Equilibrium statistical mechanics

CERN Document Server

Mayer, J E

1968-01-01

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

Statistical formulation of gravitational radiation reaction

International Nuclear Information System (INIS)

Schutz, B.F.

1980-01-01

A new formulation of the radiation-reaction problem is proposed, which is simpler than alternatives which have been used before. The new approach is based on the initial-value problem, uses approximations which need be uniformly valid only in compact regions of space-time, and makes no time-asymmetric assumptions (no a priori introduction of retarded potentials or outgoing-wave asymptotic conditions). It defines radiation reaction to be the expected evolution of a source obtained by averaging over a statistical ensemble of initial conditions. The ensemble is chosen to reflect one's complete lack of information (in real systems) about the initial data for the radiation field. The approach is applied to the simple case of a weak-field, slow-motion source in general relativity, where it yields the usual expressions for radiation reaction when the gauge is chosen properly. There is a discussion of gauge freedom, and another of the necessity of taking into account reaction corrections to the particle-conservation equation. The analogy with the second law of thermodynamics is very close, and suggests that the electromagnetic and thermodynamic arrows of time are the same. Because the formulation is based on the usual initial-value problem, it has no spurious ''runaway'' solutions

Statistical mechanics

CERN Document Server

Davidson, Norman

2003-01-01

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

What is Quantum Mechanics? A Minimal Formulation

Science.gov (United States)

Friedberg, R.; Hohenberg, P. C.

2018-03-01

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.

Lectures on statistical mechanics

CERN Document Server

Bowler, M G

1982-01-01

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

Statistical mechanics

CERN Document Server

Schwabl, Franz

2006-01-01

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

Statistical mechanics

CERN Document Server

Jana, Madhusudan

2015-01-01

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

Statistical mechanics of nonequilibrium liquids

CERN Document Server

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

1990-01-01

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

Statistical mechanics of superconductivity

CERN Document Server

Kita, Takafumi

2015-01-01

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

Statistical mechanics in JINR

International Nuclear Information System (INIS)

Tonchev, N.; Shumovskij, A.S.

1986-01-01

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

History Matching Through a Smooth Formulation of Multiple-Point Statistics

DEFF Research Database (Denmark)

Melnikova, Yulia; Zunino, Andrea; Lange, Katrine

2014-01-01

and the mismatch with multiple-point statistics. As a result, in the framework of the Bayesian approach, such a solution belongs to a high posterior region. The methodology, while applicable to any inverse problem with a training-image-based prior, is especially beneficial for problems which require expensive......We propose a smooth formulation of multiple-point statistics that enables us to solve inverse problems using gradient-based optimization techniques. We introduce a differentiable function that quantifies the mismatch between multiple-point statistics of a training image and of a given model. We...... show that, by minimizing this function, any continuous image can be gradually transformed into an image that honors the multiple-point statistics of the discrete training image. The solution to an inverse problem is then found by minimizing the sum of two mismatches: the mismatch with data...

Random path formulation of nonrelativistic quantum mechanics

International Nuclear Information System (INIS)

Roncadelli, M.

1993-01-01

Quantum amplitudes satisfy (almost) the same calculus that probabilities obey in the theory of classical stochastic diffusion processes. As a consequence of this structural analogy, a new formulation of (nonrelativistic) quantum mechanics naturally arises as the quantum counterpart of the Langevin description of (classical) stochastic diffusion processes. Quantum fluctuations are simulated here by a Fresnel white noise (FWN), which is a (real) white noise with imaginary diffusion constant, whose functional (pseudo) measure yields the amplitude distribution for its configurations. Central to this approach is the idea that classical dynamical trajectories in configuration space are perturbed by the FWN. Hence, a single (arbitrary) classical dynamical path gets replaced by a family of quantum random paths (QRPs) - one for each FWN sample - all originating from the same space-time point (x', t'). The QRPs are the basic objects of the present formulation and are given by a Langevin equation with the FWN, whose drift is controlled by a (arbitrary) solution to the classical Hamilton-Jacobi equation. So, our approach is manifestly based on classical dynamics. Now, a transition amplitude is associated with each QRP: it gives the amplitude that a particle starting from (x', t') will reach (x'', t'') by travelling just along the considered QRP. The quantum mechanical propagator (x'', t'' modul x', t') then emerges as the FWN average of the transition amplitude along a QRP. Thus, quantum mechanics looks like classical mechanics as perturbed by the FWN. The general structure of this formulation is discussed in detail, along with some practical and conceptual implications. (author). 14 refs

Statistical mechanics in a nutshell

CERN Document Server

Peliti, Luca

2011-01-01

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

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)

Current algebra, statistical mechanics and quantum models

Science.gov (United States)

Vilela Mendes, R.

2017-11-01

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

Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics

International Nuclear Information System (INIS)

Goldfarb, Yair; Degani, Ilan; Tannor, David J.

2006-01-01

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared--it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification - a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10 -7 calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity

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.

Statistical mechanics rigorous results

CERN Document Server

Ruelle, David

1999-01-01

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

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

International Nuclear Information System (INIS)

Tadaki, Kohtaro

2010-01-01

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

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

CERN Document Server

Hill, Terrell L

1956-01-01

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

Hamiltonian formulation and statistics of an attracting system of nonlinear oscillators

International Nuclear Information System (INIS)

Tasso, H.

1987-10-01

An attracting system of r nonlinear oscillators of an extended van der Pol type was investigated with respect to Hamiltonian formulation. The case of r=2 is rather simple, though nontrivial. For r>2 the tests with Jacobi's identity and Frechet derivatives are negative if Hamiltonians in the natural variables are looked for. Independently, a Liouville theorem is proved and equilibrium statistics is made possible, which leads to a Gaussian distribution in the natural variables. (orig.)

Artificial intelligence in pharmaceutical product formulation: neural computing

OpenAIRE

Svetlana Ibrić; Jelena Petrović; Jelena Parojčić; Zorica Djurić

2009-01-01

The properties of a formulation are determined not only by the ratios in which the ingredients are combined but also by the processing conditions. Although the relationships between the ingredient levels, processing conditions, and product performance may be known anecdotally, they can rarely be quantified. In the past, formulators tended to use statistical techniques to model their formulations, relying on response surfaces to provide a mechanism for optimazation. However, the optimization b...

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

Science.gov (United States)

Ohzeki, Masayuki

2015-03-01

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

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

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

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

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

OpenAIRE

Săvoiu, Gheorghe

2008-01-01

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

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.)

Significance of Strain in Formulation in Theory of Solid Mechanics

Science.gov (United States)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.

2003-01-01

The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.

Hydrogen atom in the phase-space formulation of quantum mechanics

International Nuclear Information System (INIS)

Gracia-Bondia, J.M.

1984-01-01

Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way

Modern Thermodynamics with Statistical Mechanics

CERN Document Server

Helrich, Carl S

2009-01-01

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

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.)

Playing at Statistical Mechanics

Science.gov (United States)

Clark, Paul M.; And Others

1974-01-01

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

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

International Nuclear Information System (INIS)

Prugovecki, E.

1978-01-01

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

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.

Quadratic Jordan formulation of quantum mechanics and construction of Lie (super)algebras from Jordan (super)algebras

International Nuclear Information System (INIS)

Guenaydin, M.

1979-05-01

Quadratic Jordan formulation of quantum mechanics in terms of Jordan triple product is presented. This formulation extends to the case of octonionic quantum mechanics for which no Hilbert space formulation exists. Using ternary algebraic techniques we then five the constructions of the derivation, structure and Tits-Koecher (Moebius) algebras of Jordan superalgebras. (orig.) [de

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

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics

International Nuclear Information System (INIS)

Tosiek, J.; Brzykcy, P.

2013-01-01

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function

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

Graphene Statistical Mechanics

Science.gov (United States)

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

2015-03-01

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

Nonequilibrium statistical mechanics ensemble method

CERN Document Server

Eu, Byung Chan

1998-01-01

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

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

An introduction to thermodynamics and statistical mechanics

CERN Document Server

Saxena, A K

2016-01-01

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

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.

Learning Predictive Statistics: Strategies and Brain Mechanisms.

Science.gov (United States)

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

2017-08-30

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

Statistical mechanics and applications in condensed matter

CERN Document Server

Di Castro, Carlo

2015-01-01

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

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

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Science.gov (United States)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

An alternative formulation of classical mechanics based on an analogy with thermodynamics

International Nuclear Information System (INIS)

Teruel, Ginés R Pérez

2013-01-01

We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analysed under coordinate transformations. When invariance under different kinds of transformations is considered the new formulation is found to be completely equivalent to the usual Lagrangian formulation, recovering well-established results such as conservation of angular momentum. Furthermore, a natural generalization of the Poisson bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, L ' =-L, it is possible to establish an exact one-to-one mathematical correspondence between the thermodynamic potentials and the new potentials of classical mechanics. (paper)

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

Energy Technology Data Exchange (ETDEWEB)

Reyes, A.

2006-07-01

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

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.)

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

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

Vaccine instability in the cold chain: mechanisms, analysis and formulation strategies.

Science.gov (United States)

Kumru, Ozan S; Joshi, Sangeeta B; Smith, Dawn E; Middaugh, C Russell; Prusik, Ted; Volkin, David B

2014-09-01

Instability of vaccines often emerges as a key challenge during clinical development (lab to clinic) as well as commercial distribution (factory to patient). To yield stable, efficacious vaccine dosage forms for human use, successful formulation strategies must address a combination of interrelated topics including stabilization of antigens, selection of appropriate adjuvants, and development of stability-indicating analytical methods. This review covers key concepts in understanding the causes and mechanisms of vaccine instability including (1) the complex and delicate nature of antigen structures (e.g., viruses, proteins, carbohydrates, protein-carbohydrate conjugates, etc.), (2) use of adjuvants to further enhance immune responses, (3) development of physicochemical and biological assays to assess vaccine integrity and potency, and (4) stabilization strategies to protect vaccine antigens and adjuvants (and their interactions) during storage. Despite these challenges, vaccines can usually be sufficiently stabilized for use as medicines through a combination of formulation approaches combined with maintenance of an efficient cold chain (manufacturing, distribution, storage and administration). Several illustrative case studies are described regarding mechanisms of vaccine instability along with formulation approaches for stabilization within the vaccine cold chain. These include live, attenuated (measles, polio) and inactivated (influenza, polio) viral vaccines as well as recombinant protein (hepatitis B) vaccines. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Compressional, mechanical and release properties of a novel gum in paracetamol tablet formulations

Directory of Open Access Journals (Sweden)

Adedokun Musiliu O.

2014-09-01

Full Text Available The binding properties of Eucalyptus gum obtained from the incised trunk of Eucalyptus tereticornis, were evaluated in paracetamol tablet formulations, in comparison with that of Gelatin B.P. In so doing, the compression properties were analyzed using density measurements and the compression equations of Heckel, Kawakita and Gurham. In our work, the mechanical properties of the tablets were assessed using the crushing strength and friability of the tablets, while the drug release properties of the tablets were assessed using disintegration and dissolution times. The results of the study reveal that tablet formulations incorporating Eucalyptus gum as binder, exhibited faster onset and higher amount of plastic deformation during compression than those containing gelatin. What is more, the Gurnham equation could be used as a substitute for the Kawakita equation in describing the compression properties of pharmaceutical tablets. Furthermore, the crushing strength, disintegration and dissolution times of the tablets increased with binder concentration, while friability values decreased. We noted that no significant differences in properties exist between formulations derived from the two binders (p > 0.05 exist. While tablets incorporating gelatin exhibited higher values for mechanical properties, Eucalyptus gum tablets had better balance between mechanical and release properties - as seen from the CSFR/Dt values. Tablets of good mechanical and release properties were prepared using Eucalyptus gum as a binder, and, therefore, it could serve as an alternative binder in producing tablets with good mechanical strength and fast drug release.

Journey Through Statistical Mechanics

Science.gov (United States)

Yang, C. N.

2013-05-01

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

Statistical crack mechanics

International Nuclear Information System (INIS)

Dienes, J.K.

1993-01-01

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

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

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.)

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

Effect of formulation of alginate beads on their mechanical behavior and stiffness

Institute of Scientific and Technical Information of China (English)

Eng-Seng Chan; Tek-Kaun Lim; Wan-Ping Voo; Ravindra Pogaku; Beng Ti Tey; Zhibing Zhang

2011-01-01

The aim of this work was to determine the effect of formulation of alginate beads on their mechanical behavior and stiffness when compressed at high speed. The alginate beads were formulated using different types and concentrations of alginate and gelling cations and were produced using an extrusiondripping method. Single wet beads were compressed at a speed of 40 mm/min, and their elastic limits were investigated, and the corresponding force versus displacement data were obtained. The Young's moduli of the beads were determined from the force versus displacement data using the Hertz's contact mechanics theory. The alginate beads were found to exhibit plastic behavior when they were compressed beyond 50％ with the exception of copper-alginate beads for which yield occured at lower deformation.Alginate beads made of higher guluronic acid contents and gelling cations of higher chemical affinity were found to have greater stiffness. Increasing the concentration of alginate and gelling ions also generated a similar effect. At such a compression speed, the values of Young's modulus of the beads were found to be in the range between 250 and 900 kPa depending on the bead formulation.

Statistical mechanics of multipartite entanglement

Science.gov (United States)

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

2009-02-01

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

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

Statistical mechanics in the context of special relativity.

Science.gov (United States)

Kaniadakis, G

2002-11-01

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

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)

Generalized statistical mechanics approaches to earthquakes and tectonics

Science.gov (United States)

Papadakis, Giorgos; Michas, Georgios

2016-01-01

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

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

A signed particle formulation of non-relativistic quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-09-15

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.

A statistical mechanical approach to restricted integer partition functions

Science.gov (United States)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-05-01

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

Applied statistical thermodynamics

CERN Document Server

Lucas, Klaus

1991-01-01

The book guides the reader from the foundations of statisti- cal thermodynamics including the theory of intermolecular forces to modern computer-aided applications in chemical en- gineering and physical chemistry. The approach is new. The foundations of quantum and statistical mechanics are presen- ted in a simple way and their applications to the prediction of fluid phase behavior of real systems are demonstrated. A particular effort is made to introduce the reader to expli- cit formulations of intermolecular interaction models and to show how these models influence the properties of fluid sy- stems. The established methods of statistical mechanics - computer simulation, perturbation theory, and numerical in- tegration - are discussed in a style appropriate for newcom- ers and are extensively applied. Numerous worked examples illustrate how practical calculations should be carried out.

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.

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

Annotations to quantum statistical mechanics

CERN Document Server

Kim, In-Gee

2018-01-01

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

Microcanonical ensemble formulation of lattice gauge theory

International Nuclear Information System (INIS)

Callaway, D.J.E.; Rahman, A.

1982-01-01

A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed

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

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)

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

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

International Nuclear Information System (INIS)

Ng, Felix S.L.

2016-01-01

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

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

Equilibrium statistical mechanics of lattice models

CERN Document Server

Lavis, David A

2015-01-01

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

Statistical models and NMR analysis of polymer microstructure

Science.gov (United States)

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 approach to inverse statistical mechanics

Science.gov (United States)

Habeck, Michael

2014-05-01

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

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.

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

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

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

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.

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

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

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

The probability representation as a new formulation of quantum mechanics

International Nuclear Information System (INIS)

Man'ko, Margarita A; Man'ko, Vladimir I

2012-01-01

We present a new formulation of conventional quantum mechanics, in which the notion of a quantum state is identified via a fair probability distribution of the position measured in a reference frame of the phase space with rotated axes. In this formulation, the quantum evolution equation as well as the equation for finding energy levels are expressed as linear equations for the probability distributions that determine the quantum states. We also give the integral transforms relating the probability distribution (called the tomographic-probability distribution or the state tomogram) to the density matrix and the Wigner function and discuss their connection with the Radon transform. Qudit states are considered and the invertible map of the state density operators onto the probability vectors is discussed. The tomographic entropies and entropic uncertainty relations are reviewed. We demonstrate the uncertainty relations for the position and momentum and the entropic uncertainty relations in the tomographic-probability representation, which is suitable for an experimental check of the uncertainty relations.

Quality of comminuted sausages formulated from mechanically deboned poultry meat.

Science.gov (United States)

Mielnik, Maria B; Aaby, Kjersti; Rolfsen, Knut; Ellekjær, Marit R; Nilsson, Astrid

2002-05-01

Comminuted sausages formulated with mechanically deboned poultry meat-MDPM (turkey or chicken, frame or neck) treated in different ways before production (vacuum packed MDPM or air packed skeletons deboned at production) and stored frozen for 6 or 18 weeks have been studied using a full-factorial design and chemical, physical and sensory analysis. MDPM was obtained from a Beehive separator. Comminuted sausages with MDPM from turkey frames, stored at -25 °C as skeletons, packed in air for 18 weeks developed marked rancid odour and flavour which could also be detected by thiobarbituric acid reactive substances (TBARS) and the concentration of volatile compounds. Vacuum packed mechanically deboned meat irrespective of species and carcass part could be stored for up to 18 weeks and used in formulation of sausages without any serious changes in their sensory profiles. Instrumental colour differences between sausages were mainly due to species. Turkey sausages were darker, redder and less yellow than chicken sausages. Moisture and fat contents were influenced by carcass part and to a lesser extent depended on species and storage time. Principal least squares regression (PLS2) showed close relationships between instrumental parameters and sensory attributes. TBARS, hexanal and volatile compounds were highly correlated with rancid flavour while redness (a(∗)) was strongly related to sensory colour hue and colour strength.

Why irreversibility? The formulation of classical and quantum mechanics for nonintegrable systems

International Nuclear Information System (INIS)

Prigogine, I.

1995-01-01

Nonintegrable Poincare systems with a continuous spectrum lead to the appearance of diffusive terms in the frame of classical or quantum dynamics. These terms break time symmetry. They lead, therefore, to limitations to classical trajectory theory and of wave-function formalism. These diffusive terms correspond to well-defined classes of dynamical processes. The diffusive effects are amplified in situations corresponding to persistent interactions. As a result, we have to include, already, in the fundamental dynamical description the two basic aspects, probability and irreversibility, which are so conspicuous on the macroscopic level. We have to formulate both classical and quantum mechanics on the Liouville level of probability distributions. For integrable systems, we recover the usual formulation of classical or quantum mechanics. Instead of being primitive concepts, which cannot be further analyzed, trajectories and wave functions appear as special solutions of the Liouville-von Neumann equations. This extension of classical and quantum dynamics permits us to unify the two concepts of nature that we inherited from the nineteenth century, based, on the one hand, on dynamical time-reversible laws and, on the other, on an evolutionary view associated to entropy. It leads also to a unified formulation of quantum theory, avoiding the conventional dual structure based on Schroedinger's equation, on the one hand, and on the open-quotes collapseclose quotes of the wave function, on the other. A dynamical interpretation is given to processes such as decoherence or approach to equilibrium without any appeal to extra dynamic considerations. There is a striking parallelism between classical and quantum theory. For large Poincare systems (LPS), we have, in general, both a open-quotes collapseclose quotes of trajectories and of wave functions. In both cases, we need a generalized formulation of dynamics in terms of probability distributions or density matrices

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.

Combined use of MSWI bottom ash and fly ash as aggregate in concrete formulation: environmental and mechanical considerations.

Science.gov (United States)

Ginés, O; Chimenos, J M; Vizcarro, A; Formosa, J; Rosell, J R

2009-09-30

This paper reports the experimental results obtained after casting concrete formulated with different mix proportions of municipal solid waste incineration (MSWI) by-products, bottom ash (BA) and air pollution control fly ash (APCFA), as aggregates. Several tests were performed to determine the properties of the mixed proportions. Mechanical properties of the formulations, such as compressive strength, were also determined, and two different leaching tests were performed to study their environmental effects. Some suitable concrete formulations were obtained for the 95/5 and 90/10 BA/APCFA mix proportions. These formulations showed the highest compressive strength test results, above 15 MPa, and the lowest amount of released trace metals in reference to the leaching test. The leaching mechanisms involved in the release of trace metals for the best formulations were also studied, revealing that the washing-off process may play an important role. Given the experimental data it can be concluded that these concrete mix proportions are suitable for use as non-structural concrete.

An adhesive contact mechanics formulation based on atomistically induced surface traction

Energy Technology Data Exchange (ETDEWEB)

Fan, Houfu [Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 (United States); Ren, Bo [Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551 (United States); Li, Shaofan, E-mail: shaofan@berkeley.edu [Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720 (United States)

2015-12-01

In this work, we have developed a novel multiscale computational contact formulation based on the generalized Derjuguin approximation for continua that are characterized by atomistically enriched constitutive relations in order to study macroscopic interaction between arbitrarily shaped deformable continua. The proposed adhesive contact formulation makes use of the microscopic interaction forces between individual particles in the interacting bodies. In particular, the double-layer volume integral describing the contact interaction (energy, force vector, matrix) is converted into a double-layer surface integral through a mathematically consistent approach that employs the divergence theorem and a special partitioning technique. The proposed contact model is formulated in the nonlinear continuum mechanics framework and implemented using the standard finite element method. With no large penalty constant, the stiffness matrix of the system will in general be well-conditioned, which is of great significance for quasi-static analysis. Three numerical examples are presented to illustrate the capability of the proposed method. Results indicate that with the same mesh configuration, the finite element computation based on the surface integral approach is faster and more accurate than the volume integral based approach. In addition, the proposed approach is energy preserving even in a very long dynamic simulation.

(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 ...

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

Science.gov (United States)

der, R.

1987-01-01

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

Statistical mechanics of complex networks

CERN Document Server

Rubi, Miguel; Diaz-Guilera, Albert

2003-01-01

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

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 ...

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

Science.gov (United States)

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

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

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

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

International Nuclear Information System (INIS)

Velazquez Abad, Luisberis

2012-01-01

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

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)

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)

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

Science.gov (United States)

Ichiyanagi, Masakazu

1995-11-01

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

Introduction to quantum statistical mechanics

CERN Document Server

Bogolyubov, N N

2010-01-01

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

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

An introduction to statistical mechanics and thermodynamics

CERN Document Server

Swendsen, Robert H

2012-01-01

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

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

CERN Document Server

Hemmo, Meir

2012-01-01

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

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 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.

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second-Order Perturbation Theory

Science.gov (United States)

Matsubara, Takahiko

2003-02-01

We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, two-dimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDM-like models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

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)

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

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 ...

Statistical mechanics and the physics of fluids

CERN Document Server

Tosi, Mario

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

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

Science.gov (United States)

Bovier, Anton

2006-06-01

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

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 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

Artificial intelligence in pharmaceutical product formulation: neural computing

Directory of Open Access Journals (Sweden)

Svetlana Ibrić

2009-10-01

Full Text Available The properties of a formulation are determined not only by the ratios in which the ingredients are combined but also by the processing conditions. Although the relationships between the ingredient levels, processing conditions, and product performance may be known anecdotally, they can rarely be quantified. In the past, formulators tended to use statistical techniques to model their formulations, relying on response surfaces to provide a mechanism for optimazation. However, the optimization by such a method can be misleading, especially if the formulation is complex. More recently, advances in mathematics and computer science have led to the development of alternative modeling and data mining techniques which work with a wider range of data sources: neural networks (an attempt to mimic the processing of the human brain; genetic algorithms (an attempt to mimic the evolutionary process by which biological systems self-organize and adapt, and fuzzy logic (an attempt to mimic the ability of the human brain to draw conclusions and generate responses based on incomplete or imprecise information. In this review the current technology will be examined, as well as its application in pharmaceutical formulation and processing. The challenges, benefits and future possibilities of neural computing will be discussed.

Intermediate release formulations of diclofenac potassium tablets for IVIVC.

Science.gov (United States)

Ali, Huma; Shoaib, Muhammad Harris; Zafar, Farya; Bushra, Rabia; Yasmin, Riffat; Siddiqui, Shehla; Alam, Zafar M

2016-07-01

In recent days response surface methodology (RSM) has widely been applied for development and optimization of cost effective formulations with required quality. Study comprised of three steps including micromeritic comparison of different powder blends of placebo and diclofenac potassium (DP), formulation designing with CCRD (Design Expert, version 7.0.0), and stability testing of selected formulations by using R Gui. Ten formulations (F11-F20) were developed using microcrystalline cellulose (Avicel PH-102) (X1) (13-72%), methocel K15M (X2) (6.59-23.4%) and magnesium stearate (X3) (1.32-4.68%), while responses were % friability and % drug release. Blending rate constant was determined at 3, 6, 9 and 12 minutes. The results of physicochemical parameters were found within acceptable limits. After in vitro testing at pH 1.2, pH 4.5 and pH 6.8, mechanism of drug release, kinetic analysis and statistical evaluation were carried out by model - independent, model-dependent and one-way ANOVA methods. Most formulations followed zero order kinetics at higher pH. Fickian release (0.326 ≤ n ≤0.449) was observed with β greater than 0.5 and less than 1. ANOVA indicated no significant variation within and between formulations as p-values were found to be > 0.05.

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 mechanics of budget-constrained auctions

OpenAIRE

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

2009-01-01

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

Statistical physics a prelude and fugue for engineers

CERN Document Server

Piazza, Roberto

2017-01-01

This book, provides a general introduction to the ideas and methods of statistical mechanics with the principal aim of meeting the needs of Master’s students in chemical, mechanical, and materials science engineering. Extensive introductory information is presented on many general physics topics in which students in engineering are inadequately trained, ranging from the Hamiltonian formulation of classical mechanics to basic quantum mechanics, electromagnetic fields in matter, intermolecular forces, and transport phenomena. Since engineers should be able to apply physical concepts, the book also focuses on the practical applications of statistical physics to material science and to cutting-edge technologies, with brief but informative sections on, for example, interfacial properties, disperse systems, nucleation, magnetic materials, superfluidity, and ultralow temperature technologies. The book adopts a graded approach to learning, the opening four basic-level chapters being followed by advanced “starred�...

Statistical mechanics of the vertex-cover problem

Science.gov (United States)

Hartmann, Alexander K.; Weigt, Martin

2003-10-01

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

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 Mechanics and Black Hole Thermodynamics

OpenAIRE

Carlip, Steven

1997-01-01

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

A general contact mechanical formulation of multilayered structures and its application to deconvolute thickness/mechanical properties of glue used in surface force apparatus.

Science.gov (United States)

Math, Souvik; Horn, Roger; Jayaram, Vikram; Biswas, Sanjay Kumar

2007-04-15

Currently data obtained from surface force apparatus experiments are convoluted with the mechanical response of glue of unknown thickness, used to bond mica sheets to the substrates. This paper describes a formulation to precisely deconvolute out the forces between the mica sheets by determining the thickness of glue, knowing the mechanical properties of the glue. The formulation consists of a general solution based on the noniterative Hankel transform of the Laplace equation. The generality is achieved by treating all the layers except the one in contact as an effective lumped system consisting of a set of springs in series, where each spring represents a layer. The solution is validated by nanoindentation of trilayer systems consisting of layers with widely diverse mechanical properties, some differing from each other by three orders of magnitude. SFA experiments are done with carefully metered slabs of glue. The proposed method is validated by comparing the actual glue thicknesses with those determined using the present analysis.

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

Quantum formalism for classical statistics

Science.gov (United States)

Wetterich, C.

2018-06-01

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

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

Statistical mechanics of directed models of polymers in the square lattice

CERN Document Server

Rensburg, J V

2003-01-01

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

A 'general boundary' formulation for quantum mechanics and quantum gravity

International Nuclear Information System (INIS)

Oeckl, Robert

2003-01-01

I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such 'general boundary' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a 'general boundary' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three-dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four-dimensional quantum gravity

Formulation and optimization of chronomodulated press-coated tablet of carvedilol by Box–Behnken statistical design

Directory of Open Access Journals (Sweden)

Satwara RS

2012-08-01

Full Text Available Rohan S Satwara, Parul K PatelDepartment of Pharmaceutics, Babaria Institute of Pharmacy, Vadodara, Gujarat, IndiaObjective: The primary objective of the present investigation was to formulate and optimize chronomodulated press-coated tablets to deliver the antihypertensive carvedilol at an effective quantity predawn, when a blood pressure spike is typically observed in most hypertensive patients.Experimental work: Preformulation studies and drug excipient compatibility studies were carried out for carvedilol and excipients. Core tablets (6 mm containing carvedilol and 10-mm press-coated tablets were prepared by direct compression. The Box–Behnken experimental design was applied to these press-coated tablets (F1–F15 formula with differing concentrations of rate-controlling polymers. Hydroxypropyl methyl cellulose K4M, ethyl cellulose, and K-carrageenan were used as rate-controlling polymers in the outer layer. These tablets were subjected to various precompression and postcompression tests. The optimized batch was derived both by statistically (using desirability function and graphically (using Design Expert® 8; Stat-Ease Inc. Tablets formulated using the optimized formulas were then evaluated for lag time and in vitro dissolution.Results and discussion: Results of preformulation studies were satisfactory. No interaction was observed between carvedilol and excipients by ultraviolet, Fourier transform infrared spectroscopy, and dynamic light scattering analysis. The results of precompression studies and postcompression studies were within limits. The varying lag time and percent cumulative carvedilol release after 8 h was optimized to obtain a formulation that offered a release profile with 6 h lag time, followed by complete carvedilol release after 8 h. The results showed no significant bias between predicted response and actual response for the optimized formula.Conclusion: Bedtime dosing of chronomodulated press-coated tablets may offer a

Statistical Mechanics of Turbulent Dynamos

Science.gov (United States)

Shebalin, John V.

2014-01-01

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

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

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

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

Displaced Path Integral Formulation for the Momentum Distribution of Quantum Particles

Science.gov (United States)

Lin, Lin; Morrone, Joseph A.; Car, Roberto; Parrinello, Michele

2010-09-01

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

Principles of thermodynamics and statistical mechanics

CERN Document Server

Lawden, D F

2005-01-01

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

Braid group, knot theory and statistical mechanics II

CERN Document Server

Yang Chen Ning

1994-01-01

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

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

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

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

Science.gov (United States)

Eroglu, Sertac

2014-10-01

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

Realistic thermodynamic and statistical-mechanical measures for neural synchronization.

Science.gov (United States)

Kim, Sang-Yoon; Lim, Woochang

2014-04-15

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

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

Science.gov (United States)

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping

Science.gov (United States)

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

2018-05-01

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

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

Early years of Computational Statistical Mechanics

Science.gov (United States)

Mareschal, Michel

2018-05-01

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

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

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.

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

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

Introduction to the Lie-admissible treatment of non-potential interactions in Newtonian, statistical, and particle mechanics

International Nuclear Information System (INIS)

Santilli, R.M.

1982-01-01

Views on the experimental origin, theoretical formulation, and mathematical structure of nonpotential interactions in Newtonian, statistical, and particle mechanics are presented. The simplest but most dominant consideration of this introduction is the expectation that the charge distribution of hadrons is not perfectly rigid, but admits deformations under suitable impacts with other hadrons. These rather natural deformations then imply: (1) the breaking of the SU(2)-spin symmetry for the interior strong problem, with the understanding that conventional, conserved, total spin quantities are recovered in the exterior treatment; (2) the consequential necessary breaking of the T- and P-symmetries, also for the interior strong problem, owing to the explicit dependence of the discrete operators on spin, with the understanding that the center-of-mass trajectories of closed strong systems recover the T- and P-symmetries; and (3) the origin of irreversibility at the most elemental level of nature, via the nonpotential interactions originating from mutual penetrations and overlappings of hadrons under strong interactions

Is quantum theory a form of statistical mechanics?

Science.gov (United States)

Adler, S. L.

2007-05-01

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

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 model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

Science.gov (United States)

Rizvi, Mohd Suhail; Pal, Anupam

2014-09-01

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

Science.gov (United States)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

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)

Statistical mechanics and the evolution of polygenic quantitative traits

NARCIS (Netherlands)

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

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

STATISTICAL DISTRIBUTION PATTERNS IN MECHANICAL AND FATIGUE PROPERTIES OF METALLIC MATERIALS

OpenAIRE

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

1997-01-01

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

Statistical physics of black holes as quantum-mechanical systems

OpenAIRE

Giddings, Steven B.

2013-01-01

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

A statistical mechanics approach to mixing in stratified fluids

OpenAIRE

Venaille , Antoine; Gostiaux , Louis; Sommeria , Joël

2016-01-01

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

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

Reliability, Sensitivity, and Specificity of Case Formulations for Comorbid Profiles in Interpersonal Reconstructive Therapy: Addressing Mechanisms of Psychopathology.

Science.gov (United States)

Critchfield, Kenneth L; Benjamin, Lorna Smith; Levenick, Kathleen

2015-08-01

Interpersonal Reconstructive Therapy (IRT) case formulations describe psychosocial mechanisms of affective and personality pathology in ways that enhance the effectiveness of psychotherapy for individuals. With a valid and reliable IRT case formulation, a clinician is in a better position to draw upon effective techniques to maximize treatment effects. The case formulation and treatment models for IRT were described in depth along with the IRT treatment model by Benjamin (2003/2006). Data in this report from 93 adult inpatients with complex and comorbid presentations suggest that the case formulation is highly reliable and unique to individuals, and that symptoms reflect current interpersonal stresses linked to early interactions involving forms of hostility in relation with attachment figures and corresponding to three basic patterns in adulthood: identification (be like him or her), recapitulation (act as you did with him or her), and introjection (treat yourself as you were treated).

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

Science.gov (United States)

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

2010-06-01

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

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.

A Look Behind the Salt Curve: An Examination of Thickening Mechanisms in Shampoo Formulations

Science.gov (United States)

Penfield, Kevin

2008-07-01

Dynamic oscillatory rheological measurements are used to examine two mechanisms for thickening simple shampoo formulations. The salt curve, in which viscosity of a surfactant solution is maximized at intermediate levels of salt, is shown to be due to the variation in relaxation time; this is found to correlate with variation in the degree of entanglement per micelle. This is contrasted with the effect of PEG-150 distearate, which alters viscosity through a change in modulus.

A κ-generalized statistical mechanics approach to income analysis

Science.gov (United States)

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

2009-02-01

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

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

Why quantum mechanics?

International Nuclear Information System (INIS)

Landsberg, P.T.

1988-01-01

It is suggested that an oversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of a classical uncertainty relation for a very simple model. The existence of universal motion, i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter

To a causal formulation of quantum mechanics

International Nuclear Information System (INIS)

Brody, T.A.; Cetto, A.M.; Pena, L. de la

1979-01-01

This paper consists of two parts. In the first one we analyze the elements that a theory of quantum mechanics (QM) must contain in order to provide a physical explanation of the most notable quantum features (random behaviour, wave-particle duality, discrete spectra). We conclude that the theory that possesses the qualitative elements required is stochastic electrodynamics (SED), according to which the quantum behavior of the electron arises from its interaction with the stochastic electromagnetic background fiel associated with the zero-point energy. In the second part we show that the postulates of SED are suitable for the construction of a theory of the motion of the electron from which QM may be derived as an approximate description; hence, the mathematical formalism of QM too is justified by SED. Thus, the present theory generalizes QM and moreover, provides an objective statistical interpretation of it. (author)

Alternative derivations of the statistical mechanical distribution laws.

Science.gov (United States)

Wall, F T

1971-08-01

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

Geometry and topology in hamiltonian dynamics and statistical mechanics

CERN Document Server

Pettini, Marco

2007-01-01

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

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.

Some aspects of the formulation of alginate dental impression materials--setting characteristics and mechanical properties.

Science.gov (United States)

Nallamuthu, Navina A; Braden, Michael; Patel, Mangala P

2012-07-01

To study the role of the various components of alginate dental impression materials. Experimental materials were formulated and their physical properties characterized and compared to commercially available counterparts (Neocolloid, Palgat Plus and Blueprint Cremix). Properties examined were: dimensional stability and weight change in water and artificial saliva; setting behavior; Shore A hardness and tear energy. The role of magnesium oxide was also investigated. Weight changes in water and artificial saliva can be attributed to an initial thermodynamic potential owing to the ionic content of the alginate, causing water to diffuse into the material. Water is then driven back out following a reversal of this potential. Hardness results for experimental materials were within the range obtained from the commercial materials. The hardness value for an experimental formulation that did not contain magnesium oxide was lower than values from the other experimental materials that did. Tear energies for all three experimental materials were greater than those of the commercial products. There were statistically significant differences between the two experimental materials that contained magnesium oxide and one that did not. With regard to setting time, statistically significant differences were seen between commercial materials and two of the experimental materials. The experimental material that did not contain magnesium oxide had a considerably longer setting time than all of the other materials tested. The key role of magnesium oxide in the setting reaction and the effect on hardness have been demonstrated and discussed. Copyright © 2012 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

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

2009-07-01

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

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

SRB states and nonequilibrium statistical mechanics close to equilibrium

OpenAIRE

Gallavotti, Giovannni; Ruelle, David

1996-01-01

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

Thermodynamics and statistical mechanics an integrated approach

CERN Document Server

Hardy, Robert J

2014-01-01

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

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

Prolonged release matrix tablet of pyridostigmine bromide: formulation and optimization using statistical methods.

Science.gov (United States)

Bolourchian, Noushin; Rangchian, Maryam; Foroutan, Seyed Mohsen

2012-07-01

The aim of this study was to design and optimize a prolonged release matrix formulation of pyridostigmine bromide, an effective drug in myasthenia gravis and poisoning with nerve gas, using hydrophilic - hydrophobic polymers via D-optimal experimental design. HPMC and carnauba wax as retarding agents as well as tricalcium phosphate were used in matrix formulation and considered as independent variables. Tablets were prepared by wet granulation technique and the percentage of drug released at 1 (Y(1)), 4 (Y(2)) and 8 (Y(3)) hours were considered as dependent variables (responses) in this investigation. These experimental responses were best fitted for the cubic, cubic and linear models, respectively. The optimal formulation obtained in this study, consisted of 12.8 % HPMC, 24.4 % carnauba wax and 26.7 % tricalcium phosphate, had a suitable prolonged release behavior followed by Higuchi model in which observed and predicted values were very close. The study revealed that D-optimal design could facilitate the optimization of prolonged release matrix tablet containing pyridostigmine bromide. Accelerated stability studies confirmed that the optimized formulation remains unchanged after exposing in stability conditions for six months.

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

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)

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)

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

Directory of Open Access Journals (Sweden)

Ray Amritansu

2014-01-01

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

Connes distance function on fuzzy sphere and the connection between geometry and statistics

International Nuclear Information System (INIS)

Devi, Yendrembam Chaoba; Chakraborty, Biswajit; Prajapat, Shivraj; Mukhopadhyay, Aritra K.; Scholtz, Frederik G.

2015-01-01

An algorithm to compute Connes spectral distance, adaptable to the Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics, was developed earlier by introducing the appropriate spectral triple and used to compute infinitesimal distances in the Moyal plane, revealing a deep connection between geometry and statistics. In this paper, using the same algorithm, the Connes spectral distance has been calculated in the Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial coordinates satisfy the su(2) algebra. This has been computed for both the discrete and the Perelemov’s SU(2) coherent state. Here also, we get a connection between geometry and statistics which is shown by computing the infinitesimal distance between mixed states on the quantum Hilbert space of a particular fuzzy sphere, indexed by n ∈ ℤ/2

Design and formulation of nano-sized spray dried efavirenz. Part I: Influence of formulation parameters

CSIR Research Space (South Africa)

Katata, L

2012-10-01

Full Text Available statistical design with an L8 orthogonal array, was implemented to optimise the formulation parameters of PCL-EFV nanoparticles. The types of sugar (lactose or trehalose), surfactant concentration and solvent (dichloromethane and ethyl acetate) were chosen...

Addressing the statistical mechanics of planet orbits in the solar system

Science.gov (United States)

Mogavero, Federico

2017-10-01

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

Effects of the Formulations of Silicon-Based Composite Anodes on their Mechanical, Storage, and Electrochemical Properties.

Science.gov (United States)

Assresahegn, Birhanu Desalegn; Bélanger, Daniel

2017-10-23

In this work, the effects of the formulation of silicon-based composite anodes on their mechanical, storage, and electrochemical properties were investigated. The electrode formulation was changed through the use of hydrogenated or modified (through the covalent attachment of a binding additive such as polyacrylic acid) silicon and acetylene black or graphene sheets as conducting additives. A composite anode with a covalently grafted binder had the highest elongation without breakages and strong adhesion to the current collector. These mechanical properties depend significantly on the conductive carbon additive used and the use of graphene sheets instead of acetylene black can improve elongation and adhesion significantly. After 180 days of storage under ambient conditions, the electronic conductivity and discharge capacity of the modified silicon electrode showed much smaller decreases in these properties than those of the hydrogenated silicon composite electrode, indicating that the modification can result in passivation and a constant composition of the active material. Moreover, the composite Si anode has a high packing density. Consequently, thin-film electrodes with very high material loadings can be prepared without decreased electrochemical performance. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of thermal and chemical modifications on the mechanical and release properties of paracetamol tablet formulations containing corn, cassava and sweet potato starches as filler-binders

Directory of Open Access Journals (Sweden)

Mariam Vbamiunomhene Lawal

2015-07-01

Conclusions: Modification of the experimental starches improved the mechanical and release properties of directly compressed paracetamol tablet formulations. Thus, they can be developed for use as pharmaceutical excipients in specific formulations.

S-matrix formulation of thermodynamics with N-body scatterings

Energy Technology Data Exchange (ETDEWEB)

Lo, Pok Man [University of Wroclaw, Institute of Theoretical Physics, Wroclaw (Poland); Extreme Matter Institute EMMI, GSI, Darmstadt (Germany)

2017-08-15

We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics. A generalized phase shift function suitable for studying the thermal contribution of N → N processes is motivated and examined in various models. Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out. Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering. (orig.)

Statistical mechanical perturbation theory of solid-vapor interfacial free energy

NARCIS (Netherlands)

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

2017-01-01

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

Statistical Mechanical Perturbation Theory of Solid−Vapor Interfacial Free Energy

NARCIS (Netherlands)

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

2017-01-01

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

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.)

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-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 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 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

Evaluation of anti-inflammatory potential of the multidrug herbomineral formulation in male Wistar rats against rheumatoid arthritis

Directory of Open Access Journals (Sweden)

Snehal S Patel

2013-01-01

Full Text Available Background: Immunological and inflammatory mechanisms, which may play a role in a number of disorders like rheumatoid arthritis (RA. Ancient ayurvedic physicians had developed certain dietary and therapeutic measures to arrest or prevent these disorders. Objective: Rheuma off gold (RG is a herbomineral formulation recommended by ayurvedic medical practitioners for treatment of RA. This study was carried out to lend scientific evidence to the efficacy claim for RG in the management of RA in folklore medicine. Materials and Methods: Arthritis was induced by complete Freund′s adjuvant. Treatment with formulation 100 mg/kg and dexamethasone 2 mg/kg was given to rats intragastrically once a day from day 1 to day 21 and after which estimation of physical, biochemical, and hematological parameters were carried out. Results: Treatment of formulation to adjuvant induced arthritic animal showed statistically significant ( P < 0.05 improvement in physical parameters like arthritic index, paw edema, paw thickness as well as reduction of inflammatory markers like C-reactive protein, serum rheumatoid factor, erythrocyte sedimentation rate. The treatment also produced statistically significant ( P < 0.05 increase in hemoglobin percent and improvement in splenomegaly and thymus index. In the histopathological examination, ameliorative effect of formulation was observed in hyperplasia of synovium, pannus formation, and destruction of the joint space. Conclusion: The results obtained in experiments indicated that the formulation significantly inhibited the adjuvant-induced arthritis which was comparable to dexamethasone and had preferable anti-inflammatory effect without significant side effect. Thus, the formulation may be a potential preventive or therapeutic candidate for the treatment of chronic inflammation and arthritis.

Statistical field theory of futures commodity prices

Science.gov (United States)

Baaquie, Belal E.; Yu, Miao

2018-02-01

The statistical theory of commodity prices has been formulated by Baaquie (2013). Further empirical studies of single (Baaquie et al., 2015) and multiple commodity prices (Baaquie et al., 2016) have provided strong evidence in support the primary assumptions of the statistical formulation. In this paper, the model for spot prices (Baaquie, 2013) is extended to model futures commodity prices using a statistical field theory of futures commodity prices. The futures prices are modeled as a two dimensional statistical field and a nonlinear Lagrangian is postulated. Empirical studies provide clear evidence in support of the model, with many nontrivial features of the model finding unexpected support from market data.

Quality by design approach for formulation, evaluation and statistical optimization of diclofenac-loaded ethosomes via transdermal route.

Science.gov (United States)

Jain, Shashank; Patel, Niketkumar; Madan, Parshotam; Lin, Senshang

2015-06-01

The objective of this study was to fabricate and understand ethosomal formulations of diclofenac (DF) for enhanced anti-inflammatory activity using quality by design approach. DF-loaded ethosomal formulations were prepared using 4 × 5 full-factorial design with phosphatidylcholine:cholesterol (PC:CH) ratios ranging between 50:50 and 90:10, and ethanol concentration ranging between 0% and 30% as formulation variables. These formulations were characterized in terms of physicochemical properties and skin permeation kinetics. The interaction of formulation variables had a significant effect on both physicochemical properties and permeation kinetics. The results of multivariate regression analysis illustrated that vesicle size and elasticity of ethosomes were the dominating physicochemical properties affecting skin permeation, and could be suitably controlled by manipulation of formulation variables to optimize the formulation and enhance the skin permeation of DF-loaded ethosomes. The optimized formulation had ethanol concentration of 22.9% and PC:CH ratio of 88.4:11.6, with vesicle size of 144 ± 5 nm, zeta potential of -23.0 ± 3.76 mV, elasticity of 2.48 ± 0.75 and entrapment efficiency of 71 ± 4%. Permeation flux for the optimized formulation was 12.9 ± 1.0 µg/h cm(2), which was significantly higher than the drug-loaded conventional liposome, ethanolic or aqueous solution. The in vivo study indicated that optimized ethosomal hydrogel exhibited enhanced anti-inflammatory activity compared with liposomal and plain drug hydrogel formulations.

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

Directory of Open Access Journals (Sweden)

Evgeni B. Starikov

2018-02-01

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

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

On the statistical mechanics of species abundance distributions.

Science.gov (United States)

Bowler, Michael G; Kelly, Colleen K

2012-09-01

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

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

Science.gov (United States)

Gogolin, Christian; Eisert, Jens

2016-05-01

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

Statistical mechanics in the context of special relativity. II.

Science.gov (United States)

Kaniadakis, G

2005-09-01

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

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

Science.gov (United States)

Sinitskiy, Anton V; Voth, Gregory A

2015-09-07

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

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

Electrochemical mechanism and kinetics studies of haloperidol and its assay in commercial formulations

International Nuclear Information System (INIS)

Ribeiro, Francisco W.P.; Soares, Janete E.S.; Becker, Helena; De Souza, Djenaine; Lima-Neto, Pedro de; Correia, Adriana N.

2011-01-01

The kinetics and mechanism for electrochemical reduction of haloperidol, a psychotherapeutic drug used in the treatment of schizophrenia, were studied using square wave and cyclic voltammetries allied to a hanging mercury drop electrode. The experimental and voltammetric parameters were optimized at 0.04 mol L -1 Brinton-Robinson buffer (pH 10), with a pulse potential frequency of 100 s -1 , a pulse amplitude of 30 mV and scan increment of 2 mV. Two well-defined peaks were observed, which exhibited properties of fast electron transfer with a strong adsorption process of reactants and products on the electrode surface. The first peak was related to a fast and reversible anion-radical formation originating from the reduction of the carbonyl group, and the second was related to the irreversible reduction of the anion-radical previously formed. Analytical parameters such as: linearity range, equation of the analytical curves, correlation coefficients, detection and quantification limits, recovery efficiency, and relative standard deviation for intraday and interday were compared to similar results obtained by use of the UV-vis spectrophotometry technique, and the analytical results obtained in commercial formulations show that the voltammetric procedure using a hanging mercury drop electrode is suitable for analyzing haloperidol in complex commercial formulation samples.

Electrochemical mechanism and kinetics studies of haloperidol and its assay in commercial formulations

Energy Technology Data Exchange (ETDEWEB)

Ribeiro, Francisco W.P. [Departamento de Quimica Analitica e Fisico-Quimica, Centro de Ciencias, Universidade Federal do Ceara, Bloco 940 Campus do Pici 60455-970, Fortaleza, CE (Brazil); Soares, Janete E.S. [Departamento de Farmacia, Faculdade de Farmacia, Odontologia e Enfermagem, Universidade Federal do Ceara, Rua Capitao Francisco Pedro, 1210 Rodolfo Teofilo 60430-370, Fortaleza, CE (Brazil); Becker, Helena; De Souza, Djenaine; Lima-Neto, Pedro de [Departamento de Quimica Analitica e Fisico-Quimica, Centro de Ciencias, Universidade Federal do Ceara, Bloco 940 Campus do Pici 60455-970, Fortaleza, CE (Brazil); Correia, Adriana N., E-mail: adriana@ufc.b [Departamento de Quimica Analitica e Fisico-Quimica, Centro de Ciencias, Universidade Federal do Ceara, Bloco 940 Campus do Pici 60455-970, Fortaleza, CE (Brazil)

2011-02-01

The kinetics and mechanism for electrochemical reduction of haloperidol, a psychotherapeutic drug used in the treatment of schizophrenia, were studied using square wave and cyclic voltammetries allied to a hanging mercury drop electrode. The experimental and voltammetric parameters were optimized at 0.04 mol L{sup -1} Brinton-Robinson buffer (pH 10), with a pulse potential frequency of 100 s{sup -1}, a pulse amplitude of 30 mV and scan increment of 2 mV. Two well-defined peaks were observed, which exhibited properties of fast electron transfer with a strong adsorption process of reactants and products on the electrode surface. The first peak was related to a fast and reversible anion-radical formation originating from the reduction of the carbonyl group, and the second was related to the irreversible reduction of the anion-radical previously formed. Analytical parameters such as: linearity range, equation of the analytical curves, correlation coefficients, detection and quantification limits, recovery efficiency, and relative standard deviation for intraday and interday were compared to similar results obtained by use of the UV-vis spectrophotometry technique, and the analytical results obtained in commercial formulations show that the voltammetric procedure using a hanging mercury drop electrode is suitable for analyzing haloperidol in complex commercial formulation samples.

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

NARCIS (Netherlands)

van Lith, J.H.

2001-01-01

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

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.)

Sources of Error and the Statistical Formulation of M S: m b Seismic Event Screening Analysis

Science.gov (United States)

Anderson, D. N.; Patton, H. J.; Taylor, S. R.; Bonner, J. L.; Selby, N. D.

2014-03-01

The Comprehensive Nuclear-Test-Ban Treaty (CTBT), a global ban on nuclear explosions, is currently in a ratification phase. Under the CTBT, an International Monitoring System (IMS) of seismic, hydroacoustic, infrasonic and radionuclide sensors is operational, and the data from the IMS is analysed by the International Data Centre (IDC). The IDC provides CTBT signatories basic seismic event parameters and a screening analysis indicating whether an event exhibits explosion characteristics (for example, shallow depth). An important component of the screening analysis is a statistical test of the null hypothesis H 0: explosion characteristics using empirical measurements of seismic energy (magnitudes). The established magnitude used for event size is the body-wave magnitude (denoted m b) computed from the initial segment of a seismic waveform. IDC screening analysis is applied to events with m b greater than 3.5. The Rayleigh wave magnitude (denoted M S) is a measure of later arriving surface wave energy. Magnitudes are measurements of seismic energy that include adjustments (physical correction model) for path and distance effects between event and station. Relative to m b, earthquakes generally have a larger M S magnitude than explosions. This article proposes a hypothesis test (screening analysis) using M S and m b that expressly accounts for physical correction model inadequacy in the standard error of the test statistic. With this hypothesis test formulation, the 2009 Democratic Peoples Republic of Korea announced nuclear weapon test fails to reject the null hypothesis H 0: explosion characteristics.

A Note on Burg’s Modified Entropy in Statistical Mechanics

Directory of Open Access Journals (Sweden)

Amritansu Ray

2016-02-01

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

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

Statistical mechanics of driven diffusive systems

CERN Document Server

Schmittmann, B

1995-01-01

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

Engineering quantum mechanics

CERN Document Server

Ahn, Doyeol

2011-01-01

A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...

Transdermal delivery of diclofenac using water-in-oil microemulsion: formulation and mechanistic approach of drug skin permeation.

Science.gov (United States)

Thakkar, Priyanka J; Madan, Parshotam; Lin, Senshang

2014-05-01

The objective of the present investigation was to enhance skin permeation of diclofenac using water-in-oil microemulsion and to elucidate its skin permeation mechanism. The w/o microemulsion formulations were selected based on constructed pseudoternary phase diagrams depending on water solubilization capacity and thermodynamic stability. These formulations were also subjected to physical characterization based on droplet size, viscosity, pH and conductivity. Permeation of diclofenac across rat skin using side-by-side permeation cells from selected w/o microemulsion formulations were evaluated and compared with control formulations. The selected w/o microemulsion formulations were thermodynamically stable, and incorporation of diclofenac sodium into microemulsion did not affect the phase behavior of system. All microemulsion formulations had very low viscosity (11-17 cps) and droplet size range of 30-160 nm. Microemulsion formulations exhibited statistically significant increase in diclofenac permeation compared to oily solution, aqueous solution and oil-Smix solution. Higher skin permeation of diclofenac was observed with low Smix concentration and smaller droplet size. Increase in diclofenac loading in aqueous phase decreased the partition of diclofenac. Diclofenac from the oil phase of microemulsion could directly partition into skin, while diclofenac from the aqueous droplets was carried through skin by carrier effect.

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

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)

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

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Abe, Sumiyoshi

2014-11-01

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown, in particular, how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

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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

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

International Nuclear Information System (INIS)

Israel, W.; Kandrup, H.E.

1984-01-01

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

Influence of dioctyl phthalate (DOP) on the mechanical, optical and thermal properties of formulations for the industrial manufacture of radiation sterilizable medical disposables

Science.gov (United States)

Ahmed, Shamshad; Mehmood, Mazhar; Iqbal, Rashid

2010-03-01

Shelf life of the formulations designed for the industrial manufacture of radiation sterilizable syringes and other medical disposables is a very important issue world over. Radiation compatible formulations were developed earlier in the laboratory by the incorporation of primary and secondary antioxidants along with processing stabilizers in a random polypropylene copolymer. It has been reported in literature that the mobilizing agents namely hydrocarbons, greases, wax and the plasticizer, dioctyl phthalate (DOP) impart radiation resistance to the polypropylene by providing free volume. It was envisaged that the addition of DOP to the afore-mentioned formulation might favorably influence the mechanical, optical and thermal properties of our formulation. To study the influence of addition of DOP on the afore-mentioned properties, the addition of 1%, 2% and 3% of the mobilizer was made, followed by the irradiation of resulting heat pressed sheets to the industrial standard dose of 25 kGy. Two important characteristic mechanical properties to determine the suitability of the radiation sterilized materials comprise angle of breakage and the haze percent. After irradiation and even on accelerated ageing of the irradiated material, the angle of breakage of heat press sheets of formulations containing 1%, 2% and 3% of DOP was found to be 180°, demonstrating the role of DOP, in imparting additional radiation stability. In case of the irradiated control sample, the angle of breakage was much lower. In the heat pressed sheets containing the DOP, a remarkable retention in the tensile strength, percentage elongation at break, along with improved thermal stability was observed. The formulation devoid of DOP demonstrated poor retention of the afore-mentioned characteristic properties .The observed improvement in thermal stability of the formulations containing DOP hints at the likely possibility of reuse of these materials by autoclaving which is considered an additional

Influence of dioctyl phthalate (DOP) on the mechanical, optical and thermal properties of formulations for the industrial manufacture of radiation sterilizable medical disposables

International Nuclear Information System (INIS)

Ahmed, Shamshad; Mehmood, Mazhar; Iqbal, Rashid

2010-01-01

Shelf life of the formulations designed for the industrial manufacture of radiation sterilizable syringes and other medical disposables is a very important issue world over. Radiation compatible formulations were developed earlier in the laboratory by the incorporation of primary and secondary antioxidants along with processing stabilizers in a random polypropylene copolymer. It has been reported in literature that the mobilizing agents namely hydrocarbons, greases, wax and the plasticizer, dioctyl phthalate (DOP) impart radiation resistance to the polypropylene by providing free volume. It was envisaged that the addition of DOP to the afore-mentioned formulation might favorably influence the mechanical, optical and thermal properties of our formulation. To study the influence of addition of DOP on the afore-mentioned properties, the addition of 1%, 2% and 3% of the mobilizer was made, followed by the irradiation of resulting heat pressed sheets to the industrial standard dose of 25 kGy. Two important characteristic mechanical properties to determine the suitability of the radiation sterilized materials comprise angle of breakage and the haze percent. After irradiation and even on accelerated ageing of the irradiated material, the angle of breakage of heat press sheets of formulations containing 1%, 2% and 3% of DOP was found to be 180 deg, demonstrating the role of DOP, in imparting additional radiation stability. In case of the irradiated control sample, the angle of breakage was much lower. In the heat pressed sheets containing the DOP, a remarkable retention in the tensile strength, percentage elongation at break, along with improved thermal stability was observed. The formulation devoid of DOP demonstrated poor retention of the afore-mentioned characteristic properties .The observed improvement in thermal stability of the formulations containing DOP hints at the likely possibility of reuse of these materials by autoclaving which is considered an additional

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

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

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

NARCIS (Netherlands)

Marcolli, Matilde; Cornelissen, Gunther

2014-01-01

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

Geometric statistical inference

International Nuclear Information System (INIS)

Periwal, Vipul

1999-01-01

A reparametrization-covariant formulation of the inverse problem of probability is explicitly solved for finite sample sizes. The inferred distribution is explicitly continuous for finite sample size. A geometric solution of the statistical inference problem in higher dimensions is outlined

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

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de Gier, Jan; Warnaar, Ole

2006-07-01

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

Langevin formulation of quantum dynamics

International Nuclear Information System (INIS)

Roncadelli, M.

1989-03-01

We first show that nonrelativistic quantum mechanics formulated at imaginary-(h/2 π) can formally be viewed as the Fokker-Planck description of a frictionless brownian motion, which occurs (in general) in an absorbing medium. We next offer a new formulation of quantum mechanics, which is basically the Langevin treatment of this brownian motion. Explicitly, we derive a noise-average representation for the transition probability W(X'',t''|X',t'), in terms of the solutions to a Langevin equation with a Gaussian white-noise. Upon analytic continuation back to real-(h/2 π),W(X'',t''|X',t') becomes the propagator of the original Schroedinger equation. Our approach allows for a straightforward application to quantum dynamical problems of the mathematical techniques of classical stochastic processes. Moreover, computer simulations of quantum mechanical systems can be carried out by using numerical programs based on the Langevin dynamics. (author). 19 refs, 1 tab

A sympletic formulation of relativistic particle dynamics

International Nuclear Information System (INIS)

Tulczyjew, W.M.

1977-01-01

Particle mechanics is formulated in terms of sympletic relations and infinitesimal symplectic relations. Generating functions of symplectic relations are shown to be classical counterparts of Green's functions of wave mechanics. (author)

From inverse problems to learning: a Statistical Mechanics approach

Science.gov (United States)

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

2018-01-01

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

A simplectic formulation of relativistic particle dynamics

International Nuclear Information System (INIS)

Tulczyjew, W.M.

1976-12-01

Particle mechanics is formulated in terms of symplectic relations and infinitesimal symplectic relations. Generating functions of symplectic relations are shown to be classical counterparts of Green's functions of wave mechanics. (orig.) [de

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

Science.gov (United States)

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

2009-01-01

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

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

Science.gov (United States)

Ingber, Lester

1994-05-01

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

Influence of Brazilian vegetable oils on mechanical resistence of hair fiber

Directory of Open Access Journals (Sweden)

Maria Valéria Velasco

2015-02-01

Full Text Available Associating the global trend of incorporating active compounds and plants in cosmetic formulations and the vast Brazilian biodiversity, the present work aimed to study the incorporation of Brazilian vegetable oils in hair conditioner formulations, evaluating the mechanical resistance of hair fibers. The following oils were incorporated into base formulations at 5.0 % (w/w: babassu, buriti, andiroba and pequi. The formulations were applied to samples of Caucasian hair, followed by several washing steps, then the evaluation of mechanical strength. It was found that there was no statistically significant difference in mechanical resistance between samples treated with oils and the control between the first and seventh wash cycles. This fact can be explained by the possible low penetration of oils into the cortex, a region responsible for the mechanical properties of the hair fiber, since the grease composition disfavors its diffusion. The common effects of vegetable oils on the cuticle, such as filling in cracks or cavities, lubrication, and increased protein hydrophobicity cannot be excluded. The oils tested in this work were not able to raise or protect hair tresses. However, additional studies are required in order to establish the effects of oil treatments, particularly in damaged hair.

Controlled release hydrophilic matrix tablet formulations of isoniazid: design and in vitro studies.

Science.gov (United States)

Hiremath, Praveen S; Saha, Ranendra N

2008-01-01

The aim of the present investigation was to develop oral controlled release matrix tablet formulations of isoniazid using hydroxypropyl methylcellulose (HPMC) as a hydrophilic release retardant polymer and to study the influence of various formulation factors like proportion of the polymer, polymer viscosity grade, compression force, and release media on the in vitro release characteristics of the drug. The formulations were developed using wet granulation technology. The in vitro release studies were performed using US Pharmacopoeia type 1 apparatus (basket method) in 900 ml of pH 7.4 phosphate buffer at 100 rpm. The release kinetics was analyzed using Korsmeyer-Peppas model. The release profiles were also analyzed using statistical method (one-way analysis of variance) and f (2) metric values. The release profiles found to follow Higuchi's square root kinetics model irrespective of the polymer ratio and the viscosity grade used. The results in the present investigation confirm that the release rate of the drug from the HPMC matrices is highly influenced by the drug/HPMC ratio and viscosity grade of the HPMC. Also, the effect of compression force and release media was found to be significant on the release profiles of isoniazid from HPMC matrix tablets. The release mechanism was found to be anomalous non-Fickian diffusion in all the cases. In the present investigation, a series of controlled release formulations of isoniazid were developed with different release rates and duration so that these formulations could further be assessed from the in vivo bioavailability studies. The formulations were found to be stable and reproducible.

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

International Nuclear Information System (INIS)

Rogers, F.J.

1984-01-01

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

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

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

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

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

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

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

International Nuclear Information System (INIS)

Daicic, J.; Frankel, N.E.

1993-01-01

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

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

International Nuclear Information System (INIS)

Boyanovsky, D.; Naon, C.M.

1990-01-01

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

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

Two statistical mechanics aspects of complex networks

Science.gov (United States)

Thurner, Stefan; Biely, Christoly

2006-12-01

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

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

Science.gov (United States)

Aslin, Richard N

2017-01-01

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

Thermodynamic Bethe ansatz with Haldane statistics

International Nuclear Information System (INIS)

Bytsko, A.G.; Fring, A.

1998-01-01

We derive the thermodynamic Bethe ansatz equation for the situation in which the statistical interaction of a multi-particle system is governed by Haldane statistics. We formulate a macroscopical equivalence principle for such systems. Particular CDD ambiguities play a distinguished role in compensating the ambiguity in the exclusion statistics. We derive Y-systems related to generalized statistics. We discuss several fermionic, bosonic and anyonic versions of affine Toda field theories and Calogero-Sutherland type models in the context of generalized statistics. (orig.)

Proof of the Spin Statistics Connection 2: Relativistic Theory

Science.gov (United States)

Santamato, Enrico; De Martini, Francesco

2017-12-01

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

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

International Nuclear Information System (INIS)

Gonchar, N.S.

1986-01-01

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

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

Bioavailability of two oral formulations of triazolam using radioreceptor assay

Energy Technology Data Exchange (ETDEWEB)

Lapka, R; Cepelakova, H; Rejholec, V; Franc, Z

1986-04-01

The radioreceptor assay (RRA) was used to quantitate plasma triazolam concentration in eight female volunteers following single 0.5 mg doses of two tablet formulations in a cross-over study. Bioavailability in terms of area under the plasma concentration versus time curve, maximum plasma concentration, time to maximum, and mean residence time was not statistically significantly different from one formulation to the other.

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

NARCIS (Netherlands)

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

2004-01-01

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

Formulation and Evaluation of Tramadol HCl Matrix Tablets Using ...

African Journals Online (AJOL)

Formulation and Evaluation of Tramadol HCl Matrix Tablets Using Carbopol ... to 83 % compared with the release rate of 99 % for the formulation with D:P ratio of 10:3. Kinetic analysis indicates that drug release mechanism was anomalous ...

[Efficient Pharmaceutical Formulation Designs and Their Development Using Mathematical and Statistical Analysis].

Science.gov (United States)

Iwao, Yasunori

2015-01-01

With the aim of directly predicting the functionality and mechanism of pharmaceutical excipients, we investigated an analysis method based on available surface area (S(t)), which is the surface area of a drug in direct contact with the external solvent during dissolution. First, to study the effect of lubricant concentration on the dissolution rate of acetaminophen (APAP), the dissolution behaviors as well as the change over time in S(t) of APAP tablets were examined. In the dissolution tests, a retarded dissolution of APAP was not observed with new lubricant triglycerin full behenate (TR-FB), whereas magnesium stearate (Mg-St) retarded the dissolution. The S(t) profiles for APAP with Mg-St at>0.5% showed downward curvature indicating a gradual decrease in surface area over time. Conversely, with TR-FB, even when its concentration was increased, the S(t) profile for APAP had a maximum value. The differences between Mg-St and TR-FB could be explained by the differences in extensibility deriving from their morphology. Next, we evaluated the effect of disintegtant concentration using five disintegrants. When disintegrant was added to ethenzamide tablet formulation, an increase in the dissolution rate and S(t) dependent on disintegrant concentration was observed, according to the type of disintegrant. It was found that the water absorption ability of disintegrants had strong correlations with the parameters of S(t). Taken together, this study demonstrates that analysis of S(t) can directly provide useful information, especially about the functionality of pharmaceutical excipients.

Thermodynamics and statistical mechanics an integrated approach

CERN Document Server

Shell, M Scott

2015-01-01

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

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

International Nuclear Information System (INIS)

Haken, H.

1980-01-01

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

Variational and potential formulation for stochastic partial differential equations

International Nuclear Information System (INIS)

Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T

2006-01-01

Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)

Application of statistical experimental design to study the formulation variables influencing the coating process of lidocaine liposomes.

Science.gov (United States)

González-Rodríguez, M L; Barros, L B; Palma, J; González-Rodríguez, P L; Rabasco, A M

2007-06-07

In this paper, we have used statistical experimental design to investigate the effect of several factors in coating process of lidocaine hydrochloride (LID) liposomes by a biodegradable polymer (chitosan, CH). These variables were the concentration of CH coating solution, the dripping rate of this solution on the liposome colloidal dispersion, the stirring rate, the time since the liposome production to the liposome coating and finally the amount of drug entrapped into liposomes. The selected response variables were drug encapsulation efficiency (EE, %), coating efficiency (CE, %) and zeta potential. Liposomes were obtained by thin-layer evaporation method. They were subsequently coated with CH according the experimental plan provided by a fractional factorial (2(5-1)) screening matrix. We have used spectroscopic methods to determine the zeta potential values. The EE (%) assay was carried out in dialysis bags and the brilliant red probe was used to determine CE (%) due to its property of forming molecular complexes with CH. The graphic analysis of the effects allowed the identification of the main formulation and technological factors by the analysis of the selected responses and permitted the determination of the proper level of these factors for the response improvement. Moreover, fractional design allowed quantifying the interactions between the factors, which will consider in next experiments. The results obtained pointed out that LID amount was the predominant factor that increased the drug entrapment capacity (EE). The CE (%) response was mainly affected by the concentration of the CH solution and the stirring rate, although all the interactions between the main factors have statistical significance.

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.

Institutional statism: an overview of the formulation of the taxi recapitalisation policy

Directory of Open Access Journals (Sweden)

D. van Schalkwyk

2008-07-01

Full Text Available This article provides an overview of the government’s formulation of the taxi recapitalisation policy which is aimed at regulating the minibus taxi industry. Coupled with a brief social and politico-historical context of the policy, the aim is to highlight the government’s statist conduct in the formulation of the recapitalisation policy. The minibus taxi industry started to fulfil a prominent role in the 1970s as a result of a loophole in the legislation of the former apartheid government. It is currently the most accessible mode of public transport and conveys 65 per cent of the country’s commuters daily. Consequently, the Industry is an imperative force to be considered by the government in its formulation of transport policies. However, the industry is characterised by numerous problems, including a high rate of minibus taxis involved in accidents, unroadworthy vehicles and violence. It is in this context that the government formulated both the original and revised versions of the recapitalisation policy. However, the formulation of the policy has been problematic. The government followed a statist approach during the formulation process when it directed the course of the process according to its interests and without adequate consultation with relevant role players.

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)

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)

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Formulation and Evaluation of Ascorbic acid Tablets by Direct ...

African Journals Online (AJOL)

Formulation and Evaluation of Ascorbic acid Tablets by Direct Compression using Microcrystalline Starch as a Direct Compression Excipient. ... Abstract. PURPOSE: To evaluate the tableting properties of microcrystalline starch (MCS) used as a direct ... RESULTS: Mechanical properties of tablets formulated with MCS were

Intercomparison of chemical mechanisms for air quality policy formulation and assessment under North American conditions.

Science.gov (United States)

Derwent, Richard

2017-07-01

The intercomparison of seven chemical mechanisms for their suitability for air quality policy formulation and assessment is described. Box modeling techniques were employed using 44 sets of background environmental conditions covering North America to constrain the chemical development of the longer lived species. The selected mechanisms were modified to enable an unbiased assessment of the adequacy of the parameterizations of photochemical ozone production from volatile organic compound (VOC) oxidation in the presence of NO x . Photochemical ozone production rates responded differently to 30% NO x and VOC reductions with the different mechanisms, despite the striking similarities between the base-case ozone production rates. The 30% reductions in NO x and VOCs also produced changes in OH. The responses in OH to 30% reductions in NO x and VOCs appeared to be more sensitive to mechanism choice, compared with the responses in the photochemical ozone production rates. Although 30% NO x reductions generally led to decreases in OH, 30% reductions in VOCs led to increases in OH, irrespective of mechanism choice and background environmental conditions. The different mechanisms therefore gave different OH responses to NO x and VOC reductions and so would give different responses in terms of changes in the fate and behavior of air toxics, acidification and eutrophication, and fine particle formation compared with others, in response to ozone control strategies. Policymakers need to understand that there are likely to be inherent differences in the responses to ozone control strategies between different mechanisms, depending on background environmental conditions and the extents of NO x and VOC reductions under consideration. The purpose of this paper is to compare predicted ozone responses to NO x and VOC reductions with seven chemical mechanisms under North American conditions. The good agreement found between the tested mechanisms should provide some support for their

Statistical fluid mechanics

CERN Document Server

Monin, A S

2007-01-01

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

Multiscale representation of generating and correlation functions for some models of statistical mechanics and quantum field theory

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

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

Science.gov (United States)

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

2018-05-01

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

Evaluation of mechanical properties of steel wire ropes by statistical methods

Directory of Open Access Journals (Sweden)

Boroška Ján

1999-12-01

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

Finite Elements Based on Strong and Weak Formulations for Structural Mechanics: Stability, Accuracy and Reliability

Directory of Open Access Journals (Sweden)

Francesco Tornabene

2017-07-01

Full Text Available The authors are presenting a novel formulation based on the Differential Quadrature (DQ method which is used to approximate derivatives and integrals. The resulting scheme has been termed strong and weak form finite elements (SFEM or WFEM, according to the numerical scheme employed in the computation. Such numerical methods are applied to solve some structural problems related to the mechanical behavior of plates and shells, made of isotropic or composite materials. The main differences between these two approaches rely on the initial formulation – which is strong or weak (variational – and the implementation of the boundary conditions, that for the former include the continuity of stresses and displacements, whereas in the latter can consider the continuity of the displacements or both. The two methodologies consider also a mapping technique to transform an element of general shape described in Cartesian coordinates into the same element in the computational space. Such technique can be implemented by employing the classic Lagrangian-shaped elements with a fixed number of nodes along the element edges or blending functions which allow an “exact mapping” of the element. In particular, the authors are employing NURBS (Not-Uniform Rational B-Splines for such nonlinear mapping in order to use the “exact” shape of CAD designs.

Physical-Mechanical characterization of cosmetic formulations and correlation between instrumental measurements and sensorial properties.

Science.gov (United States)

Calixto, L S; Maia Campos, P M B G

2017-10-01

The correct choice of raw materials in the development of cosmetic formulations is essential for obtaining stable and pleasant skin care products. Therefore, rheological, texture and sensory analyses are important to understand the behaviour and stability of the formulations. In this context, the aim of this study was to develop cosmetic formulations containing or not (vehicle) UV filters and chicory root extract, to evaluate their stability as well as to characterize their physical and texture properties and correlate them with the sensory attributes. Four formulations containing organic UV filters and chicory extract, each alone or in combination, were developed and evaluated for 180 days with a cone and plate rheometer, a texture analyzer and consumer's sensorial analysis. Thus, the data obtained were correlated to observe the different influences. The developed formulations remained stable after 180 days regarding macroscopic aspects, organoleptic characteristics and pH values. The addition of the UV filters alone and in combination with the active substance resulted in significant increases in rheology properties, viscosity and consistency. The formulation with the active ingredient showed significant decreases in the texture parameters after 180 days, mainly due to its polysaccharide inulin. All formulations obtained high scores in sensorial parameters. A strong correlation was mainly found between spreadability and work of shear, and between the texture parameters. The raw materials strongly influenced the physical, texture and sensorial parameters. Finally, the UV filters showed a greater influence on the results of the formulations than the chicory root extract. In conclusion, the association of the mentioned methods allows the correct choice of ingredients and their combinations. © 2017 Society of Cosmetic Scientists and the Société Française de Cosmétologie.

Generalized quantum statistics

International Nuclear Information System (INIS)

Chou, C.

1992-01-01

In the paper, a non-anyonic generalization of quantum statistics is presented, in which Fermi-Dirac statistics (FDS) and Bose-Einstein statistics (BES) appear as two special cases. The new quantum statistics, which is characterized by the dimension of its single particle Fock space, contains three consistent parts, namely the generalized bilinear quantization, the generalized quantum mechanical description and the corresponding statistical mechanics

Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

Science.gov (United States)

Cierniak, Robert; Lorent, Anna

2016-09-01

The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. Copyright © 2016 Elsevier Ltd. All rights reserved.

The Brandeis Dice Problem and Statistical Mechanics

Science.gov (United States)

van Enk, Steven J.

2014-11-01

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

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

International Nuclear Information System (INIS)

Tsallis, Constantino; Tirnakli, Ugur

2010-01-01

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

Casein Films: The Effects of Formulation, Environmental Conditions and the Addition of Citric Pectin on the Structure and Mechanical Properties

Directory of Open Access Journals (Sweden)

Laetitia M. Bonnaillie

2014-07-01

Full Text Available Thin casein films for food packaging applications reportedly possess good strength and low oxygen permeability, but low elasticity and high sensitivity to moisture. Modifying the films to target specific behaviors depending on environmental conditions can enable a variety of commercial applications for casein-based films. The mechanical properties of solvent-cast (15% solids calcium-caseinate/glycerol films (CaCas:Gly ratio of 3:1 were characterized as a function of processing and environmental conditions, including film thickness, solution formulation and ambient humidity (from 22% to 70% relative humidity (RH at ~20 °C. At constant RH, the elongation at break (EAB had a strong positive dependence on the film thickness. When RH increased, the tensile strength (TS and modulus (E decreased approximately linearly, while EAB increased. From 0.05% to 1% (w/w of citric pectin (CP was then incorporated into CaCas/Gly films following seven different formulations (mixing sequences, to alter the protein network and to evaluate the effects of CP on the tensile properties of CaCas/Gly/CP films. At constant film thickness and ~60% RH, the addition of 0.1% or 1.0% CP to the films considerably increased or decreased EAB, TS and E in different directions and to different extents, depending on the formulation, while optical micrographs also showed vastly differing network configurations, suggesting complex formulation- and stoichiometry-dependent casein-pectin interactions within the dried films. Depending on the desired film properties and utilization conditions, pectin may be a useful addition to casein film formulations for food packaging applications.

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

Czech Academy of Sciences Publication Activity Database

Jackson, G.; Nezbeda, Ivo

2011-01-01

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

A study on the design, formulation and effectiveness of chewing gums containing Chlorhexidine Gluconate in the prevention of dental plaque

Directory of Open Access Journals (Sweden)

Kolahi Kazerani G

2003-08-01

Full Text Available Statement of Problem: The role of the microbial plaque in caries etiology and periodontal diseases has been"nproved and the mechanical methods for plaque control have special limitations, consequently, chemical"nmethods have been suggested. One of the most effective materials is Chlorhexidine Gluconate that is"ncommonly used as mouth rinses. However, the medicated formulations of chewing gums, due to several"nproperties, have been paid attention. It should be noted that a new formulation to satisfy the consumers' taste"nseems necessary."nPurpose: The aim of this study was to present a new formulation for chewing gums containing chlorhexidine"nto achieve a pleasant taste coupled with their effectiveness and anti-plaque properties maintenance."nMaterials and Methods: In this double blind, crossover, prospective clinical trial, 18 volunteers were"ninvestigated. Chlorhexidine Gluconate was used and added to the gum-base by Manitole. In order to cover the"nbitter taste of the drug Aspartam, mint essence and Mentole were used. After gums production, the profile of"ndrug dissolution was evaluated by jaw movement simulating system. It took 5 days to study each type of"nchewing gums without any mechanical plaque control method. Medicated and placebo chewing gums were"nidentical in shape, size, color and formulation. The washout period was 2 days. Chewing gums were used"nevery 12 hours for 20 minutes. To determine plaque score, Turesky- Gilmore- Glickman modification index"nwas used. Other variables including: subjective evaluation of taste, cleansing effect and taste disturbance were"nassessed through filling a checklist. The data were analyzed by Paired t test and Wilcoxon test."nResults: During 20 mins, 80% of the drug was released from the gum-base. The mean difference of plaque"nscore between the initial and final stages at the first trial was -0.1589 and at the second trial was 2.994 which"nwas statistically significant (P<0.001. Subjective

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

Science.gov (United States)

Ingber, Lester

1991-09-01

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

Multiple commodities in statistical microeconomics: Model and market

Science.gov (United States)

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.

Shrinkage / stress reduction and mechanical properties improvement in restorative composites formulated with thio-urethane oligomers.

Science.gov (United States)

Bacchi, Atais; Yih, Jonathan A; Platta, Jacqueline; Knight, Joseph; Pfeifer, Carmem S

2018-02-01

Thio-urethane oligomers (TUs) have been shown to favorably modify methacrylate networks to reduce stress and significantly increase fracture toughness. Since those are very desirable features in dental applications, the objective of this work was to characterize restorative composites formulated with the addition of TUs. TUs were synthesized by combining thiols - pentaerythritol tetra-3-mercaptopropionate (PETMP) or trimethylol-tris-3-mercaptopropionate (TMP) - with isocyanates - 1,6-Hexanediol-diissocyante (HDDI) (aliphatic) or 1,3-bis(1-isocyanato-1-methylethyl)benzene (BDI) (aromatic) or dicyclohexylmethane 4,4'-Diisocyanate (HMDI) (cyclic), at 1:2 isocyanate:thiol, leaving pendant thiols. 20wt% TU were added to BisGMA-TEGDMA (70-30%). To this organic matrix, 70wt% silanated inorganic fillers were added. Near-IR was used to follow methacrylate conversion and rate of polymerization (Rp max ). Mechanical properties were evaluated in three-point bending (ISO 4049) for flexural strength/modulus (FS/FM) and toughness (T), and notched specimens (ASTM Standard E399-90) for fracture toughness (K IC ). Polymerization stress (PS) was measured on the Bioman. Volumetric shrinkage (VS) was measured with the bonded disk technique. Glass transition temperature (Tg) and heterogeneity of network were obtained with dynamic mechanical analysis. The addition of TUs led to an increase in mechanical properties (except for Tg and FS). Fracture toughness ranged from 1.6-1.94MPam 1/2 for TU-modified groups, an increase of 33-61% in relation to the control (1.21 ± 0.1MPam 1/2 ). Toughness showed a two-fold increase in relation to the control: from 0.91MPa to values ranging from 1.70-1.95MPa. Flexural modulus was statistically higher for the TU-modified groups. The Tg, as expected, decreased for all TU groups due to the greater flexibility imparted to the network (which also explains the increase in toughness and fracture toughness). Narrower tan-delta peaks suggest more homogeneous

Bioequivalence of a new liquid formulation of benazepril compared with the reference tablet product.

Science.gov (United States)

Kelers, K; Devi, J L; Anderson, G A; Zahra, P; Vine, J H; Whittem, T

2013-08-01

To compare the bioequivalence and 'switchability' of two formulations of benazepril (tablet and liquid) after oral administration. Randomised cross-over design, followed by parallel comparison. Twelve mixed-breed dogs were administered either a tablet (Group A) or liquid formulation (Group B) of benazepril orally at 0.45 mg/kg daily for 4 days. With no washout period, the dogs then received the alternative treatment at the same dose for a further 4 days. Blood samples taken prior to treatment and serially after treatment were analysed for plasma concentrations of benazepril and benazeprilat and the activity and concentration of angiotensin-converting enzyme (ACE). The calculated percentage inhibition of ACE was defined as the primary outcome variable. No statistically significant differences were found between groups A and B for any variable evaluated. The mean (± SD) percentage of ACE inhibition was 85.5 ± 7.04% for the liquid formulation and 85.9 ± 6.66% for the tablet formulation. The mean of the ratios was 1.00 (80% confidence interval 0.96-1.04). No evaluated effect term (sequence, formulation or period) had any statistical effect on any outcome variable. This study supports a conclusion that, based on pharmacodynamic response, the liquid formulation of benazepril is bioequivalent to the reference tablet formulation. Further, the lack of a sequence effect supports the switchability of these two formulations. © 2013 Australian Veterinary Association.

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

Science.gov (United States)

Niss, Martin

2009-01-01

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

USING STATISTICAL SURVEY IN ECONOMICS

Directory of Open Access Journals (Sweden)

Delia TESELIOS

2012-01-01

Full Text Available Statistical survey is an effective method of statistical investigation that involves gathering quantitative data, which is often preferred in statistical reports due to the information which can be obtained regarding the entire population studied by observing a part of it. Therefore, because of the information provided, polls are used in many research areas. In economics, statistics are used in the decision making process in choosing competitive strategies in the analysis of certain economic phenomena, the formulation of forecasts. Economic study presented in this paper is to illustrate how a simple random sampling is used to analyze the existing parking spaces situation in a given locality.

Putative skin-protective formulations in preventing and/or inhibiting experimentally-produced irritant and allergic contact dermatitis.

Science.gov (United States)

Zhai, H; Willard, P; Maibach, H I

1999-10-01

The effectiveness of skin protective formulations was evaluated in a previously-described in vivo human model. All formulations failed to inhibit ammonium hydroxide and urea irritation. Only paraffin wax in cetyl alcohol statistically (plauryl sulfate irritation. Paraffin wax in cetyl alcohol was quantitatively the most effective formulation. These results suggest that some formulations may provide protective effects against certain, but not all, irritants or allergens.

Statistical mechanics of fluids under internal constraints: Rigorous results for the one-dimensional hard rod fluid

International Nuclear Information System (INIS)

Corti, D.S.; Debenedetti, P.G.

1998-01-01

The rigorous statistical mechanics of metastability requires the imposition of internal constraints that prevent access to regions of phase space corresponding to inhomogeneous states. We derive exactly the Helmholtz energy and equation of state of the one-dimensional hard rod fluid under the influence of an internal constraint that places an upper bound on the distance between nearest-neighbor rods. This type of constraint is relevant to the suppression of boiling in a superheated liquid. We determine the effects of this constraint upon the thermophysical properties and internal structure of the hard rod fluid. By adding an infinitely weak and infinitely long-ranged attractive potential to the hard core, the fluid exhibits a first-order vapor-liquid transition. We determine exactly the equation of state of the one-dimensional superheated liquid and show that it exhibits metastable phase equilibrium. We also derive statistical mechanical relations for the equation of state of a fluid under the action of arbitrary constraints, and show the connection between the statistical mechanics of constrained and unconstrained ensembles. copyright 1998 The American Physical Society

Formulation and Evaluation of Rifampicin Liposomes for Buccal Drug Delivery.

Science.gov (United States)

Lankalapalli, Srinivas; Tenneti, V S Vinai Kumar

2016-01-01

Drug delivery through liposomes offers several advantages, but still challenging to the researchers for the use of liposomes as carriers in drug delivery due to their poor physical stability, unpredictable drug encapsulation and systemic availability of the loaded drug. The present investigation was planned with an objective to prepare Rifampicin loaded liposomes by using response surface methodology of statistical 32 factorial design and further to formulate them into pastilles for deliver through buccal route thereby to enhance systemic absorption. Rifampicin liposomes were prepared by using different ratios of soya lecithin and cholesterol by solvent Injection method. These liposomes were characterized by using optical microscopy, Scanning Electron Microscopy (SEM) and evaluated for particle size, entrapment efficiency (EE), in vitro and ex vivo drug release. Main effects and interaction terms of the formulation variables were evaluated quantitatively using a mathematical statistical model approach showing that both independent variables have significant (P value value: 0.0273), percentage entrapment efficiency (P value: 0.0096), percentage drug release through dialysis membrane (P value: 0.0047) and percentage drug release through porcine buccal membrane (P value: 0.0019). The statistical factorial design of liposomal formulations fulfilled all the requirements of the target set and exhibited suitable values for the selected test parameters. Pastilles were prepared for liposomes using glycerol gelatin base and were found to be soft, smooth with uniform drug content and drug release.

Ether formulations of relativity

International Nuclear Information System (INIS)

Duffy, M.C.

1980-01-01

Contemporary ether theories are surveyed and criticised, especially those formally identical to orthodox Relativity. The historical development of Relativity, Special and General, in terms of an ether, is briefly indicated. Classical interpretations of Generalized Relativity using ether are compared to Euclidean formulations using a background space. The history of a sub-group of theories, formulating a 'new' Relativity involving modified transforms, is outlined. According to the theory with which they agree, recent supposed detections of drift are classified and criticised. Cosmological evidence suggesting an ether is mentioned. Only ether theories formally identical to Relativity have been published in depth. They stand criticised as being contrary to the positivist spirit. The history of mechanical analogues is traced, from Hartley's representing gravitating matter as spherical standing waves, to recent suggestions that vortex-sponge might model electromagnetic, quantum, uncertainty and faster-than-light phenomena. Contemporary theories are particular physical theories, themselves 'second interpretations' of a primary mathematical model. Mechanical analogues are auxiliary, not necessary, to other theory, disclosing relationships between classical and non-classical descriptions of assemblies charging state. The ether-relativity polemic, part of a broader dispute about relativity, is founded on mistaken conceptions of the roles of mathematical and physical models, mechanical analogues; and a distored view of history, which indicates that ether theories have become relativistic. (author)

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

DEFF Research Database (Denmark)

Pomogaev, Vladimir; Pomogaeva, Anna; Avramov, Pavel

2011-01-01

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

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

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

International Nuclear Information System (INIS)

Oefverbeck, P.; Oestberg, G.

1977-01-01

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

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

Science.gov (United States)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-06-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

International Nuclear Information System (INIS)

Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

2012-01-01

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.

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

International Nuclear Information System (INIS)

Ichinose, Shoichi

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Cohen, E G.D.

1985-01-01

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

Statistical black-hole thermodynamics

International Nuclear Information System (INIS)

Bekenstein, J.D.

1975-01-01

Traditional methods from statistical thermodynamics, with appropriate modifications, are used to study several problems in black-hole thermodynamics. Jaynes's maximum-uncertainty method for computing probabilities is used to show that the earlier-formulated generalized second law is respected in statistically averaged form in the process of spontaneous radiation by a Kerr black hole discovered by Hawking, and also in the case of a Schwarzschild hole immersed in a bath of black-body radiation, however cold. The generalized second law is used to motivate a maximum-entropy principle for determining the equilibrium probability distribution for a system containing a black hole. As an application we derive the distribution for the radiation in equilibrium with a Kerr hole (it is found to agree with what would be expected from Hawking's results) and the form of the associated distribution among Kerr black-hole solution states of definite mass. The same results are shown to follow from a statistical interpretation of the concept of black-hole entropy as the natural logarithm of the number of possible interior configurations that are compatible with the given exterior black-hole state. We also formulate a Jaynes-type maximum-uncertainty principle for black holes, and apply it to obtain the probability distribution among Kerr solution states for an isolated radiating Kerr hole

Aftershock Energy Distribution by Statistical Mechanics Approach

Science.gov (United States)

Daminelli, R.; Marcellini, A.

2015-12-01

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

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

Science.gov (United States)

Pearce, Marcus T

2018-05-11

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

Mechanical Properties Studies of Components Formulation for Mixing Process Contain of Polypropylene, Polyethylene, and Aluminium Powder

Science.gov (United States)

Hamsi, A.; Dinzi, R.

2017-03-01

Certain powder and others components can induce toxic reactions if not properly handled in the mixing stage. During handling, the small particles can become airborne and be trapped in the lungs, another concern is inhomogeneities in the mixing process. Uniform quantities of the particles of the components are needed in all portions of the mixture. This paper reports the results of mechanical properties studies of mixing three components formulation for mixing process. Contain of Polyethylene (PE), Polyprophylene (PP) and Aluminium Powder. Powder mixer, Autodesk mold flow and computer based on excell method was carried out to study the influence of each formulation component on the flow %, PE 20% and Aluminium powder 2%. Macroscopic optic and macro photo was carried out to identify the homogenity of mixing, tensile test for identify the strength of component after mixing. Finally the optimal tensile test with composition PP 785,PE 20% and Aluminium powder 2% at speed 52 rpm, temperature 1500C, the tensile strength 20,92 N/mm2. At temperature 1600C, speed 100 rpm the optimum tensile strength 17,91 N/mm2. The result of simulation autodesk mold flow adviser the filling time 6 seconds. Otherwise on manual hot hidraulic press the time of filling 10 seconds.

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

Directory of Open Access Journals (Sweden)

Sheng Wang

2007-10-01

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

A statistical mechanical model of economics

Science.gov (United States)

Lubbers, Nicholas Edward Williams

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

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 shear lag model - unraveling the size effect in hierarchical composites.

Science.gov (United States)

Wei, Xiaoding; Filleter, Tobin; Espinosa, Horacio D

2015-05-01

Numerous experimental and computational studies have established that the hierarchical structures encountered in natural materials, such as the brick-and-mortar structure observed in sea shells, are essential for achieving defect tolerance. Due to this hierarchy, the mechanical properties of natural materials have a different size dependence compared to that of typical engineered materials. This study aimed to explore size effects on the strength of bio-inspired staggered hierarchical composites and to define the influence of the geometry of constituents in their outstanding defect tolerance capability. A statistical shear lag model is derived by extending the classical shear lag model to account for the statistics of the constituents' strength. A general solution emerges from rigorous mathematical derivations, unifying the various empirical formulations for the fundamental link length used in previous statistical models. The model shows that the staggered arrangement of constituents grants composites a unique size effect on mechanical strength in contrast to homogenous continuous materials. The model is applied to hierarchical yarns consisting of double-walled carbon nanotube bundles to assess its predictive capabilities for novel synthetic materials. Interestingly, the model predicts that yarn gauge length does not significantly influence the yarn strength, in close agreement with experimental observations. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

What type of statistical model to choose for the analysis of radioimmunoassays

International Nuclear Information System (INIS)

Huet, S.

1984-01-01

The current techniques used for statistical analysis of radioimmunoassays are not very satisfactory for either the statistician or the biologist. They are based on an attempt to make the response curve linear to avoid complicated computations. The present article shows that this practice has considerable effects (often neglected) on the statistical assumptions which must be formulated. A more strict analysis is proposed by applying the four-parameter logistic model. The advantages of this method are: the statistical assumptions formulated are based on observed data, and the model can be applied to almost all radioimmunoassays [fr

A Cultural Formulation Approach to Career Assessment and Career Counseling with Asian American Clients

Science.gov (United States)

Leong, Frederick T. L.; Hardin, Erin E.; Gupta, Arpana

2010-01-01

Using the cultural formulations approach to career assessment and career counseling, the current article applies it specifically to Asian American clients. The approach is illustrated by using the "Diagnostic and Statistical Manual of Mental Disorders" fourth edition ("DSM-IV") Outline for Cultural Formulations that consists of the following five…

Experimental statistics

CERN Document Server

Natrella, Mary Gibbons

1963-01-01

Formulated to assist scientists and engineers engaged in army ordnance research and development programs, this well-known and highly regarded handbook is a ready reference for advanced undergraduate and graduate students as well as for professionals seeking engineering information and quantitative data for designing, developing, constructing, and testing equipment. Topics include characterizing and comparing the measured performance of a material, product, or process; general considerations in planning experiments; statistical techniques for analyzing extreme-value data; use of transformations

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

KAUST Repository

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

2014-01-01

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

THE STUDY ON THE EFFECT OF FORMULATION VARIABLES ON IN VITRO FLOATING TIME AND THE RELEASE PROPERTIES OF A FLOATING DRUG DELIVERY SYSTEM BY A STATISTICAL OPTIMIZATION TECHNIQUE

Directory of Open Access Journals (Sweden)

C. NARENDRA

2008-03-01

Full Text Available The present investigation concerns the evaluation of the effect of formulation variables on in vitro floating time and the release properties in developing a floating drug delivery system (FDDS containing a highly water soluble drug metoprolol tartrate (MT in the presence of a gas generating agent. A 32 full factorial design was employed in formulating the FDDS containing hydroxyl propylmethylcellulose (HPMC K4M and sodium carboxymethylcellulose (NaCMC as swellable polymers. Drug-to-polymer ratio and polymer-to-polymer ratio were included as independent variables. The main effect and the interaction terms were quantitatively evaluated by a quadratic model to predict formulations with the floating time desired, and the release properties. It was found that only drug-to-polymer ratio and its quadratic term were found to be significantly affective for all the response variables. Non-Fickian transport was confirmed as a release mechanism from the optimized formulations. The desirability function was used to optimize the response variables, each having a different target, and the observed responses were highly agreed with experimental values. The results demonstrate the feasibility of the model in the development of FDDS containing a highly water-soluble drug MT.

Post electrical or lightning injury syndrome: a proposal for an American Psychiatric Association's Diagnostic and Statistical Manual formulation with implications for treatment.

Science.gov (United States)

Andrews, Christopher J; Reisner, Andrew D; Cooper, Mary Ann

2017-09-01

In the past, victims of electrical and lightning injuries have been assessed in a manner lacking a systematic formulation, and against ad hoc criteria, particularly in the area of neuropsychological disability. In this manner patients have, for example, only been partially treated, been poorly or incorrectly diagnosed, and have been denied the full benefit of compensation for their injuries. This paper contains a proposal for diagnostic criteria particularly for the neuropsychological aspects of the post injury syndrome. It pays attention to widely published consistent descriptions of the syndrome, and a new cluster analysis of post electrical injury patients. It formulates a proposal which could be incorporated into future editions of the American Psychiatric Association's Diagnostic and Statistical Manual (DSM). The major neuropsychological consequences include neurocognitive dysfunction, and memory subgroup dysfunction, with ongoing consequences, and sometimes including progressive or delayed psychiatric, cognitive, and/or neurological symptoms. The proposed diagnostic criteria insist on a demonstrated context for the injury, both specifying the shock circumstance, and also physical consequences. It allows for a certain delay in onset of symptoms. It recognizes exclusory conditions. The outcome is a proposal for a DSM classification for the post electrical or lightning injury syndrome. This proposal is considered important for grounding patient treatment, and for further treatment trials. Options for treatment in electrical or lightning injury are summarised, and future trials are foreshadowed.

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

Fractal multiplication of electron avalanches and streamers: new mechanism of electrical breakdown?

International Nuclear Information System (INIS)

Ficker, T

2007-01-01

Long-lasting problems concerning peculiar statistical behaviour of high populated electron avalanches have been analysed. These avalanches are precursors of streamer breakdown in gases. The present streamer theory fails in explaining severe systematic deviations from the Furry statistics that is believed to be a governing statistical law. Such a deviated behaviour of high populated avalanches seems to be a consequence of a special pre-breakdown mechanism that is rather different from that known so far in discharge physics. This analysis tends towards formulating a modified theoretical concept supplementing the streamer theory by a new statistical view of pre-streamer states. The correctness of the concept is corroborated by a series of experiments

Testing quantum mechanics at DaφNe

International Nuclear Information System (INIS)

Di Domenica, A.

1997-01-01

After a brief introduction to EPR-paradox and Bell's inequality, it is shown that a Bell-like inequality can be formulated for the neutral kaon system at a Φ-factory using the Pauli spin formalism, in our case called K-spin, and taking into account CP violation. Experimental methods to reveal tiny violations of this inequality by quantum mechanics are discussed. The statistical accuracy achievable at DAΦNE, the Frascati Φ-factory, seems adequate to successfully perform such a test. (author)

A statistical study on fracture toughness data of Japanese RPVS

International Nuclear Information System (INIS)

Sakai, Y.; Ogura, N.

1987-01-01

In a cooperative study for investigating fracture toughness on pressure vessel steels produced in Japan, a number of heats of ASTM A533B cl.1 and A508 cl.3 steels have been studied. Approximately 3000 fracture toughness data and 8000 mechanical properties data were obtained and filed in a computer data bank. Statistical characterization of toughness data in the transition region has been carried out using the computer data bank. Curve fitting technique for toughness data has been examined. Approach using the function to model the transition behaviours of each toughness has been applied. The aims of fitting curve technique were as follows; (1) Summarization of an enormous toughness data base to permit comparison heats, materials and testing methods; (2) Investigating the relationships among static, dynamic and arrest toughness; (3) Examining the ASME K(IR) curve statistically. The methodology used in this study for analyzing a large quantity of fracture toughness data was found to be useful for formulating a statistically based K(IR) curve. (orig./HP)

Maximization of Tsallis entropy in the combinatorial formulation

International Nuclear Information System (INIS)

Suyari, Hiroki

2010-01-01

This paper presents the mathematical reformulation for maximization of Tsallis entropy S q in the combinatorial sense. More concretely, we generalize the original derivation of Maxwell-Boltzmann distribution law to Tsallis statistics by means of the corresponding generalized multinomial coefficient. Our results reveal that maximization of S 2-q under the usual expectation or S q under q-average using the escort expectation are naturally derived from the combinatorial formulations for Tsallis statistics with respective combinatorial dualities, that is, one for additive duality and the other for multiplicative duality.

Relationship between the generalized equivalent uniform dose formulation and the Poisson statistics-based tumor control probability model

International Nuclear Information System (INIS)

Zhou Sumin; Das, Shiva; Wang Zhiheng; Marks, Lawrence B.

2004-01-01

The generalized equivalent uniform dose (GEUD) model uses a power-law formalism, where the outcome is related to the dose via a power law. We herein investigate the mathematical compatibility between this GEUD model and the Poisson statistics based tumor control probability (TCP) model. The GEUD and TCP formulations are combined and subjected to a compatibility constraint equation. This compatibility constraint equates tumor control probability from the original heterogeneous target dose distribution to that from the homogeneous dose from the GEUD formalism. It is shown that this constraint equation possesses a unique, analytical closed-form solution which relates radiation dose to the tumor cell survival fraction. It is further demonstrated that, when there is no positive threshold or finite critical dose in the tumor response to radiation, this relationship is not bounded within the realistic cell survival limits of 0%-100%. Thus, the GEUD and TCP formalisms are, in general, mathematically inconsistent. However, when a threshold dose or finite critical dose exists in the tumor response to radiation, there is a unique mathematical solution for the tumor cell survival fraction that allows the GEUD and TCP formalisms to coexist, provided that all portions of the tumor are confined within certain specific dose ranges

An Alternate, Egg-Free Radiolabeled Meal Formulation for Gastric-Emptying Scintigraphy.

Science.gov (United States)

Garrigue, Philippe; Bodin-Hullin, Aurore; Gonzalez, Sandra; Sala, Quentin; Guillet, Benjamin

2017-07-01

Tc-radiolabeled scrambled eggs (SEs) are most often used as the ingested solid phase for gastric-emptying scintigraphy, leading egg-reluctant patients to avoid the examination. We formulated and validated 2 egg-free alternate meals, in the absence of any commercialized formulation: chocolate mug cake (MC) and scrambled tofu (ST). Six healthy volunteers underwent gastric-emptying scintigraphy after ingesting Tc-radiolabeled MC, ST, or SE. Gastric retention indexes did not change significantly between formulations (% of overtime variation to SE: MC 7.75% ± 7.1%, ST 7.17% ± 5.8%; P = 0.6618, not statistically significant), suggesting MC and ST as interesting egg-free alternatives.

Statistical experimental design for refractory coatings

International Nuclear Information System (INIS)

McKinnon, J.A.; Standard, O.C.

2000-01-01

The production of refractory coatings on metal casting moulds is critically dependent on the development of suitable rheological characteristics, such as viscosity and thixotropy, in the initial coating slurry. In this paper, the basic concepts of mixture design and analysis are applied to the formulation of a refractory coating, with illustration by a worked example. Experimental data of coating viscosity versus composition are fitted to a statistical model to obtain a reliable method of predicting the optimal formulation of the coating. Copyright (2000) The Australian Ceramic Society

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

Science.gov (United States)

Pohorille, Andrew

2006-01-01

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

Shnirelman peak in the level spacing statistics

International Nuclear Information System (INIS)

Chirikov, B.V.; Shepelyanskij, D.L.

1994-01-01

The first results on the statistical properties of the quantum quasidegeneracy are presented. A physical interpretation of the Shnirelman theorem predicted the bulk quasidegeneracy is given. The conditions for the strong impact of the degeneracy on the quantum level statistics are formulated which allows to extend the application of the Shnirelman theorem into a broad class of quantum systems. 14 refs., 3 figs

In-vitro release of diclofenac diethylammonium from lipid-based formulations.

Science.gov (United States)

Parsaee, Siamak; Sarbolouki, Mohammad N; Parnianpour, Mohamad

2002-07-08

This article presents the preparation and topical performance of some new lipid-based formulations of diclofenac, namely (a) a diclofenac aqueous gel containing mixed micelles (sodium cholate:egg lecithin molar ratio 0.55); (b) diclofenac lotion that contains soya lecithin, ethanol and buffer; and (c) diclofenac lipogel containing egg lecithin, isopropyl myristate, propylene glycol and ethanol. Gel formulations were prepared using Carbomer 934. Release of diclofenac from all formulations was monitored via dialysis through Spectra/por membrane into phosphate buffer (0.2 M pH=7.4) using a Franz cell. Drug release profile and diffusion coefficients were compared with brand formulation (Geigy's Vlotaren Emulgel). Statistical analysis of data show that the diffusion coefficient of the drug from these formulations rank according to the following order: Diclofenac lotion (D=5.308x10(-7) cm(2)/s) >lipogel (D=2.102 x 10(-7) cm(2)/s) >Voltaren Emulgel (1.518 x 10(-7) cm(2)/s) >aqueous gel mixed micelle (0.966 x 10(-7) cm(2)/s). These results show that diclofenac lotion and lipogel maybe more suitable formulations than the conventional topical dosage form.

Statistical mechanics of high-density bond percolation

Science.gov (United States)

Timonin, P. N.

2018-05-01

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

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)

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

Science.gov (United States)

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

2007-01-01

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

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

Science.gov (United States)

Steffen, Jason H.

2008-12-01

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

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

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.

Optimization of primaquine diphosphate tablet formulation for controlled drug release using the mixture experimental design.

Science.gov (United States)

Duque, Marcelo Dutra; Kreidel, Rogério Nepomuceno; Taqueda, Maria Elena Santos; Baby, André Rolim; Kaneko, Telma Mary; Velasco, Maria Valéria Robles; Consiglieri, Vladi Olga

2013-01-01

A tablet formulation based on hydrophilic matrix with a controlled drug release was developed, and the effect of polymer concentrations on the release of primaquine diphosphate was evaluated. To achieve this purpose, a 20-run, four-factor with multiple constraints on the proportions of the components was employed to obtain tablet compositions. Drug release was determined by an in vitro dissolution study in phosphate buffer solution at pH 6.8. The polynomial fitted functions described the behavior of the mixture on simplex coordinate systems to study the effects of each factor (polymer) on tablet characteristics. Based on the response surface methodology, a tablet composition was optimized with the purpose of obtaining a primaquine diphosphate release closer to a zero order kinetic. This formulation released 85.22% of the drug for 8 h and its kinetic was studied regarding to Korsmeyer-Peppas model, (Adj-R(2) = 0.99295) which has confirmed that both diffusion and erosion were related to the mechanism of the drug release. The data from the optimized formulation were very close to the predictions from statistical analysis, demonstrating that mixture experimental design could be used to optimize primaquine diphosphate dissolution from hidroxypropylmethyl cellulose and polyethylene glycol matrix tablets.

Comments on Brodsky's statistical methods for evaluating epidemiological results, and reply by Brodsky, A

International Nuclear Information System (INIS)

Frome, E.L.; Khare, M.

1980-01-01

Brodsky's paper 'A Statistical Method for Testing Epidemiological Results, as applied to the Hanford Worker Population', (Health Phys., 36, 611-628, 1979) proposed two test statistics for use in comparing the survival experience of a group of employees and controls. This letter states that both of the test statistics were computed using incorrect formulas and concludes that the results obtained using these statistics may also be incorrect. In his reply Brodsky concurs with the comments on the proper formulation of estimates of pooled standard errors in constructing test statistics but believes that the erroneous formulation does not invalidate the major points, results and discussions of his paper. (author)

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

International Nuclear Information System (INIS)

Yeh, L.

1992-01-01

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

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).

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 analysis of Gaussian labeled-unlabeled classification problems

International Nuclear Information System (INIS)

Tanaka, Toshiyuki

2013-01-01

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

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)

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)

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

Science.gov (United States)

Lehoucq, R B; Sears, Mark P

2011-09-01

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

A general formulation of discrete-time quantum mechanics: Restrictions on the action and the relation of unitarity to the existence theorem for initial-value problems

International Nuclear Information System (INIS)

Khorrami, M.

1995-01-01

A general formulation for discrete-time quantum mechanics, based on Feynman's method in ordinary quantum mechanics, is presented. It is shown that the ambiguities present in ordinary quantum mechanics (due to noncommutativity of the operators), are no longer present here. Then the criteria for the unitarity of the evolution operator are examined. It is shown that the unitarity of the evolution operator puts restrictions on the form of the action, and also implies the existence of a solution for the classical initial-value problem. 13 refs

Cetirizine release from cyclodextrin formulated compressed chewing gum

DEFF Research Database (Denmark)

Stojanov, Mladen; Larsen, Kim Lambertsen

2012-01-01

release patterns, but with variations in the total amount released. Chewing gum formulated with cetirizine alone, demonstrated a release of 75% after 8 min of chewing. The presence of CDs resulted in increased cetirizine release. The analysis of variance (ANOVA) demonstrated that parameters with the most...... the statistical analysis (ANOVA) demonstrated significance in the release (P

Aspects of statistical consulting not taught by acedemia

DEFF Research Database (Denmark)

Kenett, R.; Thyregod, Poul

2006-01-01

Education in statistics is preparing for statistical analysis but not necessarily for statistical consulting. The objective of this paper is to explore the phases that precede and follow statistical analysis. Specifically these include: problem elicitation, data collection and, following statisti......Education in statistics is preparing for statistical analysis but not necessarily for statistical consulting. The objective of this paper is to explore the phases that precede and follow statistical analysis. Specifically these include: problem elicitation, data collection and, following...... statistical data analysis, formulation of findings, and presentation of findings, and recommendations. Some insights derived from a literature review and real-life case studies are provided. Areas for joint research by statisticians and cognitive scientists are outlined....

Testing quantum mechanics at Da{phi}Ne

Energy Technology Data Exchange (ETDEWEB)

Di Domenica, A. [Rome Univ. 2 (Italy). Dipt. di Fisica

1997-12-31

After a brief introduction to EPR-paradox and Bell`s inequality, it is shown that a Bell-like inequality can be formulated for the neutral kaon system at a {Phi}-factory using the Pauli spin formalism, in our case called K-spin, and taking into account CP violation. Experimental methods to reveal tiny violations of this inequality by quantum mechanics are discussed. The statistical accuracy achievable at DA{Phi}NE, the Frascati {Phi}-factory, seems adequate to successfully perform such a test. (author) 13 refs.

Statistical descriptions of polydisperse turbulent two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Minier, Jean-Pierre, E-mail: jean-pierre.minier@edf.fr

2016-12-15

Disperse two-phase flows are flows containing two non-miscible phases where one phase is present as a set of discrete elements dispersed in the second one. These discrete elements, or ‘particles’, can be droplets, bubbles or solid particles having different sizes. This situation encompasses a wide range of phenomena, from nano-particles and colloids sensitive to the molecular fluctuations of the carrier fluid to inertia particles transported by the large-scale motions of turbulent flows and, depending on the phenomenon studied, a broad spectrum of approaches have been developed. The aim of the present article is to analyze statistical models of particles in turbulent flows by addressing this issue as the extension of the classical formulations operating at a molecular or meso-molecular level of description. It has a three-fold purpose: (1) to bring out the thread of continuity between models for discrete particles in turbulent flows (above the hydrodynamical level of description) and classical mesoscopic formulations of statistical physics (below the hydrodynamical level); (2) to reveal the specific challenges met by statistical models in turbulence; (3) to establish a methodology for modeling particle dynamics in random media with non-zero space and time correlations. The presentation is therefore centered on organizing the different approaches, establishing links and clarifying physical foundations. The analysis of disperse two-phase flow models is developed by discussing: first, approaches of classical statistical physics; then, by considering models for single-phase turbulent flows; and, finally, by addressing current formulations for discrete particles in turbulent flows. This brings out that particle-based models do not cease to exist above the hydrodynamical level and offer great interest when combined with proper stochastic formulations to account for the lack of equilibrium distributions and scale separation. In the course of this study, general

Mucoadhesive in situ gel formulation for vaginal delivery of clotrimazole: formulation, preparation, and in vitro/in vivo evaluation.

Science.gov (United States)

Rençber, Seda; Karavana, Sinem Yaprak; Şenyiğit, Zeynep Ay; Eraç, Bayri; Limoncu, Mine Hoşgör; Baloğlu, Esra

2017-06-01

The purpose of this study was to develop a suitable mucoadhesive in situ gel formulation of clotrimazole (CLO) for the treatment of vaginal candidiasis. For this aim, the mixture of poloxamer (PLX) 407 and 188 were used to prepare in situ gels. Hydroxypropyl methylcellulose (HPMC) K100M or E50 was added to in situ gels in 0.5% ratio to improve the mucoadhesive and mechanical properties of formulations and to prolong the residence time in vaginal cavity. After the preparation of mucoadhesive in situ gels; gelation temperature/time, viscosity, mechanical, mucoadhesive, syringeability, spreadibility and rheological properties, in vitro release behavior, and anticandidal activities were determined. Moreover vaginal retention of mucoadhesive in situ gels was investigated with in vivo distribution studies in rats. Based on the obtained results, it was found that gels prepared with 20% PLX 407, 10% PLX 188 and 0.5% HPMC K100M/E50 might be suitable for vaginal administration of CLO. In addition, the results of in vivo distribution studies showed that gel formulations remained on the vaginal mucosa even 24 h after application. In conclusion, the mucoadhesive in situ gels of CLO would be alternative candidate for treatment of vaginal candidiasis since it has suitable gel properties with good vaginal retention.

Technical Status Report: Preliminary Glass Formulation Report for INEEL HAW

International Nuclear Information System (INIS)

Peeler, D.; Reamer, I.; Vienna, J.; Crum, J.A.

1998-03-01

This study was performed by a team comprising experts in glass chemistry, glass technology, and statistics at both SRTC and PNNL. This joint effort combined the strengths of each discipline and site to quickly develop a glass formulation for specific INEEL HAW

Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow

Science.gov (United States)

Farrell, Brian F.; Ioannou, Petros J.

2017-08-01

This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium

Introduction to analytical mechanics

CERN Document Server

Gamalath, KAILW

2011-01-01

INTRODUCTION TO ANALYTICAL MECHANICS is an attempt to introduce the modern treatment of classical mechanics so that transition to many fields in physics can be made with the least difficulty. This book deal with the formulation of Newtonian mechanics, Lagrangian dynamics, conservation laws relating to symmetries, Hamiltonian dynamics Hamilton's principle, Poisson brackets, canonical transformations which are invaluable in formulating the quantum mechanics and Hamilton-Jacobi equation which provides the transition to wave mechanics.

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

Science.gov (United States)

Viaggiu, Stefano

2017-05-01

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

Global and Local Mechanical Responses for Necking of Rectangular Bars Using Updated and Total Lagrangian Finite Element Formulations

Directory of Open Access Journals (Sweden)

Claudio A. Careglio

2016-01-01

Full Text Available In simulations of forged and stamping processes using the finite element method, load displacement paths and three-dimensional stress and strains states should be well and reliably represented. The simple tension test is a suitable and economical tool to calibrate constitutive equations with finite strains and plasticity for those simulations. A complex three-dimensional stress and strain states are developed when this test is done on rectangular bars and the necking phenomenon appears. In this work, global and local numerical results of the mechanical response of rectangular bars subjected to simple tension test obtained from two different finite element formulations are compared and discussed. To this end, Updated and Total Lagrangian formulations are used in order to get the three-dimensional stress and strain states. Geometric changes together with strain and stress distributions at the cross section where necking occurs are assessed. In particular, a detailed analysis of the effective plastic strain, stress components in axial and transverse directions and pressure, and deviatoric stress components is presented. Specific numerical results are also validated with experimental measurements comparing, in turn, the performance of the two numerical approaches used in this study.

p-Adic quantum mechanics

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1988-01-01

Quantum mechanics above the field of p-adic numbers is constructed. Three formulations of p-adic quantum mechanics are considered: 1) quantum mechanics with complex-valued wave functions and p-adic coordinates and pulses; an approach based on Weyl representation is suggested; 2) the probability (Euclidean) formulation; 3) the secondary quantization representation (Fock representation) with p-adic wave functions

Molecular Theory of the Living Cell Concepts, Molecular Mechanisms, and Biomedical Applications

CERN Document Server

Ji, Sungchul

2012-01-01

This book presents a comprehensive molecular theory of the living cell based on over thirty concepts, principles and laws imported from thermodynamics, statistical mechanics, quantum mechanics, chemical kinetics, informatics, computer science, linguistics, semiotics, and philosophy. The author formulates physically, chemically and enzymologically realistic molecular mechanisms to account for the basic living processes such as ligand-receptor interactions, protein folding, single-molecule enzymic catalysis, force-generating mechanisms in molecular motors, signal transduction, regulation of the genome-wide RNA metabolism, morphogenesis, the micro-macro coupling in coordination dynamics, the origin of life, and the mechanisms of biological evolution itself. Possible solutions to basic and practical problems facing contemporary biology and biomedical sciences have been suggested, including pharmacotheragnostics and personalized medicine.

Mechanism for enhanced absorption of a solid dispersion formulation of LY2300559 using the artificial stomach duodenum model.

Science.gov (United States)

Polster, Christopher S; Wu, Sy-Juen; Gueorguieva, Ivelina; Sperry, David C

2015-04-06

An artificial stomach duodenum (ASD) model has been used to demonstrate the performance difference between two formulations of LY2300559, a low-solubility acidic developmental drug. The two formulations investigated were a conventional high-shear wet granulation (HSWG) formulation and a solid dispersion formulation. A pharmacokinetic study in humans demonstrated the enhanced performance of the solid dispersion formulation relative to the HSWG formulation. The Cmax and AUC of the solid dispersion was 2.6 and 1.9 times greater, respectively, compared to the HSWG formulation. In the ASD, the solid dispersion formulation performance was characterized by three main phases: (1) rapid release in the stomach, creating a supersaturated concentration of drug, (2) precipitation in the stomach, and (3) rapid redissolution of the precipitate in the duodenum to concentration levels that are supersaturated relative to crystalline drug. A series of complementary experiments were employed to describe this performance behavior mechanistically. Imaging experiments with a pH indicating dye showed that local pH gradients from meglumine in the solid dispersion formulation were responsible for creating a high initial supersaturation concentration in the stomach. Upon dissipation of meglumine, the drug precipitated in the stomach as an amorphous solid. Because the precipitated drug is in an amorphous form, it can then rapidly redissolve as it transits to the more neutral environment of the duodenum. This unexpected sequence of physical state changes gives a mechanistic explanation for the enhanced in vivo performance of the solid dispersion formulation relative to the HSWG formulation.

The Statistical Mechanics of Ideal MHD Turbulence

Science.gov (United States)

Shebalin, John V.

2003-01-01

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

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

Statistics with JMP graphs, descriptive statistics and probability

CERN Document Server

Goos, Peter

2015-01-01

Peter Goos, Department of Statistics, University ofLeuven, Faculty of Bio-Science Engineering and University ofAntwerp, Faculty of Applied Economics, BelgiumDavid Meintrup, Department of Mathematics and Statistics,University of Applied Sciences Ingolstadt, Faculty of MechanicalEngineering, GermanyThorough presentation of introductory statistics and probabilitytheory, with numerous examples and applications using JMPDescriptive Statistics and Probability provides anaccessible and thorough overview of the most important descriptivestatistics for nominal, ordinal and quantitative data withpartic

Bioreducible liposomes for gene delivery: from the formulation to the mechanism of action.

Directory of Open Access Journals (Sweden)

Gabriele Candiani

Full Text Available BACKGROUND: A promising strategy to create stimuli-responsive gene delivery systems is to exploit the redox gradient between the oxidizing extracellular milieu and the reducing cytoplasm in order to disassemble DNA/cationic lipid complexes (lipoplexes. On these premises, we previously described the synthesis of SS14 redox-sensitive gemini surfactant for gene delivery. Although others have attributed the beneficial effects of intracellular reducing environment to reduced glutathione (GSH, these observations cannot rule out the possible implication of the redox milieu in its whole on transfection efficiency of bioreducible transfectants leaving the determinants of DNA release largely undefined. METHODOLOGY/PRINCIPAL FINDINGS: With the aim of addressing this issue, SS14 was here formulated into binary and ternary 100 nm-extruded liposomes and the effects of the helper lipid composition and of the SS14/helper lipids molar ratio on chemical-physical and structural parameters defining transfection effectiveness were investigated. Among all formulations tested, DOPC/DOPE/SS14 at 25:50:25 molar ratio was the most effective in transfection studies owing to the presence of dioleoyl chains and phosphatidylethanolamine head groups in co-lipids. The increase in SS14 content up to 50% along DOPC/DOPE/SS14 liposome series yielded enhanced transfection, up to 2.7-fold higher than that of the benchmark Lipofectamine 2000, without altering cytotoxicity of the corresponding lipoplexes at charge ratio 5. Secondly, we specifically investigated the redox-dependent mechanisms of gene delivery into cells through tailored protocols of transfection in GSH-depleted and repleted vs. increased oxidative stress conditions. Importantly, GSH specifically induced DNA release in batch and in vitro. CONCLUSIONS/SIGNIFICANCE: The presence of helper lipids carrying unsaturated dioleoyl chains and phosphatidylethanolamine head groups significantly improved transfection efficiencies

Formulation And Evaluation Of Bilayer Tablet for Bimodal Release of Venlafaxine Hydrochloride

Directory of Open Access Journals (Sweden)

Munira eMomin

2015-07-01

Full Text Available The aim of the present research was to develop a bilayer tablet of venlafexine hydrochloride for bimodal drug release. In the present investigation authors have tried to explore Fenugreek Mucilage (FNM for bioadhesive sustained release layer. The attempt has been made to combine FNM with well studied bioahesive polymers like Hydroxy Propyl Methyl Cellulose, Carbopol and Xanthan Gum. The formulations were evaluated for swelling Index, ex-vivo bioadhesion, water uptake studies, in-vitro drug release and dissolution kinetics was studied. Substantial bioadhesion force (2.4±0.023 gms and tablet adhesion retention time (24±2 hrs was observed with FNM and HPMC combination at 80:20 ratio. The dissolution kinetics followed the Higuchi model (R2 =0.9913 via a non-Fickian diffusion controlled release mechanism after the initial burst. The 32 full factorial design was employed in the present study. The type of polymers used in combination with FNM (X1 and percent polymer replaced with FNM (X2 were taken as independent formulations variables. The selected responses, bioadhesion force (0.11-0.25±0.023gm, amount of drug released in 10 h, Y10 (78.20–95.78±1.24 % and bioadhesive strength, (19-24±2hrs presented good correlation with the selected independent variables. Statistical analysis (ANOVA of the optimized bilayer formulations showed no significant difference in the cumulative amount of drug release after 15 min, but significant difference (p < 0.05 in the amount of drug released after 1 hr till 12 h from optimized formulations was observed. The natural mucilage like FNM could be successfully incorporated into tablet with only 20% replacement with HPMC and it showed good bioadhesiveness and sustained drug release.

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

Science.gov (United States)

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

1997-03-01

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

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

Science.gov (United States)

Ingber, Lester

1984-06-01

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

Physical-chemical characterization of different hydrogels Formulations

International Nuclear Information System (INIS)

Rodriguez, Y.; Romero, M.; Soler, I.; Saldivar, D.

2001-01-01

They were carried out swelling studies at 37 0C of different hydrogels formulations whose composition was the following one: 3% PEG-1000, 1% Agar and concentrations of PVP and NVP 7, 10 and 14% and a maximum thickness of 2 mm, this formulations were irradiated to 25 kGy in a self-shield irradiator of 60Co and the same time studies of the mechanical properties. It was obtained that the hydrogels of PVP absorbs more water than those of NVP. It was described pseudo-Fickian s kinetic whose exponent diffusional is in the following range: 0.5 0.6

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

International Nuclear Information System (INIS)

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

1981-01-01

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

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density functional formulation and nature of steady-state forces

International Nuclear Information System (INIS)

Hyldgaard, P

2012-01-01

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted ‘DBT’, provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the

Characterization of absorption enhancers for orally administered therapeutic peptides in tablet formulations - Applying statistical learning

DEFF Research Database (Denmark)

Welling, Søren Havelund

. In the Caco-2 model all reagents are pre-dissolved, and therefore the assay cannot predict critical solubility issues and bile salt interactions in the final tablet formulation. A QSAR solubility model was built to foresee and avoid slow tablet dissolution. Due to enzyme kinetics, slow tablet dissolution...

Clinical pharmacology of novel anticancer drug formulations

NARCIS (Netherlands)

Stuurman, F.E.

2013-01-01

Studies outlined in this thesis describe the impact of drug formulations on pharmacology of anticancer drugs. It consists of four parts and starts with a review describing the mechanisms of low oral bioavailability of anti-cancer drugs and strategies for improvement of the bioavailability. The

Bottlenecks in the development of topical analgesics: molecule, formulation, dose-finding, and phase III design

Directory of Open Access Journals (Sweden)

Keppel Hesselink JM

2017-03-01

Full Text Available Jan M Keppel Hesselink,1 David J Kopsky,2 Stephen M Stahl3 1Institute Neuropathic Pain, Bosch en Duin, the Netherlands; 2Institute Neuropathic Pain, Amsterdam, the Netherlands; 3University of California San Diego, La Jolla, CA, USA Abstract: Topical analgesics can be defined as topical formulations containing analgesics or co-analgesics. Since 2000, interest in such formulations has been on the rise. There are, however, four critical issues in the research and development phases of topical analgesics: 1 The selection of the active pharmaceutical ingredient. Analgesics and co-analgesics differ greatly in their mechanism of action, and it is required to find the most optimal fit between such mechanisms of action and the pathogenesis of the targeted (neuropathic pain. 2 Issues concerning the optimized formulation. For relevant clinical efficacy, specific characteristics for the selected vehicle (eg, cream base or gel base are required, depending on the physicochemical characteristics of the active pharmaceutical ingredient(s to be delivered. 3 Well-designed phase II dose-finding studies are required, and, unfortunately, such trials are missing. In fact, we will demonstrate that underdosing is one of the major hurdles to detect meaningful and statistically relevant clinical effects of topical analgesics. 4 Selection of clinical end points and innovatively designed phase III trials. End point selection can make or break a trial. For instance, to include numbness together with tingling as a composite end point for neuropathic pain seems stretching the therapeutic impact of an analgesic too far. Given the fast onset of action of topical analgesics (usually within 30 minutes, enrichment designs might enhance the chances for success, as the placebo response might decrease. Topical analgesics may become promising inroads for the treatment of neuropathic pain, once sufficient attention is given to these four key aspects. Keywords: topical, analgesics

Statistical mechanics of lattice systems a concrete mathematical introduction

CERN Document Server

Friedli, Sacha

2017-01-01

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

Statistical mechanics of competitive resource allocation using agent-based models

Science.gov (United States)

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

2015-01-01

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

Quantum Mechanics and the Principle of Least Radix Economy

Science.gov (United States)

Garcia-Morales, Vladimir

2015-03-01

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

Validation of flexible multibody dynamics beam formulations using benchmark problems

Energy Technology Data Exchange (ETDEWEB)

Bauchau, Olivier A., E-mail: obauchau@umd.edu [University of Maryland (United States); Betsch, Peter [Karlsruhe Institute of Technology (Germany); Cardona, Alberto [CIMEC (UNL/Conicet) (Argentina); Gerstmayr, Johannes [Leopold-Franzens Universität Innsbruck (Austria); Jonker, Ben [University of Twente (Netherlands); Masarati, Pierangelo [Politecnico di Milano (Italy); Sonneville, Valentin [Université de Liège (Belgium)

2016-05-15

As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.

Comparative study on the predictability of statistical models (RSM and ANN) on the behavior of optimized buccoadhesive wafers containing Loratadine and their in vivo assessment.

Science.gov (United States)

Chakraborty, Prithviraj; Parcha, Versha; Chakraborty, Debarupa D; Ghosh, Amitava

2016-01-01

Buccoadhesive wafer dosage form containing Loratadine is formulated utilizing Formulation by Design (FbD) approach incorporating sodium alginate and lactose monohydrate as independent variable employing solvent casting method. The wafers were statistically optimized using Response Surface Methodology (RSM) and Artificial Neural Network algorithm (ANN) for predicting physicochemical and physico-mechanical properties of the wafers as responses. Morphologically wafers were tested using SEM. Quick disintegration of the samples was examined employing Optical Contact Angle (OCA). The comparison of the predictability of RSM and ANN showed a high prognostic capacity of RSM model over ANN model in forecasting mechanical and physicochemical properties of the wafers. The in vivo assessment of the optimized buccoadhesive wafer exhibits marked increase in bioavailability justifying the administration of Loratadine through buccal route, bypassing hepatic first pass metabolism.

Infant Statistical Learning

Science.gov (United States)

Saffran, Jenny R.; Kirkham, Natasha Z.

2017-01-01

Perception involves making sense of a dynamic, multimodal environment. In the absence of mechanisms capable of exploiting the statistical patterns in the natural world, infants would face an insurmountable computational problem. Infant statistical learning mechanisms facilitate the detection of structure. These abilities allow the infant to compute across elements in their environmental input, extracting patterns for further processing and subsequent learning. In this selective review, we summarize findings that show that statistical learning is both a broad and flexible mechanism (supporting learning from different modalities across many different content areas) and input specific (shifting computations depending on the type of input and goal of learning). We suggest that statistical learning not only provides a framework for studying language development and object knowledge in constrained laboratory settings, but also allows researchers to tackle real-world problems, such as multilingualism, the role of ever-changing learning environments, and differential developmental trajectories. PMID:28793812

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

Science.gov (United States)

Verkley, Wim; Severijns, Camiel

2014-05-01

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

Formulations and algorithms for problems on rock mass and support deformation during mining

Science.gov (United States)

Seryakov, VM

2018-03-01

The analysis of problem formulations to calculate stress-strain state of mine support and surrounding rocks mass in rock mechanics shows that such formulations incompletely describe the mechanical features of joint deformation in the rock mass–support system. The present paper proposes an algorithm to take into account the actual conditions of rock mass and support interaction and the algorithm implementation method to ensure efficient calculation of stresses in rocks and support.

Influence of cellulose derivative and ethylene glycol on optimization of lornoxicam transdermal formulation.

Science.gov (United States)

Shahzad, Yasser; Khan, Qalandar; Hussain, Talib; Shah, Syed Nisar Hussain

2013-10-01

Lornoxicam containing topically applied lotions were formulated and optimized with the aim to deliver it transdermally. The formulated lotions were evaluated for pH, viscosity and in vitro permeation studies through silicone membrane using Franz diffusion cells. Data were fitted to linear, quadratic and cubic models and best fit model was selected to investigate the influence of variables, namely hydroxypropyl methylcellulose (HPMC) and ethylene glycol (EG) on permeation of lornoxicam from topically applied lotion formulations. The best fit quadratic model revealed that low level of HPMC and intermediate level of EG in the formulation was optimum for enhancing the drug flux across silicone membrane. FT-IR analysis confirmed absence of drug-polymer interactions. Selected optimized lotion formulation was then subjected to accelerated stability testing, sensatory perception testing and in vitro permeation across rabbit skin. The drug flux from the optimized lotion across rabbit skin was significantly better that that from the control formulation. Furthermore, sensatory perception test rated a higher acceptability while lotion was stable over stability testing period. Therefore, use of Box-Wilson statistical design successfully elaborated the influence of formulation variables on permeation of lornoxicam form topical formulations, thus, helped in optimization of the lotion formulation. Copyright © 2013 Elsevier B.V. All rights reserved.

Bohmian mechanics. The physics and mathematics of quantum theory

International Nuclear Information System (INIS)

Duerr, Detlef; Teufel, Stefan

2009-01-01

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

Bohmian mechanics. The physics and mathematics of quantum theory

Energy Technology Data Exchange (ETDEWEB)

Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.

2009-07-01

Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

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.

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

Directory of Open Access Journals (Sweden)

Abhishek Majhi

2017-12-01

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

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

Performance of mixed formulations for the particle finite element method in soil mechanics problems

Science.gov (United States)

Monforte, Lluís; Carbonell, Josep Maria; Arroyo, Marcos; Gens, Antonio

2017-07-01

This paper presents a computational framework for the numerical analysis of fluid-saturated porous media at large strains. The proposal relies, on one hand, on the particle finite element method (PFEM), known for its capability to tackle large deformations and rapid changing boundaries, and, on the other hand, on constitutive descriptions well established in current geotechnical analyses (Darcy's law; Modified Cam Clay; Houlsby hyperelasticity). An important feature of this kind of problem is that incompressibility may arise either from undrained conditions or as a consequence of material behaviour; incompressibility may lead to volumetric locking of the low-order elements that are typically used in PFEM. In this work, two different three-field mixed formulations for the coupled hydromechanical problem are presented, in which either the effective pressure or the Jacobian are considered as nodal variables, in addition to the solid skeleton displacement and water pressure. Additionally, several mixed formulations are described for the simplified single-phase problem due to its formal similitude to the poromechanical case and its relevance in geotechnics, since it may approximate the saturated soil behaviour under undrained conditions. In order to use equal-order interpolants in displacements and scalar fields, stabilization techniques are used in the mass conservation equation of the biphasic medium and in the rest of scalar equations. Finally, all mixed formulations are assessed in some benchmark problems and their performances are compared. It is found that mixed formulations that have the Jacobian as a nodal variable perform better.

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

Science.gov (United States)

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

2017-08-01

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

Statistical gamma transitions in {sup 174}Hf

Energy Technology Data Exchange (ETDEWEB)

Farris, L P; Cizewski, J A; Brinkman, M J; Henry, R G; Lee, C S [Rutgers--the State Univ., New Brunswick, NJ (United States); Khoo, T L; Janssens, R V.F.; Moore, E F; Carpenter, M P; Ahmad, I; Lauritsen, T [Argonne National Lab., IL (United States); Kolata, J J; Beard, K B; Ye, B; Garg, U [Notre Dame Univ., IN (United States); Kaplan, M S; Saladin, J X; Winchell, D [Pittsburgh Univ., PA (United States)

1992-08-01

The statistical spectrum extracted from the {sup 172}Yb({alpha},2n){sup 174}Hf reaction was fit with Monte Carlo simulations using a modified GDR E1 strength function and several formulations of the level density. (author). 15 refs., 1 tab., 3 figs.

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.)

Formulations with green clay for acne-prone skin: evaluation of rheology and sensory

Directory of Open Access Journals (Sweden)

Maria Cibelle Pauli Lungatto

2014-11-01

Full Text Available Acne is an inflammatory skin condition that develops in pilosebaceous follicles, affecting mainly the onset of puberty. Among the numerous chemicals with dermatological and cosmetic purpose, traded and prescribed, raw materials of mineral origin have been often sought in formulations aimed at treating and / or preventing acne. This work aimed at the development of cosmetic preparations including green clay and sensory analysis of the formulations. Four formulations containing 2.5 % to 5 % green clay, in the presence or absence of dimethicone were prepared. The rheological behavior of the samples was analyzed at time 0, 24 hours, 30 days, 60 days and 90 days, using a cone and plate type rheometer (DVII + viscometer, Brookfiel. Sensory analyses of the formulations were also made. It can be concluded that all formulations exhibited pseudoplastic behavior and, through statistical analysis, it was found that there were no significant differences in acceptance between the formulations with or without dimethicone in the attributes of spreadability, stickiness, color and sensation after application. However, in regard to the attribute of odor, it was found that there was a greater acceptance in formulations to which dimethicone was added.

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

International Nuclear Information System (INIS)

Gross, D.H.E.

2006-01-01

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

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

An Explicit Formulation of Singularity-Free Dynamic Equations of Mechanical Systems in Lagrangian Form---Part one: Single Rigid Bodies

Directory of Open Access Journals (Sweden)

Pål Johan From

2012-04-01

Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with

Statistical Physics An Introduction

CERN Document Server

Yoshioka, Daijiro

2007-01-01

This book provides a comprehensive presentation of the basics of statistical physics. The first part explains the essence of statistical physics and how it provides a bridge between microscopic and macroscopic phenomena, allowing one to derive quantities such as entropy. Here the author avoids going into details such as Liouville’s theorem or the ergodic theorem, which are difficult for beginners and unnecessary for the actual application of the statistical mechanics. In the second part, statistical mechanics is applied to various systems which, although they look different, share the same mathematical structure. In this way readers can deepen their understanding of statistical physics. The book also features applications to quantum dynamics, thermodynamics, the Ising model and the statistical dynamics of free spins.

Superfield formulation of stochastic quantization for gauge theories

International Nuclear Information System (INIS)

Egoryan, Ed.Sh.; Manvelian, R.P.

1990-01-01

Using gauge symmetry localization relative to superspace coordinates an extended stochastic action for the Yang-Mills field possessing supergauge invariance is obtained. This allows to formulate correctly a mechanism of stochastic reduction for gauge theories beyond the framework of perturbation theory. 12 refs

Formulation and Characterization of Potential Antifungal Oleogel with Essential Oil of Thyme

Directory of Open Access Journals (Sweden)

Giedre Kasparaviciene

2018-01-01

Full Text Available The aim of this research was to formulate oleogel with thyme essential oil with potential antimicrobial activity, design optimal formulation, and evaluate the influence of ingredients on texture parameters of preparation. Central composite design was applied to statistical optimization of colloidal silica and paraffin oil mixture for the modeling of oleogel delivery system. The influence of designed formulations on response variables (texture parameters, firmness, cohesiveness, consistency, and index of viscosity, was evaluated. Quality of essential oil of thyme was assessed by determinate concentration of thymol and carvacrol using gas chromatography with flame ionization detection (GC-FID. Microbiological tests have shown that oleogel with thyme essential oil affects Candida albicans microorganism when thyme essential oil’s concentration is 0,05% in oleogel mixture.

The statistical mechanics of financial markets

CERN Document Server

Voit, Johannes

2003-01-01

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

Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Lauwers, P G

1990-12-01

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

Controlled-release, pegylation, liposomal formulations: new mechanisms in the delivery of injectable drugs.

Science.gov (United States)

Reddy, K R

2000-01-01

To review recent developments in novel injectable drug delivery mechanisms and outline the advantages and disadvantages of each. A MEDLINE (1995-January 2000) search using the terms polyethylene glycol, liposomes, polymers, polylactic acid, and controlled release was conducted. Additional references were identified by scanning bibliographies. All articles were considered for inclusion. Abstracts were included only if they were judged to add critical information not otherwise available in the medical literature. A number of systems that alter the delivery of injectable drugs have been developed in attempts to improve pharmacodynamic and pharmacokinetic properties of therapeutic agents. New drug delivery systems can be produced either through a change in formulation (e.g., continuous-release products, liposomes) or an addition to the drug molecule (e.g., pegylation). Potential advantages of new delivery mechanisms include an increased or prolonged duration of pharmacologic activity, a decrease in adverse effects, and increased patient compliance and quality of life. Injectable continuous-release systems deliver drugs in a controlled, predetermined fashion and are particularly appropriate when it is important to avoid large fluctuations in plasma drug concentrations. Encapsulating a drug within a liposome can produce a prolonged half-life and a shift of distribution toward tissues with increased capillary permeability (e.g., tumors, infected tissue). Pegylation provides a method for modification of therapeutic proteins to minimize many of the limitations (e.g., poor stability, short half-life, immunogenicity) associated with these agents. Pegylation of therapeutic proteins is an established process with new applications. However, not all pegylated proteins are alike, and each requires optimization on a protein-by-protein basis to derive maximum clinical benefit. The language required to describe each pegylated therapeutic protein must be more precise to accurately

Statistical physics

CERN Document Server

Sadovskii, Michael V

2012-01-01

This volume provides a compact presentation of modern statistical physics at an advanced level. Beginning with questions on the foundations of statistical mechanics all important aspects of statistical physics are included, such as applications to ideal gases, the theory of quantum liquids and superconductivity and the modern theory of critical phenomena. Beyond that attention is given to new approaches, such as quantum field theory methods and non-equilibrium problems.

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

Science.gov (United States)

Ingber, Lester; Nunez, Paul L

2011-02-01

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

Statistical investigation of expected wave energy and its reliability

International Nuclear Information System (INIS)

Ozger, M.; Altunkaynak, A.; Sen, Z.

2004-01-01

The statistical behavior of wave energy at a single site is derived by considering simultaneous variations in the period and wave height. In this paper, the general wave power formulation is derived by using the theory of perturbation. This method leads to a general formulation of the wave power expectation and other statistical parameter expressions, such as standard deviation and coefficient of variation. The statistical parameters, namely the mean value and variance of wave energy, are found in terms of the simple statistical parameters of period, significant wave height and zero up-crossing period. The elegance of these parameters is that they are distribution free. These parameters provide a means for defining the wave energy distribution function by employing the Chebyschev's inequality. Subsequently, an approximate probability distribution function of the wave energy is also derived for assessment of risk and reliability associated with wave energy. Necessary simple charts are given for risk and reliability assessments. Two procedures are presented for such assessments in wave energy calculations and the applications of these procedures are provided for wave energy potential assessment in the regions of the Pacific Ocean off the west coast of U.S. (author)

Statistical investigation of expected wave energy and its reliability

International Nuclear Information System (INIS)

Oezger, Mehmet; Altunkaynak, Abduesselam; Sen, Zekai

2004-01-01

The statistical behavior of wave energy at a single site is derived by considering simultaneous variations in the period and wave height. In this paper, the general wave power formulation is derived by using the theory of perturbation. This method leads to a general formulation of the wave power expectation and other statistical parameter expressions, such as standard deviation and coefficient of variation. The statistical parameters, namely the mean value and variance of wave energy, are found in terms of the simple statistical parameters of period, significant wave height and zero up-crossing period. The elegance of these parameters is that they are distribution free. These parameters provide a means for defining the wave energy distribution function by employing the Chebyschev's inequality. Subsequently, an approximate probability distribution function of the wave energy is also derived for assessment of risk and reliability associated with wave energy. Necessary simple charts are given for risk and reliability assessments. Two procedures are presented for such assessments in wave energy calculations and the applications of these procedures are provided for wave energy potential assessment in the regions of the Pacific Ocean off the west coast of U.S

Bioequivalence of a new cyclosporine a formulation to Neoral.

Science.gov (United States)

David-Neto, Elias; Kakehashi, Erica; Alves, Cristiane Feres; Pereira, Lilian M; de Castro, Maria Cristina R; de Mattos, Renata Maciel; Sumita, Nairo Massakazu; Romano, Paschoalina; Mendes, Maria Elizabete; Nahas, William Carlos; Ianhez, Luiz Estevam

2004-02-01

New cyclosporine A (CsA) formulations must prove their bioequivalence to Neoral, the reference CsA formulation, to allow free prescription for the patients. The aim of this study was to compare the pharmacokinetics (PK) of a new CsA formulation (Zinograf-ME), produced by Strides-Arcolab, to Neoral and to demonstrate their interchangeability in stable renal transplant recipients. Twelve-hour PK studies were obtained from 18 (13 M/5 F) adult patients (mean age 44.7 +/- 12 years). They received their renal allografts from 13 cadaver and 5 living donors. Before enrollment, all patients were receiving a third generic CsA for a mean of 48 months. Nine patients were also under azathioprine and 9 under mycophenolate mofetil; 17 received prednisone. A single oral dose of either Zinograf or Neoral was administered. The first PK study was performed with one formulation, and 1 week later, a second PK was done with the other formulation. During the washout period, patients continued taking the third CsA formulation. The drug substitution was done milligram-for-milligram. The CsA whole-blood level was measured by TDx immunoassay. Mean +/- SD of area under the curve (AUC), maximum concentration (C(max)), and concentration at the second hour (C2) of Zinograf were not statistically different from those with Neoral (4019 +/- 1466 vs 3971 +/- 1325 ng x h/mL, 998 +/- 376 vs 1021 +/- 356 ng/mL, and 707 +/- 254 vs 734 +/- 229 ng/mL, respectively). In the same way, the Zinograf 90% confidence interval for either C(max) (-123, +77 ng/mL) or AUC (-214, +311 ng.mL/h) were within the Neoral bioequivalence interval for the same parameters (+/-204 ng/mL and +/-794 ng x mL/h, respectively). These data demonstrate that the ZinografME CsA formulation is bioequivalent to Neoral.

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

International Nuclear Information System (INIS)

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

1977-09-01

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

The formulation of the essential oil of Piper aduncum Linnaeus (Piperales: Piperaceae) increases its efficacy as an insect repellent.

Science.gov (United States)

Mamood, S N H; Hidayatulfathi, O; Budin, S B; Ahmad Rohi, G; Zulfakar, M H

2017-02-01

The essential oil (EO) of Piper aduncum Linnaeus, known as 'sireh lada' to locals Malaysian, has the potential to be used as an alternative to synthetic insect repellents such as N,N-diethyl-meta-toluamide. However, the EO's efficacy as a repellent decreases after application due to the high volatility of its active ingredients. A number of studies have showed that optimizing the formulation of plant-based EOs can improve their efficacy as repellents. The present study sought to evaluate the effectiveness of 10% P. aduncum EO in ethanol and in three different semisolid formulations: ointment, cream and gel. These formulations were tested on Aedes aegypti under laboratory conditions. Each formulation was applied to the subject's hands, which were then inserted into a cage containing 25 nulliparous A. aegypti. The number of mosquitoes landing on or biting each subject's hand was recorded, and the repellency percentage, landing/biting percentage and protection time for each of the formulations were compared. There were no statistically significant differences between the semisolid EO formulations with regards to the repellency percentage and the landing/biting percentage at 4 h post-application. All three semisolid EO formulations were able to repel >65% of the A. aegypti at 4 h post-application. The EO ointment formulation provided a protection time (182.5 ± 16.01 min) that was statistically significantly longer than that associated with the EO gel formulation (97.5 ± 14.93 min). Meanwhile, the EO cream formulation provided a protection time of 162.5 ± 6.29 min. As the EO cream and ointment formulations displayed better repellent properties than the EO gel formulation, they appear to be the most promising P. aduncum EO formulations to be developed and commercialized as alternatives to synthetic repellents.

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

A Fourth Order Formulation of DDM for Crack Analysis in Brittle Solids

Directory of Open Access Journals (Sweden)

Abolfazl Abdollahipour

2017-01-01

Full Text Available A fourth order formulation of the displacement discontinuity method (DDM is proposed for the crack analysis of brittle solids such as rocks, glasses, concretes and ceramics. A fourth order boundary collocation scheme is used for the discretization of each boundary element (the source element. In this approach, the source boundary element is divided into five sub-elements each recognized by a central node where the displacement discontinuity components are to be numerically evaluated. Three different formulating procedures are presented and their corresponding discretization schemes are discussed. A new discretization scheme is also proposed to use the fourth order formulation for the special crack tip elements which may be used to increase the accuracy of the stress and displacement fields near the crack ends. Therefore, these new crack tips discretizing schemes are also improved by using the proposed fourth order displacement discontinuity formulation and the corresponding shape functions for a bunch of five special crack tip elements. Some example problems in brittle fracture mechanics are solved for estimating the Mode I and Mode II stress intensity factors near the crack ends. These semi-analytical results are compared to those cited in the fracture mechanics literature whereby the high accuracy of the fourth order DDM formulation is demonstrated.

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

International Nuclear Information System (INIS)

Dinariev, O.Yu.

2000-01-01

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

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

Formulation optimization of transdermal meloxicam potassium-loaded mesomorphic phases containing ethanol, oleic acid and mixture surfactant using the statistical experimental design methodology.

Science.gov (United States)

Huang, Chi-Te; Tsai, Chia-Hsun; Tsou, Hsin-Yeh; Huang, Yaw-Bin; Tsai, Yi-Hung; Wu, Pao-Chu

2011-01-01

Response surface methodology (RSM) was used to develop and optimize the mesomorphic phase formulation for a meloxicam transdermal dosage form. A mixture design was applied to prepare formulations which consisted of three independent variables including oleic acid (X(1)), distilled water (X(2)) and ethanol (X(3)). The flux and lag time (LT) were selected as dependent variables. The result showed that using mesomorphic phases as vehicles can significantly increase flux and shorten LT of drug. The analysis of variance showed that the permeation parameters of meloxicam from formulations were significantly influenced by the independent variables and their interactions. The X(3) (ethanol) had the greatest potential influence on the flux and LT, followed by X(1) and X(2). A new formulation was prepared according to the independent levels provided by RSM. The observed responses were in close agreement with the predicted values, demonstrating that RSM could be successfully used to optimize mesomorphic phase formulations.

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

International Nuclear Information System (INIS)

Kushnirenko, A.N.

1989-01-01

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

Probability and Bayesian statistics

CERN Document Server

1987-01-01

This book contains selected and refereed contributions to the "Inter­ national Symposium on Probability and Bayesian Statistics" which was orga­ nized to celebrate the 80th birthday of Professor Bruno de Finetti at his birthplace Innsbruck in Austria. Since Professor de Finetti died in 1985 the symposium was dedicated to the memory of Bruno de Finetti and took place at Igls near Innsbruck from 23 to 26 September 1986. Some of the pa­ pers are published especially by the relationship to Bruno de Finetti's scientific work. The evolution of stochastics shows growing importance of probability as coherent assessment of numerical values as degrees of believe in certain events. This is the basis for Bayesian inference in the sense of modern statistics. The contributions in this volume cover a broad spectrum ranging from foundations of probability across psychological aspects of formulating sub­ jective probability statements, abstract measure theoretical considerations, contributions to theoretical statistics an...

Fractional statistics and quantum theory

CERN Document Server

Khare, Avinash

1997-01-01

This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced research workers with a reasonable background in quantum and statistical mechanics. The main emphasis will be on explaining new concepts. Topics in the first part of the book includes the flux tube model of anyons, the braid group and quantum and statistical mechanics of noninteracting anyon gas. The second part of the book provides a detailed discussion about f

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

International Nuclear Information System (INIS)

Daunys, Mykolas; Sniuolis, Raimondas

2006-01-01

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

Introduction to the basic concepts of modern physics special relativity, quantum and statistical physics

CERN Document Server

Becchi, Carlo Maria

2016-01-01

This is the third edition of a well-received textbook on modern physics theory. This book provides an elementary but rigorous and self-contained presentation of the simplest theoretical framework that will meet the needs of undergraduate students. In addition, a number of examples of relevant applications and an appropriate list of solved problems are provided.Apart from a substantial extension of the proposed problems, the new edition provides more detailed discussion on Lorentz transformations and their group properties, a deeper treatment of quantum mechanics in a central potential, and a closer comparison of statistical mechanics in classical and in quantum physics. The first part of the book is devoted to special relativity, with a particular focus on space-time relativity and relativistic kinematics. The second part deals with Schrödinger's formulation of quantum mechanics. The presentation concerns mainly one-dimensional problems, but some three-dimensional examples are discussed in detail. The third...

Statistical Mechanics and Applications in Condensed Matter

Science.gov (United States)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

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

Statistical Mechanics of Money, Income, and Wealth

Science.gov (United States)

Yakovenko, Victor

2006-03-01

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

Formulation of gastroretentive floating drug delivery system using hydrophilic polymers and its in vitro characterization

Directory of Open Access Journals (Sweden)

Venkata Srikanth Meka

2014-04-01

Full Text Available The aim of the present research is to formulate and evaluate the gastroretentive floating drug delivery system of antihypertensive drug, propranolol HCl. Gastroretentive floating tablets (GRFT were prepared by using a synthetic hydrophilic polymer polyethylene oxide of different grades such as PEO WSR N-12 K and PEO 18 NF as release retarding polymers and calcium carbonate as gas generating agent. The GRFT were compressed by direct compression strategy and the tablets were evaluated for physico-chemical properties, in vitro buoyancy, swelling studies, in vitro dissolution studies and release mechanism studies. From the dissolution and buoyancy studies, F 9 was selected as an optimized formulation. The optimized formulation followed zero order rate kinetics with non-Fickian diffusion mechanism. The optimized formulation was characterised with FTIR studies and observed no interaction between the drug and the polymers.

Finite element analysis of structures through unified formulation

CERN Document Server

Carrera, Erasmo; Petrolo, Marco; Zappino, Enrico

2014-01-01

The finite element method (FEM) is a computational tool widely used to design and analyse  complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same ''fundamental nucleus'' that comes from geometrical relations and Hooke''s law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D...

Recent advances in co-amorphous drug formulations

DEFF Research Database (Denmark)

Dengale, Swapnil Jayant; Grohganz, Holger; Rades, Thomas

2016-01-01

with other amorphous stabilization techniques. Because of this, several research groups started to investigate the co-amorphous formulation approach, resulting in an increasing amount of scientific publications over the last few years. This study provides an overview of the co-amorphous field and its recent......Co-amorphous drug delivery systems have recently gained considerable interest in the pharmaceutical field because of their potential to improve oral bioavailability of poorly water-soluble drugs through drug dissolution enhancement as a result of the amorphous nature of the material. A co...... findings. In particular, we investigate co-amorphous formulations from the viewpoint of solid dispersions, describe their formation and mechanism of stabilization, study their impact on dissolution and in vivo performance and briefly outline the future potentials....

Evaluation of observables in statistical multifragmentation theories

International Nuclear Information System (INIS)

Cole, A.J.

1989-01-01

The canonical formulation of equilibrium statistical multifragmentation is examined. It is shown that the explicit construction of observables (average values) by sampling the partition probabilities is unnecessary insofar as closed expressions in the form of recursion relations can be obtained quite easily. Such expressions may conversely be used to verify the sampling algorithms

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

Science.gov (United States)

Shinzato, Takashi

2016-12-01

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

Methods of statistical physics

CERN Document Server

Akhiezer, Aleksandr I

1981-01-01

Methods of Statistical Physics is an exposition of the tools of statistical mechanics, which evaluates the kinetic equations of classical and quantized systems. The book also analyzes the equations of macroscopic physics, such as the equations of hydrodynamics for normal and superfluid liquids and macroscopic electrodynamics. The text gives particular attention to the study of quantum systems. This study begins with a discussion of problems of quantum statistics with a detailed description of the basics of quantum mechanics along with the theory of measurement. An analysis of the asymptotic be

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

Science.gov (United States)

Gautestad, Arild O

2012-09-07

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

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

Science.gov (United States)

Charles, Alexandre; Ballard, Patrick

2016-08-01

The dynamics of mechanical systems with a finite number of degrees of freedom (discrete mechanical systems) is governed by the Lagrange equation which is a second-order differential equation on a Riemannian manifold (the configuration manifold). The handling of perfect (frictionless) unilateral constraints in this framework (that of Lagrange's analytical dynamics) was undertaken by Schatzman and Moreau at the beginning of the 1980s. A mathematically sound and consistent evolution problem was obtained, paving the road for many subsequent theoretical investigations. In this general evolution problem, the only reaction force which is involved is a generalized reaction force, consistently with the virtual power philosophy of Lagrange. Surprisingly, such a general formulation was never derived in the case of frictional unilateral multibody dynamics. Instead, the paradigm of the Coulomb law applying to reaction forces in the real world is generally invoked. So far, this paradigm has only enabled to obtain a consistent evolution problem in only some very few specific examples and to suggest numerical algorithms to produce computational examples (numerical modeling). In particular, it is not clear what is the evolution problem underlying the computational examples. Moreover, some of the few specific cases in which this paradigm enables to write down a precise evolution problem are known to show paradoxes: the Painlevé paradox (indeterminacy) and the Kane paradox (increase in kinetic energy due to friction). In this paper, we follow Lagrange's philosophy and formulate the frictional unilateral multibody dynamics in terms of the generalized reaction force and not in terms of the real-world reaction force. A general evolution problem that governs the dynamics is obtained for the first time. We prove that all the solutions are dissipative; that is, this new formulation is free of Kane paradox. We also prove that some indeterminacy of the Painlevé paradox is fixed in this

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

Czech Academy of Sciences Publication Activity Database

Andrey, Ladislav; Erzan, R.

2002-01-01

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

Mechanism of charity activity

Directory of Open Access Journals (Sweden)

Roman B. Golovkin

2015-12-01

Full Text Available Objective to establish the essential properties of the mechanism of charitable activities and to formulate the concept of quotmechanism of charitable activityquot. Methods the objective of the study is achieved using the complex of methods which are based on the interaction of dialectical and metaphysical analysis the epistemological properties of which allowed to reveal various aspects of the charitable activities mechanism functioning taking into account the principles of comprehensiveness complexity specificity and objectivity of the research. Results the rules are stated of using the term quotmechanismquot to characterize actions of state and law the essence of the charity mechanism is defined the definition of quotthe mechanism of charitable activity quot is formulated. Scientific novelty for the first time at theoretical level in legal science the definition of quotthe mechanism of charitable activityquot is formulated and its essential properties are set. Practical significance the research will contribute to improving the legal regulation in the field of philanthropy as well as to improving the efficiency and quality of charitable activity in the Russian Federation. nbsp

Statistical methods and materials characterisation

International Nuclear Information System (INIS)

Wallin, K.R.W.

2010-01-01

Statistics is a wide mathematical area, which covers a myriad of analysis and estimation options, some of which suit special cases better than others. A comprehensive coverage of the whole area of statistics would be an enormous effort and would also be outside the capabilities of this author. Therefore, this does not intend to be a textbook on statistical methods available for general data analysis and decision making. Instead it will highlight a certain special statistical case applicable to mechanical materials characterization. The methods presented here do not in any way rule out other statistical methods by which to analyze mechanical property material data. (orig.)

Molecular Mechanism of Enhanced Anticancer Effect of Nanoparticle Formulated LY2835219 via p16-CDK4/6-pRb Pathway in Colorectal Carcinoma Cell Line

Directory of Open Access Journals (Sweden)

Xu Tang

2016-01-01

Full Text Available LY2835219 is a dual inhibitor to CDK4 and CDK6. This study was to prepare LY2835219-loaded chitosan nanoparticles (CNP/LY and LY2835219-loaded hyaluronic acid-conjugated chitosan nanoparticles (HACNP/LY and revealed their anticancer effect and influence on p16-CDK4/6-pRb pathway against colon cell line. The nanoparticle sizes of CNP/LY and HACNP/LY were approximately 195±39.6 nm and 217±31.1 nm, respectively. The zeta potentials of CNP/LY and HACNP/LY were 37.3±1.5 mV and 30.3±2.2 mV, respectively. And the preparation process showed considerable drug encapsulation efficiency and loading efficiency. LY2835219, CNP/LY, and HACNP/LY inhibited HT29 cell proliferation with 0.68, 0.54, and 0.30 μM of IC50, respectively. G1 phase was arrested by LY2835219 and its formulations. Furthermore, inhibition of CDK4/6 by LY2835219 formulations induced CDK4, CDK6, cyclin D1, and pRb decrease and p16 increase at both protein and mRNA levels. Overall, nanoparticle formulated LY2835219 could enhance the cytotoxicity and cell cycle arrest, and HACNP/LY strengthened the trend furtherly compared to CNP/LY. It is the first time to demonstrate the anticancer effect and mechanism against HT29 by LY2835219 and its nanoparticles. The drug and its nanoparticle formulations delay the cell growth and arrest cell cycle through p16-CDK4/6-pRb pathway, while the nanoparticle formulated LY2835219 could strengthen the process.

Energy policy formulation and energy administration in South Africa

International Nuclear Information System (INIS)

Du Plessis, S.J.P.

1983-01-01

The evolvement of the governmental energy administrative mechanisms is discussed. Energy policy formulation and the role of the Department of Mineral and Energy Affairs in this regard are outlined. The energy administrative process, with reference to various energy carriers and specific spheres of the South African energy economy is discussed. It is indicated that close co-operation between the public and private energy sectors should result in mutual understanding of each others' practical problems and objectives, and should contribute towards the process of judicious energy policy formulation and administration in the interests of the national well-being

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

Science.gov (United States)

Blumenfeld, Raphael

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

Boundary-integral equation formulation for time-dependent inelastic deformation in metals

Energy Technology Data Exchange (ETDEWEB)

Kumar, V; Mukherjee, S

1977-01-01

The mathematical structure of various constitutive relations proposed in recent years for representing time-dependent inelastic deformation behavior of metals at elevated temperatues has certain features which permit a simple formulation of the three-dimensional inelasticity problem in terms of real time rates. A direct formulation of the boundary-integral equation method in terms of rates is discussed for the analysis of time-dependent inelastic deformation of arbitrarily shaped three-dimensional metallic bodies subjected to arbitrary mechanical and thermal loading histories and obeying constitutive relations of the kind mentioned above. The formulation is based on the assumption of infinitesimal deformations. Several illustrative examples involving creep of thick-walled spheres, long thick-walled cylinders, and rotating discs are discussed. The implementation of the method appears to be far easier than analogous BIE formulations that have been suggested for elastoplastic problems.

Mechanical properties of bioactive glass putty formulations

NARCIS (Netherlands)

van Gestel, N.A.P.; Geurts, J.A.P.; Hulsen, D.J.W.; Hofmann, S.; Ito, K.; van Rietbergen, B.; Arts, J.J.C.

2016-01-01

Introduction: Bioactive glass (BAG) has been studied widely and seems to be a very promising biomaterial in regeneration of large bone defects and osteomyelitis treatment, because of its bone bonding and antibacterial properties[1]-[5]. Its high stiffness could potentially also enable mechanical

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

Science.gov (United States)

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

2014-02-01

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

Generalized statistics and the rishon hypothesis

Energy Technology Data Exchange (ETDEWEB)

Jarvis, P.D. (Tasmania Univ., Sandy Bay (Australia). Dept. of Physics); Green, H.S. (Adelaide Univ. (Australia). Dept. of Mathematical Physics)

1983-01-01

It is pointed out that the proposal of Harari and others, that leptons and quarks should be regarded as composites, consisting of rishons or quips, can be formulated as a field theory in terms of two fundamental spinor fields which satisfy a new generalization of quantum statistics. The requirement of macroscopic causality determines which of the many combinations of rishons may be observed as isolated particles.

Tablet coating by injection molding technology - Optimization of coating formulation attributes and coating process parameters.

Science.gov (United States)

Desai, Parind M; Puri, Vibha; Brancazio, David; Halkude, Bhakti S; Hartman, Jeremy E; Wahane, Aniket V; Martinez, Alexander R; Jensen, Keith D; Harinath, Eranda; Braatz, Richard D; Chun, Jung-Hoon; Trout, Bernhardt L

2018-01-01

We developed and evaluated a solvent-free injection molding (IM) coating technology that could be suitable for continuous manufacturing via incorporation with IM tableting. Coating formulations (coating polymers and plasticizers) were prepared using hot-melt extrusion and screened via stress-strain analysis employing a universal testing machine. Selected coating formulations were studied for their melt flow characteristics. Tablets were coated using a vertical injection molding unit. Process parameters like softening temperature, injection pressure, and cooling temperature played a very important role in IM coating processing. IM coating employing polyethylene oxide (PEO) based formulations required sufficient room humidity (>30% RH) to avoid immediate cracks, whereas other formulations were insensitive to the room humidity. Tested formulations based on Eudrajit E PO and Kollicoat IR had unsuitable mechanical properties. Three coating formulations based on hydroxypropyl pea starch, PEO 1,000,000 and Opadry had favorable mechanical (35% elongation, >95×10 4 J/m 3 toughness) and melt flow (>0.4g/min) characteristics, that rendered acceptable IM coats. These three formulations increased the dissolution time by 10, 15 and 35min, respectively (75% drug release), compared to the uncoated tablets (15min). Coated tablets stored in several environmental conditions remained stable to cracking for the evaluated 8-week time period. Copyright © 2017 Elsevier B.V. All rights reserved.

Experimental Ion Exchange Column With SuperLig 639 And Simulant Formulation

Energy Technology Data Exchange (ETDEWEB)

Morse, Megan; Nash, C.

2013-08-26

SuperLig®639 ion exchange resin was tested as a retrieval mechanism for pertechnetate, through decontamination of a perrhenate spiked 5M Simple Average Na{sup +} Mass Based Simulant. Testing included batch contacts and a three-column ion exchange campaign. A decontamination of perrhenate exceeding 99% from the liquid feed was demonstrated. Analysis of the first formulation of a SBS/WESP simulant found unexpectedly low concentrations of soluble aluminum. Follow-on work will complete the formulation.

A statistical mechanics approach to Granovetter theory

Science.gov (United States)

Barra, Adriano; Agliari, Elena

2012-05-01

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

Statistical Thermodynamics and Microscale Thermophysics

Science.gov (United States)

Carey, Van P.

1999-08-01

Many exciting new developments in microscale engineering are based on the application of traditional principles of statistical thermodynamics. In this text Van Carey offers a modern view of thermodynamics, interweaving classical and statistical thermodynamic principles and applying them to current engineering systems. He begins with coverage of microscale energy storage mechanisms from a quantum mechanics perspective and then develops the fundamental elements of classical and statistical thermodynamics. Subsequent chapters discuss applications of equilibrium statistical thermodynamics to solid, liquid, and gas phase systems. The remainder of the book is devoted to nonequilibrium thermodynamics of transport phenomena and to nonequilibrium effects and noncontinuum behavior at the microscale. Although the text emphasizes mathematical development, Carey includes many examples and exercises to illustrate how the theoretical concepts are applied to systems of scientific and engineering interest. In the process he offers a fresh view of statistical thermodynamics for advanced undergraduate and graduate students, as well as practitioners, in mechanical, chemical, and materials engineering.

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)

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

Science.gov (United States)

Oravec, Heather Ann; Daniels, Christopher C.

2014-01-01

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

Statistical Physics

CERN Document Server

Wannier, Gregory Hugh

1966-01-01

Until recently, the field of statistical physics was traditionally taught as three separate subjects: thermodynamics, statistical mechanics, and kinetic theory. This text, a forerunner in its field and now a classic, was the first to recognize the outdated reasons for their separation and to combine the essentials of the three subjects into one unified presentation of thermal physics. It has been widely adopted in graduate and advanced undergraduate courses, and is recommended throughout the field as an indispensable aid to the independent study and research of statistical physics.Designed for