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Sample records for statistical mechanics perspective

  1. Statistical mechanics

    CERN Document Server

    Davidson, Norman

    2003-01-01

    Clear and readable, this fine text assists students in achieving a grasp of the techniques and limitations of statistical mechanics. The treatment follows a logical progression from elementary to advanced theories, with careful attention to detail and mathematical development, and is sufficiently rigorous for introductory or intermediate graduate courses.Beginning with a study of the statistical mechanics of ideal gases and other systems of non-interacting particles, the text develops the theory in detail and applies it to the study of chemical equilibrium and the calculation of the thermody

  2. Statistical mechanics

    CERN Document Server

    Schwabl, Franz

    2006-01-01

    The completely revised new edition of the classical book on Statistical Mechanics covers the basic concepts of equilibrium and non-equilibrium statistical physics. In addition to a deductive approach to equilibrium statistics and thermodynamics based on a single hypothesis - the form of the microcanonical density matrix - this book treats the most important elements of non-equilibrium phenomena. Intermediate calculations are presented in complete detail. Problems at the end of each chapter help students to consolidate their understanding of the material. Beyond the fundamentals, this text demonstrates the breadth of the field and its great variety of applications. Modern areas such as renormalization group theory, percolation, stochastic equations of motion and their applications to critical dynamics, kinetic theories, as well as fundamental considerations of irreversibility, are discussed. The text will be useful for advanced students of physics and other natural sciences; a basic knowledge of quantum mechan...

  3. Statistical mechanics

    CERN Document Server

    Jana, Madhusudan

    2015-01-01

    Statistical mechanics is self sufficient, written in a lucid manner, keeping in mind the exam system of the universities. Need of study this subject and its relation to Thermodynamics is discussed in detail. Starting from Liouville theorem gradually, the Statistical Mechanics is developed thoroughly. All three types of Statistical distribution functions are derived separately with their periphery of applications and limitations. Non-interacting ideal Bose gas and Fermi gas are discussed thoroughly. Properties of Liquid He-II and the corresponding models have been depicted. White dwarfs and condensed matter physics, transport phenomenon - thermal and electrical conductivity, Hall effect, Magneto resistance, viscosity, diffusion, etc. are discussed. Basic understanding of Ising model is given to explain the phase transition. The book ends with a detailed coverage to the method of ensembles (namely Microcanonical, canonical and grand canonical) and their applications. Various numerical and conceptual problems ar...

  4. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

    Science.gov (United States)

    Sinitskiy, Anton V; Voth, Gregory A

    2015-09-07

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

  5. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

    International Nuclear Information System (INIS)

    Sinitskiy, Anton V.; Voth, Gregory A.

    2015-01-01

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

  6. Statistical mechanics of solitons

    International Nuclear Information System (INIS)

    Bishop, A.

    1980-01-01

    The status of statistical mechanics theory (classical and quantum, statics and dynamics) is reviewed for 1-D soliton or solitary-wave-bearing systems. Primary attention is given to (i) perspective for existing results with evaluation and representative literature guide; (ii) motivation and status report for remaining problems; (iii) discussion of connections with other 1-D topics

  7. Principles of classical statistical mechanics: A perspective from the notion of complementarity

    International Nuclear Information System (INIS)

    Velazquez Abad, Luisberis

    2012-01-01

    Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the complementarity between two descriptions that are unified in thermodynamics: (i) the parametrization of the system macrostate in terms of mechanical macroscopic observablesI=(I i ), and (ii) the dynamical description that explains the evolution of a system towards the thermodynamic equilibrium. As expected, such a complementarity is related to the uncertainty relations of classical statistical mechanics ΔI i Δη i ≥k. Here, k is the Boltzmann constant, η i =∂S(I|θ)/∂I i are the restituting generalized forces derived from the entropy S(I|θ) of a closed system, which is found in an equilibrium situation driven by certain control parameters θ=(θ α ). These arguments constitute the central ingredients of a reformulation of classical statistical mechanics from the notion of complementarity. In this new framework, Einstein postulate of classical fluctuation theory dp(I|θ)∼exp[S(I|θ)/k]dI appears as the correspondence principle between classical statistical mechanics and thermodynamics in the limit k→0, while the existence of uncertainty relations can be associated with the non-commuting character of certain operators. - Highlights: ► There exists a direct analogy between quantum and classical statistical mechanics. ► Statistical form of Le Chatellier principle leads to the uncertainty principle. ► Einstein postulate is simply the correspondence principle. ► Complementary quantities are associated with non-commuting operators.

  8. Equilibrium statistical mechanics

    CERN Document Server

    Jackson, E Atlee

    2000-01-01

    Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction t

  9. Lectures on statistical mechanics

    CERN Document Server

    Bowler, M G

    1982-01-01

    Anyone dissatisfied with the almost ritual dullness of many 'standard' texts in statistical mechanics will be grateful for the lucid explanation and generally reassuring tone. Aimed at securing firm foundations for equilibrium statistical mechanics, topics of great subtlety are presented transparently and enthusiastically. Very little mathematical preparation is required beyond elementary calculus and prerequisites in physics are limited to some elementary classical thermodynamics. Suitable as a basis for a first course in statistical mechanics, the book is an ideal supplement to more convent

  10. Equilibrium statistical mechanics

    CERN Document Server

    Mayer, J E

    1968-01-01

    The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t

  11. An analysis of a large dataset on immigrant integration in Spain. The Statistical Mechanics perspective on Social Action

    Science.gov (United States)

    Barra, Adriano; Contucci, Pierluigi; Sandell, Rickard; Vernia, Cecilia

    2014-02-01

    How does immigrant integration in a country change with immigration density? Guided by a statistical mechanics perspective we propose a novel approach to this problem. The analysis focuses on classical integration quantifiers such as the percentage of jobs (temporary and permanent) given to immigrants, mixed marriages, and newborns with parents of mixed origin. We find that the average values of different quantifiers may exhibit either linear or non-linear growth on immigrant density and we suggest that social action, a concept identified by Max Weber, causes the observed non-linearity. Using the statistical mechanics notion of interaction to quantitatively emulate social action, a unified mathematical model for integration is proposed and it is shown to explain both growth behaviors observed. The linear theory instead, ignoring the possibility of interaction effects would underestimate the quantifiers up to 30% when immigrant densities are low, and overestimate them as much when densities are high. The capacity to quantitatively isolate different types of integration mechanisms makes our framework a suitable tool in the quest for more efficient integration policies.

  12. Statistical mechanics in JINR

    International Nuclear Information System (INIS)

    Tonchev, N.; Shumovskij, A.S.

    1986-01-01

    The history of investigations, conducted at the JINR in the field of statistical mechanics, beginning with the fundamental works by Bogolyubov N.N. on superconductivity microscopic theory is presented. Ideas, introduced in these works and methods developed in them, have largely determined the ways for developing statistical mechanics in the JINR and Hartree-Fock-Bogolyubov variational principle has become an important method of the modern nucleus theory. A brief review of the main achievements, connected with the development of statistical mechanics methods and their application in different fields of physical science is given

  13. Statistical mechanics of superconductivity

    CERN Document Server

    Kita, Takafumi

    2015-01-01

    This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction, and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematical clarity based on ...

  14. Playing at Statistical Mechanics

    Science.gov (United States)

    Clark, Paul M.; And Others

    1974-01-01

    Discussed are the applications of counting techniques of a sorting game to distributions and concepts in statistical mechanics. Included are the following distributions: Fermi-Dirac, Bose-Einstein, and most probable. (RH)

  15. Statistical mechanics rigorous results

    CERN Document Server

    Ruelle, David

    1999-01-01

    This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

  16. Statistical mechanics of anyons

    International Nuclear Information System (INIS)

    Arovas, D.P.

    1985-01-01

    We study the statistical mechanics of a two-dimensional gas of free anyons - particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter. (orig.)

  17. Statistics: a Bayesian perspective

    National Research Council Canada - National Science Library

    Berry, Donald A

    1996-01-01

    ...: it is the only introductory textbook based on Bayesian ideas, it combines concepts and methods, it presents statistics as a means of integrating data into the significant process, it develops ideas...

  18. Einstein's statistical mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Baracca, A; Rechtman S, R

    1985-08-01

    The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject.

  19. Einstein's statistical mechanics

    International Nuclear Information System (INIS)

    Baracca, A.; Rechtman S, R.

    1985-01-01

    The foundation of equilibrium classical statistical mechanics were laid down in 1902 independently by Gibbs and Einstein. The latter's contribution, developed in three papers published between 1902 and 1904, is usually forgotten and when not, rapidly dismissed as equivalent to Gibb's. We review in detail Einstein's ideas on the foundations of statistical mechanics and show that they constitute the beginning of a research program that led Einstein to quantum theory. We also show how these ideas may be used as a starting point for an introductory course on the subject. (author)

  20. Wave Mechanics or Wave Statistical Mechanics

    International Nuclear Information System (INIS)

    Qian Shangwu; Xu Laizi

    2007-01-01

    By comparison between equations of motion of geometrical optics and that of classical statistical mechanics, this paper finds that there should be an analogy between geometrical optics and classical statistical mechanics instead of geometrical mechanics and classical mechanics. Furthermore, by comparison between the classical limit of quantum mechanics and classical statistical mechanics, it finds that classical limit of quantum mechanics is classical statistical mechanics not classical mechanics, hence it demonstrates that quantum mechanics is a natural generalization of classical statistical mechanics instead of classical mechanics. Thence quantum mechanics in its true appearance is a wave statistical mechanics instead of a wave mechanics.

  1. Journey Through Statistical Mechanics

    Science.gov (United States)

    Yang, C. N.

    2013-05-01

    My first involvement with statistical mechanics and the many body problem was when I was a student at The National Southwest Associated University in Kunming during the war. At that time Professor Wang Zhu-Xi had just come back from Cambridge, England, where he was a student of Fowler, and his thesis was on phase transitions, a hot topic at that time, and still a very hot topic today...

  2. Causality Statistical Perspectives and Applications

    CERN Document Server

    Berzuini, Carlo; Bernardinell, Luisa

    2012-01-01

    A state of the art volume on statistical causality Causality: Statistical Perspectives and Applications presents a wide-ranging collection of seminal contributions by renowned experts in the field, providing a thorough treatment of all aspects of statistical causality. It covers the various formalisms in current use, methods for applying them to specific problems, and the special requirements of a range of examples from medicine, biology and economics to political science. This book:Provides a clear account and comparison of formal languages, concepts and models for statistical causality. Addr

  3. Graphene Statistical Mechanics

    Science.gov (United States)

    Bowick, Mark; Kosmrlj, Andrej; Nelson, David; Sknepnek, Rastko

    2015-03-01

    Graphene provides an ideal system to test the statistical mechanics of thermally fluctuating elastic membranes. The high Young's modulus of graphene means that thermal fluctuations over even small length scales significantly stiffen the renormalized bending rigidity. We study the effect of thermal fluctuations on graphene ribbons of width W and length L, pinned at one end, via coarse-grained Molecular Dynamics simulations and compare with analytic predictions of the scaling of width-averaged root-mean-squared height fluctuations as a function of distance along the ribbon. Scaling collapse as a function of W and L also allows us to extract the scaling exponent eta governing the long-wavelength stiffening of the bending rigidity. A full understanding of the geometry-dependent mechanical properties of graphene, including arrays of cuts, may allow the design of a variety of modular elements with desired mechanical properties starting from pure graphene alone. Supported by NSF grant DMR-1435794

  4. Statistical crack mechanics

    International Nuclear Information System (INIS)

    Dienes, J.K.

    1993-01-01

    Although it is possible to simulate the ground blast from a single explosive shot with a simple computer algorithm and appropriate constants, the most commonly used modelling methods do not account for major changes in geology or shot energy because mechanical features such as tectonic stresses, fault structure, microcracking, brittle-ductile transition, and water content are not represented in significant detail. An alternative approach for modelling called Statistical Crack Mechanics is presented in this paper. This method, developed in the seventies as a part of the oil shale program, accounts for crack opening, shear, growth, and coalescence. Numerous photographs and micrographs show that shocked materials tend to involve arrays of planar cracks. The approach described here provides a way to account for microstructure and give a representation of the physical behavior of a material at the microscopic level that can account for phenomena such as permeability, fragmentation, shear banding, and hot-spot formation in explosives

  5. Semiclassical statistical mechanics

    International Nuclear Information System (INIS)

    Stratt, R.M.

    1979-04-01

    On the basis of an approach devised by Miller, a formalism is developed which allows the nonperturbative incorporation of quantum effects into equilibrium classical statistical mechanics. The resulting expressions bear a close similarity to classical phase space integrals and, therefore, are easily molded into forms suitable for examining a wide variety of problems. As a demonstration of this, three such problems are briefly considered: the simple harmonic oscillator, the vibrational state distribution of HCl, and the density-independent radial distribution function of He 4 . A more detailed study is then made of two more general applications involving the statistical mechanics of nonanalytic potentials and of fluids. The former, which is a particularly difficult problem for perturbative schemes, is treated with only limited success by restricting phase space and by adding an effective potential. The problem of fluids, however, is readily found to yield to a semiclassical pairwise interaction approximation, which in turn permits any classical many-body model to be expressed in a convenient form. The remainder of the discussion concentrates on some ramifications of having a phase space version of quantum mechanics. To test the breadth of the formulation, the task of constructing quantal ensemble averages of phase space functions is undertaken, and in the process several limitations of the formalism are revealed. A rather different approach is also pursued. The concept of quantum mechanical ergodicity is examined through the use of numerically evaluated eigenstates of the Barbanis potential, and the existence of this quantal ergodicity - normally associated with classical phase space - is verified. 21 figures, 4 tables

  6. Topics in statistical mechanics

    International Nuclear Information System (INIS)

    Elser, V.

    1984-05-01

    This thesis deals with four independent topics in statistical mechanics: (1) the dimer problem is solved exactly for a hexagonal lattice with general boundary using a known generating function from the theory of partitions. It is shown that the leading term in the entropy depends on the shape of the boundary; (2) continuum models of percolation and self-avoiding walks are introduced with the property that their series expansions are sums over linear graphs with intrinsic combinatorial weights and explicit dimension dependence; (3) a constrained SOS model is used to describe the edge of a simple cubic crystal. Low and high temperature results are derived as well as the detailed behavior near the crystal facet; (4) the microscopic model of the lambda-transition involving atomic permutation cycles is reexamined. In particular, a new derivation of the two-component field theory model of the critical behavior is presented. Results for a lattice model originally proposed by Kikuchi are extended with a high temperature series expansion and Monte Carlo simulation. 30 references

  7. Statistical mechanics of nonequilibrium liquids

    CERN Document Server

    Evans, Denis J; Craig, D P; McWeeny, R

    1990-01-01

    Statistical Mechanics of Nonequilibrium Liquids deals with theoretical rheology. The book discusses nonlinear response of systems and outlines the statistical mechanical theory. In discussing the framework of nonequilibrium statistical mechanics, the book explains the derivation of a nonequilibrium analogue of the Gibbsian basis for equilibrium statistical mechanics. The book reviews the linear irreversible thermodynamics, the Liouville equation, and the Irving-Kirkwood procedure. The text then explains the Green-Kubo relations used in linear transport coefficients, the linear response theory,

  8. Statistical fluid mechanics

    CERN Document Server

    Monin, A S

    2007-01-01

    ""If ever a field needed a definitive book, it is the study of turbulence; if ever a book on turbulence could be called definitive, it is this book."" - ScienceWritten by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. The first volume begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulenc

  9. Statistical mechanics in a nutshell

    CERN Document Server

    Peliti, Luca

    2011-01-01

    Statistical mechanics is one of the most exciting areas of physics today, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. Statistical Mechanics in a Nutshell offers the most concise, self-contained introduction to this rapidly developing field. Requiring only a background in elementary calculus and elementary mechanics, this book starts with the basics, introduces the most important developments in classical statistical mechanics over the last thirty years, and guides readers to the very threshold of today

  10. Nonequilibrium statistical physics a modern perspective

    CERN Document Server

    Livi, Roberto

    2017-01-01

    Statistical mechanics has been proven to be successful at describing physical systems at thermodynamic equilibrium. Since most natural phenomena occur in nonequilibrium conditions, the present challenge is to find suitable physical approaches for such conditions: this book provides a pedagogical pathway that explores various perspectives. The use of clear language, and explanatory figures and diagrams to describe models, simulations and experimental findings makes the book a valuable resource for undergraduate and graduate students, and also for lecturers organizing teaching at varying levels of experience in the field. Written in three parts, it covers basic and traditional concepts of nonequilibrium physics, modern aspects concerning nonequilibrium phase transitions, and application-orientated topics from a modern perspective. A broad range of topics is covered, including Langevin equations, Levy processes, directed percolation, kinetic roughening and pattern formation.

  11. Introduction to quantum statistical mechanics

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Bogolyubov, N.N.

    1980-01-01

    In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

  12. QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

    International Nuclear Information System (INIS)

    Geiger, G.

    2000-01-01

    The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

  13. Renyi statistics in equilibrium statistical mechanics

    International Nuclear Information System (INIS)

    Parvan, A.S.; Biro, T.S.

    2010-01-01

    The Renyi statistics in the canonical and microcanonical ensembles is examined both in general and in particular for the ideal gas. In the microcanonical ensemble the Renyi statistics is equivalent to the Boltzmann-Gibbs statistics. By the exact analytical results for the ideal gas, it is shown that in the canonical ensemble, taking the thermodynamic limit, the Renyi statistics is also equivalent to the Boltzmann-Gibbs statistics. Furthermore it satisfies the requirements of the equilibrium thermodynamics, i.e. the thermodynamical potential of the statistical ensemble is a homogeneous function of first degree of its extensive variables of state. We conclude that the Renyi statistics arrives at the same thermodynamical relations, as those stemming from the Boltzmann-Gibbs statistics in this limit.

  14. Quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C.

    2010-01-01

    Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

  15. Modern Thermodynamics with Statistical Mechanics

    CERN Document Server

    Helrich, Carl S

    2009-01-01

    With the aim of presenting thermodynamics in as simple and as unified a form as possible, this textbook starts with an introduction to the first and second laws and then promptly addresses the complete set of the potentials in a subsequent chapter and as a central theme throughout. Before discussing modern laboratory measurements, the book shows that the fundamental quantities sought in the laboratory are those which are required for determining the potentials. Since the subjects of thermodynamics and statistical mechanics are a seamless whole, statistical mechanics is treated as integral part of the text. Other key topics such as irreversibility, the ideas of Ilya Prigogine, chemical reaction rates, equilibrium of heterogeneous systems, and transition-state theory serve to round out this modern treatment. An additional chapter covers quantum statistical mechanics due to active current research in Bose-Einstein condensation. End-of-chapter exercises, chapter summaries, and an appendix reviewing fundamental pr...

  16. Bayesian approach to inverse statistical mechanics

    Science.gov (United States)

    Habeck, Michael

    2014-05-01

    Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

  17. Applying Statistical Mechanics to pixel detectors

    International Nuclear Information System (INIS)

    Pindo, Massimiliano

    2002-01-01

    Pixel detectors, being made of a large number of active cells of the same kind, can be considered as significant sets to which Statistical Mechanics variables and methods can be applied. By properly redefining well known statistical parameters in order to let them match the ones that actually characterize pixel detectors, an analysis of the way they work can be performed in a totally new perspective. A deeper understanding of pixel detectors is attained, helping in the evaluation and comparison of their intrinsic characteristics and performance

  18. Statistical ensembles in quantum mechanics

    International Nuclear Information System (INIS)

    Blokhintsev, D.

    1976-01-01

    The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

  19. Statistical mechanics of multipartite entanglement

    Science.gov (United States)

    Facchi, P.; Florio, G.; Marzolino, U.; Parisi, G.; Pascazio, S.

    2009-02-01

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.

  20. Statistical mechanics of multipartite entanglement

    Energy Technology Data Exchange (ETDEWEB)

    Facchi, P [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); Florio, G; Pascazio, S [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Marzolino, U [Dipartimento di Fisica Teorica, Universita di Trieste, Strada Costiera 11, 34014 Trieste (Italy); Parisi, G [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, 00185 Roma, Italy, Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM, 00185 Roma (Italy)

    2009-02-06

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.

  1. Statistical mechanics of multipartite entanglement

    International Nuclear Information System (INIS)

    Facchi, P; Florio, G; Pascazio, S; Marzolino, U; Parisi, G

    2009-01-01

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics

  2. Introductory statistics and analytics a resampling perspective

    CERN Document Server

    Bruce, Peter C

    2014-01-01

    Concise, thoroughly class-tested primer that features basic statistical concepts in the concepts in the context of analytics, resampling, and the bootstrapA uniquely developed presentation of key statistical topics, Introductory Statistics and Analytics: A Resampling Perspective provides an accessible approach to statistical analytics, resampling, and the bootstrap for readers with various levels of exposure to basic probability and statistics. Originally class-tested at one of the first online learning companies in the discipline, www.statistics.com, the book primarily focuses on application

  3. Statistical Mechanics of Prion Diseases

    International Nuclear Information System (INIS)

    Slepoy, A.; Singh, R. R. P.; Pazmandi, F.; Kulkarni, R. V.; Cox, D. L.

    2001-01-01

    We present a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., mad cow disease) with concomitant prion protein misfolding and aggregation. Our studies lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self-averaging. We model ''species barriers'' to prion infection and assess a related treatment protocol

  4. Statistical mechanics of black holes

    International Nuclear Information System (INIS)

    Harms, B.; Leblanc, Y.

    1992-01-01

    We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried by a single black hole. Schwarzschild black holes are found to obey the statistical bootstrap condition. In all cases, the microcanonical temperature is identical to the Hawking temperature of the most massive black hole in the gas. U(1) charges in general break the bootstrap property. The problems of black-hole decay and of quantum coherence are also addressed

  5. Statistical perspectives on inverse problems

    DEFF Research Database (Denmark)

    Andersen, Kim Emil

    of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...

  6. Nonequilibrium statistical mechanics ensemble method

    CERN Document Server

    Eu, Byung Chan

    1998-01-01

    In this monograph, nonequilibrium statistical mechanics is developed by means of ensemble methods on the basis of the Boltzmann equation, the generic Boltzmann equations for classical and quantum dilute gases, and a generalised Boltzmann equation for dense simple fluids The theories are developed in forms parallel with the equilibrium Gibbs ensemble theory in a way fully consistent with the laws of thermodynamics The generalised hydrodynamics equations are the integral part of the theory and describe the evolution of macroscopic processes in accordance with the laws of thermodynamics of systems far removed from equilibrium Audience This book will be of interest to researchers in the fields of statistical mechanics, condensed matter physics, gas dynamics, fluid dynamics, rheology, irreversible thermodynamics and nonequilibrium phenomena

  7. Statistical mechanics of complex networks

    CERN Document Server

    Rubi, Miguel; Diaz-Guilera, Albert

    2003-01-01

    Networks can provide a useful model and graphic image useful for the description of a wide variety of web-like structures in the physical and man-made realms, e.g. protein networks, food webs and the Internet. The contributions gathered in the present volume provide both an introduction to, and an overview of, the multifaceted phenomenology of complex networks. Statistical Mechanics of Complex Networks also provides a state-of-the-art picture of current theoretical methods and approaches.

  8. Statistical mechanics of economics I

    Energy Technology Data Exchange (ETDEWEB)

    Kusmartsev, F.V., E-mail: F.Kusmartsev@lboro.ac.u [Department of Physics, Loughborough University, Leicestershire, LE11 3TU (United Kingdom)

    2011-02-07

    We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one.

  9. Statistical mechanics of economics I

    International Nuclear Information System (INIS)

    Kusmartsev, F.V.

    2011-01-01

    We show that statistical mechanics is useful in the description of financial crisis and economics. Taking a large amount of instant snapshots of a market over an interval of time we construct their ensembles and study their statistical interference. This results in a probability description of the market and gives capital, money, income, wealth and debt distributions, which in the most cases takes the form of the Bose-Einstein distribution. In addition, statistical mechanics provides the main market equations and laws which govern the correlations between the amount of money, debt, product, prices and number of retailers. We applied the found relations to a study of the evolution of the economics in USA between the years 1996 to 2008 and observe that over that time the income of a major population is well described by the Bose-Einstein distribution which parameters are different for each year. Each financial crisis corresponds to a peak in the absolute activity coefficient. The analysis correctly indicates the past crises and predicts the future one.

  10. Statistical mechanics and Lorentz violation

    International Nuclear Information System (INIS)

    Colladay, Don; McDonald, Patrick

    2004-01-01

    The theory of statistical mechanics is studied in the presence of Lorentz-violating background fields. The analysis is performed using the Standard-Model Extension (SME) together with a Jaynesian formulation of statistical inference. Conventional laws of thermodynamics are obtained in the presence of a perturbed hamiltonian that contains the Lorentz-violating terms. As an example, properties of the nonrelativistic ideal gas are calculated in detail. To lowest order in Lorentz violation, the scalar thermodynamic variables are only corrected by a rotationally invariant combination of parameters that mimics a (frame dependent) effective mass. Spin-couplings can induce a temperature-independent polarization in the classical gas that is not present in the conventional case. Precision measurements in the residual expectation values of the magnetic moment of Fermi gases in the limit of high temperature may provide interesting limits on these parameters

  11. Statistical mechanics of cellular automata

    International Nuclear Information System (INIS)

    Wolfram, S.

    1983-01-01

    Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions approx. =1.59 or approx. =1.69. With ''random'' initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed

  12. Statistical mechanics and field theory

    International Nuclear Information System (INIS)

    Samuel, S.A.

    1979-05-01

    Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references

  13. Introduction to quantum statistical mechanics

    CERN Document Server

    Bogolyubov, N N

    2010-01-01

    Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.

  14. Annotations to quantum statistical mechanics

    CERN Document Server

    Kim, In-Gee

    2018-01-01

    This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He st...

  15. Statistical mechanics of violent relaxation

    International Nuclear Information System (INIS)

    Shu, F.H.

    1978-01-01

    We reexamine the foundations of Lynden-Bell's statistical mechanical discussion of violent relaxation in collisionless stellar systems. We argue that Lynden-Bell's formulation in terms of a continuum description introduces unnecessary complications, and we consider a more conventional formulation in terms of particles. We then find the exclusion principle discovered by Lynden-Bell to be quantitatively important only at phase densities where two-body encounters are no longer negligible. Since the edynamical basis for the exclusion principle vanishes in such cases anyway, Lynden-Bell statistics always reduces in practice to Maxwell-Boltzmann statistics when applied to stellar systems. Lynden-Bell also found the equilibrium distribution function generally to be a sum of Maxwellians with velocity dispersions dependent on the phase density at star formation. We show that this difficulty vanishes in the particulate description for an encounterless stellar system as long as stars of different masses are initially well mixed in phase space. Our methods also demonstrate the equivalence between Gibbs's formalism which uses the microcanonical ensemble and Boltzmann's formalism which uses a coarse-grained continuum description. In addition, we clarify the concept of irreversible behavior on a macroscopic scale for an encounterless stellar system. Finally, we comment on the use of unusual macroscopic constraints to simulate the effects of incomplete relaxation

  16. Statistical mechanics of program systems

    International Nuclear Information System (INIS)

    Neirotti, Juan P; Caticha, Nestor

    2006-01-01

    We discuss the collective behaviour of a set of operators and variables that constitute a program and the emergence of meaningful computational properties in the language of statistical mechanics. This is done by appropriately modifying available Monte Carlo methods to deal with hierarchical structures. The study suggests, in analogy with simulated annealing, a method to automatically design programs. Reasonable solutions can be found, at low temperatures, when the method is applied to simple toy problems such as finding an algorithm that determines the roots of a function or one that makes a nonlinear regression. Peaks in the specific heat are interpreted as signalling phase transitions which separate regions where different algorithmic strategies are used to solve the problem

  17. Statistical Mechanics of Turbulent Flows

    International Nuclear Information System (INIS)

    Cambon, C

    2004-01-01

    This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

  18. Statistical Mechanics of Turbulent Dynamos

    Science.gov (United States)

    Shebalin, John V.

    2014-01-01

    Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much

  19. Agile manufacturing from a statistical perspective

    Energy Technology Data Exchange (ETDEWEB)

    Easterling, R.G. [Sandia National Labs., Albuquerque, NM (United States). New Initiatives Dept.

    1995-10-01

    The objective of agile manufacturing is to provide the ability to quickly realize high-quality, highly-customized, in-demand products at a cost commensurate with mass production. More broadly, agility in manufacturing, or any other endeavor, is defined as change-proficiency; the ability to thrive in an environment of unpredictable change. This report discusses the general direction of the agile manufacturing initiative, including research programs at the National Institute of Standards and Technology (NIST), the Department of Energy, and other government agencies, but focuses on agile manufacturing from a statistical perspective. The role of statistics can be important because agile manufacturing requires the collection and communication of process characterization and capability information, much of which will be data-based. The statistical community should initiate collaborative work in this important area.

  20. A Statistical Perspective on Highly Accelerated Testing

    Energy Technology Data Exchange (ETDEWEB)

    Thomas, Edward V. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-02-01

    Highly accelerated life testing has been heavily promoted at Sandia (and elsewhere) as a means to rapidly identify product weaknesses caused by flaws in the product's design or manufacturing process. During product development, a small number of units are forced to fail at high stress. The failed units are then examined to determine the root causes of failure. The identification of the root causes of product failures exposed by highly accelerated life testing can instigate changes to the product's design and/or manufacturing process that result in a product with increased reliability. It is widely viewed that this qualitative use of highly accelerated life testing (often associated with the acronym HALT) can be useful. However, highly accelerated life testing has also been proposed as a quantitative means for "demonstrating" the reliability of a product where unreliability is associated with loss of margin via an identified and dominating failure mechanism. It is assumed that the dominant failure mechanism can be accelerated by changing the level of a stress factor that is assumed to be related to the dominant failure mode. In extreme cases, a minimal number of units (often from a pre-production lot) are subjected to a single highly accelerated stress relative to normal use. If no (or, sufficiently few) units fail at this high stress level, some might claim that a certain level of reliability has been demonstrated (relative to normal use conditions). Underlying this claim are assumptions regarding the level of knowledge associated with the relationship between the stress level and the probability of failure. The primary purpose of this document is to discuss (from a statistical perspective) the efficacy of using accelerated life testing protocols (and, in particular, "highly accelerated" protocols) to make quantitative inferences concerning the performance of a product (e.g., reliability) when in fact there is lack-of-knowledge and uncertainty concerning

  1. Quantum mechanics as applied mathematical statistics

    International Nuclear Information System (INIS)

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-01-01

    Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

  2. Statistical mechanics principles and selected applications

    CERN Document Server

    Hill, Terrell L

    1956-01-01

    ""Excellent … a welcome addition to the literature on the subject."" - ScienceBefore the publication of this standard, oft-cited book, there were few if any statistical-mechanics texts that incorporated reviews of both fundamental principles and recent developments in the field.In this volume, Professor Hill offers just such a dual presentation - a useful account of basic theory and of its applications, made accessible in a comprehensive format. The book opens with concise, unusually clear introductory chapters on classical statistical mechanics, quantum statistical mechanics and the relatio

  3. Understanding Statistics and Statistics Education: A Chinese Perspective

    Science.gov (United States)

    Shi, Ning-Zhong; He, Xuming; Tao, Jian

    2009-01-01

    In recent years, statistics education in China has made great strides. However, there still exists a fairly large gap with the advanced levels of statistics education in more developed countries. In this paper, we identify some existing problems in statistics education in Chinese schools and make some proposals as to how they may be overcome. We…

  4. Thermalized solutions, statistical mechanics and turbulence

    Indian Academy of Sciences (India)

    2015-02-20

    Feb 20, 2015 ... In this study, we examine the intriguing connection between turbulence and equilibrium statistical mechanics. There are several recent works which emphasize this connection. Thus in the last ... Current Issue : Vol. 90, Issue 6.

  5. Science Academies' Refresher Course in Statistical Mechanics

    Indian Academy of Sciences (India)

    2018-02-27

    Feb 27, 2018 ... Post Graduate and Research Department of Physics. Bishop Moore ... The Course will cover the basic and advanced topics of Statistical. Mechanics ... Courses of good standing for promotion, vide notification. F3-1/2009 ...

  6. Is there a statistical mechanics of turbulence?

    International Nuclear Information System (INIS)

    Kraichnan, R.H.; Chen, S.Y.

    1988-09-01

    The statistical-mechanical treatment of turbulence is made questionable by strong nonlinearity and strong disequilibrium that result in the creation of ordered structures imbedded in disorder. Model systems are described which may provide some hope that a compact, yet faithful, statistical description of turbulence nevertheless is possible. Some essential dynamic features of the models are captured by low-order statistical approximations despite strongly non-Gaussian behavior. 31 refs., 5 figs

  7. Projection operator techniques in nonequilibrium statistical mechanics

    International Nuclear Information System (INIS)

    Grabert, H.

    1982-01-01

    This book is an introduction to the application of the projection operator technique to the statistical mechanics of irreversible processes. After a general introduction to the projection operator technique and statistical thermodynamics the Fokker-Planck and the master equation approach are described together with the response theory. Then, as applications the damped harmonic oscillator, simple fluids, and the spin relaxation are considered. (HSI)

  8. The large deviation approach to statistical mechanics

    International Nuclear Information System (INIS)

    Touchette, Hugo

    2009-01-01

    The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

  9. The large deviation approach to statistical mechanics

    Science.gov (United States)

    Touchette, Hugo

    2009-07-01

    The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein’s theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

  10. The Dirac equation in classical statistical mechanics

    International Nuclear Information System (INIS)

    Ord, G.N.

    2002-01-01

    The Dirac equation, usually obtained by 'quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic continuation, making the model 'self-quantizing'. This provides a new context for the Dirac equation, distinct from its usual context in relativistic quantum mechanics

  11. Emergence of quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C

    2009-01-01

    The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

  12. An introduction to thermodynamics and statistical mechanics

    CERN Document Server

    Saxena, A K

    2016-01-01

    An Introduction to Thermodynamics and Statistical Mechanics aims to serve as a text book for undergraduate hons.and postgraduate students of physics. The book covers First Law of Thermodynamics, Entropy and Second Law ofThermodynamics, Thermodynamic Relations, The Statistical Basis of Thermodynamics, Microcanonical Ensemble,Classical Statistical and Canonical Distribution, Grand Canonical Ensemble, Quantum Statistical Mechanics, PhaseTransitions, Fluctuations, Irreversible Processes and Transport Phenomena (Diffusion).SALIENT FEATURES:iC* Offers students a conceptual development of the subjectiC* Review questions at the end of chapters.NEW TO THE SECOND EDITIONiC* PVT SurfacesiC* Real Heat EnginesiC* Van der Waals Models (Qualitative Considerations)iC* Cluster ExpansioniC* Brownian Motion (Einstein's Theory)

  13. Learning Predictive Statistics: Strategies and Brain Mechanisms.

    Science.gov (United States)

    Wang, Rui; Shen, Yuan; Tino, Peter; Welchman, Andrew E; Kourtzi, Zoe

    2017-08-30

    When immersed in a new environment, we are challenged to decipher initially incomprehensible streams of sensory information. However, quite rapidly, the brain finds structure and meaning in these incoming signals, helping us to predict and prepare ourselves for future actions. This skill relies on extracting the statistics of event streams in the environment that contain regularities of variable complexity from simple repetitive patterns to complex probabilistic combinations. Here, we test the brain mechanisms that mediate our ability to adapt to the environment's statistics and predict upcoming events. By combining behavioral training and multisession fMRI in human participants (male and female), we track the corticostriatal mechanisms that mediate learning of temporal sequences as they change in structure complexity. We show that learning of predictive structures relates to individual decision strategy; that is, selecting the most probable outcome in a given context (maximizing) versus matching the exact sequence statistics. These strategies engage distinct human brain regions: maximizing engages dorsolateral prefrontal, cingulate, sensory-motor regions, and basal ganglia (dorsal caudate, putamen), whereas matching engages occipitotemporal regions (including the hippocampus) and basal ganglia (ventral caudate). Our findings provide evidence for distinct corticostriatal mechanisms that facilitate our ability to extract behaviorally relevant statistics to make predictions. SIGNIFICANCE STATEMENT Making predictions about future events relies on interpreting streams of information that may initially appear incomprehensible. Past work has studied how humans identify repetitive patterns and associative pairings. However, the natural environment contains regularities that vary in complexity from simple repetition to complex probabilistic combinations. Here, we combine behavior and multisession fMRI to track the brain mechanisms that mediate our ability to adapt to

  14. Statistical mechanics and applications in condensed matter

    CERN Document Server

    Di Castro, Carlo

    2015-01-01

    This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between ...

  15. Fluctuations of physical values in statistical mechanics

    International Nuclear Information System (INIS)

    Zaripov, R.G.

    1999-01-01

    The new matrix inequalities for the boundary of measurement accuracy of physical values in the ensemble of quantum systems were obtained. The multidimensional thermodynamical parameter measurement is estimated. The matrix inequalities obtained are quantum analogs of the Cramer-Rao information inequalities in mathematical statistics. The quantity of information in quantum mechanical measurement, connected with the boundaries of jointly measurable values in one macroscopic experiment was determined. The lower boundary of the variance of estimation of multidimensional quantum mechanical parameter was found. (author)

  16. (ajst) statistical mechanics model for orientational

    African Journals Online (AJOL)

    Science and Engineering Series Vol. 6, No. 2, pp. 94 - 101. STATISTICAL MECHANICS MODEL FOR ORIENTATIONAL. MOTION OF TWO-DIMENSIONAL RIGID ROTATOR. Malo, J.O. ... there is no translational motion and that they are well separated so .... constant and I is the moment of inertia of a linear rotator. Thus, the ...

  17. Statistical-mechanical formulation of Lyapunov exponents

    International Nuclear Information System (INIS)

    Tanase-Nicola, Sorin; Kurchan, Jorge

    2003-01-01

    We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed

  18. Multiparticle quantum mechanics obeying fractional statistics

    International Nuclear Information System (INIS)

    Wu, Y.

    1984-01-01

    We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

  19. Statistical mechanics and the foundations of thermodynamics

    International Nuclear Information System (INIS)

    Loef, A.M.

    1979-01-01

    An introduction to classical statistical mechanics and its relation to thermodynamics is presented. Emphasis is put on getting a detailed and logical presentation of the foundations of thermodynamics based on the maximum entropy principles which govern the values taken by macroscopic variables according to the laws of large numbers

  20. Statistical mechanics of systems of unbounded spins

    Energy Technology Data Exchange (ETDEWEB)

    Lebowitz, J L [Yeshiva Univ., New York (USA). Belfer Graduate School of Science; Presutti, E [L' Aquila Univ. (Italy). Istituto di Matematica

    1976-11-01

    We develop the statistical mechanics of unbounded n-component spin systems interacting via potentials which are superstable and strongly tempered. The uniqueness of the equilibrium state is then proven for one component ferromagnetic spins whose free energy is differentiable with respect to the magnetic field.

  1. Stability and equilibrium in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Kastler, Daniel.

    1975-01-01

    A derivation of the Gibbs Ansatz, base of the equilibrium statistical mechanics is provided from a stability requirements, in technical connection with the harmonic analysis of non-commutative dynamical systems. By the same token a relation is established between stability and the positivity of Hamiltonian in the zero temperature case [fr

  2. Infinite Random Graphs as Statistical Mechanical Models

    DEFF Research Database (Denmark)

    Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria

    2011-01-01

    We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...

  3. Nonextensive statistical mechanics of ionic solutions

    International Nuclear Information System (INIS)

    Varela, L.M.; Carrete, J.; Munoz-Sola, R.; Rodriguez, J.R.; Gallego, J.

    2007-01-01

    Classical mean-field Poisson-Boltzmann theory of ionic solutions is revisited in the theoretical framework of nonextensive Tsallis statistics. The nonextensive equivalent of Poisson-Boltzmann equation is formulated revisiting the statistical mechanics of liquids and the Debye-Hueckel framework is shown to be valid for highly diluted solutions even under circumstances where nonextensive thermostatistics must be applied. The lowest order corrections associated to nonadditive effects are identified for both symmetric and asymmetric electrolytes and the behavior of the average electrostatic potential in a homogeneous system is analytically and numerically analyzed for various values of the complexity measurement nonextensive parameter q

  4. An introduction to statistical mechanics and thermodynamics

    CERN Document Server

    Swendsen, Robert H

    2012-01-01

    This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is the development ofentropy based on Boltzmann's 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. D

  5. Quantum mechanics as a natural generalization of classical statistical mechanics

    International Nuclear Information System (INIS)

    Xu Laizi; Qian Shangwu

    1994-01-01

    By comparison between equations of motion of geometrical optics (GO) and that of classical statistical mechanics (CSM), it is found that there should be an analogy between GO and CSM instead of GO and classical mechanics (CM). Furthermore, by comparison between the classical limit (CL) of quantum mechanics (QM) and CSM, the authors find that CL of QM is CSM not CM, hence they demonstrated that QM is a natural generalization of CSM instead of CM

  6. Analogies between classical statistical mechanics and quantum mechanics

    International Nuclear Information System (INIS)

    Uehara, M.

    1986-01-01

    Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

  7. Statistical learning from a regression perspective

    CERN Document Server

    Berk, Richard A

    2016-01-01

    This textbook considers statistical learning applications when interest centers on the conditional distribution of the response variable, given a set of predictors, and when it is important to characterize how the predictors are related to the response. As a first approximation, this can be seen as an extension of nonparametric regression. This fully revised new edition includes important developments over the past 8 years. Consistent with modern data analytics, it emphasizes that a proper statistical learning data analysis derives from sound data collection, intelligent data management, appropriate statistical procedures, and an accessible interpretation of results. A continued emphasis on the implications for practice runs through the text. Among the statistical learning procedures examined are bagging, random forests, boosting, support vector machines and neural networks. Response variables may be quantitative or categorical. As in the first edition, a unifying theme is supervised learning that can be trea...

  8. Cellular automata and statistical mechanical models

    International Nuclear Information System (INIS)

    Rujan, P.

    1987-01-01

    The authors elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata. Transient and stationary properties of probabilistic automata are linked to surface and bulk properties, respectively, of restricted statistical mechanical systems. It is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata. Some exact results are derived, including duality transformations, exact mappings, disorder, and linear solutions. Many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties. This approach is considered to be a first step toward the design of fully parallel, probabilistic systems whose computational abilities rely on the cooperative behavior of their components

  9. Mathematical methods in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Fishman, L.

    1977-01-01

    The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

  10. Equilibrium statistical mechanics of lattice models

    CERN Document Server

    Lavis, David A

    2015-01-01

    Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg—Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi—Hijmans—De Boer hierarchy of approximations. In Part III the use of alge...

  11. Statistical mechanics and the physics of fluids

    CERN Document Server

    Tosi, Mario

    This volume collects the lecture notes of a course on statistical mechanics, held at Scuola Normale Superiore di Pisa for third-to-fifth year students in physics and chemistry. Three main themes are covered in the book. The first part gives a compact presentation of the foundations of statistical mechanics and their connections with thermodynamics. Applications to ideal gases of material particles and of excitation quanta are followed by a brief introduction to a real classical gas and to a weakly coupled classical plasma, and by a broad overview on the three states of matter.The second part is devoted to fluctuations around equilibrium and their correlations. Coverage of liquid structure and critical phenomena is followed by a discussion of irreversible processes as exemplified by diffusive motions and by the dynamics of density and heat fluctuations. Finally, the third part is an introduction to some advanced themes: supercooling and the glassy state, non-Newtonian fluids including polymers and liquid cryst...

  12. Nonextensive statistical mechanics and high energy physics

    Directory of Open Access Journals (Sweden)

    Tsallis Constantino

    2014-04-01

    Full Text Available The use of the celebrated Boltzmann-Gibbs entropy and statistical mechanics is justified for ergodic-like systems. In contrast, complex systems typically require more powerful theories. We will provide a brief introduction to nonadditive entropies (characterized by indices like q, which, in the q → 1 limit, recovers the standard Boltzmann-Gibbs entropy and associated nonextensive statistical mechanics. We then present somerecent applications to systems such as high-energy collisions, black holes and others. In addition to that, we clarify and illustrate the neat distinction that exists between Lévy distributions and q-exponential ones, a point which occasionally causes some confusion in the literature, very particularly in the LHC literature

  13. Zeno dynamics in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Schmidt, Andreas U

    2003-01-01

    We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium

  14. Introductory statistical mechanics for electron storage rings

    International Nuclear Information System (INIS)

    Jowett, J.M.

    1986-07-01

    These lectures introduce the beam dynamics of electron-positron storage rings with particular emphasis on the effects due to synchrotron radiation. They differ from most other introductions in their systematic use of the physical principles and mathematical techniques of the non-equilibrium statistical mechanics of fluctuating dynamical systems. A self-contained exposition of the necessary topics from this field is included. Throughout the development, a Hamiltonian description of the effects of the externally applied fields is maintained in order to preserve the links with other lectures on beam dynamics and to show clearly the extent to which electron dynamics in non-Hamiltonian. The statistical mechanical framework is extended to a discussion of the conceptual foundations of the treatment of collective effects through the Vlasov equation

  15. International Conference on Trends and Perspectives in Linear Statistical Inference

    CERN Document Server

    Rosen, Dietrich

    2018-01-01

    This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference. .

  16. Statistical algebraic approach to quantum mechanics

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2001-01-01

    The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

  17. Exactly soluble problems in statistical mechanics

    International Nuclear Information System (INIS)

    Yang, C.N.

    1983-01-01

    In the last few years, a number of two-dimensional classical and one-dimensional quantum mechanical problems in statistical mechanics have been exactly solved. Although these problems range over models of diverse physical interest, their solutions were obtained using very similar mathematical methods. In these lectures, the main points of the methods are discussed. In this introductory lecture, an overall survey of all these problems without going into the detailed method of solution is given. In later lectures, they shall concentrate on one particular problem: the delta function interaction in one dimension, and go into the details of that problem

  18. Classical statistical mechanics approach to multipartite entanglement

    Energy Technology Data Exchange (ETDEWEB)

    Facchi, P [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); Florio, G; Pascazio, S [Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari (Italy); Marzolino, U [Dipartimento di Fisica, Universita di Trieste, and Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, I-34014 Trieste (Italy); Parisi, G [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , Piazzale Aldo Moro 2, Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM (Italy)

    2010-06-04

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

  19. Classical statistical mechanics approach to multipartite entanglement

    Science.gov (United States)

    Facchi, P.; Florio, G.; Marzolino, U.; Parisi, G.; Pascazio, S.

    2010-06-01

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

  20. Classical statistical mechanics approach to multipartite entanglement

    International Nuclear Information System (INIS)

    Facchi, P; Florio, G; Pascazio, S; Marzolino, U; Parisi, G

    2010-01-01

    We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

  1. Statistical Mechanics and Black Hole Thermodynamics

    OpenAIRE

    Carlip, Steven

    1997-01-01

    Black holes are thermodynamic objects, but despite recent progress, the ultimate statistical mechanical origin of black hole temperature and entropy remains mysterious. Here I summarize an approach in which the entropy is viewed as arising from ``would-be pure gauge'' degrees of freedom that become dynamical at the horizon. For the (2+1)-dimensional black hole, these degrees of freedom can be counted, and yield the correct Bekenstein-Hawking entropy; the corresponding problem in 3+1 dimension...

  2. Statistical mechanics of budget-constrained auctions

    OpenAIRE

    Altarelli, F.; Braunstein, A.; Realpe-Gomez, J.; Zecchina, R.

    2009-01-01

    Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution,...

  3. The statistical mechanics of learning a rule

    International Nuclear Information System (INIS)

    Watkin, T.L.H.; Rau, A.; Biehl, M.

    1993-01-01

    A summary is presented of the statistical mechanical theory of learning a rule with a neural network, a rapidly advancing area which is closely related to other inverse problems frequently encountered by physicists. By emphasizing the relationship between neural networks and strongly interacting physical systems, such as spin glasses, the authors show how learning theory has provided a workshop in which to develop new, exact analytical techniques

  4. Statistical mechanics of the majority game

    International Nuclear Information System (INIS)

    Kozlowski, P; Marsili, M

    2003-01-01

    The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield-like Hamiltonian. On the basis of replica symmetric calculations, we draw the phase diagram, which contains the analogue of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations

  5. Metastability in Field Theory and Statistical Mechanics

    International Nuclear Information System (INIS)

    Carvalho, C.A. de.

    1984-01-01

    After a phase transition analysis which can occur in the framework of a scalar field theory, at finite temperature and in presence of a external field, possibles metastable situations are studied and also how is their relationship with the transitions. In both cases it is used a semiclassical approximation to the theory which, in Statistical Mechanics, corresponds to the droplet-bubble model. (L.C.) [pt

  6. Ontology matching evaluation : A statistical perspective

    NARCIS (Netherlands)

    Mohammadi, M.; Hofman, W.J.; Tan, Y.H.

    2016-01-01

    This paper proposes statistical approaches to test if the difference between two ontology matchers is real. Specifically, the performances of the matchers over multiple data sets are obtained and based on their performances, the conclusion can be drawn whether one method is better than one another

  7. Ontology matching evaluation : A statistical perspective

    NARCIS (Netherlands)

    Mohammadi, M.; Hofman, Wout; Tan, Y.

    2016-01-01

    This paper proposes statistical approaches to test if the difference between two ontology matchers is real. Specifically, the performances of the matchers over multiple data sets are obtained and based on their performances, the conclusion can be drawn whether one method is better than one

  8. Statistical mechanics for a class of quantum statistics

    International Nuclear Information System (INIS)

    Isakov, S.B.

    1994-01-01

    Generalized statistical distributions for identical particles are introduced for the case where filling a single-particle quantum state by particles depends on filling states of different momenta. The system of one-dimensional bosons with a two-body potential that can be solved by means of the thermodynamic Bethe ansatz is shown to be equivalent thermodynamically to a system of free particles obeying statistical distributions of the above class. The quantum statistics arising in this way are completely determined by the two-particle scattering phases of the corresponding interacting systems. An equation determining the statistical distributions for these statistics is derived

  9. Statistical mechanics of lattice Boson field theory

    International Nuclear Information System (INIS)

    1976-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region

  10. Quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Jegerlehner, F.

    1975-01-01

    At first a heuristic understanding is given how the relation between quantum field theory and statistical mechanics near phase transitions comes about. A long range scale invariant theory is constructed, critical indices are calculated and the relations among them are proved, field theoretical Kadanoff-scale transformations are formulated and scaling corrections calculated. A precise meaning to many of Kadanoffs considerations and a model matching Wegners phenomenological scheme is given. It is shown, that soft parametrization is most transparent for the discussion of scaling behaviour. (BJ) [de

  11. Statistical mechanics of spatial evolutionary games

    International Nuclear Information System (INIS)

    Miekisz, Jacek

    2004-01-01

    We discuss the long-run behaviour of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash equilibria. We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We use concepts and techniques of statistical mechanics to study game-theoretic models. In order to obtain results in the case of the so-called potential games, we analyse the thermodynamic limit of the appropriate models of interacting particles

  12. Statistical mechanics out of equilibrium the irreversibility

    International Nuclear Information System (INIS)

    Alvarez Estrada, R. F.

    2001-01-01

    A Round Table about the issue of Irreversibility and related matters has taken place during the last (20th) Statistical Mechanics Conference, held in Paris (July 1998). This article tries to provide a view (necessarily limited, and hence, uncompleted) of some approaches to the subject: the one based upon deterministic chaos (which is currently giving rise to a very active research) and the classical interpretation due to Boltzmann. An attempt has been made to write this article in a self-contained way, and to avoid a technical presentation wherever possible. (Author) 29 refs

  13. Principles of thermodynamics and statistical mechanics

    CERN Document Server

    Lawden, D F

    2005-01-01

    A thorough exploration of the universal principles of thermodynamics and statistical mechanics, this volume explains the applications of these essential rules to a multitude of situations arising in physics and engineering. It develops their use in a variety of circumstances-including those involving gases, crystals, and magnets-in order to illustrate general methods of analysis and to provide readers with all the necessary background to continue in greater depth with specific topics.Author D. F. Lawden has considerable experience in teaching this subject to university students of varied abili

  14. Thermodynamics and statistical mechanics an integrated approach

    CERN Document Server

    Hardy, Robert J

    2014-01-01

    This textbook brings together the fundamentals of the macroscopic and microscopic aspects of thermal physics by presenting thermodynamics and statistical mechanics as complementary theories based on small numbers of postulates. The book is designed to give the instructor flexibility in structuring courses for advanced undergraduates and/or beginning graduate students and is written on the principle that a good text should also be a good reference. The presentation of thermodynamics follows the logic of Clausius and Kelvin while relating the concepts involved to familiar phenomena and the mod

  15. Statistical mechanics of lattice boson field theory

    International Nuclear Information System (INIS)

    Baker, G.A. Jr.

    1977-01-01

    A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references

  16. Early years of Computational Statistical Mechanics

    Science.gov (United States)

    Mareschal, Michel

    2018-05-01

    Evidence that a model of hard spheres exhibits a first-order solid-fluid phase transition was provided in the late fifties by two new numerical techniques known as Monte Carlo and Molecular Dynamics. This result can be considered as the starting point of computational statistical mechanics: at the time, it was a confirmation of a counter-intuitive (and controversial) theoretical prediction by J. Kirkwood. It necessitated an intensive collaboration between the Los Alamos team, with Bill Wood developing the Monte Carlo approach, and the Livermore group, where Berni Alder was inventing Molecular Dynamics. This article tells how it happened.

  17. Networking—a statistical physics perspective

    International Nuclear Information System (INIS)

    Yeung, Chi Ho; Saad, David

    2013-01-01

    Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. (topical review)

  18. A clinical perspective of accelerated statistical reconstruction

    International Nuclear Information System (INIS)

    Hutton, B.F.; Hudson, H.M.; Beekman, F.J.

    1997-01-01

    Although the potential benefits of maximum likelihood reconstruction have been recognised for many years, the technique has only recently found widespread popularity in clinical practice. Factors which have contributed to the wider acceptance include improved models for the emission process, better understanding of the properties of the algorithm and, not least, the practicality of application with the development of acceleration schemes and the improved speed of computers. The objective in this article is to present a framework for applying maximum likelihood reconstruction for a wide range of clinically based problems. The article draws particularly on the experience of the three authors in applying an acceleration scheme involving use of ordered subsets to a range of applications. The potential advantages of statistical reconstruction techniques include: (a) the ability to better model the emission and detection process, in order to make the reconstruction converge to a quantitative image, (b) the inclusion of a statistical noise model which results in better noise characteristics, and (c) the possibility to incorporate prior knowledge about the distribution being imaged. The great flexibility in adapting the reconstruction for a specific model results in these techniques having wide applicability to problems in clinical nuclear medicine. (orig.). With 8 figs., 1 tab

  19. Networking—a statistical physics perspective

    Science.gov (United States)

    Yeung, Chi Ho; Saad, David

    2013-03-01

    Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.

  20. Statistical mechanics and the foundations of thermodynamics

    International Nuclear Information System (INIS)

    Martin-Loef, A.

    1979-01-01

    These lectures are designed as an introduction to classical statistical mechanics and its relation to thermodynamics. They are intended to bridge the gap between the treatment of the subject in physics text books and the modern presentations of mathematically rigorous results. We shall first introduce the probability distributions, ensembles, appropriate for describing systems in equilibrium and consider some of their basic physical applications. We also discuss the problem of approach to equilibrium and how irreversibility comes into the dynamics. We then give a detailed description of how the law of large numbers for macrovariables in equilibrium is derived from the fact that entropy is an extensive quantity in the thermodynamic limit. We show in a natural way how to split the energy changes in an thermodynamical process into work and heat leading to a derivation of the first and second laws of thermodynamics from the rules of thermodynamical equilibrium. We have elaborated this part in detail because we feel it is quite satisfactory, that the establishment of the limit of thermodynamic functions as achieved in the modern development of the mathematical aspects of statistical mechanics allows a more general and logically clearer presentation of the bases of thermodynamics. We close these lectures by presenting the basic facts about fluctuation theory. The treatment aims to be reasonably self-contained both concerning the physics and mathematics needed. No knowledge of quantum mechanics is presupposed. Since we spent a large part on mathematical proofs and give many technical facts these lectures are probably most digestive for the mathematically inclined reader who wants to understand the physics of the subject. (HJ)

  1. Cratering statistics on asteroids: Methods and perspectives

    Science.gov (United States)

    Chapman, C.

    2014-07-01

    Crater size-frequency distributions (SFDs) on the surfaces of solid-surfaced bodies in the solar system have provided valuable insights about planetary surface processes and about impactor populations since the first spacecraft images were obtained in the 1960s. They can be used to determine relative age differences between surficial units, to obtain absolute model ages if the impactor flux and scaling laws are understood, to assess various endogenic planetary or asteroidal processes that degrade craters or resurface units, as well as assess changes in impactor populations across the solar system and/or with time. The first asteroid SFDs were measured from Galileo images of Gaspra and Ida (cf., Chapman 2002). Despite the superficial simplicity of these studies, they are fraught with many difficulties, including confusion by secondary and/or endogenic cratering and poorly understood aspects of varying target properties (including regoliths, ejecta blankets, and nearly-zero-g rubble piles), widely varying attributes of impactors, and a host of methodological problems including recognizability of degraded craters, which is affected by illumination angle and by the ''personal equations'' of analysts. Indeed, controlled studies (Robbins et al. 2014) demonstrate crater-density differences of a factor of two or more between experienced crater counters. These inherent difficulties have been especially apparent in divergent results for Vesta from different members of the Dawn Science Team (cf. Russell et al. 2013). Indeed, they have been exacerbated by misuse of a widely available tool (Craterstats: hrscview.fu- berlin.de/craterstats.html), which incorrectly computes error bars for proper interpretation of cumulative SFDs, resulting in derived model ages specified to three significant figures and interpretations of statistically insignificant kinks. They are further exacerbated, and for other small-body crater SFDs analyzed by the Berlin group, by stubbornly adopting

  2. Perspectives of ukrainian mechanical engineering development

    OpenAIRE

    Dyrda, E.; Schepetkova, A.; Galushko, O.

    2013-01-01

    Theses are devoted to problems and perspectives of Ukrainian mechanical engineering development. Role of mechanical engineering in national economy is described. Problems of mechanical engineering, such as losing the cometetive advantages, production decreasing, debts growing, ineffective assets structure, are investigated. Influence of European integration process on mechanical engineering enterprises is discussed.

  3. A statistical mechanical interpretation of algorithmic information theory: Total statistical mechanical interpretation based on physical argument

    International Nuclear Information System (INIS)

    Tadaki, Kohtaro

    2010-01-01

    The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp. 425-434, 2008] and [K. Tadaki, Proceedings of LFCS'09, Springer's LNCS, vol. 5407, pp. 422-440, 2009], where we introduced the notion of thermodynamic quantities, such as partition function Z(T), free energy F(T), energy E(T), statistical mechanical entropy S(T), and specific heat C(T), into AIT. We then discovered that, in the interpretation, the temperature T equals to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate by means of program-size complexity. Furthermore, we showed that this situation holds for the temperature T itself, which is one of the most typical thermodynamic quantities. Namely, we showed that, for each of the thermodynamic quantities Z(T), F(T), E(T), and S(T) above, the computability of its value at temperature T gives a sufficient condition for T is an element of (0,1) to satisfy the condition that the partial randomness of T equals to T. In this paper, based on a physical argument on the same level of mathematical strictness as normal statistical mechanics in physics, we develop a total statistical mechanical interpretation of AIT which actualizes a perfect correspondence to normal statistical mechanics. We do this by identifying a microcanonical ensemble in the framework of AIT. As a result, we clarify the statistical mechanical meaning of the thermodynamic quantities of AIT.

  4. Two statistical mechanics aspects of complex networks

    Science.gov (United States)

    Thurner, Stefan; Biely, Christoly

    2006-12-01

    By adopting an ensemble interpretation of non-growing rewiring networks, network theory can be reduced to a counting problem of possible network states and an identification of their associated probabilities. We present two scenarios of how different rewirement schemes can be used to control the state probabilities of the system. In particular, we review how by generalizing the linking rules of random graphs, in combination with superstatistics and quantum mechanical concepts, one can establish an exact relation between the degree distribution of any given network and the nodes’ linking probability distributions. In a second approach, we control state probabilities by a network Hamiltonian, whose characteristics are motivated by biological and socio-economical statistical systems. We demonstrate that a thermodynamics of networks becomes a fully consistent concept, allowing to study e.g. ‘phase transitions’ and computing entropies through thermodynamic relations.

  5. Statistical mechanics of magnetized pair Fermi gas

    International Nuclear Information System (INIS)

    Daicic, J.; Frankel, N.E.; Kowalenko, V.

    1993-01-01

    Following previous work on the magnetized pair Bose gas this contribution presents the statistical mechanics of the charged relativistic Fermi gas with pair creation in d spatial dimensions. Initially, the gas in no external fields is studied. As a result, expansions for the various thermodynamic functions are obtained in both the μ/m→0 (neutrino) limit, and about the point μ/m =1, where μ is the chemical potential. The thermodynamics of a gas of quantum-number conserving massless fermions is also discussed. Then a complete study of the pair Fermi gas in a homogeneous magnetic field, is presented investigating the behavior of the magnetization over a wide range of field strengths. The inclusion of pairs leads to new results for the net magnetization due to the paramagnetic moment of the spins and the diamagnetic Landau orbits. 20 refs

  6. Thermodynamics and statistical mechanics an integrated approach

    CERN Document Server

    Shell, M Scott

    2015-01-01

    Learn classical thermodynamics alongside statistical mechanics with this fresh approach to the subjects. Molecular and macroscopic principles are explained in an integrated, side-by-side manner to give students a deep, intuitive understanding of thermodynamics and equip them to tackle future research topics that focus on the nanoscale. Entropy is introduced from the get-go, providing a clear explanation of how the classical laws connect to the molecular principles, and closing the gap between the atomic world and thermodynamics. Notation is streamlined throughout, with a focus on general concepts and simple models, for building basic physical intuition and gaining confidence in problem analysis and model development. Well over 400 guided end-of-chapter problems are included, addressing conceptual, fundamental, and applied skill sets. Numerous worked examples are also provided together with handy shaded boxes to emphasize key concepts, making this the complete teaching package for students in chemical engineer...

  7. Current algebra, statistical mechanics and quantum models

    Science.gov (United States)

    Vilela Mendes, R.

    2017-11-01

    Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

  8. Statistical mechanics of budget-constrained auctions

    International Nuclear Information System (INIS)

    Altarelli, F; Braunstein, A; Realpe-Gomez, J; Zecchina, R

    2009-01-01

    Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise

  9. Statistical mechanics of budget-constrained auctions

    Science.gov (United States)

    Altarelli, F.; Braunstein, A.; Realpe-Gomez, J.; Zecchina, R.

    2009-07-01

    Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.

  10. Generalized bond percolation and statistical mechanics

    International Nuclear Information System (INIS)

    Tsallis, C.

    1978-05-01

    A generalization of traditional bond percolation is performed, in the sens that bonds have now the possibility of partially transmitting the information (a fact which leads to the concept of 'fidelity' of the bond), and also in the sens that, besides the normal tendency to equiprobability, the bonds are allowed to substantially change the information. Furthermore the fidelity is allowed, to become an aleatory variable, and the operational rules concerning the associated distribution laws are determined. Thermally quenched random bonds and the whole body of Statistical Mechanics become particular cases of this formalism, which is in general adapted to the treatment of all problems whose main characteristic is to preserve a part of the information through a long path or array (critical phenomena, regime changements, thermal random models, etc). Operationally it provides a quick method for the calculation of the equivalent probability of complex clusters within the traditional bond percolation problem [pt

  11. Statistical mechanics of dense granular media

    International Nuclear Information System (INIS)

    Coniglio, A; Fierro, A; Nicodemi, M; Ciamarra, M Pica; Tarzia, M

    2005-01-01

    We discuss some recent results on the statistical mechanics approach to dense granular media. In particular, by analytical mean field investigation we derive the phase diagram of monodisperse and bidisperse granular assemblies. We show that 'jamming' corresponds to a phase transition from a 'fluid' to a 'glassy' phase, observed when crystallization is avoided. The nature of such a 'glassy' phase turns out to be the same as found in mean field models for glass formers. This gives quantitative evidence for the idea of a unified description of the 'jamming' transition in granular media and thermal systems, such as glasses. We also discuss mixing/segregation transitions in binary mixtures and their connections to phase separation and 'geometric' effects

  12. Statistical mechanics of driven diffusive systems

    CERN Document Server

    Schmittmann, B

    1995-01-01

    Far-from-equilibrium phenomena, while abundant in nature, are not nearly as well understood as their equilibrium counterparts. On the theoretical side, progress is slowed by the lack of a simple framework, such as the Boltzmann-Gbbs paradigm in the case of equilibrium thermodynamics. On the experimental side, the enormous structural complexity of real systems poses serious obstacles to comprehension. Similar difficulties have been overcome in equilibrium statistical mechanics by focusing on model systems. Even if they seem too simplistic for known physical systems, models give us considerable insight, provided they capture the essential physics. They serve as important theoretical testing grounds where the relationship between the generic physical behavior and the key ingredients of a successful theory can be identified and understood in detail. Within the vast realm of non-equilibrium physics, driven diffusive systems form a subset with particularly interesting properties. As a prototype model for these syst...

  13. BOOK REVIEW: Statistical Mechanics of Turbulent Flows

    Science.gov (United States)

    Cambon, C.

    2004-10-01

    This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

  14. Aftershock Energy Distribution by Statistical Mechanics Approach

    Science.gov (United States)

    Daminelli, R.; Marcellini, A.

    2015-12-01

    The aim of our work is to research the most probable distribution of the energy of aftershocks. We started by applying one of the fundamental principles of statistical mechanics that, in case of aftershock sequences, it could be expressed as: the greater the number of different ways in which the energy of aftershocks can be arranged among the energy cells in phase space the more probable the distribution. We assume that each cell in phase space has the same possibility to be occupied, and that more than one cell in the phase space can have the same energy. Seeing that seismic energy is proportional to products of different parameters, a number of different combinations of parameters can produce different energies (e.g., different combination of stress drop and fault area can release the same seismic energy). Let us assume that there are gi cells in the aftershock phase space characterised by the same energy released ɛi. Therefore we can assume that the Maxwell-Boltzmann statistics can be applied to aftershock sequences with the proviso that the judgment on the validity of this hypothesis is the agreement with the data. The aftershock energy distribution can therefore be written as follow: n(ɛ)=Ag(ɛ)exp(-βɛ)where n(ɛ) is the number of aftershocks with energy, ɛ, A and β are constants. Considering the above hypothesis, we can assume g(ɛ) is proportional to ɛ. We selected and analysed different aftershock sequences (data extracted from Earthquake Catalogs of SCEC, of INGV-CNT and other institutions) with a minimum magnitude retained ML=2 (in some cases ML=2.6) and a time window of 35 days. The results of our model are in agreement with the data, except in the very low energy band, where our model resulted in a moderate overestimation.

  15. A quantum information approach to statistical mechanics

    International Nuclear Information System (INIS)

    Cuevas, G.

    2011-01-01

    The field of quantum information and computation harnesses and exploits the properties of quantum mechanics to perform tasks more efficiently than their classical counterparts, or that may uniquely be possible in the quantum world. Its findings and techniques have been applied to a number of fields, such as the study of entanglement in strongly correlated systems, new simulation techniques for many-body physics or, generally, to quantum optics. This thesis aims at broadening the scope of quantum information theory by applying it to problems in statistical mechanics. We focus on classical spin models, which are toy models used in a variety of systems, ranging from magnetism, neural networks, to quantum gravity. We tackle these models using quantum information tools from three different angles. First, we show how the partition function of a class of widely different classical spin models (models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. We prove this by first establishing a relation between partition functions and quantum states, and then transforming the corresponding quantum states to each other. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proof is based on a relation between partition functions and quantum circuits, which allows us to determine the quantum computational complexity of the partition function by studying the corresponding quantum circuit. Finally, we outline the possibility of applying quantum information concepts and tools to certain models of dis- crete quantum gravity. The latter provide a natural route to generalize our results, insofar as the central quantity has the form of a partition function, and as classical spin models are used as toy models of matter. (author)

  16. The Brandeis Dice Problem and Statistical Mechanics

    Science.gov (United States)

    van Enk, Steven J.

    2014-11-01

    Jaynes invented the Brandeis Dice Problem as a simple illustration of the MaxEnt (Maximum Entropy) procedure that he had demonstrated to work so well in Statistical Mechanics. I construct here two alternative solutions to his toy problem. One, like Jaynes' solution, uses MaxEnt and yields an analog of the canonical ensemble, but at a different level of description. The other uses Bayesian updating and yields an analog of the micro-canonical ensemble. Both, unlike Jaynes' solution, yield error bars, whose operational merits I discuss. These two alternative solutions are not equivalent for the original Brandeis Dice Problem, but become so in what must, therefore, count as the analog of the thermodynamic limit, M-sided dice with M → ∞. Whereas the mathematical analogies between the dice problem and Stat Mech are quite close, there are physical properties that the former lacks but that are crucial to the workings of the latter. Stat Mech is more than just MaxEnt.

  17. The Statistical Mechanics of Ideal MHD Turbulence

    Science.gov (United States)

    Shebalin, John V.

    2003-01-01

    Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

  18. Plasma Soliton Turbulence and Statistical Mechanics

    International Nuclear Information System (INIS)

    Treumann, R.A.; Pottelette, R.

    1999-01-01

    Collisionless kinetic plasma turbulence is described approximately in terms of a superposition of non-interacting solitary waves. We discuss the relevance of such a description under astrophysical conditions. Several types of solitary waves may be of interest in this relation as generators of turbulence and turbulent transport. A consistent theory of turbulence can be given only in a few particular cases when the description can be reduced to the Korteweg-de Vries equation or some other simple equation like the Kadomtsev-Petviashvili equation. It turns out that the soliton turbulence is usually energetically harder than the ordinary weakly turbulent plasma description. This implies that interaction of particles with such kinds of turbulence can lead to stronger acceleration than in ordinary turbulence. However, the description in our model is only classical and non-relativistic. Transport in solitary turbulence is most important for drift wave turbulence. Such waves form solitary drift wave vortices which may provide cross-field transport. A more general discussion is given on transport. In a model of Levy flight trapping of particles in solitons (or solitary turbulence) one finds that the residence time of particles in the region of turbulence may be described by a generalized Lorentzian probability distribution. It is shown that under collisionless equilibrium conditions far away from thermal equilibrium such distributions are natural equilibrium distributions. A consistent thermodynamic description of such media can be given in terms of a generalized Lorentzian statistical mechanics and thermodynamics. (author)

  19. Statistical mechanics, gravity, and Euclidean theory

    International Nuclear Information System (INIS)

    Fursaev, Dmitri V.

    2002-01-01

    A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigenvalue problems which depend non-linearly on the spectral parameter. We present a method to deal with such problems. In particular, we demonstrate how some results of the spectral theory of second-order elliptic operators, such as heat kernel asymptotics, can be extended to a class of non-linear spectral problems. The method is used to trace down the relation between the canonical definition of the free energy based on summation over the modes and the covariant definition given in Euclidean quantum gravity. As an application, high-temperature asymptotics of the free energy and of the thermal part of the stress-energy tensor in the presence of rotation are derived. We also discuss statistical mechanics in the presence of Killing horizons where canonical and Euclidean theories are related in a non-trivial way

  20. Probabilistic cellular automata: Some statistical mechanical considerations

    International Nuclear Information System (INIS)

    Lebowitz, J.L.; Maes, C.; Speer, E.R.

    1990-01-01

    Spin systems evolving in continuous or discrete time under the action of stochastic dynamics are used to model phenomena as diverse as the structure of alloys and the functioning of neural networks. While in some cases the dynamics are secondary, designed to produce a specific stationary measure whose properties one is interested in studying, there are other cases in which the only available information is the dynamical rule. Prime examples of the former are computer simulations, via Glauber dynamics, of equilibrium Gibbs measures with a specified interaction potential. Examples of the latter include various types of majority rule dynamics used as models for pattern recognition and for error-tolerant computations. The present note discusses ways in which techniques found useful in equilibrium statistical mechanics can be applied to a particular class of models of the latter types. These are cellular automata with noise: systems in which the spins are updated stochastically at integer times, simultaneously at all sites of some regular lattice. These models were first investigated in detail in the Soviet literature of the late sixties and early seventies. They are now generally referred to as Stochastic or Probabilistic Cellular Automata (PCA), and may be considered to include deterministic automata (CA) as special limits. 16 refs., 3 figs

  1. A statistical mechanical model of economics

    Science.gov (United States)

    Lubbers, Nicholas Edward Williams

    Statistical mechanics pursues low-dimensional descriptions of systems with a very large number of degrees of freedom. I explore this theme in two contexts. The main body of this dissertation explores and extends the Yard Sale Model (YSM) of economic transactions using a combination of simulations and theory. The YSM is a simple interacting model for wealth distributions which has the potential to explain the empirical observation of Pareto distributions of wealth. I develop the link between wealth condensation and the breakdown of ergodicity due to nonlinear diffusion effects which are analogous to the geometric random walk. Using this, I develop a deterministic effective theory of wealth transfer in the YSM that is useful for explaining many quantitative results. I introduce various forms of growth to the model, paying attention to the effect of growth on wealth condensation, inequality, and ergodicity. Arithmetic growth is found to partially break condensation, and geometric growth is found to completely break condensation. Further generalizations of geometric growth with growth in- equality show that the system is divided into two phases by a tipping point in the inequality parameter. The tipping point marks the line between systems which are ergodic and systems which exhibit wealth condensation. I explore generalizations of the YSM transaction scheme to arbitrary betting functions to develop notions of universality in YSM-like models. I find that wealth vi condensation is universal to a large class of models which can be divided into two phases. The first exhibits slow, power-law condensation dynamics, and the second exhibits fast, finite-time condensation dynamics. I find that the YSM, which exhibits exponential dynamics, is the critical, self-similar model which marks the dividing line between the two phases. The final chapter develops a low-dimensional approach to materials microstructure quantification. Modern materials design harnesses complex

  2. A statistical mechanics approach to Granovetter theory

    Science.gov (United States)

    Barra, Adriano; Agliari, Elena

    2012-05-01

    In this paper we try to bridge breakthroughs in quantitative sociology/econometrics, pioneered during the last decades by Mac Fadden, Brock-Durlauf, Granovetter and Watts-Strogatz, by introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors. Our model relies on a pairwise Hamiltonian for decision-maker interactions which naturally extends the multi-populations approaches by shifting and biasing the pattern definitions of a Hopfield model of neural networks. Once introduced, the model is investigated through graph theory (to recover Granovetter and Watts-Strogatz results) and statistical mechanics (to recover Mac-Fadden and Brock-Durlauf results). Due to the internal symmetries of our model, the latter is obtained as the relaxation of a proper Markov process, allowing even to study its out-of-equilibrium properties. The method used to solve its equilibrium is an adaptation of the Hamilton-Jacobi technique recently introduced by Guerra in the spin-glass scenario and the picture obtained is the following: shifting the patterns from [-1,+1]→[0.+1] implies that the larger the amount of similarities among decision makers, the stronger their relative influence, and this is enough to explain both the different role of strong and weak ties in the social network as well as its small-world properties. As a result, imitative interaction strengths seem essentially a robust request (enough to break the gauge symmetry in the couplings), furthermore, this naturally leads to a discrete choice modelization when dealing with the external influences and to imitative behavior à la Curie-Weiss as the one introduced by Brock and Durlauf.

  3. Statistical Mechanics of Money, Income, and Wealth

    Science.gov (United States)

    Yakovenko, Victor

    2006-03-01

    In Ref. [1], we proposed an analogy between the exponential Boltzmann-Gibbs distribution of energy in physics and the equilibrium probability distribution of money in a closed economic system. Analogously to energy, money is locally conserved in interactions between economic agents, so the thermal Boltzmann-Gibbs distribution function is expected for money. Since then, many researchers followed and expanded this idea [2]. Much work was done on the analysis of empirical data, mostly on income, for which a lot of tax and census data is available. We demonstrated [3] that income distribution in the USA has a well-defined two-class structure. The majority of population (97-99%) belongs to the lower class characterized by the exponential Boltzmann-Gibbs (``thermal'') distribution. The upper class (1-3% of population) has a Pareto power-law (``superthermal'') distribution, whose parameters change in time with the rise and fall of stock market. We proposed a concept of equilibrium inequality in a society, based on the principle of maximal entropy, and quantitatively demonstrated that it applies to the majority of population. Income distribution in other countries shows similar patterns. For more references, see http://www2.physics.umd.edu/˜yakovenk/econophysics.html. References: [1] A. A. Dragulescu and V. M. Yakovenko, ``Statistical mechanics of money'', Eur. Phys. J. B 17, 723 (2000). [2] ``Econophysics of Wealth Distributions'', edited by A. Chatterjee, S. Yarlagadda, and B. K. Chakrabarti, Springer, 2005. [3] A. C. Silva and V. M. Yakovenko, ``Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001'', Europhys. Lett. 69, 304 (2005).

  4. Statistical Mechanics and Applications in Condensed Matter

    Science.gov (United States)

    Di Castro, Carlo; Raimondi, Roberto

    2015-08-01

    Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

  5. Statistical Mechanics of Temporal and Interacting Networks

    Science.gov (United States)

    Zhao, Kun

    In the last ten years important breakthroughs in the understanding of the topology of complexity have been made in the framework of network science. Indeed it has been found that many networks belong to the universality classes called small-world networks or scale-free networks. Moreover it was found that the complex architecture of real world networks strongly affects the critical phenomena defined on these structures. Nevertheless the main focus of the research has been the characterization of single and static networks. Recently, temporal networks and interacting networks have attracted large interest. Indeed many networks are interacting or formed by a multilayer structure. Example of these networks are found in social networks where an individual might be at the same time part of different social networks, in economic and financial networks, in physiology or in infrastructure systems. Moreover, many networks are temporal, i.e. the links appear and disappear on the fast time scale. Examples of these networks are social networks of contacts such as face-to-face interactions or mobile-phone communication, the time-dependent correlations in the brain activity and etc. Understanding the evolution of temporal and multilayer networks and characterizing critical phenomena in these systems is crucial if we want to describe, predict and control the dynamics of complex system. In this thesis, we investigate several statistical mechanics models of temporal and interacting networks, to shed light on the dynamics of this new generation of complex networks. First, we investigate a model of temporal social networks aimed at characterizing human social interactions such as face-to-face interactions and phone-call communication. Indeed thanks to the availability of data on these interactions, we are now in the position to compare the proposed model to the real data finding good agreement. Second, we investigate the entropy of temporal networks and growing networks , to provide

  6. Statistical methods and applications from a historical perspective selected issues

    CERN Document Server

    Mignani, Stefania

    2014-01-01

    The book showcases a selection of peer-reviewed papers, the preliminary versions of which were presented at a conference held 11-13 June 2011 in Bologna and organized jointly by the Italian Statistical Society (SIS), the National Institute of Statistics (ISTAT) and the Bank of Italy. The theme of the conference was "Statistics in the 150 years of the Unification of Italy." The celebration of the anniversary of Italian unification provided the opportunity to examine and discuss the methodological aspects and applications from a historical perspective and both from a national and international point of view. The critical discussion on the issues of the past has made it possible to focus on recent advances, considering the studies of socio-economic and demographic changes in European countries.

  7. The scientifiv way of thinking in statistics, statistical physics and quantum mechanics

    OpenAIRE

    Săvoiu, Gheorghe

    2008-01-01

    This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

  8. The scientific way of thinking in statistics, statistical physics and quantum mechanics

    OpenAIRE

    Săvoiu, Gheorghe

    2008-01-01

    This paper focuses on the way of thinking in both classical and modern Physics and Statistics, Statistical Mechanics or Statistical Physics and Quantum Mechanics. These different statistical ways of thinking and their specific methods have generated new fields for new activities and new scientific disciplines, like Econophysics (between Economics and Physics), Sociophysics (between Sociology and Physics), Mediaphysics (between all media and comunication sciences), etc. After describing some r...

  9. The statistical mechanics of financial markets

    CERN Document Server

    Voit, Johannes

    2003-01-01

    From the reviews of the first edition - "Provides an excellent introduction for physicists interested in the statistical properties of financial markets. Appropriately early in the book the basic financial terms such as shorts, limit orders, puts, calls, and other terms are clearly defined. Examples, often with graphs, augment the reader’s understanding of what may be a plethora of new terms and ideas… [This is] an excellent starting point for the physicist interested in the subject. Some of the book’s strongest features are its careful definitions, its detailed examples, and the connection it establishes to physical systems." PHYSICS TODAY "This book is excellent at illustrating the similarities of financial markets with other non-equilibrium physical systems. [...] In summary, a very good book that offers more than just qualitative comparisons of physics and finance." (www.quantnotes.com) This highly-praised introductory treatment describes parallels between statistical physics and finance - both thos...

  10. Changing viewer perspectives reveals constraints to implicit visual statistical learning.

    Science.gov (United States)

    Jiang, Yuhong V; Swallow, Khena M

    2014-10-07

    Statistical learning-learning environmental regularities to guide behavior-likely plays an important role in natural human behavior. One potential use is in search for valuable items. Because visual statistical learning can be acquired quickly and without intention or awareness, it could optimize search and thereby conserve energy. For this to be true, however, visual statistical learning needs to be viewpoint invariant, facilitating search even when people walk around. To test whether implicit visual statistical learning of spatial information is viewpoint independent, we asked participants to perform a visual search task from variable locations around a monitor placed flat on a stand. Unbeknownst to participants, the target was more often in some locations than others. In contrast to previous research on stationary observers, visual statistical learning failed to produce a search advantage for targets in high-probable regions that were stable within the environment but variable relative to the viewer. This failure was observed even when conditions for spatial updating were optimized. However, learning was successful when the rich locations were referenced relative to the viewer. We conclude that changing viewer perspective disrupts implicit learning of the target's location probability. This form of learning shows limited integration with spatial updating or spatiotopic representations. © 2014 ARVO.

  11. Statistical mechanics of microscopically thin thermalized shells

    Science.gov (United States)

    Kosmrlj, Andrej

    Recent explosion in fabrication of microscopically thin free standing structures made from graphene and other two-dimensional materials has led to a renewed interest in the mechanics of such structures in presence of thermal fluctuations. Since late 1980s it has been known that for flat solid sheets thermal fluctuations effectively increase the bending rigidity and reduce the bulk and shear moduli in a scale-dependent fashion. However, much is still unknown about the mechanics of thermalized flat sheets of complex geometries and about the mechanics of thermalized shells with non-zero background curvature. In this talk I will present recent development in the mechanics of thermalized ribbons, spherical shells and cylindrical tubes. Long ribbons are found to behave like hybrids between flat sheets with renormalized elastic constants and semi-flexible polymers, and these results can be used to predict the mechanics of graphene kirigami structures. Contrary to the anticipated behavior for ribbons, the non-zero background curvature of shells leads to remarkable novel phenomena. In shells, thermal fluctuations effectively generate negative surface tension, which can significantly reduce the critical buckling pressure for spherical shells and the critical axial load for cylindrical tubes. For large shells this thermally generated load becomes big enough to spontaneously crush spherical shells and cylindrical tubes even in the absence of external loads. I will comment on the relevance for crushing of microscopic shells (viral capsids, bacteria, microcapsules) due to osmotic shocks and for crushing of nanotubes.

  12. A statistical mechanical model for equilibrium ionization

    International Nuclear Information System (INIS)

    Macris, N.; Martin, P.A.; Pule, J.

    1990-01-01

    A quantum electron interacts with a classical gas of hard spheres and is in thermal equilibrium with it. The interaction is attractive and the electron can form a bound state with the classical particles. It is rigorously shown that in a well defined low density and low temperature limit, the ionization probability for the electron tends to the value predicted by the Saha formula for thermal ionization. In this regime, the electron is found to be in a statistical mixture of a bound and a free state. (orig.)

  13. Equilibrium statistical mechanics on correlated random graphs

    Science.gov (United States)

    Barra, Adriano; Agliari, Elena

    2011-02-01

    Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]\\to [0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved.

  14. Equilibrium statistical mechanics on correlated random graphs

    International Nuclear Information System (INIS)

    Barra, Adriano; Agliari, Elena

    2011-01-01

    Biological and social networks have recently attracted great attention from physicists. Among several aspects, two main ones may be stressed: a non-trivial topology of the graph describing the mutual interactions between agents and, typically, imitative, weighted, interactions. Despite such aspects being widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a priori assumptions and, in most cases, implement constant intensities for links. Here we propose a simple shift [-1,+1]→[0,+1] in the definition of patterns in a Hopfield model: a straightforward effect is the conversion of frustration into dilution. In fact, we show that by varying the bias of pattern distribution, the network topology (generated by the reciprocal affinities among agents, i.e. the Hebbian rule) crosses various well-known regimes, ranging from fully connected, to an extreme dilution scenario, then to completely disconnected. These features, as well as small-world properties, are, in this context, emergent and no longer imposed a priori. The model is throughout investigated also from a thermodynamics perspective: the Ising model defined on the resulting graph is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. Overall, our findings show that, at least at equilibrium, dilution (of whatever kind) simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations is that, within our approach, replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible subgraphs belonging to the main one investigated: as a consequence, for these objects a closure for a self-consistent relation is achieved

  15. Statistical mechanics of reacting dense plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Rogers, F.J.

    1978-11-22

    A review of the quantum statistical theory of strongly coupled many component plasmas is given. The theoretical development is shown to consist of six separate parts. Compensation between bound and scattering state contributions to the partition function and use of the shifted Debye energy levels are important aspects of the analysis. The results are valid when the electrons are moderately coupled to the heavy ions, i.e., ..lambda../sub e..cap alpha../* < 1, but no restriction is placed on the coupling between heavy ions. Another restriction is that lambda/lambda/sub D/ < 1, i.e., the thermal deBroglie wavelength is less than the Debye length. Numerical calculations of PV/N/sub 0/kT and C/sub V/ are given for a Rubidium plasma.

  16. Statistical mechanics of human resource allocation

    Science.gov (United States)

    Inoue, Jun-Ichi; Chen, He

    2014-03-01

    We provide a mathematical platform to investigate the network topology of agents, say, university graduates who are looking for their positions in labor markets. The basic model is described by the so-called Potts spin glass which is well-known in the research field of statistical physics. In the model, each Potts spin (a tiny magnet in atomic scale length) represents the action of each student, and it takes a discrete variable corresponding to the company he/she applies for. We construct the energy to include three distinct effects on the students' behavior, namely, collective effect, market history and international ranking of companies. In this model system, the correlations (the adjacent matrix) between students are taken into account through the pairwise spin-spin interactions. We carry out computer simulations to examine the efficiency of the model. We also show that some chiral representation of the Potts spin enables us to obtain some analytical insights into our labor markets. This work was financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science No. 25330278.

  17. Statistical Mechanics of Japanese Labor Markets

    Science.gov (United States)

    Chen, He

    We introduce a probabilistic model to analyze job-matching processes of recent Japanese labor markets, in particular, for university graduates by means of statistical physics. To make a model of the market efficiently, we take into account several hypotheses. Namely, each company fixes the (business year independent) number of opening positions for newcomers. The ability of gathering newcomers depends on the result of job matching process in past business years. This fact means that the ability of the company is weakening if the company did not make their quota or the company gathered applicants too much over the quota. All university graduates who are looking for their jobs can access the public information about the ranking of companies. By assuming the above essential key points, we construct the local energy function of each company and describe the probability that an arbitrary company gets students at each business year by a Boltzmann-Gibbs distribution. We evaluate the relevant physical quantities such as the employment rate and Gini index. We discuss social inequalities in labor markets, and provide some ways to improve these situations, such as the informal job offer rate, the job-worker mismatch between students and companies. Graduate School of Information Science and Technology.

  18. Statistical mechanics of a cat's cradle

    Science.gov (United States)

    Shen, Tongye; Wolynes, Peter G.

    2006-11-01

    It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a variety of phase transitions as a function of temperature and extension. The results of self-consistent phonon calculations for the regular networks agree very well with computer simulations at finite temperature. The analytic theory also yields a rigidity onset (mechanical percolation) and the fraction of extended bonds for random networks. There is very good agreement with the simulations by Delaney et al (2005 Europhys. Lett. 72 990). The mean field theory reveals a nontranslationally invariant phase with self-generated heterogeneity of tautness, representing 'antiferroelasticity'.

  19. Statistical Mechanics of Thin Spherical Shells

    Directory of Open Access Journals (Sweden)

    Andrej Košmrlj

    2017-01-01

    Full Text Available We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated “pressure.” Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

  20. African perspectives on the clean development mechanism

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1999-08-01

    The papers, which are all written from an African perspective, are an important contribution to the debate surrounding the relevance and applicability of the Clean Development Mechanism in Africa. In addition to sector-specific discussions on the prospects for CDM in the energy, transport, industry and forestry sectors, various authors have attempted to tackle complex issues related to the instituional design of CDM, its mode of operation, participatory implementation and methodological questions such as baselines and additionality. (au)

  1. A statistical mechanical approach to restricted integer partition functions

    Science.gov (United States)

    Zhou, Chi-Chun; Dai, Wu-Sheng

    2018-05-01

    The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.

  2. Statistical mechanics for a system with imperfections: pt. 1

    International Nuclear Information System (INIS)

    Choh, S.T.; Kahng, W.H.; Um, C.I.

    1982-01-01

    Statistical mechanics is extended to treat a system where parts of the Hamiltonian are randomly varying. As the starting point of the theory, the statistical correlation among energy levels is neglected, allowing use of the central limit theorem of the probability theory. (Author)

  3. A New Perspective on Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Kong, Otto C W

    2011-01-01

    Based on a linear realization formulation of a quantum relativity, - proposed relativity for 'quantum space-time', we introduce the new Poincare-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. While there is supposed to be not separate notion of classical and quantum mechanics at the level of the very unconventional quantum relativity, the Poincare-Snyder relativity is more like a mathematically extended form of Einstein relativity on which we can write down a formal canonical classical and quantum mechanics. We discuss how the Poincare-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and present a first look of the interesting picture from the new perspective.

  4. Quantum mechanics and field theory with fractional spin and statistics

    International Nuclear Information System (INIS)

    Forte, S.

    1992-01-01

    Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

  5. Statistical-mechanical entropy by the thin-layer method

    International Nuclear Information System (INIS)

    Feng, He; Kim, Sung Won

    2003-01-01

    G. Hooft first studied the statistical-mechanical entropy of a scalar field in a Schwarzschild black hole background by the brick-wall method and hinted that the statistical-mechanical entropy is the statistical origin of the Bekenstein-Hawking entropy of the black hole. However, according to our viewpoint, the statistical-mechanical entropy is only a quantum correction to the Bekenstein-Hawking entropy of the black-hole. The brick-wall method based on thermal equilibrium at a large scale cannot be applied to the cases out of equilibrium such as a nonstationary black hole. The statistical-mechanical entropy of a scalar field in a nonstationary black hole background is calculated by the thin-layer method. The condition of local equilibrium near the horizon of the black hole is used as a working postulate and is maintained for a black hole which evaporates slowly enough and whose mass is far greater than the Planck mass. The statistical-mechanical entropy is also proportional to the area of the black hole horizon. The difference from the stationary black hole is that the result relies on a time-dependent cutoff

  6. Fracture mechanics and statistical mechanics of reinforced elastomeric blends

    CERN Document Server

    Heinrich, Gert; Kaliske, Michael; Klüppel, Manfred; Schneider, Konrad; Vilgis, Thomas

    2013-01-01

    Elastomers are found in many applications ranging from technology to daily life applications for example in tires, drive systems, sealings and print rollers. Dynamical operation conditions put extremely high demands on the performance and stability of these materials and their elastic and flow properties can be easily adjusted by simple manipulations on their elastic and viscous properties. However, the required service life suffers often from material damage as a result of wear processes such as abrasion and wear fatigue, mostly caused by crack formation and propagation. This book covers interdisciplinary research between physics, physical chemistry, material sciences and engineering of elastomers within the range from nanometres to millimetres and connects these aspects with the constitutive material properties. The different chapters describe reliable lifetime and durability predictions based on new fracture mechanical testing concepts and advanced material-theoretical methods which are finally implemented...

  7. Maximum entropy principle and hydrodynamic models in statistical mechanics

    International Nuclear Information System (INIS)

    Trovato, M.; Reggiani, L.

    2012-01-01

    This review presents the state of the art of the maximum entropy principle (MEP) in its classical and quantum (QMEP) formulation. Within the classical MEP we overview a general theory able to provide, in a dynamical context, the macroscopic relevant variables for carrier transport in the presence of electric fields of arbitrary strength. For the macroscopic variables the linearized maximum entropy approach is developed including full-band effects within a total energy scheme. Under spatially homogeneous conditions, we construct a closed set of hydrodynamic equations for the small-signal (dynamic) response of the macroscopic variables. The coupling between the driving field and the energy dissipation is analyzed quantitatively by using an arbitrary number of moments of the distribution function. Analogously, the theoretical approach is applied to many one-dimensional n + nn + submicron Si structures by using different band structure models, different doping profiles, different applied biases and is validated by comparing numerical calculations with ensemble Monte Carlo simulations and with available experimental data. Within the quantum MEP we introduce a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is then asserted as fundamental principle of quantum statistical mechanics. Accordingly, we have developed a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theory is formulated both in thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ħ 2 , being ħ the reduced Planck constant. In particular, by using an arbitrary number of moments, we prove that: i) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives both of the

  8. The mirror mechanism: recent findings and perspectives

    Science.gov (United States)

    Rizzolatti, Giacomo; Fogassi, Leonardo

    2014-01-01

    Mirror neurons are a specific type of visuomotor neuron that discharge both when a monkey executes a motor act and when it observes a similar motor act performed by another individual. In this article, we review first the basic properties of these neurons. We then describe visual features recently investigated which indicate that, besides encoding the goal of motor acts, mirror neurons are modulated by location in space of the observed motor acts, by the perspective from which the others’ motor acts are seen, and by the value associated with the object on which others’ motor acts are performed. In the last part of this article, we discuss the role of the mirror mechanism in planning actions and in understanding the intention underlying the others’ motor acts. We also review some human studies suggesting that motor intention in humans may rely, as in the monkey, on the mirror mechanism. PMID:24778385

  9. Brief introduction to Lie-admissible formulations in statistical mechanics

    International Nuclear Information System (INIS)

    Fronteau, J.

    1981-01-01

    The present article is a summary of the essential ideas and results published in previous articles, the aim here being to describe the situation in a schematic way for the benefit of non-specialists. The non-truncated Liouville theorem and equation, natural introduction of Lie-admissible formulations into statistical mechanics, the notion of a statistical quasi-particle, and transition towards the notion of fine thermodynamics are discussed

  10. The road to Maxwell's demon conceptual foundations of statistical mechanics

    CERN Document Server

    Hemmo, Meir

    2012-01-01

    Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

  11. Statistical mechanics of low-density parity-check codes

    Energy Technology Data Exchange (ETDEWEB)

    Kabashima, Yoshiyuki [Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)

    2004-02-13

    We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems. (topical review)

  12. Statistical mechanics of low-density parity-check codes

    International Nuclear Information System (INIS)

    Kabashima, Yoshiyuki; Saad, David

    2004-01-01

    We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multi-spin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems. (topical review)

  13. Gravitational lensing of gravitational waves: a statistical perspective

    Science.gov (United States)

    Li, Shun-Sheng; Mao, Shude; Zhao, Yuetong; Lu, Youjun

    2018-05-01

    In this paper, we study the strong gravitational lensing of gravitational waves (GWs) from a statistical perspective, with particular focus on the high frequency GWs from stellar binary black hole coalescences. These are most promising targets for ground-based detectors such as Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) and the proposed Einstein Telescope (ET) and can be safely treated under the geometrical optics limit for GW propagation. We perform a thorough calculation of the lensing rate, by taking account of effects caused by the ellipticity of lensing galaxies, lens environments, and magnification bias. We find that in certain GW source rate scenarios, we should be able to observe strongly lensed GW events once per year (˜1 yr-1) in the aLIGO survey at its design sensitivity; for the proposed ET survey, the rate could be as high as ˜80 yr-1. These results depend on the estimate of GW source abundance, and hence can be correspondingly modified with an improvement in our understanding of the merger rate of stellar binary black holes. We also compute the fraction of four-image lens systems in each survey, predicting it to be ˜30 per cent for the aLIGO survey and ˜6 per cent for the ET survey. Finally, we evaluate the possibility of missing some images due to the finite survey duration, by presenting the probability distribution of lensing time delays. We predict that this selection bias will be insignificant in future GW surveys, as most of the lens systems ({˜ } 90{per cent}) will have time delays less than ˜1 month, which will be far shorter than survey durations.

  14. A NEW STATISTICAL PERSPECTIVE TO THE COSMIC VOID DISTRIBUTION

    International Nuclear Information System (INIS)

    Pycke, J-R; Russell, E.

    2016-01-01

    In this study, we obtain the size distribution of voids as a three-parameter redshift-independent log-normal void probability function (VPF) directly from the Cosmic Void Catalog (CVC). Although many statistical models of void distributions are based on the counts in randomly placed cells, the log-normal VPF that we obtain here is independent of the shape of the voids due to the parameter-free void finder of the CVC. We use three void populations drawn from the CVC generated by the Halo Occupation Distribution (HOD) Mocks, which are tuned to three mock SDSS samples to investigate the void distribution statistically and to investigate the effects of the environments on the size distribution. As a result, it is shown that void size distributions obtained from the HOD Mock samples are satisfied by the three-parameter log-normal distribution. In addition, we find that there may be a relation between the hierarchical formation, skewness, and kurtosis of the log-normal distribution for each catalog. We also show that the shape of the three-parameter distribution from the samples is strikingly similar to the galaxy log-normal mass distribution obtained from numerical studies. This similarity between void size and galaxy mass distributions may possibly indicate evidence of nonlinear mechanisms affecting both voids and galaxies, such as large-scale accretion and tidal effects. Considering the fact that in this study, all voids are generated by galaxy mocks and show hierarchical structures in different levels, it may be possible that the same nonlinear mechanisms of mass distribution affect the void size distribution.

  15. Limiting processes in non-equilibrium classical statistical mechanics

    International Nuclear Information System (INIS)

    Jancel, R.

    1983-01-01

    After a recall of the basic principles of the statistical mechanics, the results of ergodic theory, the transient at the thermodynamic limit and his link with the transport theory near the equilibrium are analyzed. The fundamental problems put by the description of non-equilibrium macroscopic systems are investigated and the kinetic methods are stated. The problems of the non-equilibrium statistical mechanics are analyzed: irreversibility and coarse-graining, macroscopic variables and kinetic description, autonomous reduced descriptions, limit processes, BBGKY hierarchy, limit theorems [fr

  16. Generalized statistical mechanics approaches to earthquakes and tectonics

    Science.gov (United States)

    Papadakis, Giorgos; Michas, Georgios

    2016-01-01

    Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes. PMID:28119548

  17. Statistical physics of black holes as quantum-mechanical systems

    OpenAIRE

    Giddings, Steven B.

    2013-01-01

    Some basic features of black-hole statistical mechanics are investigated, assuming that black holes respect the principles of quantum mechanics. Care is needed in defining an entropy S_bh corresponding to the number of microstates of a black hole, given that the black hole interacts with its surroundings. An open question is then the relationship between this entropy and the Bekenstein-Hawking entropy S_BH. For a wide class of models with interactions needed to ensure unitary quantum evolutio...

  18. A statistical mechanics approach to mixing in stratified fluids

    OpenAIRE

    Venaille , Antoine; Gostiaux , Louis; Sommeria , Joël

    2016-01-01

    Accepted for the Journal of Fluid Mechanics; Predicting how much mixing occurs when a given amount of energy is injected into a Boussinesq fluid is a longstanding problem in stratified turbulence. The huge number of degrees of freedom involved in these processes renders extremely difficult a deterministic approach to the problem. Here we present a statistical mechanics approach yielding a prediction for a cumulative, global mixing efficiency as a function of a global Richard-son number and th...

  19. Molecular dynamics and Monte Carlo calculations in statistical mechanics

    International Nuclear Information System (INIS)

    Wood, W.W.; Erpenbeck, J.J.

    1976-01-01

    Monte Carlo and molecular dynamics calculations on statistical mechanical systems is reviewed giving some of the more significant recent developments. It is noted that the term molecular dynamics refers to the time-averaging technique for hard-core and square-well interactions and for continuous force-law interactions. Ergodic questions, methodology, quantum mechanical, Lorentz, and one-dimensional, hard-core, and square and triangular-well systems, short-range soft potentials, and other systems are included. 268 references

  20. SRB states and nonequilibrium statistical mechanics close to equilibrium

    OpenAIRE

    Gallavotti, Giovannni; Ruelle, David

    1996-01-01

    Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing previous results. In this framework we give a general proof of the Onsager reciprocity relations.

  1. Two-dimensional models in statistical mechanics and field theory

    International Nuclear Information System (INIS)

    Koberle, R.

    1980-01-01

    Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

  2. Mathematics of statistical mechanics and the chaos theory

    International Nuclear Information System (INIS)

    Llave, R. de la; Haro, A.

    2000-01-01

    Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs

  3. Braid group, knot theory and statistical mechanics II

    CERN Document Server

    Yang Chen Ning

    1994-01-01

    The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.

  4. Statistical mechanics and the evolution of polygenic quantitative traits

    NARCIS (Netherlands)

    Barton, N.H.; De Vladar, H.P.

    The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified

  5. Grassmann methods in lattice field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Bilgici, E.; Gattringer, C.; Huber, P.

    2006-01-01

    Full text: In two dimensions models of loops can be represented as simple Grassmann integrals. In our work we explore the generalization of these techniques to lattice field theories and statistical mechanic systems in three and four dimensions. We discuss possible strategies and applications for representations of loop and surface models as Grassmann integrals. (author)

  6. Geometry and topology in hamiltonian dynamics and statistical mechanics

    CERN Document Server

    Pettini, Marco

    2007-01-01

    Explores the foundations of hamiltonian dynamical systems and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. This book provides an overview of the research in the area. Using geometrical thinking to solve fundamental problems in these areas could be highly productive

  7. Statistical mechanics in the context of special relativity.

    Science.gov (United States)

    Kaniadakis, G

    2002-11-01

    In Ref. [Physica A 296, 405 (2001)], starting from the one parameter deformation of the exponential function exp(kappa)(x)=(sqrt[1+kappa(2)x(2)]+kappax)(1/kappa), a statistical mechanics has been constructed which reduces to the ordinary Boltzmann-Gibbs statistical mechanics as the deformation parameter kappa approaches to zero. The distribution f=exp(kappa)(-beta E+betamu) obtained within this statistical mechanics shows a power law tail and depends on the nonspecified parameter beta, containing all the information about the temperature of the system. On the other hand, the entropic form S(kappa)= integral d(3)p(c(kappa) f(1+kappa)+c(-kappa) f(1-kappa)), which after maximization produces the distribution f and reduces to the standard Boltzmann-Shannon entropy S0 as kappa-->0, contains the coefficient c(kappa) whose expression involves, beside the Boltzmann constant, another nonspecified parameter alpha. In the present effort we show that S(kappa) is the unique existing entropy obtained by a continuous deformation of S0 and preserving unaltered its fundamental properties of concavity, additivity, and extensivity. These properties of S(kappa) permit to determine unequivocally the values of the above mentioned parameters beta and alpha. Subsequently, we explain the origin of the deformation mechanism introduced by kappa and show that this deformation emerges naturally within the Einstein special relativity. Furthermore, we extend the theory in order to treat statistical systems in a time dependent and relativistic context. Then, we show that it is possible to determine in a self consistent scheme within the special relativity the values of the free parameter kappa which results to depend on the light speed c and reduces to zero as c--> infinity recovering in this way the ordinary statistical mechanics and thermodynamics. The statistical mechanics here presented, does not contain free parameters, preserves unaltered the mathematical and epistemological structure of

  8. Fundamental link between system theory and statistical mechanics

    International Nuclear Information System (INIS)

    Atmanspacher, H.; Scheingraber, H.

    1987-01-01

    A fundamental link between system theory and statistical mechanics has been found to be established by the Kolmogorov entropy. By this quantity the temporal evolution of dynamical systems can be classified into regular, chaotic, and stochastic processes. Since K represents a measure for the internal information creation rate of dynamical systems, it provides an approach to irreversibility. The formal relationship to statistical mechanics is derived by means of an operator formalism originally introduced by Prigogine. For a Liouville operator L and an information operator M tilde acting on a distribution in phase space, it is shown that i[L, M tilde] = KI (I = identity operator). As a first consequence of this equivalence, a relation is obtained between the chaotic correlation time of a system and Prigogine's concept of a finite duration of presence. Finally, the existence of chaos in quantum systems is discussed with respect to the existence of a quantum mechanical time operator

  9. Assessment Methods in Statistical Education An International Perspective

    CERN Document Server

    Bidgood, Penelope; Jolliffe, Flavia

    2010-01-01

    This book is a collaboration from leading figures in statistical education and is designed primarily for academic audiences involved in teaching statistics and mathematics. The book is divided in four sections: (1) Assessment using real-world problems, (2) Assessment statistical thinking, (3) Individual assessment (4) Successful assessment strategies.

  10. Statistical mechanics of two-dimensional and geophysical flows

    International Nuclear Information System (INIS)

    Bouchet, Freddy; Venaille, Antoine

    2012-01-01

    The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasi-geostrophic equations, the specificity of two-dimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations and mean field approach) and thermodynamic concepts (ensemble inequivalence and negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations is provided. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states. In this last case, forces and dissipation are in a statistical balance; fluxes of conserved quantity characterize the system and microcanonical or other equilibrium measures no longer describe the system.

  11. Statistical fracture mechanics approach to the strength of brittle rock

    International Nuclear Information System (INIS)

    Ratigan, J.L.

    1981-06-01

    Statistical fracture mechanics concepts used in the past for rock are critically reviewed and modifications are proposed which are warranted by (1) increased understanding of fracture provided by modern fracture mechanics and (2) laboratory test data both from the literature and from this research. Over 600 direct and indirect tension tests have been performed on three different rock types; Stripa Granite, Sierra White Granite and Carrara Marble. In several instances assumptions which are common in the literature were found to be invalid. A three parameter statistical fracture mechanics model with Mode I critical strain energy release rate as the variant is presented. Methodologies for evaluating the parameters in this model as well as the more commonly employed two parameter models are discussed. The experimental results and analysis of this research indicate that surfacially distributed flaws, rather than volumetrically distributed flaws are responsible for rupture in many testing situations. For several of the rock types tested, anisotropy (both in apparent tensile strength and size effect) precludes the use of contemporary statistical fracture mechanics models

  12. On the statistical-mechanical meaning of the Bousso bound

    International Nuclear Information System (INIS)

    Pesci, Alessandro

    2008-01-01

    The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property holds, emerging when the attempt is made to apply the bound to thin layers of matter. This property consists of the existence of an ultimate lower limit l* to the thickness of the slices for which a statistical-mechanical description is viable, depending l* on the thermodynamical variables which define the state of the system locally. This limiting scale, found to be in general much larger than the Planck scale (so that no Planck scale physics must be necessarily invoked to justify it), appears not related to gravity and this suggests that the generalized entropy bound is likely to be rooted on conventional flat-spacetime statistical mechanics, with the maximum admitted entropy being however actually determined also by gravity. Some examples of ideal fluids are considered in order to identify the mechanisms which can set a lower limit to the statistical-mechanical description and these systems are found to respect the lower limiting scale l*. The photon gas, in particular, appears to seemingly saturate this limiting scale and the consequence is drawn that for systems consisting of a single slice of a photon gas with thickness l*, the generalized Bousso bound is saturated. It is argued that this seems to open the way to a peculiar understanding of black hole entropy: if an entropy can meaningfully (i.e. with a second law) be assigned to a black hole, the value A/4 for it (where A is the area of the black hole) is required simply by (conventional) statistical mechanics coupled to general relativity

  13. Modeling CCN effects on tropical convection: An statistical perspective

    Science.gov (United States)

    Carrio, G. G.; Cotton, W. R.; Massie, S. T.

    2012-12-01

    This modeling study examines the response of tropical convection to the enhancement of CCN concentrations from a statistical perspective. The sensitivity runs were performed using RAMS version 6.0, covering almost the entire Amazonian Aerosol Characterization Experiment period (AMAZE, wet season of 2008). The main focus of the analysis was the indirect aerosol effects on the probability density functions (PDFs) of various cloud properties. RAMS was configured to work with four two-way interactive nested grids with 42 vertical levels and horizontal grid spacing of 150, 37.5, 7.5, and 1.5 km. Grids 2 and 3 were used to simulate the synoptic and mesoscale environments, while grid 4 was used to resolve deep convection. Comparisons were made using the finest grid with a domain size of 300 X 300km, approximately centered on the city of Manaus (3.1S, 60.01W). The vertical grid was stretched using with 75m spacing at the finest levels to provide better resolution within the first 1.5 km, and the model top extended to approximately 22 km above ground level. RAMS was initialized on February 10 2008 (00:00 UTC), the length of simulations was 32 days, and GSF data were used for initialization and nudging of the coarser-grid boundaries. The control run considered a CCN concentration of 300cm-3 while other several other simulations considered an influx of higher CCN concentrations (up to 1300/cc) . The latter concentration was observed near the end of the AMAZE project period. Both direct and indirect effects of these CCN particles were considered. Model output data (finest grid) every 15 min were used to compute the PDFs for each model level. When increasing aerosol concentrations, significant impacts were simulated for the PDFs of the water contents of various hydrometeors, vertical motions, area with precipitation, latent heat releases, among other quantities. In most cases, they exhibited a peculiar non-monotonic response similar to that seen in two previous studies of ours

  14. A κ-generalized statistical mechanics approach to income analysis

    International Nuclear Information System (INIS)

    Clementi, F; Gallegati, M; Kaniadakis, G

    2009-01-01

    This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of κ-generalized statistics, is derived that is particularly suitable for describing the whole spectrum of incomes, from the low–middle income region up to the high income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters is revealed as very powerful

  15. A κ-generalized statistical mechanics approach to income analysis

    Science.gov (United States)

    Clementi, F.; Gallegati, M.; Kaniadakis, G.

    2009-02-01

    This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of κ-generalized statistics, is derived that is particularly suitable for describing the whole spectrum of incomes, from the low-middle income region up to the high income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters is revealed as very powerful.

  16. Statistical Mechanics Analysis of ATP Binding to a Multisubunit Enzyme

    International Nuclear Information System (INIS)

    Zhang Yun-Xin

    2014-01-01

    Due to inter-subunit communication, multisubunit enzymes usually hydrolyze ATP in a concerted fashion. However, so far the principle of this process remains poorly understood. In this study, from the viewpoint of statistical mechanics, a simple model is presented. In this model, we assume that the binding of ATP will change the potential of the corresponding enzyme subunit, and the degree of this change depends on the state of its adjacent subunits. The probability of enzyme in a given state satisfies the Boltzmann's distribution. Although it looks much simple, this model can fit the recent experimental data of chaperonin TRiC/CCT well. From this model, the dominant state of TRiC/CCT can be obtained. This study provide a new way to understand biophysical processe by statistical mechanics analysis. (interdisciplinary physics and related areas of science and technology)

  17. Algebraic methods in statistical mechanics and quantum field theory

    CERN Document Server

    Emch, Dr Gérard G

    2009-01-01

    This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained descriptions of the mathematical methods.The four-part treatment begins with a survey of algebraic approaches to certain phys

  18. Statistical mechanics of complex neural systems and high dimensional data

    International Nuclear Information System (INIS)

    Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya

    2013-01-01

    Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? Second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks. (paper)

  19. Generalized Statistical Mechanics at the Onset of Chaos

    Directory of Open Access Journals (Sweden)

    Alberto Robledo

    2013-11-01

    Full Text Available Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii dynamical hierarchies with modular organization; and (iv limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.

  20. Applying contemporary philosophy in mathematics and statistics education : The perspective of inferentialism

    NARCIS (Netherlands)

    Schindler, Maike; Mackrell, Kate; Pratt, Dave; Bakker, A.

    2017-01-01

    Schindler, M., Mackrell, K., Pratt, D., & Bakker, A. (2017). Applying contemporary philosophy in mathematics and statistics education: The perspective of inferentialism. In G. Kaiser (Ed.). Proceedings of the 13th International Congress on Mathematical Education, ICME-13

  1. Realistic thermodynamic and statistical-mechanical measures for neural synchronization.

    Science.gov (United States)

    Kim, Sang-Yoon; Lim, Woochang

    2014-04-15

    Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential VG in computational neuroscience. The time-averaged fluctuation of VG plays the role of a "thermodynamic" order parameter O used for describing the synchrony-asynchrony transition in neural systems. Population spike synchronization may be well visualized in the raster plot of neural spikes. The degree of neural synchronization seen in the raster plot is well measured in terms of a "statistical-mechanical" spike-based measure Ms introduced by considering the occupation and the pacing patterns of spikes. The global potential VG is also used to give a reference global cycle for the calculation of Ms. Hence, VG becomes an important collective quantity because it is associated with calculation of both O and Ms. However, it is practically difficult to directly get VG in real experiments. To overcome this difficulty, instead of VG, we employ the instantaneous population spike rate (IPSR) which can be obtained in experiments, and develop realistic thermodynamic and statistical-mechanical measures, based on IPSR, to make practical characterization of the neural synchronization in both computational and experimental neuroscience. Particularly, more accurate characterization of weak sparse spike synchronization can be achieved in terms of realistic statistical-mechanical IPSR-based measure, in comparison with the conventional measure based on VG. Copyright © 2014. Published by Elsevier B.V.

  2. Statistical Mechanics of Disordered Systems - Series: Cambridge Series in Statistical and Probabilistic Mathematics (No. 18)

    Science.gov (United States)

    Bovier, Anton

    2006-06-01

    Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail. Comprehensive introduction to an active and fascinating area of research Clear exposition that builds to the state of the art in the mathematics of spin glasses Written by a well-known and active researcher in the field

  3. Introduction to nonequilibrium statistical mechanics with quantum field theory

    International Nuclear Information System (INIS)

    Kita, Takafumi

    2010-01-01

    In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

  4. Alternative derivations of the statistical mechanical distribution laws.

    Science.gov (United States)

    Wall, F T

    1971-08-01

    A new approach is presented for the derivation of statistical mechanical distribution laws. The derivations are accomplished by minimizing the Helmholtz free energy under constant temperature and volume, instead of maximizing the entropy under constant energy and volume. An alternative method involves stipulating equality of chemical potential, or equality of activity, for particles in different energy levels. This approach leads to a general statement of distribution laws applicable to all systems for which thermodynamic probabilities can be written. The methods also avoid use of the calculus of variations, Lagrangian multipliers, and Stirling's approximation for the factorial. The results are applied specifically to Boltzmann, Fermi-Dirac, and Bose-Einstein statistics. The special significance of chemical potential and activity is discussed for microscopic systems.

  5. Thermodynamics and statistical mechanics. [thermodynamic properties of gases

    Science.gov (United States)

    1976-01-01

    The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

  6. Is quantum theory a form of statistical mechanics?

    Science.gov (United States)

    Adler, S. L.

    2007-05-01

    We give a review of the basic themes of my recent book: Adler S L 2004 Quantum Theory as an Emergent Phenomenon (Cambridge: Cambridge University Press). We first give motivations for considering the possibility that quantum mechanics is not exact, but is instead an accurate asymptotic approximation to a deeper level theory. For this deeper level, we propose a non-commutative generalization of classical mechanics, that we call "trace dynamics", and we give a brief survey of how it works, considering for simplicity only the bosonic case. We then discuss the statistical mechanics of trace dynamics and give our argument that with suitable approximations, the Ward identities for trace dynamics imply that ensemble averages in the canonical ensemble correspond to Wightman functions in quantum field theory. Thus, quantum theory emerges as the statistical thermodynamics of trace dynamics. Finally, we argue that Brownian motion corrections to this thermodynamics lead to stochastic corrections to the Schrödinger equation, of the type that have been much studied in the "continuous spontaneous localization" model of objective state vector reduction. In appendices to the talk, we give details of the existence of a conserved operator in trace dynamics that encodes the structure of the canonical algebra, of the derivation of the Ward identities, and of the proof that the stochastically-modified Schrödinger equation leads to state vector reduction with Born rule probabilities.

  7. Statistical mechanical analysis of LMFBR fuel cladding tubes

    International Nuclear Information System (INIS)

    Poncelet, J.-P.; Pay, A.

    1977-01-01

    The most important design requirement on fuel pin cladding for LMFBR's is its mechanical integrity. Disruptive factors include internal pressure from mixed oxide fuel fission gas release, thermal stresses and high temperature creep, neutron-induced differential void-swelling as a source of stress in the cladding and irradiation creep of stainless steel material, corrosion by fission products. Under irradiation these load-restraining mechanisms are accentuated by stainless steel embrittlement and strength alterations. To account for the numerous uncertainties involved in the analysis by theoretical models and computer codes statistical tools are unavoidably requested, i.e. Monte Carlo simulation methods. Thanks to these techniques, uncertainties in nominal characteristics, material properties and environmental conditions can be linked up in a correct way and used for a more accurate conceptual design. First, a thermal creep damage index is set up through a sufficiently sophisticated clad physical analysis including arbitrary time dependence of power and neutron flux as well as effects of sodium temperature, burnup and steel mechanical behavior. Although this strain limit approach implies a more general but time consuming model., on the counterpart the net output is improved and e.g. clad temperature, stress and strain maxima may be easily assessed. A full spectrum of variables are statistically treated to account for their probability distributions. Creep damage probability may be obtained and can contribute to a quantitative fuel probability estimation

  8. Representative volume size: A comparison of statistical continuum mechanics and statistical physics

    Energy Technology Data Exchange (ETDEWEB)

    AIDUN,JOHN B.; TRUCANO,TIMOTHY G.; LO,CHI S.; FYE,RICHARD M.

    1999-05-01

    In this combination background and position paper, the authors argue that careful work is needed to develop accurate methods for relating the results of fine-scale numerical simulations of material processes to meaningful values of macroscopic properties for use in constitutive models suitable for finite element solid mechanics simulations. To provide a definite context for this discussion, the problem is couched in terms of the lack of general objective criteria for identifying the size of the representative volume (RV) of a material. The objective of this report is to lay out at least the beginnings of an approach for applying results and methods from statistical physics to develop concepts and tools necessary for determining the RV size, as well as alternatives to RV volume-averaging for situations in which the RV is unmanageably large. The background necessary to understand the pertinent issues and statistical physics concepts is presented.

  9. The Phenomena Implied by the New Economy from Statistics Perspective

    Directory of Open Access Journals (Sweden)

    Giani GRADINARU

    2006-01-01

    Full Text Available The rapidity of the informational society to transform into an information and knowledge society determines a perspective on the New Economy which would consider the Internet market and the effect of the Internet information on all economic agents, and the effect of knowledge as economic factor, which imposes the recognition of intangible goods, in general, in the making of economic value as well as the requirements for achieving a lasting society, which cannot be possible but inside the knowledge society, and which would impose in the society economy new technologies, and most important, changes in orientation according to the classic economic thinking.

  10. A statistical physics perspective on criticality in financial markets

    International Nuclear Information System (INIS)

    Bury, Thomas

    2013-01-01

    Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believed to be critical by analogy to physical systems, but little statistically founded evidence has been given. Through a data-based methodology and comparison to simulations inspired by the statistical physics of complex systems, we show that the Dow Jones and index sets are not rigorously critical. However, financial systems are closer to criticality in the crash neighborhood. (paper)

  11. Methodological difficulties of conducting agroecological studies from a statistical perspective

    DEFF Research Database (Denmark)

    Bianconi, A.; Dalgaard, Tommy; Manly, Bryan F J

    2013-01-01

    Statistical methods for analysing agroecological data might not be able to help agroecologists to solve all of the current problems concerning crop and animal husbandry, but such methods could well help agroecologists to assess, tackle, and resolve several agroecological issues in a more reliable...... and accurate manner. Therefore, our goal in this paper is to discuss the importance of statistical tools for alternative agronomic approaches, because alternative approaches, such as organic farming, should not only be promoted by encouraging farmers to deploy agroecological techniques, but also by providing...

  12. Nonequilibrium statistical mechanics and stochastic thermodynamics of small systems

    International Nuclear Information System (INIS)

    Tu Zhanchun

    2014-01-01

    Thermodynamics is an old subject. The research objects in conventional thermodynamics are macroscopic systems with huge number of particles. In recent 30 years, thermodynamics of small systems is a frontier topic in physics. Here we introduce nonequilibrium statistical mechanics and stochastic thermodynamics of small systems. As a case study, we construct a Canot-like cycle of a stochastic heat engine with a single particle controlled by a time-dependent harmonic potential. We find that the efficiency at maximum power is 1 - √T c /T h , where Tc and Th are the temperatures of cold bath and hot bath, respectively. (author)

  13. Statistical mechanics of attractor neural network models with synaptic depression

    International Nuclear Information System (INIS)

    Igarashi, Yasuhiko; Oizumi, Masafumi; Otsubo, Yosuke; Nagata, Kenji; Okada, Masato

    2009-01-01

    Synaptic depression is known to control gain for presynaptic inputs. Since cortical neurons receive thousands of presynaptic inputs, and their outputs are fed into thousands of other neurons, the synaptic depression should influence macroscopic properties of neural networks. We employ simple neural network models to explore the macroscopic effects of synaptic depression. Systems with the synaptic depression cannot be analyzed due to asymmetry of connections with the conventional equilibrium statistical-mechanical approach. Thus, we first propose a microscopic dynamical mean field theory. Next, we derive macroscopic steady state equations and discuss the stabilities of steady states for various types of neural network models.

  14. From inverse problems to learning: a Statistical Mechanics approach

    Science.gov (United States)

    Baldassi, Carlo; Gerace, Federica; Saglietti, Luca; Zecchina, Riccardo

    2018-01-01

    We present a brief introduction to the statistical mechanics approaches for the study of inverse problems in data science. We then provide concrete new results on inferring couplings from sampled configurations in systems characterized by an extensive number of stable attractors in the low temperature regime. We also show how these result are connected to the problem of learning with realistic weak signals in computational neuroscience. Our techniques and algorithms rely on advanced mean-field methods developed in the context of disordered systems.

  15. Statistical mechanics of socio-economic systems with heterogeneous agents

    International Nuclear Information System (INIS)

    De Martino, Andrea; Marsili, Matteo

    2006-01-01

    We review the statistical mechanics approach to the study of the emerging collective behaviour of systems of heterogeneous interacting agents. The general framework is presented through examples in such contexts as ecosystem dynamics and traffic modelling. We then focus on the analysis of the optimal properties of large random resource-allocation problems and on Minority Games and related models of speculative trading in financial markets, discussing a number of extensions including multi-asset models, majority games and models with asymmetric information. Finally, we summarize the main conclusions and outline the major open problems and limitations of the approach. (topical review)

  16. Rural farmers' perspectives on stock theft: police crime statistics ...

    African Journals Online (AJOL)

    Rural farmers are not only facing challenges of severe drought blamed on the El Nino weather pattern, but the stock theft as well. The South African Police's annual crime statistics report and surveys indicates that rural livestock farmers are mostly affected by stock theft in South Africa. The costs paid by these farmers to ...

  17. Statistical mechanical analysis of LMFBR fuel cladding tubes

    International Nuclear Information System (INIS)

    Poncelet, J.-P.; Pay, A.

    1977-01-01

    The most important design requirement on fuel pin cladding for LMFBR's is its mechanical integrity. Disruptive factors include internal pressure from mixed oxide fuel fission gas release, thermal stresses and high temperature creep, neutron-induced differential void-swelling as a source of stress in the cladding and irradiation creep of stainless steel material, corrosion by fission products. Under irradiation these load-restraining mechanisms are accentuated by stainless steel embrittlement and strength alterations. To account for the numerous uncertainties involved in the analysis by theoretical models and computer codes statistical tools are unavoidably requested, i.e. Monte Carlo simulation methods. Thanks to these techniques, uncertainties in nominal characteristics, material properties and environmental conditions can be linked up in a correct way and used for a more accurate conceptual design. (Auth.)

  18. Multiple-shock initiation via statistical crack mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Dienes, J.K.; Kershner, J.D.

    1998-12-31

    Statistical Crack Mechanics (SCRAM) is a theoretical approach to the behavior of brittle materials that accounts for the behavior of an ensemble of microcracks, including their opening, shear, growth, and coalescence. Mechanical parameters are based on measured strain-softening behavior. In applications to explosive and propellant sensitivity it is assumed that closed cracks act as hot spots, and that the heating due to interfacial friction initiates reactions which are modeled as one-dimensional heat flow with an Arrhenius source term, and computed in a subscale grid. Post-ignition behavior of hot spots is treated with the burn model of Ward, Son and Brewster. Numerical calculations using SCRAM-HYDROX are compared with the multiple-shock experiments of Mulford et al. in which the particle velocity in PBX 9501 is measured with embedded wires, and reactions are initiated and quenched.

  19. Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

    International Nuclear Information System (INIS)

    Remler, E.A.

    1977-01-01

    A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

  20. Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

    Science.gov (United States)

    Budiyono, Agung; Rohrlich, Daniel

    2017-11-03

    Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

  1. Introduction to quantum mechanics a time-dependent perspective

    CERN Document Server

    Tannor, David J

    2007-01-01

    "Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.

  2. Statistical mechanics in the context of special relativity. II.

    Science.gov (United States)

    Kaniadakis, G

    2005-09-01

    The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

  3. Statistical mechanics of the vertex-cover problem

    Science.gov (United States)

    Hartmann, Alexander K.; Weigt, Martin

    2003-10-01

    We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping the VC to a hard-core lattice gas, and then applying techniques such as the replica trick or the cavity approach. Using these methods, the phase diagram of the VC could be obtained exactly for connectivities c e, the solution of the VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the VC. Finally, we describe recent results for the VC when studied on other ensembles of finite- and infinite-dimensional graphs.

  4. Statistical mechanics of the vertex-cover problem

    International Nuclear Information System (INIS)

    Hartmann, Alexander K; Weigt, Martin

    2003-01-01

    We review recent progress in the study of the vertex-cover problem (VC). The VC belongs to the class of NP-complete graph theoretical problems, which plays a central role in theoretical computer science. On ensembles of random graphs, VC exhibits a coverable-uncoverable phase transition. Very close to this transition, depending on the solution algorithm, easy-hard transitions in the typical running time of the algorithms occur. We explain a statistical mechanics approach, which works by mapping the VC to a hard-core lattice gas, and then applying techniques such as the replica trick or the cavity approach. Using these methods, the phase diagram of the VC could be obtained exactly for connectivities c e, the solution of the VC exhibits full replica symmetry breaking. The statistical mechanics approach can also be used to study analytically the typical running time of simple complete and incomplete algorithms for the VC. Finally, we describe recent results for the VC when studied on other ensembles of finite- and infinite-dimensional graphs

  5. Statistical mechanics of learning orthogonal signals for general covariance models

    International Nuclear Information System (INIS)

    Hoyle, David C

    2010-01-01

    Statistical mechanics techniques have proved to be useful tools in quantifying the accuracy with which signal vectors are extracted from experimental data. However, analysis has previously been limited to specific model forms for the population covariance C, which may be inappropriate for real world data sets. In this paper we obtain new statistical mechanical results for a general population covariance matrix C. For data sets consisting of p sample points in R N we use the replica method to study the accuracy of orthogonal signal vectors estimated from the sample data. In the asymptotic limit of N,p→∞ at fixed α = p/N, we derive analytical results for the signal direction learning curves. In the asymptotic limit the learning curves follow a single universal form, each displaying a retarded learning transition. An explicit formula for the location of the retarded learning transition is obtained and we find marked variation in the location of the retarded learning transition dependent on the distribution of population covariance eigenvalues. The results of the replica analysis are confirmed against simulation

  6. Statistical learning: a powerful mechanism that operates by mere exposure.

    Science.gov (United States)

    Aslin, Richard N

    2017-01-01

    How do infants learn so rapidly and with little apparent effort? In 1996, Saffran, Aslin, and Newport reported that 8-month-old human infants could learn the underlying temporal structure of a stream of speech syllables after only 2 min of passive listening. This demonstration of what was called statistical learning, involving no instruction, reinforcement, or feedback, led to dozens of confirmations of this powerful mechanism of implicit learning in a variety of modalities, domains, and species. These findings reveal that infants are not nearly as dependent on explicit forms of instruction as we might have assumed from studies of learning in which children or adults are taught facts such as math or problem solving skills. Instead, at least in some domains, infants soak up the information around them by mere exposure. Learning and development in these domains thus appear to occur automatically and with little active involvement by an instructor (parent or teacher). The details of this statistical learning mechanism are discussed, including how exposure to specific types of information can, under some circumstances, generalize to never-before-observed information, thereby enabling transfer of learning. WIREs Cogn Sci 2017, 8:e1373. doi: 10.1002/wcs.1373 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

  7. Statistical methods in the mechanical design of fuel assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Radsak, C.; Streit, D.; Muench, C.J. [AREVA NP GmbH, Erlangen (Germany)

    2013-07-01

    The mechanical design of a fuel assembly is still being mainly performed in a de terministic way. This conservative approach is however not suitable to provide a realistic quantification of the design margins with respect to licensing criter ia for more and more demanding operating conditions (power upgrades, burnup increase,..). This quantification can be provided by statistical methods utilizing all available information (e.g. from manufacturing, experience feedback etc.) of the topic under consideration. During optimization e.g. of the holddown system certain objectives in the mechanical design of a fuel assembly (FA) can contradict each other, such as sufficient holddown forces enough to prevent fuel assembly lift-off and reducing the holddown forces to minimize axial loads on the fuel assembly structure to ensure no negative effect on the control rod movement.By u sing a statistical method the fuel assembly design can be optimized much better with respect to these objectives than it would be possible based on a deterministic approach. This leads to a more realistic assessment and safer way of operating fuel assemblies. Statistical models are defined on the one hand by the quanti le that has to be maintained concerning the design limit requirements (e.g. one FA quantile) and on the other hand by the confidence level which has to be met. Using the above example of the holddown force, a feasible quantile can be define d based on the requirement that less than one fuel assembly (quantile > 192/19 3 [%] = 99.5 %) in the core violates the holddown force limit w ith a confidence of 95%. (orig.)

  8. A statistical perspective on association studies of psychiatric disorders

    DEFF Research Database (Denmark)

    Foldager, Leslie

    2014-01-01

    Gene-gene (GxG) and gene-environment (GxE) interactions likely play an important role in the aetiology of complex diseases like psychiatric disorders. Thus, we aim at investigating methodological aspects of and apply methods from statistical genetics taking interactions into account. In addition we...... genes and maternal infection by virus. Paper 3 presents the initial steps (mainly data construction) of an ongoing simulation study aiming at guiding decisions by comparing methods for GxE interaction analysis including both traditional two-step logistic regression, exhaustive searches using efficient...... these markers. However, the validity of the identified haplotypes is also checked by inferring phased haplotypes from genotypes. Haplotype analysis is also used in paper 5 which is otherwise an example of a focused approach to narrow down a previously found signal to search for more precise positions of disease...

  9. From statistic mechanic outside equilibrium to transport equations

    International Nuclear Information System (INIS)

    Balian, R.

    1995-01-01

    This lecture notes give a synthetic view on the foundations of non-equilibrium statistical mechanics. The purpose is to establish the transport equations satisfied by the relevant variables, starting from the microscopic dynamics. The Liouville representation is introduced, and a projection associates with any density operator , for given choice of relevant observables, a reduced density operator. An exact integral-differential equation for the relevant variables is thereby derived. A short-memory approximation then yields the transport equations. A relevant entropy which characterizes the coarseness of the description is associated with each level of description. As an illustration, the classical gas, with its three levels of description and with the Chapman-Enskog method, is discussed. (author). 3 figs., 5 refs

  10. Statistical mechanics of lattice systems a concrete mathematical introduction

    CERN Document Server

    Friedli, Sacha

    2017-01-01

    This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie–Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin–Wagner and Lee–Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov–Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make i...

  11. Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

    Energy Technology Data Exchange (ETDEWEB)

    Alamino, Roberto C; Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)

    2007-10-12

    Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases.

  12. Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

    International Nuclear Information System (INIS)

    Alamino, Roberto C; Saad, David

    2007-01-01

    Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases

  13. Statistical mechanics of the fashion game on random networks

    International Nuclear Information System (INIS)

    Sun, YiFan

    2016-01-01

    A model of fashion on networks is studied. This model consists of two groups of agents that are located on a network and have opposite viewpoints towards being fashionable: behaving consistently with either the majority or the minority of adjacent agents. Checking whether the fashion game has a pure Nash equilibrium (pure NE) is a non-deterministic polynomial complete problem. Using replica-symmetric mean field theory, the largest proportion of satisfied agents and the region where at least one pure NE should exist are determined for several types of random networks. Furthermore, a quantitive analysis of the asynchronous best response dynamics yields the phase diagram of existence and detectability of pure NE in the fashion game on some random networks. (paper: classical statistical mechanics, equilibrium and non-equilibrium).

  14. Statistical mechanics of sparse generalization and graphical model selection

    International Nuclear Information System (INIS)

    Lage-Castellanos, Alejandro; Pagnani, Andrea; Weigt, Martin

    2009-01-01

    One of the crucial tasks in many inference problems is the extraction of an underlying sparse graphical model from a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penalty term, the L p norm of the model parameters, with p≤1 for efficient dilution. Here we propose a statistical mechanics analysis of the problem in the setting of perceptron memorization and generalization. Using a replica approach, we are able to evaluate the relative performance of naive dilution (obtained by learning without dilution, following by applying a threshold to the model parameters), L 1 dilution (which is frequently used in convex optimization) and L 0 dilution (which is optimal but computationally hard to implement). Whereas both L p diluted approaches clearly outperform the naive approach, we find a small region where L 0 works almost perfectly and strongly outperforms the simpler to implement L 1 dilution

  15. Anomalous behavior of q-averages in nonextensive statistical mechanics

    International Nuclear Information System (INIS)

    Abe, Sumiyoshi

    2009-01-01

    A generalized definition of average, termed the q-average, is widely employed in the field of nonextensive statistical mechanics. Recently, it has however been pointed out that such an average value may behave unphysically under specific deformations of probability distributions. Here, the following three issues are discussed and clarified. Firstly, the deformations considered are physical and may be realized experimentally. Secondly, in view of the thermostatistics, the q-average is unstable in both finite and infinite discrete systems. Thirdly, a naive generalization of the discussion to continuous systems misses a point, and a norm better than the L 1 -norm should be employed for measuring the distance between two probability distributions. Consequently, stability of the q-average is shown not to be established in all of the cases

  16. Statistical mechanics of the interacting Yang-Mills instanton gas

    International Nuclear Information System (INIS)

    Ilgenfritz, E.-M.; Mueller-Preussker, M.

    1980-01-01

    Within the framework of the dilute gas approximation the instanton gas with dipole-like interaction is studied, including hard-core repulsion necessarily implied by the consistency of this approximation. A new, selfconsistent scheme is obtained of instanton calculations provided by a cooperative suppression of large instantons instead of the usual ad hoc infrared cut-off. Diluteness is better under control by a single, regularization prescription independent parameter. Functional methods known from statistical mechanics are used to treat the hard-core and dipole interactions simultaneously. The permeability of the instanton gas is calculated and used to discuss the Gell-Mann-Low β-function in the intermediate coupling range. The results are confronted with recent lattice calculations

  17. On the statistical mechanics of species abundance distributions.

    Science.gov (United States)

    Bowler, Michael G; Kelly, Colleen K

    2012-09-01

    A central issue in ecology is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to species abundance distributions (SADs) shows that simple ecological properties could account for the near universal features observed. These properties are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth and death rates. They underpin the neutral theory of Hubbell (2001), the master equation approach of Volkov et al. (2003, 2005) and the idiosyncratic (extreme niche) theory of Pueyo et al. (2007); they result in an underlying log series SAD, regardless of neutral or niche dynamics. The success of statistical mechanics in this application implies that communities are in dynamic equilibrium and hence that niches must be flexible and that temporal fluctuations on all sorts of scales are likely to be important in community structure. Copyright © 2012 Elsevier Inc. All rights reserved.

  18. Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

    International Nuclear Information System (INIS)

    Kogut, J.B.

    1984-01-01

    Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

  19. Greenhouse mechanization: State of the art and future perspective

    NARCIS (Netherlands)

    Henten, van E.

    2006-01-01

    This paper reviews the state of the art and future perspective of greenhouse mechanization. Driving forces for mechanization are identified. Dutch greenhouse crop production is used as an example. Analysis of a generic crop production process combined with a review of the state of the art in

  20. Phloem physics: mechanisms, constraints, and perspectives.

    Science.gov (United States)

    Jensen, Kaare H

    2018-04-13

    Plants have evolved specialized vascular tissues for the distribution of energy, water, nutrients, and for communication. The phloem transports sugars from photosynthetic source regions (e.g. mature leaves) to sugar sinks (e.g. developing tissues such as buds, flowers, roots). Moreover, chemical signals such as hormones, RNAs and proteins also move in the phloem. Basic physical processes strongly limit phloem anatomy and function. This paper provides an overview of recent research and perspectives on phloem biomechanics and the physical constraints relevant to sugar transport in plants. Copyright © 2018 Elsevier Ltd. All rights reserved.

  1. Statistical characteristics of mechanical heart valve cavitation in accelerated testing.

    Science.gov (United States)

    Wu, Changfu; Hwang, Ned H C; Lin, Yu-Kweng M

    2004-07-01

    Cavitation damage has been observed on mechanical heart valves (MHVs) undergoing accelerated testing. Cavitation itself can be modeled as a stochastic process, as it varies from beat to beat of the testing machine. This in-vitro study was undertaken to investigate the statistical characteristics of MHV cavitation. A 25-mm St. Jude Medical bileaflet MHV (SJM 25) was tested in an accelerated tester at various pulse rates, ranging from 300 to 1,000 bpm, with stepwise increments of 100 bpm. A miniature pressure transducer was placed near a leaflet tip on the inflow side of the valve, to monitor regional transient pressure fluctuations at instants of valve closure. The pressure trace associated with each beat was passed through a 70 kHz high-pass digital filter to extract the high-frequency oscillation (HFO) components resulting from the collapse of cavitation bubbles. Three intensity-related measures were calculated for each HFO burst: its time span; its local root-mean-square (LRMS) value; and the area enveloped by the absolute value of the HFO pressure trace and the time axis, referred to as cavitation impulse. These were treated as stochastic processes, of which the first-order probability density functions (PDFs) were estimated for each test rate. Both the LRMS value and cavitation impulse were log-normal distributed, and the time span was normal distributed. These distribution laws were consistent at different test rates. The present investigation was directed at understanding MHV cavitation as a stochastic process. The results provide a basis for establishing further the statistical relationship between cavitation intensity and time-evolving cavitation damage on MHV surfaces. These data are required to assess and compare the performance of MHVs of different designs.

  2. The role of angular momentum conservation law in statistical mechanics

    Directory of Open Access Journals (Sweden)

    I.M. Dubrovskii

    2008-12-01

    Full Text Available Within the limits of Khinchin ideas [A.Y. Khinchin, Mathematical Foundation of Statistical Mechanics. NY, Ed. Dover, 1949] the importance of momentum and angular momentum conservation laws was analyzed for two cases: for uniform magnetic field and when magnetic field is absent. The law of momentum conservation does not change the density of probability distribution in both cases, just as it is assumed in the conventional theory. It is shown that in systems where the kinetic energy depends only on particle momenta canonically conjugated with Cartesian coordinates being their diagonal quadric form,the angular momentum conservation law changes the density of distribution of the system only in case the full angular momentum of a system is not equal to zero. In the gas of charged particles in a uniform magnetic field the density of distribution also varies if the angular momentum is zero [see Dubrovskii I.M., Condensed Matter Physics, 2206, 9, 23]. Two-dimensional gas of charged particles located within a section of an endless strip filled with gas in magnetic field is considered. Under such conditions the angular momentum is not conserved. Directional particle flows take place close to the strip boundaries, and, as a consequence, the phase trajectory of the considered set of particles does not remain within the limited volume of the phase space. In order to apply a statistical thermodynamics method, it was suggested to consider near-boundary trajectories relative to a reference system that moves uniformly. It was shown that if the diameter of an orbit having average thermal energy is much smaller than a strip width, the corrections to thermodynamic functions are small depending on magnetic field. Only the average velocity of near-boundary particles that form near-boundary electric currents creating the paramagnetic moment turn out to be essential.

  3. Multi-agent Negotiation Mechanisms for Statistical Target Classification in Wireless Multimedia Sensor Networks

    Directory of Open Access Journals (Sweden)

    Sheng Wang

    2007-10-01

    Full Text Available The recent availability of low cost and miniaturized hardware has allowedwireless sensor networks (WSNs to retrieve audio and video data in real worldapplications, which has fostered the development of wireless multimedia sensor networks(WMSNs. Resource constraints and challenging multimedia data volume makedevelopment of efficient algorithms to perform in-network processing of multimediacontents imperative. This paper proposes solving problems in the domain of WMSNs fromthe perspective of multi-agent systems. The multi-agent framework enables flexible networkconfiguration and efficient collaborative in-network processing. The focus is placed ontarget classification in WMSNs where audio information is retrieved by microphones. Todeal with the uncertainties related to audio information retrieval, the statistical approachesof power spectral density estimates, principal component analysis and Gaussian processclassification are employed. A multi-agent negotiation mechanism is specially developed toefficiently utilize limited resources and simultaneously enhance classification accuracy andreliability. The negotiation is composed of two phases, where an auction based approach isfirst exploited to allocate the classification task among the agents and then individual agentdecisions are combined by the committee decision mechanism. Simulation experiments withreal world data are conducted and the results show that the proposed statistical approachesand negotiation mechanism not only reduce memory and computation requi

  4. Multi-agent Negotiation Mechanisms for Statistical Target Classification in Wireless Multimedia Sensor Networks

    Science.gov (United States)

    Wang, Xue; Bi, Dao-wei; Ding, Liang; Wang, Sheng

    2007-01-01

    The recent availability of low cost and miniaturized hardware has allowed wireless sensor networks (WSNs) to retrieve audio and video data in real world applications, which has fostered the development of wireless multimedia sensor networks (WMSNs). Resource constraints and challenging multimedia data volume make development of efficient algorithms to perform in-network processing of multimedia contents imperative. This paper proposes solving problems in the domain of WMSNs from the perspective of multi-agent systems. The multi-agent framework enables flexible network configuration and efficient collaborative in-network processing. The focus is placed on target classification in WMSNs where audio information is retrieved by microphones. To deal with the uncertainties related to audio information retrieval, the statistical approaches of power spectral density estimates, principal component analysis and Gaussian process classification are employed. A multi-agent negotiation mechanism is specially developed to efficiently utilize limited resources and simultaneously enhance classification accuracy and reliability. The negotiation is composed of two phases, where an auction based approach is first exploited to allocate the classification task among the agents and then individual agent decisions are combined by the committee decision mechanism. Simulation experiments with real world data are conducted and the results show that the proposed statistical approaches and negotiation mechanism not only reduce memory and computation requirements in WMSNs but also significantly enhance classification accuracy and reliability. PMID:28903223

  5. Irradiation creep mechanism: an experimental perspective

    International Nuclear Information System (INIS)

    Garner, F.A.; Gelles, D.S.

    1988-01-01

    The object of this effort is to determine the mechanisms involved in radiation-induced deformation of structural materials and to apply these insights for extrapolation of available fast reactor data to fusion-relevant conditions. An extensive review was conducted of a variety of radiation-induced microstructural data, searching for microstructural records of various irradiation creep mechanisms. It was found that the stress-affected evolution of dislocation microstructure during irradiation is considerably more complex than envisioned in most theoretical modeling studies, particularly in the types of interactive feedback mechanisms operating. Reasonably conclusive evidence was found for a SIPA-type mechanism (stress-induced preferential absorption) operating on both Frank loops and network dislocations. Stress-induced preferential loop nucleation (SIPN) processes may also participate but are thought to be overshadowed by the stronger action of the SIPA-type processes operating on Frank interstitial loops. It was not possible to discern from microstructural evidence between second-order SIPA and first-order SIPA mechanisms, the latter arising from anisotropic diffusion. Evidence was presented, however, that validates the operation of stress-induced preferential unfaulting of Frank loops and stress-induced growth of previously stressed material following removal of applied stress. Dislocation glide mechanisms are also participating but the rate appears to be controlled by SIPA-type climb processes. Applied stresses were shown to generate very anisotropic distributions of Burgers vector in the irradiation-induced microstructure. 108 references, 15 figures, 1 table

  6. Statistical mechanics of high-density bond percolation

    Science.gov (United States)

    Timonin, P. N.

    2018-05-01

    High-density (HD) percolation describes the percolation of specific κ -clusters, which are the compact sets of sites each connected to κ nearest filled sites at least. It takes place in the classical patterns of independently distributed sites or bonds in which the ordinary percolation transition also exists. Hence, the study of series of κ -type HD percolations amounts to the description of classical clusters' structure for which κ -clusters constitute κ -cores nested one into another. Such data are needed for description of a number of physical, biological, and information properties of complex systems on random lattices, graphs, and networks. They range from magnetic properties of semiconductor alloys to anomalies in supercooled water and clustering in biological and social networks. Here we present the statistical mechanics approach to study HD bond percolation on an arbitrary graph. It is shown that the generating function for κ -clusters' size distribution can be obtained from the partition function of the specific q -state Potts-Ising model in the q →1 limit. Using this approach we find exact κ -clusters' size distributions for the Bethe lattice and Erdos-Renyi graph. The application of the method to Euclidean lattices is also discussed.

  7. Nonextensive statistical mechanics: a brief review of its present status

    Directory of Open Access Journals (Sweden)

    CONSTANTINO TSALLIS

    2002-09-01

    Full Text Available We briefly review the present status of nonextensive statistical mechanics. We focus on (i the central equations of the formalism, (ii the most recent applications in physics and other sciences, (iii the a priori determination (from microscopic dynamics of the entropic index q for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative and long-range interacting many-body hamiltonian classical systems.Revisamos sumariamente o estado presente da mecânica estatística não-extensiva. Focalizamos em (i as equacões centrais do formalismo; (ii as aplicações mais recentes na física e em outras ciências, (iii a determinação a priori (da dinâmica microscópica do índice entrópico q para duas classes importantes de sistemas físicos, a saber, mapas de baixa dimensão (tanto dissipativos quanto conservativos e sistemas clássicos hamiltonianos de muitos corpos com interações de longo alcance.

  8. Universal biology and the statistical mechanics of early life

    Science.gov (United States)

    Goldenfeld, Nigel; Biancalani, Tommaso; Jafarpour, Farshid

    2017-11-01

    All known life on the Earth exhibits at least two non-trivial common features: the canonical genetic code and biological homochirality, both of which emerged prior to the Last Universal Common Ancestor state. This article describes recent efforts to provide a narrative of this epoch using tools from statistical mechanics. During the emergence of self-replicating life far from equilibrium in a period of chemical evolution, minimal models of autocatalysis show that homochirality would have necessarily co-evolved along with the efficiency of early-life self-replicators. Dynamical system models of the evolution of the genetic code must explain its universality and its highly refined error-minimization properties. These have both been accounted for in a scenario where life arose from a collective, networked phase where there was no notion of species and perhaps even individuality itself. We show how this phase ultimately terminated during an event sometimes known as the Darwinian transition, leading to the present epoch of tree-like vertical descent of organismal lineages. These examples illustrate concrete examples of universal biology: the quest for a fundamental understanding of the basic properties of living systems, independent of precise instantiation in chemistry or other media. This article is part of the themed issue 'Reconceptualizing the origins of life'.

  9. The statistical mechanics of vortex-acoustic ion wave turbulence

    International Nuclear Information System (INIS)

    Giles, M.J.

    1980-01-01

    The equilibrium statistical mechanics of electrostatic ion wave turbulence is studied within the framework of a continuum ion flow with adiabatic electrons. The wave field consists in general of two components, namely ion-acoustic and ion vortex modes. It is shown that the latter can significantly affect the equilibria on account of their ability both to emit and to scatter ion sound. Exact equilibria for the vortex-acoustic wave field are given in terms of a canonical distribution and the correlation functions are expressed in terms of a generating functional. Detailed calculations are carried out for the case in which the dominant coupling is an indirect interaction of the vortex modes mediated by the sound field. An equation for the spectrum of the vortex modes is obtained for this case, which is shown to possess a simple exact solution. This solution shows that the spectrum of fluctuations changes considerably as the total energy increases. Condensed vortex states could occur in the plasma sheet of the earth's magnetosphere and it is shown that the predicted ratio of the mean ion energy to the mean electron energy is consistent with the trend of observed values. (author)

  10. Statistical mechanics and stability of random lattice field theory

    International Nuclear Information System (INIS)

    Baskaran, G.

    1984-01-01

    The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities. (orig.)

  11. Statistical mechanics approach to 1-bit compressed sensing

    International Nuclear Information System (INIS)

    Xu, Yingying; Kabashima, Yoshiyuki

    2013-01-01

    Compressed sensing is a framework that makes it possible to recover an N-dimensional sparse vector x∈R N from its linear transformation y∈R M of lower dimensionality M 1 -norm-based signal recovery scheme for 1-bit compressed sensing using statistical mechanics methods. We show that the signal recovery performance predicted by the replica method under the replica symmetric ansatz, which turns out to be locally unstable for modes breaking the replica symmetry, is in good consistency with experimental results of an approximate recovery algorithm developed earlier. This suggests that the l 1 -based recovery problem typically has many local optima of a similar recovery accuracy, which can be achieved by the approximate algorithm. We also develop another approximate recovery algorithm inspired by the cavity method. Numerical experiments show that when the density of nonzero entries in the original signal is relatively large the new algorithm offers better performance than the abovementioned scheme and does so with a lower computational cost. (paper)

  12. A Simulational approach to teaching statistical mechanics and kinetic theory

    International Nuclear Information System (INIS)

    Karabulut, H.

    2005-01-01

    A computer simulation demonstrating how Maxwell-Boltzmann distribution is reached in gases from a nonequilibrium distribution is presented. The algorithm can be generalized to the cases of gas particles (atoms or molecules) with internal degrees of freedom such as electronic excitations and vibrational-rotational energy levels. Another generalization of the algorithm is the case of mixture of two different gases. By choosing the collision cross sections properly one can create quasi equilibrium distributions. For example by choosing same atom cross sections large and different atom cross sections very small one can create mixture of two gases with different temperatures where two gases slowly interact and come to equilibrium in a long time. Similarly, for the case one kind of atom with internal degrees of freedom one can create situations that internal degrees of freedom come to the equilibrium much later than translational degrees of freedom. In all these cases the equilibrium distribution that the algorithm gives is the same as expected from the statistical mechanics. The algorithm can also be extended to cover the case of chemical equilibrium where species A and B react to form AB molecules. The laws of chemical equilibrium can be observed from this simulation. The chemical equilibrium simulation can also help to teach the elusive concept of chemical potential

  13. An Introduction to Thermodynamics and Statistical Mechanics - 2nd Edition

    Science.gov (United States)

    Stowe, Keith

    2003-03-01

    This introductory textbook for standard undergraduate courses in thermodynamics has been completely rewritten. Starting with an overview of important quantum behaviours, the book teaches students how to calculate probabilities, in order to provide a firm foundation for later chapters. It introduces the ideas of classical thermodynamics and explores them both in general and as they are applied to specific processes and interactions. The remainder of the book deals with statistical mechanics - the study of small systems interacting with huge reservoirs. The changes to this second edition have been made after more than 10 years classroom testing and student feedback. Each topic ends with a boxed summary of ideas and results, and every chapter contains numerous homework problems, covering a broad range of difficulties. Answers are given to odd numbered problems, and solutions to even problems are available to instructors at www.cambridge.org/9780521865579. The entire book has been re-written and now covers more topics It has a greater number of homework problems which range in difficulty from warm-ups to challenges It is concise and has an easy reading style

  14. USNCTAM perspectives on mechanics in medicine

    Science.gov (United States)

    Bao, Gang; Bazilevs, Yuri; Chung, Jae-Hyun; Decuzzi, Paolo; Espinosa, Horacio D.; Ferrari, Mauro; Gao, Huajian; Hossain, Shaolie S.; Hughes, Thomas J. R.; Kamm, Roger D.; Liu, Wing Kam; Marsden, Alison; Schrefler, Bernhard

    2014-01-01

    Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies. PMID:24872502

  15. USNCTAM perspectives on mechanics in medicine.

    Science.gov (United States)

    Bao, Gang; Bazilevs, Yuri; Chung, Jae-Hyun; Decuzzi, Paolo; Espinosa, Horacio D; Ferrari, Mauro; Gao, Huajian; Hossain, Shaolie S; Hughes, Thomas J R; Kamm, Roger D; Liu, Wing Kam; Marsden, Alison; Schrefler, Bernhard

    2014-08-06

    Over decades, the theoretical and applied mechanics community has developed sophisticated approaches for analysing the behaviour of complex engineering systems. Most of these approaches have targeted systems in the transportation, materials, defence and energy industries. Applying and further developing engineering approaches for understanding, predicting and modulating the response of complicated biomedical processes not only holds great promise in meeting societal needs, but also poses serious challenges. This report, prepared for the US National Committee on Theoretical and Applied Mechanics, aims to identify the most pressing challenges in biological sciences and medicine that can be tackled within the broad field of mechanics. This echoes and complements a number of national and international initiatives aiming at fostering interdisciplinary biomedical research. This report also comments on cultural/educational challenges. Specifically, this report focuses on three major thrusts in which we believe mechanics has and will continue to have a substantial impact. (i) Rationally engineering injectable nano/microdevices for imaging and therapy of disease. Within this context, we discuss nanoparticle carrier design, vascular transport and adhesion, endocytosis and tumour growth in response to therapy, as well as uncertainty quantification techniques to better connect models and experiments. (ii) Design of biomedical devices, including point-of-care diagnostic systems, model organ and multi-organ microdevices, and pulsatile ventricular assistant devices. (iii) Mechanics of cellular processes, including mechanosensing and mechanotransduction, improved characterization of cellular constitutive behaviour, and microfluidic systems for single-cell studies. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  16. Graphene Mechanics: Current Status and Perspectives

    Czech Academy of Sciences Publication Activity Database

    Galiotis, C.; Frank, Otakar; Koukaras, E. N.; Sfyris, D.

    2015-01-01

    Roč. 6, JUL 2015 (2015), s. 121-140 ISSN 1947-5438 R&D Projects: GA ČR GA14-15357S Institutional support: RVO:61388955 Keywords : mechanical properties * 2D materials * membranes Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 5.211, year: 2015

  17. Statistical mechanics of polymer networks of any topology

    International Nuclear Information System (INIS)

    Duplantier, B.

    1989-01-01

    The statistical mechanics is considered of any polymer network with a prescribed topology, in dimension d, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made to O(ε 2 ), where d = 4 -ε, of the basic critical dimensions σ L associated with any L=leg vertex (L ≥ 1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent γ G of any network G to O(ε 2 ), including L-leg star polymers. The infinite sets of contact critical exponents θ between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents θ 0 , θ 1 , θ 2 calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimension d = 4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the Θ-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constituting L-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents σ L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled

  18. On some boundary value problems in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Angelescu, N.

    1978-01-01

    The following two topics of equilibrium quantum statistical mechanics are discussed in this thesis: (i) the independence of the thermodynamic limit of grand-canonical pressure on the boundary conditions; (ii) the magnetic properties of free quantum gases. Problem (i) is handled with a functional integration technique. Wiener-type conditional measures are constructed for a given domain and a general class of mixed conditions on its boundary, these measures are used to write down Feynman-Kac formulae for the kernels of exp(-βH), where H is the Hamiltonian of N interacting particles in the given domain. These measures share the property that they assign the same mass as the usual Wiener measure to any set of trajectories not intersecting the boundary. Local estimates on the kernels of exp(-βH) are derived, which imply independence of the pressure on the boundary conditions in the thermodynamic limit. Problem (ii) has a historical development: since Landau's work (1930), much discussion has been devoted to the influence of the finite size on the susceptibility. In finite volume, Dirichlet boundary conditions are imposed, on the ground that they ensure gauge invariance. The thermodynamic limit of the pressure is proved, using again functional integration. The functional measure is now complex but absolutely continuous with respect to Wiener measure, so the usual local estimates hold true. The controversy in the literature was concentrated on the commutativity of the operations of H-derivation and thermodynamic limit, so the existence of this limit for the zero-field susceptibility and its surface term are proved separately, demonstrating this commutativity. The proof relies on the following result of independent interest: the perturbation theory of self-adjoint trace-class semigroups is trace-class convergent and analytic. (author)

  19. Proper body mechanics from an engineering perspective.

    Science.gov (United States)

    Mohr, Edward G

    2010-04-01

    The economic viability of the manual therapy practitioner depends on the number of massages/treatments that can be given in a day or week. Fatigue or injuries can have a major impact on the income potential and could ultimately reach the point which causes the practitioner to quit the profession, and seek other, less physically demanding, employment. Manual therapy practitioners in general, and massage therapists in particular, can utilize a large variety of body postures while giving treatment to a client. The hypothesis of this paper is that there is an optimal method for applying force to the client, which maximizes the benefit to the client, and at the same time minimizes the strain and effort required by the practitioner. Two methods were used to quantifiably determine the effect of using "poor" body mechanics (Improper method) and "best" body mechanics (Proper/correct method). The first approach uses computer modeling to compare the two methods. Both postures were modeled, such that the biomechanical effects on the practitioner's elbow, shoulder, hip, knee and ankle joints could be calculated. The force applied to the client, along with the height and angle of application of the force, was held constant for the comparison. The second approach was a field study of massage practitioners (n=18) to determine their maximal force capability, again comparing methods using "Improper and Proper body mechanics". Five application methods were tested at three different application heights, using a digital palm force gauge. Results showed that there was a definite difference between the two methods, and that the use of correct body mechanics can have a large impact on the health and well being of the massage practitioner over both the short and long term. Copyright 2009 Elsevier Ltd. All rights reserved.

  20. Sensitivity filtering from a continuum mechanics perspective

    DEFF Research Database (Denmark)

    Sigmund, Ole; Maute, Kurt

    2012-01-01

    In topology optimization filtering is a popular approach for preventing numerical instabilities. This short note shows that the well-known sensitivity filtering technique, that prevents checkerboards and ensures mesh-independent designs in density-based topology optimization, is equivalent to min...... to minimizing compliance for nonlocal elasticity problems known from continuum mechanics. Hence, the note resolves the long-standing quest for finding an explanation and physical motivation for the sensitivity filter....

  1. Counting in Lattices: Combinatorial Problems from Statistical Mechanics.

    Science.gov (United States)

    Randall, Dana Jill

    In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and self-avoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is counting self-avoiding walks in lattices. This problem arises in the study of the thermodynamics of long polymer chains in dilute solution. While there are a number of Monte Carlo algorithms used to count self -avoiding walks in practice, these are heuristic and their correctness relies on unproven conjectures. In contrast, we present an efficient algorithm which relies on a single, widely-believed conjecture that is simpler than preceding assumptions and, more importantly, is one which the algorithm itself can test. Thus our algorithm is reliable, in the sense that it either outputs answers that are guaranteed, with high probability, to be correct, or finds a counterexample to the conjecture. In either case we know we can trust our results and the algorithm is guaranteed to run in polynomial time. This is the first algorithm for counting self-avoiding walks in which the error bounds are rigorously controlled. This work was supported in part by an AT&T graduate fellowship, a University of

  2. Public and patient involvement in quantitative health research: A statistical perspective.

    Science.gov (United States)

    Hannigan, Ailish

    2018-06-19

    The majority of studies included in recent reviews of impact for public and patient involvement (PPI) in health research had a qualitative design. PPI in solely quantitative designs is underexplored, particularly its impact on statistical analysis. Statisticians in practice have a long history of working in both consultative (indirect) and collaborative (direct) roles in health research, yet their perspective on PPI in quantitative health research has never been explicitly examined. To explore the potential and challenges of PPI from a statistical perspective at distinct stages of quantitative research, that is sampling, measurement and statistical analysis, distinguishing between indirect and direct PPI. Statistical analysis is underpinned by having a representative sample, and a collaborative or direct approach to PPI may help achieve that by supporting access to and increasing participation of under-represented groups in the population. Acknowledging and valuing the role of lay knowledge of the context in statistical analysis and in deciding what variables to measure may support collective learning and advance scientific understanding, as evidenced by the use of participatory modelling in other disciplines. A recurring issue for quantitative researchers, which reflects quantitative sampling methods, is the selection and required number of PPI contributors, and this requires further methodological development. Direct approaches to PPI in quantitative health research may potentially increase its impact, but the facilitation and partnership skills required may require further training for all stakeholders, including statisticians. © 2018 The Authors Health Expectations published by John Wiley & Sons Ltd.

  3. Equilibrium statistical mechanics for self-gravitating systems: local ergodicity and extended Boltzmann-Gibbs/White-Narayan statistics

    Science.gov (United States)

    He, Ping

    2012-01-01

    The long-standing puzzle surrounding the statistical mechanics of self-gravitating systems has not yet been solved successfully. We formulate a systematic theoretical framework of entropy-based statistical mechanics for spherically symmetric collisionless self-gravitating systems. We use an approach that is very different from that of the conventional statistical mechanics of short-range interaction systems. We demonstrate that the equilibrium states of self-gravitating systems consist of both mechanical and statistical equilibria, with the former characterized by a series of velocity-moment equations and the latter by statistical equilibrium equations, which should be derived from the entropy principle. The velocity-moment equations of all orders are derived from the steady-state collisionless Boltzmann equation. We point out that the ergodicity is invalid for the whole self-gravitating system, but it can be re-established locally. Based on the local ergodicity, using Fermi-Dirac-like statistics, with the non-degenerate condition and the spatial independence of the local microstates, we rederive the Boltzmann-Gibbs entropy. This is consistent with the validity of the collisionless Boltzmann equation, and should be the correct entropy form for collisionless self-gravitating systems. Apart from the usual constraints of mass and energy conservation, we demonstrate that the series of moment or virialization equations must be included as additional constraints on the entropy functional when performing the variational calculus; this is an extension to the original prescription by White & Narayan. Any possible velocity distribution can be produced by the statistical-mechanical approach that we have developed with the extended Boltzmann-Gibbs/White-Narayan statistics. Finally, we discuss the questions of negative specific heat and ensemble inequivalence for self-gravitating systems.

  4. Clean development mechanism: Perspectives from developing countries

    Energy Technology Data Exchange (ETDEWEB)

    Sari, Agus P.; Meyers, Stephen

    1999-06-01

    This paper addresses the political acceptability and workability of CDM by and in developing countries. At COP-3 in Kyoto in 1997, the general position among developing countries changed from strong rejection of joint implementation to acceptance of CDM. The outgrowth of CDM from a proposal from Brazil to establish a Clean Development Fund gave developing countries a sense of ownership of the idea. More importantly, establishing support for sustainable development as a main goal for CDM overcame the resistance of many developing countries to accept a carbon trading mechanism. The official acceptance of CDM is not a guarantee of continued acceptance, however. Many developing countries expect CDM to facilitate a substantial transfer of technology and other resources to support economic growth. There is concern that Annex I countries may shift official development assistance into CDM in order to gain carbon credits, and that development priorities could suffer as a result. Some fear that private investments could be skewed toward projects that yield carbon credits. Developing country governments are wary regarding the strong role of the private sector envisioned for CDM. Increasing the awareness and capacity of the private sector in developing countries to initiate and implement CDM projects needs to be a high priority. While private sector partnerships will be the main vehicle for resource transfer in CDM, developing country governments want to play a strong role in overseeing and guiding the process so that it best serves their development goals. Most countries feel that establishment of criteria for sustainable development should be left to individual countries. A key issue is how CDM can best support the strengthening of local capacity to sustain and replicate projects that serve both climate change mitigation and sustainable development objectives.There is support among developing countries for commencing CDM as soon as possible. Since official commencement must

  5. Student Understanding of Taylor Series Expansions in Statistical Mechanics

    Science.gov (United States)

    Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.

    2013-01-01

    One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann…

  6. Statistical mechanics of learning: A variational approach for real data

    International Nuclear Information System (INIS)

    Malzahn, Doerthe; Opper, Manfred

    2002-01-01

    Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators for generalization errors that are based on training data alone

  7. A Statistical Mechanics Approach to Approximate Analytical Bootstrap Averages

    DEFF Research Database (Denmark)

    Malzahn, Dorthe; Opper, Manfred

    2003-01-01

    We apply the replica method of Statistical Physics combined with a variational method to the approximate analytical computation of bootstrap averages for estimating the generalization error. We demonstrate our approach on regression with Gaussian processes and compare our results with averages...

  8. Statistical mechanics and the description of the early universe I

    DEFF Research Database (Denmark)

    Pessah, Martin Elias; F. Torres, Diego; Vucetich, H.

    2001-01-01

    We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related with the ......We analyze how the thermal history of the universe is influenced by the statistical description, assuming a deviation from the usual Bose-Einstein, Fermi-Dirac and Boltzmann-Gibbs distribution functions. These deviations represent the possible appearance of non-extensive effects related...... and to place limits to the range of its validity. The corrections obtained will change with temperature, and consequently, the bounds on the possible amount of non-extensivity will also change with time. We generalize results which can be used in other contexts as well, as the Boltzmann equation and the Saha...

  9. Erwin Schroedinger: Collected papers V. 1. Contributions to statistical mechanics

    International Nuclear Information System (INIS)

    Schroedinger, E.

    1984-01-01

    38 publications reprinted in this volume show that the interest for statistical problems accompanied Schroedinger during his entire scientific career. Already in his second paper he worked on the magnetism of solid states. The classical considerations come close to the heart of diamagnetism and also to the origin of paramagnetism. In classical investigations of the specific heat Schroedinger helped through abstract theory but also by analysing a gigantic amount of experimental material. In 1926 he and F. Kohlrausch actually played the 'Urngame of Ehrenfest' as a model of the H-curve and published the results. Inclination towards experimenting, sequences of measurements and statistical evaluation of experimental data led to papers on the foundation of the theory of probability, where he tries to put the subjective probability concept on into a systematic framework. Two earlier papers on dynamics of the elastic chain remained particularly valuable. By solving the initial value problem with Bessel-functions this many-body-problem is led to an explicit discussion. These studies are likely to be the roots of another keynote in Schroedinger's thinking, namely, the irreversibility. 1945 a statistical theory of chain-reactions was published under the inconspicuous title of 'Probability Problems in Nuclear Chemistry'. In his last work Schroedinger turns off in a wrong direction: it is that energy should only be a statistical concept and should not be conserved in elementary processes, but somehow only in the mean. These short remarks only illuminate the diversity of the material in this volume, but testify Schroedinger's deep understanding in this field. (W.K.)

  10. Student understanding of Taylor series expansions in statistical mechanics

    Directory of Open Access Journals (Sweden)

    Trevor I. Smith

    2013-08-01

    Full Text Available One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.

  11. Student understanding of Taylor series expansions in statistical mechanics

    Science.gov (United States)

    Smith, Trevor I.; Thompson, John R.; Mountcastle, Donald B.

    2013-12-01

    One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.

  12. Quantum statistical mechanics selected works of N N Bogolubov

    CERN Document Server

    Bogolyubov, N N

    2015-01-01

    In this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles. Contents: On the Theory of Superfluidit

  13. On second quantization methods applied to classical statistical mechanics

    International Nuclear Information System (INIS)

    Matos Neto, A.; Vianna, J.D.M.

    1984-01-01

    A method of expressing statistical classical results in terms of mathematical entities usually associated to quantum field theoretical treatment of many particle systems (Fock space, commutators, field operators, state vector) is discussed. It is developed a linear response theory using the 'second quantized' Liouville equation introduced by Schonberg. The relationship of this method to that of Prigogine et al. is briefly analyzed. The chain of equations and the spectral representations for the new classical Green's functions are presented. Generalized operators defined on Fock space are discussed. It is shown that the correlation functions can be obtained from Green's functions defined with generalized operators. (Author) [pt

  14. Application of few-body methods to statistical mechanics

    International Nuclear Information System (INIS)

    Bolle, D.

    1981-01-01

    This paper reviews some of the methods to study the thermodynamic properties of a macroscopic system in terms of the scattering processes between the constituent particles in the system. In particular, we discuss the time delay approach to the virial expansion and the use of the arrangement channel quantum mechanics formulation in kinetic theory. (orig.)

  15. Statistics

    CERN Document Server

    Hayslett, H T

    1991-01-01

    Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the

  16. Nonequilibrium statistical mechanics of systems with long-range interactions

    Energy Technology Data Exchange (ETDEWEB)

    Levin, Yan, E-mail: levin@if.ufrgs.br; Pakter, Renato, E-mail: pakter@if.ufrgs.br; Rizzato, Felipe B., E-mail: rizzato@if.ufrgs.br; Teles, Tarcísio N., E-mail: tarcisio.teles@fi.infn.it; Benetti, Fernanda P.C., E-mail: fbenetti@if.ufrgs.br

    2014-02-01

    Systems with long-range (LR) forces, for which the interaction potential decays with the interparticle distance with an exponent smaller than the dimensionality of the embedding space, remain an outstanding challenge to statistical physics. The internal energy of such systems lacks extensivity and additivity. Although the extensivity can be restored by scaling the interaction potential with the number of particles, the non-additivity still remains. Lack of additivity leads to inequivalence of statistical ensembles. Before relaxing to thermodynamic equilibrium, isolated systems with LR forces become trapped in out-of-equilibrium quasi-stationary states (qSSs), the lifetime of which diverges with the number of particles. Therefore, in the thermodynamic limit LR systems will not relax to equilibrium. The qSSs are attained through the process of collisionless relaxation. Density oscillations lead to particle–wave interactions and excitation of parametric resonances. The resonant particles escape from the main cluster to form a tenuous halo. Simultaneously, this cools down the core of the distribution and dampens out the oscillations. When all the oscillations die out the ergodicity is broken and a qSS is born. In this report, we will review a theory which allows us to quantitatively predict the particle distribution in the qSS. The theory is applied to various LR interacting systems, ranging from plasmas to self-gravitating clusters and kinetic spin models.

  17. Nuclear multifragmentation, its relation to general physics. A rich test ground of the fundamentals of statistical mechanics

    International Nuclear Information System (INIS)

    Gross, D.H.E.

    2006-01-01

    Heat can flow from cold to hot at any phase separation even in macroscopic systems. Therefore also Lynden-Bell's famous gravo-thermal catastrophe must be reconsidered. In contrast to traditional canonical Boltzmann-Gibbs statistics this is correctly described only by microcanonical statistics. Systems studied in chemical thermodynamics (ChTh) by using canonical statistics consist of several homogeneous macroscopic phases. Evidently, macroscopic statistics as in chemistry cannot and should not be applied to non-extensive or inhomogeneous systems like nuclei or galaxies. Nuclei are small and inhomogeneous. Multifragmented nuclei are even more inhomogeneous and the fragments even smaller. Phase transitions of first order and especially phase separations therefore cannot be described by a (homogeneous) canonical ensemble. Taking this serious, fascinating perspectives open for statistical nuclear fragmentation as test ground for the basic principles of statistical mechanics, especially of phase transitions, without the use of the thermodynamic limit. Moreover, there is also a lot of similarity between the accessible phase space of fragmenting nuclei and inhomogeneous multistellar systems. This underlines the fundamental significance for statistical physics in general. (orig.)

  18. Statistical mechanics of flux lines in high-temperature superconductors

    International Nuclear Information System (INIS)

    Dasgupta, C.

    1992-01-01

    The shortness of the low temperature coherence lengths of high T c materials leads to new mechanisms of pinning of flux lines. Lattice periodic modulations of the order parameters itself acts to pin vortex lines in regions of the unit cell were the order parameter is small. A presentation of flux creep and flux noise at low temperature and magnetic fields in terms of motion of simple metastable defects on flux lines is made, with a calculation of flux lattice melting. 12 refs

  19. Nonextensive statistical mechanics approach to electron trapping in degenerate plasmas

    Science.gov (United States)

    Mebrouk, Khireddine; Gougam, Leila Ait; Tribeche, Mouloud

    2016-06-01

    The electron trapping in a weakly nondegenerate plasma is reformulated and re-examined by incorporating the nonextensive entropy prescription. Using the q-deformed Fermi-Dirac distribution function including the quantum as well as the nonextensive statistical effects, we derive a new generalized electron density with a new contribution proportional to the electron temperature T, which may dominate the usual thermal correction (∼T2) at very low temperatures. To make the physics behind the effect of this new contribution more transparent, we analyze the modifications arising in the propagation of ion-acoustic solitary waves. Interestingly, we find that due to the nonextensive correction, our plasma model allows the possibility of existence of quantum ion-acoustic solitons with velocity higher than the Fermi ion-sound velocity. Moreover, as the nonextensive parameter q increases, the critical temperature Tc beyond which coexistence of compressive and rarefactive solitons sets in, is shifted towards higher values.

  20. Elements of statistical thermodynamics

    CERN Document Server

    Nash, Leonard K

    2006-01-01

    Encompassing essentially all aspects of statistical mechanics that appear in undergraduate texts, this concise, elementary treatment shows how an atomic-molecular perspective yields new insights into macroscopic thermodynamics. 1974 edition.

  1. Einstein's Approach to Statistical Mechanics: The 1902-04 Papers

    Science.gov (United States)

    Peliti, Luca; Rechtman, Raúl

    2017-05-01

    We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-1904 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways.

  2. Statistical mechanics of sensing and communications: Insights and techniques

    International Nuclear Information System (INIS)

    Murayama, T; Davis, P

    2008-01-01

    In this article we review a basic model for analysis of large sensor networks from the point of view of collective estimation under bandwidth constraints. We compare different sensing aggregation levels as alternative 'strategies' for collective estimation: moderate aggregation from a moderate number of sensors for which communication bandwidth is enough that data encoding can be reversible, and large scale aggregation from very many sensors - in which case communication bandwidth constraints require the use of nonreversible encoding. We show the non-trivial trade-off between sensing quality, which can be increased by increasing the number of sensors, and communication quality under bandwidth constraints, which decreases if the number of sensors is too large. From a practical standpoint, we verify that such a trade-off exists in constructively defined communications schemes. We introduce a probabilistic encoding scheme and define rate distortion models that are suitable for analysis of the large network limit. Our description shows that the methods and ideas from statistical physics can play an important role in formulating effective models for such schemes

  3. Statistics

    Science.gov (United States)

    Links to sources of cancer-related statistics, including the Surveillance, Epidemiology and End Results (SEER) Program, SEER-Medicare datasets, cancer survivor prevalence data, and the Cancer Trends Progress Report.

  4. PGT: A Statistical Approach to Prediction and Mechanism Design

    Science.gov (United States)

    Wolpert, David H.; Bono, James W.

    One of the biggest challenges facing behavioral economics is the lack of a single theoretical framework that is capable of directly utilizing all types of behavioral data. One of the biggest challenges of game theory is the lack of a framework for making predictions and designing markets in a manner that is consistent with the axioms of decision theory. An approach in which solution concepts are distribution-valued rather than set-valued (i.e. equilibrium theory) has both capabilities. We call this approach Predictive Game Theory (or PGT). This paper outlines a general Bayesian approach to PGT. It also presents one simple example to illustrate the way in which this approach differs from equilibrium approaches in both prediction and mechanism design settings.

  5. New paradigm for drug developments--from emerging market statistical perspective.

    Science.gov (United States)

    Quan, Hui; Chen, Xun; Zhang, Ji; Zhao, Peng-Liang

    2013-11-01

    Paradigm for new drug development has changed dramatically over the last decade. Even though new technology increases efficiency in many aspects, partially due to much more stringent regulatory requirements, it actually now takes longer and costs more to develop a new drug. To deal with challenge, some initiatives are taken by the pharmaceutical industry. These initiatives include exploring emerging markets, conducting global trials and building research and development centers in emerging markets to curb spending. It is particularly the current trend that major pharmaceutical companies offshore a part of their biostatistical support to China. In this paper, we first discuss the skill set for trial statisticians in the new era. We then elaborate on some of the approaches for acquiring statistical talent and capacity in general, particularly in emerging markets. We also make some recommendations on the use of the PDUFA strategy and collaborations among industry, health authority and academia from emerging market statistical perspective. © 2013.

  6. Impact initiation of explosives and propellants via statistical crack mechanics

    Science.gov (United States)

    Dienes, J. K.; Zuo, Q. H.; Kershner, J. D.

    2006-06-01

    A statistical approach has been developed for modeling the dynamic response of brittle materials by superimposing the effects of a myriad of microcracks, including opening, shear, growth and coalescence, taking as a starting point the well-established theory of penny-shaped cracks. This paper discusses the general approach, but in particular an application to the sensitivity of explosives and propellants, which often contain brittle constituents. We examine the hypothesis that the intense heating by frictional sliding between the faces of a closed crack during unstable growth can form a hot spot, causing localized melting, ignition, and fast burn of the reactive material adjacent to the crack. Opening and growth of a closed crack due to the pressure of burned gases inside the crack and interactions of adjacent cracks can lead to violent reaction, with detonation as a possible consequence. This approach was used to model a multiple-shock experiment by Mulford et al. [1993. Initiation of preshocked high explosives PBX-9404, PBX-9502, PBX-9501, monitored with in-material magnetic gauging. In: Proceedings of the 10th International Detonation Symposium, pp. 459-467] involving initiation and subsequent quenching of chemical reactions in a slab of PBX 9501 impacted by a two-material flyer plate. We examine the effects of crack orientation and temperature dependence of viscosity of the melt on the response. Numerical results confirm our theoretical finding [Zuo, Q.H., Dienes, J.K., 2005. On the stability of penny-shaped cracks with friction: the five types of brittle behavior. Int. J. Solids Struct. 42, 1309-1326] that crack orientation has a significant effect on brittle behavior, especially under compressive loading where interfacial friction plays an important role. With a reasonable choice of crack orientation and a temperature-dependent viscosity obtained from molecular dynamics calculations, the calculated particle velocities compare well with those measured using

  7. The problem of phase transitions in statistical mechanics

    International Nuclear Information System (INIS)

    Martynov, Georgii A

    1999-01-01

    The first part of this review deals with the single-phase approach to the statistical theory of phase transitions. This approach is based on the assumption that a first-order phase transition is due to the loss of stability of the parent phase. We demonstrate that it is practically impossible to find the coordinates of the transition points using this criterion in the framework of the global Gibbs theory which describes the state of the entire macroscopic system. On the basis of the Ornstein-Zernike equation we formulate a local approach that analyzes the state of matter inside the correlation sphere of radius R c ∼ 10 A. This approach is proved to be as rigorous as the Gibbs theory. In the context of the local approach we formulate a criterion that allows finding the transition points without calculating the chemical potential and the pressure of the second conjugate phase. In the second part of the review we consider second-order phase transitions (critical phenomena). The Kadanoff-Wilson theory of critical phenomena is analyzed, based on the global Gibbs approach. Again we use the Ornstein-Zernike equation to formulate a local theory of critical phenomena. With regard to experimentally established quantities this theory yields precisely the same results as the Kadanoff-Wilson theory; secondly, the local approach allows the prediction of many previously unknown details of critical phenomena, and thirdly, the local approach paves the way for constructing a unified theory of liquids that will describe the behavior of matter not only in the regular domain of the phase diagram, but also at the critical point and in its vicinity. (reviews of topical problems)

  8. Application of nonequilibrium quantum statistical mechanics to homogeneous nucleation

    International Nuclear Information System (INIS)

    Larson, A.R.; Cantrell, C.D.

    1978-01-01

    The master equation for cluster growth and evaporation is derived from many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory has been generalized to include system and reservoir states that are not separate entities. Formulae for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulae for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud-chamber and nozzle experiments, which measure water

  9. Parallelism in computations in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Clementi, E.; Corongiu, G.; Detrich, J.H.

    1985-01-01

    Often very fundamental biochemical and biophysical problems defy simulations because of limitations in today's computers. We present and discuss a distributed system composed of two IBM 4341 s and/or an IBM 4381 as front-end processors and ten FPS-164 attached array processors. This parallel system - called LCAP - has presently a peak performance of about 110 Mflops; extensions to higher performance are discussed. Presently, the system applications use a modified version of VM/SP as the operating system: description of the modifications is given. Three applications programs have been migrated from sequential to parallel: a molecular quantum mechanical, a Metropolis-Monte Carlo and a molecular dynamics program. Descriptions of the parallel codes are briefly outlined. Use of these parallel codes has already opened up new capabilities for our research. The very positive performance comparisons with today's supercomputers allow us to conclude that parallel computers and programming, of the type we have considered, represent a pragmatic answer to many computationally intensive problems. (orig.)

  10. Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics

    International Nuclear Information System (INIS)

    1978-08-01

    The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references

  11. Statistics

    International Nuclear Information System (INIS)

    2005-01-01

    For the years 2004 and 2005 the figures shown in the tables of Energy Review are partly preliminary. The annual statistics published in Energy Review are presented in more detail in a publication called Energy Statistics that comes out yearly. Energy Statistics also includes historical time-series over a longer period of time (see e.g. Energy Statistics, Statistics Finland, Helsinki 2004.) The applied energy units and conversion coefficients are shown in the back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supplies and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes, precautionary stock fees and oil pollution fees

  12. New Perspectives on the Charging Mechanisms of Supercapacitors

    Science.gov (United States)

    2016-01-01

    Supercapacitors (or electric double-layer capacitors) are high-power energy storage devices that store charge at the interface between porous carbon electrodes and an electrolyte solution. These devices are already employed in heavy electric vehicles and electronic devices, and can complement batteries in a more sustainable future. Their widespread application could be facilitated by the development of devices that can store more energy, without compromising their fast charging and discharging times. In situ characterization methods and computational modeling techniques have recently been developed to study the molecular mechanisms of charge storage, with the hope that better devices can be rationally designed. In this Perspective, we bring together recent findings from a range of experimental and computational studies to give a detailed picture of the charging mechanisms of supercapacitors. Nuclear magnetic resonance experiments and molecular dynamics simulations have revealed that the electrode pores contain a considerable number of ions in the absence of an applied charging potential. Experiments and computer simulations have shown that different charging mechanisms can then operate when a potential is applied, going beyond the traditional view of charging by counter-ion adsorption. It is shown that charging almost always involves ion exchange (swapping of co-ions for counter-ions), and rarely occurs by counter-ion adsorption alone. We introduce a charging mechanism parameter that quantifies the mechanism and allows comparisons between different systems. The mechanism is found to depend strongly on the polarization of the electrode, and the choice of the electrolyte and electrode materials. In light of these advances we identify new directions for supercapacitor research. Further experimental and computational work is needed to explain the factors that control supercapacitor charging mechanisms, and to establish the links between mechanisms and performance

  13. Statistics

    International Nuclear Information System (INIS)

    2001-01-01

    For the year 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1999, Statistics Finland, Helsinki 2000, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions from the use of fossil fuels, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in 2000, Energy exports by recipient country in 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products

  14. Statistics

    International Nuclear Information System (INIS)

    2000-01-01

    For the year 1999 and 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g., Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-March 2000, Energy exports by recipient country in January-March 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products

  15. Statistics

    International Nuclear Information System (INIS)

    1999-01-01

    For the year 1998 and the year 1999, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy Review appear in more detail from the publication Energiatilastot - Energy Statistics issued annually, which also includes historical time series over a longer period (see e.g. Energiatilastot 1998, Statistics Finland, Helsinki 1999, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-June 1999, Energy exports by recipient country in January-June 1999, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products

  16. Statistics

    International Nuclear Information System (INIS)

    2003-01-01

    For the year 2002, part of the figures shown in the tables of the Energy Review are partly preliminary. The annual statistics of the Energy Review also includes historical time-series over a longer period (see e.g. Energiatilastot 2001, Statistics Finland, Helsinki 2002). The applied energy units and conversion coefficients are shown in the inside back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supply and total consumption of electricity GWh, Energy imports by country of origin in January-June 2003, Energy exports by recipient country in January-June 2003, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Excise taxes, precautionary stock fees on oil pollution fees on energy products

  17. Statistics

    International Nuclear Information System (INIS)

    2004-01-01

    For the year 2003 and 2004, the figures shown in the tables of the Energy Review are partly preliminary. The annual statistics of the Energy Review also includes historical time-series over a longer period (see e.g. Energiatilastot, Statistics Finland, Helsinki 2003, ISSN 0785-3165). The applied energy units and conversion coefficients are shown in the inside back cover of the Review. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in GDP, energy consumption and electricity consumption, Carbon dioxide emissions from fossile fuels use, Coal consumption, Consumption of natural gas, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices in heat production, Fuel prices in electricity production, Price of electricity by type of consumer, Average monthly spot prices at the Nord pool power exchange, Total energy consumption by source and CO 2 -emissions, Supplies and total consumption of electricity GWh, Energy imports by country of origin in January-March 2004, Energy exports by recipient country in January-March 2004, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Price of natural gas by type of consumer, Price of electricity by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Excise taxes, precautionary stock fees on oil pollution fees

  18. Statistics

    International Nuclear Information System (INIS)

    2000-01-01

    For the year 1999 and 2000, part of the figures shown in the tables of the Energy Review are preliminary or estimated. The annual statistics of the Energy also includes historical time series over a longer period (see e.g., Energiatilastot 1999, Statistics Finland, Helsinki 2000, ISSN 0785-3165). The inside of the Review's back cover shows the energy units and the conversion coefficients used for them. Explanatory notes to the statistical tables can be found after tables and figures. The figures presents: Changes in the volume of GNP and energy consumption, Changes in the volume of GNP and electricity, Coal consumption, Natural gas consumption, Peat consumption, Domestic oil deliveries, Import prices of oil, Consumer prices of principal oil products, Fuel prices for heat production, Fuel prices for electricity production, Carbon dioxide emissions, Total energy consumption by source and CO 2 -emissions, Electricity supply, Energy imports by country of origin in January-June 2000, Energy exports by recipient country in January-June 2000, Consumer prices of liquid fuels, Consumer prices of hard coal, natural gas and indigenous fuels, Average electricity price by type of consumer, Price of district heating by type of consumer, Excise taxes, value added taxes and fiscal charges and fees included in consumer prices of some energy sources and Energy taxes and precautionary stock fees on oil products

  19. STATISTICAL DISTRIBUTION PATTERNS IN MECHANICAL AND FATIGUE PROPERTIES OF METALLIC MATERIALS

    OpenAIRE

    Tatsuo, SAKAI; Masaki, NAKAJIMA; Keiro, TOKAJI; Norihiko, HASEGAWA; Department of Mechanical Engineering, Ritsumeikan University; Department of Mechanical Engineering, Toyota College of Technology; Department of Mechanical Engineering, Gifu University; Department of Mechanical Engineering, Gifu University

    1997-01-01

    Many papers on the statistical aspect of materials strength have been collected and reviewed by The Research Group for Statistical Aspects of Materials Strength.A book of "Statistical Aspects of Materials Strength" was written by this group, and published in 1992.Based on the experimental data compiled in this book, distribution patterns of mechanical properties are systematically surveyed paying an attention to metallic materials.Thus one can obtain the fundamental knowledge for a reliabilit...

  20. Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives

    International Nuclear Information System (INIS)

    Lomholt, Michael A; Miao Ling

    2006-01-01

    Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy

  1. A perspective on quantum mechanics calculations in ADMET predictions.

    Science.gov (United States)

    Bowen, J Phillip; Güner, Osman F

    2013-01-01

    Understanding the molecular basis of drug action has been an important objective for pharmaceutical scientists. With the increasing speed of computers and the implementation of quantum chemistry methodologies, pharmacodynamic and pharmacokinetic problems have become more computationally tractable. Historically the former has been the focus of drug design, but within the last two decades efforts to understand the latter have increased. It takes about fifteen years and over $1 billion dollars for a drug to go from laboratory hit, through lead optimization, to final approval by the U.S. Food and Drug Administration. While the costs have increased substantially, the overall clinical success rate for a compound to emerge from clinical trials is approximately 10%. Most of the attrition rate can be traced to ADMET (absorption, distribution, metabolism, excretion, and toxicity) problems, which is a powerful impetus to study these issues at an earlier stage in drug discovery. Quantum mechanics offers pharmaceutical scientists the opportunity to investigate pharmacokinetic problems at the molecular level prior to laboratory preparation and testing. This review will provide a perspective on the use of quantum mechanics or a combination of quantum mechanics coupled with other classical methods in the pharmacokinetic phase of drug discovery. A brief overview of the essential features of theory will be discussed, and a few carefully selected examples will be given to highlight the computational methods.

  2. Nanoparticle-Cell Interaction: A Cell Mechanics Perspective.

    Science.gov (United States)

    Septiadi, Dedy; Crippa, Federica; Moore, Thomas Lee; Rothen-Rutishauser, Barbara; Petri-Fink, Alke

    2018-05-01

    Progress in the field of nanoparticles has enabled the rapid development of multiple products and technologies; however, some nanoparticles can pose both a threat to the environment and human health. To enable their safe implementation, a comprehensive knowledge of nanoparticles and their biological interactions is needed. In vitro and in vivo toxicity tests have been considered the gold standard to evaluate nanoparticle safety, but it is becoming necessary to understand the impact of nanosystems on cell mechanics. Here, the interaction between particles and cells, from the point of view of cell mechanics (i.e., bionanomechanics), is highlighted and put in perspective. Specifically, the ability of intracellular and extracellular nanoparticles to impair cell adhesion, cytoskeletal organization, stiffness, and migration are discussed. Furthermore, the development of cutting-edge, nanotechnology-driven tools based on the use of particles allowing the determination of cell mechanics is emphasized. These include traction force microscopy, colloidal probe atomic force microscopy, optical tweezers, magnetic manipulation, and particle tracking microrheology. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  3. Statistics, synergy, and mechanism of multiple photogeneration of excitons in quantum dots: Fundamental and applied aspects

    International Nuclear Information System (INIS)

    Oksengendler, B. L.; Turaeva, N. N.; Uralov, I.; Marasulov, M. B.

    2012-01-01

    The effect of multiple exciton generation is analyzed based on statistical physics, quantum mechanics, and synergetics. Statistical problems of the effect of multiple exciton generation (MEG) are broadened and take into account not only exciton generation, but also background excitation. The study of the role of surface states of quantum dots is based on the synergy of self-catalyzed electronic reactions. An analysis of the MEG mechanism is based on the idea of electronic shaking using the sudden perturbation method in quantum mechanics. All of the above-mentioned results are applied to the problem of calculating the limiting efficiency to transform solar energy into electric energy. (authors)

  4. Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives

    DEFF Research Database (Denmark)

    Lomholt, Michael Andersen; Miao, L.

    2006-01-01

    Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which...... the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties....... A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different...

  5. Epigenetic Mechanisms and Therapeutic Perspectives for Neurodevelopmental Disorders

    Directory of Open Access Journals (Sweden)

    Kunio Miyake

    2012-04-01

    Full Text Available The number of children with mild neurodevelopmental disorders, such as autism, has been recently increasing in advanced countries. This increase is probably caused by environmental factors rather than genetic factors, because it is unlikely that genetic mutation rates suddenly increased within a short period. Epigenetics is a mechanism that regulates gene expression, depending not on the underlying DNA sequence but on the chemical modifications of DNA and histone proteins. Because mental stress can alter the epigenetic status in neuronal cells, environmental factors may alter brain function through epigenetic changes. However, one advantage of epigenetic changes is their reversibility. Therefore, diseases due to abnormal epigenetic regulation are theoretically treatable. In fact, several drugs for treating mental diseases are known to have restoring effects on aberrant epigenetic statuses, and a novel therapeutic strategy targeting gene has been developed. In this review, we discuss epigenetic mechanisms of congenital and acquired neurodevelopmental disorders, drugs with epigenetic effects, novel therapeutic strategies for epigenetic diseases, and future perspectives in epigenetic medicine.

  6. A Statistical Perspective on Running with Prosthetic Lower-Limbs: An Advantage or Disadvantage?

    Directory of Open Access Journals (Sweden)

    Hossein Hassani

    2014-11-01

    Full Text Available Technological developments have led to the increased use of carbon fiber and prosthetic lower-limbs in running events at the Paralympic Games. This study aims to exploit a series of statistical techniques in order to prepare a response to the vital question of whether utilizing prosthetic feet can affect an athletes ability when running competitively at the Paralympics Games by comparing both within and between different classifications. The study also considers the differences between running on biological limbs and prosthetic lower-limbs from a mechanical point of view. The results from the male 100 m, 200 m and 400 m at the 2012 London Paralympic Games have been the source of this investigation. The investigation provides statistical evidence to propose that the number of prosthetic limbs used and the structure of such limbs have a significant impact on the outcome of track events at the Paralympic Games.

  7. To the problem of the statistical basis of evaluation of the mechanical safety factor

    International Nuclear Information System (INIS)

    Tsyganov, S.V.

    2009-01-01

    The methodology applied for the safety factor assessment of the WWER fuel cycles uses methods and terms of statistics. Value of the factor is calculated on the basis of estimation of probability to meet predefined limits. Such approach demands the special attention to the statistical properties of parameters of interest. Considering the mechanical constituents of the engineering factor it is assumed uncertainty factors of safety parameters are stochastic values. It characterized by probabilistic distributions that can be unknown. Traditionally in the safety factor assessment process the unknown parameters are estimated from the conservative points of view. This paper analyses how the refinement of the factors distribution parameters is important for the assessment of the mechanical safety factor. For the analysis the statistical approach is applied for modelling of different type of factor probabilistic distributions. It is shown the significant influence of the shape and parameters of distributions for some factors on the value of mechanical safety factor. (Authors)

  8. Statistical mechanics of directed models of polymers in the square lattice

    CERN Document Server

    Rensburg, J V

    2003-01-01

    Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce...

  9. To the problem of the statistical basis of evaluation of the mechanical safety factor

    International Nuclear Information System (INIS)

    Tsyganov, S.

    2009-01-01

    The methodology applied for the safety factor assessment of the VVER fuel cycles uses methods and terms of statistics. Value of the factor is calculated on the basis of estimation of probability to meet predefined limits. Such approach demands the special attention to the statistical properties of parameters of interest. Considering the mechanical constituents of the engineering factor it is assumed uncertainty factors of safety parameters are stochastic values. It characterized by probabilistic distributions that can be unknown. Traditionally in the safety factor assessment process the unknown parameters are estimated from the conservative points of view. This paper analyses how the refinement of the factors distribution parameters is important for the assessment of the mechanical safety factor. For the analysis the statistical approach is applied for modelling of different type of factor probabilistic distributions. It is shown the significant influence of the shape and parameters of distributions for some factors on the value of mechanical safety factor. (author)

  10. Menzerath-Altmann Law: Statistical Mechanical Interpretation as Applied to a Linguistic Organization

    Science.gov (United States)

    Eroglu, Sertac

    2014-10-01

    The distribution behavior described by the empirical Menzerath-Altmann law is frequently encountered during the self-organization of linguistic and non-linguistic natural organizations at various structural levels. This study presents a statistical mechanical derivation of the law based on the analogy between the classical particles of a statistical mechanical organization and the distinct words of a textual organization. The derived model, a transformed (generalized) form of the Menzerath-Altmann model, was termed as the statistical mechanical Menzerath-Altmann model. The derived model allows interpreting the model parameters in terms of physical concepts. We also propose that many organizations presenting the Menzerath-Altmann law behavior, whether linguistic or not, can be methodically examined by the transformed distribution model through the properly defined structure-dependent parameter and the energy associated states.

  11. A statistical mechanical approach for the computation of the climatic response to general forcings

    Directory of Open Access Journals (Sweden)

    V. Lucarini

    2011-01-01

    Full Text Available The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing

  12. Mechanisms and applications of plant growth promoting rhizobacteria: Current perspective

    Directory of Open Access Journals (Sweden)

    Munees Ahemad

    2014-01-01

    Full Text Available Plant growth promoting rhizobacteria are the soil bacteria inhabiting around/on the root surface and are directly or indirectly involved in promoting plant growth and development via production and secretion of various regulatory chemicals in the vicinity of rhizosphere. Generally, plant growth promoting rhizobacteria facilitate the plant growth directly by either assisting in resource acquisition (nitrogen, phosphorus and essential minerals or modulating plant hormone levels, or indirectly by decreasing the inhibitory effects of various pathogens on plant growth and development in the forms of biocontrol agents. Various studies have documented the increased health and productivity of different plant species by the application of plant growth promoting rhizobacteria under both normal and stressed conditions. The plant-beneficial rhizobacteria may decrease the global dependence on hazardous agricultural chemicals which destabilize the agro-ecosystems. This review accentuates the perception of the rhizosphere and plant growth promoting rhizobacteria under the current perspectives. Further, explicit outlooks on the different mechanisms of rhizobacteria mediated plant growth promotion have been described in detail with the recent development and research. Finally, the latest paradigms of applicability of these beneficial rhizobacteria in different agro-ecosystems have been presented comprehensively under both normal and stress conditions to highlight the recent trends with the aim to develop future insights.

  13. Do infants retain the statistics of a statistical learning experience? Insights from a developmental cognitive neuroscience perspective.

    Science.gov (United States)

    Gómez, Rebecca L

    2017-01-05

    Statistical structure abounds in language. Human infants show a striking capacity for using statistical learning (SL) to extract regularities in their linguistic environments, a process thought to bootstrap their knowledge of language. Critically, studies of SL test infants in the minutes immediately following familiarization, but long-term retention unfolds over hours and days, with almost no work investigating retention of SL. This creates a critical gap in the literature given that we know little about how single or multiple SL experiences translate into permanent knowledge. Furthermore, different memory systems with vastly different encoding and retention profiles emerge at different points in development, with the underlying memory system dictating the fidelity of the memory trace hours later. I describe the scant literature on retention of SL, the learning and retention properties of memory systems as they apply to SL, and the development of these memory systems. I propose that different memory systems support retention of SL in infant and adult learners, suggesting an explanation for the slow pace of natural language acquisition in infancy. I discuss the implications of developing memory systems for SL and suggest that we exercise caution in extrapolating from adult to infant properties of SL.This article is part of the themed issue 'New frontiers for statistical learning in the cognitive sciences'. © 2016 The Author(s).

  14. Ergodic theory, interpretations of probability and the foundations of statistical mechanics

    NARCIS (Netherlands)

    van Lith, J.H.

    2001-01-01

    The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time

  15. An introduction to conformal invariance in quantum field theory and statistical mechanics

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Naon, C.M.

    1990-01-01

    The subject of conformal invariance provides an extraordinarly successful and productive symbiosis between statistical mechanics and quantum field theory. The main goal of this paper, which is tailored to a wide audience, is to give an introduction to such vast subject (C.P.)

  16. The steady state of heterogeneous catalysis, studied by first-principles statistical mechanics

    NARCIS (Netherlands)

    Reuter, K.; Frenkel, D.; Scheffler, M.

    2004-01-01

    The turnover frequency of the catalytic oxidation of CO at RuO2(110) was calculated as a function of temperature and partial pressures using ab initio statistical mechanics. The underlying energetics of the gas-phase molecules, dissociation, adsorption, surface diffusion, surface chemical reactions,

  17. Completely X-symmetric S-matrices corresponding to theta functions and models of statistical mechanics

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.; Chudnovsky, G.V.

    1981-01-01

    We consider general expressions of factorized S-matrices with Abelian symmetry expressed in terms of theta-functions. These expressions arise from representations of the Heisenberg group. New examples of factorized S-matrices lead to a large class of completely integrable models of statistical mechanics which generalize the XYZ-model of the eight-vertex model. (orig.)

  18. Metamodelling Messages Conveyed in Five Statistical Mechanical Textbooks from 1936 to 2001

    Science.gov (United States)

    Niss, Martin

    2009-01-01

    Modelling is a significant aspect of doing physics and it is important how this activity is taught. This paper focuses on the explicit or implicit messages about modelling conveyed to the student in the treatments of phase transitions in statistical mechanics textbooks at beginning graduate level. Five textbooks from the 1930s to the present are…

  19. Statistical mechanical perturbation theory of solid-vapor interfacial free energy

    NARCIS (Netherlands)

    Kalikmanov, Vitalij Iosifovitsj; Hagmeijer, Rob; Venner, Cornelis H.

    2017-01-01

    The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

  20. Statistical Mechanical Perturbation Theory of Solid−Vapor Interfacial Free Energy

    NARCIS (Netherlands)

    Kalikmanov, V.I.; Hagmeijer, R.; Venner, C.H.

    2017-01-01

    The solid–vapor interfacial free energy γsv plays an important role in a number of physical phenomena, such as adsorption, wetting, and adhesion. We propose a closed form expression for the orientation averaged value of this quantity using a statistical mechanical perturbation approach developed in

  1. Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions

    NARCIS (Netherlands)

    Marcolli, Matilde; Cornelissen, Gunther

    2014-01-01

    The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory. We introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium

  2. Fundamental problems in statistical mechanics VI. Proceedings of the sixth international summer school

    Energy Technology Data Exchange (ETDEWEB)

    Cohen, E G.D.

    1985-01-01

    The following topics were dealt with: walks, walls and ordering in low dimensions; renormalisation of fluids; wetting transition; phases and phase transitions; liquid-vapour interface; statistical mechanics in lattice gauge theory; hydrodynamic instabilities; complex dynamics and chaos; dynamical transitions; phase separation and pattern formation; kinetic theory of clustering; localisation.

  3. Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications

    International Nuclear Information System (INIS)

    Tsallis, Constantino; Tirnakli, Ugur

    2010-01-01

    We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy shown. Among others, we focus on possible realizations of the q-generalized Central Limit Theorem, including at the edge of chaos of the logistic map, and for quasi-stationary states of many-body long-range-interacting Hamiltonian systems.

  4. Statistical evaluation of the mechanical properties of high-volume class F fly ash concretes

    KAUST Repository

    Yoon, Seyoon; Monteiro, Paulo J.M.; Macphee, Donald E.; Glasser, Fredrik P.; Imbabi, Mohammed Salah-Eldin

    2014-01-01

    the authors experimentally and statistically investigated the effects of mix-design factors on the mechanical properties of high-volume class F fly ash concretes. A total of 240 and 32 samples were produced and tested in the laboratory to measure compressive

  5. Some properties of the representation of the quasilocal observables in statistical mechanics and quantum field theory

    International Nuclear Information System (INIS)

    Testard, D.; Centre National de la Recherche Scientifique, 13 - Marseille

    1977-09-01

    For a finite non zero temperature state in Statistical Mechanics it is proved that the factor obtained in the corresponding representation of the quasilocal algebra has the property of Araki. The same result also holds for the 'wedge-algebras' of a hermitian scalar Wightman field

  6. Statistical and stochastic aspects of the delocalization problem in quantum mechanics

    International Nuclear Information System (INIS)

    Claverie, P.; Diner, S.

    1976-01-01

    The space-time behaviour of electrons in atoms and molecules is reviewed. The wave conception of the electron is criticized and the poverty of the non-reductionist attitude is underlined. Further, the two main interpretations of quantum mechanics are recalled: the Copenhagen and the Statistical Interpretations. The meaning and the successes of the Statistical Interpretation are explained and it is shown that it does not solve all problems because quantum mechanics is irreducible to a classical statistical theory. The fluctuation of the particle number and its relationship to loge theory, delocalization and correlation is studied. Finally, different stochastic models for microphysics are reviewed. The markovian Fenyes-Nelson process allows an interpretation of the original heuristic considerations of Schroedinger. Non-markov processes with Schroedinger time evolution are shown to be equivalent to the base state analysis of Feynmann but they are unsatisfactory from a probabilistic point of view. Stochastic electrodynamics is presented as the most satisfactory conception nowadays

  7. Derivation of some new distributions in statistical mechanics using maximum entropy approach

    Directory of Open Access Journals (Sweden)

    Ray Amritansu

    2014-01-01

    Full Text Available The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E., Fermi Dirac(F.D. & Intermediate Statistics(I.S. distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.

  8. Statistical mechanics provides novel insights into microtubule stability and mechanism of shrinkage.

    Directory of Open Access Journals (Sweden)

    Ishutesh Jain

    2015-02-01

    Full Text Available Microtubules are nano-machines that grow and shrink stochastically, making use of the coupling between chemical kinetics and mechanics of its constituent protofilaments (PFs. We investigate the stability and shrinkage of microtubules taking into account inter-protofilament interactions and bending interactions of intrinsically curved PFs. Computing the free energy as a function of PF tip position, we show that the competition between curvature energy, inter-PF interaction energy and entropy leads to a rich landscape with a series of minima that repeat over a length-scale determined by the intrinsic curvature. Computing Langevin dynamics of the tip through the landscape and accounting for depolymerization, we calculate the average unzippering and shrinkage velocities of GDP protofilaments and compare them with the experimentally known results. Our analysis predicts that the strength of the inter-PF interaction (E(s(m has to be comparable to the strength of the curvature energy (E(b(m such that E(s(m - E(b(m ≈ 1kBT, and questions the prevalent notion that unzippering results from the domination of bending energy of curved GDP PFs. Our work demonstrates how the shape of the free energy landscape is crucial in explaining the mechanism of MT shrinkage where the unzippered PFs will fluctuate in a set of partially peeled off states and subunit dissociation will reduce the length.

  9. Nonequilibrium phase transitions and bifurcations of limit cycles and tori- a new research topic for statistical mechanics mechanics

    International Nuclear Information System (INIS)

    Haken, H.

    1980-01-01

    In the development of statistical mechanics we can more or less distinguish between two steps. First of all the main objective of statistical mechanics had been to give thermodynamics a solid theoretical basis starting from the microscopic world. The next step has then been performed in parallel with the development of irreversible thermodynamics dealing with processes close to thermal equilibrium. The problems dealt with here are mainly transport and relaxation processes. Over the past years it has become apparent that there is a third field, namely processes far away from thermal equilibrium. The particular interest in those processes stems from the fact that in such situations order can be generated on a macroscopic scale. The ordered states can be maintained by a flux of energy or matter through, these systems. In the realm of synergetjcs we have studied numerous examples and we now know that the occurrence of many of the ordered structures is governed by the same basic principles. (author)

  10. Statistical mechanics of dense plasmas and implications for the plasma polarization shift

    International Nuclear Information System (INIS)

    Rogers, F.J.

    1984-01-01

    A brief description of the statistical mechanics of reacting, dense, plasmas is given. The results do not support a Debye-like polarization shift at low density. It is shown that the electronic charge density factors into a strongly quantum mechanical part, that is not much affected by many body correlations and a weakly quantum mechanical part, that is considerably effected by many body correlations. The few body charge density is obtained from direct solution of the Schroedinger equation and the many body charge density is obtained from the hypernetted chain equation through the introduction of a pseudopotential

  11. Many-body problem in quantum mechanics and quantum statistical mechanics

    International Nuclear Information System (INIS)

    Lee, T.D.; Yang, C.N.

    1983-01-01

    This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/

  12. Statistical mechanical analysis of the linear vector channel in digital communication

    International Nuclear Information System (INIS)

    Takeda, Koujin; Hatabu, Atsushi; Kabashima, Yoshiyuki

    2007-01-01

    A statistical mechanical framework to analyze linear vector channel models in digital wireless communication is proposed for a large system. The framework is a generalization of that proposed for code-division multiple-access systems in Takeda et al (2006 Europhys. Lett. 76 1193) and enables the analysis of the system in which the elements of the channel transfer matrix are statistically correlated with each other. The significance of the proposed scheme is demonstrated by assessing the performance of an existing model of multi-input multi-output communication systems

  13. Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

    Science.gov (United States)

    Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael

    2011-02-01

    This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.

  14. Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

    Science.gov (United States)

    Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando; Preskill, John; Svore, Krysta M.

    2018-05-01

    Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p3DCC (1 )≃1.9 % and p3DCC (2 )≃27.6 % . We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

  15. Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems.

    Science.gov (United States)

    Gogolin, Christian; Eisert, Jens

    2016-05-01

    We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state statistical mechanics, the eigenstate thermalisation hypothesis, the equivalence of ensembles, non-equilibration dynamics following global and local quenches as well as ramps. We also address initial state independence, absence of thermalisation, and many-body localisation. We elucidate the role played by key concepts for these phenomena, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles, and quantum (non-)integrability. We put emphasis on rigorous approaches and present the most important results in a unified language.

  16. Statistical mechanical foundation of the peridynamic nonlocal continuum theory: energy and momentum conservation laws.

    Science.gov (United States)

    Lehoucq, R B; Sears, Mark P

    2011-09-01

    The purpose of this paper is to derive the energy and momentum conservation laws of the peridynamic nonlocal continuum theory using the principles of classical statistical mechanics. The peridynamic laws allow the consideration of discontinuous motion, or deformation, by relying on integral operators. These operators sum forces and power expenditures separated by a finite distance and so represent nonlocal interaction. The integral operators replace the differential divergence operators conventionally used, thereby obviating special treatment at points of discontinuity. The derivation presented employs a general multibody interatomic potential, avoiding the standard assumption of a pairwise decomposition. The integral operators are also expressed in terms of a stress tensor and heat flux vector under the assumption that these fields are differentiable, demonstrating that the classical continuum energy and momentum conservation laws are consequences of the more general peridynamic laws. An important conclusion is that nonlocal interaction is intrinsic to continuum conservation laws when derived using the principles of statistical mechanics.

  17. Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory

    Science.gov (United States)

    Ingber, Lester

    1994-05-01

    Previous papers in this series of statistical mechanics of neocortical interactions (SMNI) have detailed a development from the relatively microscopic scales of neurons up to the macroscopic scales as recorded by electroencephalography (EEG), requiring an intermediate mesocolumnar scale to be developed at the scale of minicolumns (~=102 neurons) and macrocolumns (~=105 neurons). Opportunity was taken to view SMNI as sets of statistical constraints, not necessarily describing specific synaptic or neuronal mechanisms, on neuronal interactions, on some aspects of short-term memory (STM), e.g., its capacity, stability, and duration. A recently developed c-language code, pathint, provides a non-Monte Carlo technique for calculating the dynamic evolution of arbitrary-dimension (subject to computer resources) nonlinear Lagrangians, such as derived for the two-variable SMNI problem. Here, pathint is used to explicitly detail the evolution of the SMNI constraints on STM.

  18. Statistical-mechanical lattice models for protein-DNA binding in chromatin

    International Nuclear Information System (INIS)

    Teif, Vladimir B; Rippe, Karsten

    2010-01-01

    Statistical-mechanical lattice models for protein-DNA binding are well established as a method to describe complex ligand binding equilibria measured in vitro with purified DNA and protein components. Recently, a new field of applications has opened up for this approach since it has become possible to experimentally quantify genome-wide protein occupancies in relation to the DNA sequence. In particular, the organization of the eukaryotic genome by histone proteins into a nucleoprotein complex termed chromatin has been recognized as a key parameter that controls the access of transcription factors to the DNA sequence. New approaches have to be developed to derive statistical-mechanical lattice descriptions of chromatin-associated protein-DNA interactions. Here, we present the theoretical framework for lattice models of histone-DNA interactions in chromatin and investigate the (competitive) DNA binding of other chromosomal proteins and transcription factors. The results have a number of applications for quantitative models for the regulation of gene expression.

  19. Addressing the statistical mechanics of planet orbits in the solar system

    Science.gov (United States)

    Mogavero, Federico

    2017-10-01

    The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position and velocity of the planets are replaced by the probability density function (PDF) of their orbital elements. It is natural to set up this kind of approach in the framework of statistical mechanics. In the present paper, I focus on the collisionless excitation of eccentricities and inclinations via gravitational interactions in a planetary system. The future planet trajectories in the solar system constitute the prototype of this kind of dynamics. I thus address the statistical mechanics of the solar system planet orbits and try to reproduce the PDFs numerically constructed by Laskar (2008, Icarus, 196, 1). I show that the microcanonical ensemble of the Laplace-Lagrange theory accurately reproduces the statistics of the giant planet orbits. To model the inner planets I then investigate the ansatz of equiprobability in the phase space constrained by the secular integrals of motion. The eccentricity and inclination PDFs of Earth and Venus are reproduced with no free parameters. Within the limitations of a stationary model, the predictions also show a reasonable agreement with Mars PDFs and that of Mercury inclination. The eccentricity of Mercury demands in contrast a deeper analysis. I finally revisit the random walk approach of Laskar to the time dependence of the inner planet PDFs. Such a statistical theory could be combined with direct numerical simulations of planet trajectories in the context of planet formation, which is likely to be a chaotic process.

  20. A cross-culture, cross-gender comparison of perspective taking mechanisms

    OpenAIRE

    Kessler, Klaus; Cao, Liyu; O'Shea, Kieran J.; Wang, Hong Fang

    2014-01-01

    Being able to judge another person's visuo-spatial perspective is an essential social skill, hence we investigated the generalizability of the involved mechanisms across cultures and genders. Developmental, cross-species, and our own previous research suggest that two different forms of perspective taking can be distinguished, which are subserved by two distinct mechanisms. The simpler form relies on inferring another's line-of-sight, whereas the more complex form depends on embodied transfor...

  1. A study of outliers in statistical distributions of mechanical properties of structural steels

    International Nuclear Information System (INIS)

    Oefverbeck, P.; Oestberg, G.

    1977-01-01

    The safety against failure of pressure vessels can be assessed by statistical methods, so-called probabilistic fracture mechanics. The data base for such estimations is admittedly rather meagre, making it necessary to assume certain conventional statistical distributions. Since the failure rates arrived at are low, for nuclear vessels of the order of 10 - to 10 - per year, the extremes of the variables involved, among other things the mechanical properties of the steel used, are of particular interest. A question sometimes raised is whether outliers, or values exceeding the extremes in the assumed distributions, might occur. In order to explore this possibility a study has been made of strength values of three qualities of structural steels, available in samples of up to about 12,000. Statistical evaluation of these samples with respect to outliers, using standard methods for this purpose, revealed the presence of such outliers in most cases, with a frequency of occurrence of, typically, a few values per thousand, estimated by the methods described. Obviously, statistical analysis alone cannot be expected to shed any light on the causes of outliers. Thus, the interpretation of these results with respect to their implication for the probabilistic estimation of the integrety of pressure vessels must await further studies of a similar nature in which the test specimens corresponding to outliers can be recovered and examined metallographically. For the moment the results should be regarded only as a factor to be considered in discussions of the safety of pressure vessels. (author)

  2. Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

    International Nuclear Information System (INIS)

    Ichinose, Shoichi

    2010-01-01

    A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

  3. PREFACE: Counting Complexity: An international workshop on statistical mechanics and combinatorics

    Science.gov (United States)

    de Gier, Jan; Warnaar, Ole

    2006-07-01

    On 10-15 July 2005 the conference `Counting Complexity: An international workshop on statistical mechanics and combinatorics' was held on Dunk Island, Queensland, Australia in celebration of Tony Guttmann's 60th birthday. Dunk Island provided the perfect setting for engaging in almost all of Tony's life-long passions: swimming, running, food, wine and, of course, plenty of mathematics and physics. The conference was attended by many of Tony's close scientific friends from all over the world, and most talks were presented by his past and present collaborators. This volume contains the proceedings of the meeting and consists of 24 refereed research papers in the fields of statistical mechanics, condensed matter physics and combinatorics. These papers provide an excellent illustration of the breadth and scope of Tony's work. The very first contribution, written by Stu Whittington, contains an overview of the many scientific achievements of Tony over the past 40 years in mathematics and physics. The organizing committee, consisting of Richard Brak, Aleks Owczarek, Jan de Gier, Emma Lockwood, Andrew Rechnitzer and Ole Warnaar, gratefully acknowledges the Australian Mathematical Society (AustMS), the Australian Mathematical Sciences Institute (AMSI), the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), the ARC Complex Open Systems Research Network (COSNet), the Institute of Physics (IOP) and the Department of Mathematics and Statistics of The University of Melbourne for financial support in organizing the conference. Tony, we hope that your future years in mathematics will be numerous. Count yourself lucky! Tony Guttman

  4. Essays on the statistical mechanics of the labor market and implications for the distribution of earned income

    Science.gov (United States)

    Schneider, Markus P. A.

    This dissertation contributes to two areas in economics: the understanding of the distribution of earned income and to Bayesian analysis of distributional data. Recently, physicists claimed that the distribution of earned income is exponential (see Yakovenko, 2009). The first chapter explores the perspective that the economy is a statistical mechanical system and the implication for labor market outcomes is considered critically. The robustness of the empirical results that lead to the physicists' claims, the significance of the exponential distribution in statistical mechanics, and the case for a conservation law in economics are discussed. The conclusion reached is that physicists' conception of the economy is too narrow even within their chosen framework, but that their overall approach is insightful. The dual labor market theory of segmented labor markets is invoked to understand why the observed distribution may be a mixture of distributional components, corresponding to different generating mechanisms described in Reich et al. (1973). The application of informational entropy in chapter II connects this work to Bayesian analysis and maximum entropy econometrics. The analysis follows E. T. Jaynes's treatment of Wolf's dice data, but is applied to the distribution of earned income based on CPS data. The results are calibrated to account for rounded survey responses using a simple simulation, and answer the graphical analyses by physicists. The results indicate that neither the income distribution of all respondents nor of the subpopulation used by physicists appears to be exponential. The empirics do support the claim that a mixture with exponential and log-normal distributional components ts the data. In the final chapter, a log-linear model is used to fit the exponential to the earned income distribution. Separating the CPS data by gender and marital status reveals that the exponential is only an appropriate model for a limited number of subpopulations, namely

  5. The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved

    International Nuclear Information System (INIS)

    Samaj, L

    2003-01-01

    The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid model is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics and the large-distance asymptotic behaviour of the two-body correlation functions

  6. Dimensionally regularized Tsallis' statistical mechanics and two-body Newton's gravitation

    Science.gov (United States)

    Zamora, J. D.; Rocca, M. C.; Plastino, A.; Ferri, G. L.

    2018-05-01

    Typical Tsallis' statistical mechanics' quantifiers like the partition function and the mean energy exhibit poles. We are speaking of the partition function Z and the mean energy 〈 U 〉 . The poles appear for distinctive values of Tsallis' characteristic real parameter q, at a numerable set of rational numbers of the q-line. These poles are dealt with dimensional regularization resources. The physical effects of these poles on the specific heats are studied here for the two-body classical gravitation potential.

  7. Evaluation of mechanical properties of steel wire ropes by statistical methods

    Directory of Open Access Journals (Sweden)

    Boroška Ján

    1999-12-01

    Full Text Available The contribution deals with the evaluation of mechanical properties of steel wire ropes using statistical methods from the viewpoint of the quality of single wires as well as the internal construction of the wire ropes. The evaluation is based on the loading capacity calculated from the strength, number of folds and torsions. For the better ilustration, a box plot has been constructed.

  8. Are Statisticians Cold-Blooded Bosses? A New Perspective on the "Old" Concept of Statistical Population

    Science.gov (United States)

    Lu, Yonggang; Henning, Kevin S. S.

    2013-01-01

    Spurred by recent writings regarding statistical pragmatism, we propose a simple, practical approach to introducing students to a new style of statistical thinking that models nature through the lens of data-generating processes, not populations. (Contains 5 figures.)

  9. Introduction to conformal invariance in statistical mechanics and to random surface models

    International Nuclear Information System (INIS)

    David, F.

    1995-01-01

    In the first part of these lectures I give a brief and somewhat superficial introduction to the techniques of conformal invariance and to a few applications in statistical mechanics in two dimensions. My purpose is to introduce the basic ideas and some standard results for the students who are not familiar with the theory, and to introduce concepts and tools which will be useful for the other lecturers, rather than to give a complete and up to date review of the subject. In the second part I discuss several problems in the statistical mechanics of two dimensional random surfaces and membranes. As an introduction, I present some basic facts about the statistical mechanics of one-dimensional objects and polymers, which are classical examples of objects with critical properties. Then I emphasize the special role of curvature energy and of the elastic energy associated with the internal structure of membranes, and the corresponding models of random surfaces. Finally, I discuss the specific problem of self-avoiding tethered surfaces, whose critical properties are still poorly understood, and for which the applicability of some basic techniques of field theory, such as renormalization group calculations, has been understood only recently. (orig.)

  10. Statistical learning and probabilistic prediction in music cognition: mechanisms of stylistic enculturation.

    Science.gov (United States)

    Pearce, Marcus T

    2018-05-11

    Music perception depends on internal psychological models derived through exposure to a musical culture. It is hypothesized that this musical enculturation depends on two cognitive processes: (1) statistical learning, in which listeners acquire internal cognitive models of statistical regularities present in the music to which they are exposed; and (2) probabilistic prediction based on these learned models that enables listeners to organize and process their mental representations of music. To corroborate these hypotheses, I review research that uses a computational model of probabilistic prediction based on statistical learning (the information dynamics of music (IDyOM) model) to simulate data from empirical studies of human listeners. The results show that a broad range of psychological processes involved in music perception-expectation, emotion, memory, similarity, segmentation, and meter-can be understood in terms of a single, underlying process of probabilistic prediction using learned statistical models. Furthermore, IDyOM simulations of listeners from different musical cultures demonstrate that statistical learning can plausibly predict causal effects of differential cultural exposure to musical styles, providing a quantitative model of cultural distance. Understanding the neural basis of musical enculturation will benefit from close coordination between empirical neuroimaging and computational modeling of underlying mechanisms, as outlined here. © 2018 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals, Inc. on behalf of New York Academy of Sciences.

  11. On the geometry of the spin-statistics connection in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Reyes, A.

    2006-07-01

    The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishability and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be

  12. Perspective: Ab initio force field methods derived from quantum mechanics

    Science.gov (United States)

    Xu, Peng; Guidez, Emilie B.; Bertoni, Colleen; Gordon, Mark S.

    2018-03-01

    It is often desirable to accurately and efficiently model the behavior of large molecular systems in the condensed phase (thousands to tens of thousands of atoms) over long time scales (from nanoseconds to milliseconds). In these cases, ab initio methods are difficult due to the increasing computational cost with the number of electrons. A more computationally attractive alternative is to perform the simulations at the atomic level using a parameterized function to model the electronic energy. Many empirical force fields have been developed for this purpose. However, the functions that are used to model interatomic and intermolecular interactions contain many fitted parameters obtained from selected model systems, and such classical force fields cannot properly simulate important electronic effects. Furthermore, while such force fields are computationally affordable, they are not reliable when applied to systems that differ significantly from those used in their parameterization. They also cannot provide the information necessary to analyze the interactions that occur in the system, making the systematic improvement of the functional forms that are used difficult. Ab initio force field methods aim to combine the merits of both types of methods. The ideal ab initio force fields are built on first principles and require no fitted parameters. Ab initio force field methods surveyed in this perspective are based on fragmentation approaches and intermolecular perturbation theory. This perspective summarizes their theoretical foundation, key components in their formulation, and discusses key aspects of these methods such as accuracy and formal computational cost. The ab initio force fields considered here were developed for different targets, and this perspective also aims to provide a balanced presentation of their strengths and shortcomings. Finally, this perspective suggests some future directions for this actively developing area.

  13. Bayesian Statistical Mechanics: Entropy-Enthalpy Compensation and Universal Equation of State at the Tip of Pen

    Directory of Open Access Journals (Sweden)

    Evgeni B. Starikov

    2018-02-01

    Full Text Available This work has shown the way to put the formal statistical-mechanical basement under the hotly debated notion of enthalpy-entropy compensation. The possibility of writing down the universal equation of state based upon the statistical mechanics is discussed here.

  14. Solvability of a class of systems of infinite-dimensional integral equations and their application in statistical mechanics

    International Nuclear Information System (INIS)

    Gonchar, N.S.

    1986-01-01

    This paper presents a mathematical method developed for investigating a class of systems of infinite-dimensional integral equations which have application in statistical mechanics. Necessary and sufficient conditions are obtained for the uniqueness and bifurcation of the solution of this class of systems of equations. Problems of equilibrium statistical mechanics are considered on the basis of this method

  15. A statistical mechanics model for free-for-all airplane passenger boarding

    Energy Technology Data Exchange (ETDEWEB)

    Steffen, Jason H.; /Fermilab

    2008-08-01

    I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty.

  16. A statistical mechanics model for free-for-all airplane passenger boarding

    Science.gov (United States)

    Steffen, Jason H.

    2008-12-01

    I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics, where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty.

  17. Statistical mechanics of gravitons in a box and the black hole entropy

    Science.gov (United States)

    Viaggiu, Stefano

    2017-05-01

    This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index ℓ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy 〈 E 〉 results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole internal energy U is provided by its ADM rest energy, without invoking particular quantum gravity theories. This seriously suggests that the interior of a black hole can be composed of trapped gravitons at a thermodynamical temperature proportional by a factor ≃ 2 to the horizon temperature Th.

  18. A statistical mechanics model for free-for-all airplane passenger boarding

    International Nuclear Information System (INIS)

    Steffen, Jason H.; Fermilab

    2008-01-01

    I discuss a model for free-for-all passenger boarding which is employed by some discount air carriers. The model is based on the principles of statistical mechanics where each seat in the aircraft has an associated energy which reflects the preferences of travelers. As each passenger enters the airplane they select their seats using Boltzmann statistics, proceed to that location, load their luggage, sit down, and the partition function seen by remaining passengers is modified to reflect this fact. I discuss the various model parameters and make qualitative comparisons of this passenger boarding model with those that involve assigned seats. The model can be used to predict the probability that certain seats will be occupied at different times during the boarding process. These results might provide a useful description of this boarding method. The model is a relatively unusual application of undergraduate level physics and describes a situation familiar to many students and faculty

  19. Implementation of Statistical Process Control: Evaluating the Mechanical Performance of a Candidate Silicone Elastomer Docking Seal

    Science.gov (United States)

    Oravec, Heather Ann; Daniels, Christopher C.

    2014-01-01

    The National Aeronautics and Space Administration has been developing a novel docking system to meet the requirements of future exploration missions to low-Earth orbit and beyond. A dynamic gas pressure seal is located at the main interface between the active and passive mating components of the new docking system. This seal is designed to operate in the harsh space environment, but is also to perform within strict loading requirements while maintaining an acceptable level of leak rate. In this study, a candidate silicone elastomer seal was designed, and multiple subscale test articles were manufactured for evaluation purposes. The force required to fully compress each test article at room temperature was quantified and found to be below the maximum allowable load for the docking system. However, a significant amount of scatter was observed in the test results. Due to the stochastic nature of the mechanical performance of this candidate docking seal, a statistical process control technique was implemented to isolate unusual compression behavior from typical mechanical performance. The results of this statistical analysis indicated a lack of process control, suggesting a variation in the manufacturing phase of the process. Further investigation revealed that changes in the manufacturing molding process had occurred which may have influenced the mechanical performance of the seal. This knowledge improves the chance of this and future space seals to satisfy or exceed design specifications.

  20. Statistical analysis of the factors that influenced the mechanical properties improvement of cassava starch films

    Science.gov (United States)

    Monteiro, Mayra; Oliveira, Victor; Santos, Francisco; Barros Neto, Eduardo; Silva, Karyn; Silva, Rayane; Henrique, João; Chibério, Abimaelle

    2017-08-01

    In order to obtain cassava starch films with improved mechanical properties in relation to the synthetic polymer in the packaging production, a complete factorial design 23 was carried out in order to investigate which factor significantly influences the tensile strength of the biofilm. The factors to be investigated were cassava starch, glycerol and modified clay contents. Modified bentonite clay was used as a filling material of the biofilm. Glycerol was the plasticizer used to thermoplastify cassava starch. The factorial analysis suggested a regression model capable of predicting the optimal mechanical property of the cassava starch film from the maximization of the tensile strength. The reliability of the regression model was tested by the correlation established with the experimental data through the following statistical analyse: Pareto graph. The modified clay was the factor of greater statistical significance on the observed response variable, being the factor that contributed most to the improvement of the mechanical property of the starch film. The factorial experiments showed that the interaction of glycerol with both modified clay and cassava starch was significant for the reduction of biofilm ductility. Modified clay and cassava starch contributed to the maximization of biofilm ductility, while glycerol contributed to the minimization.

  1. Students' Perspectives of Using Cooperative Learning in a Flipped Statistics Classroom

    Science.gov (United States)

    Chen, Liwen; Chen, Tung-Liang; Chen, Nian-Shing

    2015-01-01

    Statistics has been recognised as one of the most anxiety-provoking subjects to learn in the higher education context. Educators have continuously endeavoured to find ways to integrate digital technologies and innovative pedagogies in the classroom to eliminate the fear of statistics. The purpose of this study is to systematically identify…

  2. Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography

    Science.gov (United States)

    Ingber, Lester

    1991-09-01

    A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single-neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked-potential data being collected to investigate genetic predispositions to alcoholism and to extract brain ``signatures'' of short-term memory. Using the numerical algorithm of very fast simulated reannealing, it is demonstrated that SMNI can indeed fit these data within experimentally observed ranges of its underlying neuronal-synaptic parameters, and the quantitative modeling results are used to examine physical neocortical mechanisms to discriminate high-risk and low-risk populations genetically predisposed to alcoholism. Since this study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent with EEG data during selective attention tasks and with neocortical mechanisms describing short-term memory previously published using this approach. This paper explicitly identifies similar nonlinear stochastic mechanisms of interaction at the microscopic-neuronal, mesoscopic-columnar, and macroscopic-regional scales of neocortical interactions. These results give strong quantitative support for an accurate intuitive picture, portraying

  3. Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

    Science.gov (United States)

    Pohorille, Andrew

    2006-01-01

    The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described

  4. Portfolio selection problem with liquidity constraints under non-extensive statistical mechanics

    International Nuclear Information System (INIS)

    Zhao, Pan; Xiao, Qingxian

    2016-01-01

    In this study, we consider the optimal portfolio selection problem with liquidity limits. A portfolio selection model is proposed in which the risky asset price is driven by the process based on non-extensive statistical mechanics instead of the classic Wiener process. Using dynamic programming and Lagrange multiplier methods, we obtain the optimal policy and value function. Moreover, the numerical results indicate that this model is considerably different from the model based on the classic Wiener process, the optimal strategy is affected by the non-extensive parameter q, the increase in the investment in the risky asset is faster at a larger parameter q and the increase in wealth is similar.

  5. Portfolio optimization problem with nonidentical variances of asset returns using statistical mechanical informatics

    Science.gov (United States)

    Shinzato, Takashi

    2016-12-01

    The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We defined two characteristic quantities of an optimal portfolio, namely, minimal investment risk and investment concentration, in order to solve the portfolio optimization problem and analytically determined their asymptotical behaviors using replica analysis. Numerical experiments were also performed, and a comparison between the results of our simulation and those obtained via replica analysis validated our proposed method.

  6. PREFACE: International Workshop on Statistical-Mechanical Informatics 2008 (IW-SMI 2008)

    Science.gov (United States)

    Hayashi, Masahito; Inoue, Jun-ichi; Kabashima, Yoshiyuki; Tanaka, Kazuyuki

    2009-01-01

    Statistical mechanical informatics (SMI) is an approach that applies physics to information science, in which many-body problems in information processing are tackled using statistical mechanics methods. In the last decade, the use of SMI has resulted in great advances in research into classical information processing, in particular, theories of information and communications, probabilistic inference and combinatorial optimization problems. It is expected that the success of SMI can be extended to quantum systems. The importance of many-body problems is also being recognized in quantum information theory (QIT), for which quantification of entanglement of bipartite systems has recently been almost completely established after considerable effort. SMI and QIT are sufficiently well developed that it is now appropriate to consider applying SMI to quantum systems and developing many-body theory in QIT. This combination of SMI and QIT is highly likely to contribute significantly to the development of both research fields. The International Workshop on Statistical-Mechanical Informatics has been organized in response to this situation. This workshop, held at Sendai International Conference Center, Sendai, Japan, 14-17 September 2008, and sponsored by the Grant-in-Aid for Scientific Research on Priority Areas `Deepening and Expansion of Statistical Mechanical Informatics (DEX-SMI)' (Head investigator: Yoshiyuki Kabashima, Tokyo Institute of Technology) (Project http://dex-smi.sp.dis.titech.ac.jp/DEX-SMI), was intended to provide leading researchers with strong interdisciplinary interests in QIT and SMI with the opportunity to engage in intensive discussions. The aim of the workshop was to expand SMI to quantum systems and QIT research on quantum (entangled) many-body systems, to discuss possible future directions, and to offer researchers the opportunity to exchange ideas that may lead to joint research initiatives. We would like to thank the contributors of the workshop

  7. Statistical mechanics of Fermi-Pasta-Ulam chains with the canonical ensemble

    Science.gov (United States)

    Demirel, Melik C.; Sayar, Mehmet; Atılgan, Ali R.

    1997-03-01

    Low-energy vibrations of a Fermi-Pasta-Ulam-Β (FPU-Β) chain with 16 repeat units are analyzed with the aid of numerical experiments and the statistical mechanics equations of the canonical ensemble. Constant temperature numerical integrations are performed by employing the cubic coupling scheme of Kusnezov et al. [Ann. Phys. 204, 155 (1990)]. Very good agreement is obtained between numerical results and theoretical predictions for the probability distributions of the generalized coordinates and momenta both of the chain and of the thermal bath. It is also shown that the average energy of the chain scales linearly with the bath temperature.

  8. Statistical mechanics of a one-component fluid of charged hard rods in 1D

    International Nuclear Information System (INIS)

    Vericat, F.; Blum, L.

    1986-09-01

    The statistical mechanics of a classical one component system of charged hard rods in a neutralizing background is investigated in 1D stressing on the effects of the hard core interactions over the thermodynamic and the structure of the system. The crystalline status of the system at all temperatures and densities and the absence of phase transitions is shown by extending previous results of Baxter and Kunz on the one-component plasma of point particles. Explicit expressions for the thermodynamic functions and the one-particle correlation function are given in the limits of small and strong couplings. (author)

  9. Reason of method of density functional in classical and quantum statistical mechanisms

    International Nuclear Information System (INIS)

    Dinariev, O.Yu.

    2000-01-01

    Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

  10. Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity

    Science.gov (United States)

    Ingber, Lester

    1984-06-01

    A theory developed by the author to describe macroscopic neocortical interactions demonstrates that empirical values of chemical and electrical parameters of synaptic interactions establish several minima of the path-integral Lagrangian as a function of excitatory and inhibitory columnar firings. The number of possible minima, their time scales of hysteresis and probable reverberations, and their nearest-neighbor columnar interactions are all consistent with well-established empirical rules of human short-term memory. Thus, aspects of conscious experience are derived from neuronal firing patterns, using modern methods of nonlinear nonequilibrium statistical mechanics to develop realistic explicit synaptic interactions.

  11. Existence and uniqueness of Gibbs states for a statistical mechanical polyacetylene model

    International Nuclear Information System (INIS)

    Park, Y.M.

    1987-01-01

    One-dimensional polyacetylene is studied as a model of statistical mechanics. In a semiclassical approximation the system is equivalent to a quantum XY model interacting with unbounded classical spins in one-dimensional lattice space Z. By establishing uniform estimates, an infinite-volume-limit Hilbert space, a strongly continuous time evolution group of unitary operators, and an invariant vector are constructed. Moreover, it is proven that any infinite-limit state satisfies Gibbs conditions. Finally, a modification of Araki's relative entropy method is used to establish the uniqueness of Gibbs states

  12. Statistical mechanics of directed models of polymers in the square lattice

    International Nuclear Information System (INIS)

    Rensburg, E J Janse van

    2003-01-01

    Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce partition functions and free energies, and then investigate these using the general framework of critical phenomena. Generating function and statistical mechanics approaches are closely related. For example, questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function, and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function. In this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented. These methods include decomposition methods leading to functional recursions, as well as the Temperley method (that is implemented by creating a combinatorial object, one slice at a time). A constant term formulation of the generating function will also be reviewed. The thermodynamic features and critical behaviour in models of directed paths may be

  13. Non-extensive statistical mechanics and black hole entropy from quantum geometry

    Directory of Open Access Journals (Sweden)

    Abhishek Majhi

    2017-12-01

    Full Text Available Using non-extensive statistical mechanics, the Bekenstein–Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero–Immirzi parameter (γ. The arbitrariness of γ is encoded in the strength of the “bias” created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of γ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.

  14. The nano-mechanical signature of Ultra High Performance Concrete by statistical nanoindentation techniques

    International Nuclear Information System (INIS)

    Sorelli, Luca; Constantinides, Georgios; Ulm, Franz-Josef; Toutlemonde, Francois

    2008-01-01

    Advances in engineering the microstructure of cementitious composites have led to the development of fiber reinforced Ultra High Performance Concretes (UHPC). The scope of this paper is twofold, first to characterize the nano-mechanical properties of the phases governing the UHPC microstructure by means of a novel statistical nanoindentation technique; then to upscale those nanoscale properties, by means of continuum micromechanics, to the macroscopic scale of engineering applications. In particular, a combined investigation of nanoindentation, scanning electron microscope (SEM) and X-ray Diffraction (XRD) indicates that the fiber-matrix transition zone is relatively defect free. On this basis, a four-level multiscale model with defect free interfaces allows to accurately determine the composite stiffness from the measured nano-mechanical properties. Besides evidencing the dominant role of high density calcium silicate hydrates and the stiffening effect of residual clinker, the suggested model may become a useful tool for further optimizing cement-based engineered composites

  15. Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

    International Nuclear Information System (INIS)

    Ng, Felix S.L.

    2016-01-01

    We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

  16. Statistical evaluation of low cycle loading curves parameters for structural materials by mechanical characteristics

    International Nuclear Information System (INIS)

    Daunys, Mykolas; Sniuolis, Raimondas

    2006-01-01

    About 300 welded joint materials that are used in nuclear power energy were tested under monotonous tension and low cycle loading in Kaunas University of Technology together with St. Peterburg Central Research Institute of Structural Materials in 1970-2000. The main mechanical, low cycle loading and fracture characteristics of base metals, weld metals and some heat-affected zones of welded joints metals were determined during these experiments. Analytical dependences of low cycle fatigue parameters on mechanical characteristics of structural materials were proposed on the basis of a large number of experimental data, obtained by the same methods and testing equipment. When these dependences are used, expensive low cycle fatigue tests may be omitted and it is possible to compute low cycle loading curves parameters and lifetime for structural materials according to the main mechanical characteristics given in technical manuals. Dependences of low cycle loading curves parameters on mechanical characteristics for several groups of structural materials used in Russian nuclear power energy are obtained by statistical methods and proposed in this paper

  17. Statistical mechanics of binary mixture adsorption in metal-organic frameworks in the osmotic ensemble

    Science.gov (United States)

    Dunne, Lawrence J.; Manos, George

    2018-03-01

    Although crucial for designing separation processes little is known experimentally about multi-component adsorption isotherms in comparison with pure single components. Very few binary mixture adsorption isotherms are to be found in the literature and information about isotherms over a wide range of gas-phase composition and mechanical pressures and temperature is lacking. Here, we present a quasi-one-dimensional statistical mechanical model of binary mixture adsorption in metal-organic frameworks (MOFs) treated exactly by a transfer matrix method in the osmotic ensemble. The experimental parameter space may be very complex and investigations into multi-component mixture adsorption may be guided by theoretical insights. The approach successfully models breathing structural transitions induced by adsorption giving a good account of the shape of adsorption isotherms of CO2 and CH4 adsorption in MIL-53(Al). Binary mixture isotherms and co-adsorption-phase diagrams are also calculated and found to give a good description of the experimental trends in these properties and because of the wide model parameter range which reproduces this behaviour suggests that this is generic to MOFs. Finally, a study is made of the influence of mechanical pressure on the shape of CO2 and CH4 adsorption isotherms in MIL-53(Al). Quite modest mechanical pressures can induce significant changes to isotherm shapes in MOFs with implications for binary mixture separation processes. This article is part of the theme issue `Modern theoretical chemistry'.

  18. A statistical model of uplink inter-cell interference with slow and fast power control mechanisms

    KAUST Repository

    Tabassum, Hina

    2013-09-01

    Uplink power control is in essence an interference mitigation technique that aims at minimizing the inter-cell interference (ICI) in cellular networks by reducing the transmit power levels of the mobile users while maintaining their target received signal quality levels at base stations. Power control mechanisms directly impact the interference dynamics and, thus, affect the overall achievable capacity and consumed power in cellular networks. Due to the stochastic nature of wireless channels and mobile users\\' locations, it is important to derive theoretical models for ICI that can capture the impact of design alternatives related to power control mechanisms. To this end, we derive and verify a novel statistical model for uplink ICI in Generalized-K composite fading environments as a function of various slow and fast power control mechanisms. The derived expressions are then utilized to quantify numerically key network performance metrics that include average resource fairness, average reduction in power consumption, and ergodic capacity. The accuracy of the derived expressions is validated via Monte-Carlo simulations. Results are generated for multiple network scenarios, and insights are extracted to assess various power control mechanisms as a function of system parameters. © 1972-2012 IEEE.

  19. Neocortical dynamics at multiple scales: EEG standing waves, statistical mechanics, and physical analogs.

    Science.gov (United States)

    Ingber, Lester; Nunez, Paul L

    2011-02-01

    The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical columns via short-ranged non-myelinated fibers. A mechanical model consisting of a stretched string with attached nonlinear springs demonstrates the general idea. The string produces standing waves analogous to large-scale coherent EEG observed in some brain states. The attached springs are analogous to the smaller (mesoscopic) scale columnar dynamics. Generally, we expect string displacement and EEG at all scales to result from both global and local phenomena. A statistical mechanics of neocortical interactions (SMNI) calculates oscillatory behavior consistent with typical EEG, within columns, between neighboring columns via short-ranged non-myelinated fibers, across cortical regions via myelinated fibers, and also derives a string equation consistent with the global EEG model. Copyright © 2010 Elsevier Inc. All rights reserved.

  20. A statistical model of uplink inter-cell interference with slow and fast power control mechanisms

    KAUST Repository

    Tabassum, Hina; Yilmaz, Ferkan; Dawy, Zaher; Alouini, Mohamed-Slim

    2013-01-01

    Uplink power control is in essence an interference mitigation technique that aims at minimizing the inter-cell interference (ICI) in cellular networks by reducing the transmit power levels of the mobile users while maintaining their target received signal quality levels at base stations. Power control mechanisms directly impact the interference dynamics and, thus, affect the overall achievable capacity and consumed power in cellular networks. Due to the stochastic nature of wireless channels and mobile users' locations, it is important to derive theoretical models for ICI that can capture the impact of design alternatives related to power control mechanisms. To this end, we derive and verify a novel statistical model for uplink ICI in Generalized-K composite fading environments as a function of various slow and fast power control mechanisms. The derived expressions are then utilized to quantify numerically key network performance metrics that include average resource fairness, average reduction in power consumption, and ergodic capacity. The accuracy of the derived expressions is validated via Monte-Carlo simulations. Results are generated for multiple network scenarios, and insights are extracted to assess various power control mechanisms as a function of system parameters. © 1972-2012 IEEE.

  1. A unified treatment of dynamics and scattering in classical and quantum statistical mechanics

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1978-01-01

    The common formal features of classical and quantum statistical mechanics are investigated at three separate levels: at the level of L 2 spaces of wave-packets on GAMMA-space, of Liouville spaces B 2 consisting of density operators constructed from such wave-packets, and of phase-space representation spaces P of GAMMA distribution functions. It is shown that at the last level the formal similarities become so outstanding that all key quantities in P-space, such as Liouville operators, Hamiltonian functions, position and momentum observables, etc., are represented by expressions which to the zeroth order in (h/2π) coincide in the classical and quantum case, and in some instances coincide completely. Scattering theory on the B 2 Liouville spaces takes on the same formal appearance for classical and quantum statistical mechanics, and to the zeroth order in (h/2π) it coincides in both cases. This makes possible the formulation of a classical approximation to quantum scattering, and of a computational scheme for determining rhosup(out) from rhosup(in) for successive order of (h/2π). (Auth.)

  2. Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion.

    Science.gov (United States)

    Gautestad, Arild O

    2012-09-07

    Animals moving under the influence of spatio-temporal scaling and long-term memory generate a kind of space-use pattern that has proved difficult to model within a coherent theoretical framework. An extended kind of statistical mechanics is needed, accounting for both the effects of spatial memory and scale-free space use, and put into a context of ecological conditions. Simulations illustrating the distinction between scale-specific and scale-free locomotion are presented. The results show how observational scale (time lag between relocations of an individual) may critically influence the interpretation of the underlying process. In this respect, a novel protocol is proposed as a method to distinguish between some main movement classes. For example, the 'power law in disguise' paradox-from a composite Brownian motion consisting of a superposition of independent movement processes at different scales-may be resolved by shifting the focus from pattern analysis at one particular temporal resolution towards a more process-oriented approach involving several scales of observation. A more explicit consideration of system complexity within a statistical mechanical framework, supplementing the more traditional mechanistic modelling approach, is advocated.

  3. A Note on Burg’s Modified Entropy in Statistical Mechanics

    Directory of Open Access Journals (Sweden)

    Amritansu Ray

    2016-02-01

    Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

  4. Statistical-Mechanical Analysis of Pre-training and Fine Tuning in Deep Learning

    Science.gov (United States)

    Ohzeki, Masayuki

    2015-03-01

    In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning — pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the extraction of features from the training data as a margin criterion in a high-dimensional feature-vector space. The self-organized classifier is then supplied with small amounts of labelled data, as in deep learning. Although we employ a simple single-layer perceptron model, rather than directly analyzing a multi-layer neural network, we find a nontrivial phase transition that is dependent on the number of unlabelled data in the generalization error of the resultant classifier. In this sense, we evaluate the efficacy of the unsupervised learning component of deep learning. The analysis is performed by the replica method, which is a sophisticated tool in statistical mechanics. We validate our result in the manner of deep learning, using a simple iterative algorithm to learn the weight vector on the basis of belief propagation.

  5. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

    Science.gov (United States)

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

  6. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

    Science.gov (United States)

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

  7. Statistical mechanics of relativistic spin-1 bosons in a magnetic field

    International Nuclear Information System (INIS)

    Daicic, J.; Frankel, N.E.

    1993-01-01

    This paper investigates the statistical mechanics of a gas of spin-1 particles with pair creation in a homogeneous magnetic field. It is shown that expansions for the thermodynamic potential and magnetization in fields below the mass scale of the constituent particles are well behaved. However, when the field is at or above the mass scale, an intrinsic pathology of the single-particle energy spectrum manifests itself in the statistical mechanics of the system. Whilst for the spin-0 and spin-1/2 analog of this system there seemed to be no barrier ab initio to the field strength, the nature of the vacuum, and the role of interactions, were always borne in mind as matters to be considered in a high-order treatment, particularly when the field was at or above the mass scale. In the spin-1 case, the pathology in the single-particle energy spectrum heralds this from the beginning, and seems to be a warning that a single particle non-interacting picture of physics at high energies needs some reconsideration. 10 refs

  8. Outcome and Perspectives from the First IAEA International Technical Meeting on Statistical Methodologies for Safeguards

    International Nuclear Information System (INIS)

    Norman, C.; Binner, R.; Peter, N. J.; Wuester, J.; Zhao, K.; Krieger, T.; Walczak-Typke, A.C.; Richet, S.; Portaix, C.G.; Martin, K.; Bonner, E.R.

    2015-01-01

    Statistical and probabilistic methodologies have always played a fundamental role in the field of safeguards. In-field inspection approaches are based on sampling algorithms and random verification schemes designed to achieve a designed detection probability for defects of interest (e.g., missing material, indicators of tampering with containment and other equipment, changes of design). In addition, the evaluation of verification data with a view to drawing soundly based safeguards conclusions rests on the application of various advanced statistical methodologies. The considerable progress of information technology in the field of data processing and computational capabilities as well as the evolution of safeguards concepts and the steep increase in the volume of verification data in the last decades call for the review and modernization of safeguards statistical methodologies, not only to improve the efficiency of the analytical processes but also to address new statistical and probabilistic questions. Modern computer-intensive approaches are also needed to fully exploit the large body of verification data collected over the years in the increasing number and diversifying types of nuclear fuel cycle facilities in the world. The first biennial IAEA International Technical Meeting on Statistical Methodologies for Safeguards was held in Vienna from the 16 to 18 October 2013. Recommendations and a working plan were drafted which identify and chart necessary steps to review, harmonize, update and consolidate statistical methodologies for safeguards. Three major problem spaces were identified: Random Verification Schemes, Estimation of Uncertainties and Statistical Evaluation of Safeguards Verification Data for which a detailed list of objectives and actions to be taken were established. Since the meeting, considerable progress was made to meet these objectives. The actions undertaken and their outcome are presented in this paper. (author)

  9. The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model

    Science.gov (United States)

    Verkley, Wim; Severijns, Camiel

    2014-05-01

    Lorenz [1] has devised a dynamical system that has proved to be very useful as a benchmark system in geophysical fluid dynamics. The system in its simplest form consists of a periodic array of variables that can be associated with an atmospheric field on a latitude circle. The system is driven by a constant forcing, is damped by linear friction and has a simple advection term that causes the model to behave chaotically if the forcing is large enough. Our aim is to predict the statistics of Lorenz' model on the basis of a given average value of its total energy - obtained from a numerical integration - and the assumption of statistical stationarity. Our method is the principle of maximum entropy [2] which in this case reads: the information entropy of the system's probability density function shall be maximal under the constraints of normalization, a given value of the average total energy and statistical stationarity. Statistical stationarity is incorporated approximately by using `stationarity constraints', i.e., by requiring that the average first and possibly higher-order time-derivatives of the energy are zero in the maximization of entropy. The analysis [3] reveals that, if the first stationarity constraint is used, the resulting probability density function rather accurately reproduces the statistics of the individual variables. If the second stationarity constraint is used as well, the correlations between the variables are also reproduced quite adequately. The method can be generalized straightforwardly and holds the promise of a viable non-equilibrium statistical mechanics of the forced-dissipative systems of geophysical fluid dynamics. [1] E.N. Lorenz, 1996: Predictability - A problem partly solved, in Proc. Seminar on Predictability (ECMWF, Reading, Berkshire, UK), Vol. 1, pp. 1-18. [2] E.T. Jaynes, 2003: Probability Theory - The Logic of Science (Cambridge University Press, Cambridge). [3] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy

  10. An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference

    Science.gov (United States)

    Bakker, Arthur; Ben-Zvi, Dani; Makar, Katie

    2017-12-01

    To understand how statistical and other types of reasoning are coordinated with actions to reduce uncertainty, we conducted a case study in vocational education that involved statistical hypothesis testing. We analyzed an intern's research project in a hospital laboratory in which reducing uncertainties was crucial to make a valid statistical inference. In his project, the intern, Sam, investigated whether patients' blood could be sent through pneumatic post without influencing the measurement of particular blood components. We asked, in the process of making a statistical inference, how are reasons and actions coordinated to reduce uncertainty? For the analysis, we used the semantic theory of inferentialism, specifically, the concept of webs of reasons and actions—complexes of interconnected reasons for facts and actions; these reasons include premises and conclusions, inferential relations, implications, motives for action, and utility of tools for specific purposes in a particular context. Analysis of interviews with Sam, his supervisor and teacher as well as video data of Sam in the classroom showed that many of Sam's actions aimed to reduce variability, rule out errors, and thus reduce uncertainties so as to arrive at a valid inference. Interestingly, the decisive factor was not the outcome of a t test but of the reference change value, a clinical chemical measure of analytic and biological variability. With insights from this case study, we expect that students can be better supported in connecting statistics with context and in dealing with uncertainty.

  11. Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

    International Nuclear Information System (INIS)

    Rebhan, E.

    2005-01-01

    The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

  12. New perspectives on mechanisms of sound generation in songbirds

    DEFF Research Database (Denmark)

    Goller, Franz; Larsen, Ole Næsbye

    2002-01-01

    -tone mechanism similar to human phonation with the labia forming a pneumatic valve. The classical avian model proposed that vibrations of the thin medial tympaniform membranes are the primary sound generating mechanism. As a direct test of these two hypotheses we ablated the medial tympaniform membranes in two......The physical mechanisms of sound generation in the vocal organ, the syrinx, of songbirds have been investigated mostly with indirect methods. Recent direct endoscopic observation identified vibrations of the labia as the principal sound source. This model suggests sound generation in a pulse...... atmosphere) as well as direct (labial vibration during tonal sound) measurements of syringeal vibrations support a vibration-based soundgenerating mechanism even for tonal sounds....

  13. How Medical Statistics has been established at the University of Freiburg: a historical perspective

    Directory of Open Access Journals (Sweden)

    Schumacher, Martin

    2005-06-01

    Full Text Available This contribution gives an outline on the reasons why the Faculty of Medicine at the University of Freiburg established an Institute of Medical Statistics and Documentation about fourty years ago as one of the first in Germany. It will be shown that the Professor of Medical Microbiology and Hygiene at that time initiated and promoted this development being himself motivated by the successful implementation of a vaccine against poliomyelitis through rigorous design, conduct and statistical analysis of a large scale field trial.

  14. Dysfunctions of the contemporary family from the perspective of judicial statistics

    Directory of Open Access Journals (Sweden)

    DANUTA KOWALCZYK

    2017-10-01

    Full Text Available The problems connected with the dysfunctions of the contemporary family are the subject of the study. Judicial statistics related mostly to the proceedings of family courts have been employed in the analysis. Emphasis has been placed on the problems related to the marital bond and parental responsibility. Statistical data suggests that there are some negative phenomena in both of these realms. Divorce and separation still constitute the cause of the incompleteness of family environments. Th e level of court interference in how parental responsibility is exercised which serves to protect children from the hazards of the lack of proper care is still not decreased.

  15. Statistical evaluation of the mechanical properties of high-volume class F fly ash concretes

    KAUST Repository

    Yoon, Seyoon

    2014-03-01

    High-Volume Fly Ash (HVFA) concretes are seen by many as a feasible solution for sustainable, low embodied carbon construction. At the moment, fly ash is classified as a waste by-product, primarily of thermal power stations. In this paper the authors experimentally and statistically investigated the effects of mix-design factors on the mechanical properties of high-volume class F fly ash concretes. A total of 240 and 32 samples were produced and tested in the laboratory to measure compressive strength and Young\\'s modulus respectively. Applicability of the CEB-FIP (Comite Euro-international du Béton - Fédération Internationale de la Précontrainte) and ACI (American Concrete Institute) Building Model Code (Thomas, 2010; ACI Committee 209, 1982) [1,2] to the experimentally-derived mechanical property data for HVFA concretes was established. Furthermore, using multiple linear regression analysis, Mean Squared Residuals (MSRs) were obtained to determine whether a weight- or volume-based mix proportion is better to predict the mechanical properties of HVFA concrete. The significance levels of the design factors, which indicate how significantly the factors affect the HVFA concrete\\'s mechanical properties, were determined using analysis of variance (ANOVA) tests. The results show that a weight-based mix proportion is a slightly better predictor of mechanical properties than volume-based one. The significance level of fly ash substitution rate was higher than that of w/b ratio initially but reduced over time. © 2014 Elsevier Ltd. All rights reserved.

  16. REDD+ and the Clean Development Mechanism: A comparative perspective

    Directory of Open Access Journals (Sweden)

    Lovleen Bhullar

    2013-04-01

    Full Text Available The program, ‘Reducing Emissions from Deforestation and Forest Degradation’ (REDD, which operates within the international climate change policy framework, is projected to emerge as one of the key climate change mitigation mechanisms for developing countries. The existing Afforestation/Reforestation (A/R mechanism, operating under the Clean Development Mechanism of the Kyoto Protocol to the United Nations Framework Convention on Climate Change, may prove useful for drawing lessons for the emerging REDD program, since both mechanisms represent flexible means for developed countries to achieve compliance with their mitigation targets under the Kyoto Protocol. The possible means include CDM as the basis for a project-based approach for the implementation of REDD (if adopted or the inclusion of REDD within CDM. This article compares the features of A/R CDM and REDD, identifies similarities and differences, and analyses the extent to which the former can provide guidance for the development of a carbon governance mechanism for REDD.

  17. Current perspectives on the mechanism of action of artemisinins.

    Science.gov (United States)

    Golenser, Jacob; Waknine, Judith H; Krugliak, Miriam; Hunt, Nicholas H; Grau, Georges E

    2006-12-01

    Artemisinin derivatives are the most recent single drugs approved and introduced for public antimalarial treatment. Although their recommended use is for treatment of Plasmodium falciparum infection, these drugs also act against other parasites, as well as against tumor cells. The mechanisms of action attributed to artemisinin include interference with parasite transport proteins, disruption of parasite mitochondrial function, modulation of host immune function and inhibition of angiogenesis. Artemisinin combination therapies are currently the preferred treatment for malaria. These combinations may prevent the induction of parasite drug resistance. However, in view of the multiple mechanisms involved, especially when additional drugs are used, the combined therapy should be carefully examined for antagonistic effects. It is now a general theory that the crucial mechanism is interference with plasmodial SERCA. Therefore, future development of resistance may be associated with overproduction or mutations of this transporter. However, a general mechanism, such as alterations in general drug transport pathways, is feasible. In this article, we review the evidence for each mechanism of action suggested.

  18. Mapping Psychology Students' Perspective on Group Peer-Tutoring in Statistics

    Science.gov (United States)

    Cantinotti, Michael; Désormeaux-Moreau, Marjorie; Balbinotti, Marcos

    2017-01-01

    Students in psychology generally have difficulties to successfully accomplish mandatory courses in statistics. Group peer-tutoring is a pedagogical strategy to support them with a peer that has already successfully mastered the content of such a course. In order to specifically tailor group peer-tutoring to the needs of students and to sustain…

  19. The Statistical Knowledge Gap in Higher Degree by Research Students: The Supervisors' Perspective

    Science.gov (United States)

    Baglin, James; Hart, Claire; Stow, Sarah

    2017-01-01

    This study sought to gain an understanding of the current statistical training and support needs for Australian Higher Degree by Research (HDR) students and their supervisors. The data reported herein are based on the survey responses of 191 (18.7%) eligible supervisors from a single Australian institution. The survey was composed of both…

  20. The CEO performance effect : Statistical issues and a complex fit perspective

    NARCIS (Netherlands)

    Blettner, D.P.; Chaddad, F.R.; Bettis, R.

    2012-01-01

    How CEOs affect strategy and performance is important to strategic management research. We show that sophisticated statistical analysis alone is problematic for establishing the magnitude and causes of CEO impact on performance. We discuss three problem areas that substantially distort the

  1. Perspectives and realities of teaching statistics at a superior school of business administration

    Science.gov (United States)

    Nunes, Sandra

    2016-06-01

    This paper aims to describe the reality of the teaching of statistics in a superior school of business administration in Portugal. It is supported in a twenty years of experience teaching several disciplines belonging to the scientific area of Mathematics such as: Statistics and Probability, Data Analysis, Calculus, Algebra and Numerical Analysis. This experience is not limited to school of business administration but also in engineering and health courses and in all these schools there has been a substantial increase of failure in these disciplines. I intend to present the main difficulties that teachers encounter. These difficulties are due to a diversity of problems. A leading cause is undoubtedly the huge heterogeneity of the level of knowledge that students have. The large number of students in each class it is also a massive problem. I must point out that, in my opinion, the introduction of the Bologna process has aggravated this situation. The assumption of reduced classroom hours and an increase in self-study is extremely penalizing for such students. There are many challenges that teachers have to face: How to teach statistics to a class where more than half the students cannot interpret the basic concepts of mathematics? Is the approach of teaching statistics through software beneficial? Should the teaching of statistics be addressed in a more practical way? How can we install a critical thinking in the students, to enable them to use the knowledge acquired to solve problems? How can we deal and prevent the failure that is increasing each year? These are only a few questions that all the teachers need an answer.

  2. Fluid mechanics of eating, swallowing and digestion - overview and perspectives.

    Science.gov (United States)

    Engmann, Jan; Burbidge, Adam S

    2013-02-26

    From a very simplistic viewpoint, the human digestive system can be regarded as a long tube (with dramatic variations in diameter, cross-section, wall properties, pumping mechanisms, regulating valves and in-line sensors). We single out a few fluid mechanical phenomena along the trajectory of a food bolus from the mouth to the small intestine and discuss how they influence sensorial perception, safe transport, and nutrient absorption from a bolus. The focus is on lubrication flows between the tongue and palate, the oropharyngeal stage of swallowing and effects of flow on absorption in the small intestine. Specific challenges and opportunities in this research area are highlighted.

  3. Contemplating compliance: European compliance mechanisms in international perspective

    NARCIS (Netherlands)

    Koops, C.E.

    2014-01-01

    How can international organizations make their Member States comply with the rules of the organization? Which is the more effective method: to coax and entice, to argue and persuade, or to threaten and punish? On the basis of which criteria should a compliance mechanism be construed and applied,

  4. Mechanics of the brain: perspectives, challenges, and opportunities.

    Science.gov (United States)

    Goriely, Alain; Geers, Marc G D; Holzapfel, Gerhard A; Jayamohan, Jayaratnam; Jérusalem, Antoine; Sivaloganathan, Sivabal; Squier, Waney; van Dommelen, Johannes A W; Waters, Sarah; Kuhl, Ellen

    2015-10-01

    The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today's open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

  5. Physics colloquium: Single-electron counting in quantum metrology and in statistical mechanics

    CERN Multimedia

    Geneva University

    2011-01-01

    GENEVA UNIVERSITY Ecole de physique Département de physique nucléaire et corspusculaire 24, quai Ernest-Ansermet 1211 Genève 4 Tél.: (022) 379 62 73 Fax: (022) 379 69 92olé   Lundi 17 octobre 2011 17h00 - Ecole de Physique, Auditoire Stueckelberg PHYSICS COLLOQUIUM « Single-electron counting in quantum metrology and in statistical mechanics » Prof. Jukka Pekola Low Temperature Laboratory, Aalto University Helsinki, Finland   First I discuss the basics of single-electron tunneling and its potential applications in metrology. My main focus is in developing an accurate source of single-electron current for the realization of the unit ampere. I discuss the principle and the present status of the so-called single- electron turnstile. Investigation of errors in transporting electrons one by one has revealed a wealth of observations on fundamental phenomena in mesoscopic superconductivity, including individual Andreev...

  6. Statistical mechanics of competitive resource allocation using agent-based models

    Science.gov (United States)

    Chakraborti, Anirban; Challet, Damien; Chatterjee, Arnab; Marsili, Matteo; Zhang, Yi-Cheng; Chakrabarti, Bikas K.

    2015-01-01

    Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

  7. Excitation functions of parameters in Erlang distribution, Schwinger mechanism, and Tsallis statistics in RHIC BES program

    International Nuclear Information System (INIS)

    Gao, Li-Na; Liu, Fu-Hu; Lacey, Roy A.

    2016-01-01

    Experimental results of the transverse-momentum distributions of φ mesons and Ω hyperons produced in gold-gold (Au-Au) collisions with different centrality intervals, measured by the STAR Collaboration at different energies (7.7, 11.5, 19.6, 27, and 39 GeV) in the beam energy scan (BES) program at the relativistic heavy-ion collider (RHIC), are approximately described by the single Erlang distribution and the two-component Schwinger mechanism. Moreover, the STAR experimental transverse-momentum distributions of negatively charged particles, produced in Au-Au collisions at RHIC BES energies, are approximately described by the two-component Erlang distribution and the single Tsallis statistics. The excitation functions of free parameters are obtained from the fit to the experimental data. A weak softest point in the string tension in Ω hyperon spectra is observed at 7.7 GeV. (orig.)

  8. Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties.

    Science.gov (United States)

    Simon, Cory M; Braun, Efrem; Carraro, Carlo; Smit, Berend

    2017-01-17

    Some nanoporous, crystalline materials possess dynamic constituents, for example, rotatable moieties. These moieties can undergo a conformation change in response to the adsorption of guest molecules, which qualitatively impacts adsorption behavior. We pose and solve a statistical mechanical model of gas adsorption in a porous crystal whose cages share a common ligand that can adopt two distinct rotational conformations. Guest molecules incentivize the ligands to adopt a different rotational configuration than maintained in the empty host. Our model captures inflections, steps, and hysteresis that can arise in the adsorption isotherm as a signature of the rotating ligands. The insights disclosed by our simple model contribute a more intimate understanding of the response and consequence of rotating ligands integrated into porous materials to harness them for gas storage and separations, chemical sensing, drug delivery, catalysis, and nanoscale devices. Particularly, our model reveals design strategies to exploit these moving constituents and engineer improved adsorbents with intrinsic thermal management for pressure-swing adsorption processes.

  9. Statistical-mechanics analysis of Gaussian labeled-unlabeled classification problems

    International Nuclear Information System (INIS)

    Tanaka, Toshiyuki

    2013-01-01

    The labeled-unlabeled classification problem in semi-supervised learning is studied via statistical-mechanics approach. We analytically investigate performance of a learner with an equal-weight mixture of two symmetrically-located Gaussians, performing posterior mean estimation of the parameter vector on the basis of a dataset consisting of labeled and unlabeled data generated from the same probability model as that assumed by the learner. Under the assumption of replica symmetry, we have analytically obtained a set of saddle-point equations, which allows us to numerically evaluate performance of the learner. On the basis of the analytical result we have observed interesting phenomena, in particular the coexistence of good and bad solutions, which may happen when the number of unlabeled data is relatively large compared with that of labeled data

  10. Granular statistical mechanics - Building on the legacy of Sir Sam Edwards

    Science.gov (United States)

    Blumenfeld, Raphael

    When Sir Sam Edwards laid down the foundations for the statistical mechanics of jammed granular materials he opened a new field in soft condensed matter and many followed. In this presentation we review briefly the Edwards formalism and some of its less discussed consequences. We point out that the formalism is useful for other classes of systems - cellular and porous materials. A certain shortcoming of the original formalism is then discussed and a modification to overcome it is proposed. Finally, a derivation of an equation of state with the new formalism is presented; the equation of state is analogous to the PVT relation for thermal gases, relating the volume, the boundary stress and measures of the structural and stress fluctuations. NUDT, Changsha, China, Imperial College London, UK, Cambridge University, UK.

  11. Noise and the statistical mechanics of distributed transport in a colony of interacting agents

    Science.gov (United States)

    Katifori, Eleni; Graewer, Johannes; Ronellenfitsch, Henrik; Mazza, Marco G.

    Inspired by the process of liquid food distribution between individuals in an ant colony, in this work we consider the statistical mechanics of resource dissemination between interacting agents with finite carrying capacity. The agents move inside a confined space (nest), pick up the food at the entrance of the nest and share it with other agents that they encounter. We calculate analytically and via a series of simulations the global food intake rate for the whole colony as well as observables describing how uniformly the food is distributed within the nest. Our model and predictions provide a useful benchmark to assess which strategies can lead to efficient food distribution within the nest and also to what level the observed food uptake rates and efficiency in food distribution are due to stochastic fluctuations or specific food exchange strategies by an actual ant colony.

  12. Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lauwers, P G

    1990-12-01

    Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

  13. Conceptual developments of non-equilibrium statistical mechanics in the early days of Japan

    Science.gov (United States)

    Ichiyanagi, Masakazu

    1995-11-01

    This paper reviews the research in nonequilibrium statistical mechanics made in Japan in the period between 1930 and 1960. Nearly thirty years have passed since the discovery of the exact formula for the electrical conductivity. With the rise of the linear response theory, the methods and results of which are quickly grasped by anyone, its rationale was pushed aside and even at the stage where the formulation was still incomplete some authors hurried to make physical applications. Such an attitude robbed it of most of its interest for the average physicist, who would approach an understanding of some basic concept, not through abstract and logical analysis but by simply increasing his technical experiences with the concept. The purpose of this review is to rescue the linear response theory from being labeled a mathematical tool and to show that it has considerable physical content. Many key papers, originally written in Japanese, are reproduced.

  14. Moral foundations in an interacting neural networks society: A statistical mechanics analysis

    Science.gov (United States)

    Vicente, R.; Susemihl, A.; Jericó, J. P.; Caticha, N.

    2014-04-01

    The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by the recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighbourhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents when disagreeing. We consider a family of learning algorithms parametrized by δ, that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter δ at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustain less opinion diversity. We discuss predictions of the model and propose possible experimental tests.

  15. Ants in a labyrinth: a statistical mechanics approach to the division of labour.

    Directory of Open Access Journals (Sweden)

    Thomas Owen Richardson

    2011-04-01

    Full Text Available Division of labour (DoL is a fundamental organisational principle in human societies, within virtual and robotic swarms and at all levels of biological organisation. DoL reaches a pinnacle in the insect societies where the most widely used model is based on variation in response thresholds among individuals, and the assumption that individuals and stimuli are well-mixed. Here, we present a spatially explicit model of DoL. Our model is inspired by Pierre de Gennes' 'Ant in a Labyrinth' which laid the foundations of an entire new field in statistical mechanics. We demonstrate the emergence, even in a simplified one-dimensional model, of a spatial patterning of individuals and a right-skewed activity distribution, both of which are characteristics of division of labour in animal societies. We then show using a two-dimensional model that the work done by an individual within an activity bout is a sigmoidal function of its response threshold. Furthermore, there is an inverse relationship between the overall stimulus level and the skewness of the activity distribution. Therefore, the difference in the amount of work done by two individuals with different thresholds increases as the overall stimulus level decreases. Indeed, spatial fluctuations of task stimuli are minimised at these low stimulus levels. Hence, the more unequally labour is divided amongst individuals, the greater the ability of the colony to maintain homeostasis. Finally, we show that the non-random spatial distribution of individuals within biological and social systems could be caused by indirect (stigmergic interactions, rather than direct agent-to-agent interactions. Our model links the principle of DoL with principles in the statistical mechanics and provides testable hypotheses for future experiments.

  16. Statistical physics as an approximate method of many-body quantum mechanics in the representation of occupation numbers

    International Nuclear Information System (INIS)

    Kushnirenko, A.N.

    1989-01-01

    An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems

  17. Thermo-dynamical contours of electronic-vibrational spectra simulated using the statistical quantum-mechanical methods

    DEFF Research Database (Denmark)

    Pomogaev, Vladimir; Pomogaeva, Anna; Avramov, Pavel

    2011-01-01

    Three polycyclic organic molecules in various solvents focused on thermo-dynamical aspects were theoretically investigated using the recently developed statistical quantum mechanical/classical molecular dynamics method for simulating electronic-vibrational spectra. The absorption bands of estradiol...

  18. A mathematical model for HIV and hepatitis C co-infection and its assessment from a statistical perspective.

    Science.gov (United States)

    Castro Sanchez, Amparo Yovanna; Aerts, Marc; Shkedy, Ziv; Vickerman, Peter; Faggiano, Fabrizio; Salamina, Guiseppe; Hens, Niel

    2013-03-01

    The hepatitis C virus (HCV) and the human immunodeficiency virus (HIV) are a clear threat for public health, with high prevalences especially in high risk groups such as injecting drug users. People with HIV infection who are also infected by HCV suffer from a more rapid progression to HCV-related liver disease and have an increased risk for cirrhosis and liver cancer. Quantifying the impact of HIV and HCV co-infection is therefore of great importance. We propose a new joint mathematical model accounting for co-infection with the two viruses in the context of injecting drug users (IDUs). Statistical concepts and methods are used to assess the model from a statistical perspective, in order to get further insights in: (i) the comparison and selection of optional model components, (ii) the unknown values of the numerous model parameters, (iii) the parameters to which the model is most 'sensitive' and (iv) the combinations or patterns of values in the high-dimensional parameter space which are most supported by the data. Data from a longitudinal study of heroin users in Italy are used to illustrate the application of the proposed joint model and its statistical assessment. The parameters associated with contact rates (sharing syringes) and the transmission rates per syringe-sharing event are shown to play a major role. Copyright © 2013 Elsevier B.V. All rights reserved.

  19. 8th Liblice Conference on the Statistical Mechanics of Liquids - Brno, Czech Republic, 13-18 June 2010 FOREWORD

    Czech Academy of Sciences Publication Activity Database

    Jackson, G.; Nezbeda, Ivo

    2011-01-01

    Roč. 190, 1 Sp.I:Sl (2011), s. 1-2 ISSN 0026-8976. [Liblice Conference on the Statistical Mechanics of Liquids /8./. Brno, 13.06.2010-18.06.2010] Institutional research plan: CEZ:AV0Z40720504 Keywords : editorial material * theories of liquids * statistical mechanics Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.819, year: 2011

  20. Biochemical mechanisms of signaling: perspectives in plants under arsenic stress.

    Science.gov (United States)

    Islam, Ejazul; Khan, Muhammad Tahir; Irem, Samra

    2015-04-01

    Plants are the ultimate food source for humans, either directly or indirectly. Being sessile in nature, they are exposed to various biotic and abiotic stresses because of changing climate that adversely effects their growth and development. Contamination of heavy metals is one of the major abiotic stresses because of anthropogenic as well as natural factors which lead to increased toxicity and accumulation in plants. Arsenic is a naturally occurring metalloid toxin present in the earth crust. Due to its presence in terrestrial and aquatic environments, it effects the growth of plants. Plants can tolerate arsenic using several mechanisms like phytochelation, vacuole sequestration and activation of antioxidant defense systems. Several signaling mechanisms have evolved in plants that involve the use of proteins, calcium ions, hormones, reactive oxygen species and nitric oxide as signaling molecules to cope with arsenic toxicity. These mechanisms facilitate plants to survive under metal stress by activating their defense systems. The pathways by which these stress signals are perceived and responded is an unexplored area of research and there are lots of gaps still to be filled. A good understanding of these signaling pathways can help in raising the plants which can perform better in arsenic contaminated soil and water. In order to increase the survival of plants in contaminated areas there is a strong need to identify suitable gene targets that can be modified according to needs of the stakeholders using various biotechnological techniques. This review focuses on the signaling mechanisms of plants grown under arsenic stress and will give an insight of the different sensory systems in plants. Furthermore, it provides the knowledge about several pathways that can be exploited to develop plant cultivars which are resistant to arsenic stress or can reduce its uptake to minimize the risk of arsenic toxicity through food chain thus ensuring food security. Copyright © 2015

  1. Comparison of Predictive Contract Mechanisms from an Information Theory Perspective

    OpenAIRE

    Zhang, Xin; Ward, Tomas; McLoone, Seamus

    2012-01-01

    Inconsistency arises across a Distributed Virtual Environment due to network latency induced by state changes communications. Predictive Contract Mechanisms (PCMs) combat this problem through reducing the amount of messages transmitted in return for perceptually tolerable inconsistency. To date there are no methods to quantify the efficiency of PCMs in communicating this reduced state information. This article presents an approach derived from concepts in information theory for a dee...

  2. Statistical mechanics and dynamics of solvable models with long-range interactions

    International Nuclear Information System (INIS)

    Campa, Alessandro; Dauxois, Thierry; Ruffo, Stefano

    2009-01-01

    For systems with long-range interactions, the two-body potential decays at large distances as V(r)∼1/r α , with α≤d, where d is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics, two-dimensional elasticity, charged and dipolar systems. Although such systems can be made extensive, they are intrinsically non additive: the sum of the energies of macroscopic subsystems is not equal to the energy of the whole system. Moreover, the space of accessible macroscopic thermodynamic parameters might be non convex. The violation of these two basic properties of the thermodynamics of short-range systems is at the origin of ensemble inequivalence. In turn, this inequivalence implies that specific heat can be negative in the microcanonical ensemble, and temperature jumps can appear at microcanonical first order phase transitions. The lack of convexity allows us to easily spot regions of parameter space where ergodicity may be broken. Historically, negative specific heat had been found for gravitational systems and was thought to be a specific property of a system for which the existence of standard equilibrium statistical mechanics itself was doubted. Realizing that such properties may be present for a wider class of systems has renewed the interest in long-range interactions. Here, we present a comprehensive review of the recent advances on the statistical mechanics and out-of-equilibrium dynamics of solvable systems with long-range interactions. The core of the review consists in the detailed presentation of the concept of ensemble inequivalence, as exemplified by the exact solution, in the microcanonical and canonical ensembles, of mean-field type models. Remarkably, the entropy of all these models can be obtained using the method of large deviations. Long-range interacting systems display an extremely slow relaxation towards thermodynamic equilibrium and, what is more striking, the convergence towards quasi-stationary states. The

  3. Molecular mechanisms of depression: perspectives on new treatment strategies.

    Science.gov (United States)

    Lang, Undine E; Borgwardt, Stefan

    2013-01-01

    observed by ketamine, which acts via the glutamatergic system. Hence, GABA, AMPA, EAAT, NMDA- and metabotropic glutamate receptors (mGluR1 to mGluR8) have gained interest in depression recently. Alternative, causative or also easy available treatment strategies beyond serotonin and noradrenaline reuptake inhibition might be a major topic of future psychiatric care. In this review, an attempt is made to overview concepts of the disease and search for perspectives on antidepressant treatment strategies beyond approved medications. Copyright © 2013 S. Karger AG, Basel.

  4. Molecular Mechanisms of Depression: Perspectives on New Treatment Strategies

    Directory of Open Access Journals (Sweden)

    Undine E. Lang

    2013-05-01

    effect has also been observed by ketamine, which acts via the glutamatergic system. Hence, GABA, AMPA, EAAT, NMDA- and metabotropic glutamate receptors (mGluR1 to mGluR8 have gained interest in depression recently. Alternative, causative or also easy available treatment strategies beyond serotonin and noradrenaline reuptake inhibition might be a major topic of future psychiatric care. In this review, an attempt is made to overview concepts of the disease and search for perspectives on antidepressant treatment strategies beyond approved medications.

  5. Pesticides and human chronic diseases: Evidences, mechanisms, and perspectives

    International Nuclear Information System (INIS)

    Mostafalou, Sara; Abdollahi, Mohammad

    2013-01-01

    Along with the wide use of pesticides in the world, the concerns over their health impacts are rapidly growing. There is a huge body of evidence on the relation between exposure to pesticides and elevated rate of chronic diseases such as different types of cancers, diabetes, neurodegenerative disorders like Parkinson, Alzheimer, and amyotrophic lateral sclerosis (ALS), birth defects, and reproductive disorders. There is also circumstantial evidence on the association of exposure to pesticides with some other chronic diseases like respiratory problems, particularly asthma and chronic obstructive pulmonary disease (COPD), cardiovascular disease such as atherosclerosis and coronary artery disease, chronic nephropathies, autoimmune diseases like systemic lupus erythematous and rheumatoid arthritis, chronic fatigue syndrome, and aging. The common feature of chronic disorders is a disturbance in cellular homeostasis, which can be induced via pesticides' primary action like perturbation of ion channels, enzymes, receptors, etc., or can as well be mediated via pathways other than the main mechanism. In this review, we present the highlighted evidence on the association of pesticide's exposure with the incidence of chronic diseases and introduce genetic damages, epigenetic modifications, endocrine disruption, mitochondrial dysfunction, oxidative stress, endoplasmic reticulum stress and unfolded protein response (UPR), impairment of ubiquitin proteasome system, and defective autophagy as the effective mechanisms of action. - Highlights: ► There is a link between exposure to pesticides and incidence of chronic diseases. ► Genotoxicity and proteotoxicity are two main involved mechanisms. ► Epigenetic knowledge may help diagnose the relationships. ► Efficient policies on safe use of pesticides should be set up

  6. Pesticides and human chronic diseases: Evidences, mechanisms, and perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Mostafalou, Sara; Abdollahi, Mohammad, E-mail: Mohammad.Abdollahi@UToronto.Ca

    2013-04-15

    Along with the wide use of pesticides in the world, the concerns over their health impacts are rapidly growing. There is a huge body of evidence on the relation between exposure to pesticides and elevated rate of chronic diseases such as different types of cancers, diabetes, neurodegenerative disorders like Parkinson, Alzheimer, and amyotrophic lateral sclerosis (ALS), birth defects, and reproductive disorders. There is also circumstantial evidence on the association of exposure to pesticides with some other chronic diseases like respiratory problems, particularly asthma and chronic obstructive pulmonary disease (COPD), cardiovascular disease such as atherosclerosis and coronary artery disease, chronic nephropathies, autoimmune diseases like systemic lupus erythematous and rheumatoid arthritis, chronic fatigue syndrome, and aging. The common feature of chronic disorders is a disturbance in cellular homeostasis, which can be induced via pesticides' primary action like perturbation of ion channels, enzymes, receptors, etc., or can as well be mediated via pathways other than the main mechanism. In this review, we present the highlighted evidence on the association of pesticide's exposure with the incidence of chronic diseases and introduce genetic damages, epigenetic modifications, endocrine disruption, mitochondrial dysfunction, oxidative stress, endoplasmic reticulum stress and unfolded protein response (UPR), impairment of ubiquitin proteasome system, and defective autophagy as the effective mechanisms of action. - Highlights: ► There is a link between exposure to pesticides and incidence of chronic diseases. ► Genotoxicity and proteotoxicity are two main involved mechanisms. ► Epigenetic knowledge may help diagnose the relationships. ► Efficient policies on safe use of pesticides should be set up.

  7. Perspectives and challenges in statistical physics and complex systems for the next decade

    CERN Document Server

    Raposo, Ernesto P; Gomes Eleutério da Luz, Marcos

    2014-01-01

    Statistical Physics (SP) has followed an unusual evolutionary path in science. Originally aiming to provide a fundamental basis for another important branch of Physics, namely Thermodynamics, SP gradually became an independent field of research in its own right. But despite more than a century of steady progress, there are still plenty of challenges and open questions in the SP realm. In fact, the area is still rapidly evolving, in contrast to other branches of science, which already have well defined scopes and borderlines of applicability. This difference is due to the steadily expanding num

  8. Antiulcer properties of fruits and vegetables: A mechanism based perspective.

    Science.gov (United States)

    Harsha, Choudhary; Banik, Kishore; Bordoloi, Devivasha; Kunnumakkara, Ajaikumar B

    2017-10-01

    Gastric ulcer is the damage caused to mucosal layer of the stomach under the action of various factors like high levels of acid and pepsin, invasion by Helicobacter pylori, etc. Although most cases have been controlled and the rate of ulcer occurrence has reduced over the last few decades, gastric ulcer still holds a prime concern today. A range of palliative medicines comprising proton pump inhibitors, H2 receptor antagonists, COX-2 inhibitors (coxibs) is widely in use and patients have also been administered with acid suppression therapies. But these remedies aggravate the condition of patients causing severe side effects, or rather impart temporary relief. Therefore, it is highly imperative to develop safe and effective therapies for the treatment of gastric ulcer. Nature provides us various fruits and vegetables that can combat gastric ulcer through multiple mechanisms; predominantly via antioxidant, anti-inflammatory, antisecretory, antimicrobial, anticholinergic and cytoprotective activity, inhibition of small intestinal propulsion etc. Various phytochemicals from fruits and vegetables such as phenolics, flavonoids, tannins and saponins play a vital role in the prevention and cure of gastric ulcer. This review is a compendium of all fruits and vegetables known for their profound antiulcer effect and their underlying mechanisms of action. Copyright © 2017 Elsevier Ltd. All rights reserved.

  9. Undercut tolerances in industry from a fracture mechanic perspective

    Directory of Open Access Journals (Sweden)

    Steimbreger Ceferino

    2018-01-01

    Full Text Available Fatigue is an important damage mechanism that particularly affects welded components, since they are likely to present residual stresses, inhomogeneities and stress raisers. Assessment of cyclic load effects on welds has concerned both industries and scientist for decades; unexpected failure must be prevented and at the same time, structures must withstand design loads with minimum requirements of material. All these facts together with economic issues have lead to the creation of normative that rule designing and construction of welded components. Particularly, toe undercuts are generally found in large structures, and large scatter and disagreement exists towards their significance and effects. Documents usually limit only their depth without considering radius, width or length, and there is currently no explanation to that fact. Understanding the damaging process will also help to set less conservative tolerances, with consequent cost reduction due to less demanding inspection. The present paper deals with a fracture mechanic approach that uses the Resistance Curve concept to predict fatigue limit of welded components with undercuts. Results revealed that depth is the most influencing variable, and it can be used as the limiting parameter in design regulations. Moreover, good correlation was obtained with FAT values normally assigned to this kind of defect.

  10. Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

    Science.gov (United States)

    Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

    We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of

  11. Precipitation projections under GCMs perspective and Turkish Water Foundation (TWF) statistical downscaling model procedures

    Science.gov (United States)

    Dabanlı, İsmail; Şen, Zekai

    2018-04-01

    The statistical climate downscaling model by the Turkish Water Foundation (TWF) is further developed and applied to a set of monthly precipitation records. The model is structured by two phases as spatial (regional) and temporal downscaling of global circulation model (GCM) scenarios. The TWF model takes into consideration the regional dependence function (RDF) for spatial structure and Markov whitening process (MWP) for temporal characteristics of the records to set projections. The impact of climate change on monthly precipitations is studied by downscaling Intergovernmental Panel on Climate Change-Special Report on Emission Scenarios (IPCC-SRES) A2 and B2 emission scenarios from Max Plank Institute (EH40PYC) and Hadley Center (HadCM3). The main purposes are to explain the TWF statistical climate downscaling model procedures and to expose the validation tests, which are rewarded in same specifications as "very good" for all stations except one (Suhut) station in the Akarcay basin that is in the west central part of Turkey. Eventhough, the validation score is just a bit lower at the Suhut station, the results are "satisfactory." It is, therefore, possible to say that the TWF model has reasonably acceptable skill for highly accurate estimation regarding standard deviation ratio (SDR), Nash-Sutcliffe efficiency (NSE), and percent bias (PBIAS) criteria. Based on the validated model, precipitation predictions are generated from 2011 to 2100 by using 30-year reference observation period (1981-2010). Precipitation arithmetic average and standard deviation have less than 5% error for EH40PYC and HadCM3 SRES (A2 and B2) scenarios.

  12. The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

    Science.gov (United States)

    der, R.

    1987-01-01

    The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transformwidetilde{C}(z)) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z=∞ and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover,widetilde{C}(z) may be expressed by a Laurent series expansion in positive and negative powers of z, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions ofwidetilde{C}(z) as obtained from the application of conventional many-body techniques to the calculation

  13. A developmental perspective on neuroeconomic mechanisms of contingency management.

    Science.gov (United States)

    Stanger, Catherine; Budney, Alan J; Bickel, Warren K

    2013-06-01

    This paper provides a developmental overview of relevant theory and research on delay discounting and neuroeconomics, and their implications for contingency management (CM) approaches to treatment. Recent advances in the neuroscience of decision making have the potential to inform treatment development for adolescent substance use in general, and CM treatments in particular. CM interventions may be informed by research on delay discounting, a type of decision making that reflects how individuals value immediate versus delayed rewards. Delay discounting reliably distinguishes substance abusers from nonabusers and is a significant predictor of individual differences in response to substance use treatments. Discounting may also be important in predicting response to CM, as CM attempts to directly influence this decision-making process, shifting the preference from the immediate rewards of use to delayed rewards for choosing not to use. Multiple neural processes underlie decision making, and those processes have implications for adolescent substance abuse. There are significant neurodevelopmental processes that differentiate adolescents from adults. These processes are implicated in delay discounting, suggesting that adolescence may reflect a period of plasticity in temporal decision making. Understanding the neural mechanisms of delay discounting has led to promising working memory interventions directly targeting the executive functions that underlie individual choices. These interventions may be particularly helpful in combination with CM interventions that offer immediate rewards for brief periods of abstinence, and may show particular benefit in adolescence due to the heightened neural plasticity of systems that underlie temporal discounting in adolescence. 2013 APA, all rights reserved

  14. Oxidative Stress in Neurodegenerative Diseases: Mechanisms and Therapeutic Perspectives

    Directory of Open Access Journals (Sweden)

    Ailton Melo

    2011-01-01

    Full Text Available The incidence and prevalence of neurodegenerative diseases (ND increase with life expectancy. This paper reviews the role of oxidative stress (OS in ND and pharmacological attempts to fight against reactive oxygen species (ROS-induced neurodegeneration. Several mechanisms involved in ROS generation in neurodegeneration have been proposed. Recent articles about molecular pathways involved in ROS generation were reviewed. The progress in the development of neuroprotective therapies has been hampered because it is difficult to define targets for treatment and determine what should be considered as neuroprotective. Therefore, the attention was focused on researches about pharmacological targets that could protect neurons against OS. Since it is necessary to look for genes as the ultimate controllers of all biological processes, this paper also tried to identify gerontogenes involved in OS and neurodegeneration. Since neurons depend on glial cells to survive, recent articles about the functioning of these cells in aging and ND were also reviewed. Finally, clinical trials testing potential neuroprotective agents were critically reviewed. Although several potential drugs have been screened in in vitro and in vivo models of ND, these results were not translated in benefit of patients, and disappointing results were obtained in the majority of clinical trials.

  15. Protein logic: a statistical mechanical study of signal integration at the single-molecule level.

    Science.gov (United States)

    de Ronde, Wiet; Rein ten Wolde, Pieter; Mugler, Andrew

    2012-09-05

    Information processing and decision-making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years, however, both experimentalists and theorists have begun to appreciate that cellular decision-making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well-known statistical mechanical model. As an example system, we focus on receptors that bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce what to our knowledge is a novel idea: that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  16. A Framework for Structural Systems Based on the Principles of Statistical Mechanics

    Directory of Open Access Journals (Sweden)

    Rabindranath Andujar

    2014-11-01

    Full Text Available A framework is proposed in which certain well-known concepts of statistical mechanics and thermodynamics can be used and applied to characterize structural systems of interconnected Timoshenko beam elements. We first make the assimilation to a network of nodes linked by potential energy functions that are derived from the stiffness properties of the beams. Then we define a series of thermodynamic quantities inherent to a given structure (i.e., internal energy, heat, pressure, temperature, entropy, and kinetic energy. With the exception of entropy, all of them have the dimensions of energy. In order to test this new framework, a series of experiments was performed on four structural specimens within the elastic regime. Their configurations were taken from the seismic regulations known as Eurocode 8 in order to have a better based reference for our comparisons. The results are then explained within this new framework. Very interesting correlations have been found between the parameters given in the code and our concepts.

  17. Statistical mechanics of few-particle systems: exact results for two useful models

    Science.gov (United States)

    Miranda, Enrique N.

    2017-11-01

    The statistical mechanics of small clusters (n ˜ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B , as in the thermodynamic case, while within the microcanonical formalism the limit value is k B (1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.

  18. Nonequilibrium statistical mechanics in the general theory of relativity. I. A general formalism

    International Nuclear Information System (INIS)

    Israel, W.; Kandrup, H.E.

    1984-01-01

    This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The objecct here is the development of a tractable theory for self-gravitating systems. It is argued that the ''state'' of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. By mapping the true physics onto a fictitious ''background'' spacetime, which may be chosen to satisfy some ''average'' field equations, one then obtains a useful covariant notion of ''evolution'' in response to a fluctuating ''gravitational force.'' For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as ''localized'' in space and time, one obtains a tractable kinetic equation which reduces, in the Newtonian limit, to the stardard Landau equation

  19. Characterization of adaptive statistical iterative reconstruction algorithm for dose reduction in CT: A pediatric oncology perspective

    International Nuclear Information System (INIS)

    Brady, S. L.; Yee, B. S.; Kaufman, R. A.

    2012-01-01

    Purpose: This study demonstrates a means of implementing an adaptive statistical iterative reconstruction (ASiR™) technique for dose reduction in computed tomography (CT) while maintaining similar noise levels in the reconstructed image. The effects of image quality and noise texture were assessed at all implementation levels of ASiR™. Empirically derived dose reduction limits were established for ASiR™ for imaging of the trunk for a pediatric oncology population ranging from 1 yr old through adolescence/adulthood. Methods: Image quality was assessed using metrics established by the American College of Radiology (ACR) CT accreditation program. Each image quality metric was tested using the ACR CT phantom with 0%–100% ASiR™ blended with filtered back projection (FBP) reconstructed images. Additionally, the noise power spectrum (NPS) was calculated for three common reconstruction filters of the trunk. The empirically derived limitations on ASiR™ implementation for dose reduction were assessed using (1, 5, 10) yr old and adolescent/adult anthropomorphic phantoms. To assess dose reduction limits, the phantoms were scanned in increments of increased noise index (decrementing mA using automatic tube current modulation) balanced with ASiR™ reconstruction to maintain noise equivalence of the 0% ASiR™ image. Results: The ASiR™ algorithm did not produce any unfavorable effects on image quality as assessed by ACR criteria. Conversely, low-contrast resolution was found to improve due to the reduction of noise in the reconstructed images. NPS calculations demonstrated that images with lower frequency noise had lower noise variance and coarser graininess at progressively higher percentages of ASiR™ reconstruction; and in spite of the similar magnitudes of noise, the image reconstructed with 50% or more ASiR™ presented a more smoothed appearance than the pre-ASiR™ 100% FBP image. Finally, relative to non-ASiR™ images with 100% of standard dose across the

  20. Characterization of adaptive statistical iterative reconstruction algorithm for dose reduction in CT: A pediatric oncology perspective

    Energy Technology Data Exchange (ETDEWEB)

    Brady, S. L.; Yee, B. S.; Kaufman, R. A. [Department of Radiological Sciences, St. Jude Children' s Research Hospital, Memphis, Tennessee 38105 (United States)

    2012-09-15

    Purpose: This study demonstrates a means of implementing an adaptive statistical iterative reconstruction (ASiR Trade-Mark-Sign ) technique for dose reduction in computed tomography (CT) while maintaining similar noise levels in the reconstructed image. The effects of image quality and noise texture were assessed at all implementation levels of ASiR Trade-Mark-Sign . Empirically derived dose reduction limits were established for ASiR Trade-Mark-Sign for imaging of the trunk for a pediatric oncology population ranging from 1 yr old through adolescence/adulthood. Methods: Image quality was assessed using metrics established by the American College of Radiology (ACR) CT accreditation program. Each image quality metric was tested using the ACR CT phantom with 0%-100% ASiR Trade-Mark-Sign blended with filtered back projection (FBP) reconstructed images. Additionally, the noise power spectrum (NPS) was calculated for three common reconstruction filters of the trunk. The empirically derived limitations on ASiR Trade-Mark-Sign implementation for dose reduction were assessed using (1, 5, 10) yr old and adolescent/adult anthropomorphic phantoms. To assess dose reduction limits, the phantoms were scanned in increments of increased noise index (decrementing mA using automatic tube current modulation) balanced with ASiR Trade-Mark-Sign reconstruction to maintain noise equivalence of the 0% ASiR Trade-Mark-Sign image. Results: The ASiR Trade-Mark-Sign algorithm did not produce any unfavorable effects on image quality as assessed by ACR criteria. Conversely, low-contrast resolution was found to improve due to the reduction of noise in the reconstructed images. NPS calculations demonstrated that images with lower frequency noise had lower noise variance and coarser graininess at progressively higher percentages of ASiR Trade-Mark-Sign reconstruction; and in spite of the similar magnitudes of noise, the image reconstructed with 50% or more ASiR Trade-Mark-Sign presented a more

  1. Natural time analysis and Tsallis non-additive entropy statistical mechanics.

    Science.gov (United States)

    Sarlis, N. V.; Skordas, E. S.; Varotsos, P.

    2016-12-01

    Upon analyzing the seismic data in natural time and employing a sliding natural time window comprising a number of events that would occur in a few months, it has been recently uncovered[1] that a precursory Seismic Electric Signals activity[2] initiates almost simultaneously with the appearance of a minimum in the fluctuations of the order parameter of seismicity [3]. Such minima have been ascertained [4] during periods of the magnitude time series exhibiting long range correlations [5] a few months before all earthquakes of magnitude 7.6 or larger that occurred in the entire Japanese area from 1 January 1984 to 11 March 2011 (the day of the M9 Tohoku-Oki earthquake). Before and after these minima, characteristic changes of the temporal correlations between earthquake magnitudes are observed which cannot be captured by Tsallis non-additive entropy statistical mechanics in the frame of which it has been suggested that kappa distributions arise [6]. Here, we extend the study concerning the existence of such minima in a large area that includes Aegean Sea and its surrounding area which exhibits in general seismo-tectonics [7] different than that of the entire Japanese area. References P. A. Varotsos et al., Tectonophysics, 589 (2013) 116. P. Varotsos and M. Lazaridou, Tectonophysics 188 (1991) 321. P.A. Varotsos et al., Phys Rev E 72 (2005) 041103. N. V. Sarlis et al., Proc Natl Acad Sci USA 110 (2013) 13734. P. A. Varotsos, N. V. Sarlis, and E. S. Skordas, J Geophys Res Space Physics 119 (2014), 9192, doi: 10.1002/2014JA0205800. G. Livadiotis, and D. J. McComas, J Geophys Res 114 (2009) A11105, doi:10.1029/2009JA014352. S. Uyeda et al., Tectonophysics, 304 (1999) 41.

  2. Statistical Comparison of the Baseline Mechanical Properties of NBG-18 and PCEA Graphite

    Energy Technology Data Exchange (ETDEWEB)

    Mark C. Carroll; David T. Rohrbaugh

    2013-08-01

    High-purity graphite is the core structural material of choice in the Very High Temperature Reactor (VHTR), a graphite-moderated, helium-cooled design that is capable of producing process heat for power generation and for industrial process that require temperatures higher than the outlet temperatures of present nuclear reactors. The Baseline Graphite Characterization Program is endeavoring to minimize the conservative estimates of as-manufactured mechanical and physical properties by providing comprehensive data that captures the level of variation in measured values. In addition to providing a comprehensive comparison between these values in different nuclear grades, the program is also carefully tracking individual specimen source, position, and orientation information in order to provide comparisons and variations between different lots, different billets, and different positions from within a single billet. This report is a preliminary comparison between the two grades of graphite that were initially favored in the two main VHTR designs. NBG-18, a medium-grain pitch coke graphite from SGL formed via vibration molding, was the favored structural material in the pebble-bed configuration, while PCEA, a smaller grain, petroleum coke, extruded graphite from GrafTech was favored for the prismatic configuration. An analysis of the comparison between these two grades will include not only the differences in fundamental and statistically-significant individual strength levels, but also the differences in variability in properties within each of the grades that will ultimately provide the basis for the prediction of in-service performance. The comparative performance of the different types of nuclear grade graphites will continue to evolve as thousands more specimens are fully characterized from the numerous grades of graphite being evaluated.

  3. Statistical mechanics of a time-homogeneous system of money and antimoney

    Science.gov (United States)

    Schmitt, Matthias; Schacker, Andreas; Braun, Dieter

    2014-03-01

    Financial crises appear throughout human history. While there are many schools of thought on what the actual causes of such crises are, it has been suggested that the creation of credit money might be a source of financial instability. We discuss how the credit mechanism in a system of fractional reserve banking leads to non-local transfers of purchasing power that also affect non-involved agents. To overcome this issue, we impose the local symmetry of time homogeneity on the monetary system. A bi-currency system of non-bank assets (money) and bank assets (antimoney) is considered. A payment is either made by passing on money or by receiving antimoney. As a result, a free floating exchange rate between non-bank assets and bank assets is established. Credit creation is replaced by the simultaneous transfer of money and antimoney at a negotiated exchange rate. This is in contrast to traditional discussions of full reserve banking, which stalls creditary lending. With money and antimoney, the problem of credit crunches is mitigated while a full time symmetry of the monetary system is maintained. As a test environment for such a monetary system, we discuss an economy of random transfers. Random transfers are a strong criterion to probe the stability of monetary systems. The analysis using statistical physics provides analytical solutions and confirms that a money-antimoney system could be functional. Equally important to the probing of the stability of such a monetary system is the question of how to implement the credit default dynamics. This issue remains open.

  4. Statistical mechanics of a time-homogeneous system of money and antimoney

    International Nuclear Information System (INIS)

    Schmitt, Matthias; Schacker, Andreas; Braun, Dieter

    2014-01-01

    Financial crises appear throughout human history. While there are many schools of thought on what the actual causes of such crises are, it has been suggested that the creation of credit money might be a source of financial instability. We discuss how the credit mechanism in a system of fractional reserve banking leads to non-local transfers of purchasing power that also affect non-involved agents. To overcome this issue, we impose the local symmetry of time homogeneity on the monetary system. A bi-currency system of non-bank assets (money) and bank assets (antimoney) is considered. A payment is either made by passing on money or by receiving antimoney. As a result, a free floating exchange rate between non-bank assets and bank assets is established. Credit creation is replaced by the simultaneous transfer of money and antimoney at a negotiated exchange rate. This is in contrast to traditional discussions of full reserve banking, which stalls creditary lending. With money and antimoney, the problem of credit crunches is mitigated while a full time symmetry of the monetary system is maintained. As a test environment for such a monetary system, we discuss an economy of random transfers. Random transfers are a strong criterion to probe the stability of monetary systems. The analysis using statistical physics provides analytical solutions and confirms that a money–antimoney system could be functional. Equally important to the probing of the stability of such a monetary system is the question of how to implement the credit default dynamics. This issue remains open

  5. A Statistical Study on VLF Subionospheric Perturbations Associated with Major Earthquakes: A View from Focal Mechanism

    Science.gov (United States)

    Kawano, T.; Tatsuta, K.; Hobara, Y.

    2015-12-01

    Continuous monitoring of signal amplitudes of worldwide VLF transmitters is a powerful tool to study the lower ionospheric condition. Although, lower ionospheric perturbations prior to some of the major earthquakes have been reported for years, their occurrence and coupling mechanism between the ground and overlaying ionosphere prior to the earthquakes are not clear yet. In this paper, we carried out a statistical analysis based on the nighttime averaged signal amplitude data from the UEC's VLF/LF transmitter observation network. Two hundred forty three earthquakes were occurred within the 5th Fresnel zone of transmitter-receiver paths around Japan during the time period of 2007 to 2012. These earthquakes were characterized into three different groups based on the Centroid-Moment-Tensor (CMT) solution such as reverse fault type, normal fault type and stress slip type. The ionospheric anomaly was identified by a large change in the VLF/LF amplitude during nighttime. As a result, we found the ionospheric perturbations associated with both ground and sea earthquakes. Remarkably, the reverse fault type earthquakes have the highest occurrence rate of ionospheric perturbation among the three types both for sea (41%) and ground events (61%). The occurrence rates for normal type fault are 35% and 56% for sea and ground earthquakes respectively and the same for stress slip type are 39% and 20% for sea and ground earthquakes respectively. In both cases the occurrence rates are smaller than the reverse fault type. The clear difference of occurrence rate of the ionospheric perturbations may indicate that the coupling efficiency of seismic activity into the overlaying ionosphere is controlled by the pressure in the earth's crust. This gives us further physical insight of Lithosphere-Atmosphere-Ionosphere (LAI) coupling processes.

  6. Moyal products-a new perspective on quasi-Hermitian quantum mechanics

    International Nuclear Information System (INIS)

    Scholtz, F G; Geyer, H B

    2006-01-01

    The rationale for introducing non-Hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-Hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-Hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric

  7. An Overview of a Class of Clock Synchronization Algorithms for Wireless Sensor Networks: A Statistical Signal Processing Perspective

    Directory of Open Access Journals (Sweden)

    Xu Wang

    2015-08-01

    Full Text Available Recently, wireless sensor networks (WSNs have drawn great interest due to their outstanding monitoring and management potential in medical, environmental and industrial applications. Most of the applications that employ WSNs demand all of the sensor nodes to run on a common time scale, a requirement that highlights the importance of clock synchronization. The clock synchronization problem in WSNs is inherently related to parameter estimation. The accuracy of clock synchronization algorithms depends essentially on the statistical properties of the parameter estimation algorithms. Recently, studies dedicated to the estimation of synchronization parameters, such as clock offset and skew, have begun to emerge in the literature. The aim of this article is to provide an overview of the state-of-the-art clock synchronization algorithms for WSNs from a statistical signal processing point of view. This article focuses on describing the key features of the class of clock synchronization algorithms that exploit the traditional two-way message (signal exchange mechanism. Upon introducing the two-way message exchange mechanism, the main clock offset estimation algorithms for pairwise synchronization of sensor nodes are first reviewed, and their performance is compared. The class of fully-distributed clock offset estimation algorithms for network-wide synchronization is then surveyed. The paper concludes with a list of open research problems pertaining to clock synchronization of WSNs.

  8. Mechanical behaviour of alkali-activated blast furnace slag-activated metakaolin blended pastes. Statistical study

    Directory of Open Access Journals (Sweden)

    Higuera, I.

    2012-06-01

    Full Text Available The study and development of alternative, more ecoefficient binders than portland cement are attracting a good deal of scientific and technological interest. Binders obtained from the chemical interaction between calcium silico-aluminous materials and highly alkaline solutions are one of several types of such possible cements. The present paper discusses the mechanical behaviour and mineralogical composition of blended pastes made from NaOH-activated vitreous blast furnace slag and metakaolin. The aim of the study was to determine how parameters such as the slag/metakaolin ratio, activating solution concentration and curing temperature affect strength development in these binders. A statistical study was conducted to establish the impact of each variable and model strength behaviour in these alkaline cements. The conclusion drawn is that activator concentration and the slag/metakaolin ratio are both determinant parameters.

    El estudio y desarrollo de cementos alternativos y más eco-eficientes que el cemento Portland es un tema de gran impacto a nivel científico y tecnológico. Entre esos posibles cementos se encuentran los cementos alcalinos que son materiales conglomerantes obtenidos por la interacción química de materiales silico-aluminosos cálcicos y disoluciones fuertemente alcalinas. En el presente trabajo se estudia el comportamiento mecánico y la composición mineralógica de mezclas de escoria vítrea de horno alto y metacaolín activadas alcalinamente con disoluciones de NaOH. El objetivo de este estudio es conocer cómo afectan parámetros tales como la relación escoria/metacaolín, la concentración de la disolución activadora y la temperatura de curado, al desarrollo resistente de las mezclas. A través del estudio estadístico realizado se ha podido establecer la influencia de cada variable y modelizar el comportamiento resistente de estos cementos alcalinos. Se concluye que la concentración del activador y la relaci

  9. Mathematics of statistical mechanics and the chaos theory; Las matematicas de la mecanica estadistica y de la teoria del caos

    Energy Technology Data Exchange (ETDEWEB)

    Llave, R. de la; Haro, A.

    2000-07-01

    Statistical mechanics requires a language that unifies probabilistic and deterministic description of physical systems. We describe briefly some of the mathematical ideas needed for this unification. These ideas have also proved important in the study of chaotic systems. (Author) 17 refs.

  10. Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

    International Nuclear Information System (INIS)

    Yeh, L.

    1992-01-01

    The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite- mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena

  11. The Sigmoid Transfer Function and the Gain-threshold Exponential Dependence for Neurons from Statistical Mechanics Treatment

    Czech Academy of Sciences Publication Activity Database

    Andrey, Ladislav; Erzan, R.

    2002-01-01

    Roč. 52, č. 12 (2002), s. 1349-1356 ISSN 0011-4626 R&D Projects: GA ČR GA305/02/1487 Institutional research plan: AV0Z1030915 Keywords : nonlinear gain curve * gain-threshold dependence * non-monotone transfer function * statistical mechanics Subject RIV: BA - General Mathematics Impact factor: 0.311, year: 2002

  12. Phase Transitions in Combinatorial Optimization Problems Basics, Algorithms and Statistical Mechanics

    CERN Document Server

    Hartmann, Alexander K

    2005-01-01

    A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary

  13. A cross-culture, cross-gender comparison of perspective taking mechanisms.

    Science.gov (United States)

    Kessler, Klaus; Cao, Liyu; O'Shea, Kieran J; Wang, Hongfang

    2014-06-22

    Being able to judge another person's visuo-spatial perspective is an essential social skill, hence we investigated the generalizability of the involved mechanisms across cultures and genders. Developmental, cross-species, and our own previous research suggest that two different forms of perspective taking can be distinguished, which are subserved by two distinct mechanisms. The simpler form relies on inferring another's line-of-sight, whereas the more complex form depends on embodied transformation into the other's orientation in form of a simulated body rotation. Our current results suggest that, in principle, the same basic mechanisms are employed by males and females in both, East-Asian (EA; Chinese) and Western culture. However, we also confirmed the hypothesis that Westerners show an egocentric bias, whereas EAs reveal an other-oriented bias. Furthermore, Westerners were slower overall than EAs and showed stronger gender differences in speed and depth of embodied processing. Our findings substantiate differences and communalities in social cognition mechanisms across genders and two cultures and suggest that cultural evolution or transmission should take gender as a modulating variable into account.

  14. On application of non—extensive statistical mechanics to studying ecological diversity

    International Nuclear Information System (INIS)

    Van Xuan, Le; Lan, Nguyen Tri; Viet, Nguyen Ai

    2016-01-01

    The concept of Tsallis entropy provides an extension of thermodynamics and statistical physics. In the ecology, Tsallis entropy is proposed to be a new class of diversity indices S_q which covers many common diversity indices found in ecological literature. As a new statistical model for the Whittaker plots describing species abundance distribution, the truncated exponential distribution is used to calculate the diversity and evenness indices. The obtained results in new model are graphically compared with those in previous publication in the same field of interests, and shows a good agreement. A further development of a thermodynamic theory of ecological systems that is consistent with entropic approach of statistical physics is motivated. (paper)

  15. Geological and Rock Mechanics Perspectives for Underground Coal Gasification in India

    Science.gov (United States)

    Singh, Ajay K.; Singh, Rajendra

    2017-07-01

    The geological resources of coal in India are more than 308 billion tonnes upto a depth of 1200 m, out of which proved reserve has been reported at around 130 billion tonnes. There is an increasing requirement to increase the energy extraction efficiency from coal as the developmental prospects of India increase. Underground coal gasification (UCG) is a potential mechanism which may be utilized for extraction of deep-seated coal reserves. Some previous studies suggest that lignites from Gujarat and Rajasthan, along with tertiary coals from northeastern India can be useful from the point of view of UCG. We discuss some geological literature available for these areas. Coming to the rock mechanics perspectives, during UCG the rock temperature is considerable high. At this temperature, most empirical models of rock mechanics may not be applied. In this situation, the challenges for numerical modelling of UCG sites increases manifold. We discuss some of the important modelling geomechanical issues related to UCG in India.

  16. Study of energy fluctuation effect on the statistical mechanics of equilibrium systems

    International Nuclear Information System (INIS)

    Lysogorskiy, Yu V; Wang, Q A; Tayurskii, D A

    2012-01-01

    This work is devoted to the modeling of energy fluctuation effect on the behavior of small classical thermodynamic systems. It is known that when an equilibrium system gets smaller and smaller, one of the major quantities that becomes more and more uncertain is its internal energy. These increasing fluctuations can considerably modify the original statistics. The present model considers the effect of such energy fluctuations and is based on an overlapping between the Boltzmann-Gibbs statistics and the statistics of the fluctuation. Within this o verlap statistics , we studied the effects of several types of energy fluctuations on the probability distribution, internal energy and heat capacity. It was shown that the fluctuations can considerably change the temperature dependence of internal energy and heat capacity in the low energy range and at low temperatures. Particularly, it was found that, due to the lower energy limit of the systems, the fluctuations reduce the probability for the low energy states close to the lowest energy and increase the total average energy. This energy increasing is larger for lower temperatures, making negative heat capacity possible for this case.

  17. Classical and statistical mechanics of celestial-scale spinning strings: Rotating space elevators

    Science.gov (United States)

    Golubović, L.; Knudsen, S.

    2009-05-01

    We introduce novel and unique class of dynamical systems, Rotating Space Elevators (RSE). The RSEs are multiply rotating systems of strings reaching into outer space. Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. The RSEs exhibit interesting nonlinear dynamics and statistical physics phenomena.

  18. Learning Curves and Bootstrap Estimates for Inference with Gaussian Processes: A Statistical Mechanics Study

    DEFF Research Database (Denmark)

    Malzahn, Dorthe; Opper, Manfred

    2003-01-01

    We employ the replica method of statistical physics to study the average case performance of learning systems. The new feature of our theory is that general distributions of data can be treated, which enables applications to real data. For a class of Bayesian prediction models which are based...... on Gaussian processes, we discuss Bootstrap estimates for learning curves....

  19. Statistical Thermodynamics and Microscale Thermophysics

    Science.gov (United States)

    Carey, Van P.

    1999-08-01

    Many exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. In this text Van Carey offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. He begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and then develops the fundamental elements of classical and statistical thermodynamics. Subsequent chapters discuss applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems. The remainder of the book is devoted to nonequilibrium thermodynamics of transport phenomena and to nonequilibrium effects and noncontinuum behavior at the microscale. Although the text emphasizes mathematical development, Carey includes many examples and exercises to illustrate how the theoretical concepts are applied to systems of scientific and engineering interest. In the process he offers a fresh view of statistical thermodynamics for advanced undergraduate and graduate students, as well as practitioners, in mechanical, chemical, and materials engineering.

  20. Neocortical Dynamics at Multiple Scales: EEG Standing Waves, Statistical Mechanics, and Physical Analogs

    OpenAIRE

    Ingber, Lester; Nunez, Paul L.

    2010-01-01

    The dynamic behavior of scalp potentials (EEG) is apparently due to some combination of global and local processes with important top-down and bottom-up interactions across spatial scales. In treating global mechanisms, we stress the importance of myelinated axon propagation delays and periodic boundary conditions in the cortical-white matter system, which is topologically close to a spherical shell. By contrast, the proposed local mechanisms are multiscale interactions between cortical colum...

  1. Phase Transitions in Combinatorial Optimization Problems: Basics, Algorithms and Statistical Mechanics

    Science.gov (United States)

    Hartmann, Alexander K.; Weigt, Martin

    2005-10-01

    A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.

  2. Quantum mechanics of the fractional-statistics gas: Random-phase approximation

    International Nuclear Information System (INIS)

    Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.

    1992-01-01

    A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)

  3. Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow

    Science.gov (United States)

    Farrell, Brian F.; Ioannou, Petros J.

    2017-08-01

    This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium

  4. Appplication of statistical mechanical methods to the modeling of social networks

    Science.gov (United States)

    Strathman, Anthony Robert

    With the recent availability of large-scale social data sets, social networks have become open to quantitative analysis via the methods of statistical physics. We examine the statistical properties of a real large-scale social network, generated from cellular phone call-trace logs. We find this network, like many other social networks to be assortative (r = 0.31) and clustered (i.e., strongly transitive, C = 0.21). We measure fluctuation scaling to identify the presence of internal structure in the network and find that structural inhomogeneity effectively disappears at the scale of a few hundred nodes, though there is no sharp cutoff. We introduce an agent-based model of social behavior, designed to model the formation and dissolution of social ties. The model is a modified Metropolis algorithm containing agents operating under the basic sociological constraints of reciprocity, communication need and transitivity. The model introduces the concept of a social temperature. We go on to show that this simple model reproduces the global statistical network features (incl. assortativity, connected fraction, mean degree, clustering, and mean shortest path length) of the real network data and undergoes two phase transitions, one being from a "gas" to a "liquid" state and the second from a liquid to a glassy state as function of this social temperature.

  5. Statistical mechanics of fluids under internal constraints: Rigorous results for the one-dimensional hard rod fluid

    International Nuclear Information System (INIS)

    Corti, D.S.; Debenedetti, P.G.

    1998-01-01

    The rigorous statistical mechanics of metastability requires the imposition of internal constraints that prevent access to regions of phase space corresponding to inhomogeneous states. We derive exactly the Helmholtz energy and equation of state of the one-dimensional hard rod fluid under the influence of an internal constraint that places an upper bound on the distance between nearest-neighbor rods. This type of constraint is relevant to the suppression of boiling in a superheated liquid. We determine the effects of this constraint upon the thermophysical properties and internal structure of the hard rod fluid. By adding an infinitely weak and infinitely long-ranged attractive potential to the hard core, the fluid exhibits a first-order vapor-liquid transition. We determine exactly the equation of state of the one-dimensional superheated liquid and show that it exhibits metastable phase equilibrium. We also derive statistical mechanical relations for the equation of state of a fluid under the action of arbitrary constraints, and show the connection between the statistical mechanics of constrained and unconstrained ensembles. copyright 1998 The American Physical Society

  6. For a science of layered mechanisms: beyond laws, statistics, and correlations.

    Science.gov (United States)

    Castelfranchi, Cristiano

    2014-01-01

    Two general claims are made in this work. First, we need several different layers of "theory," in particular for understanding human behavior. These layers should concern: the cognitive (mental) representations and mechanisms; the neural underlying processes; the evolutionary history and adaptive functions of our cognition and behaviors; the emergent and complex social structures and dynamics, their relation and feedbacks on individual minds and behaviors, and the relationship between internal regulating goals and the external functions/roles of our conduct; the historical and cultural mechanisms shaping our minds and behaviors; the developmental paths. Second, we do not just need "predictions" and "laws" but also "explanations"; that is, we need to identify the mechanisms producing (here-and-now, or diachronically) a given phenomenon. "Laws" are not enough; they are simply descriptive and predictive; we need the "why" and "how." Correlations are not enough (and they are frequently misleading). We need computational models of the processes postulated in our theories.

  7. Statistical model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

    Science.gov (United States)

    Rizvi, Mohd Suhail; Pal, Anupam

    2014-09-01

    The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. The role of nonequilibrium thermo-mechanical statistics in modern technologies and industrial processes: an overview

    OpenAIRE

    Rodrigues, Clóves G.; Silva, Antônio A. P.; Silva, Carlos A. B.; Vasconcellos, Áurea R.; Ramos, J. Galvão; Luzzi, Roberto

    2010-01-01

    The nowadays notable development of all the modern technology, fundamental for the progress and well being of world society, imposes a great deal of stress in the realm of basic Physics, more precisely on Thermo-Statistics. We do face situations in electronics and optoelectronics involving physical-chemical systems far-removed-from equilibrium, where ultrafast (in pico- and femto-second scale) and non-linear processes are present. Further, we need to be aware of the rapid unfolding of nano-te...

  9. Quantum-statistical mechanics of an atom-dimer mixture: Lee-Yang cluster expansion approach

    International Nuclear Information System (INIS)

    Ohkuma, Takahiro; Ueda, Masahito

    2006-01-01

    We use the Lee-Yang cluster expansion method to study quantum-statistical properties of a mixture of interconvertible atoms and dimers, where the dimers form in a two-body bound state of the atoms. We point out an infinite series of cluster diagrams whose summation leads to the Bose-Einstein condensation of the dimers below a critical temperature. Our theory captures some important features of a cold atom-dimer mixture such as interconversion of atoms and dimers and properties of the mixture at the unitarity limit

  10. Thermodynamics and statistical mechanics of some hydrides of the lanthanides and actinides

    International Nuclear Information System (INIS)

    Mintz, M.H.

    1976-06-01

    This work deals mainly with the thermodynamic and physical properties of the hydrides of the lanthanides and actinides. In addition, statistical models have been developed and applied to metal-hydrogen systems. A kinetic study of the uranium-hydrogen system was performed. The thermodynamic properties of the hydrides of neptunium, thorium, praseodymium, neodymium, samarium and europium were determined. In addition the samarium-europium-hydrogen ternary system was investigated. Moessbauer effect measurements of cubic neptunium hydrides were interpreted according to a model presented. A comparison. (author)

  11. Mechanical fasteners used in historical Siberian shipbuilding: perspectives for metallurgical analysis

    Science.gov (United States)

    Goncharov, A. E.; Mednikov, D. M.; Karelin, N. M.; Nasyrov, I. R.

    2017-10-01

    Recent discoveries of shipwrecked vessels in the northern reaches of the river Yenisei led to a number of questions concerning the history of shipbuilding in Siberia and the technical features of the first vessels of the industrial era to navigate the Northern Sea Route and the Yenisei. One of these questions addresses the features of mechanical fasteners used in the construction of the Siberian vessels. The answer to this question may provide information on how the first vessels, constructed in Siberia during the 1870’s, were able to sail the high seas of the Arctic Ocean and reach European ports. In this paper, we provide a description of iron mechanical fasteners obtained from one shipwrecked vessel and discuss on the perspectives of a metallurgical analysis This research has been funded by a grant of the Russian Fund of Humanities Research (Russian Fund of Fundamental Research) and the Krasnoyarsk Regional Science Fund under Grant number 16-11-24010.

  12. Nitinol Stents in the Femoropopliteal Artery: A Mechanical Perspective on Material, Design, and Performance.

    Science.gov (United States)

    Maleckis, Kaspars; Anttila, Eric; Aylward, Paul; Poulson, William; Desyatova, Anastasia; MacTaggart, Jason; Kamenskiy, Alexey

    2018-05-01

    Endovascular stenting has matured into a commonly used treatment for peripheral arterial disease (PAD) due to its minimally invasive nature and associated reductions in short-term morbidity and mortality. The mechanical properties of the superelastic Nitinol alloy have played a major role in the explosion of peripheral artery stenting, with modern stents demonstrating reasonable resilience and durability. Yet in the superficial femoral and popliteal arteries, even the newest generation Nitinol stents continue to demonstrate clinical outcomes that leave significant room for improvement. Restenosis and progression of native arterial disease often lead to recurrence of symptoms and reinterventions that increase morbidity and health care expenditures. One of the main factors thought to be associated with stent failure in the femoropopliteal artery (FPA) is the unique and highly dynamic mechanical environment of the lower limb. Clinical and experimental data demonstrate that the FPA undergoes significant deformations with limb flexion. It is hypothesized that the inability of many existing stent designs to conform to these deformations likely plays a role in reconstruction failure, as repetitive movements of the leg and thigh combine with mechanical mismatch between the artery and the stent and result in mechanical damage to both the artery and the stent. In this review we will identify challenges and provide a mechanical perspective of FPA stenting, and then discuss current research directions with promise to provide a better understanding of Nitinol, specific features of stent design, and improved characterization of the biomechanical environment of the FPA to facilitate development of better stents for patients with PAD.

  13. Modular reweighting software for statistical mechanical analysis of biased equilibrium data

    Science.gov (United States)

    Sindhikara, Daniel J.

    2012-07-01

    Here a simple, useful, modular approach and software suite designed for statistical reweighting and analysis of equilibrium ensembles is presented. Statistical reweighting is useful and sometimes necessary for analysis of equilibrium enhanced sampling methods, such as umbrella sampling or replica exchange, and also in experimental cases where biasing factors are explicitly known. Essentially, statistical reweighting allows extrapolation of data from one or more equilibrium ensembles to another. Here, the fundamental separable steps of statistical reweighting are broken up into modules - allowing for application to the general case and avoiding the black-box nature of some “all-inclusive” reweighting programs. Additionally, the programs included are, by-design, written with little dependencies. The compilers required are either pre-installed on most systems, or freely available for download with minimal trouble. Examples of the use of this suite applied to umbrella sampling and replica exchange molecular dynamics simulations will be shown along with advice on how to apply it in the general case. New version program summaryProgram title: Modular reweighting version 2 Catalogue identifier: AEJH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 179 118 No. of bytes in distributed program, including test data, etc.: 8 518 178 Distribution format: tar.gz Programming language: C++, Python 2.6+, Perl 5+ Computer: Any Operating system: Any RAM: 50-500 MB Supplementary material: An updated version of the original manuscript (Comput. Phys. Commun. 182 (2011) 2227) is available Classification: 4.13 Catalogue identifier of previous version: AEJH_v1_0 Journal reference of previous version: Comput. Phys. Commun. 182 (2011) 2227 Does the new

  14. For a science of layered mechanisms: beyond laws, statistics, and correlations

    Directory of Open Access Journals (Sweden)

    Cristiano eCastelfranchi

    2014-06-01

    Full Text Available Two general claims are made in this work. First, we need several different layers of theory, in particular for understanding human behavior. These layers should concern: the cognitive (mental representations and mechanisms; the neural underlying processes; the evolutionary history and adaptive functions of our cognition and behaviors; the emergent and complex social structures and dynamics, their relation and feedbacks on individual minds and behaviors, and the relationship between internal regulating goals and the external functions/roles of our conduct; the historical and cultural mechanisms shaping our minds and behaviors; the developmental paths. Second, we do not just need predictions and laws but also explanations; that is, we need to identify the mechanisms producing (here-and-now, or diachronically a given phenomenon. Laws are not enough; they are simply descriptive and predictive; we need the why and how. Correlations are not enough (and they are frequently misleading. We need computational models of the processes postulated in our theories.Reductionism, Cognitive architecture, Emergence, Intentions, Functions, Computer modeling and simulation, Proximate causes

  15. Statistical grand rounds: understanding the mechanism: mediation analysis in randomized and nonrandomized studies.

    Science.gov (United States)

    Mascha, Edward J; Dalton, Jarrod E; Kurz, Andrea; Saager, Leif

    2013-10-01

    In comparative clinical studies, a common goal is to assess whether an exposure, or intervention, affects the outcome of interest. However, just as important is to understand the mechanism(s) for how the intervention affects outcome. For example, if preoperative anemia was shown to increase the risk of postoperative complications by 15%, it would be important to quantify how much of that effect was due to patients receiving intraoperative transfusions. Mediation analysis attempts to quantify how much, if any, of the effect of an intervention on outcome goes though prespecified mediator, or "mechanism" variable(s), that is, variables sitting on the causal pathway between exposure and outcome. Effects of an exposure on outcome can thus be divided into direct and indirect, or mediated, effects. Mediation is claimed when 2 conditions are true: the exposure affects the mediator and the mediator (adjusting for the exposure) affects the outcome. Understanding how an intervention affects outcome can validate or invalidate one's original hypothesis and also facilitate further research to modify the responsible factors, and thus improve patient outcome. We discuss the proper design and analysis of studies investigating mediation, including the importance of distinguishing mediator variables from confounding variables, the challenge of identifying potential mediators when the exposure is chronic versus acute, and the requirements for claiming mediation. Simple designs are considered, as well as those containing multiple mediators, multiple outcomes, and mixed data types. Methods are illustrated with data collected by the National Surgical Quality Improvement Project (NSQIP) and utilized in a companion paper which assessed the effects of preoperative anemic status on postoperative outcomes.

  16. Path integrals in quantum mechanics, statistics, polymer physics, and financial markets

    CERN Document Server

    Kleinert, Hagen

    2009-01-01

    This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p

  17. Predicting the lung compliance of mechanically ventilated patients via statistical modeling

    International Nuclear Information System (INIS)

    Ganzert, Steven; Kramer, Stefan; Guttmann, Josef

    2012-01-01

    To avoid ventilator associated lung injury (VALI) during mechanical ventilation, the ventilator is adjusted with reference to the volume distensibility or ‘compliance’ of the lung. For lung-protective ventilation, the lung should be inflated at its maximum compliance, i.e. when during inspiration a maximal intrapulmonary volume change is achieved by a minimal change of pressure. To accomplish this, one of the main parameters is the adjusted positive end-expiratory pressure (PEEP). As changing the ventilator settings usually produces an effect on patient's lung mechanics with a considerable time delay, the prediction of the compliance change associated with a planned change of PEEP could assist the physician at the bedside. This study introduces a machine learning approach to predict the nonlinear lung compliance for the individual patient by Gaussian processes, a probabilistic modeling technique. Experiments are based on time series data obtained from patients suffering from acute respiratory distress syndrome (ARDS). With a high hit ratio of up to 93%, the learned models could predict whether an increase/decrease of PEEP would lead to an increase/decrease of the compliance. However, the prediction of the complete pressure–volume relation for an individual patient has to be improved. We conclude that the approach is well suitable for the given problem domain but that an individualized feature selection should be applied for a precise prediction of individual pressure–volume curves. (paper)

  18. Short-period atmospheric gravity waves - A study of their statistical properties and source mechanisms

    Science.gov (United States)

    Gedzelman, S. D.

    1983-01-01

    Gravity waves for the one year period beginning 19 October 1976 around Palisades, New York, are investigated to determine their statistical properties and sources. The waves have typical periods of 10 min, pressure amplitudes of 3 Pa and velocities of 30 m/s. In general, the largest, amplitude waves occur during late fall and early winter when the upper tropospheric winds directly overhead are fastest and the static stability of the lower troposphere is greatest. Mean wave amplitudes correlate highly with the product of the mean maximum wind speed and the mean low level stratification directly aloft. A distinct diurnal variation of wave amplitudes with the largest waves occurring in the pre-dawn hours is also observed as a result of the increased static stability then. The majority of waves are generated by shear instability; however, a number of waves are generated by distant sources such as nuclear detonations or large thunderstorms. The waves with distant sources can be distinguished on the basis of their generally much higher coherency across the grid and velocities that depart markedly from the wind velocity at any point in the sounding.

  19. Degradation of creatinine using boron-doped diamond electrode: Statistical modeling and degradation mechanism.

    Science.gov (United States)

    Zhang, Zhefeng; Xian, Jiahui; Zhang, Chunyong; Fu, Degang

    2017-09-01

    This study investigated the degradation performance and mechanism of creatinine (a urine metabolite) with boron-doped diamond (BDD) anodes. Experiments were performed using a synthetic creatinine solution containing two supporting electrolytes (NaCl and Na 2 SO 4 ). A three-level central composite design was adopted to optimize the degradation process, a mathematical model was thus constructed and used to explore the optimum operating conditions. A maximum mineralization percentage of 80% following with full creatinine removal had been achieved within 120 min of electrolysis, confirming the strong oxidation capability of BDD anodes. Moreover, the results obtained suggested that supporting electrolyte concentration should be listed as one of the most important parameters in BDD technology. Lastly, based on the results from quantum chemistry calculations and LC/MS analyses, two different reaction pathways which governed the electrocatalytic oxidation of creatinine irrespective of the supporting electrolytes were identified. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. Statistical mechanical characteristics of slip-ring induction motors when direct current braking

    Energy Technology Data Exchange (ETDEWEB)

    Kedzior, W; Muchorowski, J; Pienkowski, K

    1980-09-01

    This paper evaluates methods of braking high capacity belt conveyors used in brown coal surface mines in Poland. Complications associated with belt conveyor braking, particularly when a conveyor moves down a slope, are analyzed. A method of calculating mechanical characteristics of wound-rotor induction motors during direct current braking taking into account saturation of magnetic circuit is presented. Characteristics of the SZUr motor with 630 kW power, used in brown coal mining, are also given. Analyses show that motor operation can be efficiently braked in two ways: 1. by changing additional resistance in rotor circuit (e.g. using thyristor controller); 2. by changing intensity of electric current supplied to stator winding (e.g. using a rectifier). (3 refs.) (In Polish)

  1. Molecular Dynamics Simulation and Statistics Analysis Reveals the Defense Response Mechanism in Plants

    Science.gov (United States)

    Liu, Zhichao; Zhao, Yunjie; Zeng, Chen; Computational Biophysics Lab Team

    As the main protein of the bacterial flagella, flagellin plays an important role in perception and defense response. The newly discovered locus, FLS2, is ubiquitously expressed. FLS2 encodes a putative receptor kinase and shares many homologies with some plant resistance genes and even with some components of immune system of mammals and insects. In Arabidopsis, FLS2 perception is achieved by the recognition of epitope flg22, which induces FLS2 heteromerization with BAK1 and finally the plant immunity. Here we use both analytical methods such as Direct Coupling Analysis (DCA) and Molecular Dynamics (MD) Simulations to get a better understanding of the defense mechanism of FLS2. This may facilitate a redesign of flg22 or de-novo design for desired specificity and potency to extend the immune properties of FLS2 to other important crops and vegetables.

  2. Maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems.

    Science.gov (United States)

    Vasconcelos, Giovani L; Salazar, Domingos S P; Macêdo, A M S

    2018-02-01

    A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.

  3. Statistical mechanics of the self-gravitating gas: II. Local physical magnitudes and fractal structures

    International Nuclear Information System (INIS)

    Vega, H.J. de; Sanchez, N.

    2002-01-01

    We complete our study of the self-gravitating gas by computing the fluctuations around the saddle point solution for the three statistical ensembles (grand canonical, canonical and microcanonical). Although the saddle point is the same for the three ensembles, the fluctuations change from one ensemble to the other. The zeroes of the small fluctuations determinant determine the position of the critical points for each ensemble. This yields the domains of validity of the mean field approach. Only the S-wave determinant exhibits critical points. Closed formulae for the S- and P-wave determinants of fluctuations are derived. The local properties of the self-gravitating gas in thermodynamic equilibrium are studied in detail. The pressure, energy density, particle density and speed of sound are computed and analyzed as functions of the position. The equation of state turns out to be locally p(r→ )=Tρ V (r→ ) as for the ideal gas. Starting from the partition function of the self-gravitating gas, we prove in this microscopic calculation that the hydrostatic description yielding locally the ideal gas equation of state is exact in the N=∞ limit. The dilute nature of the thermodynamic limit (N∼L→∞ with N/L fixed) together with the long range nature of the gravitational forces play a crucial role in obtaining such ideal gas equation. The self-gravitating gas being inhomogeneous, we have PV/[NT]=f(η)≤1 for any finite volume V. The inhomogeneous particle distribution in the ground state suggests a fractal distribution with Haussdorf dimension D, D is slowly decreasing with increasing density, 1< D<3. The average distance between particles is computed in Monte Carlo simulations and analytically in the mean field approach. A dramatic drop at the phase transition is exhibited, clearly illustrating the properties of the collapse

  4. Exact matrix treatment of statistical mechanical lattice model of adsorption induced gate opening in metal-organic frameworks

    International Nuclear Information System (INIS)

    Dunne, Lawrence J; Manos, George

    2015-01-01

    Here we present a statistical mechanical lattice model which is exactly solvable using a matrix method and allows treatment of adsorption induced gate opening structural transformations of metal-organic frameworks which are nanoporous materials with exceptional adsorption properties. Modelling of these structural changes presents a serious theoretical challenge when the solid and gas species are treated in an even handed way. This exactly solvable model complements other simulation based approaches. The methodology presented here highlights the competition between the potential for adsorption and the energy required for structural transition as a driving force for the features in the adsorption isotherms. (paper)

  5. Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics

    Directory of Open Access Journals (Sweden)

    Pan Zhao

    2018-01-01

    Full Text Available In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.

  6. Couplings in D(2,1;α) superconformal mechanics from the SU(2) perspective

    Energy Technology Data Exchange (ETDEWEB)

    Galajinsky, Anton [Laboratory of Mathematical Physics, Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

    2017-03-09

    Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;α) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some phase space can be extended to a representation of the Lie superalgebra corresponding to D(2,1;α). Novel couplings of arbitrary number of supermultiplets of the type (1,4,3) and (0,4,4) to a single supermultiplet of either the type (3,4,1), or (4,4,0) are constructed. D(2,1;α) superconformal mechanics describing superparticles propagating near the horizon of the extreme Reissner-Nordström-AdS-dS black hole in four and five dimensions is considered. The parameter α is linked to the cosmological constant.

  7. Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging

    International Nuclear Information System (INIS)

    Moireau, Philippe; Chapelle, Dominique; Tallec, Patrick Le

    2009-01-01

    We propose an effective filtering methodology designed to perform estimation in a distributed mechanical system using position measurements. As in a previously introduced method, the filter is inspired by robust control feedback, but here we take full advantage of the estimation specificity to choose a feedback law that can act on displacements instead of velocities and still retain the same kind of dissipativity property which guarantees robustness. This is very valuable in many applications for which positions are more readily available than velocities, as in medical imaging. We provide an in-depth analysis of the proposed procedure, as well as detailed numerical assessments using a test problem inspired by cardiac biomechanics, as medical diagnosis assistance is an important perspective for this approach. The method is formulated first for measurements based on Lagrangian displacements, but we then derive a nonlinear extension allowing us to instead consider segmented images, which of course is even more relevant in medical applications

  8. Nitinol Stents in the Femoropopliteal Artery: A Mechanical Perspective on Material, Design, and Performance

    Science.gov (United States)

    Maleckis, Kaspars; Anttila, Eric; Aylward, Paul; Poulson, William; Desyatova, Anastasia; MacTaggart, Jason; Kamenskiy, Alexey

    2018-01-01

    Endovascular stenting has matured into a commonly used treatment for peripheral arterial disease (PAD) due to its minimally invasive nature and associated reductions in short-termmorbidity and mortality. The mechanical properties of the superelastic Nitinol alloy have played a major role in the explosion of peripheral artery stenting, with modern stents demonstrating reasonable resilience and durability. Yet in the superficial femoral and popliteal arteries, even the newest generation Nitinol stents continue to demonstrate clinical outcomes that leave significant room for improvement. Restenosis and progression of native arterial disease often lead to recurrence of symptoms and reinterventions that increase morbidity and health care expenditures. One of the main factors thought to be associated with stent failure in the femoropopliteal artery (FPA) is the unique and highly dynamic mechanical environment of the lower limb. Clinical and experimental data demonstrate that the FPA undergoes significant deformations with limb flexion. It is hypothesized that the inability of many existing stent designs to conform to these deformations likely plays a role in reconstruction failure, as repetitive movements of the leg and thigh combine with mechanical mismatch between the artery and the stent and result in mechanical damage to both the artery and the stent. In this review we will identify challenges and provide a mechanical perspective of FPA stenting, and then discuss current research directions with promise to provide a better understanding of Nitinol, specific features of stent design, and improved characterization of the biomechanical environment of the FPA to facilitate development of better stents for patients with PAD. PMID:29470746

  9. Quantum and Statistical Mechanics Applied to Singlet Carbenes, Pericyclic Reactions, and Condensed Phase Phenomena

    Science.gov (United States)

    Evanseck, Jeffrey Donald

    The completed research covers a broad range of theoretical applications in organic chemistry. It is divided into three chapters which covers the chemistry of singlet carbenes (Chapter 1), substituent effects in pericyclic rearrangements (Chapter 2), and the effects of solvent on the reactivity of organic reactions (Chapter 3). The selectivity between 1,2- and 1,4-intramolecular additions to restricted diene systems has been investigated. A decrease in activation energy for the intramolecular cycloaddition is noted for systems which approach the idealized geometry found with intermolecular addition of carbenes to olefins. Direct substitution at the carbene site dramatically effects the predicted activation barriers for 1,2-hydrogen shifts. An excellent correlation between the activation energy and a substituents sigma_sp {rm R}{rm o} parameters has been demonstrated. The long standing problem of orbital alignment influences on the selectivity of 1,2-hydrogen arrangements shows significant geometric distortions, yet has little influence on the rates of singlet alkylcarbene rearrangements. The exo-selectivities observed for 1,2-shifts in rigid systems are explained by torsional and steric interactions which develop in the transition structures. Substituent effects on pericyclic reactions have been computed for several conrotatory and disrotatory electrocyclizations. The six-electron disrotatory electrocyclization of 1-substituted hexatrienes displays a strong electronic component in determining stereoselectivity, despite incredible steric interference. The eight-electron conrotatory electrocyclization transition structure of 1-substituted octatetraene has an unusual helical transition structure which does not differentiate between substituent position. The effects of solvents on the acidity differences between E and Z esters has supplemented earlier ab initio quantum mechanical results on the enhanced acidity of Meldrum's acid. Monte Carlo simulations predict a

  10. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    International Nuclear Information System (INIS)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki

    2011-01-01

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3–6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3–4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: ► This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. ► A Boltzmann distribution is studied among iron lines of various excitation levels. ► We find an overpopulation of the high-lying energy levels from the normal distribution. ► It is caused through Penning-type collision of iron atom with argon metastable atom.

  11. Boltzmann statistical consideration on the excitation mechanism of iron atomic lines emitted from glow discharge plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Lei; Kashiwakura, Shunsuke; Wagatsuma, Kazuaki, E-mail: wagatuma@imr.tohoku.ac.jp

    2011-11-15

    A Boltzmann plot for many iron atomic lines having excitation energies of 3.3-6.9 eV was investigated in glow discharge plasmas when argon or neon was employed as the plasma gas. The plot did not show a linear relationship over a wide range of the excitation energy, but showed that the emission lines having higher excitation energies largely deviated from a normal Boltzmann distribution whereas those having low excitation energies (3.3-4.3 eV) well followed it. This result would be derived from an overpopulation among the corresponding energy levels. A probable reason for this is that excitations for the high-lying excited levels would be caused predominantly through a Penning-type collision with the metastable atom of argon or neon, followed by recombination with an electron and then stepwise de-excitations which can populate the excited energy levels just below the ionization limit of iron atom. The non-thermal excitation occurred more actively in the argon plasma rather than the neon plasma, because of a difference in the number density between the argon and the neon metastables. The Boltzmann plots yields important information on the reason why lots of Fe I lines assigned to high-lying excited levels can be emitted from glow discharge plasmas. - Highlights: Black-Right-Pointing-Pointer This paper shows the excitation mechanism of Fe I lines from a glow discharge plasma. Black-Right-Pointing-Pointer A Boltzmann distribution is studied among iron lines of various excitation levels. Black-Right-Pointing-Pointer We find an overpopulation of the high-lying energy levels from the normal distribution. Black-Right-Pointing-Pointer It is caused through Penning-type collision of iron atom with argon metastable atom.

  12. Statistical Analysis of Categorical Time Series of Atmospheric Elementary Circulation Mechanisms - Dzerdzeevski Classification for the Northern Hemisphere.

    Science.gov (United States)

    Brenčič, Mihael

    2016-01-01

    Northern hemisphere elementary circulation mechanisms, defined with the Dzerdzeevski classification and published on a daily basis from 1899-2012, are analysed with statistical methods as continuous categorical time series. Classification consists of 41 elementary circulation mechanisms (ECM), which are assigned to calendar days. Empirical marginal probabilities of each ECM were determined. Seasonality and the periodicity effect were investigated with moving dispersion filters and randomisation procedure on the ECM categories as well as with the time analyses of the ECM mode. The time series were determined as being non-stationary with strong time-dependent trends. During the investigated period, periodicity interchanges with periods when no seasonality is present. In the time series structure, the strongest division is visible at the milestone of 1986, showing that the atmospheric circulation pattern reflected in the ECM has significantly changed. This change is result of the change in the frequency of ECM categories; before 1986, the appearance of ECM was more diverse, and afterwards fewer ECMs appear. The statistical approach applied to the categorical climatic time series opens up new potential insight into climate variability and change studies that have to be performed in the future.

  13. Tsallis non-extensive statistical mechanics in the ionospheric detrended total electron content during quiet and storm periods

    Science.gov (United States)

    Ogunsua, B. O.; Laoye, J. A.

    2018-05-01

    In this paper, the Tsallis non-extensive q-statistics in ionospheric dynamics was investigated using the total electron content (TEC) obtained from two Global Positioning System (GPS) receiver stations. This investigation was carried out considering the geomagnetically quiet and storm periods. The micro density variation of the ionospheric total electron content was extracted from the TEC data by method of detrending. The detrended total electron content, which represent the variation in the internal dynamics of the system was further analyzed using for non-extensive statistical mechanics using the q-Gaussian methods. Our results reveals that for all the analyzed data sets the Tsallis Gaussian probability distribution (q-Gaussian) with value q > 1 were obtained. It was observed that there is no distinct difference in pattern between the values of qquiet and qstorm. However the values of q varies with geophysical conditions and possibly with local dynamics for the two stations. Also observed are the asymmetric pattern of the q-Gaussian and a highly significant level of correlation for the q-index values obtained for the storm periods compared to the quiet periods between the two GPS receiver stations where the TEC was measured. The factors responsible for this variation can be mostly attributed to the varying mechanisms resulting in the self-reorganization of the system dynamics during the storm periods. The result shows the existence of long range correlation for both quiet and storm periods for the two stations.

  14. Exact results in nonequilibrium statistical mechanics: Formalism and applications in chemical kinetics and single-molecule free energy estimation

    Science.gov (United States)

    Adib, Artur B.

    In the last two decades or so, a collection of results in nonequilibrium statistical mechanics that departs from the traditional near-equilibrium framework introduced by Lars Onsager in 1931 has been derived, yielding new fundamental insights into far-from-equilibrium processes in general. Apart from offering a more quantitative statement of the second law of thermodynamics, some of these results---typified by the so-called "Jarzynski equality"---have also offered novel means of estimating equilibrium quantities from nonequilibrium processes, such as free energy differences from single-molecule "pulling" experiments. This thesis contributes to such efforts by offering three novel results in nonequilibrium statistical mechanics: (a) The entropic analog of the Jarzynski equality; (b) A methodology for estimating free energies from "clamp-and-release" nonequilibrium processes; and (c) A directly measurable symmetry relation in chemical kinetics similar to (but more general than) chemical detailed balance. These results share in common the feature of remaining valid outside Onsager's near-equilibrium regime, and bear direct applicability in protein folding kinetics as well as in single-molecule free energy estimation.

  15. The determinants of bond angle variability in protein/peptide backbones: A comprehensive statistical/quantum mechanics analysis.

    Science.gov (United States)

    Improta, Roberto; Vitagliano, Luigi; Esposito, Luciana

    2015-11-01

    The elucidation of the mutual influence between peptide bond geometry and local conformation has important implications for protein structure refinement, validation, and prediction. To gain insights into the structural determinants and the energetic contributions associated with protein/peptide backbone plasticity, we here report an extensive analysis of the variability of the peptide bond angles by combining statistical analyses of protein structures and quantum mechanics calculations on small model peptide systems. Our analyses demonstrate that all the backbone bond angles strongly depend on the peptide conformation and unveil the existence of regular trends as function of ψ and/or φ. The excellent agreement of the quantum mechanics calculations with the statistical surveys of protein structures validates the computational scheme here employed and demonstrates that the valence geometry of protein/peptide backbone is primarily dictated by local interactions. Notably, for the first time we show that the position of the H(α) hydrogen atom, which is an important parameter in NMR structural studies, is also dependent on the local conformation. Most of the trends observed may be satisfactorily explained by invoking steric repulsive interactions; in some specific cases the valence bond variability is also influenced by hydrogen-bond like interactions. Moreover, we can provide a reliable estimate of the energies involved in the interplay between geometry and conformations. © 2015 Wiley Periodicals, Inc.

  16. Perspective

    DEFF Research Database (Denmark)

    Kussmann, Martin; Morine, Melissa J; Hager, Jörg

    2013-01-01

    We review here the status of human type 2 diabetes studies from a genetic, epidemiological, and clinical (intervention) perspective. Most studies limit analyses to one or a few omic technologies providing data of components of physiological processes. Since all chronic diseases are multifactorial...... at different time points along this longitudinal investigation are performed with a comprehensive set of omics platforms. These data sets are generated in a biological context, rather than biochemical compound class-driven manner, which we term "systems omics."...

  17. Mechanical properties of various z-stent designs: an endovascular stent-grafting perspective.

    Science.gov (United States)

    Bashar, Abul Hasan Muhammad; Kazui, Teruhisa; Washiyama, Naoki; Terada, Hitoshi; Yamashita, Katsushi; Haque, Mohammad E

    2003-08-01

    To comparatively assess the mechani-cal behavior of various clinically relevant Z-stent designs. A total of 16 Z-stents of original, biliary, spiral, and double-skirted designs (n=4 for each) were constructed using similar specifications for all. Stents were then evaluated for stiffness, snap opening force (SOF), flexibility, and displacement force using a novel tensiometer. Differences among the stents were determined using statistical methods. Stents explanted from dog aorta after a mean follow-up of 13 months were examined under a scanning electron microscope for surface defects. Forces required for about 50% reduction in diameter were 1.88 +/- 0.16 N, 3.81 +/- 0.21 N, 2.76 +/- 0.22 N, and 3.35 +/- 0.19 N for original, biliary, spiral, and skirted designs, respectively. Differences among the four designs were statistically significant at almost all points of measurement (P designs showed higher SOF values in the early measurements. Stents explanted from dog aorta after a mean duration of 13 months showed no obvious corrosion or breakage in the wire struts. Significant differences exist among the various Z-stent designs in terms of their mechanical properties. Understanding them should help to select the appropriate stent for a given lesion. 316L stainless steel shows a favorable long-term tissue interaction.

  18. Fracture mechanics and statistical modeling of ternary blends of polylactide/ethylene-acrylate copolymer /wood-flour composites

    Science.gov (United States)

    Afrifah, Kojo Agyapong

    This study examined the mechanisms of toughening the brittle bio-based poly(lactic acid) (PLA) with a biodegradable rubbery impact modifier to develop biodegradable and cost effective PLA/wood-flour composites with improved impact strength, toughness, high ductility, and flexibility. Semicrystalline and amorphous PLA grades were impact modified by melt blending with an ethylene-acrylate copolymer (EAC) impact modifier. EAC content was varied to study the effectiveness and efficiency of the impact modifier in toughening the semicrystalline and amorphous grades of the PLA. Impact strength was used to assess the effectiveness and efficiency of the EAC in toughening the blends, whereas the toughening mechanisms were determined with the phase morphologies and the miscibilities of the blends. Subsequent tensile property analyses were performed on the most efficiently toughened PLA grade. Composites were made from PLA, wood flour of various particle sizes, and EAC. Using two-level factorial design the interaction between wood flour content, wood flour particle size, and EAC content and its effect on the mechanical properties of the PLA/wood-flour composites was statistically studied. Numerical optimization was also performed to statistically model and optimize material compositions to attain mechanical properties for the PLA/wood-flour composites equivalent to at least those of unfilled PLA. The J-integral method of fracture mechanics was applied to assess the crack initiation (Jin) and complete fracture (J f) energies of the composites to account for imperfections in the composites and generate data useful for engineering designs. Morphologies of the fractured surfaces of the composites were analyzed to elucidate the failure and toughening mechanisms of the composites. The EAC impact modifier effectively improved the impact strength of the PLA/EAC blends, regardless of the PLA type. However, the EAC was more efficient in the semicrystalline grades of PLA compared to the

  19. Thermodynamics and statistical mechanics

    CERN Document Server

    Landsberg, Peter T

    1990-01-01

    Exceptionally articulate treatment combines precise mathematical style with strong physical intuition. Wide range of applications includes negative temperatures, negative heat capacities, special and general relativistic effects, black hole thermodynamics, gravitational collapse, more. Over 100 problems with worked solutions. Advanced undergraduate, graduate level. Table of applications. Useful formulas and other data.

  20. Statistical mechanics of elasticity

    CERN Document Server

    Weiner, JH

    2012-01-01

    Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.