Reorientation of Anisotropy in a Square Well Quantum Hall Sample

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金属塑性成形6)plastic anisotropy

r= r0 + 2r45 + r90 4
Point C (0, σs )
σ2
Point B
σ1
O R=1 R>1 Point A (σs, 0)
εw r= ε εt r=
width
thickness
6 Plastic anisotropy*
6.3 Normal anisotropy and planar anisotropy
Specimen taken from different directions have different 1) The cause of anisotropy -crystallographic orientation r-value. This kind of anisotropy is called planar anisotropy. Planar anisotropy is 2) Types of by characterizedanisotropy for sheet metals
6 Plastic anisotropy*
6.2 r-value
1)A useful parameter to show plastic anisotropy of a sheet metal is the The cause of anisotropy -crystallographic orientation so-called r-value, which is the ratio of plastic strains, measured from a 2) Types of anisotropy for sheet tensile specimen of sheet metal. metals

刺杀小说家英语作文摘抄

In the realm of literature,the concept of a fictional assassination is a fascinating and complex theme that has been explored in various forms.Here are some excerpts from English essays that delve into the intricacies of this subject:1.The Power of Words:In the world of fiction,a writer wields the power to create and destroy.The act of assassinating a character is a demonstration of this power,often serving as a pivotal moment in the narrative that can reshape the entire story.2.Moral Dilemmas in Storytelling:Assassinating a character in a novel is not merely a plot device it is a moral decision that the author must grapple with.It raises questions about the ethics of storytelling and the responsibility of the writer towards their creations.3.The Impact on the Reader:When a beloved character is assassinated in a novel,it can elicit strong emotional responses from the reader.This emotional connection is a testament to the power of storytelling and the deep bonds that readers form with fictional characters.4.Symbolism and Metaphor:The act of assassination in fiction often carries symbolic weight.It can represent the end of an era,the triumph of evil over good,or the inevitable consequences of certain actions.It serves as a metaphor for larger themes within the story.5.The Role of Foreshadowing:Skillful writers use foreshadowing to prepare the reader for the eventual assassination of a character.This technique can heighten the tension and anticipation,making the moment of the assassination all the more impactful.6.The Aftermath of Assassination:The death of a character is not the end of their story. The aftermath of an assassination can be just as significant as the event itself.It can lead to character growth,plot twists,and a deeper exploration of the storys themes.7.The Assassin as a Character:In some narratives,the assassin is a character in their own right.Their motivations,backstory,and moral compass add another layer of complexity to the story,inviting the reader to question the nature of justice and the blurred lines between right and wrong.8.Cultural and Historical Context:Assassination in literature can also reflect cultural and historical contexts.It can be a commentary on political assassinations,a critique of power structures,or an exploration of the human capacity for violence.9.The Unpredictability of Life:The unpredictability of life is mirrored in the unpredictability of fiction.An assassination can serve as a reminder that life is fragile andthat the threads of our existence can be severed at any moment.10.The Rebirth of a Story:In some cases,the assassination of a character can lead to the rebirth of a story.It can open up new narrative paths,introduce new characters,and provide a fresh perspective on the world the author has created.These excerpts highlight the multifaceted nature of character assassination in literature, touching on themes of power,morality,emotional impact,and narrative structure.They provide a glimpse into the rich tapestry of storytelling and the profound effects that such a dramatic event can have on a work of fiction.。

AI 艺术时代的原创会呈现怎样的形态中英互译

I want you to envision a single piece of artwork generated by artificial intelligence. When most of us think of AI art, I bet we’re imagining something like this. We’re all probably picturing something totally different.请大家想象一件由人工智能（AI）生成的艺术品。

大多数人想到AI 艺术时，我敢打赌我们想象的是这样的东西。

我们想象的东西可能完全不同。

Today, with machine learning models like DALL-E, Stable Diffusion and Midjourney, we’ve seen AI produce everything from strange life forms to imaginary influencers to entirely foreign, curious kinds of imagery. AI as a technology is fascinating to us because we’re inherently drawn to things we cannot understand.今天，有了像DALL-E、Stable Diffusion 和Midjourney 这样的机器学习模型，我们已经看到AI 可以产生各种各样的东西——从奇怪的生命形式到虚构的网红，再到完全陌生的、奇异的图像。

AI 作为一种技术对我们很有吸引力，因为我们天生就会被自己无法理解的东西所吸引。

And with neural networks processing data from thousands of other images made by people from every possible generation, every art movement, millions of images in one simple scan, they can produce visuals that are so familiar yet strikingly unfamiliar. More poetically, AI mirrors us.而且，通过神经网络处理来自每一代人、每一次艺术运动的成千上万张图像，以及一次简单扫描得到的百万张图像，AI 可以生成既熟悉又惊人陌生的视觉效果。

OSHA现场作业手册说明书

DIRECTIVE NUMBER: CPL 02-00-150 EFFECTIVE DATE: April 22, 2011 SUBJECT: Field Operations Manual (FOM)ABSTRACTPurpose: This instruction cancels and replaces OSHA Instruction CPL 02-00-148,Field Operations Manual (FOM), issued November 9, 2009, whichreplaced the September 26, 1994 Instruction that implemented the FieldInspection Reference Manual (FIRM). The FOM is a revision of OSHA’senforcement policies and procedures manual that provides the field officesa reference document for identifying the responsibilities associated withthe majority of their inspection duties. This Instruction also cancels OSHAInstruction FAP 01-00-003 Federal Agency Safety and Health Programs,May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045,Revised Field Operations Manual, June 15, 1989.Scope: OSHA-wide.References: Title 29 Code of Federal Regulations §1903.6, Advance Notice ofInspections; 29 Code of Federal Regulations §1903.14, Policy RegardingEmployee Rescue Activities; 29 Code of Federal Regulations §1903.19,Abatement Verification; 29 Code of Federal Regulations §1904.39,Reporting Fatalities and Multiple Hospitalizations to OSHA; and Housingfor Agricultural Workers: Final Rule, Federal Register, March 4, 1980 (45FR 14180).Cancellations: OSHA Instruction CPL 02-00-148, Field Operations Manual, November9, 2009.OSHA Instruction FAP 01-00-003, Federal Agency Safety and HealthPrograms, May 17, 1996.Chapter 13 of OSHA Instruction CPL 02-00-045, Revised FieldOperations Manual, June 15, 1989.State Impact: Notice of Intent and Adoption required. See paragraph VI.Action Offices: National, Regional, and Area OfficesOriginating Office: Directorate of Enforcement Programs Contact: Directorate of Enforcement ProgramsOffice of General Industry Enforcement200 Constitution Avenue, NW, N3 119Washington, DC 20210202-693-1850By and Under the Authority ofDavid Michaels, PhD, MPHAssistant SecretaryExecutive SummaryThis instruction cancels and replaces OSHA Instruction CPL 02-00-148, Field Operations Manual (FOM), issued November 9, 2009. The one remaining part of the prior Field Operations Manual, the chapter on Disclosure, will be added at a later date. This Instruction also cancels OSHA Instruction FAP 01-00-003 Federal Agency Safety and Health Programs, May 17, 1996 and Chapter 13 of OSHA Instruction CPL 02-00-045, Revised Field Operations Manual, June 15, 1989. This Instruction constitutes OSHA’s general enforcement policies and procedures manual for use by the field offices in conducting inspections, issuing citations and proposing penalties.Significant Changes∙A new Table of Contents for the entire FOM is added.∙ A new References section for the entire FOM is added∙ A new Cancellations section for the entire FOM is added.∙Adds a Maritime Industry Sector to Section III of Chapter 10, Industry Sectors.∙Revises sections referring to the Enhanced Enforcement Program (EEP) replacing the information with the Severe Violator Enforcement Program (SVEP).∙Adds Chapter 13, Federal Agency Field Activities.∙Cancels OSHA Instruction FAP 01-00-003, Federal Agency Safety and Health Programs, May 17, 1996.DisclaimerThis manual is intended to provide instruction regarding some of the internal operations of the Occupational Safety and Health Administration (OSHA), and is solely for the benefit of the Government. No duties, rights, or benefits, substantive or procedural, are created or implied by this manual. The contents of this manual are not enforceable by any person or entity against the Department of Labor or the United States. Statements which reflect current Occupational Safety and Health Review Commission or court precedents do not necessarily indicate acquiescence with those precedents.Table of ContentsCHAPTER 1INTRODUCTIONI.PURPOSE. ........................................................................................................... 1-1 II.SCOPE. ................................................................................................................ 1-1 III.REFERENCES .................................................................................................... 1-1 IV.CANCELLATIONS............................................................................................. 1-8 V. ACTION INFORMATION ................................................................................. 1-8A.R ESPONSIBLE O FFICE.......................................................................................................................................... 1-8B.A CTION O FFICES. .................................................................................................................... 1-8C. I NFORMATION O FFICES............................................................................................................ 1-8 VI. STATE IMPACT. ................................................................................................ 1-8 VII.SIGNIFICANT CHANGES. ............................................................................... 1-9 VIII.BACKGROUND. ................................................................................................. 1-9 IX. DEFINITIONS AND TERMINOLOGY. ........................................................ 1-10A.T HE A CT................................................................................................................................................................. 1-10B. C OMPLIANCE S AFETY AND H EALTH O FFICER (CSHO). ...........................................................1-10B.H E/S HE AND H IS/H ERS ..................................................................................................................................... 1-10C.P ROFESSIONAL J UDGMENT............................................................................................................................... 1-10E. W ORKPLACE AND W ORKSITE ......................................................................................................................... 1-10CHAPTER 2PROGRAM PLANNINGI.INTRODUCTION ............................................................................................... 2-1 II.AREA OFFICE RESPONSIBILITIES. .............................................................. 2-1A.P ROVIDING A SSISTANCE TO S MALL E MPLOYERS. ...................................................................................... 2-1B.A REA O FFICE O UTREACH P ROGRAM. ............................................................................................................. 2-1C. R ESPONDING TO R EQUESTS FOR A SSISTANCE. ............................................................................................ 2-2 III. OSHA COOPERATIVE PROGRAMS OVERVIEW. ...................................... 2-2A.V OLUNTARY P ROTECTION P ROGRAM (VPP). ........................................................................... 2-2B.O NSITE C ONSULTATION P ROGRAM. ................................................................................................................ 2-2C.S TRATEGIC P ARTNERSHIPS................................................................................................................................. 2-3D.A LLIANCE P ROGRAM ........................................................................................................................................... 2-3 IV. ENFORCEMENT PROGRAM SCHEDULING. ................................................ 2-4A.G ENERAL ................................................................................................................................................................. 2-4B.I NSPECTION P RIORITY C RITERIA. ..................................................................................................................... 2-4C.E FFECT OF C ONTEST ............................................................................................................................................ 2-5D.E NFORCEMENT E XEMPTIONS AND L IMITATIONS. ....................................................................................... 2-6E.P REEMPTION BY A NOTHER F EDERAL A GENCY ........................................................................................... 2-6F.U NITED S TATES P OSTAL S ERVICE. .................................................................................................................. 2-7G.H OME-B ASED W ORKSITES. ................................................................................................................................ 2-8H.I NSPECTION/I NVESTIGATION T YPES. ............................................................................................................... 2-8 V.UNPROGRAMMED ACTIVITY – HAZARD EVALUATION AND INSPECTION SCHEDULING ............................................................................ 2-9 VI.PROGRAMMED INSPECTIONS. ................................................................... 2-10A.S ITE-S PECIFIC T ARGETING (SST) P ROGRAM. ............................................................................................. 2-10B.S CHEDULING FOR C ONSTRUCTION I NSPECTIONS. ..................................................................................... 2-10C.S CHEDULING FOR M ARITIME I NSPECTIONS. ............................................................................. 2-11D.S PECIAL E MPHASIS P ROGRAMS (SEP S). ................................................................................... 2-12E.N ATIONAL E MPHASIS P ROGRAMS (NEP S) ............................................................................... 2-13F.L OCAL E MPHASIS P ROGRAMS (LEP S) AND R EGIONAL E MPHASIS P ROGRAMS (REP S) ............ 2-13G.O THER S PECIAL P ROGRAMS. ............................................................................................................................ 2-13H.I NSPECTION S CHEDULING AND I NTERFACE WITH C OOPERATIVE P ROGRAM P ARTICIPANTS ....... 2-13CHAPTER 3INSPECTION PROCEDURESI.INSPECTION PREPARATION. .......................................................................... 3-1 II.INSPECTION PLANNING. .................................................................................. 3-1A.R EVIEW OF I NSPECTION H ISTORY .................................................................................................................... 3-1B.R EVIEW OF C OOPERATIVE P ROGRAM P ARTICIPATION .............................................................................. 3-1C.OSHA D ATA I NITIATIVE (ODI) D ATA R EVIEW .......................................................................................... 3-2D.S AFETY AND H EALTH I SSUES R ELATING TO CSHO S.................................................................. 3-2E.A DVANCE N OTICE. ................................................................................................................................................ 3-3F.P RE-I NSPECTION C OMPULSORY P ROCESS ...................................................................................................... 3-5G.P ERSONAL S ECURITY C LEARANCE. ................................................................................................................. 3-5H.E XPERT A SSISTANCE. ........................................................................................................................................... 3-5 III. INSPECTION SCOPE. ......................................................................................... 3-6A.C OMPREHENSIVE ................................................................................................................................................... 3-6B.P ARTIAL. ................................................................................................................................................................... 3-6 IV. CONDUCT OF INSPECTION .............................................................................. 3-6A.T IME OF I NSPECTION............................................................................................................................................. 3-6B.P RESENTING C REDENTIALS. ............................................................................................................................... 3-6C.R EFUSAL TO P ERMIT I NSPECTION AND I NTERFERENCE ............................................................................. 3-7D.E MPLOYEE P ARTICIPATION. ............................................................................................................................... 3-9E.R ELEASE FOR E NTRY ............................................................................................................................................ 3-9F.B ANKRUPT OR O UT OF B USINESS. .................................................................................................................... 3-9G.E MPLOYEE R ESPONSIBILITIES. ................................................................................................. 3-10H.S TRIKE OR L ABOR D ISPUTE ............................................................................................................................. 3-10I. V ARIANCES. .......................................................................................................................................................... 3-11 V. OPENING CONFERENCE. ................................................................................ 3-11A.G ENERAL ................................................................................................................................................................ 3-11B.R EVIEW OF A PPROPRIATION A CT E XEMPTIONS AND L IMITATION. ..................................................... 3-13C.R EVIEW S CREENING FOR P ROCESS S AFETY M ANAGEMENT (PSM) C OVERAGE............................. 3-13D.R EVIEW OF V OLUNTARY C OMPLIANCE P ROGRAMS. ................................................................................ 3-14E.D ISRUPTIVE C ONDUCT. ...................................................................................................................................... 3-15F.C LASSIFIED A REAS ............................................................................................................................................. 3-16VI. REVIEW OF RECORDS. ................................................................................... 3-16A.I NJURY AND I LLNESS R ECORDS...................................................................................................................... 3-16B.R ECORDING C RITERIA. ...................................................................................................................................... 3-18C. R ECORDKEEPING D EFICIENCIES. .................................................................................................................. 3-18 VII. WALKAROUND INSPECTION. ....................................................................... 3-19A.W ALKAROUND R EPRESENTATIVES ............................................................................................................... 3-19B.E VALUATION OF S AFETY AND H EALTH M ANAGEMENT S YSTEM. ....................................................... 3-20C.R ECORD A LL F ACTS P ERTINENT TO A V IOLATION. ................................................................................. 3-20D.T ESTIFYING IN H EARINGS ................................................................................................................................ 3-21E.T RADE S ECRETS. ................................................................................................................................................. 3-21F.C OLLECTING S AMPLES. ..................................................................................................................................... 3-22G.P HOTOGRAPHS AND V IDEOTAPES.................................................................................................................. 3-22H.V IOLATIONS OF O THER L AWS. ....................................................................................................................... 3-23I.I NTERVIEWS OF N ON-M ANAGERIAL E MPLOYEES .................................................................................... 3-23J.M ULTI-E MPLOYER W ORKSITES ..................................................................................................................... 3-27 K.A DMINISTRATIVE S UBPOENA.......................................................................................................................... 3-27 L.E MPLOYER A BATEMENT A SSISTANCE. ........................................................................................................ 3-27 VIII. CLOSING CONFERENCE. .............................................................................. 3-28A.P ARTICIPANTS. ..................................................................................................................................................... 3-28B.D ISCUSSION I TEMS. ............................................................................................................................................ 3-28C.A DVICE TO A TTENDEES .................................................................................................................................... 3-29D.P ENALTIES............................................................................................................................................................. 3-30E.F EASIBLE A DMINISTRATIVE, W ORK P RACTICE AND E NGINEERING C ONTROLS. ............................ 3-30F.R EDUCING E MPLOYEE E XPOSURE. ................................................................................................................ 3-32G.A BATEMENT V ERIFICATION. ........................................................................................................................... 3-32H.E MPLOYEE D ISCRIMINATION .......................................................................................................................... 3-33 IX. SPECIAL INSPECTION PROCEDURES. ...................................................... 3-33A.F OLLOW-UP AND M ONITORING I NSPECTIONS............................................................................................ 3-33B.C ONSTRUCTION I NSPECTIONS ......................................................................................................................... 3-34C. F EDERAL A GENCY I NSPECTIONS. ................................................................................................................. 3-35CHAPTER 4VIOLATIONSI. BASIS OF VIOLATIONS ..................................................................................... 4-1A.S TANDARDS AND R EGULATIONS. .................................................................................................................... 4-1B.E MPLOYEE E XPOSURE. ........................................................................................................................................ 4-3C.R EGULATORY R EQUIREMENTS. ........................................................................................................................ 4-6D.H AZARD C OMMUNICATION. .............................................................................................................................. 4-6E. E MPLOYER/E MPLOYEE R ESPONSIBILITIES ................................................................................................... 4-6 II. SERIOUS VIOLATIONS. .................................................................................... 4-8A.S ECTION 17(K). ......................................................................................................................... 4-8B.E STABLISHING S ERIOUS V IOLATIONS ............................................................................................................ 4-8C. F OUR S TEPS TO BE D OCUMENTED. ................................................................................................................... 4-8 III. GENERAL DUTY REQUIREMENTS ............................................................. 4-14A.E VALUATION OF G ENERAL D UTY R EQUIREMENTS ................................................................................. 4-14B.E LEMENTS OF A G ENERAL D UTY R EQUIREMENT V IOLATION.............................................................. 4-14C. U SE OF THE G ENERAL D UTY C LAUSE ........................................................................................................ 4-23D.L IMITATIONS OF U SE OF THE G ENERAL D UTY C LAUSE. ..............................................................E.C LASSIFICATION OF V IOLATIONS C ITED U NDER THE G ENERAL D UTY C LAUSE. ..................F. P ROCEDURES FOR I MPLEMENTATION OF S ECTION 5(A)(1) E NFORCEMENT ............................ 4-25 4-27 4-27IV.OTHER-THAN-SERIOUS VIOLATIONS ............................................... 4-28 V.WILLFUL VIOLATIONS. ......................................................................... 4-28A.I NTENTIONAL D ISREGARD V IOLATIONS. ..........................................................................................4-28B.P LAIN I NDIFFERENCE V IOLATIONS. ...................................................................................................4-29 VI. CRIMINAL/WILLFUL VIOLATIONS. ................................................... 4-30A.A REA D IRECTOR C OORDINATION ....................................................................................................... 4-31B.C RITERIA FOR I NVESTIGATING P OSSIBLE C RIMINAL/W ILLFUL V IOLATIONS ........................ 4-31C. W ILLFUL V IOLATIONS R ELATED TO A F ATALITY .......................................................................... 4-32 VII. REPEATED VIOLATIONS. ...................................................................... 4-32A.F EDERAL AND S TATE P LAN V IOLATIONS. ........................................................................................4-32B.I DENTICAL S TANDARDS. .......................................................................................................................4-32C.D IFFERENT S TANDARDS. .......................................................................................................................4-33D.O BTAINING I NSPECTION H ISTORY. .....................................................................................................4-33E.T IME L IMITATIONS..................................................................................................................................4-34F.R EPEATED V. F AILURE TO A BATE....................................................................................................... 4-34G. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-35 VIII. DE MINIMIS CONDITIONS. ................................................................... 4-36A.C RITERIA ................................................................................................................................................... 4-36B.P ROFESSIONAL J UDGMENT. ..................................................................................................................4-37C. A REA D IRECTOR R ESPONSIBILITIES. .............................................................................. 4-37 IX. CITING IN THE ALTERNATIVE ............................................................ 4-37 X. COMBINING AND GROUPING VIOLATIONS. ................................... 4-37A.C OMBINING. ..............................................................................................................................................4-37B.G ROUPING. ................................................................................................................................................4-38C. W HEN N OT TO G ROUP OR C OMBINE. ................................................................................................4-38 XI. HEALTH STANDARD VIOLATIONS ....................................................... 4-39A.C ITATION OF V ENTILATION S TANDARDS ......................................................................................... 4-39B.V IOLATIONS OF THE N OISE S TANDARD. ...........................................................................................4-40 XII. VIOLATIONS OF THE RESPIRATORY PROTECTION STANDARD(§1910.134). ....................................................................................................... XIII. VIOLATIONS OF AIR CONTAMINANT STANDARDS (§1910.1000) ... 4-43 4-43A.R EQUIREMENTS UNDER THE STANDARD: .................................................................................................. 4-43B.C LASSIFICATION OF V IOLATIONS OF A IR C ONTAMINANT S TANDARDS. ......................................... 4-43 XIV. CITING IMPROPER PERSONAL HYGIENE PRACTICES. ................... 4-45A.I NGESTION H AZARDS. .................................................................................................................................... 4-45B.A BSORPTION H AZARDS. ................................................................................................................................ 4-46C.W IPE S AMPLING. ............................................................................................................................................. 4-46D.C ITATION P OLICY ............................................................................................................................................ 4-46 XV. BIOLOGICAL MONITORING. ...................................................................... 4-47CHAPTER 5CASE FILE PREPARATION AND DOCUMENTATIONI.INTRODUCTION ............................................................................................... 5-1 II.INSPECTION CONDUCTED, CITATIONS BEING ISSUED. .................... 5-1A.OSHA-1 ................................................................................................................................... 5-1B.OSHA-1A. ............................................................................................................................... 5-1C. OSHA-1B. ................................................................................................................................ 5-2 III.INSPECTION CONDUCTED BUT NO CITATIONS ISSUED .................... 5-5 IV.NO INSPECTION ............................................................................................... 5-5 V. HEALTH INSPECTIONS. ................................................................................. 5-6A.D OCUMENT P OTENTIAL E XPOSURE. ............................................................................................................... 5-6B.E MPLOYER’S O CCUPATIONAL S AFETY AND H EALTH S YSTEM. ............................................................. 5-6 VI. AFFIRMATIVE DEFENSES............................................................................. 5-8A.B URDEN OF P ROOF. .............................................................................................................................................. 5-8B.E XPLANATIONS. ..................................................................................................................................................... 5-8 VII. INTERVIEW STATEMENTS. ........................................................................ 5-10A.G ENERALLY. ......................................................................................................................................................... 5-10B.CSHO S SHALL OBTAIN WRITTEN STATEMENTS WHEN: .......................................................................... 5-10C.L ANGUAGE AND W ORDING OF S TATEMENT. ............................................................................................. 5-11D.R EFUSAL TO S IGN S TATEMENT ...................................................................................................................... 5-11E.V IDEO AND A UDIOTAPED S TATEMENTS. ..................................................................................................... 5-11F.A DMINISTRATIVE D EPOSITIONS. .............................................................................................5-11 VIII. PAPERWORK AND WRITTEN PROGRAM REQUIREMENTS. .......... 5-12 IX.GUIDELINES FOR CASE FILE DOCUMENTATION FOR USE WITH VIDEOTAPES AND AUDIOTAPES .............................................................. 5-12 X.CASE FILE ACTIVITY DIARY SHEET. ..................................................... 5-12 XI. CITATIONS. ..................................................................................................... 5-12A.S TATUTE OF L IMITATIONS. .............................................................................................................................. 5-13B.I SSUING C ITATIONS. ........................................................................................................................................... 5-13C.A MENDING/W ITHDRAWING C ITATIONS AND N OTIFICATION OF P ENALTIES. .................................. 5-13D.P ROCEDURES FOR A MENDING OR W ITHDRAWING C ITATIONS ............................................................ 5-14 XII. INSPECTION RECORDS. ............................................................................... 5-15A.G ENERALLY. ......................................................................................................................................................... 5-15B.R ELEASE OF I NSPECTION I NFORMATION ..................................................................................................... 5-15C. C LASSIFIED AND T RADE S ECRET I NFORMATION ...................................................................................... 5-16。

anisotropie磁晶各向异性

Rep.Prog.Phys.59(1996)1409–1458.Printed in the UKMagnetic anisotropy in metallic multilayersM T Johnson†,P J H Bloemen‡§,F J A den Broeder†and J J de Vries‡†Philips Research Laboratories,Prof.Holstlaan4,5656AA Eindhoven,The Netherlands‡Eindhoven University of Technology,Department of Physics,PO Box513,5600MB Eindhoven,The Netherlands Received25July1996AbstractFerromagnetic materials exhibit intrinsic‘easy’and‘hard’directions of the magnetization. This magnetic anisotropy is,from both a technological and fundamental viewpoint one of the most important properties of magnetic materials.The magnetic anisotropy in metallic magnetic multilayers forms the subject of this review article.As individual layers in a multilayer stack become thinner,the role of interfaces and surfaces may dominate that of the bulk:this is the case in many magnetic multilayers,where a perpendicular interface contribution to the magnetic anisotropy is capable of rotating the easy magnetization direction from in theﬁlm plane to perpendicular to theﬁlm plane.In this review,we show that the(in-plane)volume and(perpendicular)interface contribution to the magnetic anisotropy have been separated into terms related to mechanical stresses,crystallographic structure and the planar shape of theﬁlms.In addition,the effect of roughness,often inherent to the deposition techniques used,has been addressed theoretically.Several techniques to prepare multilayers and to characterize their growth as well as methods to determine the magnetic anisotropy are discussed.A comprehensive survey of experimental studies on the perpendicular magnetic anisotropy in metallic multilayers containing Fe,Co or Ni is presented and commented on.Two major subjects of this review are the extrinsic effects of strain,roughness and interdiffusion and the intrinsic effect of the crystallographic orientation on the magnetic anisotropy.Both effects are investigated with the help of some dedicated experimental studies.The results of the orientational dependence studies are compared with ab initio calculations.Finally,the perpendicular surface anisotropy and the in-plane step anisotropy are discussed.§Present address:Philips Research Laboratories,Prof.Holstlaan4,5656AA Eindhoven,The Netherlands 0034-4885/96/111409+50$59.50c 1996IOP Publishing Ltd14091410M T Johnson et alContentsPage1.Introduction14112.Origin of the magnetic anisotropy in thinﬁlms14142.1.Magnetic dipolar anisotropy(shape anisotropy)14142.2.Magnetocrystalline anisotropy14152.3.Magneto-elastic anisotropy14163.Techniques to determine magnetic anisotropy14193.1.Magnetization methods14193.2.Magneto-optical Kerr effect measurements14214.Sample preparation and characterization14224.1.Preparation methods14234.2.Sample characterization14275.Overview of anisotropy studies14285.1.Tables14285.2.Fe versus Ni versus Co14286.Inﬂuence of the structure on the magnetic anisotropy14316.1.Effect of roughness and interdiffusion14326.2.Magneto-elastic effects14347.Orientational dependence of the perpendicular magnetic anisotropy14387.1.Structural aspects14397.2.Interfacial and volume anisotropy14417.3.Theoretical predictions of PMA1446paring measured and calculated PMA14498.Surface versus interface anisotropy14519.Step anisotropies145210.Summary and concluding remarks1453Acknowledgments1454 References1455Magnetic anisotropy in metallic multilayers14111.IntroductionIt is an experimental fact that ferromagnetic single crystals exhibit‘easy’and‘hard’directions of the magnetization;i.e.the energy required to magnetize a crystal depends on the direction of the appliedﬁeld relative to the crystal axes.From the technological viewpoint this magnetic anisotropy is one of the most important properties of magnetic materials. Depending on the type of application,material with high,medium or low magnetic anisotropy will be required,for respective application as,for example,permanent magnets, information storage media or magnetic cores in transformers and magnetic recording heads.The physical basis that underlies a preferred magnetic moment orientation in ultrathin magneticﬁlms and multilayers can be quite different from the factors that account for the easy-axis alignment along a symmetry direction of a bulk material,and the strength can also be markedly different.The prominent presence of symmetry-breaking elements such as planar interfaces and surfaces,which automatically accompany the layered form of these systems,are the basic ingredients for this behaviour.By varying the thicknesses of the individual layers and choosing appropriate materials,it appeared possible to tailor the magnetic anisotropy.The most dramatic manifestation in this respect is the change of the preferential direction of the magnetization from the commonly observed in-plane orientation to the direction perpendicular to the plane.This phenomenon is usually referred to as perpendicular magnetic anisotropy(PMA)and is particularly important for information storage and retrieval applications.PMA plays an important role in magneto-optical(MO)recording.To write bits in MO media,the disk is heated locally by a pulse of a diode laser beam which is focused to a spot of about1µm(see alsoﬁgure1).The magnetization is reversed only in the area of the heated spot by applying a small bias counterﬁeld,which is smaller than the coerciveﬁeld ofFigure1.Schematic representation of the principle of magneto-optical recording(Zeper1991).For more information see text.1412M T Johnson et althe MO layer at room temperature but larger than the coerciveﬁeld in the heated area.Thesame laser that is used for writing also reads back the written bits(domain pattern)makinguse of the polar magneto-optical Kerr effect,the effect that the polarization of the light ischanged(i.e.rotation of the plane of linear polarization over an angleθK)upon reﬂection at a magnetic surface(Kerr1877).Since the latter is most sensitive to the perpendicularcomponent of the magnetization,one of the principle requirements of an MO medium is aperpendicular preferential orientation.Today’s MO materials,the amorphous Gd–Tb–Fe andTb–Fe–Co alloys,meet this requirement and have a sufﬁcient Kerr effect.However,apartfrom intrinsic deﬁciencies such as their susceptibility to corrosion and oxidation,their Kerreffect considerably decreases at shorter wavelengthsλof the light.They therefore oppose afurther increase in the storage density since the latter is largely determined by the diffractionlimited spot area being proportional toλ2.Several metallic magnetic multilayers appearednot to exhibit these disadvantages.This application possibility of magnetic multilayers withPMA formed one of the principle motivations for many groups to enter theﬁeld and is stillin part responsible for the current world-wide attention for these systems.In addition,newphenomena such as the interlayer exchange coupling and the giant magnetoresistance havealso attracted considerable attention in the last decade,see Fert and Bruno(1994)for arecent review on the latter two topics.The PMA is a result of a magnetic anisotropy at the interface which considerably differsfrom the magnetic anisotropy in the bulk.This type of magnetic anisotropy,a so-calledinterface or surface anisotropy,was predicted already in1954by N´e el(1954)to result fromthe lowered symmetry at the surface or interface.Theﬁrst experiments which had revealedsuch an interface anisotropy were performed in1968by Gradmann and M¨u ller(1968)onultrathin NiFeﬁlms on Cu(111).What they observed was an easy axis perpendicular to theﬁlm plane for1.8monolayers of NiFe and furthermore that the magnetic anisotropy scaledwith the reciprocalﬁlm thickness.For multilayers PMA wasﬁrst observed in1985byCarcia et al in the Co/Pd system Carcia et al(1985)and later on in several other Co-basedmultilayers:Co/Pt(Carcia1988),Co/Au(den Broeder et al1988),Co/Ru(Sakurai et al1991)and Co/Ir(den Broeder et al1991).In these studies the(effective)magnetic anisotropy energy K(J m−3)could bephenomenologically separated in a volume contribution K v(J m−3)and a contributionfrom the interfaces K s(J m−2)and approximately obeyed the relation:K=K eff=K v+2K s/t.(1) This relation just represents a weighted average of the magnetic anisotropy energy(MAE) of the interface atoms and the inner atoms of a magnetic layer of thickness t.The relation is presented under the convention that K s/d(with d the thickness of a monolayer)represents the difference between the anisotropy of the interface atoms with respect to the inner or bulk atoms.Also the layer is assumed to be bounded by two identical interfaces accounting for the prefactor2.Equation(1)is commonly used in experimental studies,and the determination of K v and K s can be obtained by a plot of the product K eff t versus t.Figure2shows a typical example of such a plot for Co/Pd multilayers(den Broeder et al1991).Here,and in the following,a positive K eff describes the case of a preferred direction of the magnetization perpendicular to the layer plane.The negative slope indicates a negative volume anisotropy K v,favouring in-plane magnetization,while the intercept at zero Co thickness indicates a positive interface anisotropy K s,favouring perpendicular magnetization.Below a certain thickness t⊥(=−2K s/K v,in this case13˚A)the interface anisotropy contribution outweighs the volume contribution,resulting in a perpendicularly magnetized system.In other words, the strong demagnetizingﬁelds which are created when tilting the magnetization out ofMagnetic anisotropy in metallic multilayers1413Figure2.MAE times the individual Co layer thickness versus the individual Co layer thicknessof Co/Pd multilayers.The vertical axis intercept equals twice the interface anisotropy,whereasthe slope gives the volume contribution.Data are taken from den Broeder et al(1991).theﬁlm plane and which are usually responsible for the orientation of the magnetization parallel to theﬁlm plane,are overcome.As will be shown later on,the volume energy corresponding to these demagnetizingﬁelds form the major contribution to K v in most cases.The many experimental results of the type shown inﬁgure2considerably stimulated theoretical work.For the bulk transition metals,it appeared very difﬁcult to calculate the magnetic anisotropy fromﬁrst principles.The order of magnitude was correct,but the predicted sign was often wrong(Daalderop et al1990a).These difﬁculties are related to the fact that the corresponding energies are very small(of the order of1meV per atom). However,for multilayers and ultrathinﬁlms,which exhibit generally larger anisotropies, much progress has recently been made.For several Co based multilayers,good agreement has been reached betweenﬁrst principles calculated anisotropies and the corresponding experimental values(Daalderop et al1990b).To increase the general understanding,these calculations can now,in principle,be used to calculate the magnetic anisotropy of magnetic layers and multilayers which cannot be made under laboratory conditions,such as free-standing monolayers;alternatively,one can make predictions for multilayers that have not been studied experimentally previously.An example of the latter is formed by Co/Ni multilayers(Daalderop et al1992).This review article is primarily concerned with the experimental aspects of the research performed on the magnetic anisotropy in thinﬁlms and multilayers.A restriction has been made to(multi)layers containing transition metals;rare-earth transition metal multilayers are not considered.Moreover,the(perpendicular)uniaxial out-of-plane anisotropy is emphasized although in-plane anisotropies will also be addressed.Earlier reviews on magnetic anisotropy were given by Heinrich and Cochran(1993)and de Jonge et al(1994).The article is organized as follows.Section2deals with the theory of several contributions to the magnetic anisotropy of magnetic thinﬁlms.The most commonly used experimental techniques to quantitatively determine the magnetic anisotropy are brieﬂy introduced in section3.In section4,a compilation of the currently used techniques to1414M T Johnson et algrow,as well as to characterizeﬁlms and multilayers,is given and the advantages and disadvantages are mentioned.An extensive overview of the measured magnetic anisotropies is given in section5.Section6is devoted to several aspects of the growth conditions andﬁlm structure which inﬂuence the PMA in magnetic multilayers,such as roughness and interdiffusion,stress and preparation methods.The orientational dependence of the magnetic anisotropy is discussed in relation with theoretical calculations in section7.The remaining sections deal with the magnetic anisotropy generated at free surfaces,section8, and surface steps,section9.In view of the limited space a selection of interesting studies has been made so as to cover,as much as possible,different aspects that are of importance for the general understanding of the magnetic anisotropy of ultrathin magnetic layers.The authors apologise to those whose work is not explicitly mentioned.Theﬁeld has become too large to cover all interesting studies in one paper.Included are tables of multilayers and sandwiches exhibiting PMA studied so far and of the orientational dependence of the PMA in Co/Pt,Co/Pd and Co/Ni multilayers.Other topics are a study on the Cu/Ni system emphasizing the importance of magneto-elastic contributions for both interface and volume anisotropy terms and a systematic experimental investigation of the relation between the magnetic anisotropy and the interface roughness.2.Origin of the magnetic anisotropy in thinﬁlmsBasically,the two main sources of the magnetic anisotropy are the magnetic dipolar interaction and the spin–orbit interaction.Due to its long range character,the dipolar interaction generally results in a contribution to the anisotropy,which depends on the shape of the specimen.It is of particular importance in thinﬁlms,and is largely responsible for the in-plane magnetization usually observed.In the absence of spin–orbit and dipolar interaction,the total energy of the electron–spin system does not depend on the direction of the magnetization.In a localized picture the spins are coupled via the spin–orbit interaction to the orbits which,in turn,are inﬂuenced by the crystal lattice.For itinerant materials the spin–orbit interaction induces a small orbital momentum,which then couples the total (spin plus orbital)magnetic moment to the crystal axes.This results in a total energy which depends on the orientation of the magnetization relative to the crystalline axes,and which reﬂects the symmetry of the crystal.This is known as the magnetocrystalline contribution to the anisotropy.The lowered symmetry at an interface strongly modiﬁes this contribution as compared to the bulk,yielding,as mentioned already,a so-called interface anisotropy as pointed out by N´e el(1954).In conjunction with the overlap in wavefunctions between neighbouring atoms,the spin–orbit interaction is also responsible for the magneto-elastic or magnetostrictive anisotropy induced in a strained system,a situation which is frequently encountered in multilayers due to the lattice mismatch between the adjacent layers.In the following subsections each of these anisotropy terms will be discussed in somewhat more detail.2.1.Magnetic dipolar anisotropy(shape anisotropy)Among the most important sources of the magnetic anisotropy in thinﬁlms is the long range magnetic dipolar interaction,which senses the outer boundaries of the sample.Neglecting the discrete nature of matter,the shape effect of the dipolar interaction in ellipsoidal ferromagnetic samples can be described,via an anisotropic demagnetizingﬁeld,H d,given by H d=−N M.Here M is the magnetization vector and N is the shape-dependent demagnetizing tensor.For a thinﬁlm,all tensor elements are zero except for the directionMagnetic anisotropy in metallic multilayers 1415perpendicular to the layer:N ⊥=1.Since the magnetostatic energy can be expressed as E d =−µ02VM ·H d d v (2)where µ0is the permeability of vacuum,it results in an anisotropy energy contribution per unit volume V of a ﬁlm of:E d =12µ0M 2s cos 2θ.(3)Here the magnetization is assumed to be uniform with a magnitude equal to the saturation magnetization M s ,and subtends an angle θwith the ﬁlm normal.According to this expression,the contribution favours an in-plane preferential orientation for the magnetization.Because the thickness of the ﬁlm does not enter into the continuum approach employed above,it contributes only to K v .It is this contribution which is mainly responsible for the negative slope of the K eff t versus t plot in ﬁgure 2.This continuum approach is common in the analysis of the experimental data.However,when the thickness of the ferromagnetic layer is reduced to only a few monolayers (ML),the ﬁlm should not,in principle,be considered as a magnetic continuum,but has to be treated as a collection of discrete magnetic dipoles on a regular lattice.Calculations made on the basis of discretely summing the dipolar interactions for ﬁlms in the range of 1–10MLs lead to the following results (Draaisma and de Jonge 1988).Depending on the symmetry of the interface,the outer layers experience a dipolar anisotropy which can be appreciably lower than the inner layers.For the inner layers,the dipolar anisotropy is rather close to the value based on the continuum approach.Consequently,the average dipolar anisotropy can be phenomenologically expressed by a volume and an interface contribution.The magnitude of the dipolar interface contribution,however,is of minor importance,and other sources of interface anisotropy,such as spin–orbit coupling,appear to be dominant.2.2.Magnetocrystalline anisotropyAs stated before,the microscopic origin of the magnetocrystalline anisotropy is the spin–orbit interaction.In principle,also the exchange interaction and the dipolar interaction could contribute to the magnetocrystalline anisotropy.The exchange interaction,however,cannot give rise to anisotropy since it is proportional to the scalar product of the spin vectors and is therefore independent of the angle between the spins and the crystal axes.The dipolar interaction energy on the other hand,does depend on the orientation of the magnetization relative to the crystal axes.In principle it results,apart from the shape contribution already discussed in subsection 2.1,in a magnetocrystalline contribution.However,for cubic crystals it can be shown from symmetry arguments that the sum of the dipole–dipole energies cancels.For structures with lower symmetry,such as hexagonal crystals,this is generally not the case.For bulk hcp cobalt however,this contribution is negligible,since the deviation of the c/a ratio from the ideal value √8/3is relatively small (−0.67%)(Daalderop et al 1990a).Consequently,the spin–orbit interaction will be primarily responsible for the magnetocrystalline anisotropy in Fe,Ni (both cubic)and Co.Before a good understanding of itinerant electron behaviour was achieved,van Vleck discussed the magnetocrystalline anisotropy (in the case of bulk)in a pair interaction model assuming localized magnetic moments (van Vleck 1937).N´e el (1954)extended this model to surfaces and showed that the reduced symmetry at the surface should result in magnetic anisotropies at the surface differing strongly from the bulk atoms.For this surface anisotropy energy he derives for fcc(111)and fcc(100)surfaces for instance,the1416M T Johnson et alrelation E=−K s cos2θ,with K s differing for(111)and(100)surfaces.Although the pair interaction model also played a role in the discussion about roughness and interdiffusion, as discussed later,and contributed signiﬁcantly to the understanding,it is fundamentally incorrect.It does not discriminate between interface and surface,nor does it give a dependence of K s on the adjacent(non-magnetic)metal.In some cases it predicts the wrong sign.Throughout this text,in fact,interface anisotropy will be considered except in section8where the surface anisotropy is discussed.A thorough understanding of the magnetocrystalline anisotropy can now be obtained from ab initio bandstructure calculations.As shown in(Daalderop1991),the symmetry and location with respect to the Fermi level of spin–orbit split or shifted states are of major importance.The symmetry of the state for instance,determines whether or not the state is split if the direction of the magnetization is perpendicular or parallel to theﬁlm plane,i.e. it determines the sign of the contribution of the state to the magnetocrystalline anisotropy. For further and more detailed discussions the reader is referred to(Daalderop et al1994).A short summary of the current status of the theory is presented in subsection7.4.2.3.Magneto-elastic anisotropyStrain in a ferromagnet changes the magnetocrystalline anisotropy and may thereby alter the direction of the magnetization.This effect is the‘inverse’of magnetostriction,the phenomenon that the sample dimensions change if the direction of the magnetization is altered.The energy per unit volume associated with this effect can,for an elastically isotropic medium with isotropic magnetostriction,be written asE me=−K me cos2θ(4) withK me=−32λσ(5) =−3λE .(6) Hereσis the stress which is related to the strain, ,via the elastic modulus E byσ=E . The magnetostriction constantλdepends on the orientation and can be positive or negative. The angleθmeasures the direction of the magnetization relative to the direction of uniform stress.If the strain in theﬁlm is non-zero,the magneto-elastic coupling contributes in principle to the effective anisotropy.When the parameters are constant(not depending on the magnetic layer thickness,t)this contribution can be identiﬁed with a volume contribution K v(compare equation(1)).Strain inﬁlms can be induced by various sources.Among them are thermal strain associated with differences in thermal expansion coefﬁcients,intrinsic strain brought about by the nature of the deposition process and strain due to non-matching lattice parameters of adjacent layers.Of particular interest in the present context,is the strain due to lattice mismatchηof a material A deposited on material B:η=(a A−a B)/a A(7) where a is the lattice parameter of material A or B.Currently this problem is described in terms of the van der Merwe model in which elastic as well as dislocation energies are considered(van der Merwe1963).Two regimes should be distinguished.If the lattice mismatch between the lattice parameters is not too large,minimizing the total energy leads to a situation whereby,below a critical thickness t c,the misﬁt can be accommodated byMagnetic anisotropy in metallic multilayers1417 introducing a tensile strain in one layer and a compressive strain in the other such that ultimately the two materials A and B adopt the same in-plane lattice parameter.This regime is called the coherent regime,the lateral planes are in full lattice-registry.The strain as well as t c depend strongly on the speciﬁc geometry(bilayer,sandwich,ﬁlm on a substrate,multilayer,etc).For a general multilayer A/B in the coherent regime, minimization of the elastic energy(12tE 2),yields in good approximation:A=−η/(1+t A E A/t B E B)(8)B=η+ A(9) with E A and E B the elastic moduli of layer A and B.For other geometries,analogous relations can be derived.Assuming that layer A is the magnetic layer,substitution of A inequation(6)gives the magneto-elastic contribution to the anisotropy K cohme =−3λE A A.Inprinciple,this contribution contains the thickness of the magnetic layer t A,and therefore may obscure the simple analysis in terms of volume and interface contributions(equation(1)). In the speciﬁc cases of t A t B and t A/t B=constant,the magneto-elastic anisotropy is independent of t A and contributes only to K v:K coh me,v=3λE Aη.(10) The elastic energy associated with the coherent situation is proportional to the strained volume.Increasing the thickness of layer A will therefore increase the elastic energy.This energy increase will not persist.At a certain critical thickness t c,already mentioned above, it becomes energetically more favourable to introduce misﬁt dislocations which partially accommodate the lattice misﬁt,allowing the uniform strain to be reduced.The lattice-registry is then partially lost and the layers become partially coherent or in short incoherent.In general,it is not an easy task to calculate the strain in the incoherent regime.In the special case of a single layer A on a rigid substrate it has been shown(Matthews1990, Chappert and Bruno1988),by minimization of the sum of the elastic energy and the energy due to dislocations,that the residual strain A,which is assumed to be uniform within the layer,can be written asA=−ηt c/t A(11) where t c,inﬁrst approximation,is given by(den Broeder et al1991):t c=Gb8|η|E A.(12)Here use was made of the simple expression for the energy of a dislocation E=1Gb2, where b is the Burgers vector of the dislocation and G the shear modulus.The critical thickness t c in the case of a thin layer A sandwiched between two identical layers B is four times larger since two layers B are elastically deformed,while there are two interfaces A/B to mediate the stress(den Broeder et al1991).Alternatively,by considering the strain ﬁeld around a misﬁt dislocation,Matthews and Blakeslee(1974,1975)derived a critical thickness:t c b =Gx4π|η|E Alnt cb+1(13)where x=1for a single layer deposited on a substrate and x=2if the stressed layer is sandwiched between two considerably thicker layers which both support coherent growth. This expression has been used for comparison with the experiment in subsection6.2.As a consequence of the speciﬁc form of equation(11),the contribution of the magneto-elastic energy,equation(6),also contains the1/t dependence.Following the common analysis1418M T Johnson et alFigure3.Theoretical thickness dependence of(a)the strain and(b)the MAE times the layerthickness in the coherent and incoherent regime.of anisotropy data as introduced by equation(1),this contribution,which is essentially generated in the volume,will emerge as an apparent interface contribution for the incoherent growth regime:K me=3λE Aηt c/t A.(14) By substituting K me=2K inc me,s/t A,the interface anisotropy is found to be:K inc me,s=3λE Aηt c.(15) It should be noted that K inc me,s does not depend onηbecause its dependence cancels against that of t c,see equations(12)and(13).An alternative,simple expression for the magneto-elastic interface contribution in the case of a sandwiched layer,can be given in terms of G and b(den Broeder et al1991)(η<0):K inc me,s=−3λGb.(16) Figure3illustrates the transition between the coherent and incoherent regime and the resulting effect observed in the magnetic anisotropy.Thus,a separate interpretation of the magnetic anisotropy must be made in the regions above and below t c(den Broeder et al1991).In the coherent region below t c,the volume anisotropy K v incorporates shape anisotropy,magnetocrystalline anisotropy(K mc)and strain anisotropy(K me,v),with interface anisotropy being solely N´e el-type.K s=K N(17)K v=−12µo M2s+K mc+K coh me,v(18)with K cohme,v as in equation(10).In this region,the inﬂuence of misﬁt strain thus appears asa volume contribution to the anisotropy.In the incoherent region above t c,the distinctive form of volume strain represented by equation(11)has been shown to lead to an apparent interface contribution:the magneto-elastic interface anisotropy(Chappert and Bruno1988), so that:K s=K N+K inc me,s(19)K v=−12µo M2s+K mc(20) with K inc me,s as in equation(15).Figure3(b)schematically illustrates the expected dependence of K eff t on t,with a marked kink appearing at the critical thickness t c.The relevance ofthis picture will be discussed by considering the Cu/Ni model system,in subsection6.2.。

动画片英语作文

Cartoons are a form of animation that has captivated audiences of all ages.They are a creative blend of art,storytelling,and technology that brings characters and stories to life in a visually engaging way.Heres a detailed look at the world of cartoons and their impact on culture and society.The History of AnimationThe roots of animation can be traced back to the early20th century,with pioneers like Walt Disney and Max Fleischer.The first animated films were handdrawn,frame by frame,which was a laborintensive process.Over time,technology has evolved,and so has the art of animation,leading to the creation of more complex and visually stunning cartoons.Types of AnimationThere are various types of animation techniques,including:Traditional Handdrawn Animation:This involves drawing each frame of the animation by hand,which is then photographed and played in sequence to create the illusion of movement.Stop Motion:Objects,often clay or plasticine figures,are physically manipulated in small increments between individually photographed frames to create the appearance of movement.Computergenerated Animation CGI:This modern technique uses computer software to model and animate characters and environments,allowing for more fluid motion and detailed visuals.Popular Cartoon GenresCartoons can be categorized into different genres,such as:Comedy:Often aimed at younger audiences,these cartoons use humor and slapstick to entertain.Action/Adventure:These cartoons feature exciting narratives with heroes overcoming obstacles and battling villains.Fantasy:They transport viewers to magical worlds with mythical creatures and enchanting landscapes.Educational:Some cartoons are designed to teach valuable lessons or impart knowledge in an engaging way.Influence on CultureCartoons have had a significant impact on popular culture.They have introduced iconic characters like Mickey Mouse,Bugs Bunny,and SpongeBob SquarePants,who have become household names.Moreover,they have influenced fashion,music,and even language,with phrases and catchphrases from cartoons becoming part of everyday speech.Educational ValueBeyond entertainment,cartoons serve as educational tools.They can help children develop language skills,enhance cognitive abilities,and foster cational cartoons often incorporate lessons about social skills,problemsolving,and basic concepts in science and math.Technological AdvancementsThe advent of digital technology has revolutionized the animation industry.Software like Adobe After Effects,Maya,and Blender has made it easier for artists to create highquality animations.Additionally,virtual reality and augmented reality are opening up new possibilities for interactive and immersive cartoon experiences.Future of AnimationThe future of animation looks promising with the continuous development of technology and storytelling techniques.We can expect more realistic animations,interactive narratives,and perhaps even personalized cartoon experiences where viewers can influence the storys outcome.ConclusionCartoons are more than just a form of entertainment they are a powerful medium for storytelling and education.As technology continues to advance,the possibilities for what can be achieved in animation are limitless,ensuring that cartoons will remain a beloved part of our culture for generations to come.。

去买奥尔良烤鸡的作文英语

As an English teacher,I will guide you through writing a descriptive essay about buying an Orleansstyle Roasted Chicken in French English.Heres how you can structure your essay:Title:The Allure of an OrleansStyle Roasted ChickenIntroduction:Begin with a captivating introduction that sets the tone for your essay.You might want to mention the cultural significance of the dish or your personal connection to it.Example:The aroma of an Orleansstyle roasted chicken is a sensory journey that transcends the mere act of cooking.It is a culinary experience that has its roots deeply embedded in the vibrant history and culture of New Orleans,a city known for its rich flavors and warm hospitality.Body Paragraph1:The History and OriginExplain the origins of the dish and how it became a staple in New Orleans cuisine.Example:The Orleansstyle roasted chicken,often associated with the famous Cajun and Creole cooking styles,has a history that is as colorful as the city itself.It is believed to have been influenced by French,Spanish,African,and Native American culinary traditions, resulting in a unique blend of flavors that is both comforting and exotic.Body Paragraph2:The PreparationDescribe the process of preparing the chicken,including the ingredients and the method.Example:Preparing an Orleansstyle roasted chicken is an art form that requires patience and precision.The chicken is marinated in a blend of herbs and spices,such as thyme, oregano,paprika,and cayenne pepper,which infuses the meat with a depth of flavor.The marinade is then sealed inside the chicken,allowing it to soak in the rich flavors overnight before being slowroasted to perfection.Body Paragraph3:The ExperienceTalk about the experience of buying and eating the chicken,including the atmosphere and the sensory details.Example:Visiting a local market to buy an Orleansstyle roasted chicken is an experience that engages all the senses.The bustling atmosphere is filled with the chatter of vendors and the laughter of locals,all against the backdrop of the tantalizing aroma of freshly roasted chicken.The moment you take your first bite,the crispy skin gives way to tender,juicy meat that is seasoned to perfection,evoking a sense of satisfaction that is both nostalgic and invigorating.Conclusion:End your essay with a conclusion that reflects on the significance of the dish and its impact on you.Example:The Orleansstyle roasted chicken is more than just a meal it is a testament to the rich cultural tapestry of New Orleans.Each bite is a celebration of the citys history,a reminder of the diverse influences that have come together to create a dish that is as unique as the city itself.It is an experience that lingers in the memory,a flavor that is as unforgettable as the city that inspired it.Remember to use descriptive language and sensory details to bring your essay to life. Enjoy the process of writing and sharing your experience with others!。

北京理工大学线性代数讲义第三章

The presentations of α and the image A (α) satisfy the following equation
to
Example 3.1. A ∈ L R3 maps the basis 1 0 1 α1 = 1 , α2 = 2 , α3 = 0 , −1 −1 −1 0 1 0 1 , α′ 3 , −1 , α′ α′ 1 = 2 = 3 = −2 0 −1
′ ′ α′ 1 , α2 , α3 is 1 23 10 1 −32 = −4 0 −13 −9
′ α′ 2 , α3 is 1 10 1 1 −4 = −15 0 −9 6
For A ∈ L(V ), Theorem 1.14 will be adopted to the following.
1. Find out the matrix representation for A with respect to the basis α1 , α2 , α3 ; 2. Find out the representations of ξ = [1 2 3]T and its image A (ξ ) with respect to the basis α1 , α2 , α3 ;
=
Hence, the representation of A with respect to the basis α1 , α2 , α3 is 1 −1 −1 1 2 A = −1 0 1 1
[α1 − α2 − α1 + α2 + α3 − α1 + 2α2 + α3 ] 1 −1 −1 1 2 [α1 α2 α3 ] −1 0 1 1

穿条纹睡衣的男孩经典语录英文

穿条纹睡衣的男孩经典语录英文1. Introduction在文学作品《穿条纹睡衣的男孩》中，作者约翰·波因特以一个八岁的纳粹德国少年的视角，讲述了纳粹集中营的悲惨故事，该故事引起了全球读者的共鸣。

小男孩在书中的独特语录也令人印象深刻，充满了对世界的好奇和对人性的纯真。

2. Classic Quotes in English以下是《穿条纹睡衣的男孩》中一些经典的英文语录：2.1 "We're not supposed to be friends, you and me. We're meant to be enemies. Did you know that?"——“我们本应该是敌人，而不是朋友。

你知道吗？”这句话体现了书中主人公布鲁诺对世界和战争的无知和好奇。

他对友谊和敌对关系的认知并不受社会常规和宗教教义的束缚，表现了他的天真和纯真。

2.2 "I don't like that word. It's a cruel word, a word that people have made up to feel big and important. So they think if they use it, people will be scared of them. The thing is, it's just a word, isn't it? Just a word."——“我不喜欢那个词。

那是个残忍的词，人们编造出来的词，为了让自己显得了不起。

这样他们就可以吓唬别人了。

可事实上，那不过是个词，是吧？仅仅是一个词。

”这句话展示了布鲁诺对“强大”和“权力”这些成人们常用的词语的质疑和挑战。

他认为这些词的能量只是来自人们对它们的恐惧和敬畏，不过是人们虚构出来的东西，这展现了他对世界的独立思考和清晰观察。

容斥原理英语范文

容斥原理英语范文The principle of inclusion-exclusion, also known as the principle of values, is a mathematical concept used to count the number of elements in a set by considering the number ofelements that belong to certain subsets.The principle states that if we want to count the number of elements in a set A, we can add the number of elements in set Ato the number of elements in set B, and then subtract the number of elements that belong to both sets A and B, as these elements have been counted twice. The formula for the principle of inclusion-exclusion is:A∪B，=，A，+，B，-，A∩BA∪B∪C，=，A，+，B，+，C，-，A∩B，-，A∩C，-，B∩C，+，A∩B∩CThis formula follows a pattern, where we add the number of elements in each set, subtract the number of elements in the intersection of every pair of sets, add the number of elementsin the intersection of every triple of sets, and so on.For example, consider a problem where we want to count the number of three-digit numbers that do not contain the digit 0, 1, or 2. We can use the principle of inclusion-exclusion to solve this problem.In conclusion, the principle of inclusion-exclusion is a powerful mathematical tool used to count the number of elements in a set by considering the number of elements that belong to certain subsets. It allows us to solve counting problems with multiple conditions or constraints by adding or subtracting the appropriate intersections of sets.。

先例现象与文学作品中宗教文化元素的翻译

先例现象与文学作品中宗教文化元素的翻译先例现象（precedent phenomenon）是指在一些领域或领域内出现的
常见现象或现象模式。

这个概念主要用于法律、政治、经济等领域，用来
指示在类似情况下可能会发生的事情。

文学作品中的宗教文化元素（religious and cultural elements in literary works）是指作品中包含的与宗教有关的信仰、仪式、符号、价
值观等元素。

这些元素可以是特定宗教的象征，也可以是对宗教思想、哲
学或生活方式的引用或描绘。

不过，具体的翻译会根据情境、作品内容和具体语境而有所调整。

以
下是两个例子的中文翻译：
Example 1:
原句：This novel explores the profound impact of religious beliefs on the characters' lives.
翻译：这部小说探讨了宗教信仰对人物生活的深远影响。

Example 2:
原句：The use of biblical allusions in the poem adds a layer of depth to the meaning.
翻译：该诗中对圣经的典故运用增添了更深层次的含义。

需要注意的是，在翻译这些宗教文化元素时，译者需要根据作品的背
景和文化差异，以及读者对这些元素的理解程度，进行恰当的调整和解释。

你对初中的感受英语作文

My journey through middle school was a rollercoaster of emotions and experiences, a period of my life that I will always look back on with a mix of nostalgia and gratitude. It was a time of growth, both academically and personally, and it set the foundation for the person I am today.The transition from elementary to middle school was a significant one. I remember feeling a mix of excitement and apprehension as I stepped into a new environment filled with unfamiliar faces and expectations. The classrooms were larger, the subjects more complex, and the teachers seemed more demanding. It was a world away from the cozy familiarity of my elementary school days.One of the most profound realizations I had during my middle school years was the importance of hard work and perseverance. The academic workload was much heavier than I had anticipated. Subjects like mathematics, science, and literature required a level of dedication and focus that I had not previously experienced. There were times when I felt overwhelmed by the pressure to perform well, but these challenges ultimately taught me the value of resilience and determination.My middle school years were also a time of exploration and selfdiscovery. I was exposed to a wide range of subjects and activities that allowed me to explore my interests and passions. I joined the schools debate team, which not only honed my public speaking skills but also instilled in me a love for critical thinking and intellectual discourse. I also discovered a passion for music and joined the school band, learning to play the flute and participating in various performances.The friendships I formed during my middle school years were another highlight. I met people from diverse backgrounds and with different perspectives, which broadened my worldview and taught me the importance of empathy and understanding. We shared our triumphs and tribulations, supported each other through exams and extracurricular activities, and created memories that I will cherish forever.However, middle school was not without its challenges. The social dynamics could be complex and sometimes intimidating. I experienced moments of selfdoubt and insecurity, particularly when it came to fitting in and being accepted by my peers. But these experiences, though difficult at the time, ultimately made me stronger and more selfaware.Looking back, I am grateful for the lessons I learned during my middle school years. They taught me the importance of hard work, the value of exploring my interests, and the power of friendship. They also helped me develop a sense of resilience and selfconfidence that has served me well in my subsequent academic and personal endeavors.In conclusion, my middle school experience was a pivotal chapter in my life. It was a time of growth, learning, and selfdiscovery that has left an indelible mark on who I am today. While there were moments of struggle and uncertainty, the overall journey was one of immense value and significance. It is a period I will always look back on with fondness and appreciation.。

Nuclear Equation of State

a r X i v :n u c l -t h /0112006v 1 3 D e c 2001Nuclear Equation of StatePawełDanielewiczNational Superconducting Cyclotron Laboratory and Department of Physics and Astronomy,Michigan State University,East Lansing,MI 48824,USA,and Gesellschaft für Schwerionenforschung mbH,D-64291Darmstadt,Germany Abstract.Nuclear equation of state plays an important role in the evolution of the Universe,in supernova explosions and,thus,in the production of heavy elements,and in stability of neutron stars.The equation constrains the two-and three-nucleon interactions and the quantum chromodynamics in nonperturbative regime.Despite the importance of the equation,though,its features had remained fairly obscure.The talk reviews new results on the equation of state from measurements of giant nuclear oscillations and from studies of particle emission in central collisions of heavy nuclei.INTRODUCTION An equation of state (EOS)is a nontrivial relation between thermodynamic variables characterizing a medium.While the term is used in its singular form in nuclear physics,actually different relations are of interest,such as between pressure p and baryon density ρand temperature T ,p (ρ,T ),or chemical potential µand T ,p (µ,T ),between energy density e and ρand T ,e (ρ,T ),etc.Some of the relations are fundamental under certain conditions,i.e.all other relations may be derived from them (such as from e (ρ)at T =0).The nuclear EOS is of interest because it affects the fate of the Universe at times t 1µs from the Big Bang and because its features are behind the supernova explo-sions.Moreover,its features ensure the stability of neutron stars.Through its effects on the evolution of the Universe,on supernovae explosions,and on neutron-star collisions,the EOS affects nucleosynthesis.Moreover,the EOS impacts central reactions of heavy nuclei.Finally,the form of the EOS constraints hadronic interactions and the nonpertur-bative quantum chromodynamics (QCD).IMPORTANCE OF EOSDifferent regimes for the strongly interacting are conveniently assessed in the µ−T plane,see Fig 1.Along the T =0axis,at µ≈930MeV ,we have the matter in heavy nuclei.The matter in the interior of neutron stars corresponds to higher chemical potentials,in combinations with low temperatures.The matter in the early Universe evolved along the temperature axis,at low baryon number content,and thus at low µ.Different regions of the plane are explored at different accelerators.In the early Universe and likely at the higher-energy accelerators,the matter crosses the transition between the hadronic matter and quark-gluon plasma.The transition is observed in numerical lattice QCD calculations as a rapid change in energy density in the temperature regionFIGURE3.Supercooling tension for the conﬁnement phase transition,after[3].FIGURE4.Phase bubbles in the region of the conﬁnement phase transition,after[3].little in the quark-gluon phase,with quarks being massless,and a lot in the hadronic phase,with massive baryons.An analogous situation takes place when seawater freezes. Then the salt appears in the areas that are last to freeze,Fig.5.There are some cautioning theoretical and experimental indications,though,regarding the scenario,that the surface tension might not be very large between in the quark-gluon and hadron phases.Supernova ExplosionsType II supernova explosions are the source of at least half of the nuclei heavier than iron around us.Only very massive stars,of masses M 8M⊙,explode.Generally,the more massive a star,the shorter it lives,burning faster due to higher density and tem-perature in its interior.A star starts out burning hydrogen,then helium and successively heavier nuclei;at each stage the products are accumulated.After a given fuel runs out, the gravitation compresses the star core raising temperature and the next fuel ignites with its burning preventing further compression.When the core consists of iron only, the burning stops.It is then up to the electron pressure(such as resisting the compres-sion of solids)to prevent the gravitational collapse of the core.However,the electronFIGURE5.Seawater analogy.pressure fails when the core exceeds the threshold Chandrasekhar mass.This is seen by examining the contributions to the energy from gravity and from an ultrarelativistic electron gas:E=−3R+N e 32p F c+... +...=15G(Nm N)2+34 1/3N4/3e+O(R).(1)The electron Fermi momentum is proportional to the cube root of electron density and, thus,is inversely proportional to core radius,p F∝ρ1/3e∝1/R.Both the gravitational andelectron energies are then inversely proportional to the radius,but the electron energy grows only as the number of electrons to the4/3power while the gravitational energy as the square power of the nucleon number.For the electron number equal to half the nucleon number,N e=N N/2,the gravity wins over electrons for core massM>M th= 5G 3/23π1/2FIGURE 8.Density proﬁle of a neutron star of mass M =1.4M ⊙,after [4].ε (MeV/fm 3)0100200300400P (M e V /f m 3)Schroedinger−based FIGURE 9.Pressure-energy relations [6]for nuclear matter,employed in astrophysical calculations.ELEMENTARY FEATURES OF THE NUCLEAR EOSEnergy MinimumThe advances in the determination of the nuclear EOS have been,generally,difﬁcult.The elementary information comes from the Weizsäcker binding-energy formula and from the systematics of nuclear density proﬁles.The Weizsäcker formula separates out the contributions to the energy associated with nuclear interactions and the interior and surface of nuclei,the contributions associated with isospin asymmetry and with Coulomb interactions,and the shell correction,−B (A ,Z )=−16MeV A +a s A 2/3+a a (A −2Z )2A 1/3−B p ,s .(3)FIGURE10.Neutron star mergers for soft(left panels)and stiff(right panels)nuclear EOS,after[7].FIGURE11.Nuclear densities deduced from electron scattering.Nuclear densities,obtained from charge densities multiplied by mass to charge number ratio,are seen to reach the same value,ρ0=0.16fm−3≃1/(6fm3),for a wide range of nuclear masses,see Fig.11.We conclude that the energy per nucleon in a uniform symmetric nuclear matter at T=0,in the absence of Coulomb interactions,has a minimum at the normal densityρ0with the energy value,relative to nucleon mass,of -16MeV,from the volume term in the binding formula,see Fig.12.As,obviously,the binding energy approaches zero for separated nucleons atρ→0,we actually know two points in the(T=0)dependence of the energy per nucleon,E/A≡e/ρ,on density. The next nontrivial feature of the energy per nucleon is its curvature in the dependence onρ,aroundρ0.This curvature is commonly quantiﬁed in terms of the so-called nuclear incompressibility,with an unusal numerical factor:K=9ρ20d2A =R2d2A.(4)The factor stems from the fact that the nuclei wereﬁrst considered as sharp-edgedFIGURE12.Energy per nucleon vs density in nuclear matter.FIGURE13.Oscillating nuclei wereﬁrst considered as sharp-edged spheres with the energy changing as a function of the radius.spheres with the energy changing as a function of the radius(Fig.13).To get an idea of what might be expected for the incompressibility,one might just run a parabola through the two known points on the curve of EFIGURE15.Energy per nucleon in nuclear matter as a function of density,from a variational calcula-tion of Ref.[10]with two-and three-nucleon interactions.primitive than the nonrelativistic ones.To get the right position of the minimum in the EOS,Fig.15,it is necessary to incor-porate three-nucleon interactions in the microscopic calculations.These interactions are not well constrained by scattering,hampering the predictive power of the theory.In this situation,one may want to turn to experiment to get the information on the EOS away from the normal density.INCOMPRESSIBILITY-GETTING OUT OF THE MINIMUM The simplest way to determine the incompressibility experimentally may seem to induce volume oscillations in a nucleus.This could be done by scatteringαparticles off a nucleus,Fig.16.For the lowest excitation,the excitation energy E∗,deduced from the ﬁnalαenergy,would be related to the classical frequency through E∗= Ω,and the latter would be related to K.Let us examine the classical energy of an oscillating nucleus:E tot= d rρm N v22AK(R−R0)22+1KA 2+K c Z(Z−1)K A E∗3 0+spectrumFIGURE18.Delivering angular momentum to a target.the quadrupole shape oscillation,cf.Fig.17.However,those oscillations transform differently under rotations and,correspondingly,the elementary excitations for those oscillations are characterized by different angular momenta,with the uniform density changes characterized by L=0.It is possible to isolate the L=0excitations by analyzing scattering at the very forward angles,Fig.18.When the alpha particle scatters off a nucleus it transfers linear and angular momenta to the nucleus.The angular momentum is limited by the product of the linear momentum transfer and the distance over which the transfer occurs,i.e.roughly the sum of projectile and target radii.At high beam energies and small angles we getL<|p−p′|R≈pθR.(9) Excitations characterized by L≥1 may suppressed by looking at scattering into the anglesθ<=138MeV,and of nuclear2matter K=K Sm/0.67∼210MeV.However,explorations with microscopic models produce different results for K A/K.In particular,relativistic models can yield results in the range K∼(250−270)MeV[13].Generally,the results are,though,on the soft side of the incompressibility.FIGURE20.0+-strength function in144Sm,determined in Ref.[12].EOS AT SUPRANORMAL DENSITIES FROM FLOW Features of EOS at supranormal densities can be inferred fromﬂow produced in col-lisions of heavy nuclei at high energies.At low impact parameters,in those collisions, macroscopic regions of high density are formed.The collectiveﬂow,that can be quanti-tatively assessed in collisions,is the particle motion characterized by space-momentum correlations of dynamic origin.Theﬂow can provide information on the pressure gener-ated in the collision.To see how theﬂow relates to pressure,we may look at the hydrodynamic Euler equation for the nuclearﬂuid,an analog of the Newton equation,in a local frame where the collective velocity vanishes,v=0:∂(e+p)to the Newton equation,we see that the pressure p=ρ2∂(e/ρ)∂t +∂ε∂r−∂ε∂p=I,(11)where I is the collision integral.Theﬁrst observable that one may want to consider to extract the information on EOS is the net radial or transverse collective energy.That energy may reach as much as half of the total kinetic energy in a reaction.Despite its magnitude,the energy is not useful for extracting the information on EOS because of the lack of information on how long the energy rge pressures acting over a short time can produce the same net collective energy as low pressures acting over a long time.This makes appearent the need for a timer in reactions.The role of the timer in reactions may be taken on by the so-called spectators.The spectator nucleons are those in the periphery of an energetic reaction,weakly affected by the reaction process,proceeding virtually at undisturbed original velocity,see Fig.21. Participant nucleons,on the other hand,are those closer to the center of the reaction, participating in violent processes,subject to matter compression and expansion in the reaction.As the participant zone expands,the spectators,moving at a prescribed pace, shadow the expansion.If the pressures in the central region are high and the expansion is rapid,the anisotropies generated by the presence of spectators are going to be strong. On the other hand,if the pressures are low and,correspondingly,the expansion of the matter is slow,the shadows left by spectators will not be very pronounced.There are different types of anisotropies in the emission that the spectators can produce.Thus,throughout the early stages of a collisions,the particles move primarily along the beam axis in the center of mass.However,during the compression stage,the participants get locked within a channel,titled at an angle,between the spectator pieces, cf.Fig.21.As a consequence,the forward and backward emitted particles acquire an average deﬂection away from the beam axis,towards the channel direction.Another anisotropy may be observed for particles emitted in the transverse directions with zero longitudinal velocity.The region with compressed matter is open to the vacuum inFIGURE21.Reaction-plane contour plots for different quantities in a124Sn+124Sn reaction at800 MeV/nucleon and b=6fm,from transport simulations by Shi[14].the direction perpendicular to the reaction plane.However,in the direction within the reaction plane the region is shadowed by the participants.Thus,more particles are expected to be transversally emitted from the participant region perpendicular than within the direction plane.The anisotropy should be stronger the faster the expansion of the compressed matter.The different anisotropies have been quantiﬁed experimentally over a wide range of bombarding energies.Figure22shows the measure of the sideward forward-backward deﬂection in Au+Au collisions as a function of the beam energy,with symbols repre-senting data.Lines represent simulations assuming different EOS.On top of theﬁgure, typical maximal densities are indicated which are reached at a given bombarding energy. Without interaction contributions to pressure,the simulations labelled cascade produce far too weak anisotropies to be compatible with data.The simulations with EOS charac-terized by the incompressibility K=167MeV yield adequate anisotropy at lower beam energies,but too low at higher energies.On the other hand,with the EOS characterized by K=380MeV,the anisotropy appears too high at virtually all energies.It should be mentioned that the incompressibilities should be considered here as merely labels for the different utilized EOS.The pressures resulting in the expansion are produced at densities signiﬁcantly higher than normal and,in fact,changing in the course of the reaction. Figure23shows next the anisotropy of emission at midrapidity or zero longitudinal velocity in the c.m.,cf.Fig.24,with symbols representing data and lines representing simulations.Again,we see that without interaction contributions to pressure,simulations cannot reproduce the measurements.The simulations with K=167MeV give too little pressure at high energies,and those with K=380MeV generally too much.A level of discrepancy is seen between data from different experiments.We see that no single EOS allows for a simultaneous description of both types of anisotropies at all energies.In particular,the K=210MeV EOS is best for the sideward anisotropy,and the K=300MeV EOS is the best for the other,so-calledFIGURE23.Ellipticﬂow excitation function for Au+Au.Data and transport calculations are respre-sented,respectively,by symbols and lines[15].FIGURE 26.Impact of the constraints on models for EOS [15].elliptic,anisotropy.We can use the discrepancy between the conclusions drawn from the two types of anisotropies as a measure of inaccuaracy of the theory and draw broad boundaries on pressure as a function of density from what is common in conclusions based on the two anisotropies.To ensure that the effects of compression dominate in the reaction over other effects,we limit ourselves to densities higher than twice the normal.The boundaries on the pressure are shown in Fig.25and they eliminate some of the more extreme models for EOS utilized in nuclear physics,such as the relativistic NL3model and models assuming a phase transition at relatively low densities,cf.Fig.26.FIGURE27.Relative particle abundancies in measurements(symbols)and calculated in the thermal freeze-out model(lines)in Ref.[17].vector resonances)have been collected with signiﬁcant background reductions and high resolution both in the energy and angle direction,allowing for improved determinations of the nuclear incompressibility.Anisotropies ofﬂow from central reactions allow to constrain the EOS at supranormal densities.The parameters of freeze-out in reactions allow to stake out the limits of the hadronic world.Additional sources of information on EOS that I had no chance to talk about include measurements of neutron-star properties, studies of nuclear systematics and lattice QCD calculations.Unconquered EOS frontiers include the dependence of EOS on the isosopin degree of freedom and the detection of the quark-gluon plasma.Theﬁrst frontier is,in particular,to be tackled at the NSCL coupled-cyclotrons and at the proposed RIA accelerator.In the baryonless regime,the second frontier is pursued at RHIC.However,the baryon-rich regime awaits stepped-up dedicated studies with good resolution in bombarding energy in the range of(2-40)GeV/nucleon.ACKNOWLEDGMENTSInformation provided by M.Itoh on giant resonances is gratefully acknowledged. This work was partially supported by the National Science Foundation under Grant PHY-0070818.∗Originalﬁgures from Refs.[1]and[4],respectively,have been utilized,with permis-sion from Elsevier Science.REFERENCES1.J.Stachel,Nucl.Phys.A654,119c(1999).2. F.Karsch,hep-lat/0106019.3. B.Kämpfer et al.,nucl-th/0011088.4.Ch.Schaab et al.,Nucl.Phys.A605,531(1996).5.N.K.Glendenning,Phys.Rev.C37,2733(1988).6. F.Weber,Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics,IoP Publishing,Bristol(1999).7.S.Rosswog et al.,Astronomy and Astrophysics341,499(1999).8.M.Baldo et al.,Phys.Rev.C41,1748(1990).9.R.Brockmann and R.Machleit,Phys.Rev.C42,1965(1990).10.A.Akmal,V.R.Pandharipande,and D.G.Ravenhall,Phys.Rev.C58,1804(1998).11.D.H.Youngblood,Nucl.Phys.A6871c(2001).12.M.Itoh et al.,Nucl.Phys.A687,52c(2001).13.D.Vretenar et al.,Nucl.Phys.A621,853(1997).14.L.Shi,P.Danielewicz and cey,Phys.Rev.C64,034601(2001).15.P.Danielewicz,W.Lynch and cey(2001),to be published.16.C.Pinkenburg et al.,Phys.Rev.Lett.83,1295(1999).17.P.Braun-Munzinger et al.,Phys.Lett.B365,1(1996).18.J.Cleymans and K.Redlich,Nucl.Phys.A661,379c(1999).。

情感细品如诗的英语作文

Emotions are the subtle threads that weave the tapestry of our lives,each strand a unique hue,each shade a testament to the depth and complexity of the human experience. In the realm of English composition,the art of capturing these emotions in poetic form is a delicate dance of words,a symphony of sentiment that resonates with the readers own inner world.To begin with,the art of emotional expression in English prose requires a keen understanding of the languages capacity for nuance.Words must be chosen with care, each one a brush stroke on the canvas of the readers mind,painting a picture that is both vivid and evocative.Adjectives and adverbs,when used sparingly and with precision,can imbue a sentence with the depth of feeling that mere nouns and verbs cannot convey alone.Consider the following example:The sun dipped below the horizon,casting a golden glow over the tranquil sea,as the gentle breeze whispered secrets to the waves.Here,the adjective golden and the verb whispered work in tandem to create a serene and enchanting scene,evoking a sense of peace and beauty that transcends the mere description of the sunset.Moreover,the use of metaphor and simile is a powerful tool in the poets arsenal,allowing for the comparison of emotions to tangible,relatable experiences.By drawing parallels between the abstract and the concrete,the writer can create a bridge between the readers own emotions and the emotions portrayed in the text.For instance:Her laughter was like a melody that danced through the air,lighting up the room with its infectious joy.In this sentence,the simile compares laughter to a melody,a universally understood expression of happiness,thereby amplifying the emotional impact of the scene. Furthermore,the rhythm and flow of the language itself can contribute to the emotional resonance of a piece.The use of rhythmic patterns,such as iambic pentameter or anapestic tetrameter,can lend a sense of musicality to the prose,making it more pleasing to the ear and,by extension,the heart.Take,for example,this excerpt:In the quiet of the night,when stars above do shine so bright,I find solace in the silence, where my heart can softly sigh.The repetition of the i sound and the consistent rhythm create a soothing,lulling effect that mirrors the tranquility of the night.Lastly,the exploration of emotions in English composition is not limited to the expression of happiness or joy.The full spectrum of human emotion,from sorrow to anger,from fear to love,can be captured in the written word.It is in the exploration of these darker,more complex emotions that the true depth of our humanity is revealed.For example:The rain fell heavy on the windowpane,a mirror to the storm that raged within my heart, each drop a tear,each gust a silent scream.Here,the metaphor of the rain and the storm serves to express the overwhelming sense of grief and turmoil,providing the reader with a poignant glimpse into the depths of emotional pain.In conclusion,the art of expressing emotions in English prose is a multifaceted endeavor, requiring a mastery of language,a keen sense of imagery,and an understanding of the power of rhythm and metaphor.When executed with skill and sensitivity,such compositions can transcend the boundaries of the page,touching the hearts and minds of readers in a way that is both profound and enduring.。

冰箱里的东西英语小作文儿

In our household,the refrigerator is a treasure trove of food,a testament to our culinary habits and the diversity of our diet.Its a place where the remnants of meals past mingle with the ingredients for future feasts,creating a symphony of scents and tastes that is uniquely ours.The Fresh Produce Drawer:At the bottom of the fridge,the crisper drawers are dedicated to fresh produce.Here, youll find a colorful array of fruits and vegetables,each carefully selected for its freshness and flavor.Apples and oranges nestle next to each other,their vibrant hues a stark contrast to the deep greens of leafy vegetables like spinach and kale.Carrots and cucumbers,with their firm textures,are often found here as well,their earthy tones adding depth to the visual feast.The Dairy Section:Amidst the cool,moist air of the fridge,the dairy section is a haven for all things creamy and k,in its various formsfullfat,skim,and almondtakes up a significant portion of the shelf space.Yogurt,both sweet and savory,is a staple,its containers lined up like little soldiers,ready to be consumed at breakfast or as a midday snack.And of course, theres always a block of cheese,its pungent aroma a reminder of the hearty meals to come.The Meat and Fish Compartment:The meat drawer is a testament to our love for protein.Here,youll find a variety of cutsbeef for stews,chicken for quick dinners,and fish for a lighter meal.The meat is carefully wrapped in butcher paper or plastic,its red hues a stark contrast to the silvery scales of the fish.This section is a favorite for those days when a hearty meal is needed to warm the soul.The Condiments and Sauces:On the door of the fridge,the shelves are dedicated to condiments and sauces,a veritable rainbow of bottles and jars.Ketchup,mustard,and mayonnaise are the reliable standbys, their familiar labels a comfort to any cook.But its the homemade sauceslike the spicy tomato sauce or the tangy vinaigrettethat truly make this section special.Each jar is a testament to the time and effort put into creating something unique and delicious.The Freezer:The freezer is a land of ice and frost,a place where time stands still for the food within. Here,youll find frozen vegetables,a backup for those days when fresh produce is scarce. Ice cream,in all its creamy glory,is a staple,its tubs nestled in the frosty depths.And then there are the frozen meals,a lifesaver for those days when cooking is the last thingon your mind.The refrigerator is more than just a place to store food its a reflection of our lifestyle,our tastes,and our memories.Each item within its doors tells a story,from the hastily grabbed breakfast yogurt to the carefully planned dinner party.Its a place of comfort,a place of sustenance,and most importantly,a place that is always ready to feed our hunger, both for food and for life.。

带有重复手法的英语作文

带有重复手法的英语作文英文回答：In the tapestry of life, repetition weaves itsintricate threads, shaping experiences, memories, and the very fabric of existence. It manifests in various forms, both subtle and overt, serving myriad purposes from enhancing memory to fostering emotional resonance.Repetition at the level of language plays a vital role in comprehension and memorization. By reiterating key concepts, ideas, or phrases, speakers and writers create a sense of familiarity and emphasis. The human brain is inherently drawn to patterns and redundancies, which facilitate the retention and retrieval of information. In education, repetition is often employed to reinforce learning and foster understanding. Repetition strengthens neural pathways in the brain, making it easier to access and recall information when needed.In the realm of art, repetition can evoke powerful emotions and create a sense of rhythm and harmony. Consider the use of repeated motifs in music, where melodies and rhythms recur, creating a sense of familiarity and emotional resonance. In visual art, repetition canestablish unity and cohesion, as well as draw attention to specific elements or create optical illusions. The repetition of shapes, colors, or patterns can elicit feelings of order, balance, and tranquility.However, the power of repetition extends beyond its cognitive and aesthetic functions. In the social sphere, repetition plays a significant role in shaping norms, traditions, and rituals. Through repeated enactments, certain behaviors and practices become ingrained in a culture, providing a sense of continuity and shared identity. Rituals, ceremonies, and social practices often involve repetition, which helps to reinforce their importance and significance.In a broader sense, the concept of repetition can be applied to the cyclical nature of human experience. Theseasons change, day follows night, and life progresses through a series of stages. This repetition provides a sense of order and predictability, but it also serves as a reminder of the transient nature of all things. It reminds us to cherish each moment and to embrace the beauty and wonder of the present.中文回答：在生活的织锦中，重复编织着错综复杂的线，塑造着经历、记忆和存在的本质。

反复的修辞手法的英语作文150

反复的修辞手法的英语作文150英文回答：In the realm of literary composition, the judicious application of rhetorical devices adds depth, resonance, and persuasiveness to discourse. Among a plethora of such techniques, repetition stands out as a powerful tool for emphasis, clarity, and emotional impact.Repetition involves the intentional reiteration of words, phrases, or ideas throughout a text. By echoing certain elements, authors can draw attention to key points, create rhythm, amplify emotions, and instill a sense of urgency.One common form of repetition is anaphora, where a word or phrase is repeated at the beginning of consecutive sentences or clauses. This technique can create a sense of momentum, build anticipation, and enhance the memorability of the message. For instance:I will not go.I will not yield.I will not be moved.Contrastingly, epistrophe employs repetition at the end of sentences or clauses, producing a sense of closure and emphasis. For example:We are all mortal.You are mortal.I am mortal.Another form of repetition is parallelism, where parallel grammatical structures are used to express similar ideas. This technique creates a sense of balance and order, and can enhance the impact of the message:The wind howled. The rain pounded. The thunder roared.Moreover, the use of synonyms or antonyms can also create a repetitive effect, known as synonymia and antanagoge, respectively. By employing words with similar or contrasting meanings, authors can subtly reinforce or juxtapose ideas.Repetition is not merely a stylistic device; it serves as a potent tool for persuasion. By echoing key points or emotional appeals, authors can amplify their impact and drive home their message. Furthermore, repetition can create a sense of unity and coherence within a text, ensuring that the reader's attention remains focused on the central theme.中文回答：在文学创作领域，巧妙运用修辞手法能为话语增添深度、共鸣和说服力。

关于动漫的英语作文

Anime,a term derived from the English word animation,has its origins in Japan and has become a global phenomenon.It refers to a style of animation that is characterized by colorful artwork,fantastical themes,and vibrant characters.Anime is not just for children it appeals to a wide range of audiences,including teenagers and adults,with its diverse genres such as action,romance,horror,and science fiction.The history of anime can be traced back to the early20th century when Japanese filmmakers began experimenting with animation techniques.However,it was not until the1960s that anime started to gain international recognition.One of the pioneers of the industry was Osamu Tezuka,who is often referred to as the godfather of anime.His work, such as Astro Boy,set the standard for storytelling and character design in the industry.Over the years,anime has evolved and diversified,reflecting the cultural,social,and technological changes in Japan.It has also been influenced by other forms of media,such as manga Japanese comics and video games.This has led to the creation of complex narratives and intricate worlds that captivate viewers.One of the key elements that make anime unique is its visual style.The art is often characterized by exaggerated facial expressions,dynamic action sequences,and detailed backgrounds.This distinctive aesthetic has been emulated by animators around the world, making anime a recognizable and influential art form.The themes and stories in anime are as varied as the art styles.Some popular themes include comingofage,friendship,and the struggle between good and evil.Anime often explores complex moral dilemmas and philosophical questions,which can provoke thought and discussion among viewers.In addition to the visual and narrative aspects,anime is known for its use of music and sound effects.The soundtracks often feature a mix of orchestral scores,pop songs,and electronic music,which complement the onscreen action and enhance the emotional impact of the story.The popularity of anime has led to the growth of a dedicated fan base,known as otaku. These fans are passionate about the medium and often engage in activities such as cosplay dressing up as their favorite characters,attending conventions,and collecting merchandise.Despite its Japanese origins,anime has been embraced by audiences worldwide.It has been dubbed or subtitled in various languages,making it accessible to nonJapanese speakers.The global appeal of anime can be attributed to its universal themes,engagingstories,and captivating visuals.In conclusion,anime is a multifaceted form of entertainment that has captured the imagination of people around the globe.Its unique blend of art,storytelling,and music has made it a beloved and enduring part of popular culture.As the industry continues to innovate and expand,the world of anime is sure to delight and inspire audiences for years to come.。

重复构成的看法英文作文

重复构成的看法英文作文英文：Repetitive constructions are a common phenomenon in language use. They can be seen in various forms such as reduplication, repetition of words, phrases, and clauses.In my opinion, repetitive constructions can serve multiple purposes in language use.Firstly, repetitive constructions can emphasize the meaning of the repeated elements. For example, in the sentence "I love love love you", the repetition of "love" emphasizes the speaker's strong affection towards the person. Similarly, in the phrase "easy peasy lemon squeezy", the repetition of "easy" emphasizes the simplicity of the task.Secondly, repetitive constructions can create a poeticor rhythmic effect in language use. For example, in the nursery rhyme "Twinkle Twinkle Little Star", the repetitionof "twinkle" and "star" creates a rhythmic and memorable effect, making it easier for children to learn and remember.Thirdly, repetitive constructions can also serve as a way of expressing emotions or attitudes. For example, inthe sentence "I am so so sorry", the repetition of "so" expresses the speaker's strong regret and apology.In summary, repetitive constructions can serve various functions in language use, including emphasizing meaning, creating poetic or rhythmic effects, and expressingemotions or attitudes.中文：重复构成在语言使用中是一个常见的现象。

力求神似的意思

Strive for a Similar Spirit"Strive for a Similar Spirit" means to make every effort to capture or replicate the essence or atmosphere of something, rather than just its literal or superficial form. This phrase is often used in the context of art, literature, translation, or any other field where a deep understanding and accurate reproduction of the original's intent and feeling is crucial.For instance, in translation, a translator might strive for a similar spirit by aiming to convey the original text's emotional and cultural nuances, rather than simply rendering it word-for-word. Similarly, an artist might strive for a similar spirit by capturing the emotional essence of a subject or scene, rather than just replicating its physical details.“力求神似”意味着尽一切努力去捕捉或复制某事物的精髓或氛围，而不仅仅是其字面或表面的形式。

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a r X i v :c o n d -m a t /0003483v 1 [c o n d -m a t .m e s -h a l l ] 30 M a r 2000Reorientation of Anisotropy in a Square Well Quantum Hall SampleW.Pan 1,2,T.Jungwirth 3,4,H.L.Stormer 5,6,D.C.Tsui 1,A.H.MacDonald 3,S.M.Girvin 3,L.Smrˇc ka 4,L.N.Pfeiﬀer 5,K.W.Baldwin 5,and K.W.West 51Department of Electrical Engineering,Princeton University,Princeton,New Jersey 085442NHMFL,Tallahassee,Florida 323103Department of Physics,Indiana University,Bloomington,Indiana 474054Institute of Physics ASCR,Cukrovarnick´a 10,16200Praha 6,Czech Republic5Bell Labs,Lucent Technologies,Murray Hill,New Jersey 079746Department of Physics and Department of Applied Physics,Columbia University,New York,New York 10027(February 1,2008)We have measured magnetotransport at half-ﬁlled high Landau levels in a quantum well with two occupied electric subbands.We ﬁnd resistivities that are isotropic in perpendicular magnetic ﬁeld but become strongly anisotropic at ν=9/2and 11/2on tilting the ﬁeld.The anisotropy appears at an in-plane ﬁeld,B ip ∼2.5T,with the easy-current direction parallel to B ip but rotates by 90◦at B ip ∼10T and points now in the same direction as in single-subband samples.This complex behavior is in quantitative agreement with theoretical calculations based on a unidirectional charge density wave state model.A two-dimensional (2D)electron gas is an attractive system for many-body physics studies [1,2].A particu-larly rich variety of phenomena associated with strong interactions among electrons appears in the regime of the fractional quantum Hall eﬀect (FQHE)[3,4].Dur-ing much of the last decade,studies of the FQHE have focused on even-denominator Landau level ﬁlling factors [5,6]such as the compressible ν=1/2state and the ν=5/2incompressible quantum Hall ﬂuid.Most re-cently,strongly anisotropic transport has been observed in high quality GaAs/Al x Ga 1−x As single heterojunctions [7–11]at ﬁlling factors ν=9/2,11/2,etc.,and in 2D hole systems [12]starting at ν=5/2.In these experiments,the magnetoresistance shows a strong peak in one cur-rent direction and a deep minimum in the perpendicular current direction.Tilting the magnetic ﬁeld away from the sample normal causes the high resistance direction to change from its original orientation to the in-plane magnetic ﬁeld direction.The origin of the magnetotransport anisotropy has not been ﬁrmly established yet.The most appealing interpre-tation suggests that the 2D electron gas spontaneously breaks the translational symmetry by forming a unidi-rectional charge density wave (UCDW),as predicted by Hartree-Fock theory [13,14].This idea has spurred much theoretical interest [15–28].Because of uncertainty about the reliability of this Hartree-Fock prediction,there has been a special emphasis [19,20]placed on tests of its abil-ity to explain experimental results on “stripe”orienta-tion in tilted magnetic ﬁelds.In particular,Jungwirth et al.[19]carried out detailed many-body RPA/Hartree-Fock calculations combined with a self-consistent local-spin-density-approximation (LSDA)description of one-particle states in experimental sample geometries.For the sample parameters of the traditional,single-interface specimens of Refs.[10,11]with a single electric subband occupied,the theory [19,20]gives stripes oriented per-pendicular to the ﬁeld,consistent with experiment.A theoretical study [19]of UCDWs in parabolic quan-tum wells that have two subbands occupied in zero mag-netic ﬁeld,has predicted much more complex behavior of the UCDW state,including stripe states induced by an in-plane ﬁeld and rotation of stripe orientation at critical in-plane ﬁeld strengths.A comparison between theory and experiment in a geometry for which this intricate be-havior occurs,constitutes an excellent test of the UCDW explanation of anisotropic transport in higher Landau levels.Since parabolic quantum wells are experimentally diﬃcult to realize and suﬀer from poor mobility we,in-stead,chose a square well structure which is expected to exhibit similarly complex behavior,provided that more than one electric subband is occupied in zero ﬁeld.Our sample,detailed in Figure 1(c),consists of a 350˚A wide GaAs quantum well bracketed between thick Al 0.24Ga 0.76As layers grown on a (100)GaAs substrate by MBE.Two Si delta-doping layers are placed symmet-rically above and below the quantum well at a distance of 800˚A .The specimen has a size of 5mm ×5mm and is contacted via eight indium contacts,placed symmet-rically around the perimeter.The electron density is es-tablished after illuminating the sample with a red light-emitting diode at ∼4.2K and we measure an electron mo-bility of µ=7×106cm 2/V s.The total electron density,n =4.6×1011cm −2,is determined from low-ﬁeld Hall data.The subband densities,n 1=3.3×1011cm −2and n 2=1.3×1011/cm −2,are obtained by Fourier analysis ofthe low-ﬁeld Shubnikov-de Haas oscillation.Their values coincide with the results of our numerical self-consistent LSDA calculation.All angular-dependent measurements were carried out at T=40mK in a top-loading dilution refrigerator equipped with an in-situ rotator[29]placed inside a33T resistive magnet.A low-frequency(∼7Hz) lock-in technique at a current I=10nA is used.We de-ﬁne the axis of rotation as the y-axis.Consequently,the in-planeﬁeld,B ip,is along the x-axis when the sample is rotated.Therefore,R xx refers to“I parallel to B ip”and R yy refers to“I perpendicular to B ip”[30].Figure1(a)shows an overview of magnetoresistance at zero-tilt.The shaded region highlights the transport features aroundν=9/2and11/2.The integer quantum Hall eﬀect(IQHE)states atν=1,2,3,···and the FQHE states atν=2/3,etc.are clearly visible.Figure1(b) shows the results of self-consistent LSDA calculations of Landau levels(measured from the bottom of the quan-tum well)in perpendicular magneticﬁeld.Figure2shows the R xx and R yy data for4<ν<6at four diﬀerent tilt anglesθ=0◦,41.2◦,67.9◦,and76.2◦. The tilt angle is determined using the shift of promi-nent QHE states,which depend only on the perpendicu-lar magneticﬁeld,B perp=B×cosθ.In the absence of B ip(θ=0◦),R xx and R yy show a peak atν=9/2and a slight dip atν=11/2and negligible anisotropy.The small diﬀerence in magnitude between R xx and R yy is probably a result of the diﬀerent contacts involved in both measurements.This practi-cally isotropic behavior of R xx and R yy is distinctively diﬀerent from results[7–11]on single-subband,single-heterojunctions,where the states atν=9/2and11/2 are strongly anisotropic in the absence of B ip.This lack of anisotropy in our sample has a simple interpretation. The diagram in Figure1(b)indicates that theν=9/2 and11/2states are theν=3/2state of the lowest Lan-dau level(N=0)in the second quantum well subband (i=2).Theν=3/2state in single subband samples ex-hibits isotropic transport,which seems to carry over to the second subband.Yet,exceptional behavior develops on tilting the specimen.Atθ=41.2◦the R xx and R yy traces are very diﬀerent from those taken at zeroﬁeld-tilt and diﬀerent from each other.Theν=9/2andν=11/2states are strongly anisotropic with the hard-axis perpendicular to B ip(R yy) and the easy-axis parallel to B ip(R xx).The direction of this tilt-induced anisotropy(TIA)is rotated by90◦as compared to the direction in traditional single-subband, single-heterojunction structures[10,11].As the tilt angle increases further,the R xx and R yy traces approach each other again atθ∼67.9◦rendering the transport nearly isotropic(Figure2(c)).Beyond this angle the anisotropy reemerges but the hard-axis and easy-axis have traded places,as seen in Figure2(d).In Figures3(a,b)we plot R xx and R yy atﬁlling factors ν=9/2and11/2versus B ip.Their general behavior is rather similar.Practically isotropic transport prevails in the range of0<B ip<2T,but there is a clear onset to anisotropy at B ip∼2.5T.The level of anisotropy rapidly increases,reaching its peak at B ip∼5.0T,whereuponthe R xx and R yy values approach each other again and cross at B ip∼10T.For higher in-planeﬁelds the trans-port is again anisotropic,but its direction has rotated by 90◦.Figures3(c,d)show the anisotropy factor,deﬁned as(R xx−R yy)/(R xx+R yy)and derived from the data of the panels above.They clearly depict the initially,prac-tically isotropic behavior followed by a strong anisotropy that rotates direction by90◦at B ip∼10T.The direction of anisotropy in single-subband samples corresponds to the high B ip direction in our double-subband specimen. We now turn to the analysis of correspondence be-tween the measured TIA and the theory based on the UCDW picture.For an inﬁnitely narrow electron layer the eﬀective2D Coulomb interaction,V( q),reduces to e−q2ℓ2/2/q(L N(q2/2))22πe2ℓ/ǫwhere L N(x)is the La-guerre polynomial, q is the wavevector,ℓis the mag-netic length,andǫis the dielectric function.Starting from N=1,zeros of L N(q2/2)occur atﬁnite q=q∗, producing a zero in the repulsive Hartree interaction at wave vectors where the attractive exchange interaction is strong.For the half-ﬁlled valence Landau level the cor-responding UCDW state consists of alternating occupied and empty stripes of electron guiding center states with a modulation period≈2π/q∗.Inﬁnite-thickness2D systems subjected to tilted mag-neticﬁelds,the dependence of the eﬀective interaction on wavevector magnitude q and orientationφrelative to the in-planeﬁeld direction can be accurately approximated [19]by V( q)=V0(q)+V2(q)cos(2φ).At B ip=0,the isotropic term V0(q)has a wavevector-dependence similar to that of the eﬀective interaction in the inﬁnitely narrow 2D layer.The corresponding curve for the valence Lan-dau level atν=9/2,shown in the top inset of Figure4, has no zeros atﬁnite q-vectors because the half-ﬁlled va-lence Landau level is the N=0state of the second sub-band(as shown in detail in Figure1(b))[31].Hence,the UCDW state is not expected to form,consistent with the isotropic transport measured in perpendicularﬁeld. Because of theﬁnite thickness of the2D system in our 350˚A wide quantum well,the orbital eﬀect of the in-plane ﬁeld causes Landau levels emanating from diﬀerent elec-tric subbands to coincide,depending on the strength of B ip.The in-planeﬁeld mixes electric and magnetic lev-els so the subband and orbit radius indices are no longer good quantum numbers.However,the eﬀect of B ip near the level(anti)crossing can sometimes be viewed approx-imately as a transfer of valence electrons from the lowest (N=0)Landau level of the second subband to a higher (N>0)Landau level of theﬁrst subband.Forﬁlling factorν=9/2,such a circumstance occurs in our sample at B ip≈3T,as seen from the top and bottom insetsof Figure4.Indeed,V0(q)is only slightly modiﬁed at low in-planeﬁelds,while a clear minimum develops for B ip>3T.As discussed above for the case of perpendic-ular magneticﬁeld it is the minimum of the interaction energy atﬁnite wavevector that opens the possibility for the formation of the UCDW state.The theoretical and experimental critical in-planeﬁelds corresponding to the onset of the UCDW and TIA,respectively,are remark-ably close.The non-zero anisotropy coeﬃcient V2(q)of the eﬀec-tive interaction at B ip>0is responsible for the non-zero UCDW anisotropy energy E A,deﬁned[19]as the total Hartree-Fock energy of stripes oriented parallel with B ip minus the total energy of stripes perpendicular to B ip. The direction of the anisotropy results from a delicate competition between electrostatic and exchange contri-butions to E A and can be determined only by an accurate calculation which takes into account details of the exper-imental conﬁguration.As shown in Figure4,the stripes align parallel with B ip at low in-planeﬁelds,consistent with the measured easy-current direction parallel with B ip.The sign of the UCDW anisotropy energy changes at B ip=10T which coincides with the experimental criticalﬁeld for the interchange of easy and hard current axes.This theoretical discussion of theν=9/2state was found to apply forν=11/2as well.In conclusion,we have observed complex transport be-havior in a two-subband QW at half-ﬁlled high Landau levels.Both the transition to an anisotropic transport state,atﬁnite B ip,and the rotation of the direction of anisotropy by90◦at higher B ip are explained quantita-tively by the UCDW picture.The close agreement be-tween complex experimental data and theoretical results leaves little doubt as to the origin of the observed trans-port anisotropies in high Landau levels.We would like to thank E.Palm and T.Murphy for experimental assistance,and N.Bonesteel,R.R.Du,and K.Yang for useful discussion.A portion of this work was performed at the National High Magnetic Field Labora-tory which is supported by NSF Cooperative Agreement No.DMR-9527035and by the State of Florida.The work at Indiana University was supported by NSF grant DMR-9714055,and at the Institute of Physics ASCR by the Grant Agency of the Czech Republic under grant 202/98/0085. D.C.T.and W.P.are supported by the DOE and the NSF.MAGNETIC FIELD [T]FIG.1.(a)Overview of magnetoresistance in perpendic-ular magnetic ﬁeld.The IQHE states (ν=1,2,3,etc.)and the FQHE states (ν=2/3,etc.)are marked by vertical lines.Shaded region highlights the transport features around ν=9/2and 11/2.(b)Self-consistent LSDA energy levels in per-pendicular ﬁeld.Index of electric subband (i)and Landau level (N)is shown for each energy level.Solid lines represent the spin-up state and dotted lines represent the spin-down state.(c)Structure of our quantum well sample.The well width is 350˚A .E F ,E 2,and E 1are the zero-ﬁeld Fermi en-ergy,second,and ﬁrst subband energy level,respectively.B perp (T)FIG.2.Magnetoresistance R xx (solid lines)and R yy (dot-ted lines)between 4<ν<6as a function of perpendicular magnetic ﬁeld,B perp ,at four tilt angles,θ.The in-plane magnetic ﬁeld B ip is along the x -axis.Stripes in the insets of panels (b)and (d)indicate the tilt-induced anisotropy (TIA)at ν=9/2and11/2.R x x a n d R y y (k Ω)B ip (T)(R x x -R y y )/(R x x +R y y )FIG.3.Amplitude of R xx (solid squares)and R yy (open squares)at ν=9/2[panel (a)]and at ν=11/2[panel (b)]as a function of B ip .Panels (c)and (d)show the anisotropy factor,deﬁned by (R xx −R yy )/(R xx +R yy )and derived from the data of the panels above.The shade regions represent the tilt-induced anisotropy (TIA)parallel with and perpendicular to B ip ,respectively.510152025B ip (T)−20−15−10−50510152025E A (10−4e 2/εl )FIG.4.Theoretical results for the ν=9/2state.Main graph:UCDW anisotropy energy as a function of in-plane magnetic ﬁeld.Top inset:the isotropic term of the ef-fective 2D Coulomb interaction multiplied by the wavevec-tor amplitude q at diﬀerent in-plane ﬁelds.Bottom inset:self-consistent LSDA Landau levels as a function of in-plane magnetic ﬁeld.Thick line is the half-ﬁlled valence Landau level.。