or of the elec-trons flowing through the molecular junction. These studies aremotivated by the appeal of miniaturization and coherent trans-port afforded by molecular electronics, combined with the great potential of spintronics to create devices for data storage and quan-tum computation 100. The experimental platforms for conducting DOI: 10.1038/NNANO.2013.91。

薛定谔—麦克斯韦尔方程径向解的存在性和多重性(英文)

In 1887, the German physicist Erwin Schrödinger proposed a radial solution to the Maxwell-Schrödinger equation. This equation describes the behavior of an electron in an atom and is used to calculate its energy levels. The radial solution was found to be valid for all values of angular momentum quantum number l, which means that it can describe any type of atomic orbital.The existence and multiplicity of this radial solution has been studied extensively since then. It has been shown that there are infinitely many solutions for each value of l, with each one corresponding to a different energy level. Furthermore, these solutions can be divided into two categories: bound states and scattering states. Bound states have negative energies and correspond to electrons that are trapped within the atom; scattering states have positive energies and correspond to electrons that escape from the atom after being excited by external radiation or collisions with other particles.The existence and multiplicity of these solutions is important because they provide insight into how atoms interact with their environment through electromagnetic radiation or collisions with other particles. They also help us understand why certain elements form molecules when combined together, as well as why some elements remain stable while others decay over time due to radioactive processes such as alpha decay or beta decay.。

SCI科技论文写作常用句型大全

一．好的论文题目是成功的一半好的论文，每一个部分都需要精雕细琢。

我们先来看看Science, Nature 子刊上用的都是些什么题目，到底这些题目暗含哪些玄机？以下是从2016年发表的论文中随机挑选的一些题目，我将其做了一下简单的分类：?reduction1. Water splitting–biosynthetic system with CO2efficiencies?exceeding?photosynthesis. (Science, 2016, 352, 1210)类似: Scalable water splitting on particulate photocatalyst sheets with a solar-to-hydrogen energy conversion efficiency?exceeding?1%?(Nature Materials 2016,15,611-615)这种题目适合哪类文章？适合于那种性能极其显着的文章（可以创纪录的文章），比如说Nocera et al. 的?Science, 2016, 352, 1210，直接与光合作用进行对比，给人的震撼是非常强的。

这种对比效果能够一下子抓住人们的眼球，吸引着读者进行阅读。

要点：使用这样的题目首先你的实验结果得够牛，你对于实验结果要足够自信，对于背景知识的了解得要足够深。

因为取这样的题目意味着你要真正达到了某一个高度。

如果明明有很多大海在那里，你个小池塘和小水坑进行比较，那么会闹笑话的。

2.1 Quantifying?the promotion of Cu catalysts by ZnO for methanol synthesis (?Science,2016, 352, 969-974.)2.2?Exploring?the origin of high optical absorption in conjugated polymers. (Nature Materials 2016,?DOI:?10.1038/nmat4645?)2.3 Promoting?solution phase discharge in Li–O2 batteries containing weakly solvatingelectrolyte?solutions (Nature Materials 2016, DOI: 10.1038/nmat4629)2.4 Reconstructing?solute-induced phase transformations within individual nanocrystals (NatureMaterials 2016,?doi:10.1038/nmat4620)2.5 Tailoring?the nature and strength of electron–phonon interactions in the SrTiO3(001) 2D electron?liquid (Nature Material, 2016, doi:10.1038/nmat4623)我简单地检索了下Nature Materials上面的文章题目，发现这种类型的题目真的非常多。

高效液相色谱法测定鸡肉中磺胺类药物残留的不确定度评定_赵健亚

高效液相色谱法测定鸡肉中磺胺类药物残留的不确定度评定赵健亚1，陈丹2，谢怀根2，肖静1,*(1.南通大学公共卫生学院，江苏南通 226019；2.南通市动物疫病预防控制中心，江苏南通 226006) 摘要：依据JJF 1059—1999《测量不确定度评定与表示》和CNAS —GL06《化学分析中不确定度的评估指南》规定的测量不确定度的基本方法，建立数学模型，分析高效液相色谱法测定鸡肉中磺胺类药物残留的不确定度来源，并对各分量进行量化，给出5种磺胺类药物残留测定结果的扩展不确定度，评定结果表明：影响检测结果不确定度的主要因素为标准曲线拟合、样品前处理过程和测量重复性等。

关键词：不确定度；磺胺；高效液相色谱法；鸡肉Uncertainty Evaluation for Determination of Sulfonamide Residues in Chicken by High Performance Liquid ChromatographyZHAO Jian-ya 1，CHEN Dan 2，XIE Huai-gen 2，XIAO Jing 1,*(1. School of Public Health, Nantong University, Nantong 226019, China ；2. Nantong Center for Animal Disease Control and Prevention, Nantong 226006, China)Abstract ：A mathematical model was established according to the basic method for uncertainty evaluation from JJF 1059—1999 and CNAS-GL06. The sources of uncertainty for determining sulfonamide residues in chicken by high performance liquid chromatography (HPLC) were analyzed and each component of uncertainty was quantified. The expanded uncertainty for ﬁ ve sulfonamides residues results was calculated. The major uncertainty sources were standard curve ﬁ tting, sample pretreatment and measurement repeatability.Key words ：uncertainty ；sulfonamides ；high performance liquid chromatography (HPLC)；chicken 中图分类号：TS207.3 文献标志码：A 文章编号：1002-6630(2013)10-0144-04doi:10.7506/spkx1002-6630-201310031收稿日期：2012-02-24基金项目：国家自然科学基金青年科学基金项目(31000539)；南通市应用研究计划项目(K2010066)作者简介：赵健亚(1980—)，女，讲师，硕士，主要从事食品安全质量控制研究。

mitochondrial control of inflammation文献讲解

mitochondrial control of inflammation文献讲解Mitochondrial Control of Inflammation: A Literature ReviewIntroduction:Inflammation is a complex physiological process that plays a crucial role in the immune response. It is initiated as a protective mechanism in response to infection, injury, or autoimmune diseases. However, sustained or dysregulated inflammation can have detrimental effects and lead to chronic diseases such as cardiovascular diseases, neurodegenerative disorders, and cancer.In recent years, there has been growing evidence suggesting a link between inflammation and mitochondrial dysfunction. Mitochondria, often referred to as the "powerhouses" of the cells, are key regulators of cellular energy production and play a vital role in various cellular processes, including inflammation. This literature review aims to summarize the current understanding of mitochondrial control of inflammation and the underlying mechanisms involved.Mitochondrial dynamics and inflammation:Mitochondria are highly dynamic organelles that constantly undergo fusion and fission processes, collectively known as mitochondrial dynamics. These processes are essential for maintaining normal mitochondrial function and cellular homeostasis. Several studies have demonstrated that dysregulation of mitochondrial dynamics can lead to an imbalance in inflammatory responses.Mitochondrial dysfunction and inflammatory signaling:Mitochondria are not only responsible for energy production but also serve as major signaling platforms in the cell. They release various molecules, including reactive oxygen species (ROS), mitochondrial DNA (mtDNA), and specific metabolites, which cantrigger innate immune responses and modulate the inflammatory signaling pathways. Dysfunctional mitochondria can release an excess amount of these signaling molecules, leading to chronic inflammation.Mitophagy and inflammation:Mitophagy is a specialized form of autophagy that selectively targets damaged or dysfunctional mitochondria for degradation. It is a crucial process that maintains mitochondrial quality control and regulates cellular inflammation. Dysfunctional mitophagy can lead to the accumulation of damaged mitochondria and the release of pro-inflammatory molecules, perpetuating chronic inflammation.Mitochondrial DNA and inflammasome activation:The presence of mitochondrial DNA in the cytosol can activate the NLRP3 inflammasome, a critical component of the innate immune system. The inflammasome activation leads to the production of pro-inflammatory cytokines, including interleukin-1β (IL-1β) and interleukin-18 (IL-18). Dysregulated inflammasome activation due to mitochondrial dysfunction can contribute to the development of chronic inflammatory diseases.Modulation of mitochondrial function for therapeutic interventions:Given the significant role of mitochondria in inflammation, targeting mitochondrial function emerges as a potential therapeutic strategy for inflammatory diseases. Several compounds have been identified that can modulate mitochondrial function and ameliorate inflammation. For example, mitochondria-targeted antioxidants have shown promising results in reducing oxidative stress and inflammation in various disease models.Conclusion:In conclusion, accumulating evidence supports the notion that mitochondrial control of inflammation is a critical process underlying the development of chronic inflammatory diseases. Dysfunctional mitochondria can disrupt the delicate balance between pro-inflammatory and anti-inflammatory responses, leading to sustained inflammation andtissue damage. Further research is needed to fully unravel the intricate mechanisms through which mitochondrial dysfunction contributes to inflammation. Targeting mitochondrial function may offer novel therapeutic avenues for the treatment of chronic inflammatory diseases.。

Instruction Manual for Q-NMR Learning Module说明书

Instructor’s GuideThis guide is intended to assist instructors in the utilization of the q-NMR learning module. While the module is designed as a stand-alone resource toaccommodate self-learners, it can also be used as an active learning resource. This instructor’s guide is designed to help1. Basic Theory Concept Questions. The questions below are also listed on the webpage that links to the Basic Theory section. These questions can be handed out in class or given as a homework assignment. Students should be able to answer these questions using the Basic Theory section of this module as an instructional resource. I would also recommend assigning the excellent web resource created by Joe Hornak, since it contains embedded animations that help clarify many difficult to understand processes in NMR. This site can be accessed directly at /htbooks/nmr/ or students can bedirected to this site in ASDL by typing its ID number, 2921, into the search box in the upper right hand corner of the site.What is spin?How does absorption of energy generate an NMR spectrum? Why is NMR less sensitive than UV-visible spectroscopy?What is chemical shift and how does it relate to resonance frequency? What is precession?How does precession produce the macroscopic magnetization (Mo)?How can the nuclear spins be manipulated to generate the NMR spectrum? What is the tip angle?What is a Free Induction Decay?How do T 1 and T 2 relaxation affect NMR spectra?2. Answers to Questions in the Basic Theory section. In addition to the conceptual questions given above, the Basic Theory section also contains aseries of simple quantitative questions, the answers of which are provided below.Question 1: How many spin states would you predict for 2H?Deuterium has a spin of 1. There for there should be 3 possible spin states: +1, 0 and -1.Question 2: Given the same magnetic field and temperature, how would the difference in population for 1H and 31P compare? For this problem we will use the equationThe difference in population for 1H and 31P will be related to the differences in their ∆E values. Since ∆E=γhB o /2π, for a fixed magnetic field the only differences between 1H and 31P is in their magnetogyric ratios.kT Elower upper e N N ∆−=468.284.10752.26)()(311==∆∆P E H EThe ratio of the N upper /N lower for 1H is e 2.468 or =11.80 times larger than the ratio of N upper /N lower for 31P.Question 3: Calculate the wavelength of electromagnetic radiation corresponding to a frequency of 500 MHz.The wavelength of electromagnetic radiation corresponding to a frequency of 500 MHz is 0.6 m.Question 4: What range of frequencies would be excited by a 10 µs rf pulse?A 10 µs rf pulse would excite a range of frequencies covering 100,000 Hz.Question 5: What are the resonance line widths of nuclei that have apparent T 2 relaxation times (i.e.T 2* values) of 1 and 2 sec.*2211T w π=Therefore, the two resonances have line widths of 0.32 and 0.16 Hz.3. Practical Aspects Concept Questions. The questions below are also listed on the webpage that links to the Practical Aspects section. These questions can be handed out in class or given as a homework assignment. Students should be able to answer these questions using the Practical Aspects section of this module as an instructional resource.How do I choose a reference standard for my Q-NMR analysis?How is the internal standard used to quantify the concentration of my analyte? What sample considerations are important in Q-NMR analysis?How do I choose the right acquisition parameters for a quantitative NMR measurement?What data processing considerations are important for obtaining accurate and precise results?4. Answers to Questions in the Practical Aspects section.Question 1. A quantitative NMR experiment is performed to quantify the amount of isopropyl alcohol in a D 2O solution. Sodium maleate (0.01021 M) is used as an internal standard. The integral obtained for the maleate resonance is 46.978. The isopropanol doublet at 1.45 ppm produces an integral of 104.43. What would youpredict for the integral of the isopropanol CH resonance as 3.99 ppm. What is the concentration of isopropanol in this solution?The isopropanol CH resonance is produced by a single proton whereas the doublet is produced by the 6 methyl protons. Therefore, the CH integral should be 1/6th that of the methyl doublet, or 17.405.To find the isopropanol concentration we first have to calculate normalized areas for isopropanol and our standard, maleate. The isopropanol(IP) doublet is comprised of 6 protons due to the two equivalent methyl groups of this compound.Normalized Area (IP) = 104.43 = 17.4056Similarly, the normalized area for maleate (MA) is:Normalized Area (MA) = 46.978 = 23.4892The concentration of the isopropanol can be calculated using the known the maleate concentration.[IP] = [MA] x Normalized Area (IP)Normalized Area (MA)[IP] = 0.01021 M x 17.405 = 0.007565 M23.489Because the accuracy of the determination depends on how well the maleate concentration is know, the standard solution should be prepared with care, using dried sodium maleate of high purity, weighing carefully a mass that is known to an appropriate number of significant figures (in this case 4), transferring the maleate quantitatively to a volumetric flask and finally dilution to the mark. Again, an appropriate solution volume must be selected to produce the desired number of significant figures given the manufacturer specifications for the glassware used.Question 2: A solution prepared for quantitative analysis using NMR was acquired by coaddition of 8 FIDs produces a spectrum with an S/N of 62.5 for the analyte signals. How many FIDs would have to be coadded to produce a spectrum with an S/N of 250?S/N increases in NMR experiments as the square root of the number of scans coadded.S/N ∝ (n)0.5To increase the S/N from 62.5 to 250 (a factor of 4 increase in S/N) would require coaddition of 16 times as many FIDs as was used to produce a spectrum withS/N of 62.5. The answer is that coaddition of 128 FIDs (8 x 16) would be required to achieve an S/N of 250.Question 3: A 1H NMR spectrum was measured using a 400.0 MHz instrument by acquisition of 8192 total data points (8192 real points) and a spectral width of 12.00 ppm. What was the acquisition time? Calculate the digital resolution of the resulting spectrum? Is this digital resolution sufficient to accurately define a peak with a width at half height of 0.5 Hz?We can calculate the acquisition time knowing the spectral width and the total number of data points.AT= NP_ = 16384__ = 1.707 sec2 SW 2 x 400 x 12DR = SW_ = 2 x 400 x 12 = 1.172 Hz/ptNP(real) 8192This would not be adequate digital resolution to accurately define a peak with a 0.5 Hz width at half height. A longer acquisition time would allow for collection of more points. Also, zero-filling could also be used to help increase the digital resolution.5. Q-NMR DrylabKHP T1 relaxation times. There are two ways of getting the T1 relaxation times for the KHP resonances. The simplest way is to have students estimate the null times for the two resonances in the inversion-recovery spectra provided. Selected spectra from the dry lab data set were used to make the figure in the Practical Aspects section of the module. Alternatively, students can process the spectra and measure resonance integrals for each peak. These can be plotted vs. the relaxation delay and fit to determine T1. The integrals we obtained are summarized in the Table below. The fits obtained using Origin 7.5 are also provided. We obtained T1 values of 4.79s and 3.11s for the KHP resonances at 7.75 and 7.61 ppm, respectively.The concentration of KHP in the stock solution is determined from the mass of KHP.Mass KHP = 0.3533 g – 0.2219 g = 0.1314 gML mol g g KHP 1287.0005.01/22.2041314.0][=×=Table 1. Inversion-recovery data for KHPDelay Integral R1 (7.75 ppm) Integral R2 (7.61 ppm) 0 s -8.34 -8.48 2 -2.38 0.07 2.5 -1.01 1.65 3 -0.14 2.81 3.5 0.8 3.78 4 1.62 4.57 6 3.87 6.86 10 6.37 8.63 15 8.28 9.67 208.959.65Inversion-recovery plot for R 1Inversion-recovery plot for R 2Malic Acid Standard Solution Determination. From the mass of malic acid weighed and the solution volume, we can calculate the concentration of this standard.Mass of MA = 0.3324g – 0.1897 g = 0.1427 g ML mol g g MA 2128.0005.01/09.1341427.0][=×=Since equal volumes of the KHP and malic acid were mixed to prepare this solution, the dilution factor can be neglected and the concentration of malic acid calculated as shown below. Here we used the integral of the resonances at 2.82 and 2.89 ppm corresponding to the inequivalent malic acid CH 2 protons.I n t e g r a lInversion-Recovery Delay I n t e g r a lInversion-Recovery DelayMM Int N N Int KHP MA KHP KHP MA MA 2142.0000.1428322.01287.0][][=××=××=Spectrum of malic acid standard solution containing KHPDetermination of Malic Acid in Apple Juice. The concentration of malic acid can similarly be calculated in an apple juice sample. Here though we will need to take into account the dilutions performed.The KHP was diluted twice in preparing this solution. First it was diluted by half with D 2O, and subsequently 100 µL of was further diluted by addition to 900 µL of apple juice for a total volume of 1 mL. The KHP concentration in the apple juice sample can be calculated as shown below. Note that the volume added in making the pH adjustment to 1.35 is not important since both the KHP and the malic acid will be diluted by the same amount. This pH adjustment is necessary to resolve the malic acid resonances from those of the other apple juice components. Because of the simplicity of the malic acid standard spectrum, pH adjustment is not needed. MM KHP KHP stock juice 00643.01000100211287.010*******][][=××=××=The malic acid concentration can then be calculated as before, providing that the dilution resulting from addition of the KHP solution is included in the calculation.MM Int N N Int KHP MA KHP KHP MA MA juice juice 0328.090010004351.042000.100643.09001000][][=×××=×××=For purposes of comparison with the table provided in the background section of this laboratory, we can convert this concentration to g/L using the molecular weight of malic acid.0.0.328 M x 134.09 g/mol = 4.40 g/L malic acid。

库什曼螺旋体英文介绍

库什曼螺旋体英文介绍《库什曼螺旋体：一种奇特的微生物》The "Kushman Spirillum: An Extraordinary Microorganism"Introduction:Microorganisms constitute a diverse range of life forms on Earth, including bacteria, viruses, fungi, and protozoa. One intriguing microbe is the Kushman spirillum, also known as the spirochete bacterium. This microorganism exhibits distinctive physical characteristics and a fascinating mode of life that has captivated the attention of scientists worldwide.Physical Description:The Kushman spirillum is a helical-shaped bacterium, resembling a tightly coiled spring or a corkscrew. Its spiral shape is the result of their unique cell structure and motility machinery, which includes periplasmic flagella. These flagella allow it to twist and rotate its body, propelling itself through the surrounding environment. With an average length of 10 to 20 micrometers, the Kushman spirillum appears as a long, thin filament under a microscope.Habitat and Distribution:These microorganisms inhabit a variety of environments, including freshwater bodies, marine ecosystems, and even gastrointestinal tracts of animals. They are often found in environments with high organic content, such as sewage and decaying matter. Kushman spirilla are known to form biofilms – communities of microorganisms attached to surfaces – in order to protect themselves and efficiently access nutrients.Metabolism:Kushman spirilla are chemoorganotrophic bacteria, meaning they obtain energy by breaking down organic compounds through respiration. They are capable of using a wide range of organic substances, including sugars, amino acids, and fatty acids, as energy sources. These microorganisms also play critical roles in various biochemical cycles, such as nitrogen and sulfur cycles, contributing to the recycling of essential elements in the ecosystem.Role in Disease:While the majority of Kushman spirilla are harmless, certain strains have been associated with diseases in humans and other animals. For example, some species of spirochetes are responsible for causing Lyme disease and syphilis. Understanding the pathogenic characteristics and mechanisms of these bacteria is essential for the development of effective treatments and preventive measures. Scientific Research:Research on Kushman spirilla is multidisciplinary, involving microbiology, genetics, molecular biology, and ecology. Scientists are keen to decipher the mechanisms of its unique helical structure, motility, and its ability to adapt to various environments. Furthermore, investigations into the genetics and metabolism of this microorganism have contributed to advancements in biotechnology, such as the production of useful enzymes and biofuels.Conclusion:The Kushman spirillum is an extraordinary microorganism that continues to fascinate scientists due to its distinct helical shape and unique biological characteristics. Its ability to adapt to diverse environments and perform various essential functions highlights its ecological importance. Furthermore, research on this microorganism has paved the way for numerous applications in biotechnology and medical science. As we delve deeper into the world of microorganisms, the Kushman spirillum remains a remarkable subject of study, unveiling the mysteries of the microbial world.。

Methods and systems for controlling the concentrat

专利名称：Methods and systems for controlling theconcentration of a component in acomposition with absorption spectroscopy发明人：Matthew L. Fisher,David L. Snyder,AshutoshMisra申请号：US10064222申请日：20020621公开号：US20030020907A1公开日：20030130专利内容由知识产权出版社提供专利附图：摘要：Provided are methods and systems for controlling the concentration of acomponent in a composition, and semiconductor processing methods and systems. One exemplary method of controlling the concentration of a component in a composition involves: providing a composition which has a liquid portion, wherein the liquid portion contains a component to be monitored; performing an absorption spectroscopy measurement on a sample of the composition; and controlling the concentration of the component in the composition based on the absorption spectroscopy measurement using a feedback control loop. The invention allows for controlling the concentration of a component in a composition, for example, a corrosion inhibitor in a chemical planarization (CMP) chemical, as well as in pre- and post-CMP storage/treatment chemicals, and can provide real time, accurate process control in a simple and robust manner.申请人：FISHER MATTHEW L.,SNYDER DAVID L.,MISRA ASHUTOSH更多信息请下载全文后查看。

分数阶多机器人的领航-跟随型环形编队控制

第38卷第1期2021年1月控制理论与应用Control Theory&ApplicationsV ol.38No.1Jan.2021分数阶多机器人的领航–跟随型环形编队控制伍锡如†,邢梦媛(桂林电子科技大学电子工程与自动化学院,广西桂林541004)摘要:针对多机器人系统的环形编队控制复杂问题,提出一种基于分数阶多机器人的环形编队控制方法,应用领航–跟随编队方法来控制多机器人系统的环形编队和目标包围,通过设计状态估测器,实现对多机器人的状态估计.由领航者获取系统中目标状态的信息,跟随者监测到领航者的状态信息并完成包围环绕编队控制,使多机器人系统形成对动态目标的目标跟踪.根据李雅普诺夫稳定性理论和米塔格定理,得到多机器人系统环形编队控制的充分条件,实现对多机器人系统对目标物的包围控制,通过对一组多机器人队列的目标包围仿真,验证了该方法的有效性.关键词:分数阶;多机器人;编队控制;环形编队;目标跟踪引用格式:伍锡如,邢梦媛.分数阶多机器人的领航–跟随型环形编队控制.控制理论与应用,2021,38(1):103–109DOI:10.7641/CTA.2020.90969Annular formation control of the leader-follower multi-robotbased on fractional orderWU Xi-ru†,XING Meng-yuan(School of Electronic Engineering and Automation,Guilin University of Electronic Technology,Guilin Guangxi541004,China) Abstract:Aiming at the complex problem of annular formation control for fractional order multi robot system,an an-nular formation control method based on fractional order multi robot is proposed.The leader follower formation method is used to control the annular formation and target envelopment of the multi robot systems.The state estimation of multi robot is realized by designing state estimator.The leader obtains the information of the target state in the system,the followers detects the status of the leader and complete annular formation control,the multi-robot system forms the target tracking of the dynamic target.According to Lyapunov stability theory and Mittag Lefﬂer’s theorem,the sufﬁcient conditions of the annular formation control for the multi robot systems are obtained in order to achieve annular formation control of the leader follower multi robot.The effectiveness of the proposed method is veriﬁed by simulation by simulation of a group of multi robot experiments.Key words:fractional order;multi-robots;formation control;annular formation;target trackingCitation:WU Xiru,XING Mengyuan.Annular formation control of the leader-follower multi-robot based on fractional order.Control Theory&Applications,2021,38(1):103–1091引言近年来,随着机器人技术的崛起和发展,各式各样的机器人技术成为了各个领域不可或缺的一部分,推动着社会的发展和进步.与此同时,机器人面临的任务也更加复杂,单个机器人已经无法独立完成应尽的责任,这就使得多机器人之间相互协作、共同完成同一个给定任务成为当前社会的研究热点.多机器人系统控制的研究主要集中在一致性问题[1]、多机器人编队控制问题[2–3]、蜂拥问题[4–5]等.其中,编队控制问题作为多机器人系统的主要研究方向之一,是国内外研究学者关注的热点问题.编队控制在生活生产、餐饮服务尤其是军事作战等领域都发挥着极大的作用.例如水下航行器在水中的自主航行和编队控制、军事作战机对空中飞行器的打击以及无人机在各行业的应用等都是多机器人编队控制上的用途[6–7].目前,多机器人编队控制方法主要有3种,其中在多机器收稿日期:2019−11−25;录用日期:2020−08−10.†通信作者.E-mail:****************;Tel.:+86132****1790.本文责任编委:黄攀峰.国家自然科学基金项目(61603107,61863007),桂林电子科技大学研究生教育创新计划项目(C99YJM00BX13)资助.Supported by the National Natural Science Foundation of China(61603107,61863007)and the Innovation Project of GUET Graduate Education (C99YJM00BX13).104控制理论与应用第38卷人系统编队控制问题上应用最广泛的是领航–跟随法[8–10];除此之外,还有基于行为法和虚拟结构法[11].基于行为的多机器人编队方法在描述系统整体时不够准确高效,且不能保证系统控制的稳定性;而虚拟结构法则存在系统灵活性不足的缺陷.领航–跟随型编队控制法具有数学分析简单、易保持队形、通信压力小等优点,被广泛应用于多机器人系统编队[12].例如,2017年,Hu等人采用分布式事件触发策略,提出一种新的自触发算法,实现了线性多机器人系统的一致性[13];Zuo等人利用李雅普诺夫函数,构造具有可变结构的全局非线性一致控制律,研究多机器人系统的鲁棒有限时间一致问题[14].考虑到分数微积分的存储特性,开发分数阶一致性控制的潜在应用具有重要意义.时中等人于2016年设计了空间遥操作分数阶PID 控制系统,提高了机器人系统的跟踪性能、抗干扰性、鲁棒性和抗时延抖动性能[15].2019年,Z Yang等人探讨了分数阶多机器人系统的领航跟随一致性问题[16].而在多机器人的环形编队控制中,对具有分数阶动力学特性的多机器人系统的研究极其有限,大部分集中在整数阶的阶段.而采用分数阶对多机器人系统目标包围编队控制进行研究,综合考虑了非局部分布式的影响,更好地描述具有遗传性质的动力学模型.使得系统的模型能更准确的反映系统的性态,对多机器人编队控制的研究非常有利.目标包围控制问题是编队控制的一个分支,是多智能体编队问题的重点研究领域.随着信息技术的高速发展,很多专家学者对多机器人系统的目标包围控制问题进行了研究探讨.例如,Kim和Sugie于2017年基于一种循环追踪策略设计分布式反馈控制律,保证了多机器人系统围绕一个目标机器人运动[17].在此基础上,Lan和Yan进行了拓展,研究了智能体包围多个目标智能体的问题,并把这个问题分为两个步骤[18]. Kowdiki K H和Barai K等人则研究了单个移动机器人对任意时变曲线的跟踪包围问题[19].Asif M考虑了机器人与目标之间的避障问题,提出了两种包围追踪控制算法;并实现了移动机器人对目标机器人的包围追踪[20].鉴于以上原因,本文采用了领航–跟随型编队控制方法来控制多机器人系统的环形编队和目标包围,通过设计状态估测器,实现对多机器人的状态估计.系统中目标状态信息只能由领航者获取,确保整个多机器人系统编队按照预期的理想编队队形进行无碰撞运动,并最终到达目标位置,对目标、领航者和跟随者的位置分析如图1(a)所示,图1(b)为编队控制后的状态.通过应用李雅普诺夫稳定性理论,得到实现多机器人系统环形编队控制的充分条件.最后通过对一组多机器人队列进行目标包围仿真,验证了该方法的有效性.(a)编队控制前(b)编队控制后图1目标、领航者和追随者的位置分析Fig.1Location analysis of targets,pilots and followers2代数图论与分数阶基础假定一个含有N个智能体的系统,通讯网络拓扑图用G={v,ε}表示,定义ε=v×v为跟随者节点之间边的集合,v={v i,i=1,2,···,N}为跟随者节点的集合.若(v i,v j)∈ε,则v i与v j为相邻节点,定义N j(t)={i|(v i,v j)∈ε,v i∈v}为相邻节点j的标签的集合.那么称第j个节点是第i 个节点的邻居节点,用N j(t)={i|(v i,v j)∈ε,v i∈v}表示第i个节点的邻居节点集合.矩阵L=D−A称为与图G对应的拉普拉斯矩阵.其中:∆是对角矩阵,对角线元素i=∑jN i a ij.若a ij=a ji,i,j∈I,则称G是无向图,否则称为有向图.如果节点v i与v j之间一组有向边(v i,v k1)(v k1,v k2)(v k2,v k3)···(v kl,v j),则称从节点v i到v j存在有向路径.定义1Riemann-Liouville(RL)分数阶微分定义:RLD atf(t)=1Γ(n−a)d nd t ntt0f(τ)(t−τ)a−n+1dτ,(1)其中:t>t0,n−1<α<n,n∈Z+,Γ(·)为伽马函数.定义2Caputo(C)分数阶微分定义:CDαtf(t)=1Γ(n−α)tt0f n(τ)(t−τ)α−n+1dτ,(2)其中:t>t0,n−1<α<n,n∈Z+,Γ(·)为伽马第1期伍锡如等:分数阶多机器人的领航–跟随型环形编队控制105函数.定义3定义具有两个参数α,β的Mittag-Lefﬂer方程为E α,β(z )=∞∑k =1z kΓ(αk +β),(3)其中:α>0,β>0.当β=1时,其单参数形式可表示为E α,1(z )=E α(z )=∞∑k =1z kΓ(αk +1).(4)引理1[21]假定存在连续可导函数x (t )∈R n ,则12C t 0D αt x T (t )x (t )=x T (t )C t 0D αt x (t ),(5)引理2[21]假定x =0是系统C t 0D αt x (t )=f (x )的平衡点,且D ⊂R n 是一个包含原点的域,R 是一个连续可微函数,x 满足以下条件:{a 1∥x ∥a V (t ) a 2∥x ∥ab ,C t 0D αt V (t ) −a 3∥x ∥ab,(6)其中:t 0,x ∈R ,α∈(0,1),a 1,a 2,a 3,a,b 为任意正常数,那么x =0就是Mittag-Lefﬂer 稳定.3系统环形编队控制考虑包含1个领航者和N 个跟随者的分数阶非线性多机器人系统.领航者的动力学方程为C t 0D αt x 0(t )=u 0(t ),(7)式中:0<α<1,x 0(t )∈R 2是领航者的位置状态,u 0(t )∈R 2是领航者的控制输入.跟随者的动力学模型如下:C t 0D αt x i (t )=u i (t ),i ∈I,(8)式中:0<α<1,x i (t )∈R 2是跟随者的位置状态,u i (t )∈R 2是跟随者i 在t 时刻的控制输入,I ={1,2,···,N }.3.1领航者控制器的设计对于领航者,选择如下控制器:u 0(t )=−k 1(x 0(t )−˜x 0(t ))−k 2sgn(x 0(t )−˜x 0(t )),(9)C t 0D αt x 0(t )=u 0(t )=−k 1(x 0(t )−˜x 0(t ))−k 2sgn(x 0(t )−˜x 0(t )).(10)设计一个李雅普诺夫函数:V (t )=12(x 0(t )−˜x 0(t ))T (x 0(t )−˜x 0(t )).(11)根据引理1,得到该李雅普诺夫函数的α阶导数如下:C 0D αt V(t )=12C 0D αt (x 0(t )−˜x 0(t ))T (x 0(t )−˜x 0(t )) (x 0(t )−˜x 0(t ))TC 0D αt (x 0(t )−˜x0(t ))=(x 0(t )−˜x 0(t ))T [C 0D αt x 0(t )−C 0D αt ˜x0(t )]=(x 0(t )−˜x 0(t ))T [−k 1(x 0(t )−˜x 0(t ))−k 2sgn(x 0(t )−˜x 0(t ))−C 0D αt ˜x0(t )]=−k 1(x 0(t )−˜x 0(t ))T (x 0(t )−˜x 0(t ))−k 2∥x 0(t )−˜x 0(t )∥−(x 0(t )−˜x 0(t ))TC 0D αt ˜x0(t )=−2k 1V (t )−k 2∥x 0(t )−˜x 0(t )∥+∥C 0D αt ˜x0(t )∥∥x 0(t )−˜x 0(t )∥=−2k 1V (t )−(k 2−∥C 0D ∝t ˜x0(t )∥)∥x 0(t )−˜x 0(t )∥ −2k 1V (t ).(12)令a 1=a 2=12,a 3=2k 1,ab =2,a >0,b >0,得到a 1∥x 0(t )−˜x 0(t )∥a V (t ) a 2∥x 0(t )−˜x 0(t )∥ab ,(13)C t 0D αt V(t ) −a 3∥x 0(t )−˜x 0(t )∥ab .(14)根据引理2,可知lim t →∞∥x 0(t )−˜x 0(t )∥=0,即x 0(t )逐渐趋近于˜x 0(t ).为了使跟随者能够跟踪观测到领航者的状态,设计了一个状态估测器.令ˆx i ∈R 2是追随者对领航者的状态估计,给出了ˆx i 的动力学方程C 0D αt ˆx i=β(∑j ∈N ia ij g ij (t )+d i g i 0(t )),(15)其中g ij =˜x j (t )−˜x i (t )∥˜x j (t )−˜x i (t )∥,˜x j (t )−˜x i (t )=0,0,˜x j (t )−˜x i (t )=0.(16)对跟随者取以下李雅普诺夫函数:V (t )=12N ∑i =1(ˆx i (t )−x 0(t ))T (ˆx i (t )−x 0(t )).(17)计算该函数的α阶导数如下:C 0D αt V(t )=12C 0D αtN ∑i =1(ˆx i (t )−x 0(t ))T (ˆx i (t )−x 0(t )) N ∑i =1(ˆx i (t )−x 0(t ))TC 0D αt (ˆx i (t )−x 0(t ))=N ∑i =1(ˆx i (t )−x 0(t ))T [C 0D αt ˆxi (t )−C 0D αt x 0(t )]=N ∑i =1(ˆx i (t )−x 0(t ))T [β(∑j ∈N ia ijˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥+d iˆx 0(t )−ˆx i (t )∥ˆx 0(t )−ˆx i (t )∥)−C 0D αt x 0(t )]=N ∑i =1(ˆx i (t )−x 0(t ))T β(∑j ∈N i a ij ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i(t )∥+106控制理论与应用第38卷d iˆx 0(t )−ˆx i (t )∥ˆx 0(t )−ˆx i (t )∥)−N ∑i =1(ˆx i (t )−x 0(t ))TC 0D αt x 0(t )=βN ∑i =1(ˆx i (t )−x 0(t ))T ∑j ∈N i a ij ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥+βN ∑i =1(ˆx i (t )−x 0(t ))Td i ˆx 0(t )−ˆx i (t )∥ˆx 0(t )−ˆx i(t )∥−N ∑i =1(ˆx i (t )−x 0(t ))TC 0D αt x 0(t ).(18)在上式中,令C 0D αt V (t )=N 1+N 2以方便后续计算,其中:N 1=βN ∑i =1(ˆx i (t )−x 0(t ))T ∑j ∈N i a ij ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥+βN ∑i =1(ˆx i (t )−x 0(t ))Td i ˆx 0(t )−ˆx i (t )∥ˆx 0(t )−ˆx i (t )∥=β2[N ∑i =1N ∑j =1a ij (ˆx i (t )−x 0(t ))T ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥+N ∑j =1N ∑i =1a ij (ˆx j (t )−x 0(t ))Tˆx i (t )−ˆx j (t )∥ˆx i (t )−ˆx j (t )∥]−βN ∑i =1d i∥ˆx 0(t )−ˆx i (t )∥2∥ˆx 0(t )−ˆx i (t )∥=β2N ∑i =1N ∑j =1a ij [(ˆx i (t )−x 0(t ))Tˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥−(ˆx j (t )−x 0(t ))T ˆx i (t )−ˆx j (t )∥ˆx i (t )−ˆx j (t )∥]−βN ∑i =1d i∥ˆx 0(t )−ˆx i (t )∥2∥ˆx 0(t )−ˆx i (t )∥=β2N ∑i =1N ∑j =1a ij [ˆx T i(t )ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥−x T 0(t )ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥−ˆx T j(t )ˆx i (t )−ˆx j (t )∥ˆx i (t )−ˆx j (t )∥+x T0(t )ˆx i (t )−ˆx j (t )∥ˆx i (t )−ˆx j (t )∥]−βN ∑i =1d i ∥ˆx 0(t )−ˆx i (t )∥=β2N ∑i =1N ∑j =1a ij [ˆx T i (t )ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥−ˆx T j (t )ˆx i (t )−ˆx j (t )∥ˆx i (t )−ˆx j (t )∥]−βN ∑i =1d i ∥ˆx 0(t )−ˆx i (t )∥2∥ˆx 0(t )−ˆx i (t )∥=β2N ∑i =1N ∑j =1a ij (ˆx T i(t )−ˆx Tj (t ))ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥−βN ∑i =1d i ∥ˆx 0(t )−ˆx i (t )∥2∥ˆx 0(t )−ˆx i (t )∥=−β(12N ∑i =1N ∑j =1a ij (ˆx T j (t )−ˆx T i (t ))×ˆx j (t )−ˆx i (t )∥ˆx j (t )−ˆx i (t )∥+N ∑i =1d i ∥ˆx 0(t )−ˆx i (t )∥2∥ˆx 0(t )−ˆx i (t )∥),(19)N 2=−N ∑i =1(ˆx i (t )−x 0(t ))TC 0D αt x 0(t )=N ∑i =1∥ˆx i (t )−x 0(t )∥∥C 0D αt x 0(t )∥×cos {ˆx i (t )−x 0(t ),−C 0D αt x 0(t )}.(20)由于∥C 0D αt x 0(t )∥k 1∥x 0(t )−˜x 0(t )∥+k 2∥sgn(x 0(t )−˜x 0(t ))∥ k 1∥x 0(t )−˜x 0(t )∥+k 2.(21)根据定义3,当lim t →∞∥x 0(t )−˜x 0(t )∥=0时,存在T >0(T 为实数),使得在t >T 时∥x 0(t )−˜x 0(t )∥ ε成立,那么对于t >T ,有0<∥C 0D αt x 0(t )∥ k 1ε+k 2=M 2,可得−N ∑i =1(ˆx i (t )−x 0(t ))TC 0D αt x 0(t )N ∑i =1∥ˆx i (t )−x 0(t )∥M 2M 2N max {∥ˆx i (t )−x 0(t )∥},(22)C 0D αt V(t ) −(β−M 2N )max i ∈I{∥ˆx i (t )−x 0(t )∥}−2β1λmin V (t ).(23)根据引理2,得lim t →∞∥ˆx i (t )−x 0(t )∥=0.(24)由上式可知,ˆx i (t )在对目标的追踪过程中逐渐趋近于x 0(t ).3.2跟随者控制器的设计在本文中,整个多机器人系统中领导者能够直接获得目标的位置信息,将这些信息传递给追随者,因此需要为每个追随者设计观测器来估计目标的状态.令ϕi (t )∈R 2由跟随者对目标i 的状态估计,给出ϕi (t )的动力学方程C 0D αt ϕi(t )=α(∑j ∈N ia ij f ij (t )+d i f i 0(t )),(25)其中f ij =ϕj (t )−ϕi (t )∥ϕj (t )−ϕi (t )∥,ϕj (t )−ϕi (t )=0,0,ϕj (t )−ϕi (t )=0.(26)取如下李雅普诺夫函数:V (t )=12N ∑i =1(ϕi (t )−r (t ))T (ϕi (t )−r (t )).(27)计算α阶导数如下:C 0D αt V(t )=第1期伍锡如等:分数阶多机器人的领航–跟随型环形编队控制10712N ∑i =1(ϕi (t )−r (t ))T (ϕi (t )−r (t )) N ∑i =1(ϕi (t )−r (t ))TC 0D αt (ϕi (t )−r (t ))=N ∑i =1(ϕi (t )−r (t ))T [C 0D αt ϕi (t )−C 0D αt r (t )]=N ∑i =1(φi (t )−r (t ))T [α(∑j ∈N ia ij f ij (t )+d i f i 0(t ))]−C 0D αt r (t )=N ∑i =1(ϕi (t )−r (t ))T α(∑j ∈N ia ij ϕj (t )−ϕi (t )∥ϕj (t )−ϕi (t )∥+d i ϕ(t )−ϕi (t )∥ϕ(t )−ϕi (t )∥)=βN ∑i =1(ϕi (t )−r (t ))T ∑j ∈N i a ijϕj (t )−ϕi (t )∥ϕj (t )−ϕi(t )∥+βN ∑i =1(ϕi (t )−r (t ))T d i ϕ(t )−ϕi (t )∥ϕ(t )−ϕi(t )∥−N ∑i =1(ϕi (t )−r (t ))TC 0D αt r (t ),(28)可得lim t →∞∥x i (t )−˜x i (t )∥=0.(29)由上式可知,x i (t )在对目标的追踪过程中逐渐趋近于˜x i (t ).4仿真结果与分析本节通过仿真结果来验证本文所提出的方法.图2为通信图,其中:V ={1,2,3,4}表示跟随者集合,0代表领导者.以5个机器人组成的队列为例进行验证,根据领航者对目标的跟随轨迹,分别进行了仿真.图2通信图Fig.2Communication diagrams假设系统中目标机器人的动态为C 0D αt r (t )=[cos t sin t ]T ,令初始值r 1(0)=r 2(0)=1,α=0.98,k 1=1,k 2=4,可知定理3中的条件是满足的.根据式(24)和式(29),随着时间趋于无穷,领航者及其跟随者的状态估计误差趋于0,这意味着领航者的状态可以由跟随者渐近精确地计算出来.令k 2>M 1,M 1=M +M ′>0,则lim t →∞∥x 0(t )−˜x 0(t )∥=0,x 0渐近收敛于领航者的真实状态.此时取时滞参数µ=0.05,实验结果见图3,由1个领航者及4个跟随者组成的多机器人系统在进行目标围堵时,最终形成了以目标机器人为中心的包围控制(见图3(b)).(a)领航者和跟随者的初始位置分析(b)编队形成后多机器人的位置关系图3目标、领航者和追随者的位置分析Fig.3Location analysis of target pilots and followers综合图4–5曲线,跟随者对领航者进行渐进跟踪,领航者同目标机器人的相对位置不变,表明该领航跟随型多机器人系统最终能与目标机器人保持期望的距离,并且不再变化.图4领航者及其跟随者的状态估计误差Fig.4The state estimation error of the leader and followers108控制理论与应用第38卷图5编队形成时领航者与目标的相对位置关系Fig.5The relative position relationship between leader andtarget仿真结果表明,多个机器人在对目标物进行包围编队时,领航者会逐渐形成以目标物运动轨迹为参照的运动路线,而跟随者则渐近的完成对领航者的跟踪(如图6所示),跟随者在对领航者进行跟踪时,会出现一定频率的抖振,但这些并不会影响该多机器人系统的目标包围编队控制.5总结本文提出了多机器人的领航–跟随型编队控制方法,选定了一台机器人作为领航者负责整个编队的路径规划任务,其余机器人作为跟随者.跟随机器人负责实时跟踪领航者,并尽可能与领航机器人之间保持队形所需的距离和角度,确保整个多机器人系统编队按照预期的理想编队队形进行无碰撞运动,并最终到达目标位置.通过建立李雅普诺夫函数和米塔格稳定性理论,得到了实现多机器人系统环形编队的充分条件,并通过对一组多机器人队列的目标包围仿真,验证了该方法的有效性.图6领航者与跟随者对目标的状态估计Fig.6State estimation of target by pilot and follower参考文献:[1]JIANG Yutao,LIU Zhongxin,CHEN Zengqiang.Distributed ﬁnite-time consensus algorithm for 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受空间位阻限制的酰胺旋转产生多重构象

受空间位阻限制的酰胺旋转产生多重构象By Tabum <译>Restricted amide rotation with steric hindrance induced multiple conformationsV.V. Krishnan a,b,⇑, Salvador Vazquez a, Kalyani Maitra a, Santanu Maitra a,⇑a Department of Chemistry, California State University, Fresno, CA 93740, United Statesb Department of Pathology and Laboratory Medicine, School of Medicine, University of California, Davis, CA 95616, United Statesa r t i c l e i n f oArticle history:Received 5 August 2017In final form 4 October 2017Available online 9 October 2017Keywords:Dynamic NMRChemical exchangeRestricted amide rotationSteric hindrance摘要C-N键的性质取决于由氮的离域孤电子对驱动的共振结构。

在N，N-二苄基-邻甲苯甲酰胺（o-DBET）中，尤其是在低温下，该分子采用具有不同NMR谱学特征的构象异构体子群的形式存在。

这种构象适应是o-DBET所独有的，而相应的邻位和间位分子没有这种行为。

变温（VT）NMR、二维交换光谱（EXSY）和定性分子模拟研究被用来证明多个竞争性相互作用如限制酰胺旋转和空间位阻效应如何引发溶液中多种分子的适应性。

关键词：动态NMR；化学交换；受限制的酰胺旋转；空间位阻1.前言酰胺中C-N键的旋转能垒与其部分双键性质有关，这种双键性质由氮原子上的孤电子对和羰基π键之间的共振相互作用产生。