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第一届凝聚态物理会议

第一届凝聚态物理会议The 1st Conference on Condensed Matter Physics2015年7月15日- 17日清华大学目录01 会议概况02 组织委员会04 会议日程•总日程•大会报告•分会场报告•海报会场会议概况为了配合凝聚态物理在中国的迅速发展和国际地位的全面提升，进一步加强国内科研工作者在不同前沿领域的交流，推进国内和国际在凝聚态物理领域的相互交流和合作，为青年学生和研究人员学习和了解国际前沿进展创造更广泛的交流平台，拟定在过去已经成功举办了13届的“凝聚态理论与材料计算国际会议”系列会议的基础上，拓宽会议的主题，特别是加强凝聚态物理实验和理论的交流与融合，于2015年7月15日－17日在北京举办“第一届凝聚态物理会议”年会。

2015年第一届凝聚态物理会议是由清华大学物理系、中国科学院物理研究所、北京大学物理学院、量子物质科学协同创新中心联合主办。

这是国内首次在凝聚态物理方面举办的大型学术交流会。

本次会议是凝聚态理论与材料计算国际会议的延续和拓展，旨在增进国内外物理学者的学术交流，分享前沿科研成果，提高国内凝聚态物理的科研水平，扩大学术声誉。

第一届凝聚态物理会议将于2015年7月15日－17日在清华大学举行。

会议主题包括：拓扑量子态和多铁性、超导和多体物理、能源和低维物理、Quantum many-body theory and statistical physics、计算凝聚态物理、量子信息及其它与凝聚态物理的交叉领域等六个主题。

本次会议共设30个专题分会，将以大会特邀报告、分会特邀报告、口头报告和张贴海报等形式进行交流探讨。

组织委员会主办单位•清华大学物理系•中国科学院物理研究所•北京大学物理学院•量子物质科学协同创新中心顾问委员会：（按姓氏拼音序）崔田、杜瑞瑞、冯世平、龚新高、解士杰、李东海、李建新、林海青、李树深、陆卫、卢仲毅、吕力、沈保根、沈健、沈志勋、苏刚、王恩哥、王孝群、王玉鹏、向涛、薛其坤、张富春、张振宇组织委员会•清华大学物理系：陈曦、薛其坤•中科院物理研究所：胡江平、戴希、方忠、丁洪、周兴江、向涛•北京大学物理学院：谢心澄分会场负责人•拓扑量子态和多铁性：胡江平、陈曦、吕力、戴希、翁红明、寇谡鹏、吴从军•超导和多体物理：孙力玲、杨义峰、刘俊明、雒建林、袁辉球、李永庆、万歆、周毅•能源和低维物理：张振宇、李泓、陈弘、赵怀周、张远波•Quantum many-body theory and statistical physics：孟子扬、张广铭、郭文安、姚宏•计算凝聚态物理：姚裕贵、段文晖、龚新高、孟胜•量子信息及其它与凝聚态物理的交叉领域：范珩、田琳、翟荟、崔晓玲会议协调人•清华大学物理系：任俊（总协调人）•中国科学院物理研究所：齐建为、刘青梅•会务组：黄文艳、唐林、井小苏、周丹、骆洁、甘翠云、付德永、杨红、肖琳、胡文婷赞助单位•清华大学物理系•量子物质科学协同创新中心•中国科学院物理研究所•北京大学物理学院2015年第一届凝聚态物理会议分会场主题：A.拓扑量子态和多铁性A1拓扑半金属IA2拓扑半金属IIA3拓扑超导体和Majorana 费米子A4多铁性材料模拟与计算A5多铁性体系B.超导和多体物理B1铬基和锰基超导体B2极端条件下的超导行为B3铁基超导B4凝聚物质的激发态和动力学理论和实验B5重费米子物理C.能源和低维物理C1锂电池中的物理C2二维材料C3二维电子系统中的物理C4硅烯的最新进展C5热电中的新物理D.Quantum many-body theory and statistical physicsD1 Recent developments in strongly correlated quantum systems ID2 Recent developments in strongly correlated quantum systems IID3 Recent developments in strongly correlated quantum systems IIID4 Recent developments in strongly correlated quantum systems IVD5 Recent developments in strongly correlated quantum systems V注意事项：为了尊重外籍邀请报告人，如无特殊情况，D分会场报告请用英文。

Complex_Dynamical_Systems_Theory

Complex Dynamical Systems Theory This article was written by Professor Alicia Juarrero, author of Dynamics in action:intentional behavior as a complex system.Complex Dynamical Systems TheoryComplexity is a systemic property. Adaptive evolving systems like ethnic cliques or complex social situations such as “knife crimes” are best understood as dynamic networks of interactions and relationships, not mere aggregates of static entities that can by analyzed by separately identifying and enumerating them. By deﬁnition, relata do not exist in individual particles, only in their inter-relationships. In short, dynamic relations, not isolated agents, constitute the basis from which complex dynamical systems theory takes its start. Thus, instead of attempting to construct the identity and dynamics of a self-organizing network from the bottom up by identifying separate individuals and only afterwards grouping them into what the investigator hopes is the appropriate aggregate, complex systems theory proceeds by letting the dynamic patterns produced by the ﬂows and processes involved identify the speciﬁc architecture in question. Because complex systems aredi ff erentiated into interlinked levels of organization – with no preferred level of granularity - the appropriate coarseness on which to ground a model is determined by the functional task of interest.Whether in the physical or social realms, if individuals are independent or even weakly interdependent no complex physical or social structure will emerge; connectivity and interaction are necessary conditions for the emergence of complexity. No closed system can spontaneously become di ff erentiated and show complex organization, form or structure. Stated di ff erently, complexity is the order that results from the interaction among multiple agents; while particles remain separate from each other, no increase in their number will ever produce organization (Brooks and Wiley 1988). In contrast to collections of isolated elements that generate Gaussian (normal) distributions that can be understood and modeled in the traditional manner, a complex system is identiﬁed by the signature “relations among components, whether static or dynamic, that constitute a composite unity as a unity of a particular kind” (Maturana 1980). The rich interactions between real complex adaptive systems and their environment also mean that because a given domain “is connected to other domains in various ways, the e ff ects of those changes might propagate through the system and out into other domains in the world, inducing changes of various degrees on all scales… . Those e ff ects might eventually travel back and lead to the disappearance of the original domain or transform its dynamics” (Chu et al. 2003).Therefore only complex dynamical systems theory and its related disciplines and tools - network theory, agent-based modeling - provide the appropriate prism through which interdependent systems such as social groups can be understood, and coherent, integrated policy recommended.BoundariesA complex dynamical system’s internal structure consists in the patterns that result from particular objects and the interactions among them. But unlike those systems characterized by linear processes that can be e ff ectively isolated from environmental inﬂuence, the external structure or boundary conditions of complex systems are as much as part of the complex system as the internal structure; the interactions between the components and the environment, that is, “the set of all [interactions not components of the system] that act or are acted on by components of [the system]” (Bunge 1979) provides the system with a causally e ff ective external structure. Although the environment of interest is thus not the total environment but the environment that a ff ects and is a ff ected by the thing in question, the feedback provides complex systems with a contextual embeddedness that makes the boundaries of complex systems typically fuzzy and di ffi cult to demarcate.From a complexity science point of view, therefore, ethnic cliques and situations such as “knife crime”, understood as dynamic “structures of process,” are not bounded by physical or geographic boundaries. In the case of ethnicity, for example, the dynamic structure of a group no doubt extends spatially into both the group’s diaspora a well as the local communities; insofar as ancient traditions, rites and rituals continue to inform and inﬂuence present practices, the dynamical system we identify as an ethnic group also extends back in time to pre-diaspora and tribal culture.The Causality of Complex SystemsThis deep contextual embeddedness of complex systems presents additionaldi ffi culties for researchers: feedback and interactions to/from embedding domains can spread causally (not as e ffi cient causes but as context-sensitive constraints), thereby expanding the domain of the system in question and propagating unforeseen side-e ff ects uncontrollably (Chu et al.). Due to the interactions that constitute them, complex adaptive systems show not only nonlinear e ff ects, but also what is often called causal spread (Wheeler and Clark 1999), a form of causalitydi ff erent from that of the more commonly understood e ffi cient causality.The connectivity and interaction required for complex systems to self-organize, and which provides them with their contextuality and causal e ffi cacy, are best understood in terms of context-sensitive constraints (Juarrero 1999) not classical billiard-ball-like (e ffi cient) causality. First order, context-dependent constraints such as nonlinear interactions like positive feedback loops and catalysts make individuals or particles strongly interdependent by altering their marginal probability. Feedback relations with the environment recalibrate the internal dynamics of complex systems to incoming signals. Doing so embeds the system in its contextual setting by e ff ectively importing the environment into the system’s very dynamical structure. Positive feedback is a temporal context-dependent constraint insofar as it incorporates the past into a system’s present structure. Because the presence of a catalyst changes the probability of a reaction’s occurrence, catalysts also function as contextual constraints insofar as they incorporate the environment into a system’s present structure. Thus individuals or organizations who play the role of social catalysts and serve as media for feedback loops are physical embodiments of bottom-up constraints that link other individuals and organizations together and embed –tightly link—their dynamic organization to its environment and its history such that the newly formed global structure is no longer independent of either.By embodying context-sensitive dependencies, feedback and catalysts are bottom-up constraints that render a system constrained by its own past experience and its environment. Complex dynamical systems thus embody the initial conditions under which they were created; their origin and trajectory constrains their future development and evolution. Because such exquisite sensitivity to initial conditions is one of the hallmarks of complex adaptive systems, these dynamical processes are also essentially historical; in Prigogine’s words, “they carry their history on their backs,” that is, their internal structure reﬂects their history. Accordingly, self-organizing networks are “path-dependent.” Any methodology that purports to understand a given complex system while at the same time ignoring or not fully understanding either its trajectory or the overall context in which it is embedded is bound to fail. The e ff ects of context-dependent constraints, therefore, are described by conditional, not marginal, probabilities. They are, in other words, functional constraints.Once closure of ﬁrst-order context sensitive constraints occurs, the resulting global dynamics presents characteristics that aggregates or sums of individuals do not; in technical terms, context-sensitive constraints are enabling constraints insofar as they precipitate the emergence of a global dynamics with an expanded phase space. The dynamic whole has greater degrees of freedom than its components individually – a narrative can tell you more than a Q&A form can. Self-organizing networks described in stories are thus multi-level dynamical systems with emergent properties that are irreducible to their component particles. These characteristics will be ignored and missed if the analytic focus is limited solely to compartmentalized components studied in isolation from each other.Qua emergent wholes, complex systems function as the boundary conditions that actively inﬂuence the behavior of their components. Insofar as individuals – children or adults - envision themselves as caught up in a particular narrative structure, we will be able to foresee their constrained behavior. Top down, narratives act as limiting constraints that restrict the degrees of freedom of their components. Whereas from a traditional mechanistic, atomistic point of view such inﬂuence was impossible, complex dynamical systems theory allows us to understand such interlevel causal relationships – ubiquitous in social systems - in a scientiﬁcally respectable way. In complex adaptive systems, interactions among individuals weave together a story; and once a narrative coalesces in the minds of an individual, or a culture in turn, and as a global system, it actively inﬂuences the behavior of the components that make it up. Only complexity science theory provides the tools to understand this kind of bottom-up and top-down causation typical of the collective behavior of human organizations. When combined with narratives as Cognitive-Edge’s SenseMaker® allows, policy makers acquire an indispensible tool with which to map current social patterns and anticipate future trends. Without an appreciation of such global dynamics it is impossible to fully understand the inter-level organizational dynamics of social groups: interacting individuals create stories which then loop back down and alter the behavior of the very individuals that constitute them.Power LawsThe relationship between (on the one hand) the context-sensitive constraints that make complex self organization possible, and the power laws that describe such systems on the other has become clearer thanks to the research of e.g. Barabasi (2002, 2003). Since many complex systems give evidence of the same dynamics atwork on multiple levels of organization (i.e., they tend to be self-similar across levels), scalability is often a central element of complexity science. Through children’s narratives it is therefore possible to capture the dynamics of an overall ethnic or social group. Because power laws are frequently “indicative of correlated, cooperative phenomena between groups of interacting agents” (Cook et al. 2004), students of complex human systems recognize that in lieu of Gaussian statistics, linear regression models, normal distributions, etc., they must model their subject matter using the more unfamiliar tools of organizational dynamics, including Pareto distributions, fractal geometries, and the like. Since extreme cases and situations are much more important than average cases and situations to most students of the human sciences, managers, policy makers, analysts and social scientists ignore power laws (which show fat or long tails, inﬁnite variance, unstable conﬁdence intervals, etc.) at their own peril.Game TheoryApplying game theory to human complex systems, exploring rational choice strategies over time, and investigating the basis of social cooperation, are just a few examples of the increasing pervasiveness of the complexity approach. In each case, the situation is treated as an evolving dynamical system with global properties that emerge from the local interactions among the participants, and between the participants and the context in which they are embedded. Such simulation modeling can capture otherwise intractable nonlinear e ff ects and thereby reveal global patterns that would have been previously out of reach.Once the usefulness of simulation models became clear, the Asian Development Bank, for example, dropped its opposition to a centuries-old management practice when Lansing’s computer model of the complex Balinese irrigation system showed the functional role of traditional water temples bore a “close resemblance to computer simulations of optimal solutions” (Lansing 2000).AttractorsAttractors are typical patterns of dynamical, interdependent behaviors of limited dimensionality and carved out from a much larger space of possible patterns and dimensions. These global structural patterns, which emerge from interactions among the system’s components through phase space, can be characterized as emergent collectives. Social networks can be characterized and studied as attractors.Ergodic behavior patterns describe what are called a system’s attractors. Only two attractors were thought to exist: (1) The dynamics of a grandfather clock’s pendulum describe a point attractor that draws the bob to a single point in phase space regardless of its original position. Equilibrium models assume that all systems they describe are of this sort; traditional economic models were equilibrium models. Not all processes can be understood as near-equilibrium and drawn into a point attractor; ecological research revealed that predator-prey relationships described a di ff erent type of attractor, (2) a periodic attractor. Unlike phenomena characterized by point attractors, predator-prey distribution, for example, typically repeat regularly in a continuous, periodic loop. It was not until the last quarter of the twentieth century that a third type of attractor, so-called strange, chaotic or complex attractors, were discovered: patterns of behavior so convoluted that it is di ffi cult todiscern any order at all; complex human systems can often be characterized as complex attractors, of which social networks are one example.Complex attractors surprised scientists when they discovered that far from being chaotic in the old sense of the word, these complex systems are characterized by a high-dimensional degree of order. Never exactly repeating, the trajectories they trace nevertheless stay within certain bounds. Far from being chaotic in the old sense of the term, these complex behavior patterns provide evidence of highly complex, context-dependent dynamic forms of organization.Attractor LandscapesIn the 1930s biologist Sewall Wright (1932) developed a model of ﬁtness landscapes intended to capture the processes natural selection by visualizing the “switch and trigger mechanisms” that precipitate a change in a system’s evolutionary trajectory. More recently, thanks to the development of computer simulation models, the dependencies and constraints embodied by attractors can also be visualized as three dimensional adaptive landscapes depicting a series of changes in a system’s relative stability and instability over time. The increased probability that a system will occupy a particular state can be represented visually as a landscape’s wells, dips or valleys that embody attractor states and behaviors; the deeper the valley the greater the propensity of its being visited and the stronger the entrainment its attractor represents. In contrast sharp peaks are saddle points representing states and behaviors from which the system shies away. These landscape features capture the impact of context-sensitive constraints over time. The set of all states that end up in a particular attractor constitutes the attractor basin; di ff erent basins are separated from each other by basin boundaries or separatrices. A system’s identity at a particular point in time captures the signature probability distribution of its dynamics – its unique adaptive landscape, so to speak. The most useful image of complex systems is its phase space portrait: its state space carved up into basins of attraction and changing over time.Since all social phenomena are complex systems it becomes extremely important for makers of social policy to be able to map these convoluted relationships as accurately as possible. Doing so allows policy makers to map a situation’s relative volatility, as well as to explore which changes to which parameters will make the situation more or less stable. Complex dynamical mapping of this sort thus provides an invaluable visual aid in phase shift prediction. Although by their very naturecomplex systems resist precise predictability,dynamical landscapes and the mathematicalsoftware that create these visual aids alsoshow decision-makers the range of “adjacentpossible” successor states an unstablesituation is likely to tip into.Dynamic landscapes depicting a series ofchanges of relative stability and instabilityover time provide a very useful way ofvisualizing the contextual and historicalconstraints embodied in the convolutedbehavior patterns described by strangeattractors. By tweaking the various parametersand ﬁlters that produce the landscapes,dynamical mapping with SenseMaker®software can provide decision-makers, forexample, with evidence of the presence of “astable pattern overall, except for those groupsthat rank high on the combination of two scales, “retributive justice” and “anger.” These dynamical landscapes also provide evidence of probable and improbable “successor states” to a given situation, information that can be invaluable, for example, for designing a particular governmental advertisement campaigns on crime prevention etc. Dynamical mapping can prove that the intended network is possible, that it can be built; it can also providing guidance on the most appropriate criteria with which to design the most e ff ective network – or disrupt a noxious one. For example, one city’s current landscape might show that it is possible to build a particular network that assists community leaders in precipitating a particular desirable phase change with respect to criminal activity– or, conversely, it can provide decision makers with information that aids and enhances the status quo. Because complex dynamical systems are uniquely individuated, dynamical systems mapping can also provide decision makers with information about whether or not the same advertisement campaign will be as e ff ective in a di ff erent city, or a di ff erent country.If a system could access every alternative with the same frequency as every other – that is, randomly – its landscape would be smooth and ﬂat, portraying an object or a situation with no propensities or dispositions, that is, with no attractors. In contrast, the increased probability that a real system will occupy a particular state can be represented as wells – dips or valleys in a landscape – that embody attractor states and behaviors that the system is more likely to occupy. The deeper the valley the greater the propensity of being visited and the stronger the entrainment of its attractor. Dynamic landscapes thus provide governmental leaders with information about how entrenched a set of attitudes or behavior patterns are, and how best to go about preserving or changing them.Topologically, ridges separating basins of attraction are called separatrices or repellers. Sharp peaks are saddle points representing states and behaviors from which the system shies away and in all likelihood will not access; the probability of their occurrence is low or nonexistent. But if a decision-maker discovers that a system is perched on a saddle point, he can rest assured that it won’t remain in that condition very long. The height of the saddle point separating one attractor from another thus also represents the unlikelihood that the system will switch to another attractor given its history, current dynamics, and the environment. Landscape valleys thus provide decision-makers with a very good indication of whether or not a systemis locked-in to that particular condition, and what the likely “adjacent possibles” might be. The steeper the attractor’s separatrix walls, the greater the improbability of the system’s making the transition. On the other hand, the deeper the valley, the stronger the attractor’s pull, and so the stronger the perturbation that would be needed to dislodge the system from that behavior pattern. Similarly, the broader the ﬂoor of a valley the greater the variability in states and behaviors that the attractor allows under its control; conversely, the narrower the valley the more speciﬁc the attractor, that is, the fewer the states and behaviors it countenances.Complex systems theory tells us that a landscape’s valleys and peaks are neither static givens nor external control mechanisms through which we can force change. They are not determinants operating as Newtonian forces. Instead they represent constrained pathways that have been constructed and continue to be modiﬁed as a result of persistent interactions between the dynamical system and its environment. Landscapes that incorporate dynamics also provide decision makers with information about the likely direction of change, and of the critical parameters that can inﬂuence the direction of that change.Co-evolutionPredator-prey relationships taught us that the dynamical landscape of a complex system, to continue with the topographical metaphor, is not ﬁxed. A predator will evolve better eyesight to see its prey, but the prey will evolve a disguise, negating the eyesight advantage. Thus “the landscape peak the predator attempted to climb has moved from under its feet, the ﬁtness peak has shifted, the landscape has deformed due to the changes in the prey. This “coevolution” means that the ﬁtness landscape seen by one creature is a dynamic, ever changing map dependent upon the actions of everything else in its surroundings. This is true for occupants of an ecosystem or a social group. It is a highly non-linear, closely coupled system - attractors that vary in both shape and position over time” (Lucas). Co-evolution with their natural and social environment is even more so of human systems than it is of animals. In the case of human beings we are always referring, therefore, to complex adaptive systems.In other words, since ﬁtness is a relative term (relative to an environmental niche), changes in a (natural, social) niche alter the ﬁtness of the individuals and species within it; in turn, changes in the relative distribution of types of individuals and species within a niche will alter the characteristics of the niche. Thus complex adaptive systems are best characterized as adapting and co-evolving with their environment.Stability versus Resilience: The Importance of Micro-diversityComplex dynamical systems theory explains the di ff erence between stability and resilience. A stable system ﬂuctuates minimally outside its stable attractor, to which it quickly returns when perturbed. Stable systems are typically brittle; they disintegrate if highly stressed. Resilient systems, on the other hand, might ﬂuctuate wildly but have the capacity to modify their structure so as to adapt and evolve. Resilient, robust systems are also called meta-stable. Co-evolution selects for resilience, not stability.Complex adaptive systems are typically resilient. And notoriously robust to random perturbations – but exquisitely vulnerable to targeted interventions, as we will see below.Understanding what causes resilience or robustness is a central issue for analysts and policy makers. For purposes of Cultural Mapping it is particularly important to understand which speciﬁc features of the dynamical relationships that make up the knife crime statistics in the city of XYZ make the situation robust or resilient; it is important, that is, to identify the system’s dynamics that allow likely participants to adapt in response to either their own dynamics or perturbations from the outside, and thereby to evolve and persist as a network, despite the removal or incarceration of many of their members. This understanding also points to avenues for intervention by the appropriate authorities. Although still a young science, complex adaptive systems theory has begun to make inroads into understanding (1) the conditions that allow these structures evolve over time in response both to their own internal dynamics and in interaction with the environment; (2) the conditions that facilitate robustness and resilience; and (3) the most e ff ective points of intervention. Jackson & Watts (2002) note that in a network context, path resistance or network resilience is equivalent to “how many errors or mutations are needed to get from some given network to an improving path leading to another network.” Peter Allen deﬁnes microdiversity more broadly than simply errors or mutations, as “a measure of the number of qualitatively di ff erent types of entity present corresponding to individuals with di ff erent attributes.” (Garnsey & McGlade 2006, 23). Chu et al. (2003) call such systemic di ff erentiation “inhomogeneity”; they too consider it a hallmark of complexity, as do Carlson & Doyle (2002). In an important article that echoes this general point, the U.S. Naval Academy’s Robert Artigiani demonstrates through two military examples that the best way to deal with unpredictable complex systems is by organizing the system so it is maximally adaptive – when leadership cannot solve the problem in advance because no one knows what the problems will be, it is important to build systems that can solve the problem for themselves. Microdiversity in the sense of internal di ff erentiation is one way to do just that. Allen, who worked extensively with Nobel Laureate Ilya Prigogine in Brussels during the earliest years of this science, has also extensively studied how micro-diversity within a natural or social system drives the qualitative changes that occur in these systems and structures over time. Allen demonstrates that if a particular variation increases an organism’s ﬁtness, natural selection will favor that variation; following the landscape metaphor, evolutionary change – i.e., increased adaptation to the environment - is tantamount to hill-climbing.Allen’s early experiments demonstrated that hill-climbing occurs “as a result of processes of ‘di ff usion’ in character space. Using di ff usion models, Allen’s research also establishes that it is micro-diversity or internal di ff erentiation that confers resilience. Further experiments conducted by Allen and his team at Cranﬁeld University (UK) subsequently conﬁrmed that successful “evolution will be driven by the amount of diversity generation to which it leads. Evolution selects for an appropriate capacity to evolve [more exploration and innovation in novel situations; less exploration in established conditions], and this will be governed by the balance between the costs of experimental ‘failures’… and the improved performance capabilities discovered by the exploration.” The conclusion Allen draws from the research is that “organizations or individuals that can adapt and transform themselves, do so as a result of the generation of micro-diversity and the interactions with micro-contextualities” (emphasis added). The system’s complex regulatory feedback and dynamics also stop cascading failures and enable thesystem to survive (Carlson & Doyle 2002). Incorporating narrative research into dynamical landscapes is a unique and powerful tool to understand and inﬂuence social systems.Understanding how information and inﬂuence disseminate throughout a social group is a key component that cuts across storylines and issues. To the extent thatdi ff usion processes identify a property that is the inverse of robustness (both pertain to the way inﬂuence or information disseminates through, or is blocked, within particular communities by components that are di ff erent – by social mavericks, ine ff ect), identifying features in a social landscape that promote desirable robustness and resilience is a central task of any decision-maker’s mission.Fail-Safe versus Safe-FailThinkers in the ﬁeld of public policy have traditionally counseled what might be called a fail-safe strategy. From Plato to Marx, the goal was always to design forms of social organization that, because they were ideal, would remain forever in equilibrium. The traditional goal of public policy makers, in other words, has been stability, the minimization of ﬂuctuations. In stark contrast to this approach, ecologist C. S. Holling argues convincingly that if the notion of resilience applies to society at all, it counsels instead a safe-fail strategy that assumes from the outset that failures will occur despite the best-laid plans. A safe-fail strategy is one “that optimizes a cost of failure and even assures that there are periodic ‘minifailures’ to prevent evolution of inﬂexibility” (Holling 1976; Juarrero-Roque 1991). It is clear that Allen’s thesis - that evolution evolves to maximize evolvability - is another way of making the same point. Social policy should pursue a goal of resilience, not stability. As this new science develops, valuable lessons are derived from studying dynamical landscapes and the networks described in cluster graphs for the way weak ties, high betweenness links, micro-diversity, and other similar features contribute to the robustness and resilience of complex adaptive networks. In turn, these insights are can inform social organization management.。

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MET TRENDS IN ENDOCRINOLOGY AND METABOLISMTRENDS IMMUNOL TRENDS IN IMMUNOLOGYTRENDS MOL MED TRENDS IN MOLECULAR MEDICINETRENDS NEUROSCI TRENDS IN NEUROSCIENCESTRENDS PHARMACOL SCI TRENDS IN PHARMACOLOGICAL SCIENCESWHO TECH REP SER WHO TECHNICAL REPORT SERIESAM J CARDIOL AMERICAN JOURNAL OF CARDIOLOGYAM J EPIDEMIOL AMERICAN JOURNAL OF EPIDEMIOLOGYAM J PATHOL AMERICAN JOURNAL OF PATHOLOGYAM J PHYSIOL-HEART C AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULA ANTIMICROB AGENTS CH ANTIMICROBIAL AGENTS AND CHEMOTHERAPYBRIT J CANCER BRITISH JOURNAL OF CANCERCANCER-AM CANCER SOC CANCERCHEST CHESTCNS NEUROL DISORD-DR CNS & Neurological Disorders-Drug Targets ENDOCRINOLOGY ENDOCRINOLOGYEUR J NEUROSCI EUROPEAN JOURNAL OF NEUROSCIENCEFREE RADICAL BIO MED FREE RADICAL BIOLOGY AND MEDICINEINFECT IMMUN INFECTION AND IMMUNITYINT J CANCER INTERNATIONAL JOURNAL OF CANCERINT J RADIAT ONCOL INTERNATIONAL JOURNAL OF RADIATION ONCOLOGY BIOL INVEST OPHTH VIS SCI INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCEJ APPL PHYSIOL JOURNAL OF APPLIED PHYSIOLOGYJ CLIN ENDOCR METAB JOURNAL OF CLINICAL ENDOCRINOLOGY AND METABOLISM J CLIN MICROBIOL JOURNAL OF CLINICAL MICROBIOLOGYJ COMP NEUROL JOURNAL OF COMPARATIVE NEUROLOGYJ IMMUNOL JOURNAL OF IMMUNOLOGYJ INFECT DIS JOURNAL OF INFECTIOUS DISEASESJ MED CHEM JOURNAL OF MEDICINAL CHEMISTRYJ NEUROCHEM JOURNAL OF NEUROCHEMISTRYJ NEUROPHYSIOL JOURNAL OF NEUROPHYSIOLOGYJ NUTR JOURNAL OF NUTRITIONJ PHARMACOL EXP THER JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPE J PHYSIOL-LONDON JOURNAL OF PHYSIOLOGY-LONDONJ UROLOGY JOURNAL OF UROLOGYJ VIROL JOURNAL OF VIROLOGYKIDNEY INT KIDNEY INTERNATIONALNEUROIMAGE NEUROIMAGENEUROSCIENCE NEUROSCIENCEPEDIATRICS PEDIATRICSRADIOLOGY RADIOLOGYTRANSPLANTATION TRANSPLANTATIONVIROLOGY VIROLOGYNATURE NATUREP NATL ACAD SCI USA PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES SCIENCE SCIENCEANN NY ACAD SCI ANNALS OF THE NEW YORK ACADEMY OF SCIENCESISSN大类名称复分大类分区是否top期刊2009年影响因子1680-7316地学1Y 4.881 0003-0007地学1Y 6.123 0930-7575地学1Y 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二叠纪-三叠纪灭绝事件

二叠纪-三叠纪灭绝事件二叠纪-三叠纪灭绝事件（Permian–Triassic extinction event）是一个大规模物种灭绝事件，发生于古生代二叠纪与中生代三叠纪之间，距今大约2亿5140万年[1][2]。

若以消失的物种来计算，当时地球上70%的陆生脊椎动物，以及高达96%的海中生物消失[3]；这次灭绝事件也造成昆虫的唯一一次大量灭绝。

计有57%的科与83%的属消失[4][5]。

在灭绝事件之后，陆地与海洋的生态圈花了数百万年才完全恢复，比其他大型灭绝事件的恢复时间更长久[3]。

此次灭绝事件是地质年代的五次大型灭绝事件中，规模最庞大的一次，因此又非正式称为大灭绝（Great Dying）[6]，或是大规模灭绝之母（Mother of all mass extinctions）[7]。

二叠纪-三叠纪灭绝事件的过程与成因仍在争议中[8]。

根据不同的研究，这次灭绝事件可分为一[1]到三[9]个阶段。

第一个小型高峰可能因为环境的逐渐改变，原因可能是海平面改变、海洋缺氧、盘古大陆形成引起的干旱气候；而后来的高峰则是迅速、剧烈的，原因可能是撞击事件、火山爆发[10]、或是海平面骤变，引起甲烷水合物的大量释放[11]。

目录? 1 年代测定? 2 灭绝模式o 2.1 海中生物o 2.2 陆地无脊椎动物o 2.3 陆地植物? 2.3.1 植物生态系统? 2.3.2 煤层缺口o 2.4 陆地脊椎动物o 2.5 灭绝模式的可能解释? 3 生态系统的复原o 3.1 海洋生态系统的改变o 3.2 陆地脊椎动物? 4 灭绝原因o 4.1 撞击事件o 4.2 火山爆发o 4.3 甲烷水合物的气化o 4.4 海平面改变o 4.5 海洋缺氧o 4.6 硫化氢o 4.7 盘古大陆的形成o 4.8 多重原因? 5 注释? 6 延伸阅读? 7 外部链接年代测定在西元二十世纪之前，二叠纪与三叠纪交界的地层很少被发现，因此科学家们很难准确地估算灭绝事件的年代与经历时间，以及影响的地理范围[12]。

伊朗法尔斯地区第三系砂岩的古地磁

a,
Dominique
Frizon de Lamotte b
a ~
' , C h a r l e s A u b o u r g a,
Jamshid Hassanzadeh
" Universitg de Cergy-Pontoise, Dept. des Sciences de la Terre (CNRS, URAI759), F95011, Cergy-Pontoise Cedex, France I~Institute of Geophysics, Tehran UniversiO, PO. Box 14155-6466, Tehran, lran
Keywords: fold-thrust belt; magnetic fabric; sandstone; weak deformation; Arc of Fars; Zagros (Iran)
1. I n t r o d u c t i o n In sedimentary rocks undergoing horizontal shortening, the initial sedimentary fabric is progressively erased and replaced by a tectonic one (Ramsay and Huber, 1983). The analysis of these initial stages of deformation during which the inherited sedimentary fabric and the tectonic fabric interact, is generally not well documented due to the subtlety of the ini-

变形预测的一种新方法

维普资讯
第２７卷第４期２００７年１月１
桂林工
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４能够自动选择最佳的网络层数和每层的神）经元数目。】．正是由于ＧＨ算法的这些优点，决定其是ＭＤ
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种实用性比较强的预测方法．用常用的ＢＰ神经网络以及ＧＨ神经网络ＭＤ
函数的离散Ｖｈｒ级数展开式ｏｅｒａ
关键词：ＧＨ算法；神经网络；变形预测；Ｂ神经网络ＭＤＰ
中图分类号：Ｐ５２８文献标志码：Ａ
数据处理的群方法（ｒｕｔｏｆａａ— ｇｏｐｍｅｄｏｔｈｎｈｄａ
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３）能够自组织多层神经网络的每层最佳结经元，由外部准则对神经元进行筛选，筛选得到的神经
摘
要：采用一种新的变形预测方法，即将ＧＤＭＨ神经网络预测方法运用到变形预测中进行短期
以及长期预测，且将预测得到的结果与采用Ｂ并Ｐ神经网络预测得到的结果进行比较．结果表明，ＧＤＭＨ神经网络是一种比较好的预测方法，变形预测中具有一定的实用性．在

量子时间晶体

a r X i v :1202.2539v 2 [q u a n t -p h ] 11 J u l 2012MIT-CTP /4348Quantum Time CrystalsFrank WilczekCenter for Theoretical PhysicsDepartment of Physics,Massachusetts Institute of Technology Cambridge Massachusetts 02139USASome subtleties and apparent diﬃculties associated with the notion of spontaneous breaking of time translation symmetry in quantum mechanics are identiﬁed and resolved.A model exhibit-ing that phenomenon is displayed.The possibility and signiﬁcance of breaking of imaginary time translation symmetry is discussed.PACS numbers:11.30-j,5.45.Xt,3.75.LmSymmetry and its spontaneous breaking is a central theme in modern physics.Perhaps no symmetry is more fundamental than time translation symmetry,since time translation symmetry underlies both the reproducibility of experience and,within the standard dynamical frame-works,the conservation of energy.So it is natural to consider the question,whether time translation symme-try might be spontaneously broken in a closed quantum-mechanical system.That is the question we will consider,and answer aﬃrmatively,here.Here we are considering the possibility of time crystals,analogous to ordinary crystals in space.They represent spontaneous emergence of a clock within a time-invariant dynamical system.Classical time crystals are considered in a companion paper [1];here the primary emphasis is on quantum theory.Several considerations might seem to make the possi-bility of quantum time crystals implausible.The Heisen-berg equation of motion for an operator with no intrinsic time dependence readsΨ|˙O|Ψ =i Ψ|[H,O ]|Ψ →Ψ=ΨE0,(1)where the last step applies to any eigenstate ΨE of H .This seems to preclude the possibility of an order pa-rameter that could indicate the spontaneous breaking of inﬁnitesimal time translation symmetry.Also,the very concept of “ground state”implies state of lowest energy;but in any state of deﬁnite energy (it seems)the Hamiltonian must act trivially.Finally,a system with spontaneous breaking of time translation symmetry in its ground state must have some sort of motion in its ground state,and is therefore perilously close to ﬁtting the deﬁnition of a perpetual motion machine.Ring Particle Model :And yet there is a familiar phys-ical phenomenon that almost does the job.A supercon-ductor,in the right circumstances,can support a stable current-carrying ground state.Speciﬁcally,this occurs if we have a superconducting ring threaded by a ﬂux that is a fraction of the ﬂux quantum.If the current is con-stant then nothing changes in time,so time translation symmetry is not broken;but clearly there is a sense in which something is moving.We can display the essence of this situation in a simple model,that displays its formal structure clearly.Con-sider a particle with charge q and unit mass,conﬁned to a ring of unit radius that is threaded by ﬂux 2πα/q .The Lagrangian,canonical (angular)momentum,and Hamil-tonian for this system are respectivelyL =12(πφ−α)2(2)πφ,through its role as generator of (angular)translations,and in view of the Heisenberg commutation relations,is realized as −i ∂2(l −α)2.(3)The lowest energy state will occur for the integer l 0that makes l −αsmallest.If αis not an integer,we will havel 0|˙φ|l 0 =l 0−α=0.(4)The case when αis half an odd integer requires spe-cial consideration.In that case we will have two distinctstates |α±12Λ=kφ/q.Note that the totalﬂux is not invariant un-der this topologically non-trivial gauge transformation,which cannot be extended smoothly oﬀthe ring,so L is modiﬁed.Second,that the operation of time-reversal T, implemented by complex conjugation of wave-functions, takes|l →|−l and leaves the dynamics invariant if simultaneouslyα→−α.Putting these observations to-gether,we see that the combined operation˜T=G2αT(5) leaves the Lagrangian invariant;it is a symmetry of the dynamics and maps|l →|2α−l .˜T interchanges |l±α →|l∓α .Thus the degeneracy between those states is a consequence of a modiﬁed time-reversal sym-metry.We can choose combinations|α+12 that simultaneously diagonalize H and˜T;for these com-binations the expectation value of˙φvanishes. Returning to the generic case:Forαthat are not half-integral time-reversal symmetry is not merely modiﬁed, but simply broken,and there is no degeneracy.How do we reconcile l0|˙φ|l0 =0with Eqn.(1)?The point is that˙φ,despite appearances,is neither the time-derivative of a legitimate operator nor the commutator of the Hamiltonian with one,sinceφ,acting on wave func-tions in Hilbert space,is multivalued.By way of contrast operators corresponding to single-valued functions ofφ, spanned by trigonometric functions O k=e ikφ,do satisfy Eqn.(1)for the eigenstates|Ψ =|l .Wave functions of the quantized ring particle model correspond to the(classical)wave functions that ap-pear in the Landau-Ginzburg theory of superconductiv-ity.Those wave functions,in turn,heuristically describe the wave function for macroscopic occupation of the single-particle quantum state appropriate to a Cooper pair,regarded as a particle.Under this correspondence, the non-vanishing expectation value of˙φfor the ground state of the ring particle subject to fractionalﬂux maps onto the persistent current in a superconducting ring. Symmetry Breaking and Observability:As mentioned previously,the choice of a ground state that violates time translation symmetryτmust be based on some criterion other than energy minimization.But what might seem to be a special diﬃculty with breakingτ,because of its connection to the Hamiltonian,actually arises in only slightly diﬀerent form for all cases of spontaneous sym-metry breaking.Consider for example the breaking of number(or dually,phase)symmetry.We characterize such breaking through a complex order parameter,Φ, that acquires a non-zero expectation value,which we can take to be real:0|Φ|0 =v=0.(6) We also have states|σ related to|0 by the symme-try operation.These are all energetically degenerate and mutually orthogonal(see below),and satisfyσ|Φ|σ =ve iσ.(7)The superposition|Ω =13 form a lump and,in view of Eqn.(4),that they will wantto move.So we can expect that the physical ground statefeatures a moving lump,which manifestly breaksτ.To make contact with the argument of the previoussection,we need an appropriate notion of locality.Forsimplicity we assume that the particles have an addi-tional integer label,besides the common angleφ,andthat the physical observables are ofﬁnite range in theadditional label.(Imagine an array of separate rings,displaced along an axis,so that the coordinates of parti-cle j are(φ,x=ja).)I will return to these conceptualissues below,after describing the construction.An appropriate Hamiltonian isH=Nj=11N−1Nj=k,1δ(φj−φk)(13)≡Nj=11∂t= N j=11∂t=1λφ,k2)E=−r2λ(1−k2λλ(20)in terms of the complete elliptic integrals E(k2),K(k2).We can solve E(k2)K(k2)=πλ2.Here dn(u,0)reduces to a con-stant,and E=−1/4.Asλincreases beyond that value krapidly approaches1,as does E(k2).dn(u,k2)→sech uand E→−λ2/8in that limit.Of course the constantsolution with E=−λ/2πexists for any value ofλ,butwhenλexceeds the critical value the inhomogeneous so-lution is more favorable energetically.These results havesimple qualitative interpretations.The hyperbolic secantis the famous soliton of the non-linear Schr¨o dinger equa-tion on a line.If that soliton is not too big it can be de-formed,without prohibitive energy cost,toﬁt on a unitcircle.The parameterβreﬂects spontaneous breaking of(ordinary)translation symmetry.Here that breaking isoccurring through a kind of phase separation.Our Hamiltonian is closely related,formally,to theLieb-Liniger model[3],but because we consider ultra-weak(∼1/N)attraction instead of repulsion,the groundstate physics is very diﬀerent.Since our extremely inho-mogeneous approximate ground state does not supportlow-energy,long-wavelength modes(apart from overalltranslation),it has no serious infrared sensitivity.Now since non-zeroαcan be interpreted as magneticﬂux through the ring,we might anticipate,from Fara-day’s law,that as we turn it on,starting fromα=0,ourlump of charge will feel a simple torque.(Note that sinceFaraday’s law is a formal consequence of the mathemat-ics of gauge potentials,its use does not require additionalhypotheses.)We can also apply“gauge transformations”,as in the discussion around Eqn.(5).These observationsare reﬂected mathematically in the following construc-tion:For any l,we solvei∂ψl2(−i∂φ−α)2ψl−λ|ψl|2ψl,(21)withψl(φ,t)=e−ilφ˜ψ(φ+(l+α)t,t)i∂˜ψ2(−i∂φ)2˜ψ−λ|˜ψ|2˜ψ+(l+α)24energy trajectory.The parameterβ,which parameterizes an orbit of(ordinary)translation symmetry,changes at a constant rate;bothτand translation symmetry are broken,but a combination remains intact.Now let us return to address the conceptual issues alluded to earlier.Our model Hamiltonian was non-local,but we required observables to be local.That schizophrenic distinction can be appropriate,since the Hamiltonian might be–and,for our rather artiﬁcial dynamics,would have to be–carefully engineered,as opposed to being constructed from easily implemented, natural observables.Moreover it is not unlikely that the assumption of all-to-all coupling could be relaxed,in par-ticular by locating the rings at the nodes of a multidimen-sional lattice and limiting the couplings to aﬁnite range. Were we literally considering charged particles con-ﬁned to a common ring,and treating the electromag-neticﬁeld dynamically,our moving lump of charge would radiate.The electromagneticﬁeld provides modes that couple to all the particles,and in eﬀect provide observers who manifestly violate the framework of Eqn.(12).That permits,and enforces,relaxation to a|k state.Simple variations can ameliorate this issue,e of multi-poles in place of single charges,embedding the system in a cavity,or simply arranging that the motion is slow.A more radical variation,that also addresses the unrealistic assumption of attraction among the charges,while still obtaining spatial non-uniformity,would be to consider charged particles on a ring that form–through repul-sion!–a Wigner lattice.Imaginary Time Crystals:In the standard treatment ofﬁnite temperature quantum systems using path inte-gral techniques,one considers conﬁgurations whose ar-guments involve imaginary values of the time,and im-poses imaginary-time periodicity in the inverse temper-atureβ=1/T.In this set-up the whole action is con-verted,in eﬀect,into a potential energy:time derivatives map onto gradients in imaginary time,which is treated on the same footing as the spatial variables.At the level of the action,there is symmetry under translations in imaginary time(iTime).But since iTime appears,in this formulation,on the same footing as the spatial variables,it is natural to consider the possibility that for appropriate systems the dominant conﬁgurations in the path integral are iTime crystals.Let the iTime crystal have preferred periodλ.Whenβis an integer multiple ofλthe crystal willﬁt without distortion,but otherwise it must be squeezed or stretched,or incorporate defects.Periodic behavior of thermodynamics quantities in1/T,with periodλ,arise,and provide an experimental diagnostic.Integration over the collective coordinate for the broken symmetry contributes to the entropy,even at zero temperature.Inspired by the spatial crystal-iTime crystal analogy,one might also consider the possibility of iTime glasses(iGlasses),which would likewise have residual entropy,but no simple order,or iQuasicrystals.Comments: 1.It is interesting to speculate that a (considerably)more elaborate quantum-mechanical sys-tem,whose states could be interpreted as collections of qubits,might be engineered to traverse,in its ground con-ﬁguration,a programmed landscape of structured states in Hilbert space over time.2.Fields or particles in the presence of a time crystal background will be subject to energy-changing processes, analogous to crystalline Umklapp processes.In either case the apparent non-conservation is in reality a trans-fer to the background.(In our earlier model,O(1/N) corrections to the background motion arise.)3.Many questions that arise in connection with any spontaneous ordering,including the nature of transitions into or out of the order atﬁnite temperature,critical dimensionality,defects and solitons,and low-energy phe-nomenology,likewise pose themselves for time crystal-lization.There are also interesting issues around the classiﬁcation of space-time periodic orderings(roughly speaking,four dimensional crystals[4]).4.The a.c.Josephson eﬀect is a semi-macroscopic oscillatory phenomenon related in spirit to time crystal-lization.It requires,however,a voltage diﬀerence that must be sustained externally.5.Quantum time crystals based on the classical time crystals of[1],which use singular Hamiltonians,can be constructed by combining the ideas of this paper with those of[5],[6].The appearance of swallowtail band structures in[7],and emergence of complicated frequency dependence in modelingﬁnite response times[1],as in[8], suggest possible areas of application. Acknowledgements I thank B.Halperin,Hong Liu,J. Maldacena,and especially Al Shapere for helpful com-ments.This work is supported in part by DOE grant DE-FG02-05ER41360.References[1]A.Shapere and F.Wilczek,Classical Time CrystalsarXiv:1202.2537(2012).[2]Compare F.Strocchi,Symmetry Breaking(Springer,sec-ond edition2008).[3]E.Lieb and W.Liniger,Phys.Rev.1301605(1963).[4]H.Brown,R.B¨u low,J.Neub¨u ser,H.Wondratschekand H.Zassenhaus Crystallographic Groups of Four-Dimensional Space(Wiley,1978).[5]M.Henneaux,C.Teitelboim,J.Zanelli Phys.Rev.A364417(1987).[6]A.Shapere,F.Wilczek Branched Quantization(paper inpreparation).[7]B.T.Seaman,L.D.Carr,M.J.Holland Phys.Rev.A72033602(2005).[8]G.Georges,G.Kotliar,W.Krauth,M.Rozenberg Rev.Mod.Phys.681(1996).。

Aesthetics of Symmetry

Aesthetics of Symmetry
Aesthetics
Aesthetics comes from the Greek word aisthetike; coined by the philosopher Alexander Gottlieb Baumgarten to mean “The science of how things are known via the senses.”
Aesthetics is defined by the Oxford English Dictionary as : 1. Concerned with beauty or the appreciation of beauty 2. Set of principles of good taste and the appreciation of beauty
Symmetry is defined by the Oxford English Dictionary as :
1. Correct or beautiful proportion of parts; balance; harmony. 2. Repitition of exactly similar parts facing each other or a center.
Types of Symmetry
There are many types of symmetry such as Directional, Rotoreflectional, Glide rቤተ መጻሕፍቲ ባይዱflectional, Helical, Scale symmetry and fractals. The most common types are reflection (bilateral or mirror symmetry), rotation, and translation. These symmetries may also be found in combinations of each other. We’ll be looking at examples of mirror symmetry, rotation, translation, and Helical.

连续和离散动力系统中两类方程的复杂动态

湖南师范大学博士学位论文连续和离散动力系统中两类方程的复杂动态姓名：***申请学位级别：博士专业：基础数学指导教师：***20100501摘要本文应用连续和离散动力系统中的分支理论、二阶平均方法、Ｍｅｌｎｉｋ－ＯＶ方法和混沌理论，首次研究连续和离散动力系统中两类方程当参数变化时不动点的分支、三频率共振解的分支和混沌动态．对于连续动力系统，首先运用Ｍｅｌｎｉｋｏｖ方法和二阶平均方法研究受悬挂轴振动和外力作用的物理单摆在周期扰动下与拟周期扰动下的复杂动态，给出在周期扰动下系统产生混沌运动的准则，在拟周期扰动下，仅能给出当Ｑ＝伽＋Ｅ以ｎ＝１，２，３，４时平均系统存在混沌的条件，而当Ｑ＝ｇｔｏ，；＋ｅ％ｎ＝５—１５时，用平均方法不能给出混沌产生的条件，这里∥和ｕ之比为无理数．同时通过数值模拟，包括二维参数平面和三维参数空间中的分支图，相应的最大Ｌｙａｐｕｎｏｖ指数图，相图以及Ｐｏｉｎｃａｘ色映射，验证了理论结果的正确性，发现了系统的一些复杂动力学行为，其中包括从周期１轨到周期２轨的分支与周期２轨到周期２轨的逆分支；混沌的突然发生：不带周期窗口的全混沌区域，带复杂周期窗口或拟周期窗口的混沌区域；混沌的突然消失，混沌转变成周期１轨；不带周期窗口的全不变环区域或全拟周期轨区域：不变环或拟周期轨突然转变与周期１轨；从一个周期１轨区域到另一个周期１轨区域或从一个拟周期轨区域到另一个拟周期轨区域的突然跳跃；周期１轨的对称断裂：内部危机；发现了许多新颖的混沌吸引子和不变环，等等．数值模拟结果表明：当调整分支参数乜，６，，ｏ与Ｑ的值时，系统动态从全混沌运动或全不变环或全拟周期轨突然转变为周期轨，这有利于控制物理单摆的运动．其次运用二阶平均方法研究受悬挂轴振动和外力作用的物理单摆的三频率共振动解的分支与混沌，运用二阶平均方法研究了当系统的固有频率咖，外力激励频率ｕ与参数频率Ｑ之比：０３０：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：佗，２：１：仉与３：１：礼时共振解的存在与分支．运用Ｍｅｌｎｉｋｏｖ方法，给出了当ｕｏ：∽：Ｑ≈１：ｍ：佗时共振解存在的条件，并通过数值模拟进行了验证．通过数值模拟，又发现了系统的许多动态，如：不带周期窗口的全不变环行为，不变环区域的串联，不带周期窗口的纯混沌行为，带复杂周期窗口的混沌行为，全周期轨区域；不变环转变为周期轨，周期轨转变为混沌，一种不变环转变为另一种不变环等动态的跳跃行为；内部危机等动态．这些动态与在周期扰动和拟周期扰动下的动态具有很大的差异，特别发现：当初始点由鞍点改变成中心时，有更多的新的不变环吸引子被找到．首次用Ｅｕｌｅｒ方法将细菌培养呼吸过程模型离散化，运用中心流形定理和分支理论，给出映射发生ｆｌｉｐ分支，Ｈｏｐｆ：分支的条件，Ｍａｒｏｔｔｏ意义下的混沌存在的条件，证明映射没有ｆｏｌｄ分支．运用数值模拟方法（包括分支图，相图，最大Ｌｙａｐｕｎｏｖ指数图，分形维数），不仅验证了理论分析结论的正确性，还发现了该映射的许多动态，如：从周期２轨到周期８轨的逆倍周期分支，从周期ｌ轨到周期４轨的逆倍周期分支，带周期窗口的混沌行为，不带周期窗口的全混沌行为，不带周期窗口的全不变环行为，从混沌转变为不变环，从不变环转变为混沌，从混沌转变为周期轨，从周期轨转变为混沌等动态的跳跃，周期轨与混沌的交替行为等．对这两个动力系统的研究，所得到的动态行为将丰富非线性动力系统的内容，对其它学科，例如，化学、物理、生物学的研究有一定的应用价值．全文共分三章．第一章是关于动力系统的分支与混沌的预备知识．简要介绍连续和离散动力系统中的中心流形定理，二阶平均方法、Ｍｅｈａｉｋｏｖ方法以及混沌的定义、特征和通向混沌的道路．第二章，深入分析与研究受悬挂轴振动和外力作用的物理单摆的复杂动态．第二节至第四节，研究在周期扰动下与拟周期扰动下系统的的动态，运用二阶平均方法与Ｍｅｌｎｉｋｏｖ方法，给出系统存在混沌的准则，数值模拟不仅验证了理论分析结果的正确性，发现了系统的一些复杂动力学行为，而且显示当Ｑ＝ｎｏ）＋姒ｎ＝７时系统也存在混沌．本部分的结果发表在ＡｃｔａＭａｔｈｅｍａｔｉｃａＡｐｐｌｉｃａｔａｅＳｉｎａｃａ，ＥｎｇｌｉｓｈＳｅｒｉｅｓ，Ｖ０１．（２６），Ｎｏ．１（２０１０），５５－７８．第五节，研究系统的三频率共振动解的分支与混沌，运用二阶平均方法给出了当系统的固有频率Ｗｏ，外力激励频率ｕ与参数频率Ｑ之比：ｗｏ：ｕ：Ｑ≈１：１：ｎ，１：２：佗，１：３：竹，２：１：ｎ与３：１：ｎ时共振解的存在条件与分支．运用Ｍｅｌｎｉｋｏｖ方法，给出了当Ｗ０：ｕ：Ｑ≈１：仇：ｎ时共振解存在的条件，并通过数值模拟进行了验证．数值模拟又发现了系统的许多动态，显示了与在周期扰动和拟周期扰动下的动态的差异，发现：当初始点由鞍点改变成中心时，有更多的新的不变环吸引子被找到．本部分的结果已被ＡｃｔａＭａｔｈｅｍａｔｉｃａＡｐｐｌｉｃａｔａｅＳｉｎａｃａ，ＥｎｇｌｉｓｈＳｅｒｉｅｓ接收．第三章，研究离散型细菌培养呼吸过程模型．应用欧拉方法将连续型细菌培养呼吸过程模型离散化，运用中心流形定理和分支理论，给出映射发生ｆｌｉｐ分支，Ｈ０ｐ吩支的条件，存在Ｍａｘｏｔｔｏ意义下的混沌的条件，证明系统不存在ｆｏｌｄ分支．运用数值模拟，验证了理论分析结果的正确性，发现了该映射的许多动态．关键词：二阶平均；Ｍｅｌｎｉｋｏｖ方法；分支；混沌；周期扰动；拟周期扰动；三频率共振；Ｍａｘｏｔｔｏ混沌．ＡＢＳＴＲＡＣＴＩｎｔｈｉｓｔｈｅｓｉｓ，ｗｅｉｎｖｅｓｔｉｇａｔｅｓｔｈｅｂｉｆｕｒｃａｔｉｏｎｏｆｆｉｘｅｄｐｏｉｎｔｓａｎｄｒｅｓｏｎａｎｔＳＯ－ｈｉｔｉｏｎｓａｎｄｃｈａｏｓｆｏｒｔｗｏｔｙｐｅｓｏｆｅｑｕａｔｉｏｎｓｉｎｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ，ｗｈｉｃｈａｌｅｎｏｔｃｏｎｓｉｄｅｒｅｄｙｅｔ，ａｓｔｈｅｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓｖａｒｙｂｙａｐ－ｐｌｙｉｎｇｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｉｅｓ，ｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ，Ｍｅｌｎｉｋｏｖｍｅｔｈｏｄａｎｄｃｈａｏｓｔｈｅｏｒｙｉｎｃｏｎｔｉｎｕｏｕｓａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ．Ｆｏｒｔｈｅｃｏｎｔｉｎｕｏｕｓｓｙｓｔｅｍ，ｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃｓｆｏｒｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．Ｆｉｒｓｔｌｙ＇ｗｅｐｒｏｖｅｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｕｎｄｅｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓｂｙｕｓｉｎｇＭｅｉｎｉｋｏｖ’ｓｍｅｔｈｏｄ．Ｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄＭｅｌｉｎｉｋｏｖ’ｓｍｅｔｈｏｄ．ｗｅｇｉｖｅｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｉｎａｖｅｒａｇｅｄｓｙｓｔｅｍｕｎｄｅｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓｆｏｒＱ＝伽＋ｅ％ｎ＝１—４，ｗｈｅｒｅｌ，ｉｓｎｏｔｒａｔｉｏｎａｌｔｏｏ，ａｎｄｃａｎ’ｔｏｆｃｈａｏｓｆｏｒ佗＝５—１５．ａｎｄｃａｌｌｓｈｏｗｔｈｅｃｈａｏｔｉｃｐｒｏｖｅｔｈｅｃｏｎｄｉｔｉｏｎｏｆｅｘｉｓｔｅｎｃｅｂｅｈａｖｉｏｒｓｆｏｒｎ＝５ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｉｎｃｌｕｄｉｎｇｂｉｆｕｒｃａｔｉｏｎｄｉａｇｒａｍｓ，ｐｈａｓｅｐｏｒｔｒａｉｔｓ，ｃｏｍｐｕｔａｔｉｏｎｏｆｍａｘｉｍｕｍＬｙａｐｕｎｏｖｅｘｐｏ－ｎｅｎｔｓａｎｄＰｏｉｎｃａｌｇｍａｐ，ｗｅｃｈｅｃｋｕｐｔｈｅｅｆｆｅｃｔｏｆｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓａｎｄｅｘｐｏｓｅｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｉｎｃｌｕｄｉｎｇｔｈｅｂｉｆｕｒｃａｔｉｏｎａｎｄｒｅｖｅｒｓｅｂｉｆｕｒｃａ－ｔｉｏｎｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｔｏｐｅｒｉｏｄ—ｔｗｏｏｒｂｉｔｓ；ａｎｄｔｈｅｏｎｓｅｔｏｆｃｈａｏｓ，ａｎｄｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｓｗｉｔｈｃｏｍｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓｏｒｗｉｔｈｃｏｍｐｌｅｘｑｕａｓｉ—ｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ；ｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｓｕｄｄｅｎｌｙｄｉｓ－ａｐｐｅａｒｉｎｇ，ｏｒｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｗｈｉｃｈｍｅａｎｓｔｈａｔｔｈｅｓｙｓｔｅｍｃａｎｂｅｓｔａｂｉｌｉｚｅｄｔｏｐｅｒｉｏｄｉｃｍｏｔｉｏｎｂｙａｄｊｕｓｔｉｎｇｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓ口，最ｆ０ａｎｄｆｌ；ａｎｄｔｈｅｏｎｓｅｔｏｆｉｎｖａｒｉａｎｔｔｏｍｓｏｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓ，ｔｈｅｅｎｔｉｒｅｉｎｖａｒｉ－ａｎｔｔｏｍｓｒｅｇｉｏｎｏｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗ，ｑｕａｓｉ－ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓｏｒｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｍ：ｔｄｄｅｎｌｙｄｉｓａｐｐｅａｒｉｎｇｏｒｃｏｎｖｅｒｔｉｎｇｔｏｐｅ－ｒｉｏｄｉｃｏｒｂｉｔ；ａｎｄｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｗｈｉｃｈｉｎｃｌｕｄｉｎｇｆｒｏｍｐｅｒｉｏｄ—ｏｎｅｏｒｂｉｔｔｏａｎｔｈｅｒｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔ，ｆｒｏｍｑｕａｓｉ—ｐｅｒｉｏｄｉｃｓｅｔｔｏａｎｏｔｈｅｒｑｕａｓｉ－ｐｅｒｉｏｄｉｃｓｅｔ；ａｎｄｔｈｅｉｎｔｅｒｌｅａｖｉｎｇｏｃｃｕｒｒｅｎｃｅｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓａｎｄｉｎｖａｌｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｏｒｑｕａｓｉ—ｐｅｒｉｏｄｉｃｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｉｎｔｅｒｉｏｒｃｒｉｓｉｓ；ａｎｄｔｈｅｓｙｍｍｅｔｒｙｂｒｅａｋｉｎｇｏｆＩＶａｎｄｉｎｖａｒｉａｎｔｔｏｍｓ．Ｉｎｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓｐａｒｔｉｃｕｌａｒ，ｔｈｅｓｙｓｔｅｍｓｈｏｗｎｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｏｒｉｎｖａｒｉａｎｔｔｏｍｓｒｅｇｉｏｎｏｒｅｎｔｉｒｅｑｕａｓｉ－ｐｅｒｉｏｄｉｃｒｅｇｉｏｎｓｕｄｄｅｎｌｙｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄｉｃｏｒｂｉｔｂｙａｄｊｕｓｔｉｎｇｔｈｅｂｉｆｕｒｃａｔｉｏｎｐａｒａｍｅｔｅｒｓＱ，正／０ａｎｄＱ，ｗｈｉｃｈｉｓｂｅｎｅｆｉｃｉａｌｔｏｔｈｅｃｏｎｔｒｏｌｏｆｍｏｔｉｏｎｓｏｆｔｈｅｐｅｎｄｕｌｕｍ．ｂｉｆｕｒｃａｔｉｏｎｓｏｆｒｅｓｏｎａｎｔｓｏｌｕ—Ｓｅｃｏｎｄｌｙ，ｗｅｉｎｖｅｓｔｉｇａｔｅｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｔｈｅｔｉｏｎｆｏｒｗ０：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：ｎ，２：１：ｔｌａｎｄ３：１：扎ｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄｇｉｖｅａｃｒｉｔｅｒｉｏｎｆｏｒｔｈｅｅｘｉｓｔｅｎｃｅｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒｗ０：ｕ：Ｑ≈１：仇：ｆｌｉｓｇｉｖｅｎｂｙｕｓｉｎｇＭｅｌｎｉｋｏｖ’Ｓｍｅｔｈｏｄａｎｄｖｅｒｉｆｙｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ，ｗｅｓｏｍｅｏｔｈｅｒｉｎｔｅｒｅｓｔｉｎｇｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｉｎｃｌｕｄｉｎｇｔｈｅｅｎｔｉｒｅｉｎｖａｒｉａｎｔｅｘｐｏｓｅｔｏｍｓｒｅｇｉｏｎ，ｔｈｅｃａｓｃａｄｅｏｆｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓ，ｔｈｅｅｎｔｉｒｅｃｈａｏｓｒｅｇｉｏｎｗｉｔｈ—ｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｃｏｍｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｔｈｅｅｎｔｉｒｅｗｈｉｃｈｉｎｃｌｕｄｉｎｇｉｎｖａｒｉａｎｔｔｏｒｕｓｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｒｅｇｉｏｎ；ｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｂｅｈａｖｉｏｒｓｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓ，ｆｒｏｍｃｈａｏｓｔｏｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｏｒｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓｔｏｃｈａｏｓ，ｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｔｏｃｈａｏｓ，ｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓｔｏａｎｏｔｈｅｒｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｉｎｔｅｒｉｏｒｃｒｉｓｉｓ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓａｔｔｒａｃｔｏｒｓａｎｄｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓ．Ｔｈｅｎｕｍｅｒｉｃａｌｒｅｓｕｌｔｓｓｌｉｏｗｔｈｅｄｉｆｆｅｒｅｎｃｅｏｆｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｉｎｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａ－ｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓｂｅｔｗｅｅｎｕｎｄｅｒｔｈｅｔｈｒｅｅｆｒｅｑｕｅｎｃｉｅｓｒｅｓｏｎａｎｔａｎｄｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｔｅｘｈｉｂｉｔｓｍａｎｙｃｏｎｄｉｔｉｏｎｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｕｎｄｅｒｔｈｅｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎｓａｎｄｗｅｆｉｎｄａｌｏｔｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｗｈｉｃｈａｒｅｄｉｆｆｅｒｅｎｔｔｏｔｈｏｓｅｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｆｏｒｔｈｅｄｉｓｃｒｅｔｅｓｙｓｔｅｍ，ｔｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆａｄｉｓｃｒｅｅｔｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｆｏｒｒｅｓｐｉｒａｔｏｒｙｐｒｏｃｅｓｓｉｎｂａｃｔｅｒｉａｌｃｕｌｔｕｒｅａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．ＴｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｆｏｒｆｌｉｐｂｉｆｕｒｃａｔｉｏｎａｎｄＨｏｐｆｂｉｆｕｒｃａｔｉｏｎａｒｅｄｅｒｉｖｅｄｂｙｕｓｉｎｇｃｅｎ－ｔｅｒｍａｎｉｆｏｌｄｔｈｅｏｒｅｍａｎｄｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｙ，ｃｏｎｄｉｔｉｏｎｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｉｎｔｈｅＳｅｌｚ．ｑｅｏｆＭａｒｏｔｔｏ’８ｄｅｆｉｎｉｔｉｏｎｏｆｃｈａｏｓｉｓｐｒｏｖｅｄ．Ｔｈｅｂｉｆｕｒｃａｔｉｏｎｄｉａｇｒａｍｓ，ＶＬｙａｐｕｎｏｖｅｘｐｏｎｅｎｔｓａｎｄｐｈａｓｅｐｏｒｔｒａｉｔｓａｒｅｇｉｖｅｎｆｏｒｄｉｆｆｅｒｅｎｔｐａｒａｍｅｔｅｒｓｏｆｔｈｅｍｏｄｅｌ，ａｎｄｔｈｅｆｒａｃｔａｌｄｉｍｅｎｓｉｏｎｏｆｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｏｆｔｈｅｍｏｄｅｌｉｓａｌｓｏｃａｌｃｕ－ｉａｔｅｄ．Ｔｈｅｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｒｅｓｕｌｔｓｎｏｔｏｎｌｙｓｈｏｗｔｈｅｃｏｎｓｉｓｔｅｎｃｅｗｉｔｈｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｕｔａｌｓｏｄｉｓｐｌａｙｔｈｅｎｅｗａｎｄｉｎｔｅｒｅｓｔｉｎｇｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｃｏｍｐａｒｅｄｗｉｔｈｔｈｅｃｏｎｔｉｍｌｏｕｓｍｏｄｅｌ，ｉｎｃｌｕｄｉｎｇｒｅｖｅｒｓｅｂｉｆｉｌｒｃａｔｉｏｎｆｒｏｍｐｅｒｉｏｄ—ｔｗｏｔｏｐｅｒｉｏｄ－ｅｉｇｈｔｏｒｂｉｔｓａｎｄｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ－ｆｏｕｒｏｒｂｉｔｓ，ｔｈｅｃａｓｃａｄｅｓｏｆｐｅｒｉｏｄ—ｄｏｕｂｌｉｎｇｂｉｆｕｒｃａｔｉｏｎｓｆｒｏｍｐｅｒｉｏｄ－ｏｎｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ—ｅｉｇｈｔｏｒｂｉｔｓａｎｄｆｒｏｍｐｅｒｉｏｄ－ｔｈｒｅｅｏｒｂｉｔｓｔｏｐｅｒｉｏｄ—ｔｗｅｌｖｅｏｒｂｉｔｓ；ａｎｄｔｈｅｏｎｓｅｔｏｆｃｈａｏｓ，ａｎｄｔｈｅｅｎｔｉｒｅｃｈａｏｔｉｃｒｅｇｉｏｎｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｃｈａｏｔｉｃｒｅｇｉｏｎｓｗｉｔｈｃｏｉｎ－ｐｌｅｘｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ，ｔｈｅｅｎｔｉｒｅｉｎｖａｒｉａｎｔｔｏｒｍｓｗｉｔｈｏｕｔｐｅｒｉｏｄｉｃｗｉｎｄｏｗｓ；ｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｃｏｎｖｅｒｔｉｎｇｔｏｐｅｒｉｏｄｉｃｏｒｂｉｔｓ；ａｎｄｔｈｅｊｕｍｐｉｎｇｂｅｈａｖｉｏｒｓｉｎｃｌｕｄｉｎｇｆｒｏｍｃｈａｏｓｔｏｉｎｖａｒｉａｎｔｔｏｍｓ，ｆｒｏｍｉｎｖａｒｉａｎｔｔｏｍｓｔｏｃｈａｏｓａｎｄｆｒｏｍｐｅｒｉｏｄｉｃｏｒｂｉｔｓｔｏｃｈａｏｓ；ａｎｄｔｈｅｉｎｔｅｒｌｅａｖｉｎｇｏｃｃｕｒｒｅｎｃｅｏｆｐｅｒｉｏｄｉｃｏｒｂｉｔｓａｎｄｉｎｖａｒｉａｎｔｔｏｍｓｂｅｈａｖｉｏｒｓ；ａｎｄｔｈｅｄｉｆｆｅｒｅｎｔｎｉｃｅｃｈａｏｔｉｃａｔｔｒａｃｔｏｒｓａｎｄｉｎｖａｒｉａｎｔｔｏｒｕｓ．Ｔｈｅｓｔｕｄｙｆｏｒｔｈｅｍｉｓｏｆｆｕｎｄａｍｅｎｔａｌａｎｄｅｖｅｎｐｒａｃｔｉｃａｌｉｎｔｅｒｅｓｔ．ＴｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆｔｈｅｓｅＳｙｓｔｅｍ８ｗｉｌｌｅｎｒｉｃｈｔｈｅｃｏｎｔｅｎｔｏｆｎｏｎｌｉｎｅａｒｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓａｎｄｗｉｌｌｂｅｕｓｅｆｕｌｉｎｏｔｈｅｒｓｕｂｊｅｃｔｓｓｕｃｈａｓｃｈｅｍｉｓｔｒｙ，ｐｈｙｓｉｃｓａｎｄｂｉｏｌｏｇｙ．Ｔｈｉｓｔｈｅｓｉｓｃｏｎｓｉｓｔｓｏｆｔｈｒｅｅｃｈａｐｔｅｒｓａｓｔｈｅｆｏｌｌｏｗｉｎｇ．Ｃｈａｐｔｅｒ１ｉｓａｂｏｕｔｐｒｅｐａｒａｔｉｏｎｋｎｏｗｌｅｄｇｅ．Ａｂｒｉｅｆｒｅｖｉｅｗｏｆｃｅｎｔｅｒｍａｎｉｆｏｌｄｔｈｅｏｒｅｍｓｆｏｒｃｏｎｔｉｎｕｍｍａｎｄｄｉｓｃｒｅｔｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｉｓｐｒｅｓｅｎｔｅｄ．Ａｔｔｈｅ８ａ工ｎｅｔｉｍｅ，ｓｏｍｅｄｅｆｉｎｉｔｉｏｎｓａｎｄｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｃｈａｏｓａｓｗｅｌｌ晒ｓｏｍｅｒｏｕｔｅｓｔｏｃｈａｏｓａｒｅｍｅｎｔｉｏｎｅｄ．Ｉｎｃｈａｐｔｅｒ２，ｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂ胁ｔｉｏｎｓｉｓｉｎｖｅｓｔｉｇａｔｅｄ．Ｉｎｓｅｃｔｉｏｎ２．２，２．３ａｎｄ２．４，ｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｉｓｔｅｎｃｅｏｆｃｈａｏｓｕｎｄｅｒｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓａｎｄｕｎｄｅｒｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓａｒｅｇｉｖｅｎｂｙｕｓｉｎｇＭｅｌｎｉｋｏｖ’Ｓｍｅｔｈｏｄａｎｄｓｅｃｏｎｄ—ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ．Ｂｙｎｕ－ｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓｗｅｎｏｔｏｎｌｙｃｈｅｃｋｕｐｔｈｅｅｆｆｅｃｔｏｆｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓａｎｄｅｘｐｏｓｅｔｈｅｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ，ｂｕｔａｌｓｏｓｈｏｗｔｈｅｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓａ８ＶＩＱ＝删＋ｆ％ｎ＝７．Ｉｎｓｅｃｔｉｏｎ２．５，ｗｅｉｎｖｅｓｔｉｇａｔｅｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｔｈｅｂｉｆｕｒｃａ－ｔｉｏｎｓｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒ峋：ｕ：Ｑ≈１：１：佗，１：２：佗，１：３：佗，２：１：ｎａｎｄ３：１：，ｌｂｙｕｓｉｎｇｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄａｎｄｇｉｖｅａｃｒｉｔｅｒｉｏｎｆｏｒｔｈｅｅｘｉｓ－ｔｅｎｃｅｏｆｒｅｓｏｎａｎｔｓｏｌｕｔｉｏｎｆｏｒ岫：ｕ：Ｑ≈１：仇：礼ｉｓｇｉｖｅｎｂｙｕｓｉｎｇＭｅｉｎｉｋ＿ｏｖ’ｓｍｅｔｈｏｄａｎｄｖｅｒｉｆｙｔｈｅｔｈｅｏｒｅｔｉｃａｌａｎａｌｙｓｉｓｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｓ．Ｂｙｍｌｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎ，ｗｅｅｘｐｏｓｅｓｏｍｅｏｔｈｅｒｉｎｔｅｒｅｓｔｉｎｇｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ．Ｔｈｅｍｌｍｅｒｉｃａｌｒｅｓｕｌｔｓｓｈｏｗｔｈｅｄｉｆｆｅｒｅｎｃｅｏｆｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｉｎｔｈｅｐｈｙｓｉｃａｌｐｅｎｄｕｌｕｍｅｑｕａ－ｔｉｏｎｗｉｔｈｓｕｓｐｅｎｓｉｏｎａｘｉｓｖｉｂｒａｔｉｏｎｓｂｅｔｗｅｅｎｕｎｄｅｒｔｈｅｔｈｒｅｅｆｒｅｑｕｅｎｃｉｅｓｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎａｎｄｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ—ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｔｅｘｈｉｂｉｔｓｍａｎｙｎｉｃｅｉｎｖａｒｉａｎｔｔｏｒｕｓｂｅｈａｖｉｏｒｓｕｎｄｅｒｔｈｅｒｅｓｏｎａｎｔｃｏｎｄｉｔｉｏｎｓａｎｄｗｅｆｉｎｄａｌｏｔｏｆｃｈａｏｔｉｃｂｅｈａｖｉｏｒｓｗｈｉｃｈａｒｅｄｉｆｆｅｒｅｎｔｔｏｔｈｏｓｅｕｎｄｅｒｔｈｅｐｅｒｉｏｄｉｃ／ｑｕａｓｉ·ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ．Ｉｎｃｈａｐｔｅｒ３，ｔｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓｏｆａｄｉｓｃｒｅｅｔｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｆｏｒｔｈｅｒｅｓｐｉｒａｔｏｒｙｐｒｏｃｅｓｓｉｎｂａｃｔｅｒｉａｌｃｕｌｔｕｒｅａｒｅｉｎｖｅｓｔｉｇａｔｅｄ．ＴｈｅｃｏｎｄｉｔｉｏｎｓｏｆｅｘｏｉｓｔｅｎｃｅｆｏｒｆｌｉｐｂｉｆｕｒｃａｔｉｏｎａｎｄＨｏｐｆｂｉｆｕｒｃａｔｉｏｎａｒｅｄｅｒｉｖｅｄｂｙｕｓｉｎｇｃｅｎｔｅｒｍａｕｌ－ｆｏｌｄｔｈｅｏｒｅｍａｎｄｂｉｆｕｒｃａｔｉｏｎｔｈｅｏｒｙ，ａｎｄｗｅｐｒｏｖｅｔｈａｔｔｈｅｒｅｉｓｎｏｆｏｌｄｂｉｆｕｒｃａｔｉｏｎ．ＴｈｅｃｈａｏｔｉｃｅｘｉｓｔｅｎｃｅｉｎｔｈｅｓｅｎｓｅｏｆＭａｒｏｔｔｏ’Ｓｄｅｆｉｎｉｔｉｏｎｏｆｃｈａｏｓｉｓｐｒｏｖｅｄ．Ｔｈｅｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｒｅｓｕｌｔｓｄｉｓｐｌａｙｓｏｍｅｎｅｗａｎｄｃｏｍｐｌｅｘｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒｓ．Ｋｅｙｗｏｒｄｓ：ｓｅｃｏｎｄ－ｏｒｄｅｒａｖｅｒａｇｉｎｇｍｅｔｈｏｄ，Ｍｅｌｎｉｋｏｖ’８ｍｅｔｈｏｄ，ｂｉｆｕｒ－ｃａｔｉｏｎ，ｃｈａｏｓ，ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ，ｑｕａｓｉ－ｐｅｒｉｏｄｉｃｐｅｒｔｕｒｂａｔｉｏｎｓ，Ｍａｒｏｔｔｏ’Ｓｃｈａｏｓ．ＶＩＩ湖南师范大学学位论文原创性声明本人郑重声明：所呈交的学位论文，是本人在导师的指导下，独立进行研究工作所取得的成果．除文中已经注明引用的内容外，本论文不含任何其他个人或集体已经发表或撰写过的作品成果．对本文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明．本人完全意识到本声明的法律结果由本人承担．靴论文作者躲槲＂年‘且ｙ日湖南师范大学学位论文版权使用授权书本学位论文作者完全了解学校有关保留、使用学位论文的规定，研究生在校攻读学位期间论文工作的知识产权单位属湖南师范大学．同意学校保留并向国家有关部门或机构送交论文的复印件和电子版，允许论文被查阅和借阅．本人授权湖南师范大学可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存和汇编本学位论文．本学位论文属于·１、保密口，在——年解密后适用本授权书．２、不保密ｄ（请在以上相应方框内打“￣／＂）作者签名：导师签名：１４７日瓣纱秘片咱日勘沙年６月∥汨连续和离散动力系统中两类方程的复杂动态１．预备知识１．１动力系统概述及其定义动力系统的研究来源于常微分方程定性理论．考虑舻中的常微分方程（组）圣＝，（卫），（１．１．１）其中，ｚ＝（ｚ。

22705900_阿尔金北缘新太古代TTG片麻岩的成因及其构造意义

苏必利尔克拉通（，）、波罗的地盾（，，；，；，；梅Ｈｅｎｒｙｅｔａｌ２０００
Ｓａｍｓｏｎｏｖａｌ２０１２ａ２０１３ｂＺｈａｏｅｔａｌ２０１５Ｚｏｎｇｅｔａｌ２０１３
ｅｔａｌ，２００５）、西格林兰克拉通（Ｐｏｌａｔｅｔａｌ，２００８）、华北克华林等，１９９７，１９９８；王忠梅等，２０１３；张建新等，２０１１；赵
ＫｅｙｗｏｒｄｓＴＴＧｇｎｅｉｓｓＺｉｒｃｏｎＳＨＲＩＭＰＵＰｂｄａｔｉｎｇＰｅｔｒｏｇｅｎｅｓｉｓＮｏｒｔｈＡｌｔｙｎＴａｇｈＴａｒｉｍＣｒａｔｏｎ
摘要塔里木克拉通前寒武纪构造演化，特别是早前寒武纪构造演化一直是地质学家讨论的焦点。本文通过对阿尔金北缘新太古代ＴＴＧ片麻岩进行详细的野外调查、岩相学观察、地球化学分析以及锆石ＳＨＲＩＭＰＵＰｂ定年来揭示该岩石的成因以及探讨塔里木克拉通早前寒武纪构造演化。锆石ＳＨＲＩＭＰＵＰｂ定年结果显示阿尔金北缘ＴＴＧ片麻岩的形成年龄为２７４０ ± １９Ｍａ，而后经历了新太古代（２４９４ ± ５３Ｍａ）混合岩化作用和古元古代（１９６２ ± ７８Ｍａ）麻粒岩相变质作用。阿尔金北缘英云闪长质片麻岩显示低的ＭｇＯ含量（１３３％～３）和（０８％Ｍｇ＃３７～５２），具有高Ｓｒ（４６９ × １０－６～７６４ × １０－６）含量、低Ｙ（４７２ × １０－６～１３５ × １０－６）和Ｙｂ（０３７ × １０－６～０９９ × １０－６）含量的特点，它们的Ｓｒ／Ｙ比值可达到４１～９９。岩石的这些特征与基性下地壳部分熔融形成的ＴＴＧ相同。并且，该新太古代ＴＴＧ片麻岩还具有正的εＮｄ（ｔ）值（０２～３６）、高的Ｎｄ同位素初始值（０５０９０８８～０５０９２６０）和古太古代两阶段模式年龄（３６２～３７０Ｇａ）。因此，阿尔金北缘新太古代ＴＴＧ片麻岩可能来源于基性下地壳部分熔融，并且岩浆源区有石榴石、角闪石和金红石的残留。综合前人的研究成果，对比相邻区域ＴＴＧ的形成时代，变质事件的记录以及太古宙地壳增生差异都指示阿尔金北缘和敦煌库鲁塔格地区可能来源于不同的大陆块体。关键词ＴＴＧ片麻岩；锆石ＳＨＲＩＭＰＵＰｂ定年；岩石成因；阿尔金北缘；塔里木克拉通中图法分类号；Ｐ５８８１２１Ｐ５９７３

Quantum Mechanics

Quantum MechanicsQuantum Mechanics is a branch of physics that deals with the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It is a complex and fascinating field of study that has revolutionized our understanding of the world around us. However, it is also a subject that can be difficult to grasp, with concepts that challenge our intuition and require us to think in new ways. In this essay, I will explore the basics of Quantum Mechanics, its implications for our understanding of reality, and some of the controversies surrounding it.One of the key principles of Quantum Mechanics is the idea of wave-particle duality. This means that particles, such as electrons, can exhibit both wave-like and particle-like behavior, depending on the context. For example, when an electron is observed, it appears as a particle, but when it is not observed, it behaves like a wave. This concept challenges our everyday understanding of the world, where objects are either particles or waves, but not both.Another important principle of Quantum Mechanics is uncertainty. Thisprinciple states that it is impossible to know both the position and momentum of a particle with absolute certainty. The more precisely we know one of these values, the less precisely we can know the other. This principle has profound implications for our understanding of causality and determinism, as it suggests that the behavior of particles is inherently unpredictable.Quantum Mechanics also introduces the concept of superposition, which is the idea that a particle can exist in multiple states at the same time. For example, an electron can exist in two different energy states simultaneously. This concept is difficult to grasp, as it challenges our everyday experience of the world, where objects are either in one state or another, but not both.One of the most famous experiments in Quantum Mechanics is the double-slit experiment. In this experiment, a beam of particles, such as electrons, is fired at a screen with two slits. When the particles pass through the slits, they create an interference pattern on a detector behind the screen, as if they had behaved like waves. This experiment demonstrates the wave-particle duality of particles and the concept of superposition.The implications of Quantum Mechanics for our understanding of reality are profound. It suggests that the world is fundamentally uncertain and that particles can exist in multiple states at the same time. This challenges our everyday experience of the world, where things are either one way or another, but not both. It also raises questions about the nature of causality and determinism, asparticles seem to behave in unpredictable ways.There are also controversies surrounding Quantum Mechanics. One of the most famous is the Einstein-Podolsky-Rosen (EPR) paradox. This paradox suggests that if two particles are entangled, meaning they have a correlated quantum state, then measuring one particle will instantaneously affect the state of the other particle, even if they are separated by large distances. This concept challenges our understanding of causality and suggests that information can travel faster thanthe speed of light, which is not allowed by relativity.Another controversy is the interpretation of Quantum Mechanics. There are several interpretations of Quantum Mechanics, each with its own strengths and weaknesses. The most popular interpretation is the Copenhagen interpretation,which suggests that the act of observation collapses the wave function of a particle, causing it to behave like a particle rather than a wave. However, this interpretation has been criticized for being too anthropocentric and for not providing a clear explanation of how the act of observation causes the collapse.In conclusion, Quantum Mechanics is a complex and fascinating field of study that challenges our understanding of the world around us. Its principles of wave-particle duality, uncertainty, and superposition have profound implications forour understanding of reality. However, there are also controversies surrounding Quantum Mechanics, such as the EPR paradox and the interpretation of the theory. Despite these challenges, Quantum Mechanics has revolutionized our understandingof the world and continues to be an active area of research and discovery.。

Finding community structure in networks using the eigenvectors of matrices

Finding community structure in networks using the eigenvectors of matrices
M. E. J. Newman
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109–1040
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the beneﬁt function known as “modularity” over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in neteasure that identiﬁes those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.

【国家自然科学基金】_夸克-胶子等离子体_基金支持热词逐年推荐_【万方软件创新助手】_20140731

科研热词推荐指数重味压低 1 部分子分布 1 薛定谔方程 1 等离子体物理 1 离子碰撞 1 核修正因子 1 手征对称性 1 强相互作用 1 夸克胶子等离子体 1 夸克胶子 1 喷注淬灭 1 体视 1 qcd相变 1 qcd 1 confinement, dynamical chiral 1 symmetry breaking,
推荐指数 1 1 1
2011年序号 1 2 3 4 5 6 7 8 9
2011年科研热词夸克-胶子等离子体相对论重离子碰撞横向不变质量谱椭圆流核修正因子奇异夸克反超氚核反物质双轻子推荐指数 2 1 1 1 1 1 1 1 1
2012年序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2013年序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
科研热词谱函数色散关系粘滞系数等离子体物质形态椭圆流探测器性色流体力学强相互作用宇宙大爆炸奇异夸克夸克胶子等离子体夸克胶子 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2009年序号 1 2 3 4 5 6 7 8 9
科研热词高能重离子碰撞量子传输粒子衰变强度干涉学强作用力夸克禁闭夸克物质多重散射 alice实验
推荐指数 1 1 1 1 1 1 1 1 1
2010年序号
科研热词 1 夸克-胶子等离子体 2 喷注-光子转换 3 光子产生
2008年序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
科研热词推荐指数高能重离子碰撞 1 集体膨胀 1 软物理 1 起伏与关联 1 色八重态产生模型 1 能量损失效应 1 粒子产生 1 碰撞几何 1 核遮蔽效应 1 核介质效应 1 强子化 1 夸克胶子等离子体 1 夸克-胶子等离子体物质 1 大型离子对撞机实验 1 光子谱仪 1 光子探测 1 alice实验 1

Cosmic

2 (4) 1 j) = p?g ? R(g) ( 3MPl ? j j2) + @ j j @ j j ? 4 F (A0 )F (A0 ) : (5) 6 8
" #
Our idea is to consider just this theory ( 4) without the Higgs potential (VHiggs (j j) = 0) but in the presence of the Einstein gravity theory with a conformally coupled scalar eld
On the Cosmological Origin of the Homogeneous Scalar Field in Uni ed Theories
V.N.Pervushin, V.I Smirichinski
Joint Institute for Nuclear Research, 141980, Dubna, Russia.
LG (g; A0 ; j o
To nd minimum of the action with the Lagrangian (5), we express it in terms of the conformal invariant variables, marked by (c), extracting the space-scale factor 6] 1
? cr + 0 +
(14)
The geometrical observables of the Friedmann Universe, in comoving frame of reference, are constructed by using the inverse conformal transformation (7) of the dynamical variables and coordinates, including the Friedmann time interval dtF = a0 d and distance DF = a0 Dc 6, 7]. 2

计算机专业英语量子计算机介绍

bits as example: It takes the fast computer several billions of
years. However, “ONE MINUTE” for a quantum computer!
以分解五百位的自然整数为例，目前最快的计算机需要用几十亿年才能完成，而用量子计算机，同样的重复频度，一分钟就可以解决。
Particles can exist in more than one state-or ‘superposition’-a exactly the same time.
Superposition:叠加
The theroy of quantum computer
The fantastic thing ：
Introduction
Maybe, the legendary age of
quantum computer is
comming！
Contents
1 From Bits to Qubits 2 The Theory of Quantum Computer 3 The Application of Quantum Computer 4 The Pioneers and Revolution
汉内克表示，“每个量子逻辑门的准确率均为90%以上，但是当所有量子逻辑门都综合起来使用，整体准确率却下降到79%。”
The 128-qubits quantum computer
This super cool machine is housed within a 10 square meter shielded room and priced 10 million dollars.

沙垚研究方法

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文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by the editor. I hope that after you download them, they can help yousolve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, our shop provides you with various types of practical materials, such as educational essays, diary appreciation, sentence excerpts, ancient poems, classic articles, topic composition, work summary, word parsing, copy excerpts,other materials and so on, want to know different data formats and writing methods, please pay attention!沙垚研究方法1. Introduction研究方法在科学研究中起着至关重要的作用，是科学研究的基础性内容。

火山的爆发：地球的脉动英语作文

Volcanic Eruptions:The Pulse of the EarthVolcanic eruptions,one of nature's most powerful and awe-inspiring phenomena,serve as a vivid reminder of the Earth's dynamic inner workings.These natural events,characterized by the explosive release of magma,gases,and ash from beneath the Earth's crust,play a crucial role in shaping our planet's landscape and atmosphere.This essay explores the significance of volcanic eruptions,highlighting their role in the Earth's geological processes,their impact on the environment and human societies,and the importance of monitoring and studying these natural phenomena.The Geological Significance of Volcanic EruptionsVolcanic eruptions are a key component of the Earth's geology,acting as a mechanism for the planet to release internal heat and pressure.The movement of tectonic plates often triggers these eruptions,especially at divergent and convergent boundaries where plates move apart or collide. As magma rises to the surface,it cools and solidifies,forming new crust and shaping the Earth's topography.Over millions of years,volcanic activity has created mountains,islands,and entire landmasses, demonstrating the planet's ever-changing nature.Environmental Impact and FertilityWhile volcanic eruptions can be destructive,they also play a vital role in replenishing the Earth's soils with nutrients.The ash and lava released during an eruption are rich in minerals that,over time,contribute to soil fertility,supporting plant growth and agriculture.For instance,the fertile soils of the Italian countryside and the Hawaiian Islands owe their richness to centuries of volcanic activity.Additionally,volcanic gases such as carbon dioxide contribute to the greenhouse effect,influencing the Earth's climate and atmospheric composition.Hazards and Human SocietyThe immediate effects of volcanic eruptions can be devastating for nearby communities,causing loss of life,destruction of property,and displacement of va flows,ash falls,and pyroclastic flows can obliterate everything in their path.Moreover,the release of volcanicash into the atmosphere can lead to respiratory health issues,disrupt air travel,and affect climate patterns globally.The eruption of Mount Tambora in1815,for example,led to the"Year Without a Summer," causing widespread crop failures and famine across the globe. Monitoring and ResearchGiven the potential hazards associated with volcanic eruptions, monitoring and research are crucial for predicting and mitigating their impact.Volcanologists use a variety of tools,including seismographs,gas sensors,and satellite imagery,to monitor volcanic activity and provide early warnings to at-risk communities.Understanding the signs of an impending eruption,such as increased seismic activity or changes in gas emissions,can save lives and minimize economic damage. ConclusionVolcanic eruptions are a testament to the Earth's vitality,reminding us of the planet's constant evolution and the forces that shape our natural world.While they pose significant risks to human society,they also enrich our environment,contributing to the cycle of renewal that sustains life on Earth.By studying and monitoring volcanic activity,we can better appreciate the complexity of our planet and learn to coexist with these powerful natural phenomena.In embracing the pulse of the Earth,we acknowledge our place within a much larger,ever-changing system.。

空间算力英文

空间算力英文Spatial Computing Power: An Exploration of Its Definition, Applications, and Future ProspectsSpatial computing power, often referred to as spatial compute or spatial AI, represents the capability of computing systems to process, analyze, and interpretspatial data. This refers to information that pertains to the physical arrangement, location, and relationships of objects in a three-dimensional space. The emergence of spatial computing power has revolutionized various fields, including robotics, autonomous vehicles, geospatial analysis, and augmented reality (AR).The core of spatial computing power lies in the ability to understand and manipulate spatial relationships. This involves not only the identification of objects and their locations but also the comprehension of how these objects interact with each other and the environment. Spatial computing systems must be able to process vast amounts of spatial data, often in real-time, to extract meaningful insights and make informed decisions.One of the key applications of spatial computing power is in robotics. Robots, especially those designed for autonomous navigation, require a deep understanding oftheir surroundings to effectively navigate and perform tasks. Spatial computing systems enable robots to map their environment, identify obstacles, and plan paths to reach their destinations. This capability is crucial for robots operating in complex, unstructured environments, such as warehouses or construction sites.Another significant area where spatial computing power finds application is in autonomous vehicles. Autonomous vehicles rely on a combination of sensors and spatial computing systems to perceive their surroundings, detect obstacles, and navigate safely. Spatial computing systems process the data from these sensors to create a detailed representation of the environment, allowing the vehicle to make informed decisions about its movement and avoid collisions.Geospatial analysis is another field that benefits from spatial computing power. Geospatial data, which includes information about the location and characteristics offeatures on the Earth's surface, is essential for understanding and managing natural resources, urban planning, and disaster response. Spatial computing systems can analyze this data to identify patterns, trends, and relationships, providing valuable insights for decision-making.Augmented reality (AR) is another exciting area where spatial computing power is making significant contributions. AR technologies overlay digital information onto the real world, creating immersive experiences that enhance our perception and interaction with the environment. Spatial computing systems are crucial for accurately mappingdigital content to the physical world, ensuring thatvirtual objects appear in the correct location and interact with the real-world environment realistically.Looking ahead, the future of spatial computing power appears bright. With the continued advancement of technologies such as AI, machine learning, and sensor fusion, we can expect spatial computing systems to become more powerful, efficient, and accurate. This will enablenew applications and use cases that further blur the lines between the physical and digital worlds.For example, we may see spatial computing power play a crucial role in the development of smart cities. By analyzing vast amounts of spatial data, these systems can optimize urban planning, transportation systems, and energy usage, creating more efficient and sustainable cities.Moreover, spatial computing power has the potential to revolutionize fields such as healthcare and education. In healthcare, spatial computing systems can aid in the accurate diagnosis and treatment of diseases by analyzing medical images and spatial data. In education, AR technologies enabled by spatial computing power can create immersive learning experiences that enhance student engagement and understanding.In conclusion, spatial computing power represents a transformative technology that is poised to revolutionize various fields. By enabling systems to understand and manipulate spatial relationships, it opens up new possibilities for robotics, autonomous vehicles, geospatial analysis, and AR. As the technology continues to evolve, wecan expect to see exciting new applications and use cases that further blur the lines between the physical and digital worlds.。

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1/3
≤ ΛEW ∼ O(250 GeV),
(3)
where ΛEW represents the electroweak symmetry breaking scale. We have inequality for there may exist other fermion condensations which are SU (2) × U (1) non-invariant. From the observed value of top mass mt ≃ 175 GeV [1], this naive argument suggests the 4-fermi interaction (1) is rather strong and is bounded from below 1/Λ2 ≥ mt /Λ3 EW due to eqs.(2) why we use the top quark (or the 4-fermi interaction (1)) to probe the symmetry breaking mechanism. From the non-standard eﬀect to e.g. Ztt vertex as shown in ﬁg.1, we would be able to study dynamical symmetry breaking physics at future colliders. 1
On the other hand, since the condensate ΨL ΨR has a non-zero SU (2) charge, it also contributes to the gauge bosons’ masses. Thus we naively expect a following inequality: ΨL ΨR
Abstract We report ﬁrst results from the investigation on probing dynamical mechanism of the electroweak symmetry breaking using top quark. We consider the case where the top mass originates from a fermion-antifermion pair condensate, which necessitates (i)strong interaction to cause condensation, and (ii)4-fermi interaction to give top mass. From the observed top mass and the unitarity constraint, we obtain, for the 4-fermi interaction (ii), lower bounds for its strength and upper bounds for its intrinsic new mass scale as we vary the type of the strong interaction (i). Bethe-Salpeter and Schwinger-Dyson equations are solved numerically to study the dynamical symmetry breaking eﬀect semi-quantitatively.
1
Department of Physics, Tohoku University Sendai, 980-77 Japan Department of Physics, Kyoto University Kyoto 606-01, Japan
3
2
Theory Group, KEK
Tsukuba, Ibaraki 305, Japan

U D

L
,
UR ,
DR ,
(4)
where these quantum numbers are chosen to cancel anomaly. Nd sets of above new fermions are introduced in the breaking sector. In order to characterize the strong interaction between the above fermion and antifermion, we introduce kernel K . For example, in the TC models where the SU (NT C ) gauge interaction cause the condensation, we can approximately write down the explicit form of the kernel K . In the improved ladder approximation in Landau gauge [4], it is written in the momentum space as [5] (momentum conﬁguration is deﬁned in ﬁg.2) K (p, q ) = C2 g 2 (p, k ) (γ µ ⊗ γ ν ) 1 (p − k )µ (p − k )ν gµν − 2 (p − k ) (p − k )2 , (6)
TU-483 May 1995
Search for Dynamical Symmetry Breaking Physics by
arXiv:hep-ph/9505371vAsaka1, N.Maekawa2, T.Moroi3† , Y.Shobuda1, and Y.Sumino1
∗ Talk given at the 5th JLC Workshop, Kawatabi, 16-17 February 1995. † Fellow of the Japan Society for the Promotion of Science.
1. Introduction successful both theoretically and experimentally. However, all the experimental tests have been done only for its gauge part and we have little knowledge on the electroweak symmetry breaking mechanism so far. In the light of the naturalness problem, we may suppose that there exists some new physics related to the electroweak symmetry breaking at the energy scale O(100GeV - 1TeV). Dynamical symmetry breaking is one of the attractive candidates for the solution to the naturalness problem. We consider this possibility and intend to study how to search dynamical symmetry breaking physics at future colliders. Here we use top quark as a probe for the symmetry breaking sector. The top quark, being much heavier than other fermions with the mass of the order of the electroweak symmetry breaking scale [1], is expected to couple most strongly to the symmetry breaking sector. In this paper, we assume the gauge symmetry is broken dynamically by a fermionantifermion pair condensate and that the top quark acquires its mass mt through a 4-fermi interaction L = 1 ΨL ΨR tR tL + h.c. , Λ2 (1) The SU (2)×U (1) gauge theory for describing the electroweak interactions has been very
and (3). It means that the new physics scale Λ is not too far from ΛEW . This is the reason
In this note, we report, as our ﬁrst results, the numerical estimation of a 4-fermi interaction which gives rise to the top mass dynamically. In this analysis, we assume a strong interaction which causes the fermion and anti-fermion pair condensate, and a 4-fermi interaction to give the top mass. For the strong interaction, we examine the non-abelian gauge interaction cases such as SU (2) or SU (3) and the ﬁxed coupling constant case. From the experimental value of mt and the unitarity constraint, we obtain lower bounds for the strength of the 4-fermi interaction and upper bounds for its intrinsic new mass scale.