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 ...
(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 ...
Equilibrium statistical mechanics of lattice models
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...
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
Current algebra, statistical mechanics and quantum models
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.
A statistical mechanical model of economics
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
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...
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.)
Statistical mechanics of the cluster Ising model
International Nuclear Information System (INIS)
Smacchia, Pietro; Amico, Luigi; Facchi, Paolo; Fazio, Rosario; Florio, Giuseppe; Pascazio, Saverio; Vedral, Vlatko
2011-01-01
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
Statistical mechanics of the cluster Ising model
Energy Technology Data Exchange (ETDEWEB)
Smacchia, Pietro [SISSA - via Bonomea 265, I-34136, Trieste (Italy); Amico, Luigi [CNR-MATIS-IMM and Dipartimento di Fisica e Astronomia Universita di Catania, C/O ed. 10, viale Andrea Doria 6, I-95125 Catania (Italy); Facchi, Paolo [Dipartimento di Matematica and MECENAS, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Fazio, Rosario [NEST, Scuola Normale Superiore and Istituto Nanoscienze - CNR, 56126 Pisa (Italy); Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Florio, Giuseppe; Pascazio, Saverio [Dipartimento di Fisica and MECENAS, Universita di Bari, I-70126 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); Vedral, Vlatko [Center for Quantum Technology, National University of Singapore, 117542 Singapore (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom)
2011-08-15
We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
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
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...
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
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.
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
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
Equilibrium statistical mechanics
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
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
Statistical mechanics of directed models of polymers in the square lattice
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...
Lectures on statistical mechanics
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
Equilibrium statistical mechanics
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
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.)
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
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
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
Statistical mechanics of superconductivity
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 ...
Playing at Statistical Mechanics
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)
Statistical mechanics rigorous results
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.
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
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.)
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.
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)
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.
A statistical mechanics model for free-for-all airplane passenger boarding
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.
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
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
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.
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
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.
Journey Through Statistical Mechanics
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...
Graphene Statistical Mechanics
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
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
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.)
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.
Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties.
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.
A statistical model of uplink inter-cell interference with slow and fast power control mechanisms
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.
A statistical model of uplink inter-cell interference with slow and fast power control mechanisms
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.
Statistical mechanics of competitive resource allocation using agent-based models
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.
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
The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model
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
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
Statistical mechanics of nonequilibrium liquids
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,
Statistical mechanics of complex networks
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.
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
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
Introduction to quantum statistical mechanics
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.
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
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
Statistical mechanics in a nutshell
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
Appplication of statistical mechanical methods to the modeling of social networks
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.
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
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
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
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.
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.
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
Modern Thermodynamics with Statistical Mechanics
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...
Statistical Mechanics of Turbulent Dynamos
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
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.)
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
Statistical mechanics of few-particle systems: exact results for two useful models
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.
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)
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)
Statistical mechanics of multipartite entanglement
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.
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.
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
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.
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.
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
Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa
2017-10-01
The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.
Nonequilibrium statistical mechanics ensemble method
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
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.
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.
Sampling, Probability Models and Statistical Reasoning Statistical
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Sampling, Probability Models and Statistical Reasoning Statistical Inference. Mohan Delampady V R Padmawar. General Article Volume 1 Issue 5 May 1996 pp 49-58 ...
Annotations to quantum statistical mechanics
Kim, In-Gee
2018-01-01
This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Bayms lectures that were presented in the book Quantum Statistical Mechanics: Greens Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Greens 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 Greens 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...
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
Periodic Ground State Configurations in a One-Dimensional Hubbard Model of Statistical Mechanics
International Nuclear Information System (INIS)
Kipnis, M. M.
2000-01-01
This paper considers an averaging procedure for the description of a particles arrangement in a Hubbard model with antiferromagnetic interactions. The arrangements are described by the devil's staircase. Completeness of the staircase is proved
On the SU(2 vertical stroke 1) WZNW model and its statistical mechanics applications
Energy Technology Data Exchange (ETDEWEB)
Saleur, H [CEA Centre d' Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique; [University of Southern California, Los Angeles, CA (United States). Dept. of Physics; Schomerus, V [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-11-15
Motivated by a careful analysis of the Laplacian on the supergroup SU(2 vertical stroke 1) we formulate a proposal for the state space of the SU(2 vertical stroke 1) WZNW model. We then use properties of sl(2 vertical stroke 1) characters to compute the partition function of the theory. In the special case of level k=1 the latter is found to agree with the properly regularized partition function for the continuum limit of the integrable sl(2 vertical stroke 1)3- anti 3 super-spin chain. Some general conclusions applicable to other WZNW models (in particular the case k=-1/2) are also drawn. (orig.)
Statistical mechanics of neocortical interactions: Constraints on 40-Hz models of short-term memory
Ingber, Lester
1995-10-01
Calculations presented in L. Ingber and P.L. Nunez, Phys. Rev. E 51, 5074 (1995) detailed the evolution of short-term memory in the neocortex, supporting the empirical 7+/-2 rule of constraints on the capacity of neocortical processing. These results are given further support when other recent models of 40-Hz subcycles of low-frequency oscillations are considered.
Monte Carlo simulation of a statistical mechanical model of multiple protein sequence alignment.
Kinjo, Akira R
2017-01-01
A grand canonical Monte Carlo (MC) algorithm is presented for studying the lattice gas model (LGM) of multiple protein sequence alignment, which coherently combines long-range interactions and variable-length insertions. MC simulations are used for both parameter optimization of the model and production runs to explore the sequence subspace around a given protein family. In this Note, I describe the details of the MC algorithm as well as some preliminary results of MC simulations with various temperatures and chemical potentials, and compare them with the mean-field approximation. The existence of a two-state transition in the sequence space is suggested for the SH3 domain family, and inappropriateness of the mean-field approximation for the LGM is demonstrated.
Statistical mechanics of a multiconnected Hopfield neural-network model in a transverse field
International Nuclear Information System (INIS)
Ma, Y.; Gong, C.
1995-01-01
The Hopfield neural-network model with p-spin interactions in the presence of a transverse field is introduced and solved exactly in the limit p→∞. In the phase diagrams drawn as a function of the temperature, the important results such as reentrance are found, and the effects of the quantum fluctuations on the phase transitions, the retrieval phase, and the storage ratio α are examined
International Nuclear Information System (INIS)
Dunne, Lawrence J; Axelsson, Anna-Karin; Alford, Neil McN; Valant, Matjaz; Manos, George
2011-01-01
Despite considerable effort, the microscopic origin of the electrocaloric (EC) effect in ferroelectric relaxors is still intensely discussed. Ferroelectric relaxors typically display a dual-peak EC effect, whose origin is uncertain. Here we present an exact statistical mechanical matrix treatment of a lattice model of polar nanoregions forming in a neutral background and use this approach to study the characteristics of the EC effect in ferroelectric relaxors under varying electric field and pressure. The dual peaks seen in the EC properties of ferroelectric relaxors are due to the formation and ordering of polar nanoregions. The model predicts significant enhancement of the EC temperature rise with pressure which may have some contribution to the giant EC effect.
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
An introduction to thermodynamics and statistical mechanics
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)
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....
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
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
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
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
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
International Nuclear Information System (INIS)
O'Carroll, M.
1993-01-01
The author considers models of statistical mechanics and quantum field theory (in the Euclidean formulation) which are treated using renormalization group methods and where the action is a small perturbation of a quadratic action. The author obtains multiscale formulas for the generating and correlation functions after n renormalization group transformations which bring out the relation with the nth effective action. The author derives and compares the formulas for different RGs. The formulas for correlation functions involve (1) two propagators which are determined by a sequence of approximate wave function renormalization constants and renormalization group operators associated with the decomposition into scales of the quadratic form and (2) field derivatives of the nth effective action. For the case of the block field open-quotes δ-functionclose quotes RG the formulas are especially simple and for asymptotic free theories only the derivatives at zero field are needed; the formulas have been previously used directly to obtain bounds on correlation functions using information obtained from the analysis of effective actions. The simplicity can be traced to an open-quotes orthogonality-of-scalesclose quotes property which follows from an implicit wavelet structure. Other commonly used RGs do not have the open-quotes orthogonality of scalesclose quotes property. 19 refs
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
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
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
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
Early years of Computational Statistical Mechanics
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.
Directory of Open Access Journals (Sweden)
R. Soundararajan
2015-01-01
Full Text Available Artificial Neural Network (ANN approach was used for predicting and analyzing the mechanical properties of A413 aluminum alloy produced by squeeze casting route. The experiments are carried out with different controlled input variables such as squeeze pressure, die preheating temperature, and melt temperature as per Full Factorial Design (FFD. The accounted absolute process variables produce a casting with pore-free and ideal fine grain dendritic structure resulting in good mechanical properties such as hardness, ultimate tensile strength, and yield strength. As a primary objective, a feed forward back propagation ANN model has been developed with different architectures for ensuring the definiteness of the values. The developed model along with its predicted data was in good agreement with the experimental data, inferring the valuable performance of the optimal model. From the work it was ascertained that, for castings produced by squeeze casting route, the ANN is an alternative method for predicting the mechanical properties and appropriate results can be estimated rather than measured, thereby reducing the testing time and cost. As a secondary objective, quantitative and statistical analysis was performed in order to evaluate the effect of process parameters on the mechanical properties of the castings.
Statistical mechanics of driven diffusive systems
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...
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)
Semiclassical statistical mechanics of fluids
International Nuclear Information System (INIS)
Singh, Y.; Sinha, S.K.
1981-01-01
The problem of calculating the equilibrium properties of fluids in the semiclassical limit when the quantum effects are small is studied. Particle distribution functions and thermodynamic quantities are defined in terms of the Slater sum and methods for evaluating the Slater sum are discussed. It is shown that the expansion method employing the usual Wigner-Kirkwood or Hemmer-Jancovici series is not suitable to treat the properties of the condensed state. Using the grand canonical ensemble and functional differentiation technique we develop cluster expansion series of the Helmholtz free energy and pair correlation functions. Using topological reduction we transform these series to more compact form involving a renormalized potential or a renormalized Mayer function. Then the convergence of the two series is improved by an optimal choice of the renormalized potential or the Mayer function. Integral equation theories are derived and used to devise perturbation methods. An application of these methods to the calculation of the virial coefficients, thermodynamic properties and the pair correlation function for model fluids is discussed. (orig.)
BOOK REVIEW: Statistical Mechanics of Turbulent Flows
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
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.
Statistical mechanics principles and selected applications
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
Thermodynamics and statistical mechanics an integrated approach
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...
Adler, Stephen L
2004-01-01
Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schr�...
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.
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 ...
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)
Exclusion statistics and integrable models
International Nuclear Information System (INIS)
Mashkevich, S.
1998-01-01
The definition of exclusion statistics, as given by Haldane, allows for a statistical interaction between distinguishable particles (multi-species statistics). The thermodynamic quantities for such statistics ca be evaluated exactly. The explicit expressions for the cluster coefficients are presented. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models. The interesting questions of generalizing this correspondence onto the higher-dimensional and the multi-species cases remain essentially open
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
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
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.
The large deviation approach to statistical mechanics
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.
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
Establishing statistical models of manufacturing parameters
International Nuclear Information System (INIS)
Senevat, J.; Pape, J.L.; Deshayes, J.F.
1991-01-01
This paper reports on the effect of pilgering and cold-work parameters on contractile strain ratio and mechanical properties that were investigated using a large population of Zircaloy tubes. Statistical models were established between: contractile strain ratio and tooling parameters, mechanical properties (tensile test, creep test) and cold-work parameters, and mechanical properties and stress-relieving temperature
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.
Exclusion statistics and integrable models
International Nuclear Information System (INIS)
Mashkevich, S.
1998-01-01
The definition of exclusion statistics that was given by Haldane admits a 'statistical interaction' between distinguishable particles (multispecies statistics). For such statistics, thermodynamic quantities can be evaluated exactly; explicit expressions are presented here for cluster coefficients. Furthermore, single-species exclusion statistics is realized in one-dimensional integrable models of the Calogero-Sutherland type. The interesting questions of generalizing this correspondence to the higher-dimensional and the multispecies cases remain essentially open; however, our results provide some hints as to searches for the models in question
A statistical mechanics approach to Granovetter theory
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.
Learning Predictive Statistics: Strategies and Brain Mechanisms.
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
Statistical mechanics and applications in condensed matter
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 ...
Aftershock Energy Distribution by Statistical Mechanics Approach
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.
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)
Amano, Ken-Ichi; Yoshidome, Takashi; Iwaki, Mitsuhiro; Suzuki, Makoto; Kinoshita, Masahiro
2010-07-28
We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1
Statistical Model of Extreme Shear
DEFF Research Database (Denmark)
Larsen, Gunner Chr.; Hansen, Kurt Schaldemose
2004-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continously increase the knowledge on wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describe the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of high-sampled full-scale time series measurements...... are consistent, given the inevitabel uncertainties associated with model as well as with the extreme value data analysis. Keywords: Statistical model, extreme wind conditions, statistical analysis, turbulence, wind loading, statistical analysis, turbulence, wind loading, wind shear, wind turbines....
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)
Statistical Mechanics and Applications in Condensed Matter
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.
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
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
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
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.
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
Statistical modeling for degradation data
Lio, Yuhlong; Ng, Hon; Tsai, Tzong-Ru
2017-01-01
This book focuses on the statistical aspects of the analysis of degradation data. In recent years, degradation data analysis has come to play an increasingly important role in different disciplines such as reliability, public health sciences, and finance. For example, information on products’ reliability can be obtained by analyzing degradation data. In addition, statistical modeling and inference techniques have been developed on the basis of different degradation measures. The book brings together experts engaged in statistical modeling and inference, presenting and discussing important recent advances in degradation data analysis and related applications. The topics covered are timely and have considerable potential to impact both statistics and reliability engineering.
Statistical modelling with quantile functions
Gilchrist, Warren
2000-01-01
Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics.Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data.Statistical Modelling with Quantile Functions adds a new dimension to the practice of stati...
A Statistical Programme Assignment Model
DEFF Research Database (Denmark)
Rosholm, Michael; Staghøj, Jonas; Svarer, Michael
When treatment effects of active labour market programmes are heterogeneous in an observable way across the population, the allocation of the unemployed into different programmes becomes a particularly important issue. In this paper, we present a statistical model designed to improve the present...... duration of unemployment spells may result if a statistical programme assignment model is introduced. We discuss several issues regarding the plementation of such a system, especially the interplay between the statistical model and case workers....
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
Bayesian approach to inverse statistical mechanics
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.
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
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
An introduction to statistical mechanics and thermodynamics
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
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
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
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
Statistical mechanics and the physics of fluids
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...
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
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
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
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.
Classical statistical mechanics approach to multipartite entanglement
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.
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.
Statistical Mechanics and Black Hole Thermodynamics
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...
Statistical mechanics of budget-constrained auctions
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,...
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
Statistical Mechanics of Temporal and Interacting Networks
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
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Statistical Model of Extreme Shear
DEFF Research Database (Denmark)
Hansen, Kurt Schaldemose; Larsen, Gunner Chr.
2005-01-01
In order to continue cost-optimisation of modern large wind turbines, it is important to continuously increase the knowledge of wind field parameters relevant to design loads. This paper presents a general statistical model that offers site-specific prediction of the probability density function...... by a model that, on a statistically consistent basis, describes the most likely spatial shape of an extreme wind shear event. Predictions from the model have been compared with results from an extreme value data analysis, based on a large number of full-scale measurements recorded with a high sampling rate...
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
Statistical Models for Social Networks
Snijders, Tom A. B.; Cook, KS; Massey, DS
2011-01-01
Statistical models for social networks as dependent variables must represent the typical network dependencies between tie variables such as reciprocity, homophily, transitivity, etc. This review first treats models for single (cross-sectionally observed) networks and then for network dynamics. For
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)
Directory of Open Access Journals (Sweden)
Ramon F. Alvarez-Estrada
2012-02-01
Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.
Sohrab, Siavash H.; Pitch, Nancy (Technical Monitor)
1999-01-01
A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).
Sensometrics: Thurstonian and Statistical Models
DEFF Research Database (Denmark)
Christensen, Rune Haubo Bojesen
. sensR is a package for sensory discrimination testing with Thurstonian models and ordinal supports analysis of ordinal data with cumulative link (mixed) models. While sensR is closely connected to the sensometrics field, the ordinal package has developed into a generic statistical package applicable......This thesis is concerned with the development and bridging of Thurstonian and statistical models for sensory discrimination testing as applied in the scientific discipline of sensometrics. In sensory discrimination testing sensory differences between products are detected and quantified by the use...... and sensory discrimination testing in particular in a series of papers by advancing Thurstonian models for a range of sensory discrimination protocols in addition to facilitating their application by providing software for fitting these models. The main focus is on identifying Thurstonian models...
Statistical models based on conditional probability distributions
International Nuclear Information System (INIS)
Narayanan, R.S.
1991-10-01
We present a formulation of statistical mechanics models based on conditional probability distribution rather than a Hamiltonian. We show that it is possible to realize critical phenomena through this procedure. Closely linked with this formulation is a Monte Carlo algorithm, in which a configuration generated is guaranteed to be statistically independent from any other configuration for all values of the parameters, in particular near the critical point. (orig.)
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
Principles of thermodynamics and statistical mechanics
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
Thermodynamics and statistical mechanics an integrated approach
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
Classical model of intermediate statistics
International Nuclear Information System (INIS)
Kaniadakis, G.
1994-01-01
In this work we present a classical kinetic model of intermediate statistics. In the case of Brownian particles we show that the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions can be obtained, just as the Maxwell-Boltzmann (MD) distribution, as steady states of a classical kinetic equation that intrinsically takes into account an exclusion-inclusion principle. In our model the intermediate statistics are obtained as steady states of a system of coupled nonlinear kinetic equations, where the coupling constants are the transmutational potentials η κκ' . We show that, besides the FD-BE intermediate statistics extensively studied from the quantum point of view, we can also study the MB-FD and MB-BE ones. Moreover, our model allows us to treat the three-state mixing FD-MB-BE intermediate statistics. For boson and fermion mixing in a D-dimensional space, we obtain a family of FD-BE intermediate statistics by varying the transmutational potential η BF . This family contains, as a particular case when η BF =0, the quantum statistics recently proposed by L. Wu, Z. Wu, and J. Sun [Phys. Lett. A 170, 280 (1992)]. When we consider the two-dimensional FD-BE statistics, we derive an analytic expression of the fraction of fermions. When the temperature T→∞, the system is composed by an equal number of bosons and fermions, regardless of the value of η BF . On the contrary, when T=0, η BF becomes important and, according to its value, the system can be completely bosonic or fermionic, or composed both by bosons and fermions
Textual information access statistical models
Gaussier, Eric
2013-01-01
This book presents statistical models that have recently been developed within several research communities to access information contained in text collections. The problems considered are linked to applications aiming at facilitating information access:- information extraction and retrieval;- text classification and clustering;- opinion mining;- comprehension aids (automatic summarization, machine translation, visualization).In order to give the reader as complete a description as possible, the focus is placed on the probability models used in the applications
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)
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.
Two statistical mechanics aspects of complex networks
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.
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
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
Statistical mechanics of budget-constrained auctions
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.
Improved model for statistical alignment
Energy Technology Data Exchange (ETDEWEB)
Miklos, I.; Toroczkai, Z. (Zoltan)
2001-01-01
The statistical approach to molecular sequence evolution involves the stochastic modeling of the substitution, insertion and deletion processes. Substitution has been modeled in a reliable way for more than three decades by using finite Markov-processes. Insertion and deletion, however, seem to be more difficult to model, and thc recent approaches cannot acceptably deal with multiple insertions and deletions. A new method based on a generating function approach is introduced to describe the multiple insertion process. The presented algorithm computes the approximate joint probability of two sequences in 0(13) running time where 1 is the geometric mean of the sequence lengths.
Statistical physics of black holes as quantum-mechanical systems
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...
Simple statistical model for branched aggregates
DEFF Research Database (Denmark)
Lemarchand, Claire; Hansen, Jesper Schmidt
2015-01-01
, given that it already has bonds with others. The model is applied here to asphaltene nanoaggregates observed in molecular dynamics simulations of Cooee bitumen. The variation with temperature of the probabilities deduced from this model is discussed in terms of statistical mechanics arguments....... The relevance of the statistical model in the case of asphaltene nanoaggregates is checked by comparing the predicted value of the probability for one molecule to have exactly i bonds with the same probability directly measured in the molecular dynamics simulations. The agreement is satisfactory......We propose a statistical model that can reproduce the size distribution of any branched aggregate, including amylopectin, dendrimers, molecular clusters of monoalcohols, and asphaltene nanoaggregates. It is based on the conditional probability for one molecule to form a new bond with a molecule...
Active Learning with Statistical Models.
1995-01-01
Active Learning with Statistical Models ASC-9217041, NSF CDA-9309300 6. AUTHOR(S) David A. Cohn, Zoubin Ghahramani, and Michael I. Jordan 7. PERFORMING...TERMS 15. NUMBER OF PAGES Al, MIT, Artificial Intelligence, active learning , queries, locally weighted 6 regression, LOESS, mixtures of gaussians...COMPUTATIONAL LEARNING DEPARTMENT OF BRAIN AND COGNITIVE SCIENCES A.I. Memo No. 1522 January 9. 1995 C.B.C.L. Paper No. 110 Active Learning with
Statistical mechanics of human resource allocation
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.
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)
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
The Brandeis Dice Problem and Statistical Mechanics
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.
The Statistical Mechanics of Ideal MHD Turbulence
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.
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
Zurek, E; Woo, T K; Firman, T K; Ziegler, T
2001-01-15
Density functional theory (DFT) has been used to calculate the energies of 36 different methylaluminoxane (MAO) cage structures with the general formula (MeAlO)n, where n ranges from 4 to 16. A least-squares fit has been used to devise a formula which predicts the total energies of the MAO with different n's giving an rms deviation of 4.70 kcal/mol. These energies in conjunction with frequency calculations based on molecular mechanics have been used to estimate the finite temperature enthalpies, entropies, and free energies for these MAO structures. Furthermore, formulas have been devised which predict finite temperature enthalpies and entropies for MAO structures of any n for a temperature range of 198.15-598.15 K. Using these formulas, the free energies at different temperatures have been predicted for MAO structures where n ranges from 17 to 30. The free energy values were then used to predict the percentage of each n found at a given temperature. Our calculations give an average n value of 18.41, 17.23, 16.89, and 15.72 at 198.15, 298.15, 398.15, and 598.15 K, respectively. Topological arguments have also been used to show that the MAO cage structure contains a limited amount of square faces as compared to octagonal and hexagonal ones. It is also suggested that the limited number of square faces with their strained Al-O bonds explain the high molar Al:catalyst ratio required for activation. Moreover, in this study we outline a general methodology which may be used to calculate the percent abundance of an equilibrium mixture of oligomers with the general formula (X)n.
Statistical Mechanics of Japanese Labor Markets
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.
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)
A statistical model for mapping morphological shape
Directory of Open Access Journals (Sweden)
Li Jiahan
2010-07-01
Full Text Available Abstract Background Living things come in all shapes and sizes, from bacteria, plants, and animals to humans. Knowledge about the genetic mechanisms for biological shape has far-reaching implications for a range spectrum of scientific disciplines including anthropology, agriculture, developmental biology, evolution and biomedicine. Results We derived a statistical model for mapping specific genes or quantitative trait loci (QTLs that control morphological shape. The model was formulated within the mixture framework, in which different types of shape are thought to result from genotypic discrepancies at a QTL. The EM algorithm was implemented to estimate QTL genotype-specific shapes based on a shape correspondence analysis. Computer simulation was used to investigate the statistical property of the model. Conclusion By identifying specific QTLs for morphological shape, the model developed will help to ask, disseminate and address many major integrative biological and genetic questions and challenges in the genetic control of biological shape and function.
Statistical Mechanics of Money, Income, and Wealth
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).
GIGMF - A statistical model program
International Nuclear Information System (INIS)
Vladuca, G.; Deberth, C.
1978-01-01
The program GIGMF computes the differential and integrated statistical model cross sections for the reactions proceeding through a compound nuclear stage. The computational method is based on the Hauser-Feshbach-Wolfenstein theory, modified to include the modern version of Tepel et al. Although the program was written for a PDP-15 computer, with 16K high speed memory, many reaction channels can be taken into account with the following restrictions: the pro ectile spin must be less than 2, the maximum spin momenta of the compound nucleus can not be greater than 10. These restrictions are due solely to the storage allotments and may be easily relaxed. The energy of the impinging particle, the target and projectile masses, the spin and paritjes of the projectile, target, emergent and residual nuclei the maximum orbital momentum and transmission coefficients for each reaction channel are the input parameters of the program. (author)
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
A κ-generalized statistical mechanics approach to income analysis
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.
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.
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
The scientifiv way of thinking in statistics, statistical physics and quantum mechanics
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...
The scientific way of thinking in statistics, statistical physics and quantum mechanics
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...
The statistical mechanics of financial markets
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...
Statistical modeling of Earth's plasmasphere
Veibell, Victoir
The behavior of plasma near Earth's geosynchronous orbit is of vital importance to both satellite operators and magnetosphere modelers because it also has a significant influence on energy transport, ion composition, and induced currents. The system is highly complex in both time and space, making the forecasting of extreme space weather events difficult. This dissertation examines the behavior and statistical properties of plasma mass density near geosynchronous orbit by using both linear and nonlinear models, as well as epoch analyses, in an attempt to better understand the physical processes that precipitates and drives its variations. It is shown that while equatorial mass density does vary significantly on an hourly timescale when a drop in the disturbance time scale index ( Dst) was observed, it does not vary significantly between the day of a Dst event onset and the day immediately following. It is also shown that increases in equatorial mass density were not, on average, preceded or followed by any significant change in the examined solar wind or geomagnetic variables, including Dst, despite prior results that considered a few selected events and found a notable influence. It is verified that equatorial mass density and and solar activity via the F10.7 index have a strong correlation, which is stronger over longer timescales such as 27 days than it is over an hourly timescale. It is then shown that this connection seems to affect the behavior of equatorial mass density most during periods of strong solar activity leading to large mass density reactions to Dst drops for high values of F10.7. It is also shown that equatorial mass density behaves differently before and after events based on the value of F10.7 at the onset of an equatorial mass density event or a Dst event, and that a southward interplanetary magnetic field at onset leads to slowed mass density growth after event onset. These behavioral differences provide insight into how solar and geomagnetic
Statistical mechanics of microscopically thin thermalized shells
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.
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.
Optimizing refiner operation with statistical modelling
Energy Technology Data Exchange (ETDEWEB)
Broderick, G [Noranda Research Centre, Pointe Claire, PQ (Canada)
1997-02-01
The impact of refining conditions on the energy efficiency of the process and on the handsheet quality of a chemi-mechanical pulp was studied as part of a series of pilot scale refining trials. Statistical models of refiner performance were constructed from these results and non-linear optimization of process conditions were conducted. Optimization results indicated that increasing the ratio of specific energy applied in the first stage led to a reduction of some 15 per cent in the total energy requirement. The strategy can also be used to obtain significant increases in pulp quality for a given energy input. 20 refs., 6 tabs.
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.
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.
Probing NWP model deficiencies by statistical postprocessing
DEFF Research Database (Denmark)
Rosgaard, Martin Haubjerg; Nielsen, Henrik Aalborg; Nielsen, Torben S.
2016-01-01
The objective in this article is twofold. On one hand, a Model Output Statistics (MOS) framework for improved wind speed forecast accuracy is described and evaluated. On the other hand, the approach explored identifies unintuitive explanatory value from a diagnostic variable in an operational....... Based on the statistical model candidates inferred from the data, the lifted index NWP model diagnostic is consistently found among the NWP model predictors of the best performing statistical models across sites....
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
Statistical mechanics of lattice systems a concrete mathematical introduction
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...
Statistical mechanics for natural flocks of birds
Bialek, William; Cavagna, Andrea; Giardina, Irene; Mora, Thierry; Silvestri, Edmondo; Viale, Massimiliano; Walczak, Aleksandra M.
2012-01-01
Flocking is a typical example of emergent collective behavior, where interactions between individuals produce collective patterns on the large scale. Here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data. We construct the minimally structured (maximum entropy) model consistent with experimental correlations in large flocks of starlings. The maximum entropy model shows that local, pairwise interactions between birds are sufficient to correctly predict the propagation of order throughout entire flocks of starlings, with no free parameters. We also find that the number of interacting neighbors is independent of flock density, confirming that interactions are ruled by topological rather than metric distance. Finally, by comparing flocks of different sizes, the model correctly accounts for the observed scale invariance of long-range correlations among the fluctuations in flight direction. PMID:22427355
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.
Quantum Statistical Mechanics on a Quantum Computer
Raedt, H. De; Hams, A.H.; Michielsen, K.; Miyashita, S.; Saito, K.; Saito, E.
2000-01-01
We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover’s database search algorithm. Some preliminary results on the stability of quantum algorithms
Quantum Statistical Mechanics on a Quantum Computer
De Raedt, H.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.
1999-01-01
We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.
Statistical mechanics of a cat's cradle
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'.
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.
Equilibrium statistical mechanics on correlated random graphs
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.
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
Is quantum theory a form of statistical mechanics?
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.
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.)
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).
Statistical modelling of fish stocks
DEFF Research Database (Denmark)
Kvist, Trine
1999-01-01
for modelling the dynamics of a fish population is suggested. A new approach is introduced to analyse the sources of variation in age composition data, which is one of the most important sources of information in the cohort based models for estimation of stock abundancies and mortalities. The approach combines...... and it is argued that an approach utilising stochastic differential equations might be advantagous in fish stoch assessments....
A statistical mechanical approach to restricted integer partition functions
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.
Statistical lung model for microdosimetry
International Nuclear Information System (INIS)
Fisher, D.R.; Hadley, R.T.
1984-03-01
To calculate the microdosimetry of plutonium in the lung, a mathematical description is needed of lung tissue microstructure that defines source-site parameters. Beagle lungs were expanded using a glutaraldehyde fixative at 30 cm water pressure. Tissue specimens, five microns thick, were stained with hematoxylin and eosin then studied using an image analyzer. Measurements were made along horizontal lines through the magnified tissue image. The distribution of air space and tissue chord lengths and locations of epithelial cell nuclei were recorded from about 10,000 line scans. The distribution parameters constituted a model of lung microstructure for predicting the paths of random alpha particle tracks in the lung and the probability of traversing biologically sensitive sites. This lung model may be used in conjunction with established deposition and retention models for determining the microdosimetry in the pulmonary lung for a wide variety of inhaled radioactive materials
Statistical modelling for ship propulsion efficiency
DEFF Research Database (Denmark)
Petersen, Jóan Petur; Jacobsen, Daniel J.; Winther, Ole
2012-01-01
This paper presents a state-of-the-art systems approach to statistical modelling of fuel efficiency in ship propulsion, and also a novel and publicly available data set of high quality sensory data. Two statistical model approaches are investigated and compared: artificial neural networks...
Actuarial statistics with generalized linear mixed models
Antonio, K.; Beirlant, J.
2007-01-01
Over the last decade the use of generalized linear models (GLMs) in actuarial statistics has received a lot of attention, starting from the actuarial illustrations in the standard text by McCullagh and Nelder [McCullagh, P., Nelder, J.A., 1989. Generalized linear models. In: Monographs on Statistics
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong; Jun, Mikyoung; Genton, Marc G.
2017-01-01
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture
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)
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.)
Statistical Models and Methods for Lifetime Data
Lawless, Jerald F
2011-01-01
Praise for the First Edition"An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ."-Choice"This is an important book, which will appeal to statisticians working on survival analysis problems."-Biometrics"A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook."-Statistics in MedicineThe statistical analysis of lifetime or response time data is a key tool in engineering,
Statistics and the shell model
International Nuclear Information System (INIS)
Weidenmueller, H.A.
1985-01-01
Starting with N. Bohr's paper on compound-nucleus reactions, we confront regular dynamical features and chaotic motion in nuclei. The shell-model and, more generally, mean-field theories describe average nuclear properties which are thus identified as regular features. The fluctuations about the average show chaotic behaviour of the same type as found in classical chaotic systems upon quantisation. These features are therefore generic and quite independent of the specific dynamics of the nucleus. A novel method to calculate fluctuations is discussed, and the results of this method are described. (orig.)
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
Fracture mechanics and statistical mechanics of reinforced elastomeric blends
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...
Statistical models and NMR analysis of polymer microstructure
Statistical models can be used in conjunction with NMR spectroscopy to study polymer microstructure and polymerization mechanisms. Thus, Bernoullian, Markovian, and enantiomorphic-site models are well known. Many additional models have been formulated over the years for additional situations. Typica...
Bayesian models: A statistical primer for ecologists
Hobbs, N. Thompson; Hooten, Mevin B.
2015-01-01
Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods—in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach.Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals.This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management.Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticiansCovers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and moreDeemphasizes computer coding in favor of basic principlesExplains how to write out properly factored statistical expressions representing Bayesian models
Statistical Model-Based Face Pose Estimation
Institute of Scientific and Technical Information of China (English)
GE Xinliang; YANG Jie; LI Feng; WANG Huahua
2007-01-01
A robust face pose estimation approach is proposed by using face shape statistical model approach and pose parameters are represented by trigonometric functions. The face shape statistical model is firstly built by analyzing the face shapes from different people under varying poses. The shape alignment is vital in the process of building the statistical model. Then, six trigonometric functions are employed to represent the face pose parameters. Lastly, the mapping function is constructed between face image and face pose by linearly relating different parameters. The proposed approach is able to estimate different face poses using a few face training samples. Experimental results are provided to demonstrate its efficiency and accuracy.
Uncertainty the soul of modeling, probability & statistics
Briggs, William
2016-01-01
This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance". The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, suc...
Automated statistical modeling of analytical measurement systems
International Nuclear Information System (INIS)
Jacobson, J.J.
1992-01-01
The statistical modeling of analytical measurement systems at the Idaho Chemical Processing Plant (ICPP) has been completely automated through computer software. The statistical modeling of analytical measurement systems is one part of a complete quality control program used by the Remote Analytical Laboratory (RAL) at the ICPP. The quality control program is an integration of automated data input, measurement system calibration, database management, and statistical process control. The quality control program and statistical modeling program meet the guidelines set forth by the American Society for Testing Materials and American National Standards Institute. A statistical model is a set of mathematical equations describing any systematic bias inherent in a measurement system and the precision of a measurement system. A statistical model is developed from data generated from the analysis of control standards. Control standards are samples which are made up at precise known levels by an independent laboratory and submitted to the RAL. The RAL analysts who process control standards do not know the values of those control standards. The object behind statistical modeling is to describe real process samples in terms of their bias and precision and, to verify that a measurement system is operating satisfactorily. The processing of control standards gives us this ability
Advanced data analysis in neuroscience integrating statistical and computational models
Durstewitz, Daniel
2017-01-01
This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanat ory frameworks, but become powerfu...
Topology for statistical modeling of petascale data.
Energy Technology Data Exchange (ETDEWEB)
Pascucci, Valerio (University of Utah, Salt Lake City, UT); Mascarenhas, Ajith Arthur; Rusek, Korben (Texas A& M University, College Station, TX); Bennett, Janine Camille; Levine, Joshua (University of Utah, Salt Lake City, UT); Pebay, Philippe Pierre; Gyulassy, Attila (University of Utah, Salt Lake City, UT); Thompson, David C.; Rojas, Joseph Maurice (Texas A& M University, College Station, TX)
2011-07-01
This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled 'Topology for Statistical Modeling of Petascale Data', funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program. Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is thus to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, our approach is based on the complementary techniques of combinatorial topology and statistical modeling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modeling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. This document summarizes the technical advances we have made to date that were made possible in whole or in part by MAPD funding. These technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modeling, and (3) new integrated topological and statistical methods.
Statistical modelling of citation exchange between statistics journals.
Varin, Cristiano; Cattelan, Manuela; Firth, David
2016-01-01
Rankings of scholarly journals based on citation data are often met with scepticism by the scientific community. Part of the scepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of researchers. The paper focuses on analysis of the table of cross-citations among a selection of statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care to avoid potential overinterpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's research assessment exercise shows strong correlation at aggregate level between assessed research quality and journal citation 'export scores' within the discipline of statistics.
Daily precipitation statistics in regional climate models
DEFF Research Database (Denmark)
Frei, Christoph; Christensen, Jens Hesselbjerg; Déqué, Michel
2003-01-01
An evaluation is undertaken of the statistics of daily precipitation as simulated by five regional climate models using comprehensive observations in the region of the European Alps. Four limited area models and one variable-resolution global model are considered, all with a grid spacing of 50 km...
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
Matrix Tricks for Linear Statistical Models
Puntanen, Simo; Styan, George PH
2011-01-01
In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and
The road to Maxwell's demon conceptual foundations of statistical mechanics
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.
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)
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)
Statistical physics of pairwise probability models
DEFF Research Database (Denmark)
Roudi, Yasser; Aurell, Erik; Hertz, John
2009-01-01
(dansk abstrakt findes ikke) Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data......: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying...
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
Generalized statistical mechanics approaches to earthquakes and tectonics
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
Distributions with given marginals and statistical modelling
Fortiana, Josep; Rodriguez-Lallena, José
2002-01-01
This book contains a selection of the papers presented at the meeting `Distributions with given marginals and statistical modelling', held in Barcelona (Spain), July 17-20, 2000. In 24 chapters, this book covers topics such as the theory of copulas and quasi-copulas, the theory and compatibility of distributions, models for survival distributions and other well-known distributions, time series, categorical models, definition and estimation of measures of dependence, monotonicity and stochastic ordering, shape and separability of distributions, hidden truncation models, diagonal families, orthogonal expansions, tests of independence, and goodness of fit assessment. These topics share the use and properties of distributions with given marginals, this being the fourth specialised text on this theme. The innovative aspect of the book is the inclusion of statistical aspects such as modelling, Bayesian statistics, estimation, and tests.
Aspects of statistical model for multifragmentation
International Nuclear Information System (INIS)
Bhattacharyya, P.; Das Gupta, S.; Mekjian, A. Z.
1999-01-01
We deal with two different aspects of an exactly soluble statistical model of fragmentation. First we show, using zero range force and finite temperature Thomas-Fermi theory, that a common link can be found between finite temperature mean field theory and the statistical fragmentation model. We show the latter naturally arises in the spinodal region. Next we show that although the exact statistical model is a canonical model and uses temperature, microcanonical results which use constant energy rather than constant temperature can also be obtained from the canonical model using saddle-point approximation. The methodology is extremely simple to implement and at least in all the examples studied in this work is very accurate. (c) 1999 The American Physical Society
Universal biology and the statistical mechanics of early life
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'.
A statistical mechanics approach to mixing in stratified fluids
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...
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
Statistical Compression for Climate Model Output
Hammerling, D.; Guinness, J.; Soh, Y. J.
2017-12-01
Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus is it important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. We decompress the data by computing conditional expectations and conditional simulations from the model given the summary statistics. Conditional expectations represent our best estimate of the original data but are subject to oversmoothing in space and time. Conditional simulations introduce realistic small-scale noise so that the decompressed fields are neither too smooth nor too rough compared with the original data. Considerable attention is paid to accurately modeling the original dataset-one year of daily mean temperature data-particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers.
Performance modeling, loss networks, and statistical multiplexing
Mazumdar, Ravi
2009-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of understanding the phenomenon of statistical multiplexing. The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the important ideas of Palm distributions associated with traffic models and their role in performance measures. Also presented are recent ideas of large buffer, and many sources asymptotics that play an important role in understanding statistical multiplexing. I
Advances in statistical models for data analysis
Minerva, Tommaso; Vichi, Maurizio
2015-01-01
This edited volume focuses on recent research results in classification, multivariate statistics and machine learning and highlights advances in statistical models for data analysis. The volume provides both methodological developments and contributions to a wide range of application areas such as economics, marketing, education, social sciences and environment. The papers in this volume were first presented at the 9th biannual meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, held in September 2013 at the University of Modena and Reggio Emilia, Italy.
Structured statistical models of inductive reasoning.
Kemp, Charles; Tenenbaum, Joshua B
2009-01-01
Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describes [corrected] 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.
Model for neural signaling leap statistics
International Nuclear Information System (INIS)
Chevrollier, Martine; Oria, Marcos
2011-01-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5 0 C, awaken regime) and Levy statistics (T = 35.5 0 C, sleeping period), characterized by rare events of long range connections.
Model for neural signaling leap statistics
Chevrollier, Martine; Oriá, Marcos
2011-03-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T = 37.5°C, awaken regime) and Lévy statistics (T = 35.5°C, sleeping period), characterized by rare events of long range connections.
Model for neural signaling leap statistics
Energy Technology Data Exchange (ETDEWEB)
Chevrollier, Martine; Oria, Marcos, E-mail: oria@otica.ufpb.br [Laboratorio de Fisica Atomica e Lasers Departamento de Fisica, Universidade Federal da ParaIba Caixa Postal 5086 58051-900 Joao Pessoa, Paraiba (Brazil)
2011-03-01
We present a simple model for neural signaling leaps in the brain considering only the thermodynamic (Nernst) potential in neuron cells and brain temperature. We numerically simulated connections between arbitrarily localized neurons and analyzed the frequency distribution of the distances reached. We observed qualitative change between Normal statistics (with T 37.5{sup 0}C, awaken regime) and Levy statistics (T = 35.5{sup 0}C, sleeping period), characterized by rare events of long range connections.
SRB states and nonequilibrium statistical mechanics close to equilibrium
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.
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
Braid group, knot theory and statistical mechanics II
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.
Statistical mechanics and the evolution of polygenic quantitative traits
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
Geometry and topology in hamiltonian dynamics and statistical mechanics
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
Quantum statistical model for hot dense matter
International Nuclear Information System (INIS)
Rukhsana Kouser; Tasneem, G.; Saleem Shahzad, M.; Shafiq-ur-Rehman; Nasim, M.H.; Amjad Ali
2015-01-01
In solving numerous applied problems, one needs to know the equation of state, photon absorption coefficient and opacity of substances employed. We present a code for absorption coefficient and opacity calculation based on quantum statistical model. A self-consistent method for the calculation of potential is used. By solving Schrödinger equation with self-consistent potential we find energy spectrum of quantum mechanical system and corresponding wave functions. In addition we find mean occupation numbers of electron states and average charge state of the substance studied. The main processes of interaction of radiation with matter included in our opacity calculation are photon absorption in spectral lines (Bound-bound), photoionization (Bound-free), inverse bremsstrahlung (Free-free), Compton and Thomson scattering. Bound-bound line shape function has contribution from natural, Doppler, fine structure, collisional and stark broadening. To illustrate the main features of the code and its capabilities, calculation of average charge state, absorption coefficient, Rosseland and Planck mean and group opacities of aluminum and iron are presented. Results are satisfactorily compared with the published data. (authors)
Statistical mechanics in the context of special relativity.
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
Statistical characteristics of mechanical heart valve cavitation in accelerated testing.
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.
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
Menzerath-Altmann Law: Statistical Mechanical Interpretation as Applied to a Linguistic Organization
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.
Growth curve models and statistical diagnostics
Pan, Jian-Xin
2002-01-01
Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.
Mechanical Systems, Classical Models
Teodorescu, Petre P
2009-01-01
This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems. The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences. Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as th...
Topology for Statistical Modeling of Petascale Data
Energy Technology Data Exchange (ETDEWEB)
Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Bremer, P. -T. [Univ. of Utah, Salt Lake City, UT (United States)
2013-10-31
Many commonly used algorithms for mathematical analysis do not scale well enough to accommodate the size or complexity of petascale data produced by computational simulations. The primary goal of this project is to develop new mathematical tools that address both the petascale size and uncertain nature of current data. At a high level, the approach of the entire team involving all three institutions is based on the complementary techniques of combinatorial topology and statistical modelling. In particular, we use combinatorial topology to filter out spurious data that would otherwise skew statistical modelling techniques, and we employ advanced algorithms from algebraic statistics to efficiently find globally optimal fits to statistical models. The overall technical contributions can be divided loosely into three categories: (1) advances in the field of combinatorial topology, (2) advances in statistical modelling, and (3) new integrated topological and statistical methods. Roughly speaking, the division of labor between our 3 groups (Sandia Labs in Livermore, Texas A&M in College Station, and U Utah in Salt Lake City) is as follows: the Sandia group focuses on statistical methods and their formulation in algebraic terms, and finds the application problems (and data sets) most relevant to this project, the Texas A&M Group develops new algebraic geometry algorithms, in particular with fewnomial theory, and the Utah group develops new algorithms in computational topology via Discrete Morse Theory. However, we hasten to point out that our three groups stay in tight contact via videconference every 2 weeks, so there is much synergy of ideas between the groups. The following of this document is focused on the contributions that had grater direct involvement from the team at the University of Utah in Salt Lake City.
Statistical mechanics of high-density bond percolation
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.
Bayesian models a statistical primer for ecologists
Hobbs, N Thompson
2015-01-01
Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods-in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probabili
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
Statistical transmutation in doped quantum dimer models.
Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P
2012-07-06
We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.
STATISTICAL MODELS OF REPRESENTING INTELLECTUAL CAPITAL
Directory of Open Access Journals (Sweden)
Andreea Feraru
2016-06-01
Full Text Available This article entitled Statistical Models of Representing Intellectual Capital approaches and analyses the concept of intellectual capital, as well as the main models which can support enterprisers/managers in evaluating and quantifying the advantages of intellectual capital. Most authors examine intellectual capital from a static perspective and focus on the development of its various evaluation models. In this chapter we surveyed the classical static models: Sveiby, Edvisson, Balanced Scorecard, as well as the canonical model of intellectual capital. Among the group of static models for evaluating organisational intellectual capital the canonical model stands out. This model enables the structuring of organisational intellectual capital in: human capital, structural capital and relational capital. Although the model is widely spread, it is a static one and can thus create a series of errors in the process of evaluation, because all the three entities mentioned above are not independent from the viewpoint of their contents, as any logic of structuring complex entities requires.
Statistical Model Checking for Biological Systems
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel
2014-01-01
Statistical Model Checking (SMC) is a highly scalable simulation-based verification approach for testing and estimating the probability that a stochastic system satisfies a given linear temporal property. The technique has been applied to (discrete and continuous time) Markov chains, stochastic...
Topology for Statistical Modeling of Petascale Data
Energy Technology Data Exchange (ETDEWEB)
Bennett, Janine Camille [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pebay, Philippe Pierre [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Pascucci, Valerio [Univ. of Utah, Salt Lake City, UT (United States); Levine, Joshua [Univ. of Utah, Salt Lake City, UT (United States); Gyulassy, Attila [Univ. of Utah, Salt Lake City, UT (United States); Rojas, Maurice [Texas A & M Univ., College Station, TX (United States)
2014-07-01
This document presents current technical progress and dissemination of results for the Mathematics for Analysis of Petascale Data (MAPD) project titled "Topology for Statistical Modeling of Petascale Data", funded by the Office of Science Advanced Scientific Computing Research (ASCR) Applied Math program.
Statistical models for optimizing mineral exploration
International Nuclear Information System (INIS)
Wignall, T.K.; DeGeoffroy, J.
1987-01-01
The primary purpose of mineral exploration is to discover ore deposits. The emphasis of this volume is on the mathematical and computational aspects of optimizing mineral exploration. The seven chapters that make up the main body of the book are devoted to the description and application of various types of computerized geomathematical models. These chapters include: (1) the optimal selection of ore deposit types and regions of search, as well as prospecting selected areas, (2) designing airborne and ground field programs for the optimal coverage of prospecting areas, and (3) delineating and evaluating exploration targets within prospecting areas by means of statistical modeling. Many of these statistical programs are innovative and are designed to be useful for mineral exploration modeling. Examples of geomathematical models are applied to exploring for six main types of base and precious metal deposits, as well as other mineral resources (such as bauxite and uranium)
Performance modeling, stochastic networks, and statistical multiplexing
Mazumdar, Ravi R
2013-01-01
This monograph presents a concise mathematical approach for modeling and analyzing the performance of communication networks with the aim of introducing an appropriate mathematical framework for modeling and analysis as well as understanding the phenomenon of statistical multiplexing. The models, techniques, and results presented form the core of traffic engineering methods used to design, control and allocate resources in communication networks.The novelty of the monograph is the fresh approach and insights provided by a sample-path methodology for queueing models that highlights the importan
Statistical models for competing risk analysis
International Nuclear Information System (INIS)
Sather, H.N.
1976-08-01
Research results on three new models for potential applications in competing risks problems. One section covers the basic statistical relationships underlying the subsequent competing risks model development. Another discusses the problem of comparing cause-specific risk structure by competing risks theory in two homogeneous populations, P1 and P2. Weibull models which allow more generality than the Berkson and Elveback models are studied for the effect of time on the hazard function. The use of concomitant information for modeling single-risk survival is extended to the multiple failure mode domain of competing risks. The model used to illustrate the use of this methodology is a life table model which has constant hazards within pre-designated intervals of the time scale. Two parametric models for bivariate dependent competing risks, which provide interesting alternatives, are proposed and examined
Algebraic methods in statistical mechanics and quantum field theory
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
Statistical physics of pairwise probability models
Directory of Open Access Journals (Sweden)
Yasser Roudi
2009-11-01
Full Text Available Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this paper, we describe how tools from statistical physics can be employed for studying and using pairwise models. We build on our previous work on the subject and study the relation between different methods for fitting these models and evaluating their quality. In particular, using data from simulated cortical networks we study how the quality of various approximate methods for inferring the parameters in a pairwise model depends on the time bin chosen for binning the data. We also study the effect of the size of the time bin on the model quality itself, again using simulated data. We show that using finer time bins increases the quality of the pairwise model. We offer new ways of deriving the expressions reported in our previous work for assessing the quality of pairwise models.
Using statistical compatibility to derive advanced probabilistic fatigue models
Czech Academy of Sciences Publication Activity Database
Fernández-Canteli, A.; Castillo, E.; López-Aenlle, M.; Seitl, Stanislav
2010-01-01
Roč. 2, č. 1 (2010), s. 1131-1140 E-ISSN 1877-7058. [Fatigue 2010. Praha, 06.06.2010-11.06.2010] Institutional research plan: CEZ:AV0Z20410507 Keywords : Fatigue models * Statistical compatibility * Functional equations Subject RIV: JL - Materials Fatigue, Friction Mechanics
Realistic thermodynamic and statistical-mechanical measures for neural synchronization.
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.
Statistical models of petrol engines vehicles dynamics
Ilie, C. O.; Marinescu, M.; Alexa, O.; Vilău, R.; Grosu, D.
2017-10-01
This paper focuses on studying statistical models of vehicles dynamics. It was design and perform a one year testing program. There were used many same type cars with gasoline engines and different mileage. Experimental data were collected of onboard sensors and those on the engine test stand. A database containing data of 64th tests was created. Several mathematical modelling were developed using database and the system identification method. Each modelling is a SISO or a MISO linear predictive ARMAX (AutoRegressive-Moving-Average with eXogenous inputs) model. It represents a differential equation with constant coefficients. It were made 64th equations for each dependency like engine torque as output and engine’s load and intake manifold pressure, as inputs. There were obtained strings with 64 values for each type of model. The final models were obtained using average values of the coefficients. The accuracy of models was assessed.
Statistical shape and appearance models of bones.
Sarkalkan, Nazli; Weinans, Harrie; Zadpoor, Amir A
2014-03-01
When applied to bones, statistical shape models (SSM) and statistical appearance models (SAM) respectively describe the mean shape and mean density distribution of bones within a certain population as well as the main modes of variations of shape and density distribution from their mean values. The availability of this quantitative information regarding the detailed anatomy of bones provides new opportunities for diagnosis, evaluation, and treatment of skeletal diseases. The potential of SSM and SAM has been recently recognized within the bone research community. For example, these models have been applied for studying the effects of bone shape on the etiology of osteoarthritis, improving the accuracy of clinical osteoporotic fracture prediction techniques, design of orthopedic implants, and surgery planning. This paper reviews the main concepts, methods, and applications of SSM and SAM as applied to bone. Copyright © 2013 Elsevier Inc. All rights reserved.
Statistical Models of Adaptive Immune populations
Sethna, Zachary; Callan, Curtis; Walczak, Aleksandra; Mora, Thierry
The availability of large (104-106 sequences) datasets of B or T cell populations from a single individual allows reliable fitting of complex statistical models for naïve generation, somatic selection, and hypermutation. It is crucial to utilize a probabilistic/informational approach when modeling these populations. The inferred probability distributions allow for population characterization, calculation of probability distributions of various hidden variables (e.g. number of insertions), as well as statistical properties of the distribution itself (e.g. entropy). In particular, the differences between the T cell populations of embryonic and mature mice will be examined as a case study. Comparing these populations, as well as proposed mixed populations, provides a concrete exercise in model creation, comparison, choice, and validation.
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
Statistical Modelling of Wind Proles - Data Analysis and Modelling
DEFF Research Database (Denmark)
Jónsson, Tryggvi; Pinson, Pierre
The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles.......The aim of the analysis presented in this document is to investigate whether statistical models can be used to make very short-term predictions of wind profiles....
Statistical modeling of geopressured geothermal reservoirs
Ansari, Esmail; Hughes, Richard; White, Christopher D.
2017-06-01
Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.
A statistical model for instable thermodynamical systems
International Nuclear Information System (INIS)
Sommer, Jens-Uwe
2003-01-01
A generic model is presented for statistical systems which display thermodynamic features in contrast to our everyday experience, such as infinite and negative heat capacities. Such system are instable in terms of classical equilibrium thermodynamics. Using our statistical model, we are able to investigate states of instable systems which are undefined in the framework of equilibrium thermodynamics. We show that a region of negative heat capacity in the adiabatic environment, leads to a first order like phase transition when the system is coupled to a heat reservoir. This phase transition takes place without a phase coexistence. Nevertheless, all intermediate states are stable due to fluctuations. When two instable system are brought in thermal contact, the temperature of the composed system is lower than the minimum temperature of the individual systems. Generally, the equilibrium states of instable system cannot be simply decomposed into equilibrium states of the individual systems. The properties of instable system depend on the environment, ensemble equivalence is broken
Metamodelling Messages Conveyed in Five Statistical Mechanical Textbooks from 1936 to 2001
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…
Logarithmic transformed statistical models in calibration
International Nuclear Information System (INIS)
Zeis, C.D.
1975-01-01
A general type of statistical model used for calibration of instruments having the property that the standard deviations of the observed values increase as a function of the mean value is described. The application to the Helix Counter at the Rocky Flats Plant is primarily from a theoretical point of view. The Helix Counter measures the amount of plutonium in certain types of chemicals. The method described can be used also for other calibrations. (U.S.)
ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING
Palas Roy; Naba Kumar Mondal; Biswajit Das; Kousik Das
2013-01-01
High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India) has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Mul...
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
Quantum statistical mechanics selected works of N N Bogolubov
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
Alternative derivations of the statistical mechanical distribution laws.
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.
Thermodynamics and statistical mechanics. [thermodynamic properties of gases
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.
A simple statistical model for geomagnetic reversals
Constable, Catherine
1990-01-01
The diversity of paleomagnetic records of geomagnetic reversals now available indicate that the field configuration during transitions cannot be adequately described by simple zonal or standing field models. A new model described here is based on statistical properties inferred from the present field and is capable of simulating field transitions like those observed. Some insight is obtained into what one can hope to learn from paleomagnetic records. In particular, it is crucial that the effects of smoothing in the remanence acquisition process be separated from true geomagnetic field behavior. This might enable us to determine the time constants associated with the dominant field configuration during a reversal.
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)
From inverse problems to learning: a Statistical Mechanics approach
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.
Growth Curve Models and Applications : Indian Statistical Institute
2017-01-01
Growth curve models in longitudinal studies are widely used to model population size, body height, biomass, fungal growth, and other variables in the biological sciences, but these statistical methods for modeling growth curves and analyzing longitudinal data also extend to general statistics, economics, public health, demographics, epidemiology, SQC, sociology, nano-biotechnology, fluid mechanics, and other applied areas. There is no one-size-fits-all approach to growth measurement. The selected papers in this volume build on presentations from the GCM workshop held at the Indian Statistical Institute, Giridih, on March 28-29, 2016. They represent recent trends in GCM research on different subject areas, both theoretical and applied. This book includes tools and possibilities for further work through new techniques and modification of existing ones. The volume includes original studies, theoretical findings and case studies from a wide range of app lied work, and these contributions have been externally r...
Statistical Modelling of the Soil Dielectric Constant
Usowicz, Boguslaw; Marczewski, Wojciech; Bogdan Usowicz, Jerzy; Lipiec, Jerzy
2010-05-01
The dielectric constant of soil is the physical property being very sensitive on water content. It funds several electrical measurement techniques for determining the water content by means of direct (TDR, FDR, and others related to effects of electrical conductance and/or capacitance) and indirect RS (Remote Sensing) methods. The work is devoted to a particular statistical manner of modelling the dielectric constant as the property accounting a wide range of specific soil composition, porosity, and mass density, within the unsaturated water content. Usually, similar models are determined for few particular soil types, and changing the soil type one needs switching the model on another type or to adjust it by parametrization of soil compounds. Therefore, it is difficult comparing and referring results between models. The presented model was developed for a generic representation of soil being a hypothetical mixture of spheres, each representing a soil fraction, in its proper phase state. The model generates a serial-parallel mesh of conductive and capacitive paths, which is analysed for a total conductive or capacitive property. The model was firstly developed to determine the thermal conductivity property, and now it is extended on the dielectric constant by analysing the capacitive mesh. The analysis is provided by statistical means obeying physical laws related to the serial-parallel branching of the representative electrical mesh. Physical relevance of the analysis is established electrically, but the definition of the electrical mesh is controlled statistically by parametrization of compound fractions, by determining the number of representative spheres per unitary volume per fraction, and by determining the number of fractions. That way the model is capable covering properties of nearly all possible soil types, all phase states within recognition of the Lorenz and Knudsen conditions. In effect the model allows on generating a hypothetical representative of
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
Encoding Dissimilarity Data for Statistical Model Building.
Wahba, Grace
2010-12-01
We summarize, review and comment upon three papers which discuss the use of discrete, noisy, incomplete, scattered pairwise dissimilarity data in statistical model building. Convex cone optimization codes are used to embed the objects into a Euclidean space which respects the dissimilarity information while controlling the dimension of the space. A "newbie" algorithm is provided for embedding new objects into this space. This allows the dissimilarity information to be incorporated into a Smoothing Spline ANOVA penalized likelihood model, a Support Vector Machine, or any model that will admit Reproducing Kernel Hilbert Space components, for nonparametric regression, supervised learning, or semi-supervised learning. Future work and open questions are discussed. The papers are: F. Lu, S. Keles, S. Wright and G. Wahba 2005. A framework for kernel regularization with application to protein clustering. Proceedings of the National Academy of Sciences 102, 12332-1233.G. Corrada Bravo, G. Wahba, K. Lee, B. Klein, R. Klein and S. Iyengar 2009. Examining the relative influence of familial, genetic and environmental covariate information in flexible risk models. Proceedings of the National Academy of Sciences 106, 8128-8133F. Lu, Y. Lin and G. Wahba. Robust manifold unfolding with kernel regularization. TR 1008, Department of Statistics, University of Wisconsin-Madison.
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.
Structural reliability in context of statistical uncertainties and modelling discrepancies
International Nuclear Information System (INIS)
Pendola, Maurice
2000-01-01
Structural reliability methods have been largely improved during the last years and have showed their ability to deal with uncertainties during the design stage or to optimize the functioning and the maintenance of industrial installations. They are based on a mechanical modeling of the structural behavior according to the considered failure modes and on a probabilistic representation of input parameters of this modeling. In practice, only limited statistical information is available to build the probabilistic representation and different sophistication levels of the mechanical modeling may be introduced. Thus, besides the physical randomness, other uncertainties occur in such analyses. The aim of this work is triple: 1. at first, to propose a methodology able to characterize the statistical uncertainties due to the limited number of data in order to take them into account in the reliability analyses. The obtained reliability index measures the confidence in the structure considering the statistical information available. 2. Then, to show a methodology leading to reliability results evaluated from a particular mechanical modeling but by using a less sophisticated one. The objective is then to decrease the computational efforts required by the reference modeling. 3. Finally, to propose partial safety factors that are evolving as a function of the number of statistical data available and as a function of the sophistication level of the mechanical modeling that is used. The concepts are illustrated in the case of a welded pipe and in the case of a natural draught cooling tower. The results show the interest of the methodologies in an industrial context. [fr
Statistical mechanics in the context of special relativity. II.
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.
Statistical mechanics of complex neural systems and high dimensional data
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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)
Thiessen, Erik D
2017-01-05
Statistical learning has been studied in a variety of different tasks, including word segmentation, object identification, category learning, artificial grammar learning and serial reaction time tasks (e.g. Saffran et al. 1996 Science 274: , 1926-1928; Orban et al. 2008 Proceedings of the National Academy of Sciences 105: , 2745-2750; Thiessen & Yee 2010 Child Development 81: , 1287-1303; Saffran 2002 Journal of Memory and Language 47: , 172-196; Misyak & Christiansen 2012 Language Learning 62: , 302-331). The difference among these tasks raises questions about whether they all depend on the same kinds of underlying processes and computations, or whether they are tapping into different underlying mechanisms. Prior theoretical approaches to statistical learning have often tried to explain or model learning in a single task. However, in many cases these approaches appear inadequate to explain performance in multiple tasks. For example, explaining word segmentation via the computation of sequential statistics (such as transitional probability) provides little insight into the nature of sensitivity to regularities among simultaneously presented features. In this article, we will present a formal computational approach that we believe is a good candidate to provide a unifying framework to explore and explain learning in a wide variety of statistical learning tasks. This framework suggests that statistical learning arises from a set of processes that are inherent in memory systems, including activation, interference, integration of information and forgetting (e.g. Perruchet & Vinter 1998 Journal of Memory and Language 39: , 246-263; Thiessen et al. 2013 Psychological Bulletin 139: , 792-814). From this perspective, statistical learning does not involve explicit computation of statistics, but rather the extraction of elements of the input into memory traces, and subsequent integration across those memory traces that emphasize consistent information (Thiessen and Pavlik
Statistical mechanics of the vertex-cover problem
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.
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
Statistical learning: a powerful mechanism that operates by mere exposure.
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.
Directory of Open Access Journals (Sweden)
Guangjian Ni
2014-01-01
Full Text Available The cochlea plays a crucial role in mammal hearing. The basic function of the cochlea is to map sounds of different frequencies onto corresponding characteristic positions on the basilar membrane (BM. Sounds enter the fluid-filled cochlea and cause deflection of the BM due to pressure differences between the cochlear fluid chambers. These deflections travel along the cochlea, increasing in amplitude, until a frequency-dependent characteristic position and then decay away rapidly. The hair cells can detect these deflections and encode them as neural signals. Modelling the mechanics of the cochlea is of help in interpreting experimental observations and also can provide predictions of the results of experiments that cannot currently be performed due to technical limitations. This paper focuses on reviewing the numerical modelling of the mechanical and electrical processes in the cochlea, which include fluid coupling, micromechanics, the cochlear amplifier, nonlinearity, and electrical coupling.
ARSENIC CONTAMINATION IN GROUNDWATER: A STATISTICAL MODELING
Directory of Open Access Journals (Sweden)
Palas Roy
2013-01-01
Full Text Available High arsenic in natural groundwater in most of the tubewells of the Purbasthali- Block II area of Burdwan district (W.B, India has recently been focused as a serious environmental concern. This paper is intending to illustrate the statistical modeling of the arsenic contaminated groundwater to identify the interrelation of that arsenic contain with other participating groundwater parameters so that the arsenic contamination level can easily be predicted by analyzing only such parameters. Multivariate data analysis was done with the collected groundwater samples from the 132 tubewells of this contaminated region shows that three variable parameters are significantly related with the arsenic. Based on these relationships, a multiple linear regression model has been developed that estimated the arsenic contamination by measuring such three predictor parameters of the groundwater variables in the contaminated aquifer. This model could also be a suggestive tool while designing the arsenic removal scheme for any affected groundwater.
Average Nuclear properties based on statistical model
International Nuclear Information System (INIS)
El-Jaick, L.J.
1974-01-01
The rough properties of nuclei were investigated by statistical model, in systems with the same and different number of protons and neutrons, separately, considering the Coulomb energy in the last system. Some average nuclear properties were calculated based on the energy density of nuclear matter, from Weizsscker-Beth mass semiempiric formulae, generalized for compressible nuclei. In the study of a s surface energy coefficient, the great influence exercised by Coulomb energy and nuclear compressibility was verified. For a good adjust of beta stability lines and mass excess, the surface symmetry energy were established. (M.C.K.) [pt
Statistical pairwise interaction model of stock market
Bury, Thomas
2013-03-01
Financial markets are a classical example of complex systems as they are compound by many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or they are agent-based models with rules designed in order to recover some empirical behaviors. Here we show that the pairwise model is actually a statistically consistent model with the observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach only based on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviors, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.
Statistical modeling to support power system planning
Staid, Andrea
This dissertation focuses on data-analytic approaches that improve our understanding of power system applications to promote better decision-making. It tackles issues of risk analysis, uncertainty management, resource estimation, and the impacts of climate change. Tools of data mining and statistical modeling are used to bring new insight to a variety of complex problems facing today's power system. The overarching goal of this research is to improve the understanding of the power system risk environment for improved operation, investment, and planning decisions. The first chapter introduces some challenges faced in planning for a sustainable power system. Chapter 2 analyzes the driving factors behind the disparity in wind energy investments among states with a goal of determining the impact that state-level policies have on incentivizing wind energy. Findings show that policy differences do not explain the disparities; physical and geographical factors are more important. Chapter 3 extends conventional wind forecasting to a risk-based focus of predicting maximum wind speeds, which are dangerous for offshore operations. Statistical models are presented that issue probabilistic predictions for the highest wind speed expected in a three-hour interval. These models achieve a high degree of accuracy and their use can improve safety and reliability in practice. Chapter 4 examines the challenges of wind power estimation for onshore wind farms. Several methods for wind power resource assessment are compared, and the weaknesses of the Jensen model are demonstrated. For two onshore farms, statistical models outperform other methods, even when very little information is known about the wind farm. Lastly, chapter 5 focuses on the power system more broadly in the context of the risks expected from tropical cyclones in a changing climate. Risks to U.S. power system infrastructure are simulated under different scenarios of tropical cyclone behavior that may result from climate
Acceleration transforms and statistical kinetic models
International Nuclear Information System (INIS)
LuValle, M.J.; Welsher, T.L.; Svoboda, K.
1988-01-01
For a restricted class of problems a mathematical model of microscopic degradation processes, statistical kinetics, is developed and linked through acceleration transforms to the information which can be obtained from a system in which the only observable sign of degradation is sudden and catastrophic failure. The acceleration transforms were developed in accelerated life testing applications as a tool for extrapolating from the observable results of an accelerated life test to the dynamics of the underlying degradation processes. A particular concern of a physicist attempting to interpreted the results of an analysis based on acceleration transforms is determining the physical species involved in the degradation process. These species may be (a) relatively abundant or (b) relatively rare. The main results of this paper are a theorem showing that for an important subclass of statistical kinetic models, acceleration transforms cannot be used to distinguish between cases a and b, and an example showing that in some cases falling outside the restrictions of the theorem, cases a and b can be distinguished by their acceleration transforms
Statistical models of a gas diffusion electrode: II. Current resistent
Energy Technology Data Exchange (ETDEWEB)
Proksch, D B; Winsel, O W
1965-07-01
The authors describe an apparatus for measuring the flow resistance of gas diffusion electrodes which is a mechanical analog of the Wheatstone bridge for measuring electric resistance. The flow resistance of a circular DSK electrode sheet, consisting of two covering layers and a working layer between them, was measured as a function of the gas pressure. While the pressure first was increased and then decreased, a hysteresis occurred, which is discussed and explained by a statistical model of a porous electrode.
Atmospheric corrosion: statistical validation of models
International Nuclear Information System (INIS)
Diaz, V.; Martinez-Luaces, V.; Guineo-Cobs, G.
2003-01-01
In this paper we discuss two different methods for validation of regression models, applied to corrosion data. One of them is based on the correlation coefficient and the other one is the statistical test of lack of fit. Both methods are used here to analyse fitting of bi logarithmic model in order to predict corrosion for very low carbon steel substrates in rural and urban-industrial atmospheres in Uruguay. Results for parameters A and n of the bi logarithmic model are reported here. For this purpose, all repeated values were used instead of using average values as usual. Modelling is carried out using experimental data corresponding to steel substrates under the same initial meteorological conditions ( in fact, they are put in the rack at the same time). Results of correlation coefficient are compared with the lack of it tested at two different signification levels (α=0.01 and α=0.05). Unexpected differences between them are explained and finally, it is possible to conclude, at least in the studied atmospheres, that the bi logarithmic model does not fit properly the experimental data. (Author) 18 refs
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.)
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
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.
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
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
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
On the statistical mechanics of species abundance distributions.
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.
Spherical Process Models for Global Spatial Statistics
Jeong, Jaehong
2017-11-28
Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.
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)
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)
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
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.
Statistical model for OCT image denoising
Li, Muxingzi
2017-08-01
Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.
Statistical 3D damage accumulation model for ion implant simulators
Hernandez-Mangas, J M; Enriquez, L E; Bailon, L; Barbolla, J; Jaraiz, M
2003-01-01
A statistical 3D damage accumulation model, based on the modified Kinchin-Pease formula, for ion implant simulation has been included in our physically based ion implantation code. It has only one fitting parameter for electronic stopping and uses 3D electron density distributions for different types of targets including compound semiconductors. Also, a statistical noise reduction mechanism based on the dose division is used. The model has been adapted to be run under parallel execution in order to speed up the calculation in 3D structures. Sequential ion implantation has been modelled including previous damage profiles. It can also simulate the implantation of molecular and cluster projectiles. Comparisons of simulated doping profiles with experimental SIMS profiles are presented. Also comparisons between simulated amorphization and experimental RBS profiles are shown. An analysis of sequential versus parallel processing is provided.
Statistical 3D damage accumulation model for ion implant simulators
International Nuclear Information System (INIS)
Hernandez-Mangas, J.M.; Lazaro, J.; Enriquez, L.; Bailon, L.; Barbolla, J.; Jaraiz, M.
2003-01-01
A statistical 3D damage accumulation model, based on the modified Kinchin-Pease formula, for ion implant simulation has been included in our physically based ion implantation code. It has only one fitting parameter for electronic stopping and uses 3D electron density distributions for different types of targets including compound semiconductors. Also, a statistical noise reduction mechanism based on the dose division is used. The model has been adapted to be run under parallel execution in order to speed up the calculation in 3D structures. Sequential ion implantation has been modelled including previous damage profiles. It can also simulate the implantation of molecular and cluster projectiles. Comparisons of simulated doping profiles with experimental SIMS profiles are presented. Also comparisons between simulated amorphization and experimental RBS profiles are shown. An analysis of sequential versus parallel processing is provided
New advances in statistical modeling and applications
Santos, Rui; Oliveira, Maria; Paulino, Carlos
2014-01-01
This volume presents selected papers from the XIXth Congress of the Portuguese Statistical Society, held in the town of Nazaré, Portugal, from September 28 to October 1, 2011. All contributions were selected after a thorough peer-review process. It covers a broad range of papers in the areas of statistical science, probability and stochastic processes, extremes and statistical applications.
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
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.
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.
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
A statistical model for predicting muscle performance
Byerly, Diane Leslie De Caix
The objective of these studies was to develop a capability for predicting muscle performance and fatigue to be utilized for both space- and ground-based applications. To develop this predictive model, healthy test subjects performed a defined, repetitive dynamic exercise to failure using a Lordex spinal machine. Throughout the exercise, surface electromyography (SEMG) data were collected from the erector spinae using a Mega Electronics ME3000 muscle tester and surface electrodes placed on both sides of the back muscle. These data were analyzed using a 5th order Autoregressive (AR) model and statistical regression analysis. It was determined that an AR derived parameter, the mean average magnitude of AR poles, significantly correlated with the maximum number of repetitions (designated Rmax) that a test subject was able to perform. Using the mean average magnitude of AR poles, a test subject's performance to failure could be predicted as early as the sixth repetition of the exercise. This predictive model has the potential to provide a basis for improving post-space flight recovery, monitoring muscle atrophy in astronauts and assessing the effectiveness of countermeasures, monitoring astronaut performance and fatigue during Extravehicular Activity (EVA) operations, providing pre-flight assessment of the ability of an EVA crewmember to perform a given task, improving the design of training protocols and simulations for strenuous International Space Station assembly EVA, and enabling EVA work task sequences to be planned enhancing astronaut performance and safety. Potential ground-based, medical applications of the predictive model include monitoring muscle deterioration and performance resulting from illness, establishing safety guidelines in the industry for repetitive tasks, monitoring the stages of rehabilitation for muscle-related injuries sustained in sports and accidents, and enhancing athletic performance through improved training protocols while reducing
Nonextensive statistical mechanics approach to electron trapping in degenerate plasmas
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.
Statistical Model Checking of Rich Models and Properties
DEFF Research Database (Denmark)
Poulsen, Danny Bøgsted
in undecidability issues for the traditional model checking approaches. Statistical model checking has proven itself a valuable supplement to model checking and this thesis is concerned with extending this software validation technique to stochastic hybrid systems. The thesis consists of two parts: the first part...... motivates why existing model checking technology should be supplemented by new techniques. It also contains a brief introduction to probability theory and concepts covered by the six papers making up the second part. The first two papers are concerned with developing online monitoring techniques...... systems. The fifth paper shows how stochastic hybrid automata are useful for modelling biological systems and the final paper is concerned with showing how statistical model checking is efficiently distributed. In parallel with developing the theory contained in the papers, a substantial part of this work...
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
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.
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)
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.)
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)
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
An Introduction to Thermodynamics and Statistical Mechanics - 2nd Edition
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
Network Data: Statistical Theory and New Models
2016-02-17
and with environmental scientists at JPL and Emory University to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution ...Beijing, May, 2013 Beijing Statistics Forum, Beijing, May, 2013 Statistics Seminar, CREST-ENSAE, Paris , March, 2013 Statistics Seminar, University...to retrieval from NASA MISR remote sensing images aerosol index AOD for air pollution monitoring and management. Satellite- retrieved Aerosol Optical
Modeling statistical properties of written text.
Directory of Open Access Journals (Sweden)
M Angeles Serrano
Full Text Available Written text is one of the fundamental manifestations of human language, and the study of its universal regularities can give clues about how our brains process information and how we, as a society, organize and share it. Among these regularities, only Zipf's law has been explored in depth. Other basic properties, such as the existence of bursts of rare words in specific documents, have only been studied independently of each other and mainly by descriptive models. As a consequence, there is a lack of understanding of linguistic processes as complex emergent phenomena. Beyond Zipf's law for word frequencies, here we focus on burstiness, Heaps' law describing the sublinear growth of vocabulary size with the length of a document, and the topicality of document collections, which encode correlations within and across documents absent in random null models. We introduce and validate a generative model that explains the simultaneous emergence of all these patterns from simple rules. As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining the non trivial organization of written text. Our research can have broad implications and practical applications in computer science, cognitive science and linguistics.
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
A generalized statistical model for the size distribution of wealth
International Nuclear Information System (INIS)
Clementi, F; Gallegati, M; Kaniadakis, G
2012-01-01
In a recent paper in this journal (Clementi et al 2009 J. Stat. Mech. P02037), we proposed a new, physically motivated, distribution function for modeling individual incomes, having its roots in the framework of the κ-generalized statistical mechanics. The performance of the κ-generalized distribution was checked against real data on personal income for the United States in 2003. In this paper we extend our previous model so as to be able to account for the distribution of wealth. Probabilistic functions and inequality measures of this generalized model for wealth distribution are obtained in closed form. In order to check the validity of the proposed model, we analyze the US household wealth distributions from 1984 to 2009 and conclude an excellent agreement with the data that is superior to any other model already known in the literature. (paper)
A generalized statistical model for the size distribution of wealth
Clementi, F.; Gallegati, M.; Kaniadakis, G.
2012-12-01
In a recent paper in this journal (Clementi et al 2009 J. Stat. Mech. P02037), we proposed a new, physically motivated, distribution function for modeling individual incomes, having its roots in the framework of the κ-generalized statistical mechanics. The performance of the κ-generalized distribution was checked against real data on personal income for the United States in 2003. In this paper we extend our previous model so as to be able to account for the distribution of wealth. Probabilistic functions and inequality measures of this generalized model for wealth distribution are obtained in closed form. In order to check the validity of the proposed model, we analyze the US household wealth distributions from 1984 to 2009 and conclude an excellent agreement with the data that is superior to any other model already known in the literature.
Statistical modelling of transcript profiles of differentially regulated genes
Directory of Open Access Journals (Sweden)
Sergeant Martin J
2008-07-01
allowed 11% of the Escherichia coli features to be fitted by an exponential function, and 25% of the Rattus norvegicus features could be described by the critical exponential model, all with statistical significance of p Conclusion The statistical non-linear regression approaches presented in this study provide detailed biologically oriented descriptions of individual gene expression profiles, using biologically variable data to generate a set of defining parameters. These approaches have application to the modelling and greater interpretation of profiles obtained across a wide range of platforms, such as microarrays. Through careful choice of appropriate model forms, such statistical regression approaches allow an improved comparison of gene expression profiles, and may provide an approach for the greater understanding of common regulatory mechanisms between genes.
Spatio-temporal statistical models with applications to atmospheric processes
International Nuclear Information System (INIS)
Wikle, C.K.
1996-01-01
This doctoral dissertation is presented as three self-contained papers. An introductory chapter considers traditional spatio-temporal statistical methods used in the atmospheric sciences from a statistical perspective. Although this section is primarily a review, many of the statistical issues considered have not been considered in the context of these methods and several open questions are posed. The first paper attempts to determine a means of characterizing the semiannual oscillation (SAO) spatial variation in the northern hemisphere extratropical height field. It was discovered that the midlatitude SAO in 500hPa geopotential height could be explained almost entirely as a result of spatial and temporal asymmetries in the annual variation of stationary eddies. It was concluded that the mechanism for the SAO in the northern hemisphere is a result of land-sea contrasts. The second paper examines the seasonal variability of mixed Rossby-gravity waves (MRGW) in lower stratospheric over the equatorial Pacific. Advanced cyclostationary time series techniques were used for analysis. It was found that there are significant twice-yearly peaks in MRGW activity. Analyses also suggested a convergence of horizontal momentum flux associated with these waves. In the third paper, a new spatio-temporal statistical model is proposed that attempts to consider the influence of both temporal and spatial variability. This method is mainly concerned with prediction in space and time, and provides a spatially descriptive and temporally dynamic model
International Nuclear Information System (INIS)
Potter, G.L.; Ellsaesser, H.W.; MacCracken, M.C.; Luther, F.M.
1978-06-01
Results from the zonal model indicate quite reasonable agreement with observation in terms of the parameters and processes that influence the radiation and energy balance calculations. The model produces zonal statistics similar to those from general circulation models, and has also been shown to produce similar responses in sensitivity studies. Further studies of model performance are planned, including: comparison with July data; comparison of temperature and moisture transport and wind fields for winter and summer months; and a tabulation of atmospheric energetics. Based on these preliminary performance studies, however, it appears that the zonal model can be used in conjunction with more complex models to help unravel the problems of understanding the processes governing present climate and climate change. As can be seen in the subsequent paper on model sensitivity studies, in addition to reduced cost of computation, the zonal model facilitates analysis of feedback mechanisms and simplifies analysis of the interactions between processes
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)
Mirman, Daniel; Estes, Katharine Graf; Magnuson, James S.
2010-01-01
Statistical learning mechanisms play an important role in theories of language acquisition and processing. Recurrent neural network models have provided important insights into how these mechanisms might operate. We examined whether such networks capture two key findings in human statistical learning. In Simulation 1, a simple recurrent network…
Impact initiation of explosives and propellants via statistical crack mechanics
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
A BRDF statistical model applying to space target materials modeling
Liu, Chenghao; Li, Zhi; Xu, Can; Tian, Qichen
2017-10-01
In order to solve the problem of poor effect in modeling the large density BRDF measured data with five-parameter semi-empirical model, a refined statistical model of BRDF which is suitable for multi-class space target material modeling were proposed. The refined model improved the Torrance-Sparrow model while having the modeling advantages of five-parameter model. Compared with the existing empirical model, the model contains six simple parameters, which can approximate the roughness distribution of the material surface, can approximate the intensity of the Fresnel reflectance phenomenon and the attenuation of the reflected light's brightness with the azimuth angle changes. The model is able to achieve parameter inversion quickly with no extra loss of accuracy. The genetic algorithm was used to invert the parameters of 11 different samples in the space target commonly used materials, and the fitting errors of all materials were below 6%, which were much lower than those of five-parameter model. The effect of the refined model is verified by comparing the fitting results of the three samples at different incident zenith angles in 0° azimuth angle. Finally, the three-dimensional modeling visualizations of these samples in the upper hemisphere space was given, in which the strength of the optical scattering of different materials could be clearly shown. It proved the good describing ability of the refined model at the material characterization as well.
Statistical Challenges in Modeling Big Brain Signals
Yu, Zhaoxia
2017-11-01
Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible solutions, and highlight future research directions.
Statistical Challenges in Modeling Big Brain Signals
Yu, Zhaoxia; Pluta, Dustin; Shen, Tong; Chen, Chuansheng; Xue, Gui; Ombao, Hernando
2017-01-01
Brain signal data are inherently big: massive in amount, complex in structure, and high in dimensions. These characteristics impose great challenges for statistical inference and learning. Here we review several key challenges, discuss possible
Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping
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.
Statistical Learning Theory: Models, Concepts, and Results
von Luxburg, Ulrike; Schoelkopf, Bernhard
2008-01-01
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory. We target at a broad audience, not necessarily machine learning researchers. This paper can serve as a starting point for people who want to get an overview on the field before diving into technical details.
Estimating preferential flow in karstic aquifers using statistical mixed models.
Anaya, Angel A; Padilla, Ingrid; Macchiavelli, Raul; Vesper, Dorothy J; Meeker, John D; Alshawabkeh, Akram N
2014-01-01
Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory-scale Geo-HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow-dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit-like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study. © 2013, National Ground Water Association.
Online Statistical Modeling (Regression Analysis) for Independent Responses
Made Tirta, I.; Anggraeni, Dian; Pandutama, Martinus
2017-06-01
Regression analysis (statistical analmodelling) are among statistical methods which are frequently needed in analyzing quantitative data, especially to model relationship between response and explanatory variables. Nowadays, statistical models have been developed into various directions to model various type and complex relationship of data. Rich varieties of advanced and recent statistical modelling are mostly available on open source software (one of them is R). However, these advanced statistical modelling, are not very friendly to novice R users, since they are based on programming script or command line interface. Our research aims to developed web interface (based on R and shiny), so that most recent and advanced statistical modelling are readily available, accessible and applicable on web. We have previously made interface in the form of e-tutorial for several modern and advanced statistical modelling on R especially for independent responses (including linear models/LM, generalized linier models/GLM, generalized additive model/GAM and generalized additive model for location scale and shape/GAMLSS). In this research we unified them in the form of data analysis, including model using Computer Intensive Statistics (Bootstrap and Markov Chain Monte Carlo/ MCMC). All are readily accessible on our online Virtual Statistics Laboratory. The web (interface) make the statistical modeling becomes easier to apply and easier to compare them in order to find the most appropriate model for the data.
Counting in Lattices: Combinatorial Problems from Statistical Mechanics.
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
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.
Statistical models for expert judgement and wear prediction
International Nuclear Information System (INIS)
Pulkkinen, U.
1994-01-01
This thesis studies the statistical analysis of expert judgements and prediction of wear. The point of view adopted is the one of information theory and Bayesian statistics. A general Bayesian framework for analyzing both the expert judgements and wear prediction is presented. Information theoretic interpretations are given for some averaging techniques used in the determination of consensus distributions. Further, information theoretic models are compared with a Bayesian model. The general Bayesian framework is then applied in analyzing expert judgements based on ordinal comparisons. In this context, the value of information lost in the ordinal comparison process is analyzed by applying decision theoretic concepts. As a generalization of the Bayesian framework, stochastic filtering models for wear prediction are formulated. These models utilize the information from condition monitoring measurements in updating the residual life distribution of mechanical components. Finally, the application of stochastic control models in optimizing operational strategies for inspected components are studied. Monte-Carlo simulation methods, such as the Gibbs sampler and the stochastic quasi-gradient method, are applied in the determination of posterior distributions and in the solution of stochastic optimization problems. (orig.) (57 refs., 7 figs., 1 tab.)
Integer Set Compression and Statistical Modeling
DEFF Research Database (Denmark)
Larsson, N. Jesper
2014-01-01
enumeration of elements may be arbitrary or random, but where statistics is kept in order to estimate probabilities of elements. We present a recursive subset-size encoding method that is able to benefit from statistics, explore the effects of permuting the enumeration order based on element probabilities......Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher compression performance. In this work, we address the case where...
Statistical modelling for social researchers principles and practice
Tarling, Roger
2008-01-01
This book explains the principles and theory of statistical modelling in an intelligible way for the non-mathematical social scientist looking to apply statistical modelling techniques in research. The book also serves as an introduction for those wishing to develop more detailed knowledge and skills in statistical modelling. Rather than present a limited number of statistical models in great depth, the aim is to provide a comprehensive overview of the statistical models currently adopted in social research, in order that the researcher can make appropriate choices and select the most suitable model for the research question to be addressed. To facilitate application, the book also offers practical guidance and instruction in fitting models using SPSS and Stata, the most popular statistical computer software which is available to most social researchers. Instruction in using MLwiN is also given. Models covered in the book include; multiple regression, binary, multinomial and ordered logistic regression, log-l...
Linear Mixed Models in Statistical Genetics
R. de Vlaming (Ronald)
2017-01-01
markdownabstractOne of the goals of statistical genetics is to elucidate the genetic architecture of phenotypes (i.e., observable individual characteristics) that are affected by many genetic variants (e.g., single-nucleotide polymorphisms; SNPs). A particular aim is to identify specific SNPs that
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.
Statistical models and methods for reliability and survival analysis
Couallier, Vincent; Huber-Carol, Catherine; Mesbah, Mounir; Huber -Carol, Catherine; Limnios, Nikolaos; Gerville-Reache, Leo
2013-01-01
Statistical Models and Methods for Reliability and Survival Analysis brings together contributions by specialists in statistical theory as they discuss their applications providing up-to-date developments in methods used in survival analysis, statistical goodness of fit, stochastic processes for system reliability, amongst others. Many of these are related to the work of Professor M. Nikulin in statistics over the past 30 years. The authors gather together various contributions with a broad array of techniques and results, divided into three parts - Statistical Models and Methods, Statistical
Bayesian Sensitivity Analysis of Statistical Models with Missing Data.
Zhu, Hongtu; Ibrahim, Joseph G; Tang, Niansheng
2014-04-01
Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.
Geometric modeling in probability and statistics
Calin, Ovidiu
2014-01-01
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader...
Challenges in dental statistics: data and modelling
Matranga, D.; Castiglia, P.; Solinas, G.
2013-01-01
The aim of this work is to present the reflections and proposals derived from the first Workshop of the SISMEC STATDENT working group on statistical methods and applications in dentistry, held in Ancona (Italy) on 28th September 2011. STATDENT began as a forum of comparison and discussion for statisticians working in the field of dental research in order to suggest new and improve existing biostatistical and clinical epidemiological methods. During the meeting, we dealt with very important to...
Addressing the statistical mechanics of planet orbits in the solar system
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.
Student Understanding of Taylor Series Expansions in Statistical Mechanics
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…
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
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...
A statistical model of future human actions
International Nuclear Information System (INIS)
Woo, G.
1992-02-01
A critical review has been carried out of models of future human actions during the long term post-closure period of a radioactive waste repository. Various Markov models have been considered as alternatives to the standard Poisson model, and the problems of parameterisation have been addressed. Where the simplistic Poisson model unduly exaggerates the intrusion risk, some form of Markov model may have to be introduced. This situation may well arise for shallow repositories, but it is less likely for deep repositories. Recommendations are made for a practical implementation of a computer based model and its associated database. (Author)
Enhanced surrogate models for statistical design exploiting space mapping technology
DEFF Research Database (Denmark)
Koziel, Slawek; Bandler, John W.; Mohamed, Achmed S.
2005-01-01
We present advances in microwave and RF device modeling exploiting Space Mapping (SM) technology. We propose new SM modeling formulations utilizing input mappings, output mappings, frequency scaling and quadratic approximations. Our aim is to enhance circuit models for statistical analysis...
Statistical models of shape optimisation and evaluation
Davies, Rhodri; Taylor, Chris
2014-01-01
Deformable shape models have wide application in computer vision and biomedical image analysis. This book addresses a key issue in shape modelling: establishment of a meaningful correspondence between a set of shapes. Full implementation details are provided.
Borsboom, D.; Haig, B.D.
2013-01-01
Unlike most other statistical frameworks, Bayesian statistical inference is wedded to a particular approach in the philosophy of science (see Howson & Urbach, 2006); this approach is called Bayesianism. Rather than being concerned with model fitting, this position in the philosophy of science
Statistical Tests for Mixed Linear Models
Khuri, André I; Sinha, Bimal K
2011-01-01
An advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these models a
Statistical modelling of traffic safety development
DEFF Research Database (Denmark)
Christens, Peter
2004-01-01
there were 6861 injury trafficc accidents reported by the police, resulting in 4519 minor injuries, 3946 serious injuries, and 431 fatalities. The general purpose of the research was to improve the insight into aggregated road safety methodology in Denmark. The aim was to analyse advanced statistical methods......, that were designed to study developments over time, including effects of interventions. This aim has been achieved by investigating variations in aggregated Danish traffic accident series and by applying state of the art methodologies to specific case studies. The thesis comprises an introduction...
Statistical image processing and multidimensional modeling
Fieguth, Paul
2010-01-01
Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something - an artery, a road, a DNA marker, an oil spill - from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over
On the one variational principle in quantum statistical mechanics
International Nuclear Information System (INIS)
Kurbatov, A.M.; Sankovich, D.P.
1980-01-01
Essential features of the approximating Hamiltonian method are reviewed. The free energy of a system can be calculated with the help of the approximating Hamiltonian, which possesses a simpler operator form than the initial model Hamiltonian. The method is applied to the following cases: model system of BCS type, model system with positive and negative coupling constants, model with nonpolynomial interaction, and model of nonideal Bose gas
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...
Fluctuations and correlations in statistical models of hadron production
International Nuclear Information System (INIS)
Gorenstein, M. I.
2012-01-01
An extension of the standard concept of the statistical ensembles is suggested. Namely, the statistical ensembles with extensive quantities fluctuating according to an externally given distribution are introduced. Applications in the statistical models of multiple hadron production in high energy physics are discussed.
Analysis and Evaluation of Statistical Models for Integrated Circuits Design
Directory of Open Access Journals (Sweden)
Sáenz-Noval J.J.
2011-10-01
Full Text Available Statistical models for integrated circuits (IC allow us to estimate the percentage of acceptable devices in the batch before fabrication. Actually, Pelgrom is the statistical model most accepted in the industry; however it was derived from a micrometer technology, which does not guarantee reliability in nanometric manufacturing processes. This work considers three of the most relevant statistical models in the industry and evaluates their limitations and advantages in analog design, so that the designer has a better criterion to make a choice. Moreover, it shows how several statistical models can be used for each one of the stages and design purposes.
Modeling of uncertainties in statistical inverse problems
International Nuclear Information System (INIS)
Kaipio, Jari
2008-01-01
In all real world problems, the models that tie the measurements to the unknowns of interest, are at best only approximations for reality. While moderate modeling and approximation errors can be tolerated with stable problems, inverse problems are a notorious exception. Typical modeling errors include inaccurate geometry, unknown boundary and initial data, properties of noise and other disturbances, and simply the numerical approximations of the physical models. In principle, the Bayesian approach to inverse problems, in which all uncertainties are modeled as random variables, is capable of handling these uncertainties. Depending on the type of uncertainties, however, different strategies may be adopted. In this paper we give an overview of typical modeling errors and related strategies within the Bayesian framework.
Interpretation of commonly used statistical regression models.
Kasza, Jessica; Wolfe, Rory
2014-01-01
A review of some regression models commonly used in respiratory health applications is provided in this article. Simple linear regression, multiple linear regression, logistic regression and ordinal logistic regression are considered. The focus of this article is on the interpretation of the regression coefficients of each model, which are illustrated through the application of these models to a respiratory health research study. © 2013 The Authors. Respirology © 2013 Asian Pacific Society of Respirology.
Statistical modeling and extrapolation of carcinogenesis data
International Nuclear Information System (INIS)
Krewski, D.; Murdoch, D.; Dewanji, A.
1986-01-01
Mathematical models of carcinogenesis are reviewed, including pharmacokinetic models for metabolic activation of carcinogenic substances. Maximum likelihood procedures for fitting these models to epidemiological data are discussed, including situations where the time to tumor occurrence is unobservable. The plausibility of different possible shapes of the dose response curve at low doses is examined, and a robust method for linear extrapolation to low doses is proposed and applied to epidemiological data on radiation carcinogenesis
Plan Recognition using Statistical Relational Models
2014-08-25
corresponding undirected model can be significantly more complex since there is no closed form solution for the maximum-likelihood set of parameters unlike in...algorithm did not scale to larger training sets, and the overall results are still not competitive with BALPs. 5In directed models, a closed form solution...opinions of ARO, DARPA, NSF or any other government agency. References Albrecht DW, Zukerman I, Nicholson AE. Bayesian models for keyhole plan
Multivariate statistical modelling based on generalized linear models
Fahrmeir, Ludwig
1994-01-01
This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of m...
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.
Statistical Modelling of Extreme Rainfall in Taiwan
L-F. Chu (Lan-Fen); M.J. McAleer (Michael); C-C. Chang (Ching-Chung)
2012-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
Statistical Modelling of Extreme Rainfall in Taiwan
L. Chu (LanFen); M.J. McAleer (Michael); C-H. Chang (Chu-Hsiang)
2013-01-01
textabstractIn this paper, the annual maximum daily rainfall data from 1961 to 2010 are modelled for 18 stations in Taiwan. We fit the rainfall data with stationary and non-stationary generalized extreme value distributions (GEV), and estimate their future behaviour based on the best fitting model.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
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.
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
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
On the Logical Development of Statistical Models.
1983-12-01
1978). "Modelos con parametros variables en el analisis de series temporales " Questiio, 4, 2, 75-87. [25] Seal, H. L. (1967). "The historical...example, a classical state-space representation of a simple time series model is: yt = it + ut Ut = *It-I + Ct (2.2) ut and et are independent normal...on its past values is displayed in the structural equation. This approach has been particularly useful in time series models. For example, model (2.2
A Noise Robust Statistical Texture Model
DEFF Research Database (Denmark)
Hilger, Klaus Baggesen; Stegmann, Mikkel Bille; Larsen, Rasmus
2002-01-01
Appearance Models segmentation framework. This is accomplished by augmenting the model with an estimate of the covariance of the noise present in the training data. This results in a more compact model maximising the signal-to-noise ratio, thus favouring subspaces rich on signal, but low on noise......This paper presents a novel approach to the problem of obtaining a low dimensional representation of texture (pixel intensity) variation present in a training set after alignment using a Generalised Procrustes analysis.We extend the conventional analysis of training textures in the Active...
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.
Student understanding of Taylor series expansions in statistical mechanics
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.
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
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.)
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
12th Workshop on Stochastic Models, Statistics and Their Applications
Rafajłowicz, Ewaryst; Szajowski, Krzysztof
2015-01-01
This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.
Materials Informatics: Statistical Modeling in Material Science.
Yosipof, Abraham; Shimanovich, Klimentiy; Senderowitz, Hanoch
2016-12-01
Material informatics is engaged with the application of informatic principles to materials science in order to assist in the discovery and development of new materials. Central to the field is the application of data mining techniques and in particular machine learning approaches, often referred to as Quantitative Structure Activity Relationship (QSAR) modeling, to derive predictive models for a variety of materials-related "activities". Such models can accelerate the development of new materials with favorable properties and provide insight into the factors governing these properties. Here we provide a comparison between medicinal chemistry/drug design and materials-related QSAR modeling and highlight the importance of developing new, materials-specific descriptors. We survey some of the most recent QSAR models developed in materials science with focus on energetic materials and on solar cells. Finally we present new examples of material-informatic analyses of solar cells libraries produced from metal oxides using combinatorial material synthesis. Different analyses lead to interesting physical insights as well as to the design of new cells with potentially improved photovoltaic parameters. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Introduction to statistical modelling: linear regression.
Lunt, Mark
2015-07-01
In many studies we wish to assess how a range of variables are associated with a particular outcome and also determine the strength of such relationships so that we can begin to understand how these factors relate to each other at a population level. Ultimately, we may also be interested in predicting the outcome from a series of predictive factors available at, say, a routine clinic visit. In a recent article in Rheumatology, Desai et al. did precisely that when they studied the prediction of hip and spine BMD from hand BMD and various demographic, lifestyle, disease and therapy variables in patients with RA. This article aims to introduce the statistical methodology that can be used in such a situation and explain the meaning of some of the terms employed. It will also outline some common pitfalls encountered when performing such analyses. © The Author 2013. Published by Oxford University Press on behalf of the British Society for Rheumatology. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Modelling the fragmentation mechanisms
International Nuclear Information System (INIS)
Bougault, R.; Durand, D.; Gulminelli, F.
1998-01-01
We have investigated the role of high amplitude collective motion in the nuclear fragmentation by using semi-classical macroscopic, as well as, microscopic simulations (BUU). These studies are motivated by the search of instabilities responsible for nuclear fragmentation. Two cases were examined: the bubble formation following the collective expansion of the compressed nucleus in case of very central reactions and, in the case of the semi-central collisions, the fast fission of the two partners issued from a binary reaction, in their corresponding Coulomb field. In the two cases the fragmentation channel is dominated by the inter-relation between the Coulomb and nuclear fields, and it is possible to obtain semi-quantitative predictions as functions of interaction parameters. The transport equations of BUU type predicts for central reactions formation of a high density transient state. Of much interest is the mechanism subsequent to de-excitation. It seems reasonable to conceive that the pressure stocked in the compressional mode manifests itself as a collective expansion of the system. As the pressure is a increasing function of the available energy one can conceive a variety of energy depending exit channels, starting from the fragmentation due the amplification of fluctuations interior to the spinodal zone up to the complete vaporization of the highly excited system. If the reached pressure is sufficiently high the reaction final state may preserve the memory of the entrance channel as a collective radial energy superimposed to the thermal disordered motion. Distributions of particles in the configuration space for both central and semi-central reactions for the Pb+Au system are presented. The rupture time is estimated to the order of 300 fm/c, and is strongly dependent on the initial temperature. The study of dependence of the rupture time on the interaction parameters is under way
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
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
Latent domain models for statistical machine translation
Hoàng, C.
2017-01-01
A data-driven approach to model translation suffers from the data mismatch problem and demands domain adaptation techniques. Given parallel training data originating from a specific domain, training an MT system on the data would result in a rather suboptimal translation for other domains. But does
Behavioral and statistical models of educational inequality
DEFF Research Database (Denmark)
Holm, Anders; Breen, Richard
2016-01-01
This paper addresses the question of how students and their families make educational decisions. We describe three types of behavioral model that might underlie decision-making and we show that they have consequences for what decisions are made. Our study thus has policy implications if we wish...
Statistical modelling of fine red wine production
Directory of Open Access Journals (Sweden)
María Rosa Castro
2010-01-01
Full Text Available Producing wine is a very important economic activity in the province of San Juan in Argentina; it is therefore most important to predict production regarding the quantity of raw material needed. This work was aimed at obtaining a model relating kilograms of crushed grape to the litres of wine so produced. Such model will be used for predicting precise future values and confidence intervals for determined quantities of crushed grapes. Data from a vineyard in the province of San Juan was thus used in this work. The sampling coefficient of correlation was calculated and a dispersion diagram was then constructed; this indicated a li- neal relationship between the litres of wine obtained and the kilograms of crushed grape. Two lineal models were then adopted and variance analysis was carried out because the data came from normal populations having the same variance. The most appropriate model was obtained from this analysis; it was validated with experimental values, a good approach being obtained.
Statistical models of global Langmuir mixing
Li, Qing; Fox-Kemper, Baylor; Breivik, Øyvind; Webb, Adrean
2017-05-01
The effects of Langmuir mixing on the surface ocean mixing may be parameterized by applying an enhancement factor which depends on wave, wind, and ocean state to the turbulent velocity scale in the K-Profile Parameterization. Diagnosing the appropriate enhancement factor online in global climate simulations is readily achieved by coupling with a prognostic wave model, but with significant computational and code development expenses. In this paper, two alternatives that do not require a prognostic wave model, (i) a monthly mean enhancement factor climatology, and (ii) an approximation to the enhancement factor based on the empirical wave spectra, are explored and tested in a global climate model. Both appear to reproduce the Langmuir mixing effects as estimated using a prognostic wave model, with nearly identical and substantial improvements in the simulated mixed layer depth and intermediate water ventilation over control simulations, but significantly less computational cost. Simpler approaches, such as ignoring Langmuir mixing altogether or setting a globally constant Langmuir number, are found to be deficient. Thus, the consequences of Stokes depth and misaligned wind and waves are important.
Sampling, Probability Models and Statistical Reasoning -RE ...
Indian Academy of Sciences (India)
random sampling allows data to be modelled with the help of probability ... g based on different trials to get an estimate of the experimental error. ... research interests lie in the .... if e is indeed the true value of the proportion of defectives in the.
Statistical Model Checking for Product Lines
DEFF Research Database (Denmark)
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2016-01-01
average cost of products (in terms of the attributes of the products’ features) and the probability of features to be (un)installed at runtime. The product lines must be modelled in QFLan, which extends the probabilistic feature-oriented language PFLan with novel quantitative constraints among features...
A Statistical Model for Energy Intensity
Directory of Open Access Journals (Sweden)
Marjaneh Issapour
2012-12-01
Full Text Available A promising approach to improve scientific literacy in regards to global warming and climate change is using a simulation as part of a science education course. The simulation needs to employ scientific analysis of actual data from internationally accepted and reputable databases to demonstrate the reality of the current climate change situation. One of the most important criteria for using a simulation in a science education course is the fidelity of the model. The realism of the events and consequences modeled in the simulation is significant as well. Therefore, all underlying equations and algorithms used in the simulation must have real-world scientific basis. The "Energy Choices" simulation is one such simulation. The focus of this paper is the development of a mathematical model for "Energy Intensity" as a part of the overall system dynamics in "Energy Choices" simulation. This model will define the "Energy Intensity" as a function of other independent variables that can be manipulated by users of the simulation. The relationship discovered by this research will be applied to an algorithm in the "Energy Choices" simulation.
Structured Statistical Models of Inductive Reasoning
Kemp, Charles; Tenenbaum, Joshua B.
2009-01-01
Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet…
Graphene growth process modeling: a physical-statistical approach
Wu, Jian; Huang, Qiang
2014-09-01
As a zero-band semiconductor, graphene is an attractive material for a wide variety of applications such as optoelectronics. Among various techniques developed for graphene synthesis, chemical vapor deposition on copper foils shows high potential for producing few-layer and large-area graphene. Since fabrication of high-quality graphene sheets requires the understanding of growth mechanisms, and methods of characterization and control of grain size of graphene flakes, analytical modeling of graphene growth process is therefore essential for controlled fabrication. The graphene growth process starts with randomly nucleated islands that gradually develop into complex shapes, grow in size, and eventually connect together to cover the copper foil. To model this complex process, we develop a physical-statistical approach under the assumption of self-similarity during graphene growth. The growth kinetics is uncovered by separating island shapes from area growth rate. We propose to characterize the area growth velocity using a confined exponential model, which not only has clear physical explanation, but also fits the real data well. For the shape modeling, we develop a parametric shape model which can be well explained by the angular-dependent growth rate. This work can provide useful information for the control and optimization of graphene growth process on Cu foil.
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.
Mechanics Model of Plug Welding
Zuo, Q. K.; Nunes, A. C., Jr.
2015-01-01
An analytical model has been developed for the mechanics of friction plug welding. The model accounts for coupling of plastic deformation (material flow) and thermal response (plastic heating). The model predictions of the torque, energy, and pull force on the plug were compared to the data of a recent experiment, and the agreements between predictions and data are encouraging.
Representation of the contextual statistical model by hyperbolic amplitudes
International Nuclear Information System (INIS)
Khrennikov, Andrei
2005-01-01
We continue the development of a so-called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric cos-interference, there exist contexts producing the hyperbolic cos-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators. This paper can be considered as the first step towards hyperbolic quantum probability. We also discuss possibilities of experimental verification of hyperbolic quantum mechanics: in physics of elementary particles, string theory as well as in experiments with nonphysical systems, e.g., in psychology, cognitive sciences, and economy
Statistical mechanical analysis of (1 + ∞) dimensional disordered systems
International Nuclear Information System (INIS)
Skantzos, Nikolaos Stavrou
2001-01-01
Valuable insight into the theory of disordered systems and spin-glasses has been offered by two classes of exactly solvable models: one-dimensional models and mean-field (infinite-range) ones, which, each carry their own specific techniques and restrictions. Both classes of models are now considered as 'exactly solvable' in the sense that in the thermodynamic limit the partition sum can been carried out analytically and the average over the disorder can be performed using methods which are well understood. In this thesis I study equilibrium properties of spin systems with a combination of one-dimensional short- and infinite-range interactions. I find that such systems, under either synchronous or asynchronous spin dynamics, and even in the absence of disorder, lead to phase diagrams with first-order transitions and regions with a multiple number of locally stable states. I then proceed to the study of recurrent neural network models with (1+∞)-dimensional interactions, and find that the competing short- and long-range forces lead to highly complex phase diagrams and that unlike infinite-range (Hopfield-type) models these phase diagrams depend crucially on the number of patterns stored, even away from saturation. To solve the statics of such models for the case of synchronous dynamics I first make a detour to solve the synchronous counterpart of the one-dimensional random-field Ising model, where I prove rigorously that the physics of the two random-field models (synchronous vs. sequential) becomes asymptotically the same, leading to an extensive ground state entropy and an infinite hierarchy of discontinuous transitions close to zero temperature. Finally, I propose and solve the statics of a spin model for the prediction of secondary structure in random hetero-polymers (which are considered as the natural first step to the study of real proteins). The model lies in the class of (1+∞)-dimensional disordered systems as a consequence of having steric- and hydrogen
Statistical Analysis and Modelling of Olkiluoto Structures
International Nuclear Information System (INIS)
Hellae, P.; Vaittinen, T.; Saksa, P.; Nummela, J.
2004-11-01
Posiva Oy is carrying out investigations for the disposal of the spent nuclear fuel at the Olkiluoto site in SW Finland. The investigations have focused on the central part of the island. The layout design of the entire repository requires characterization of notably larger areas and must rely at least at the current stage on borehole information from a rather sparse network and on the geophysical soundings providing information outside and between the holes. In this work, the structural data according to the current version of the Olkiluoto bedrock model is analyzed. The bedrock model relies much on the borehole data although results of the seismic surveys and, for example, pumping tests are used in determining the orientation and continuation of the structures. Especially in the analysis, questions related to the frequency of structures and size of the structures are discussed. The structures observed in the boreholes are mainly dipping gently to the southeast. About 9 % of the sample length belongs to structures. The proportion is higher in the upper parts of the rock. The number of fracture and crushed zones seems not to depend greatly on the depth, whereas the hydraulic features concentrate on the depth range above -100 m. Below level -300 m, the hydraulic conductivity occurs in connection of fractured zones. Especially the hydraulic features, but also fracture and crushed zones often occur in groups. The frequency of the structure (area of structures per total volume) is estimated to be of the order of 1/100m. The size of the local structures was estimated by calculating the intersection of the zone to the nearest borehole where the zone has not been detected. Stochastic models using the Fracman software by Golder Associates were generated based on the bedrock model data complemented with the magnetic ground survey data. The seismic surveys (from boreholes KR5, KR13, KR14, and KR19) were used as alternative input data. The generated models were tested by
Einstein's Approach to Statistical Mechanics: The 1902-04 Papers
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.
Statistically Based Morphodynamic Modeling of Tracer Slowdown
Borhani, S.; Ghasemi, A.; Hill, K. M.; Viparelli, E.
2017-12-01
Tracer particles are used to study bedload transport in gravel-bed rivers. One of the advantages associated with using of tracer particles is that they allow for direct measures of the entrainment rates and their size distributions. The main issue in large scale studies with tracer particles is the difference between tracer stone short term and long term behavior. This difference is due to the fact that particles undergo vertical mixing or move to less active locations such as bars or even floodplains. For these reasons the average virtual velocity of tracer particle decreases in time, i.e. the tracer slowdown. In summary, tracer slowdown can have a significant impact on the estimation of bedload transport rate or long term dispersal of contaminated sediment. The vast majority of the morphodynamic models that account for the non-uniformity of the bed material (tracer and not tracer, in this case) are based on a discrete description of the alluvial deposit. The deposit is divided in two different regions; the active layer and the substrate. The active layer is a thin layer in the topmost part of the deposit whose particles can interact with the bed material transport. The substrate is the part of the deposit below the active layer. Due to the discrete representation of the alluvial deposit, active layer models are not able to reproduce tracer slowdown. In this study we try to model the slowdown of tracer particles with the continuous Parker-Paola-Leclair morphodynamic framework. This continuous, i.e. not layer-based, framework is based on a stochastic description of the temporal variation of bed surface elevation, and of the elevation specific particle entrainment and deposition. Particle entrainment rates are computed as a function of the flow and sediment characteristics, while particle deposition is estimated with a step length formulation. Here we present one of the first implementation of the continuum framework at laboratory scale, its validation against
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'.
Hadronic equation of state in the statistical bootstrap model and linear graph theory
International Nuclear Information System (INIS)
Fre, P.; Page, R.
1976-01-01
Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed
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.
Territorial Developments Based on Graffiti: a Statistical Mechanics Approach
2011-10-28
Many animals, among which wolves , foxes and coyotes, are known to scent–mark their territories as a way of warning intruders of their presence and to...A. Lewis and R. L. Crabtree, Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone , Proc. Roy
PGT: A Statistical Approach to Prediction and Mechanism Design
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.
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
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)
Statistical mechanics of homogeneous partly pinned fluid systems.
Krakoviack, Vincent
2010-12-01
The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.
Functional summary statistics for the Johnson-Mehl model
DEFF Research Database (Denmark)
Møller, Jesper; Ghorbani, Mohammad
The Johnson-Mehl germination-growth model is a spatio-temporal point process model which among other things have been used for the description of neurotransmitters datasets. However, for such datasets parametric Johnson-Mehl models fitted by maximum likelihood have yet not been evaluated by means...... of functional summary statistics. This paper therefore invents four functional summary statistics adapted to the Johnson-Mehl model, with two of them based on the second-order properties and the other two on the nuclei-boundary distances for the associated Johnson-Mehl tessellation. The functional summary...... statistics theoretical properties are investigated, non-parametric estimators are suggested, and their usefulness for model checking is examined in a simulation study. The functional summary statistics are also used for checking fitted parametric Johnson-Mehl models for a neurotransmitters dataset....
Statistical modelling in biostatistics and bioinformatics selected papers
Peng, Defen
2014-01-01
This book presents selected papers on statistical model development related mainly to the fields of Biostatistics and Bioinformatics. The coverage of the material falls squarely into the following categories: (a) Survival analysis and multivariate survival analysis, (b) Time series and longitudinal data analysis, (c) Statistical model development and (d) Applied statistical modelling. Innovations in statistical modelling are presented throughout each of the four areas, with some intriguing new ideas on hierarchical generalized non-linear models and on frailty models with structural dispersion, just to mention two examples. The contributors include distinguished international statisticians such as Philip Hougaard, John Hinde, Il Do Ha, Roger Payne and Alessandra Durio, among others, as well as promising newcomers. Some of the contributions have come from researchers working in the BIO-SI research programme on Biostatistics and Bioinformatics, centred on the Universities of Limerick and Galway in Ireland and fu...
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
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.)
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
Statistical mechanics of dense plasmas: numerical simulation and theory
International Nuclear Information System (INIS)
DeWitt, H.E.
1977-10-01
Recent Monte Carlo calculations from Paris and from Livermore for dense one and two component plasmas have led to systematic and accurate results for the thermodynamic properties of dense Coulombic fluids. This talk will summarize the results of these numerical experiments, and the simple analytic expressions for the equation of state and other thermodynamic functions that have been obtained. The thermal energy for the one component plasma has a simple power law dependence on temperature that is identical to Monte Carlo results on strongly coupled fluids governed by l/r/sup n/ potentials. A universal model for fluids governed by simple repulsive forces is suggested. For two component plasmas the ion-sphere model is shown to accurately reproduce the Monte Carlo data for the static portion of the energy. Electron screening is included using the Lindhard dielectric function and linear response theory. Free energy expressions have been constructed for one and two component plasmas that allow easy computation of all thermodynamic functions
Petersson, K M; Nichols, T E; Poline, J B; Holmes, A P
1999-01-01
Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference. PMID:10466149
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.
Mechanical model for ductility loss
International Nuclear Information System (INIS)
Hu, W.L.
1980-01-01
A mechanical model was constructed to probe into the mechanism of ductility loss. Fracture criterion based on critical localized deformation was undertaken. Two microstructure variables were considered in the model. Namely, the strength ratio of grain boundary affected area to the matrix, Ω, and the linear fraction, x, of grain boundary affected area. A parametrical study was carried out. The study shows that the ductility is very sensitive to those microstructure parameters. The functional dependence of ductility to temperature as well as strain-rate, suggested by the model, is demonstrated to be consistent with the observation
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
Mixed deterministic statistical modelling of regional ozone air pollution
Kalenderski, Stoitchko
2011-03-17
We develop a physically motivated statistical model for regional ozone air pollution by separating the ground-level pollutant concentration field into three components, namely: transport, local production and large-scale mean trend mostly dominated by emission rates. The model is novel in the field of environmental spatial statistics in that it is a combined deterministic-statistical model, which gives a new perspective to the modelling of air pollution. The model is presented in a Bayesian hierarchical formalism, and explicitly accounts for advection of pollutants, using the advection equation. We apply the model to a specific case of regional ozone pollution-the Lower Fraser valley of British Columbia, Canada. As a predictive tool, we demonstrate that the model vastly outperforms existing, simpler modelling approaches. Our study highlights the importance of simultaneously considering different aspects of an air pollution problem as well as taking into account the physical bases that govern the processes of interest. © 2011 John Wiley & Sons, Ltd..
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.
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.
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.
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.
A Model of Statistics Performance Based on Achievement Goal Theory.
Bandalos, Deborah L.; Finney, Sara J.; Geske, Jenenne A.
2003-01-01
Tests a model of statistics performance based on achievement goal theory. Both learning and performance goals affected achievement indirectly through study strategies, self-efficacy, and test anxiety. Implications of these findings for teaching and learning statistics are discussed. (Contains 47 references, 3 tables, 3 figures, and 1 appendix.)…
Kolmogorov complexity, pseudorandom generators and statistical models testing
Czech Academy of Sciences Publication Activity Database
Šindelář, Jan; Boček, Pavel
2002-01-01
Roč. 38, č. 6 (2002), s. 747-759 ISSN 0023-5954 R&D Projects: GA ČR GA102/99/1564 Institutional research plan: CEZ:AV0Z1075907 Keywords : Kolmogorov complexity * pseudorandom generators * statistical models testing Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.341, year: 2002
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Equilibrium statistical mechanics of strongly coupled plasmas by numerical simulation
International Nuclear Information System (INIS)
DeWitt, H.E.
1977-01-01
Numerical experiments using the Monte Carlo method have led to systematic and accurate results for the thermodynamic properties of strongly coupled one-component plasmas and mixtures of two nuclear components. These talks are intended to summarize the results of Monte Carlo simulations from Paris and from Livermore. Simple analytic expressions for the equation of state and other thermodynamic functions have been obtained in which there is a clear distinction between a lattice-like static portion and a thermal portion. The thermal energy for the one-component plasma has a simple power dependence on temperature, (kT)/sup 3 / 4 /, that is identical to Monte Carlo results obtained for strongly coupled fluids governed by repulsive l/r/sup n/ potentials. For two-component plasmas the ion-sphere model is shown to accurately represent the static portion of the energy. Electron screening is included in the Monte Carlo simulations using linear response theory and the Lindhard dielectric function. Free energy expressions have been constructed for one and two component plasmas that allow easy computation of all thermodynamic functions
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
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
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
Studies on quantum field theory and statistical mechanics
International Nuclear Information System (INIS)
Zhang, S.
1987-01-01
This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather from a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable
Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
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
Improving statistical reasoning theoretical models and practical implications
Sedlmeier, Peter
1999-01-01
This book focuses on how statistical reasoning works and on training programs that can exploit people''s natural cognitive capabilities to improve their statistical reasoning. Training programs that take into account findings from evolutionary psychology and instructional theory are shown to have substantially larger effects that are more stable over time than previous training regimens. The theoretical implications are traced in a neural network model of human performance on statistical reasoning problems. This book apppeals to judgment and decision making researchers and other cognitive scientists, as well as to teachers of statistics and probabilistic reasoning.
Statistical validation of normal tissue complication probability models
Xu, Cheng-Jian; van der Schaaf, Arjen; van t Veld, Aart; Langendijk, Johannes A.; Schilstra, Cornelis
2012-01-01
PURPOSE: To investigate the applicability and value of double cross-validation and permutation tests as established statistical approaches in the validation of normal tissue complication probability (NTCP) models. METHODS AND MATERIALS: A penalized regression method, LASSO (least absolute shrinkage
Some remarks on the statistical model of heavy ion collisions
International Nuclear Information System (INIS)
Koch, V.
2003-01-01
This contribution is an attempt to assess what can be learned from the remarkable success of this statistical model in describing ratios of particle abundances in ultra-relativistic heavy ion collisions
Eigenfunction statistics for Anderson model with Hölder continuous ...
Indian Academy of Sciences (India)
The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India ... Anderson model; Hölder continuous measure; Poisson statistics. ...... [4] Combes J-M, Hislop P D and Klopp F, An optimal Wegner estimate and its application to.
A no extensive statistical model for the nucleon structure function
International Nuclear Information System (INIS)
Trevisan, Luis A.; Mirez, Carlos
2013-01-01
We studied an application of nonextensive thermodynamics to describe the structure function of nucleon, in a model where the usual Fermi-Dirac and Bose-Einstein energy distribution were replaced by the equivalent functions of the q-statistical. The parameters of the model are given by an effective temperature T, the q parameter (from Tsallis statistics), and two chemical potentials given by the corresponding up (u) and down (d) quark normalization in the nucleon.
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
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
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
Models for probability and statistical inference theory and applications
Stapleton, James H
2007-01-01
This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...
Statistical-Mechanical Analysis of Pre-training and Fine Tuning in Deep Learning
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.
Computational modelling in fluid mechanics
International Nuclear Information System (INIS)
Hauguel, A.
1985-01-01
The modelling of the greatest part of environmental or industrial flow problems gives very similar types of equations. The considerable increase in computing capacity over the last ten years consequently allowed numerical models of growing complexity to be processed. The varied group of computer codes presented are now a complementary tool of experimental facilities to achieve studies in the field of fluid mechanics. Several codes applied in the nuclear field (reactors, cooling towers, exchangers, plumes...) are presented among others [fr
Skewed factor models using selection mechanisms
Kim, Hyoung-Moon
2015-12-21
Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-tt, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.
Skewed factor models using selection mechanisms
Kim, Hyoung-Moon; Maadooliat, Mehdi; Arellano-Valle, Reinaldo B.; Genton, Marc G.
2015-01-01
Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-tt, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models using the classic open/closed book exam scores dataset.
Statistical model of stress corrosion cracking based on extended ...
Indian Academy of Sciences (India)
2016-09-07
Sep 7, 2016 ... Abstract. In the previous paper (Pramana – J. Phys. 81(6), 1009 (2013)), the mechanism of stress corrosion cracking (SCC) based on non-quadratic form of Dirichlet energy was proposed and its statistical features were discussed. Following those results, we discuss here how SCC propagates on pipe wall ...
STATISTICAL DISTRIBUTION PATTERNS IN MECHANICAL AND FATIGUE PROPERTIES OF METALLIC MATERIALS
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...
Aerodynamic and Mechanical System Modelling
DEFF Research Database (Denmark)
Jørgensen, Martin Felix
This thesis deals with mechanical multibody-systems applied to the drivetrain of a 500 kW wind turbine. Particular focus has been on gearbox modelling of wind turbines. The main part of the present project involved programming multibody systems to investigate the connection between forces, moments...
Fracture mechanics model of fragmentation
International Nuclear Information System (INIS)
Glenn, L.A.; Gommerstadt, B.Y.; Chudnovsky, A.
1986-01-01
A model of the fragmentation process is developed, based on the theory of linear elastic fracture mechanics, which predicts the average fragment size as a function of strain rate and material properties. This approach permits a unification of previous results, yielding Griffith's solution in the low-strain-rate limit and Grady's solution at high strain rates
Right-sizing statistical models for longitudinal data.
Wood, Phillip K; Steinley, Douglas; Jackson, Kristina M
2015-12-01
Arguments are proposed that researchers using longitudinal data should consider more and less complex statistical model alternatives to their initially chosen techniques in an effort to "right-size" the model to the data at hand. Such model comparisons may alert researchers who use poorly fitting, overly parsimonious models to more complex, better-fitting alternatives and, alternatively, may identify more parsimonious alternatives to overly complex (and perhaps empirically underidentified and/or less powerful) statistical models. A general framework is proposed for considering (often nested) relationships between a variety of psychometric and growth curve models. A 3-step approach is proposed in which models are evaluated based on the number and patterning of variance components prior to selection of better-fitting growth models that explain both mean and variation-covariation patterns. The orthogonal free curve slope intercept (FCSI) growth model is considered a general model that includes, as special cases, many models, including the factor mean (FM) model (McArdle & Epstein, 1987), McDonald's (1967) linearly constrained factor model, hierarchical linear models (HLMs), repeated-measures multivariate analysis of variance (MANOVA), and the linear slope intercept (linearSI) growth model. The FCSI model, in turn, is nested within the Tuckerized factor model. The approach is illustrated by comparing alternative models in a longitudinal study of children's vocabulary and by comparing several candidate parametric growth and chronometric models in a Monte Carlo study. (c) 2015 APA, all rights reserved).
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Variability aware compact model characterization for statistical circuit design optimization
Qiao, Ying; Qian, Kun; Spanos, Costas J.
2012-03-01
Variability modeling at the compact transistor model level can enable statistically optimized designs in view of limitations imposed by the fabrication technology. In this work we propose an efficient variabilityaware compact model characterization methodology based on the linear propagation of variance. Hierarchical spatial variability patterns of selected compact model parameters are directly calculated from transistor array test structures. This methodology has been implemented and tested using transistor I-V measurements and the EKV-EPFL compact model. Calculation results compare well to full-wafer direct model parameter extractions. Further studies are done on the proper selection of both compact model parameters and electrical measurement metrics used in the method.
Linear mixed models a practical guide using statistical software
West, Brady T; Galecki, Andrzej T
2006-01-01
Simplifying the often confusing array of software programs for fitting linear mixed models (LMMs), Linear Mixed Models: A Practical Guide Using Statistical Software provides a basic introduction to primary concepts, notation, software implementation, model interpretation, and visualization of clustered and longitudinal data. This easy-to-navigate reference details the use of procedures for fitting LMMs in five popular statistical software packages: SAS, SPSS, Stata, R/S-plus, and HLM. The authors introduce basic theoretical concepts, present a heuristic approach to fitting LMMs based on bo
Speech emotion recognition based on statistical pitch model
Institute of Scientific and Technical Information of China (English)
WANG Zhiping; ZHAO Li; ZOU Cairong
2006-01-01
A modified Parzen-window method, which keep high resolution in low frequencies and keep smoothness in high frequencies, is proposed to obtain statistical model. Then, a gender classification method utilizing the statistical model is proposed, which have a 98% accuracy of gender classification while long sentence is dealt with. By separation the male voice and female voice, the mean and standard deviation of speech training samples with different emotion are used to create the corresponding emotion models. Then the Bhattacharyya distance between the test sample and statistical models of pitch, are utilized for emotion recognition in speech.The normalization of pitch for the male voice and female voice are also considered, in order to illustrate them into a uniform space. Finally, the speech emotion recognition experiment based on K Nearest Neighbor shows that, the correct rate of 81% is achieved, where it is only 73.85%if the traditional parameters are utilized.
Multiple commodities in statistical microeconomics: Model and market
Baaquie, Belal E.; Yu, Miao; Du, Xin
2016-11-01
A statistical generalization of microeconomics has been made in Baaquie (2013). In Baaquie et al. (2015), the market behavior of single commodities was analyzed and it was shown that market data provides strong support for the statistical microeconomic description of commodity prices. The case of multiple commodities is studied and a parsimonious generalization of the single commodity model is made for the multiple commodities case. Market data shows that the generalization can accurately model the simultaneous correlation functions of up to four commodities. To accurately model five or more commodities, further terms have to be included in the model. This study shows that the statistical microeconomics approach is a comprehensive and complete formulation of microeconomics, and which is independent to the mainstream formulation of microeconomics.