Theory of atomic spectral emission intensity

NASA Astrophysics Data System (ADS)

Yngström, Sten

1994-07-01

The theoretical derivation of a new spectral line intensity formula for atomic radiative emission is presented. The theory is based on first principles of quantum physics, electrodynamics, and statistical physics. Quantum rules lead to revision of the conventional principle of local thermal equilibrium of matter and radiation. Study of electrodynamics suggests absence of spectral emission from fractions of the numbers of atoms and ions in a plasma due to radiative inhibition caused by electromagnetic force fields. Statistical probability methods are extended by the statement: A macroscopic physical system develops in the most probable of all conceivable ways consistent with the constraining conditions for the system. The crucial role of statistical physics in transforming quantum logic into common sense logic is stressed. The theory is strongly supported by experimental evidence.

Building on the Legacy of Professor Keenan. Entropy An Intrinsic Property of Matter

NASA Astrophysics Data System (ADS)

Gyftopoulos, Elias P.

2008-08-01

In the scientific and engineering literature, entropy—the distinguishing feature of thermodynamics from other branches of physics—is viewed with skepticism, and thought to be not a physical property of matter—like mass or energy—but a measure either of disorder in a system, or of lack of information about the physics of a system in a thermodynamic equilibrium state, and a plethora of expressions are proposed for its analytical representation. In this article, I present briefly two revolutionary nonstatistical expositions of thermodynamics (revolutionary in the sense of Thomas Kuhn, The Structure of Scientific Revolutions, U. Chicago Press, 1970) that apply to all systems (both macroscopic and microscopic, including one spin or a single particle), to all states (thermodynamic equilibrium, and not thermodynamic equilibrium), and that disclose entropy as an intrinsic property of matter. The first theory is presented without reference to quantum mechanics even though quantum theoretic ideas are lurking behind the exposition. The second theory is a unified quantum theory of mechanics and thermodynamics without statistical probabilities, that is, I am not presenting another version of statistical quantum mechanics.

Identifying Student Resources in Reasoning about Entropy and the Approach to Thermal Equilibrium

ERIC Educational Resources Information Center

Loverude, Michael

2015-01-01

As part of an ongoing project to examine student learning in upper-division courses in thermal and statistical physics, we have examined student reasoning about entropy and the second law of thermodynamics. We have examined reasoning in terms of heat transfer, entropy maximization, and statistical treatments of multiplicity and probability. In…

Experimental Determination of Dynamical Lee-Yang Zeros

NASA Astrophysics Data System (ADS)

Brandner, Kay; Maisi, Ville F.; Pekola, Jukka P.; Garrahan, Juan P.; Flindt, Christian

2017-05-01

Statistical physics provides the concepts and methods to explain the phase behavior of interacting many-body systems. Investigations of Lee-Yang zeros—complex singularities of the free energy in systems of finite size—have led to a unified understanding of equilibrium phase transitions. The ideas of Lee and Yang, however, are not restricted to equilibrium phenomena. Recently, Lee-Yang zeros have been used to characterize nonequilibrium processes such as dynamical phase transitions in quantum systems after a quench or dynamic order-disorder transitions in glasses. Here, we experimentally realize a scheme for determining Lee-Yang zeros in such nonequilibrium settings. We extract the dynamical Lee-Yang zeros of a stochastic process involving Andreev tunneling between a normal-state island and two superconducting leads from measurements of the dynamical activity along a trajectory. From the short-time behavior of the Lee-Yang zeros, we predict the large-deviation statistics of the activity which is typically difficult to measure. Our method paves the way for further experiments on the statistical mechanics of many-body systems out of equilibrium.

Magnetofermionic condensate in two dimensions

PubMed Central

Kulik, L. V.; Zhuravlev, A. S.; Dickmann, S.; Gorbunov, A. V.; Timofeev, V. B.; Kukushkin, I. V.; Schmult, S.

2016-01-01

Coherent condensate states of particles obeying either Bose or Fermi statistics are in the focus of interest in modern physics. Here we report on condensation of collective excitations with Bose statistics, cyclotron magnetoexcitons, in a high-mobility two-dimensional electron system in a magnetic field. At low temperatures, the dense non-equilibrium ensemble of long-lived triplet magnetoexcitons exhibits both a drastic reduction in the viscosity and a steep enhancement in the response to the external electromagnetic field. The observed effects are related to formation of a super-absorbing state interacting coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level form a super-emitting state. The effects are explicable from the viewpoint of a coherent condensate phase in a non-equilibrium system of two-dimensional fermions with a fully quantized energy spectrum. The condensation occurs in the space of vectors of magnetic translations, a property providing a completely new landscape for future physical investigations. PMID:27848969

From Mechanical Motion to Brownian Motion, Thermodynamics and Particle Transport Theory

ERIC Educational Resources Information Center

Bringuier, E.

2008-01-01

The motion of a particle in a medium is dealt with either as a problem of mechanics or as a transport process in non-equilibrium statistical physics. The two kinds of approach are often unrelated as they are taught in different textbooks. The aim of this paper is to highlight the link between the mechanical and statistical treatments of particle…

Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics.

PubMed

Bustamante, Carlos

2005-11-01

During the last 15 years, scientists have developed methods that permit the direct mechanical manipulation of individual molecules. Using this approach, they have begun to investigate the effect of force and torque in chemical and biochemical reactions. These studies span from the study of the mechanical properties of macromolecules, to the characterization of molecular motors, to the mechanical unfolding of individual proteins and RNA. Here I present a review of some of our most recent results using mechanical force to unfold individual molecules of RNA. These studies make it possible to follow in real time the trajectory of each molecule as it unfolds and characterize the various intermediates of the reaction. Moreover, if the process takes place reversibly it is possible to extract both kinetic and thermodynamic information from these experiments at the same time that we characterize the forces that maintain the three-dimensional structure of the molecule in solution. These studies bring us closer to the biological unfolding processes in the cell as they simulate in vitro, the mechanical unfolding of RNAs carried out in the cell by helicases. If the unfolding process occurs irreversibly, I show here that single-molecule experiments can still provide equilibrium, thermodynamic information from non-equilibrium data by using recently discovered fluctuation theorems. Such theorems represent a bridge between equilibrium and non-equilibrium statistical mechanics. In fact, first derived in 1997, the first experimental demonstration of the validity of fluctuation theorems was obtained by unfolding mechanically a single molecule of RNA. It is perhaps a sign of the times that important physical results are these days used to extract information about biological systems and that biological systems are being used to test and confirm fundamental new laws in physics.

Ordered phase and non-equilibrium fluctuation in stock market

NASA Astrophysics Data System (ADS)

Maskawa, Jun-ichi

2002-08-01

We analyze the statistics of daily price change of stock market in the framework of a statistical physics model for the collective fluctuation of stock portfolio. In this model the time series of price changes are coded into the sequences of up and down spins, and the Hamiltonian of the system is expressed by spin-spin interactions as in spin glass models of disordered magnetic systems. Through the analysis of Dow-Jones industrial portfolio consisting of 30 stock issues by this model, we find a non-equilibrium fluctuation mode on the point slightly below the boundary between ordered and disordered phases. The remaining 29 modes are still in disordered phase and well described by Gibbs distribution. The variance of the fluctuation is outlined by the theoretical curve and peculiarly large in the non-equilibrium mode compared with those in the other modes remaining in ordinary phase.

Gyrokinetic Statistical Absolute Equilibrium and Turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jian-Zhou Zhu and Gregory W. Hammett

2011-01-10

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: A finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N + 1 quantities are conserved, correspondingmore » to an energy invariant and N entropy-related invariants), the negative temperature states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less

The maximum entropy production principle: two basic questions.

PubMed

Martyushev, Leonid M

2010-05-12

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to 'prove' the principle? We adduce one more proof which is most concise today.

Gyrokinetic statistical absolute equilibrium and turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu Jianzhou; Hammett, Gregory W.

2010-12-15

A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, Q. Appl. Math. 10, 69 (1952)] is taken to study gyrokinetic plasma turbulence: a finite set of Fourier modes of the collisionless gyrokinetic equations are kept and the statistical equilibria are calculated; possible implications for plasma turbulence in various situations are discussed. For the case of two spatial and one velocity dimension, in the calculation with discretization also of velocity v with N grid points (where N+1 quantities are conserved, corresponding to an energy invariant and N entropy-related invariants), the negative temperaturemore » states, corresponding to the condensation of the generalized energy into the lowest modes, are found. This indicates a generic feature of inverse energy cascade. Comparisons are made with some classical results, such as those of Charney-Hasegawa-Mima in the cold-ion limit. There is a universal shape for statistical equilibrium of gyrokinetics in three spatial and two velocity dimensions with just one conserved quantity. Possible physical relevance to turbulence, such as ITG zonal flows, and to a critical balance hypothesis are also discussed.« less

The effect of restructuring student writing in the general chemistry laboratory on student understanding of chemistry and on students' approach to the laboratory course

NASA Astrophysics Data System (ADS)

Rudd, James Andrew, II

Many students encounter difficulties engaging with laboratory-based instruction, and reviews of research have indicated that the value of such instruction is not clearly evident. Traditional forms of writing associated with laboratory activities are commonly in a style used by professional scientists to communicate developed explanations. Students probably lack the interpretative skills of a professional, and writing in this style may not support students in learning how to develop scientific explanations. The Science Writing Heuristic (SWH) is an inquiry-based approach to laboratory instruction designed in part to promote student ability in developing such explanations. However, there is not a convincing body of evidence for the superiority of inquiry-based laboratory instruction in chemistry. In a series of studies, the performance of students using the SWH student template in place of the standard laboratory report format was compared to the performance of students using the standard format. The standard reports had Title, Purpose, Procedure, Data & Observations, Calculations & Graphs, and Discussion sections. The SWH reports had Beginning Questions & Ideas, Tests & Procedures, Observations, Claims, Evidence, and Reflection sections. The pilot study produced evidence that using the SWH improved the quality of laboratory reports, improved student performance on a laboratory exam, and improved student approach to laboratory work. A main study found that SWH students statistically exhibited a better understanding of physical equilibrium when written explanations and equations were analyzed on a lecture exam and performed descriptively better on a physical equilibrium practical exam task. In another main study, the activities covering the general equilibrium concept were restructured as an additional change, and it was found that SWH students exhibited a better understanding of chemical equilibrium as shown by statistically greater success in overcoming the common confusion of interpreting equilibrium as equal concentrations and by statistically better performance when explaining aspects of chemical equilibrium. Both main studies found that students and instructors spent less time on the SWH reports and that students preferred the SWH approach because it increased their level of mental engagement. The studies supported the conclusion that inquiry-based laboratory instruction benefits student learning and attitudes.

Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goto, Shin-itiro, E-mail: sgoto@ims.ac.jp

It has been proposed that equilibrium thermodynamics is described on Legendre submanifolds in contact geometry. It is shown in this paper that Legendre submanifolds embedded in a contact manifold can be expressed as attractors in phase space for a certain class of contact Hamiltonian vector fields. By giving a physical interpretation that points outside the Legendre submanifold can represent nonequilibrium states of thermodynamic variables, in addition to that points of a given Legendre submanifold can represent equilibrium states of the variables, this class of contact Hamiltonian vector fields is physically interpreted as a class of relaxation processes, in which thermodynamicmore » variables achieve an equilibrium state from a nonequilibrium state through a time evolution, a typical nonequilibrium phenomenon. Geometric properties of such vector fields on contact manifolds are characterized after introducing a metric tensor field on a contact manifold. It is also shown that a contact manifold and a strictly convex function induce a lower dimensional dually flat space used in information geometry where a geometrization of equilibrium statistical mechanics is constructed. Legendre duality on contact manifolds is explicitly stated throughout.« less

Statistical Physics Experiments Using Dusty Plasmas

NASA Astrophysics Data System (ADS)

Goree, John

2016-10-01

Compared to other areas of physics research, Statistical Physics is heavily dominated by theory, with comparatively little experiment. One reason for the lack of experiments is the impracticality of tracking of individual atoms and molecules within a substance. Thus, there is a need for a different kind of experimental system, one where individual particles not only move stochastically as they collide with one another, but also are large enough to allow tracking. A dusty plasma can meet this need. A dusty plasma is a partially ionized gas containing small particles of solid matter. These micron-size particles gain thousands of electronic charges by collecting more electrons than ions. Their motions are dominated by Coulomb collisions with neighboring particles. In this so-called strongly coupled plasma, the dust particles self-organize in much the same way as atoms in a liquid or solid. Unlike atoms, however, these particles are large and slow, so that they can be tracked easily by video microscopy. Advantages of dusty plasma for experimental statistical physics research include particle tracking, lack of frictional contact with solid surfaces, and avoidance of overdamped motion. Moreover, the motion of a collection of dust particles can mimic an equilibrium system with a Maxwellian velocity distribution, even though the dust particles themselves are not truly in thermal equilibrium. Nonequilibrium statistical physics can be studied by applying gradients, for example by imposing a shear flow. In this talk I will review some of our recent experiments with shear flow. First, we performed the first experimental test to verify the Fluctuation Theorem for a shear flow, showing that brief violations of the Second Law of Thermodynamics occur with the predicted probabilities, for a small system. Second, we discovered a skewness of a shear-stress distribution in a shear flow. This skewness is a phenomenon that likely has wide applicability in nonequilibrium steady states. Third, we performed the first experimental test of a statistical physics theory (the Green-Kubo model) that is widely used by physical chemists to compute viscosity coefficients, and we found that it fails. Work supported by the U.S. Department of Energy, NSF, and NASA.

Biomimetic Phases of Microtubule-Motor Mixtures

NASA Astrophysics Data System (ADS)

Ross, Jennifer

2014-03-01

We try to determine the universal principles of organization from the molecular scale that gives rise to architecture on the cellular scale. We are specifically interested in the organization of the microtubule cytoskeleton, a rigid, yet versatile network in most cell types. Microtubules in the cell are organized by motor proteins and crosslinkers. This work applies the ideas of statistical mechanics and condensed matter physics to the non-equilibrium pattern formation behind intracellular organization using the microtubule cytoskeleton as the building blocks. We examine these processes in a bottom-up manner by adding increasingly complex protein actors into the system. Our systematic experiments expose nature's laws for organization and has large impacts on biology as well as illuminating new frontiers of non-equilibrium physics.

Ensemble inequivalence and Maxwell construction in the self-gravitating ring model

NASA Astrophysics Data System (ADS)

Rocha Filho, T. M.; Silvestre, C. H.; Amato, M. A.

2018-06-01

The statement that Gibbs equilibrium ensembles are equivalent is a base line in many approaches in the context of equilibrium statistical mechanics. However, as a known fact, for some physical systems this equivalence may not be true. In this paper we illustrate from first principles the inequivalence between the canonical and microcanonical ensembles for a system with long range interactions. We make use of molecular dynamics simulations and Monte Carlo simulations to explore the thermodynamics properties of the self-gravitating ring model and discuss on what conditions the Maxwell construction is applicable.

An Integrated Approach to Thermodynamics in the Introductory Physics Course.

ERIC Educational Resources Information Center

Alonso, Marcelo; Finn, Edward J.

1995-01-01

Presents an approach to combine the empirical approach of classical thermodynamics with the structural approach of statistical mechanics. Topics covered include dynamical foundation of the first law; mechanical work, heat, radiation, and the first law; thermal equilibrium; thermal processes; thermodynamic probability; entropy; the second law;…

Anatomy of Particle Diffusion

ERIC Educational Resources Information Center

Bringuier, E.

2009-01-01

The paper analyses particle diffusion from a thermodynamic standpoint. The main goal of the paper is to highlight the conceptual connection between particle diffusion, which belongs to non-equilibrium statistical physics, and mechanics, which deals with particle motion, at the level of third-year university courses. We start out from the fact…

Cell Division and Evolution of Biological Tissues

NASA Astrophysics Data System (ADS)

Rivier, Nicolas; Arcenegui-Siemens, Xavier; Schliecker, Gudrun

A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division (fragmentation) is a local, elementary topological transformation which establishes statistical equilibrium of the structure. Statistical equilibrium is characterized by observable relations (Lewis, Aboav) between cell shapes, sizes and those of their neighbours, obtained through maximum entropy and topological correlation extending to nearest neighbours only, i.e. maximal randomness. For a two-dimensional tissue (epithelium), the distribution of cell shapes and that of mother and daughter cells can be obtained from elementary geometrical and physical arguments, except for an exponential factor favouring division of larger cells, and exponential and combinatorial factors encouraging a most symmetric division. The resulting distributions are very narrow, and stationarity severely restricts the range of an adjustable structural parameter

New physicochemical interpretations for the adsorption of food dyes on chitosan films using statistical physics treatment.

PubMed

Dotto, G L; Pinto, L A A; Hachicha, M A; Knani, S

2015-03-15

In this work, statistical physics treatment was employed to study the adsorption of food dyes onto chitosan films, in order to obtain new physicochemical interpretations at molecular level. Experimental equilibrium curves were obtained for the adsorption of four dyes (FD&C red 2, FD&C yellow 5, FD&C blue 2, Acid Red 51) at different temperatures (298, 313 and 328 K). A statistical physics formula was used to interpret these curves, and the parameters such as, number of adsorbed dye molecules per site (n), anchorage number (n'), receptor sites density (NM), adsorbed quantity at saturation (N asat), steric hindrance (τ), concentration at half saturation (c1/2) and molar adsorption energy (ΔE(a)) were estimated. The relation of the above mentioned parameters with the chemical structure of the dyes and temperature was evaluated and interpreted. Copyright © 2014 Elsevier Ltd. All rights reserved.

The Physics of Semiconductors

NASA Astrophysics Data System (ADS)

Brennan, Kevin F.

1999-02-01

Modern fabrication techniques have made it possible to produce semiconductor devices whose dimensions are so small that quantum mechanical effects dominate their behavior. This book describes the key elements of quantum mechanics, statistical mechanics, and solid-state physics that are necessary in understanding these modern semiconductor devices. The author begins with a review of elementary quantum mechanics, and then describes more advanced topics, such as multiple quantum wells. He then disusses equilibrium and nonequilibrium statistical mechanics. Following this introduction, he provides a thorough treatment of solid-state physics, covering electron motion in periodic potentials, electron-phonon interaction, and recombination processes. The final four chapters deal exclusively with real devices, such as semiconductor lasers, photodiodes, flat panel displays, and MOSFETs. The book contains many homework exercises and is suitable as a textbook for electrical engineering, materials science, or physics students taking courses in solid-state device physics. It will also be a valuable reference for practicing engineers in optoelectronics and related areas.

Teaching at the edge of knowledge: Non-equilibrium statistical physics

NASA Astrophysics Data System (ADS)

Schmittmann, Beate

2007-03-01

As physicists become increasingly interested in biological problems, we frequently find ourselves confronted with complex open systems, involving many interacting constituents and characterized by non-vanishing fluxes of mass or energy. Faced with the task of predicting macroscopic behaviors from microscopic information for these non-equilibrium systems, the familiar Gibbs-Boltzmann framework fails. The development of a comprehensive theoretical characterization of non-equilibrium behavior is one of the key challenges of modern condensed matter physics. In its absence, several approaches have been developed, from master equations to thermostatted molecular dynamics, which provide key insights into the rich and often surprising phenomenology of systems far from equilibrium. In my talk, I will address some of these methods, selecting those that are most relevant for a broad range of interdisciplinary problems from biology to traffic, finance, and sociology. The ``portability'' of these methods makes them valuable for graduate students from a variety of disciplines. To illustrate how different methods can complement each other when probing a problem from, e.g., the life sciences, I will discuss some recent attempts at modeling translation, i.e., the process by which the genetic information encoded on an mRNA is translated into the corresponding protein.

Statistical physics of vehicular traffic and some related systems

NASA Astrophysics Data System (ADS)

Chowdhury, Debashish; Santen, Ludger; Schadschneider, Andreas

2000-05-01

In the so-called “microscopic” models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a “particle”; the nature of the “interactions” among these particles is determined by the way the vehicles influence each others’ movement. Therefore, vehicular traffic, modeled as a system of interacting “particles” driven far from equilibrium, offers the possibility to study various fundamental aspects of truly nonequilibrium systems which are of current interest in statistical physics. Analytical as well as numerical techniques of statistical physics are being used to study these models to understand rich variety of physical phenomena exhibited by vehicular traffic. Some of these phenomena, observed in vehicular traffic under different circumstances, include transitions from one dynamical phase to another, criticality and self-organized criticality, metastability and hysteresis, phase-segregation, etc. In this critical review, written from the perspective of statistical physics, we explain the guiding principles behind all the main theoretical approaches. But we present detailed discussions on the results obtained mainly from the so-called “particle-hopping” models, particularly emphasizing those which have been formulated in recent years using the language of cellular automata.

Thermostatted kinetic equations as models for complex systems in physics and life sciences.

PubMed

Bianca, Carlo

2012-12-01

Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics. Copyright © 2012 Elsevier B.V. All rights reserved.

Principle of Maximum Fisher Information from Hardy’s Axioms Applied to Statistical Systems

PubMed Central

Frieden, B. Roy; Gatenby, Robert A.

2014-01-01

Consider a finite-sized, multidimensional system in a parameter state a. The system is in either a state of equilibrium or general non-equilibrium, and may obey either classical or quantum physics. L. Hardy’s mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N = max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N = max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I = Imax. This is important because many physical laws have been derived, assuming as a working hypothesis that I = Imax. These derivations include uses of the principle of Extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell’s equations, new laws of biology (e.g. of Coulomb force-directed cell development, and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I = Imax itself derives, from suitably extended Hardy axioms, thereby eliminates its need to be assumed in these derivations. Thus, uses of I = Imax and EPI express physics at its most fundamental level – its axiomatic basis in math. PMID:24229152

Statistical physics of human beings in games: Controlled experiments

NASA Astrophysics Data System (ADS)

Liang, Yuan; Huang, Ji-Ping

2014-07-01

It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings; making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system, thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.

Non-Extensive Statistical Analysis of Magnetic Field and SEPs during the March 2012 ICME event, using a multi-spacecraft approach

NASA Astrophysics Data System (ADS)

Pavlos, George; Malandraki, Olga; Pavlos, Evgenios; Iliopoulos, Aggelos; Karakatsanis, Leonidas

2017-04-01

As the solar plasma lives far from equilibrium it is an excellent laboratory for testing non-equilibrium statistical mechanics. In this study, we present the highlights of Tsallis non-extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at solar wind phenomena and magnetosphere. In this study we present some new and significant results concerning the dynamics of interplanetary coronal mass ejections (ICMEs) observed in the near Earth at L1 solar wind environment, as well as its effect in Earth's magnetosphere. The results are referred to Tsallis non-extensive statistics and in particular to the estimation of Tsallis q-triplet, (qstat, qsen, qrel) of SEPs time series observed at the interplanetary space and magnetic field time series of the ICME observed at the Earth resulting from the solar eruptive activity on March 7, 2012 at the Sun. For the magnetic field, we used a multi-spacecraft approach based on data experiments from ACE, CLUSTER 4, THEMIS-E and THEMIS-C spacecraft. For the data analysis different time periods were considered, sorted as "quiet", "shock" and "aftershock", while different space domains such as the Interplanetary space (near Earth at L1 and upstream of the Earth's bowshock), the Earth's magnetosheath and magnetotail, were also taken into account. Our results reveal significant differences in statistical and dynamical features, indicating important variations of the SEPs profile in time, and magnetic field dynamics both in time and space domains during the shock event, in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. So far, Tsallis non-extensive statistical theory and Tsallis extension of the Boltzmann-Gibbs entropy principle to the q-entropy entropy principle (Tsallis, 1988, 2009) reveal strong universality character concerning non-equilibrium dynamics (Pavlos et al. 2012a,b, 2014, 2015, 2016; Karakatsanis et al. 2013). Tsallis q-entropy principle can explain the emergence of a series of new and significant physical characteristics in distributed systems as well as in space plasmas. Such characteristics are: non-Gaussian statistics and anomalous diffusion processes, strange and fractional dynamics, multifractal, percolating and intermittent turbulence structures, multiscale and long spatio-temporal correlations, fractional acceleration and Non-Equilibrium Stationary States (NESS) or non-equilibrium self-organization process and non-equilibrium phase transition and topological phase transition processes according to Zelenyi and Milovanov (2004). In this direction, our results reveal clearly strong self-organization and development of macroscopic ordering of plasma system related to strengthen of non-extensivity, multifractality and intermittency everywhere in the space plasmas region during the CME event. Acknowledgements: This project has received funding form the European Union's Horizon 2020 research and innovation program under grant agreement No 637324.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

PubMed

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-08

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

Maximum entropy production principle for geostrophic turbulence

NASA Astrophysics Data System (ADS)

Sommeria, J.; Bouchet, F.; Chavanis, P. H.

2003-04-01

In 2D turbulence, complex stirring leads to the formation of steady organized states, once fine scale fluctuations have been filtered out. This self-organization can be explained in terms of statistical equilibrium for vorticity, as the most likely outcome of vorticity parcel rearrangements with the constraints of the conservation laws. A mixing entropy describing the vorticity rearrangements is introduced. Extension to the shallow water system has been proposed by Chavanis P.H. and Sommeria J. (2002), Phys. Rev. E. Generalization to multi-layer geostrophic flows is formally straightforward. Outside equilibrium, eddy fluxes should drive the system toward equilibrium, in the spirit of non equilibrium linear thermodynamics. This can been formalized in terms of a principle of maximum entropy production (MEP), as shown by Robert and Sommeria (1991), Phys. Rev. Lett. 69. Then a parameterization of eddy fluxes is obtained, involving an eddy diffusivity plus a drift term acting at larger scale. These two terms balance each other at equilibrium, resulting in a non trivial steady flow, which is the mean state of the statistical equilibrium. Applications of this eddy parametrization will be presented, in the context of oceanic circulation and Jupiter's Great Red Spot. Quantitative tests will be discussed, obtained by comparisons with direct numerical simulations. Kinetic models, inspired from plasma physics, provide a more precise description of the relaxation toward equilibrium, as shown by Chavanis P.H. 2000 ``Quasilinear theory of the 2D Euler equation'', Phys. Rev. Lett. 84. This approach provides relaxation equations with a form similar to the MEP, but not identical. In conclusion, the MEP provides the right trends of the system but its precise justification remains elusive.

The Physics of Polarization

NASA Astrophysics Data System (ADS)

Landi Degl'Innocenti, Egidio

2015-10-01

The introductory lecture that has been delivered at this Symposium is a condensed version of an extended course held by the author at the XII Canary Island Winter School from November 13 to November 21, 2000. The full series of lectures can be found in Landi Degl'Innocenti (2002). The original reference is organized in 20 Sections that are here itemized: 1. Introduction, 2. Description of polarized radiation, 3. Polarization and optical devices: Jones calculus and Muller matrices, 4. The Fresnel equations, 5. Dichroism and anomalous dispersion, 6. Polarization in everyday life, 7. Polarization due to radiating charges, 8. The linear antenna, 9. Thomson scattering, 10. Rayleigh scattering, 11. A digression on Mie scattering, 12. Bremsstrahlung radiation, 13. Cyclotron radiation, 14. Synchrotron radiation, 15. Polarization in spectral lines, 16. Density matrix and atomic polarization, 17. Radiative transfer and statistical equilibrium equations, 18. The amplification condition in polarized radiative transfer, and 19. Coupling radiative transfer and statistical equilibrium equations.

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

How Physicists Made Stable Lévy Processes Physically Plausible

NASA Astrophysics Data System (ADS)

Schinckus, Christophe

2013-08-01

Stable Lévy processes have very interesting properties for describing the complex behaviour of non-equilibrium dissipative systems such as turbulence, anomalous diffusion or financial markets. However, although these processes better fit the empirical data, some of their statistical properties can raise several theoretical problems in empirical applications because they generate infinite variables. Econophysicists have developed statistical solutions to make these processes physically plausible. This paper presents a review of these analytical solutions (truncations) for stable Lévy processes and how econophysicists transformed them into data-driven processes. The evolution of these analytical solutions is presented as a progressive research programme provided by (econo)physicists for theoretical problems encountered in financial economics in the 1960s and the 1970s.

Much Polyphony but Little Harmony: Otto Sackur's Groping for a Quantum Theory of Gases

NASA Astrophysics Data System (ADS)

Badino, Massimiliano; Friedrich, Bretislav

2013-09-01

The endeavor of Otto Sackur (1880-1914) was driven, on the one hand, by his interest in Nernst's heat theorem, statistical mechanics, and the problem of chemical equilibrium and, on the other hand, by his goal to shed light on classical mechanics from the quantum vantage point. Inspired by the interplay between classical physics and quantum theory, Sackur chanced to expound his personal take on the role of the quantum in the changing landscape of physics in the turbulent 1910s. We tell the story of this enthusiastic practitioner of the old quantum theory and early contributor to quantum statistical mechanics, whose scientific ontogenesis provides a telling clue about the phylogeny of his contemporaries.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

PubMed

Dixit, Purushottam D; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A

2018-01-07

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Lindemann histograms as a new method to analyse nano-patterns and phases

NASA Astrophysics Data System (ADS)

Makey, Ghaith; Ilday, Serim; Tokel, Onur; Ibrahim, Muhamet; Yavuz, Ozgun; Pavlov, Ihor; Gulseren, Oguz; Ilday, Omer

The detection, observation, and analysis of material phases and atomistic patterns are of great importance for understanding systems exhibiting both equilibrium and far-from-equilibrium dynamics. As such, there is intense research on phase transitions and pattern dynamics in soft matter, statistical and nonlinear physics, and polymer physics. In order to identify phases and nano-patterns, the pair correlation function is commonly used. However, this approach is limited in terms of recognizing competing patterns in dynamic systems, and lacks visualisation capabilities. In order to solve these limitations, we introduce Lindemann histogram quantification as an alternative method to analyse solid, liquid, and gas phases, along with hexagonal, square, and amorphous nano-pattern symmetries. We show that the proposed approach based on Lindemann parameter calculated per particle maps local number densities to material phase or particles pattern. We apply the Lindemann histogram method on dynamical colloidal self-assembly experimental data and identify competing patterns.

PREFACE: Advanced many-body and statistical methods in mesoscopic systems

NASA Astrophysics Data System (ADS)

Anghel, Dragos Victor; Sabin Delion, Doru; Sorin Paraoanu, Gheorghe

2012-02-01

It has increasingly been realized in recent times that the borders separating various subfields of physics are largely artificial. This is the case for nanoscale physics, physics of lower-dimensional systems and nuclear physics, where the advanced techniques of many-body theory developed in recent times could provide a unifying framework for these disciplines under the general name of mesoscopic physics. Other fields, such as quantum optics and quantum information, are increasingly using related methods. The 6-day conference 'Advanced many-body and statistical methods in mesoscopic systems' that took place in Constanta, Romania, between 27 June and 2 July 2011 was, we believe, a successful attempt at bridging an impressive list of topical research areas: foundations of quantum physics, equilibrium and non-equilibrium quantum statistics/fractional statistics, quantum transport, phases and phase transitions in mesoscopic systems/superfluidity and superconductivity, quantum electromechanical systems, quantum dissipation, dephasing, noise and decoherence, quantum information, spin systems and their dynamics, fundamental symmetries in mesoscopic systems, phase transitions, exactly solvable methods for mesoscopic systems, various extension of the random phase approximation, open quantum systems, clustering, decay and fission modes and systematic versus random behaviour of nuclear spectra. This event brought together participants from seventeen countries and five continents. Each of the participants brought considerable expertise in his/her field of research and, at the same time, was exposed to the newest results and methods coming from the other, seemingly remote, disciplines. The talks touched on subjects that are at the forefront of topical research areas and we hope that the resulting cross-fertilization of ideas will lead to new, interesting results from which everybody will benefit. We are grateful for the financial and organizational support from IFIN-HH, Ovidius University (where the conference took place), the Academy of Romanian Scientists and the Romanian National Authority for Scientific Research. This conference proceedings volume brings together some of the invited and contributed talks of the conference. The hope of the editors is that they will constitute reference material for applying many-body techniques to problems in mesoscopic and nuclear physics. We thank all the participants for their contribution to the success of this conference. D V Anghel and D S Delion IFIN-HH, Bucharest, Romania G S Paraoanu Aalto University, Finland Conference photograph

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems.

PubMed

Liu, Xinzijian; Liu, Jian

2018-03-14

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Path integral molecular dynamics for exact quantum statistics of multi-electronic-state systems

NASA Astrophysics Data System (ADS)

Liu, Xinzijian; Liu, Jian

2018-03-01

An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD), Liu et al. [J. Chem. Phys. 145, 024103 (2016)] and Zhang et al. [J. Chem. Phys. 147, 034109 (2017)], for quantum statistical mechanics when a single potential energy surface is involved. We first define an effective potential function that is numerically favorable for MES-PIMD and then derive corresponding estimators in MES-PIMD for evaluating various physical properties. Its application to several representative one-dimensional and multi-dimensional models demonstrates that MES-PIMD in principle offers a practical tool in either of the diabatic and adiabatic representations for studying exact quantum statistics of complex/large MES systems when the Born-Oppenheimer approximation, Condon approximation, and harmonic bath approximation are broken.

Fermi liquid, clustering, and structure factor in dilute warm nuclear matter

NASA Astrophysics Data System (ADS)

Röpke, G.; Voskresensky, D. N.; Kryukov, I. A.; Blaschke, D.

2018-02-01

Properties of nuclear systems at subsaturation densities can be obtained from different approaches. We demonstrate the use of the density autocorrelation function which is related to the isothermal compressibility and, after integration, to the equation of state. This way we connect the Landau Fermi liquid theory well elaborated in nuclear physics with the approaches to dilute nuclear matter describing cluster formation. A quantum statistical approach is presented, based on the cluster decomposition of the polarization function. The fundamental quantity to be calculated is the dynamic structure factor. Comparing with the Landau Fermi liquid theory which is reproduced in lowest approximation, the account of bound state formation and continuum correlations gives the correct low-density result as described by the second virial coefficient and by the mass action law (nuclear statistical equilibrium). Going to higher densities, the inclusion of medium effects is more involved compared with other quantum statistical approaches, but the relation to the Landau Fermi liquid theory gives a promising approach to describe not only thermodynamic but also collective excitations and non-equilibrium properties of nuclear systems in a wide region of the phase diagram.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

PubMed Central

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-01

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

Automated sampling assessment for molecular simulations using the effective sample size

PubMed Central

Zhang, Xin; Bhatt, Divesh; Zuckerman, Daniel M.

2010-01-01

To quantify the progress in the development of algorithms and forcefields used in molecular simulations, a general method for the assessment of the sampling quality is needed. Statistical mechanics principles suggest the populations of physical states characterize equilibrium sampling in a fundamental way. We therefore develop an approach for analyzing the variances in state populations, which quantifies the degree of sampling in terms of the effective sample size (ESS). The ESS estimates the number of statistically independent configurations contained in a simulated ensemble. The method is applicable to both traditional dynamics simulations as well as more modern (e.g., multi–canonical) approaches. Our procedure is tested in a variety of systems from toy models to atomistic protein simulations. We also introduce a simple automated procedure to obtain approximate physical states from dynamic trajectories: this allows sample–size estimation in systems for which physical states are not known in advance. PMID:21221418

Nonequilibrium thermodynamics and information theory: basic concepts and relaxing dynamics

NASA Astrophysics Data System (ADS)

Altaner, Bernhard

2017-11-01

Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we give a detailed didactic account on the relations between energy and entropy and thus physics and information theory. We show that thermodynamic process inequalities, like the second law, are equivalent to the requirement that an effective description for physical dynamics is strongly relaxing. From the perspective of information theory, strongly relaxing dynamics govern the irreversible convergence of a statistical ensemble towards the maximally non-commital probability distribution that is compatible with thermodynamic equilibrium parameters. In particular, Markov processes that converge to a thermodynamic equilibrium state are strongly relaxing. Our framework generalizes previous results to arbitrary open and driven systems, yielding novel thermodynamic bounds for idealized and real processes. , which features invited work from the best early-career researchers working within the scope of J. Phys. A. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Bernhard Altaner was selected by the Editorial Board of J. Phys. A as an Emerging Talent.

Non-extensive statistical analysis of magnetic field during the March 2012 ICME event using a multi-spacecraft approach

NASA Astrophysics Data System (ADS)

Pavlos, G. P.; Malandraki, O. E.; Pavlos, E. G.; Iliopoulos, A. C.; Karakatsanis, L. P.

2016-12-01

In this study we present some new and significant results concerning the dynamics of interplanetary coronal mass ejections (ICMEs) observed in the near Earth at L1 solar wind environment, as well as its effect in Earth's magnetosphere. The results are referred to Tsallis non-extensive statistics and in particular to the estimation of Tsallis q-triplet, (qstat ,qsen ,qrel) of magnetic field time series of the ICME observed at the Earth resulting from the solar eruptive activity on March 7, 2012 at the Sun. For this, we used a multi-spacecraft approach based on data experiments from ACE, CLUSTER 4, THEMIS-E and THEMIS-C spacecraft. For the data analysis different time periods were considered, sorted as ;quiet;, ;shock; and ;aftershock;, while different space domains such as the Interplanetary space (near Earth at L1 and upstream of the Earth's bowshock), the Earth's magnetosheath and magnetotail, were also taken into account. Our results reveal significant differences in statistical and dynamical features, indicating important variations of the magnetic field dynamics both in time and space domains during the shock event, in terms of rate of entropy production, relaxation dynamics and non-equilibrium meta-stable stationary states. So far, Tsallis non-extensive statistical theory and Tsallis extension of the Boltzmann-Gibbs entropy principle to the q-entropy principle (Tsallis, 1988, 2009) reveal strong universality character concerning non-equilibrium dynamics (Pavlos et al. 2012a,b, 2014a,b; Karakatsanis et al. 2013). Tsallis q-entropy principle can explain the emergence of a series of new and significant physical characteristics in distributed systems as well as in space plasmas. Such characteristics are: non-Gaussian statistics and anomalous diffusion processes, strange and fractional dynamics, multifractal, percolating and intermittent turbulence structures, multiscale and long spatio-temporal correlations, fractional acceleration and Non-Equilibrium Stationary States (NESS) or non-equilibrium self-organization process and non-equilibrium phase transition and topological phase transition processes according to Zelenyi and Milovanov (2004). In this direction, our results reveal clearly strong self-organization and development of macroscopic ordering of plasma system related to strengthen of non-extensivity, multifractality and intermittency everywhere in the space plasmas region during the CME event.

The applications of Complexity Theory and Tsallis Non-extensive Statistics at Solar Plasma Dynamics

NASA Astrophysics Data System (ADS)

Pavlos, George

2015-04-01

As the solar plasma lives far from equilibrium it is an excellent laboratory for testing complexity theory and non-equilibrium statistical mechanics. In this study, we present the highlights of complexity theory and Tsallis non extensive statistical mechanics as concerns their applications at solar plasma dynamics, especially at sunspot, solar flare and solar wind phenomena. Generally, when a physical system is driven far from equilibrium states some novel characteristics can be observed related to the nonlinear character of dynamics. Generally, the nonlinearity in space plasma dynamics can generate intermittent turbulence with the typical characteristics of the anomalous diffusion process and strange topologies of stochastic space plasma fields (velocity and magnetic fields) caused by the strange dynamics and strange kinetics (Zaslavsky, 2002). In addition, according to Zelenyi and Milovanov (2004) the complex character of the space plasma system includes the existence of non-equilibrium (quasi)-stationary states (NESS) having the topology of a percolating fractal set. The stabilization of a system near the NESS is perceived as a transition into a turbulent state determined by self-organization processes. The long-range correlation effects manifest themselves as a strange non-Gaussian behavior of kinetic processes near the NESS plasma state. The complex character of space plasma can also be described by the non-extensive statistical thermodynamics pioneered by Tsallis, which offers a consistent and effective theoretical framework, based on a generalization of Boltzmann - Gibbs (BG) entropy, to describe far from equilibrium nonlinear complex dynamics (Tsallis, 2009). In a series of recent papers, the hypothesis of Tsallis non-extensive statistics in magnetosphere, sunspot dynamics, solar flares, solar wind and space plasma in general, was tested and verified (Karakatsanis et al., 2013; Pavlos et al., 2014; 2015). Our study includes the analysis of solar plasma time series at three cases: sunspot index, solar flare and solar wind data. The non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988; 2004; 2009). The q-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using the q-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000, 2001). Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zelenyi and Milovanov's studies (Zelenyi and Milovanov, 1991; Milovanov and Zelenyi, 1993; Ruzmakin et al., 1996), (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of: (i) non-Gaussian probability distribution function P(x), (ii) multifractal scaling exponent spectrum f(a) and generalized Renyi dimension spectrum Dq, (iii) exponent spectrum J(p) of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics. Also, the q-triplet of Tsallis as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the singular value decomposition (SVD) components of the solar flares timeseries. Also the multifractal scaling exponent spectrum f(a), the generalized Renyi dimension spectrum D(q) and the spectrum J(p) of the structure function exponents were estimated experimentally and theoretically by using the q-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2000). Our analysis showed clearly the following: (a) a phase transition process in the solar flare dynamics from a high dimensional non-Gaussian self-organized critical (SOC) state to a low dimensional also non-Gaussian chaotic state, (b) strong intermittent solar corona turbulence and an anomalous (multifractal) diffusion solar corona process, which is strengthened as the solar corona dynamics makes a phase transition to low dimensional chaos, (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of the functions: (i) non-Gaussian probability distribution function P(x), (ii) f(a) and D(q), and (iii) J(p) for the solar flares timeseries and its underlying non-equilibrium solar dynamics, and (d) the solar flare dynamical profile is revealed similar to the dynamical profile of the solar corona zone as far as the phase transition process from self-organized criticality (SOC) to chaos state. However the solar low corona (solar flare) dynamical characteristics can be clearly discriminated from the dynamical characteristics of the solar convection zone. At last we present novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which can take place in Solar wind plasma system. The solar wind plasma as well as the entire solar plasma system is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields ( ) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992). References 1. T. Arimitsu, N. Arimitsu, Tsallis statistics and fully developed turbulence, J. Phys. A: Math. Gen. 33 (2000) L235. 2. T. Arimitsu, N. Arimitsu, Analysis of turbulence by statistics based on generalized entropies, Physica A 295 (2001) 177-194. 3. T. Chang, Low-dimensional behavior and symmetry braking of stochastic systems near criticality can these effects be observed in space and in the laboratory, IEEE 20 (6) (1992) 691-694. 4. U. Frisch, Turbulence, Cambridge University Press, Cambridge, UK, 1996, p. 310. 5. L.P. Karakatsanis, G.P. Pavlos, M.N. Xenakis, Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar flares dynamics, Physica A 392 (2013) 3920-3944. 6. A.V. Milovanov, Topological proof for the Alexander-Orbach conjecture, Phys. Rev. E 56 (3) (1997) 2437-2446. 7. A.V. Milovanov, L.M. Zelenyi, Fracton excitations as a driving mechanism for the self-organized dynamical structuring in the solar wind, Astrophys. Space Sci. 264 (1-4) (1999) 317-345. 8. A.V. Milovanov, Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation: large-scale behavior of the turbulent transport coefficient, Phys. Rev. E 63 (2001) 047301. 9. G.P. Pavlos, et al., Universality of non-extensive Tsallis statistics and time series analysis: Theory and applications, Physica A 395 (2014) 58-95. 10. G.P. Pavlos, et al., Tsallis non-extensive statistics and solar wind plasma complexity, Physica A 422 (2015) 113-135. 11. A.A. Ruzmaikin, et al., Spectral properties of solar convection and diffusion, ApJ 471 (1996) 1022. 12. V.E. Tarasov, Review of some promising fractional physical models, Internat. J. Modern Phys. B 27 (9) (2013) 1330005. 13. C. Tsallis, Possible generalization of BG statistics, J. Stat. Phys. J 52 (1-2) (1988) 479-487. 14. C. Tsallis, Nonextensive statistical mechanics: construction and physical interpretation, in: G.M. Murray, C. Tsallis (Eds.), Nonextensive Entropy-Interdisciplinary Applications, Oxford Univ. Press, 2004, pp. 1-53. 15. C. Tsallis, Introduction to Non-Extensive Statistical Mechanics, Springer, 2009. 16. G.M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Physics Reports 371 (2002) 461-580. 17. L.M. Zelenyi, A.V. Milovanov, Fractal properties of sunspots, Sov. Astron. Lett. 17 (6) (1991) 425. 18. L.M. Zelenyi, A.V. Milovanov, Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics, Phys.-Usp. 47 (8), (2004) 749-788.

Space-time models based on random fields with local interactions

NASA Astrophysics Data System (ADS)

Hristopulos, Dionissios T.; Tsantili, Ivi C.

2016-08-01

The analysis of space-time data from complex, real-life phenomena requires the use of flexible and physically motivated covariance functions. In most cases, it is not possible to explicitly solve the equations of motion for the fields or the respective covariance functions. In the statistical literature, covariance functions are often based on mathematical constructions. In this paper, we propose deriving space-time covariance functions by solving “effective equations of motion”, which can be used as statistical representations of systems with diffusive behavior. In particular, we propose to formulate space-time covariance functions based on an equilibrium effective Hamiltonian using the linear response theory. The effective space-time dynamics is then generated by a stochastic perturbation around the equilibrium point of the classical field Hamiltonian leading to an associated Langevin equation. We employ a Hamiltonian which extends the classical Gaussian field theory by including a curvature term and leads to a diffusive Langevin equation. Finally, we derive new forms of space-time covariance functions.

Statistical Analysis of Hubble /WFC3 Transit Spectroscopy of Extrasolar Planets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Guangwei; Deming, Drake; Knutson, Heather

2017-10-01

Transmission spectroscopy provides a window to study exoplanetary atmospheres, but that window is fogged by clouds and hazes. Clouds and haze introduce a degeneracy between the strength of gaseous absorption features and planetary physical parameters such as abundances. One way to break that degeneracy is via statistical studies. We collect all published HST /WFC3 transit spectra for 1.1–1.65 μ m water vapor absorption and perform a statistical study on potential correlations between the water absorption feature and planetary parameters. We fit the observed spectra with a template calculated for each planet using the Exo-transmit code. We express the magnitude ofmore » the water absorption in scale heights, thereby removing the known dependence on temperature, surface gravity, and mean molecular weight. We find that the absorption in scale heights has a positive baseline correlation with planetary equilibrium temperature; our hypothesis is that decreasing cloud condensation with increasing temperature is responsible for this baseline slope. However, the observed sample is also intrinsically degenerate in the sense that equilibrium temperature correlates with planetary mass. We compile the distribution of absorption in scale heights, and we find that this distribution is closer to log-normal than Gaussian. However, we also find that the distribution of equilibrium temperatures for the observed planets is similarly log-normal. This indicates that the absorption values are affected by observational bias, whereby observers have not yet targeted a sufficient sample of the hottest planets.« less

Statistical Analysis of Hubble/WFC3 Transit Spectroscopy of Extrasolar Planets

NASA Astrophysics Data System (ADS)

Fu, Guangwei; Deming, Drake; Knutson, Heather; Madhusudhan, Nikku; Mandell, Avi; Fraine, Jonathan

2018-01-01

Transmission spectroscopy provides a window to study exoplanetary atmospheres, but that window is fogged by clouds and hazes. Clouds and haze introduce a degeneracy between the strength of gaseous absorption features and planetary physical parameters such as abundances. One way to break that degeneracy is via statistical studies. We collect all published HST/WFC3 transit spectra for 1.1-1.65 micron water vapor absorption, and perform a statistical study on potential correlations between the water absorption feature and planetary parameters. We fit the observed spectra with a template calculated for each planet using the Exo-Transmit code. We express the magnitude of the water absorption in scale heights, thereby removing the known dependence on temperature, surface gravity, and mean molecular weight. We find that the absorption in scale heights has a positive baseline correlation with planetary equilibrium temperature; our hypothesis is that decreasing cloud condensation with increasing temperature is responsible for this baseline slope. However, the observed sample is also intrinsically degenerate in the sense that equilibrium temperature correlates with planetary mass. We compile the distribution of absorption in scale heights, and we find that this distribution is closer to log-normal than Gaussian. However, we also find that the distribution of equilibrium temperatures for the observed planets is similarly log-normal. This indicates that the absorption values are affected by observational bias, whereby observers have not yet targeted a sufficient sample of the hottest planets.

Statistical Analysis of Hubble/WFC3 Transit Spectroscopy of Extrasolar Planets

NASA Astrophysics Data System (ADS)

Fu, Guangwei; Deming, Drake; Knutson, Heather; Madhusudhan, Nikku; Mandell, Avi; Fraine, Jonathan

2017-10-01

Transmission spectroscopy provides a window to study exoplanetary atmospheres, but that window is fogged by clouds and hazes. Clouds and haze introduce a degeneracy between the strength of gaseous absorption features and planetary physical parameters such as abundances. One way to break that degeneracy is via statistical studies. We collect all published HST/WFC3 transit spectra for 1.1-1.65 μm water vapor absorption and perform a statistical study on potential correlations between the water absorption feature and planetary parameters. We fit the observed spectra with a template calculated for each planet using the Exo-transmit code. We express the magnitude of the water absorption in scale heights, thereby removing the known dependence on temperature, surface gravity, and mean molecular weight. We find that the absorption in scale heights has a positive baseline correlation with planetary equilibrium temperature; our hypothesis is that decreasing cloud condensation with increasing temperature is responsible for this baseline slope. However, the observed sample is also intrinsically degenerate in the sense that equilibrium temperature correlates with planetary mass. We compile the distribution of absorption in scale heights, and we find that this distribution is closer to log-normal than Gaussian. However, we also find that the distribution of equilibrium temperatures for the observed planets is similarly log-normal. This indicates that the absorption values are affected by observational bias, whereby observers have not yet targeted a sufficient sample of the hottest planets.

Inferring the parameters of a Markov process from snapshots of the steady state

NASA Astrophysics Data System (ADS)

Dettmer, Simon L.; Berg, Johannes

2018-02-01

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous configurations. We apply the method to non-equilibrium models from statistical physics and theoretical biology, including the asymmetric simple exclusion process (ASEP), the kinetic Ising model, and replicator dynamics.

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Punjabi, Alkesh; Ali, Halima

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates ({psi},{theta}) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. {psi} is the toroidal magnetic flux and {theta} is the poloidal angle. Natural canonical coordinates ({psi},{theta},{phi}) can be transformed to physical position (R,Z,{phi}) using a canonical transformation. (R,Z,{phi}) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonicalmore » coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.« less

Symplectic approach to calculation of magnetic field line trajectories in physical space with realistic magnetic geometry in divertor tokamaks

NASA Astrophysics Data System (ADS)

Punjabi, Alkesh; Ali, Halima

2008-12-01

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates (ψ,θ) from experimental data from a Grad-Shafranov equilibrium solver for a tokamak. ψ is the toroidal magnetic flux and θ is the poloidal angle. Natural canonical coordinates (ψ,θ,φ) can be transformed to physical position (R,Z,φ) using a canonical transformation. (R,Z,φ) are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates (x,y) or (R,Z), the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.

Statistical equilibrium in cometary C2. II - Swan/Phillips band ratios

NASA Technical Reports Server (NTRS)

Swamy, K. S. K.; Odell, C. R.

1979-01-01

Statistical equilibrium calculations have been made for both the triplet and ground state singlets for C2 in comets, using the exchange rate as a free parameter. The predictions of the results are consistent with optical observations and may be tested definitively by accurate observations of the Phillips and Swan band ratios. Comparison with the one reported observation indicates compatibility with a low exchange rate and resonance fluorescence statistical equilibrium.

Non-equilibrium Statistical Mechanics and the Sea Ice Thickness Distribution

NASA Astrophysics Data System (ADS)

Wettlaufer, John; Toppaladoddi, Srikanth

We use concepts from non-equilibrium statistical physics to transform the original evolution equation for the sea ice thickness distribution g (h) due to Thorndike et al., (1975) into a Fokker-Planck like conservation law. The steady solution is g (h) = calN (q) hqe - h / H , where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h << 1 , g (h) is controlled by both thermodynamics and mechanics, whereas for h >> 1 only mechanics controls g (h) . Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g (h) . This allows us to demonstrate that the ice thickness field is ergodic. The genericity of our approach provides a framework for studying the geophysical scale structure of the ice pack using methods of broad relevance in statistical mechanics. Swedish Research Council Grant No. 638-2013-9243, NASA Grant NNH13ZDA001N-CRYO and the National Science Foundation and the Office of Naval Research under OCE-1332750 for support.

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

Taverniers, Søren; Haut, Terry S; Barros, Kipton; Alexander, Francis J; Lookman, Turab

2015-11-01

In materials science and many other research areas, models are frequently inferred without considering their generalization to unseen data. We apply statistical learning using cross-validation to obtain an optimally predictive coarse-grained description of a two-dimensional kinetic nearest-neighbor Ising model with Glauber dynamics (GD) based on the stochastic Ginzburg-Landau equation (sGLE). The latter is learned from GD "training" data using a log-likelihood analysis, and its predictive ability for various complexities of the model is tested on GD "test" data independent of the data used to train the model on. Using two different error metrics, we perform a detailed analysis of the error between magnetization time trajectories simulated using the learned sGLE coarse-grained description and those obtained using the GD model. We show that both for equilibrium and out-of-equilibrium GD training trajectories, the standard phenomenological description using a quartic free energy does not always yield the most predictive coarse-grained model. Moreover, increasing the amount of training data can shift the optimal model complexity to higher values. Our results are promising in that they pave the way for the use of statistical learning as a general tool for materials modeling and discovery.

Tsallis non-extensive statistics and solar wind plasma complexity

NASA Astrophysics Data System (ADS)

Pavlos, G. P.; Iliopoulos, A. C.; Zastenker, G. N.; Zelenyi, L. M.; Karakatsanis, L. P.; Riazantseva, M. O.; Xenakis, M. N.; Pavlos, E. G.

2015-03-01

This article presents novel results revealing non-equilibrium phase transition processes in the solar wind plasma during a strong shock event, which took place on 26th September 2011. Solar wind plasma is a typical case of stochastic spatiotemporal distribution of physical state variables such as force fields (B → , E →) and matter fields (particle and current densities or bulk plasma distributions). This study shows clearly the non-extensive and non-Gaussian character of the solar wind plasma and the existence of multi-scale strong correlations from the microscopic to the macroscopic level. It also underlines the inefficiency of classical magneto-hydro-dynamic (MHD) or plasma statistical theories, based on the classical central limit theorem (CLT), to explain the complexity of the solar wind dynamics, since these theories include smooth and differentiable spatial-temporal functions (MHD theory) or Gaussian statistics (Boltzmann-Maxwell statistical mechanics). On the contrary, the results of this study indicate the presence of non-Gaussian non-extensive statistics with heavy tails probability distribution functions, which are related to the q-extension of CLT. Finally, the results of this study can be understood in the framework of modern theoretical concepts such as non-extensive statistical mechanics (Tsallis, 2009), fractal topology (Zelenyi and Milovanov, 2004), turbulence theory (Frisch, 1996), strange dynamics (Zaslavsky, 2002), percolation theory (Milovanov, 1997), anomalous diffusion theory and anomalous transport theory (Milovanov, 2001), fractional dynamics (Tarasov, 2013) and non-equilibrium phase transition theory (Chang, 1992).

Origins and properties of kappa distributions in space plasmas

NASA Astrophysics Data System (ADS)

Livadiotis, George

2016-07-01

Classical particle systems reside at thermal equilibrium with their velocity distribution function stabilized into a Maxwell distribution. On the contrary, collisionless and correlated particle systems, such as the space and astrophysical plasmas, are characterized by a non-Maxwellian behavior, typically described by the so-called kappa distributions. Empirical kappa distributions have become increasingly widespread across space and plasma physics. However, a breakthrough in the field came with the connection of kappa distributions to the solid statistical framework of Tsallis non-extensive statistical mechanics. Understanding the statistical origin of kappa distributions was the cornerstone of further theoretical developments and applications, some of which will be presented in this talk: (i) The physical meaning of thermal parameters, e.g., temperature and kappa index; (ii) the multi-particle description of kappa distributions; (iii) the phase-space kappa distribution of a Hamiltonian with non-zero potential; (iv) the Sackur-Tetrode entropy for kappa distributions, and (v) the new quantization constant, h _{*}˜10 ^{-22} Js.

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

NASA Technical Reports Server (NTRS)

Yeh, Leehwa

1993-01-01

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.

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

NASA Astrophysics Data System (ADS)

Pigolotti, Simone; Cencini, Massimo; Molina, Daniel; Muñoz, Miguel A.

2018-07-01

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D = 2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

NASA Astrophysics Data System (ADS)

Pigolotti, Simone; Cencini, Massimo; Molina, Daniel; Muñoz, Miguel A.

2017-11-01

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D = 2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

Phase Equilibrium, Chemical Equilibrium, and a Test of the Third Law: Experiments for Physical Chemistry.

ERIC Educational Resources Information Center

Dannhauser, Walter

1980-01-01

Described is an experiment designed to provide an experimental basis for a unifying point of view (utilizing theoretical framework and chemistry laboratory experiments) for physical chemistry students. Three experiments are described: phase equilibrium, chemical equilibrium, and a test of the third law of thermodynamics. (Author/DS)

Non-equilibrium dog-flea model

NASA Astrophysics Data System (ADS)

Ackerson, Bruce J.

2017-11-01

We develop the open dog-flea model to serve as a check of proposed non-equilibrium theories of statistical mechanics. The model is developed in detail. Then it is applied to four recent models for non-equilibrium statistical mechanics. Comparison of the dog-flea solution with these different models allows checking claims and giving a concrete example of the theoretical models.

Strategies for Reduced-Order Models in Uncertainty Quantification of Complex Turbulent Dynamical Systems

NASA Astrophysics Data System (ADS)

Qi, Di

Turbulent dynamical systems are ubiquitous in science and engineering. Uncertainty quantification (UQ) in turbulent dynamical systems is a grand challenge where the goal is to obtain statistical estimates for key physical quantities. In the development of a proper UQ scheme for systems characterized by both a high-dimensional phase space and a large number of instabilities, significant model errors compared with the true natural signal are always unavoidable due to both the imperfect understanding of the underlying physical processes and the limited computational resources available. One central issue in contemporary research is the development of a systematic methodology for reduced order models that can recover the crucial features both with model fidelity in statistical equilibrium and with model sensitivity in response to perturbations. In the first part, we discuss a general mathematical framework to construct statistically accurate reduced-order models that have skill in capturing the statistical variability in the principal directions of a general class of complex systems with quadratic nonlinearity. A systematic hierarchy of simple statistical closure schemes, which are built through new global statistical energy conservation principles combined with statistical equilibrium fidelity, are designed and tested for UQ of these problems. Second, the capacity of imperfect low-order stochastic approximations to model extreme events in a passive scalar field advected by turbulent flows is investigated. The effects in complicated flow systems are considered including strong nonlinear and non-Gaussian interactions, and much simpler and cheaper imperfect models with model error are constructed to capture the crucial statistical features in the stationary tracer field. Several mathematical ideas are introduced to improve the prediction skill of the imperfect reduced-order models. Most importantly, empirical information theory and statistical linear response theory are applied in the training phase for calibrating model errors to achieve optimal imperfect model parameters; and total statistical energy dynamics are introduced to improve the model sensitivity in the prediction phase especially when strong external perturbations are exerted. The validity of reduced-order models for predicting statistical responses and intermittency is demonstrated on a series of instructive models with increasing complexity, including the stochastic triad model, the Lorenz '96 model, and models for barotropic and baroclinic turbulence. The skillful low-order modeling methods developed here should also be useful for other applications such as efficient algorithms for data assimilation.

Entropy in self-similar shock profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Solitosynthesis: Cosmological evolution of non-topological solitons

NASA Technical Reports Server (NTRS)

Griest, Kim; Kolb, Edward W.

1989-01-01

The thermal creation, fusion, evaporation, and destruction of non-topological solitons (NTS) after a phase transition in the early universe is considered. By defining and following NTS statistical equilibrium and departures from it, and depending on particle physics parameters, one of three possible scenarios occurs. If reaction rates are high enough, a period of equilibrium occurs and relic abundances are determined by the freeze-out temperature. Equilibrium first drives most NTS's into their constituents (free phi particles) and then causes rapid fusion into large NTS's. If freeze-out occurs during the first phase, the NTS's are almost entirely destroyed, while if it occurs during the second phase, solitosynthesis occurs and NTS's may be cosmically relevant. For slow reaction rates the NTS's are born frozen out and have the abundance determined by the phase transition. Analytic approximations for determining the abundances are developed, and tested by numerically integrating a reaction network in an expanding universe. Unfortunately, for most of the parameter space considered, solito-destruction/evaporation occurs.

Entropy in self-similar shock profiles

DOE PAGES

Margolin, Len G.; Reisner, Jon Michael; Jordan, Pedro M.

2017-07-16

In this paper, we study the structure of a gaseous shock, and in particular the distribution of entropy within, in both a thermodynamics and a statistical mechanics context. The problem of shock structure has a long and distinguished history that we review. We employ the Navier–Stokes equations to construct a self–similar version of Becker’s solution for a shock assuming a particular (physically plausible) Prandtl number; that solution reproduces the well–known result of Morduchow & Libby that features a maximum of the equilibrium entropy inside the shock profile. We then construct an entropy profile, based on gas kinetic theory, that ismore » smooth and monotonically increasing. The extension of equilibrium thermodynamics to irreversible processes is based in part on the assumption of local thermodynamic equilibrium. We show that this assumption is not valid except for the weakest shocks. Finally, we conclude by hypothesizing a thermodynamic nonequilibrium entropy and demonstrating that it closely estimates the gas kinetic nonequilibrium entropy within a shock.« less

Statistical physics of human cooperation

NASA Astrophysics Data System (ADS)

Perc, Matjaž; Jordan, Jillian J.; Rand, David G.; Wang, Zhen; Boccaletti, Stefano; Szolnoki, Attila

2017-05-01

Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is indeed due, to a large degree, to our unparalleled other-regarding abilities. Yet, a comprehensive understanding of human cooperation remains a formidable challenge. Recent research in the social sciences indicates that it is important to focus on the collective behavior that emerges as the result of the interactions among individuals, groups, and even societies. Non-equilibrium statistical physics, in particular Monte Carlo methods and the theory of collective behavior of interacting particles near phase transition points, has proven to be very valuable for understanding counterintuitive evolutionary outcomes. By treating models of human cooperation as classical spin models, a physicist can draw on familiar settings from statistical physics. However, unlike pairwise interactions among particles that typically govern solid-state physics systems, interactions among humans often involve group interactions, and they also involve a larger number of possible states even for the most simplified description of reality. The complexity of solutions therefore often surpasses that observed in physical systems. Here we review experimental and theoretical research that advances our understanding of human cooperation, focusing on spatial pattern formation, on the spatiotemporal dynamics of observed solutions, and on self-organization that may either promote or hinder socially favorable states.

Statistical physics studies of multilayer adsorption isotherm in food materials and pore size distribution

NASA Astrophysics Data System (ADS)

Aouaini, F.; Knani, S.; Ben Yahia, M.; Ben Lamine, A.

2015-08-01

Water sorption isotherms of foodstuffs are very important in different areas of food science engineering such as for design, modeling and optimization of many processes. The equilibrium moisture content is an important parameter in models used to predict changes in the moisture content of a product during storage. A formulation of multilayer model with two energy levels was based on statistical physics and theoretical considerations. Thanks to the grand canonical ensemble in statistical physics. Some physicochemical parameters related to the adsorption process were introduced in the analytical model expression. The data tabulated in literature of water adsorption at different temperatures on: chickpea seeds, lentil seeds, potato and on green peppers were described applying the most popular models applied in food science. We also extend the study to the newest proposed model. It is concluded that among studied models the proposed model seems to be the best for description of data in the whole range of relative humidity. By using our model, we were able to determine the thermodynamic functions. The measurement of desorption isotherms, in particular a gas over a solid porous, allows access to the distribution of pore size PSD.

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach.

PubMed

Chertkov, Michael; Chernyak, Vladimir

2017-08-17

Thermostatically controlled loads, e.g., air conditioners and heaters, are by far the most widespread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control - changing from on to off, and vice versa, depending on temperature. We considered aggregation of a large group of similar devices into a statistical ensemble, where the devices operate following the same dynamics, subject to stochastic perturbations and randomized, Poisson on/off switching policy. Using theoretical and computational tools of statistical physics, we analyzed how the ensemble relaxes to a stationary distribution and established a relationship between the relaxation and the statistics of the probability flux associated with devices' cycling in the mixed (discrete, switch on/off, and continuous temperature) phase space. This allowed us to derive the spectrum of the non-equilibrium (detailed balance broken) statistical system and uncover how switching policy affects oscillatory trends and the speed of the relaxation. Relaxation of the ensemble is of practical interest because it describes how the ensemble recovers from significant perturbations, e.g., forced temporary switching off aimed at utilizing the flexibility of the ensemble to provide "demand response" services to change consumption temporarily to balance a larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

DOE PAGES

Chertkov, Michael; Chernyak, Vladimir

2017-01-17

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxationmore » and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.« less

Ensemble of Thermostatically Controlled Loads: Statistical Physics Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chertkov, Michael; Chernyak, Vladimir

Thermostatically Controlled Loads (TCL), e.g. air-conditioners and heaters, are by far the most wide-spread consumers of electricity. Normally the devices are calibrated to provide the so-called bang-bang control of temperature - changing from on to off , and vice versa, depending on temperature. Aggregation of a large group of similar devices into a statistical ensemble is considered, where the devices operate following the same dynamics subject to stochastic perturbations and randomized, Poisson on/off switching policy. We analyze, using theoretical and computational tools of statistical physics, how the ensemble relaxes to a stationary distribution and establish relation between the re- laxationmore » and statistics of the probability flux, associated with devices' cycling in the mixed (discrete, switch on/off , and continuous, temperature) phase space. This allowed us to derive and analyze spec- trum of the non-equilibrium (detailed balance broken) statistical system. and uncover how switching policy affects oscillatory trend and speed of the relaxation. Relaxation of the ensemble is of a practical interest because it describes how the ensemble recovers from significant perturbations, e.g. forceful temporary switching o aimed at utilizing flexibility of the ensemble in providing "demand response" services relieving consumption temporarily to balance larger power grid. We discuss how the statistical analysis can guide further development of the emerging demand response technology.« less

Adsorption of diclofenac and nimesulide on activated carbon: Statistical physics modeling and effect of adsorbate size

NASA Astrophysics Data System (ADS)

Sellaoui, Lotfi; Mechi, Nesrine; Lima, Éder Cláudio; Dotto, Guilherme Luiz; Ben Lamine, Abdelmottaleb

2017-10-01

Based on statistical physics elements, the equilibrium adsorption of diclofenac (DFC) and nimesulide (NM) on activated carbon was analyzed by a multilayer model with saturation. The paper aimed to describe experimentally and theoretically the adsorption process and study the effect of adsorbate size using the model parameters. From numerical simulation, the number of molecules per site showed that the adsorbate molecules (DFC and NM) were mostly anchored in both sides of the pore walls. The receptor sites density increase suggested that additional sites appeared during the process, to participate in DFC and NM adsorption. The description of the adsorption energy behavior indicated that the process was physisorption. Finally, by a model parameters correlation, the size effect of the adsorbate was deduced indicating that the molecule dimension has a negligible effect on the DFC and NM adsorption.

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

NASA Astrophysics Data System (ADS)

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.

Phase-space dynamics of opposition control in wall-bounded turbulent flows

NASA Astrophysics Data System (ADS)

Hwang, Yongyun; Ibrahim, Joseph; Yang, Qiang; Doohan, Patrick

2017-11-01

The phase-space dynamics of wall-bounded shear flow in the presence of opposition control is explored by examining the behaviours of a pair of nonlinear equilibrium solutions (exact coherent structures), edge state and life time of turbulence at low Reynolds numbers. While the control modifies statistics and phase-space location of the edge state and the lower-branch equilibrium solution very little, it is also found to regularise the periodic orbit on the edge state by reverting a period-doubling bifurcation. Only the upper-branch equilibrium solution and mean turbulent state are significantly modified by the control, and, in phase space, they gradually approach the edge state on increasing the control gain. It is found that this behaviour results in a significant reduction of the life time of turbulence, indicating that the opposition control significantly increases the probability that the turbulent solution trajectory passes through the edge state. Finally, it is shown that the opposition control increases the critical Reynolds number of the onset of the equilibrium solutions, indicating its capability of transition delay. This work is sponsored by the Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).

Modelling of electronic excitation and radiation in the Direct Simulation Monte Carlo Macroscopic Chemistry Method

NASA Astrophysics Data System (ADS)

Goldsworthy, M. J.

2012-10-01

One of the most useful tools for modelling rarefied hypersonic flows is the Direct Simulation Monte Carlo (DSMC) method. Simulator particle movement and collision calculations are combined with statistical procedures to model thermal non-equilibrium flow-fields described by the Boltzmann equation. The Macroscopic Chemistry Method for DSMC simulations was developed to simplify the inclusion of complex thermal non-equilibrium chemistry. The macroscopic approach uses statistical information which is calculated during the DSMC solution process in the modelling procedures. Here it is shown how inclusion of macroscopic information in models of chemical kinetics, electronic excitation, ionization, and radiation can enhance the capabilities of DSMC to model flow-fields where a range of physical processes occur. The approach is applied to the modelling of a 6.4 km/s nitrogen shock wave and results are compared with those from existing shock-tube experiments and continuum calculations. Reasonable agreement between the methods is obtained. The quality of the comparison is highly dependent on the set of vibrational relaxation and chemical kinetic parameters employed.

Detecting temperature fluctuations at equilibrium.

PubMed

Dixit, Purushottam D

2015-05-21

The Gibbs and the Boltzmann definition of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite-sized 'small' system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in the equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant in biophysics and nanotechnology.

Ten reasons why a thermalized system cannot be described by a many-particle wave function

NASA Astrophysics Data System (ADS)

Drossel, Barbara

2017-05-01

It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of statistical mechanics. The usual attempts to resolve this conflict for instance by appealing to decoherence or eigenstate thermalization are riddled with problems. This paper considers theoretical physics of thermalized systems as it is done in practice and shows that all approaches to thermalized systems presuppose in some form limits to linear superposition and deterministic time evolution. These considerations include, among others, the classical limit, extensivity, the concepts of entropy and equilibrium, and symmetry breaking in phase transitions and quantum measurement. As a conclusion, the paper suggests that the irreversibility and stochasticity of statistical mechanics should be taken as a real property of nature. It follows that a gas of a macroscopic number N of atoms in thermal equilibrium is best represented by a collection of N wave packets of a size of the order of the thermal de Broglie wave length, which behave quantum mechanically below this scale but classically sufficiently far beyond this scale. In particular, these wave packets must localize again after scattering events, which requires stochasticity and indicates a connection to the measurement process.

Collisional rate coefficients of C3H2 and the determination of physical conditions in molecular clouds

NASA Technical Reports Server (NTRS)

Avery, L. W.; Green, Sheldon

1989-01-01

Collisional excitation rates for C3H2, calculated using the coupled states approximation at temperatures of 10-30 K, are presented. C3H2 produces a number of spectral line pairs whose members are close together in frequency but arise from levels with different excitation energies. The rates are used in statistical equilibrium calculations to illustrate the excitation properties and density-dependent behavior of various C3H2 line ratios.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Fatigue life of metal treated by magnetic field

NASA Astrophysics Data System (ADS)

Liu, Zhao-Long; Hu, Hai-Yun; Fan, Tian-You; Xing, Xiu-San

2009-03-01

This paper investigates theoretically the influence of magnetization on fatigue life by using non-equilibrium statistical theory of fatigue fracture for metals. The fatigue microcrack growth rate is obtained from the dynamic equation of microcrack growth, where the influence of magnetization is described by an additional term in the potential energy of microcrack. The statistical value of fatigue life of metal under magnetic field is derived, which is expressed in terms of magnetic field and macrophysical as well as microphysical quantities. The fatigue life of AISI 4140 steel in static magnetic field from this theory is basically consistent with the experimental data.

Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching

NASA Astrophysics Data System (ADS)

Liu, Cheng-Wei

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

The automated design of materials far from equilibrium

NASA Astrophysics Data System (ADS)

Miskin, Marc Z.

Automated design is emerging as a powerful concept in materials science. By combining computer algorithms, simulations, and experimental data, new techniques are being developed that start with high level functional requirements and identify the ideal materials that achieve them. This represents a radically different picture of how materials become functional in which technological demand drives material discovery, rather than the other way around. At the frontiers of this field, materials systems previously considered too complicated can start to be controlled and understood. Particularly promising are materials far from equilibrium. Material robustness, high strength, self-healing and memory are properties displayed by several materials systems that are intrinsically out of equilibrium. These and other properties could be revolutionary, provided they can first be controlled. This thesis conceptualizes and implements a framework for designing materials that are far from equilibrium. We show how, even in the absence of a complete physical theory, design from the top down is possible and lends itself to producing physical insight. As a prototype system, we work with granular materials: collections of athermal, macroscopic identical objects, since these materials function both as an essential component of industrial processes as well as a model system for many non-equilibrium states of matter. We show that by placing granular materials in the context of design, benefits emerge simultaneously for fundamental and applied interests. As first steps, we use our framework to design granular aggregates with extreme properties like high stiffness, and softness. We demonstrate control over nonlinear effects by producing exotic aggregates that stiffen under compression. Expanding on our framework, we conceptualize new ways of thinking about material design when automatic discovery is possible. We show how to build rules that link particle shapes to arbitrary granular packing density. We examine how the results of a design process are contingent upon operating conditions by studying which shapes dissipate energy fastest in a granular gas. We even move to create optimization algorithms for the expressed purpose of material design, by integrating them with statistical mechanics. In all of these cases, we show that turning to machines puts a fresh perspective on materials far from equilibrium. By matching forms to functions, complexities become possibilities, motifs emerge that describe new physics, and the door opens to rational design.

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Panesi, M., E-mail: mpanesi@illinois.edu; Lani, A.

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) Amore » Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.« less

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

NASA Astrophysics Data System (ADS)

Zhang, W.; Lani, A.; Panesi, M.

2016-07-01

This work addresses the modeling of non-equilibrium phenomena in inductively coupled plasma discharges. In the proposed computational model, the electromagnetic induction equation is solved together with the set of Navier-Stokes equations in order to compute the electromagnetic and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles, with the method of Chapman and Enskog. Particle ambipolar diffusive fluxes are found by solving the Stefan-Maxwell equations with a simple iterative method. Two physico-mathematical formulations are used to model the chemical reaction processes: (1) A Local Thermodynamics Equilibrium (LTE) formulation and (2) a thermo-chemical non-equilibrium (TCNEQ) formulation. In the TCNEQ model, thermal non-equilibrium between the translational energy mode of the gas and the vibrational energy mode of individual molecules is accounted for. The electronic states of the chemical species are assumed in equilibrium with the vibrational temperature, whereas the rotational energy mode is assumed to be equilibrated with translation. Three different physical models are used to account for the coupling of chemistry and energy transfer processes. Numerical simulations obtained with the LTE and TCNEQ formulations are used to characterize the extent of non-equilibrium of the flow inside the Plasmatron facility at the von Karman Institute. Each model was tested using different kinetic mechanisms to assess the sensitivity of the results to variations in the reaction parameters. A comparison of temperatures and composition profiles at the outlet of the torch demonstrates that the flow is in non-equilibrium for operating conditions characterized by pressures below 30 000 Pa, frequency 0.37 MHz, input power 80 kW, and mass flow 8 g/s.

On the quantum Landau collision operator and electron collisions in dense plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daligault, Jérôme, E-mail: daligaul@lanl.gov

2016-03-15

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck formmore » of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.« less

On the quantum Landau collision operator and electron collisions in dense plasmas

NASA Astrophysics Data System (ADS)

Daligault, Jérôme

2016-03-01

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

An application of statistical mechanics for representing equilibrium perimeter distributions of tropical convective clouds

NASA Astrophysics Data System (ADS)

Garrett, T. J.; Alva, S.; Glenn, I. B.; Krueger, S. K.

2015-12-01

There are two possible approaches for parameterizing sub-grid cloud dynamics in a coarser grid model. The most common is to use a fine scale model to explicitly resolve the mechanistic details of clouds to the best extent possible, and then to parameterize these behaviors cloud state for the coarser grid. A second is to invoke physical intuition and some very general theoretical principles from equilibrium statistical mechanics. This approach avoids any requirement to resolve time-dependent processes in order to arrive at a suitable solution. The second approach is widely used elsewhere in the atmospheric sciences: for example the Planck function for blackbody radiation is derived this way, where no mention is made of the complexities of modeling a large ensemble of time-dependent radiation-dipole interactions in order to obtain the "grid-scale" spectrum of thermal emission by the blackbody as a whole. We find that this statistical approach may be equally suitable for modeling convective clouds. Specifically, we make the physical argument that the dissipation of buoyant energy in convective clouds is done through mixing across a cloud perimeter. From thermodynamic reasoning, one might then anticipate that vertically stacked isentropic surfaces are characterized by a power law dlnN/dlnP = -1, where N(P) is the number clouds of perimeter P. In a Giga-LES simulation of convective clouds within a 100 km square domain we find that such a power law does appear to characterize simulated cloud perimeters along isentropes, provided a sufficient cloudy sample. The suggestion is that it may be possible to parameterize certain important aspects of cloud state without appealing to computationally expensive dynamic simulations.

Principle of maximum Fisher information from Hardy's axioms applied to statistical systems.

PubMed

Frieden, B Roy; Gatenby, Robert A

2013-10-01

Consider a finite-sized, multidimensional system in parameter state a. The system is either at statistical equilibrium or general nonequilibrium, and may obey either classical or quantum physics. L. Hardy's mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number N of distinguishable states a in the system obeys N=max. This assumes that N is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which N is therefore only known approximately. Then what happens if the scope of the axiom N=max is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, I=I(max). This is important because many physical laws have been derived, assuming as a working hypothesis that I=I(max). These derivations include uses of the principle of extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell's equations, new laws of biology (e.g., of Coulomb force-directed cell development and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle I=I(max) itself derives from suitably extended Hardy axioms thereby eliminates its need to be assumed in these derivations. Thus, uses of I=I(max) and EPI express physics at its most fundamental level, its axiomatic basis in math.

``Physical Concepts in Cell Biology,'' an upper level interdisciplinary course in cell biophysics/mathematical biology

NASA Astrophysics Data System (ADS)

Vavylonis, Dimitrios

2009-03-01

I will describe my experience in developing an interdisciplinary biophysics course addressed to students at the upper undergraduate and graduate level, in collaboration with colleagues in physics and biology. The students had a background in physics, biology and engineering, and for many the course was their first exposure to interdisciplinary topics. The course did not depend on a formal knowledge of equilibrium statistical mechanics. Instead, the approach was based on dynamics. I used diffusion as a universal ``long time'' law to illustrate scaling concepts. The importance of statistics and proper counting of states/paths was introduced by calculating the maximum accuracy with which bacteria can measure the concentration of diffuse chemicals. The use of quantitative concepts and methods was introduced through specific biological examples, focusing on model organisms and extremes at the cell level. Examples included microtubule dynamic instability, the search and capture model, molecular motor cooperativity in muscle cells, mitotic spindle oscillations in C. elegans, polymerization forces and propulsion of pathogenic bacteria, Brownian ratchets, bacterial cell division and MinD oscillations.

The ideas behind self-consistent expansion

NASA Astrophysics Data System (ADS)

Schwartz, Moshe; Katzav, Eytan

2008-04-01

In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic nonlinear field theories. In some of those systems, like KPZ and related models, the interesting behavior is in the strong coupling regime, which is inaccessible by traditional perturbative treatments such as dynamical renormalization group (DRG). A useful tool in the study of such systems is the self-consistent expansion (SCE), which might be said to generate its own 'small parameter'. The self-consistent expansion (SCE) has the advantage that its structure is just that of a regular expansion, the only difference is that the simple system around which the expansion is performed is adjustable. The purpose of this paper is to present the method in a simple and understandable way that hopefully will make it accessible to a wider public working on non-equilibrium statistical physics.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

Quantum thermalization through entanglement in an isolated many-body system.

PubMed

Kaufman, Adam M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Preiss, Philipp M; Greiner, Markus

2016-08-19

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis. Copyright © 2016, American Association for the Advancement of Science.

Conceptual Integration of Chemical Equilibrium by Prospective Physical Sciences Teachers

ERIC Educational Resources Information Center

Ganaras, Kostas; Dumon, Alain; Larcher, Claudine

2008-01-01

This article describes an empirical study concerning the mastering of the chemical equilibrium concept by prospective physical sciences teachers. The main objective was to check whether the concept of chemical equilibrium had become an integrating and unifying concept for them, that is to say an operational and functional knowledge to explain and…

Stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response theory for small deviations from equilibrium, in which a general framework is constructed from the analysis of non-equilibrium states close to equilibrium. In a next step, Prigogine and others developed linear irreversible thermodynamics, which establishes relations between transport coefficients and entropy production on a phenomenological level in terms of thermodynamic forces and fluxes. However, beyond the realm of linear response no general theoretical results were available for quite a long time. This situation has changed drastically over the last 20 years with the development of stochastic thermodynamics, revealing that the range of validity of thermodynamic statements can indeed be extended deep into the non-equilibrium regime. Early developments in that direction trace back to the observations of symmetry relations between the probabilities for entropy production and entropy annihilation in non-equilibrium steady states [5-8] (nowadays categorized in the class of so-called detailed fluctuation theorems), and the derivations of the Bochkov-Kuzovlev [9, 10] and Jarzynski relations [11] (which are now classified as so-called integral fluctuation theorems). Apart from its fundamental theoretical interest, the developments in stochastic thermodynamics have experienced an additional boost from the recent experimental progress in fabricating, manipulating, controlling and observing systems on the micro- and nano-scale. These advances are not only of formidable use for probing and monitoring biological processes on the cellular, sub-cellular and molecular level, but even include the realization of a microscopic thermodynamic heat engine [12] or the experimental verification of Landauer's principle in a colloidal system [13]. The scientific program Stochastic Thermodynamics held between 4 and 15 March 2013, and hosted by The Nordic Institute for Theoretical Physics (Nordita), was attended by more than 50 scientists from the Nordic countries and elsewhere, amongst them many leading experts in the field. During the program, the most recent developments, open questions and new ideas in stochastic thermodynamics were presented and discussed. From the talks and debates, the notion of information in stochastic thermodynamics, the fundamental properties of entropy production (rate) in non-equilibrium, the efficiency of small thermodynamic machines and the characteristics of optimal protocols for the applied (cyclic) forces were crystallizing as main themes. Surprisingly, the long-studied adiabatic piston, its peculiarities and its relation to stochastic thermodynamics were also the subject of intense discussions. The comment on the Nordita program Stochastic Thermodynamics published in this issue of Physica Scripta exploits the Jarzynski relation for determining free energy differences in the adiabatic piston. This scientific program and the contribution presented here were made possible by the financial and administrative support of The Nordic Institute for Theoretical Physics.

On the Emergent Constraints of Climate Sensitivity [On proposed emergent constraints of climate sensitivity

DOE PAGES

Qu, Xin; Hall, Alex; DeAngelis, Anthony M.; ...

2018-01-11

Differences among climate models in equilibrium climate sensitivity (ECS; the equilibrium surface temperature response to a doubling of atmospheric CO2) remain a significant barrier to the accurate assessment of societally important impacts of climate change. Relationships between ECS and observable metrics of the current climate in model ensembles, so-called emergent constraints, have been used to constrain ECS. Here a statistical method (including a backward selection process) is employed to achieve a better statistical understanding of the connections between four recently proposed emergent constraint metrics and individual feedbacks influencing ECS. The relationship between each metric and ECS is largely attributable tomore » a statistical connection with shortwave low cloud feedback, the leading cause of intermodel ECS spread. This result bolsters confidence in some of the metrics, which had assumed such a connection in the first place. Additional analysis is conducted with a few thousand artificial metrics that are randomly generated but are well correlated with ECS. The relationships between the contrived metrics and ECS can also be linked statistically to shortwave cloud feedback. Thus, any proposed or forthcoming ECS constraint based on the current generation of climate models should be viewed as a potential constraint on shortwave cloud feedback, and physical links with that feedback should be investigated to verify that the constraint is real. Additionally, any proposed ECS constraint should not be taken at face value since other factors influencing ECS besides shortwave cloud feedback could be systematically biased in the models.« less

On the Emergent Constraints of Climate Sensitivity [On proposed emergent constraints of climate sensitivity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Qu, Xin; Hall, Alex; DeAngelis, Anthony M.

Differences among climate models in equilibrium climate sensitivity (ECS; the equilibrium surface temperature response to a doubling of atmospheric CO2) remain a significant barrier to the accurate assessment of societally important impacts of climate change. Relationships between ECS and observable metrics of the current climate in model ensembles, so-called emergent constraints, have been used to constrain ECS. Here a statistical method (including a backward selection process) is employed to achieve a better statistical understanding of the connections between four recently proposed emergent constraint metrics and individual feedbacks influencing ECS. The relationship between each metric and ECS is largely attributable tomore » a statistical connection with shortwave low cloud feedback, the leading cause of intermodel ECS spread. This result bolsters confidence in some of the metrics, which had assumed such a connection in the first place. Additional analysis is conducted with a few thousand artificial metrics that are randomly generated but are well correlated with ECS. The relationships between the contrived metrics and ECS can also be linked statistically to shortwave cloud feedback. Thus, any proposed or forthcoming ECS constraint based on the current generation of climate models should be viewed as a potential constraint on shortwave cloud feedback, and physical links with that feedback should be investigated to verify that the constraint is real. Additionally, any proposed ECS constraint should not be taken at face value since other factors influencing ECS besides shortwave cloud feedback could be systematically biased in the models.« less

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prigogine, I.; Balescu, R.; Henin, F.

1960-12-01

Work on nonequilibrium statistical mechanics, which allows an extension of the kinetic proof to all results of equilibrium statistical mechanics involving a finite number of degrees of freedom, is summarized. As an introduction to the general N-body problem, the scattering theory in classical mechanics is considered. The general N-body problem is considered for the case of classical mechanics, quantum mechanics with Boltzmann statistics, and quantum mechanics including quantum statistics. Six basic diagrams, which describe the elementary processes of the dynamics of correlations, were obtained. (M.C.G.)

TIME DEPENDENT NONEQUILIBRIUM IONIZATION OF TRANSITION REGION LINES OBSERVED WITH IRIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Sykora, Juan; Pontieu, Bart De; Hansteen, Viggo H.

The properties of nonstatistical equilibrium ionization of silicon and oxygen ions are analyzed in this work. We focus on five solar targets (quiet Sun; coronal hole; plage; quiescent active region, AR; and flaring AR) as observed with the Interface Region Imaging Spectrograph (IRIS). IRIS is best suited for this work owing to the high cadence (up to 0.5 s), high spatial resolution (up to 0.″32), and high signal-to-noise ratios for O iv λ1401 and Si iv λ1402. We find that the observed intensity ratio between lines of three times ionized silicon and oxygen ions depends on their total intensity and that this correlationmore » varies depending on the region observed (quiet Sun, coronal holes, plage, or active regions) and on the specific observational objects present (spicules, dynamic loops, jets, microflares, or umbra). In order to interpret the observations, we compare them with synthetic profiles taken from 2D self-consistent radiative MHD simulations of the solar atmosphere, where the statistical equilibrium or nonequilibrium treatment of silicon and oxygen is applied. These synthetic observations show vaguely similar correlations to those in the observations, i.e., between the intensity ratios and their intensities, but only in the nonequilibrium case do we find that (some of) the observations can be reproduced. We conclude that these lines are formed out of statistical equilibrium. We use our time-dependent nonequilibrium ionization simulations to describe the physical mechanisms behind these observed properties.« less

Genetic influence on exercise-induced changes in physical function among mobility-limited older adults

PubMed Central

Hsu, Fang-Chi; Brinkley, Tina E.; Carter, Christy S.; Church, Timothy S.; Dodson, John A.; Goodpaster, Bret H.; McDermott, Mary M.; Nicklas, Barbara J.; Yank, Veronica; Johnson, Julie A.; Pahor, Marco

2014-01-01

To date, physical exercise is the only intervention consistently demonstrated to attenuate age-related declines in physical function. However, variability exists in seniors' responsiveness to training. One potential source of variability is the insertion (I allele) or deletion (D allele) of a 287 bp fragment in intron 16 of the angiotensin-converting enzyme (ACE) gene. This polymorphism is known to influence a variety of physiological adaptions to exercise. However, evidence is inconclusive regarding the influence of this polymorphism on older adults' functional responses to exercise. This study aimed to evaluate the association of ACE I/D genotypes with changes in physical function among Caucasian older adults (n = 283) following 12 mo of either structured, multimodal physical activity or health education. Measures of physical function included usual-paced gait speed and performance on the Short Physical Performance Battery (SPPB). After checking Hardy-Weinberg equilibrium, we used using linear regression to evaluate the genotype*treatment interaction for each outcome. Covariates included clinic site, body mass index, age, sex, baseline score, comorbidity, and use of angiotensin receptor blockers or ACE inhibitors. Genotype frequencies [II (19.4%), ID (42.4%), DD (38.2%)] were in Hardy-Weinberg equilibrium (P > 0.05). The genotype*treatment interaction was statistically significant for both gait speed (P = 0.002) and SPPB (P = 0.020). Exercise improved gait speed by 0.06 ± 0.01 m/sec and SPPB score by 0.72 ± 0.16 points among those with at least one D allele (ID/DD carriers), but function was not improved among II carriers. Thus, ACE I/D genotype appears to play a role in modulating functional responses to exercise training in seniors. PMID:24423970

Cluster expansion for ground states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Sotiriadis, Spyros

2016-08-01

A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.

Entropy in universes evolving from initial to final de Sitter eras

NASA Astrophysics Data System (ADS)

Mimoso, José P.; Pavón, Diego

2014-05-01

This work studies the behavior of entropy in recent cosmological models that start with an initial de Sitter expansion phase, go through the conventional radiation and matter dominated eras to be followed by a final de Sitter epoch. In spite of their seemingly similarities (observationally they are close to the Λ-CDM model), different models deeply differ in their physics. The second law of thermodynamics encapsulates the underlying microscopic, statistical description, and hence we investigate it in the present work. Our study reveals that the entropy of the apparent horizon plus that of matter and radiation inside it, increases and is a concave function of the scale factor. Thus thermodynamic equilibrium is approached in the last de Sitter era, and this class of models is thermodynamically correct. Cosmological models that do not approach equilibrium appear in conflict with the second law of thermodynamics. (Based on Mimoso & Pavon 2013)

A novel energy conversion based method for velocity correction in molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Hanhui; Collaborative Innovation Center of Advanced Aero-Engine, Hangzhou 310027; Liu, Ningning

2017-05-01

Molecular dynamics (MD) simulation has become an important tool for studying micro- or nano-scale dynamics and the statistical properties of fluids and solids. In MD simulations, there are mainly two approaches: equilibrium and non-equilibrium molecular dynamics (EMD and NEMD). In this paper, a new energy conversion based correction (ECBC) method for MD is developed. Unlike the traditional systematic correction based on macroscopic parameters, the ECBC method is developed strictly based on the physical interaction processes between the pair of molecules or atoms. The developed ECBC method can apply to EMD and NEMD directly. While using MD with this method, themore » difference between the EMD and NEMD is eliminated, and no macroscopic parameters such as external imposed potentials or coefficients are needed. With this method, many limits of using MD are lifted. The application scope of MD is greatly extended.« less

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinitskiy, Anton V.; Voth, Gregory A., E-mail: gavoth@uchicago.edu

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 reductionistmore » 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.« less

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

PubMed

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.

Statistical thermodynamics of clustered populations.

PubMed

Matsoukas, Themis

2014-08-01

We present a thermodynamic theory for a generic population of M individuals distributed into N groups (clusters). We construct the ensemble of all distributions with fixed M and N, introduce a selection functional that embodies the physics that governs the population, and obtain the distribution that emerges in the scaling limit as the most probable among all distributions consistent with the given physics. We develop the thermodynamics of the ensemble and establish a rigorous mapping to regular thermodynamics. We treat the emergence of a so-called giant component as a formal phase transition and show that the criteria for its emergence are entirely analogous to the equilibrium conditions in molecular systems. We demonstrate the theory by an analytic model and confirm the predictions by Monte Carlo simulation.

OPTIMIZING THROUGH CO-EVOLUTIONARY AVALANCHES

DOE Office of Scientific and Technical Information (OSTI.GOV)

S. BOETTCHER; A. PERCUS

2000-08-01

We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by ''self-organized critically,'' a concept introduced to describe emergent complexity in many physical systems. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, extremal optimization successively replaces extremely undesirable elements of a sub-optimal solution with new, random ones. Large fluctuations, called ''avalanches,'' ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Those phase transitions are found in the parameter space of most optimization problems, and have recently been conjectured to be the origin of some of the hardest instances in computational complexity. We will demonstrate how extremal optimization can be implemented for a variety of combinatorial optimization problems. We believe that extremal optimization will be a useful tool in the investigation of phase transitions in combinatorial optimization problems, hence valuable in elucidating the origin of computational complexity.« less

Combining local search with co-evolution in a remarkably simple way

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boettcher, S.; Percus, A.

2000-05-01

The authors explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problem. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire gene-pool of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or avalanches, ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been conjectured to occur in the region of parameter space containing the hardest instances. We demonstrate how extremal optimization can be implemented for a variety of hard optimization problems. We believe that this will be a useful tool in the investigation of phase transitions in combinatorial optimization, thereby helping to elucidate the origin of computational complexity.« less

Integral Method for the Assessment of U-RANS Effectiveness in Non-Equilibrium Flows and Heat Transfer

NASA Astrophysics Data System (ADS)

Pond, Ian; Edabi, Alireza; Dubief, Yves; White, Christopher

2015-11-01

Reynolds Average Navier Stokes (RANS) modeling has established itself as a critical design tool in many engineering applications, thanks to its superior computational efficiency. The drawbacks of RANS models are well known, but not necessarily well understood: poor prediction of transition, non equilibrium flows, mixing and heat transfer, to name the ones relevant to our study. In the present study, we use a DNS of a reciprocating channel flow driven by an oscillating pressure gradient to test several low- and high-Reynolds RANS models. Temperature is introduced as a passive scalar to study heat transfer modeling. Low-Reynolds models manage to capture the overall physics of wall shear and heat flux well, yet with some phase discrepancies, whereas high Reynolds models fail. Under the microscope of the integral method for wall shear and wall heat flux, the qualitative agreement appears more serendipitous than driven by the ability of the models to capture the correct physics. The integral method is shown to be more insightful in the benchmarking of RANS models than the typical comparisons of statistical quantities. The authors acknowledges the support of NSF and DOE under grant NSF/DOE 1258697 (VT) and 1258702 (NH).

Free energy surfaces from nonequilibrium processes without work measurement

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2006-04-01

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such "clamp-and-release" processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations and analyzed in the context of tethered single-molecule experiments.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation.

PubMed

Ballard, Christopher C; Esty, C Clark; Egolf, David A

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Colloquium: Statistical mechanics of money, wealth, and income

NASA Astrophysics Data System (ADS)

Yakovenko, Victor M.; Rosser, J. Barkley, Jr.

2009-10-01

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.

Transitions between superstatistical regimes: Validity, breakdown and applications

NASA Astrophysics Data System (ADS)

Jizba, Petr; Korbel, Jan; Lavička, Hynek; Prokš, Martin; Svoboda, Václav; Beck, Christian

2018-03-01

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important rôle in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show that a multi-scale generalization of the superstatistics paradigm is more versatile, allowing to address such pertinent issues as transmutation of statistics or inter-scale stochastic behavior. To put some flesh on the bare bones, we provide a numerical evidence for a transition between two superstatistics regimes, by analyzing high-frequency (minute-tick) data for share-price returns of seven selected companies. Salient issues, such as breakdown of superstatistics in fractional diffusion processes or connection with Brownian subordination are also briefly discussed.

The Statistical Basis of Chemical Equilibria.

ERIC Educational Resources Information Center

Hauptmann, Siegfried; Menger, Eva

1978-01-01

Describes a machine which demonstrates the statistical bases of chemical equilibrium, and in doing so conveys insight into the connections among statistical mechanics, quantum mechanics, Maxwell Boltzmann statistics, statistical thermodynamics, and transition state theory. (GA)

Thermal machines beyond the weak coupling regime

NASA Astrophysics Data System (ADS)

Gallego, R.; Riera, A.; Eisert, J.

2014-12-01

How much work can be extracted from a heat bath using a thermal machine? The study of this question has a very long history in statistical physics in the weak-coupling limit, when applied to macroscopic systems. However, the assumption that thermal heat baths remain uncorrelated with associated physical systems is less reasonable on the nano-scale and in the quantum setting. In this work, we establish a framework of work extraction in the presence of quantum correlations. We show in a mathematically rigorous and quantitative fashion that quantum correlations and entanglement emerge as limitations to work extraction compared to what would be allowed by the second law of thermodynamics. At the heart of the approach are operations that capture the naturally non-equilibrium dynamics encountered when putting physical systems into contact with each other. We discuss various limits that relate to known results and put our work into the context of approaches to finite-time quantum thermodynamics.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

NASA Astrophysics Data System (ADS)

Gnesotto, F. S.; Mura, F.; Gladrow, J.; Broedersz, C. P.

2018-06-01

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Broken detailed balance and non-equilibrium dynamics in living systems: a review.

PubMed

Gnesotto, F S; Mura, F; Gladrow, J; Broedersz, C P

2018-06-01

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Influence of neural adaptation on dynamics and equilibrium state of neural activities in a ring neural network

NASA Astrophysics Data System (ADS)

Takiyama, Ken

2017-12-01

How neural adaptation affects neural information processing (i.e. the dynamics and equilibrium state of neural activities) is a central question in computational neuroscience. In my previous works, I analytically clarified the dynamics and equilibrium state of neural activities in a ring-type neural network model that is widely used to model the visual cortex, motor cortex, and several other brain regions. The neural dynamics and the equilibrium state in the neural network model corresponded to a Bayesian computation and statistically optimal multiple information integration, respectively, under a biologically inspired condition. These results were revealed in an analytically tractable manner; however, adaptation effects were not considered. Here, I analytically reveal how the dynamics and equilibrium state of neural activities in a ring neural network are influenced by spike-frequency adaptation (SFA). SFA is an adaptation that causes gradual inhibition of neural activity when a sustained stimulus is applied, and the strength of this inhibition depends on neural activities. I reveal that SFA plays three roles: (1) SFA amplifies the influence of external input in neural dynamics; (2) SFA allows the history of the external input to affect neural dynamics; and (3) the equilibrium state corresponds to the statistically optimal multiple information integration independent of the existence of SFA. In addition, the equilibrium state in a ring neural network model corresponds to the statistically optimal integration of multiple information sources under biologically inspired conditions, independent of the existence of SFA.

A Bayesian test for Hardy–Weinberg equilibrium of biallelic X-chromosomal markers

PubMed Central

Puig, X; Ginebra, J; Graffelman, J

2017-01-01

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used. PMID:28900292

Book Review:

NASA Astrophysics Data System (ADS)

Vespignani, A.

2004-09-01

Networks have been recently recognized as playing a central role in understanding a wide range of systems spanning diverse scientific domains such as physics and biology, economics, computer science and information technology. Specific examples run from the structure of the Internet and the World Wide Web to the interconnections of finance agents and ecological food webs. These networked systems are generally made by many components whose microscopic interactions give rise to global structures characterized by emergent collective behaviour and complex topological properties. In this context the statistical physics approach finds a natural application since it attempts to explain the various large-scale statistical properties of networks in terms of local interactions governing the dynamical evolution of the constituent elements of the system. It is not by chance then that many of the seminal papers in the field have been published in the physics literature, and have nevertheless made a considerable impact on other disciplines. Indeed, a truly interdisciplinary approach is required in order to understand each specific system of interest, leading to a very interesting cross-fertilization between different scientific areas defining the emergence of a new research field sometimes called network science. The book of Dorogovtsev and Mendes is the first comprehensive monograph on this new scientific field. It provides a thorough presentation of the forefront research activities in the area of complex networks, with an extensive sampling of the disciplines involved and the kinds of problems that form the subject of inquiry. The book starts with a short introduction to graphs and network theory that introduces the tools and mathematical background needed for the rest of the book. The following part is devoted to an extensive presentation of the empirical analysis of real-world networks. While for obvious reasons of space the authors cannot analyse in every detail all the various examples, they provide the reader with a general vista that makes clear the relevance of network science to a wide range of natural and man-made systems. Two chapters are then committed to the detailed exposition of the statistical physics approach to equilibrium and non-equilibrium networks. The authors are two leading players in the area of network theory and offer a very careful and complete presentation of the statistical physics theory of evolving networks. Finally, in the last two chapters, the authors focus on various consequences of network topology for dynamical and physical phenomena occurring in these kinds of structures. The book is completed by a very extensive bibliography and some useful appendices containing some technical points arising in the mathematical discussion and data analysis. The book's mathematical level is fairly advanced and allows a coherent and unified framework for the study of networked structure. The book is targeted at mathematicians, physicists and social scientists alike. It will be appreciated by everybody working in the network area, and especially by any researcher or student entering the field that would like to have a reference text on the latest developments in network science.

Far-from-Equilibrium Route to Superthermal Light in Bimodal Nanolasers

NASA Astrophysics Data System (ADS)

Marconi, Mathias; Javaloyes, Julien; Hamel, Philippe; Raineri, Fabrice; Levenson, Ariel; Yacomotti, Alejandro M.

2018-02-01

Microscale and nanoscale lasers inherently exhibit rich photon statistics due to complex light-matter interaction in a strong spontaneous emission noise background. It is well known that they may display superthermal fluctuations—photon superbunching—in specific situations due to either gain competition, leading to mode-switching instabilities, or carrier-carrier coupling in superradiant microcavities. Here we show a generic route to superbunching in bimodal nanolasers by preparing the system far from equilibrium through a parameter quench. We demonstrate, both theoretically and experimentally, that transient dynamics after a short-pump-pulse-induced quench leads to heavy-tailed superthermal statistics when projected onto the weak mode. We implement a simple experimental technique to access the probability density functions that further enables quantifying the distance from thermal equilibrium via the thermodynamic entropy. The universality of this mechanism relies on the far-from-equilibrium dynamical scenario, which can be mapped to a fast cooling process of a suspension of Brownian particles in a liquid. Our results open up new avenues to mold photon statistics in multimode optical systems and may constitute a test bed to investigate out-of-equilibrium thermodynamics using micro or nanocavity arrays.

Temperature in and out of equilibrium: A review of concepts, tools and attempts

NASA Astrophysics Data System (ADS)

Puglisi, A.; Sarracino, A.; Vulpiani, A.

2017-11-01

We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short historical survey of the key role of temperature in thermodynamics and statistical mechanics, we tackle a series of issues which have been recently reconsidered. In particular, we discuss different definitions and their relevance for energy fluctuations. The interest in such a topic has been triggered by the recent observation of negative temperatures in condensed matter experiments. Moreover, the ability to manipulate systems at the micro and nano-scale urges to understand and clarify some aspects related to the statistical properties of small systems (as the issue of temperature's ;fluctuations;). We also discuss the notion of temperature in a dynamical context, within the theory of linear response for Hamiltonian systems at equilibrium and stochastic models with detailed balance, and the generalized fluctuation-response relations, which provide a hint for an extension of the definition of temperature in far-from-equilibrium systems. To conclude we consider non-Hamiltonian systems, such as granular materials, turbulence and active matter, where a general theoretical framework is still lacking.

Essays on variational approximation techniques for stochastic optimization problems

NASA Astrophysics Data System (ADS)

Deride Silva, Julio A.

This dissertation presents five essays on approximation and modeling techniques, based on variational analysis, applied to stochastic optimization problems. It is divided into two parts, where the first is devoted to equilibrium problems and maxinf optimization, and the second corresponds to two essays in statistics and uncertainty modeling. Stochastic optimization lies at the core of this research as we were interested in relevant equilibrium applications that contain an uncertain component, and the design of a solution strategy. In addition, every stochastic optimization problem relies heavily on the underlying probability distribution that models the uncertainty. We studied these distributions, in particular, their design process and theoretical properties such as their convergence. Finally, the last aspect of stochastic optimization that we covered is the scenario creation problem, in which we described a procedure based on a probabilistic model to create scenarios for the applied problem of power estimation of renewable energies. In the first part, Equilibrium problems and maxinf optimization, we considered three Walrasian equilibrium problems: from economics, we studied a stochastic general equilibrium problem in a pure exchange economy, described in Chapter 3, and a stochastic general equilibrium with financial contracts, in Chapter 4; finally from engineering, we studied an infrastructure planning problem in Chapter 5. We stated these problems as belonging to the maxinf optimization class and, in each instance, we provided an approximation scheme based on the notion of lopsided convergence and non-concave duality. This strategy is the foundation of the augmented Walrasian algorithm, whose convergence is guaranteed by lopsided convergence, that was implemented computationally, obtaining numerical results for relevant examples. The second part, Essays about statistics and uncertainty modeling, contains two essays covering a convergence problem for a sequence of estimators, and a problem for creating probabilistic scenarios on renewable energies estimation. In Chapter 7 we re-visited one of the "folk theorems" in statistics, where a family of Bayes estimators under 0-1 loss functions is claimed to converge to the maximum a posteriori estimator. This assertion is studied under the scope of the hypo-convergence theory, and the density functions are included in the class of upper semicontinuous functions. We conclude this chapter with an example in which the convergence does not hold true, and we provided sufficient conditions that guarantee convergence. The last chapter, Chapter 8, addresses the important topic of creating probabilistic scenarios for solar power generation. Scenarios are a fundamental input for the stochastic optimization problem of energy dispatch, especially when incorporating renewables. We proposed a model designed to capture the constraints induced by physical characteristics of the variables based on the application of an epi-spline density estimation along with a copula estimation, in order to account for partial correlations between variables.

Dynamics of the microaggregate composition of chernozem in relation to changes in the content of organic matter

NASA Astrophysics Data System (ADS)

Kryshchenko, V. S.; Zamulina, I. V.; Rybyanets, T. V.; Kravtsova, N. E.; Biryukova, O. A.; Golozubov, O. M.

2016-06-01

Monitoring of soil dispersivity and humus state has been performed in the stationary profile of ordinary chernozem in the Botanic Garden of the Southern Federal University in 2009-2014. The contents of physical clay and sand are almost stable in time, which indicates a quasi-static (climax) equilibrium in the soil. Another (reversible dynamic) process occurs simultaneously: seasonal and annual variation in the mass fractions of clay and silt in physical clay. Variations of humus content in the whole soil and in its physical clay are also observed on the background of seasonal changes in precipitation and temperature. A procedure has been developed for the analysis of the polydisperse soil system with consideration for the quasi-static and dynamic equilibriums. A two-vector coordinate system has been introduced, which consists of scales for changes in the contents of physical clay and physical sand in 100 g of soil and changes in the fractions of clay and silt in 100 g of physical clay. Co-measurements of two dispersivity series of soil samples—actual dynamic and calculated under quasi-static equilibrium (ideal)—have been performed. Dynamic equilibrium coefficients, which cumulatively reflect the varying proportions of physical clay and physical sand in the soil and the mass fractions of clay and silt in physical clay, have been calculated.

Self-organization and feedback effects in the shock compressed media

NASA Astrophysics Data System (ADS)

Khantuleva, Tatyana

2005-07-01

New theoretical approach to the transport in condensed matter far from equilibrium combines methods of statistical mechanics and cybernetic physics in order to construct closed mathematical model of a system with self-organization and self-regulation. Mesoscopic effects are considered as a result of the structure formation and the feedback effects in an open system under dynamic loading. Nonequilibrium state equations had been involved to incorporate the velocity dispersion. Integrodifferential balance equations describe both wave and dissipative transport properties. Boundary conditions determine the internal scale spectra. The model is completed by the feedback that introduces the structure evolution basing the methods of cybernetic physics. The obtained results open a wide prospective for the control methods in applications to new technologies, intellectual systems and prediction of catastrophic phenomena.

Thermalization and prethermalization in isolated quantum systems: a theoretical overview

NASA Astrophysics Data System (ADS)

Mori, Takashi; Ikeda, Tatsuhiko N.; Kaminishi, Eriko; Ueda, Masahito

2018-06-01

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

Zone clearance in an infinite TASEP with a step initial condition

NASA Astrophysics Data System (ADS)

Cividini, Julien; Appert-Rolland, Cécile

2017-06-01

The TASEP is a paradigmatic model of out-of-equilibrium statistical physics, for which many quantities have been computed, either exactly or by approximate methods. In this work we study two new kinds of observables that have some relevance in biological or traffic models. They represent the probability for a given clearance zone of the lattice to be empty (for the first time) at a given time, starting from a step density profile. Exact expressions are obtained for single-time quantities, while more involved history-dependent observables are studied by Monte Carlo simulation, and partially predicted by a phenomenological approach.

Living systems do not minimize free energy. Comment on "Answering Schrödinger's question: A free-energy formulation" by Maxwell James Dèsormeau Ramstead et al.

NASA Astrophysics Data System (ADS)

Martyushev, Leonid M.

2018-03-01

The paper [1] is certainly very useful and important for understanding living systems (e.g. brain) as adaptive, self-organizing patterns. There is no need to enumerate all advantages of the paper, they are obvious. The purpose of my brief comment is to discuss one issue which, as I see it, was not thought out by the authors well enough. As a consequence, their ideas do not find as wide distribution as they otherwise could have found. This issue is related to the name selected for the principle forming the basis of their approach: free-energy principle (FEP). According to the sec. 2.1 [1]: "It asserts that all biological systems maintain their integrity by actively reducing the disorder or dispersion (i.e., entropy) of their sensory and physiological states by minimizing their variational free energy." Let us note that the authors suggested different names for the principle in their earlier works (an objective function, a function of the ensemble density encoded by the organism's configuration and the sensory data to which it is exposed, etc.), and explicitly and correctly mentioned that the free energy and entropy considered by them had nothing in common with the quantities employed in physics [2,3]. It is also obvious that a purely information-theoretic approach used by the authors with regard to the problems under study allows many other wordings and interpretations. However, in spite of this fact, in their last papers as well as in the present paper, the authors choose specifically FEP. Apparently, it may be explained by the intent to additionally base their approach on the foundation of statistical thermodynamics and therefore to demonstrate the universality of the described method. However, this is exactly what might cause misunderstandings specifically among physicists and consequently in their rejection and ignoring of FEP. The physical analogy employed by the authors has the following fundamental inconsistencies: In physics, free energy is used to describe processes occurring at constant temperatures and volumes. In physics, the minimum free energy corresponds to an equilibrium state to which an isochoric-isothermal system relaxes [4,5]. It is obvious that the biological systems considered by the authors are fundamentally non-equilibrium, do not seek equilibrium, and, in most cases, do not retain their volumes as they develop. For a biological system, the equilibrium means death, decay. Therefore, to base the idea of life on FEP is the same as to state that the pursuit of death is the purpose and meaning of life. In order to consider processes addressed by the authors, one needs functionals employed in non-equilibrium rather than equilibrium thermodynamics [6-8]. Specifically, I would like to draw their attention to the rate of change of the Gibbs energy with time, or entropy production (the maximum entropy production principle can be useful here [7,9-12]).

Statistical thermodynamics and the size distributions of tropical convective clouds.

NASA Astrophysics Data System (ADS)

Garrett, T. J.; Glenn, I. B.; Krueger, S. K.; Ferlay, N.

2017-12-01

Parameterizations for sub-grid cloud dynamics are commonly developed by using fine scale modeling or measurements to explicitly resolve the mechanistic details of clouds to the best extent possible, and then to formulating these behaviors cloud state for use within a coarser grid. A second is to invoke physical intuition and some very general theoretical principles from equilibrium statistical thermodynamics. This second approach is quite widely used elsewhere in the atmospheric sciences: for example to explain the heat capacity of air, blackbody radiation, or even the density profile or air in the atmosphere. Here we describe how entrainment and detrainment across cloud perimeters is limited by the amount of available air and the range of moist static energy in the atmosphere, and that constrains cloud perimeter distributions to a power law with a -1 exponent along isentropes and to a Boltzmann distribution across isentropes. Further, the total cloud perimeter density in a cloud field is directly tied to the buoyancy frequency of the column. These simple results are shown to be reproduced within a complex dynamic simulation of a tropical convective cloud field and in passive satellite observations of cloud 3D structures. The implication is that equilibrium tropical cloud structures can be inferred from the bulk thermodynamic structure of the atmosphere without having to analyze computationally expensive dynamic simulations.

Investigating Direct Links between Depression, Emotional Control, and Physical Punishment with Adolescent Drive for Thinness and Bulimic Behaviors, Including Possible Moderation by the Serotonin Transporter 5-HTTLPR Polymorphism.

PubMed

Rozenblat, Vanja; Ryan, Joanne; Wertheim, Eleanor H; King, Ross; Olsson, Craig A; Krug, Isabel

2017-01-01

Objectives: To examine the relationship between psychological and social factors (depression, emotional control, sexual abuse, and parental physical punishment) and adolescent drive for Thinness and Bulimic behaviors in a large community sample, and to investigate possible genetic moderation. Method: Data were drawn from the Australian Temperament Project (ATP), a population-based cohort study that has followed a representative sample of 2443 participants from infancy to adulthood across 16 waves since 1983. A subsample of 650 participants (50.2% female) of Caucasian descent who provided DNA were genotyped for a serotonin transporter promoter polymorphism ( 5-HTTLPR ). Adolescent disordered eating attitudes and behaviors were assessed using the Bulimia and Drive for Thinness scales of the Eating Disorder Inventory-2 (15-16 years). Depression and emotional control were examined at the same age using the Short Mood and Feelings Questionnaire, and an ATP-devised measure of emotional control. History of sexual abuse and physical punishment were assessed retrospectively (23-24 years) in a subsample of 467 of those providing DNA. Results: EDI-2 scores were associated with depression, emotional control, and retrospectively reported parental physical punishment. Although there was statistically significant moderation of the relationship between parental physical punishment and bulimic behaviors by 5-HTTLPR ( p = 0.0048), genotypes in this subsample were not in Hardy-Weinberg Equilibrium. No other G×E interactions were significant. Conclusion: Findings from this study affirm the central importance of psychosocial processes in disordered eating patterns in adolescence. Evidence of moderation by 5-HTTLPR was not conclusive; however, genetic moderation observed in a subsample not in Hardy-Weinberg Equilibrium warrants further investigation.

Investigating Direct Links between Depression, Emotional Control, and Physical Punishment with Adolescent Drive for Thinness and Bulimic Behaviors, Including Possible Moderation by the Serotonin Transporter 5-HTTLPR Polymorphism

PubMed Central

Rozenblat, Vanja; Ryan, Joanne; Wertheim, Eleanor H.; King, Ross; Olsson, Craig A.; Krug, Isabel

2017-01-01

Objectives: To examine the relationship between psychological and social factors (depression, emotional control, sexual abuse, and parental physical punishment) and adolescent drive for Thinness and Bulimic behaviors in a large community sample, and to investigate possible genetic moderation. Method: Data were drawn from the Australian Temperament Project (ATP), a population-based cohort study that has followed a representative sample of 2443 participants from infancy to adulthood across 16 waves since 1983. A subsample of 650 participants (50.2% female) of Caucasian descent who provided DNA were genotyped for a serotonin transporter promoter polymorphism (5-HTTLPR). Adolescent disordered eating attitudes and behaviors were assessed using the Bulimia and Drive for Thinness scales of the Eating Disorder Inventory-2 (15–16 years). Depression and emotional control were examined at the same age using the Short Mood and Feelings Questionnaire, and an ATP-devised measure of emotional control. History of sexual abuse and physical punishment were assessed retrospectively (23–24 years) in a subsample of 467 of those providing DNA. Results: EDI-2 scores were associated with depression, emotional control, and retrospectively reported parental physical punishment. Although there was statistically significant moderation of the relationship between parental physical punishment and bulimic behaviors by 5-HTTLPR (p = 0.0048), genotypes in this subsample were not in Hardy–Weinberg Equilibrium. No other G×E interactions were significant. Conclusion: Findings from this study affirm the central importance of psychosocial processes in disordered eating patterns in adolescence. Evidence of moderation by 5-HTTLPR was not conclusive; however, genetic moderation observed in a subsample not in Hardy–Weinberg Equilibrium warrants further investigation. PMID:28848475

Self-organization of grafted polyelectrolyte layers via the coupling of chemical equilibrium and physical interactions.

PubMed

Tagliazucchi, Mario; de la Cruz, Mónica Olvera; Szleifer, Igal

2010-03-23

The competition between chemical equilibrium, for example protonation, and physical interactions determines the molecular organization and functionality of biological and synthetic systems. Charge regulation by displacement of acid-base equilibrium induced by changes in the local environment provides a feedback mechanism that controls the balance between electrostatic, van der Waals, steric interactions and molecular organization. Which strategies do responsive systems follow to globally optimize chemical equilibrium and physical interactions? We address this question by theoretically studying model layers of end-grafted polyacids. These layers spontaneously form self-assembled aggregates, presenting domains of controlled local pH and whose morphologies can be manipulated by the composition of the solution in contact with the film. Charge regulation stabilizes micellar domains over a wide range of pH by reducing the local charge in the aggregate at the cost of chemical free energy and gaining in hydrophobic interactions. This balance determines the boundaries between different aggregate morphologies. We show that a qualitatively new form of organization arises from the coupling between physical interactions and protonation equilibrium. This optimization strategy presents itself with polyelectrolytes coexisting in two different and well-defined protonation states. Our results underline the need of considering the coupling between chemical equilibrium and physical interactions due to their highly nonadditive behavior. The predictions provide guidelines for the creation of responsive polymer layers presenting self-organized patterns with functional properties and they give insights for the understanding of competing interactions in highly inhomogeneous and constrained environments such as those relevant in nanotechnology and those responsible for biological cells function.

Saturated and unsaturated salt transport in peat from a constructed fen

NASA Astrophysics Data System (ADS)

Simhayov, Reuven B.; Weber, Tobias K. D.; Price, Jonathan S.

2018-02-01

The underlying processes governing solute transport in peat from an experimentally constructed fen peatland were analyzed by performing saturated and unsaturated solute breakthrough experiments using Na+ and Cl- as reactive and non-reactive solutes, respectively. We tested the performance of three solute transport models, including the classical equilibrium convection-dispersion equation (CDE), a chemical non-equilibrium one-site adsorption model (OSA) and a model to account for physical non-equilibrium, the mobile-immobile (MIM) phases. The selection was motivated by the fact that the applicability of the MIM in peat soils finds a wide consensus. However, results from inverse modeling and a robust statistical evaluation of this peat provide evidence that the measured breakthrough of the conservative tracer, Cl-, could be simulated well using the CDE. Furthermore, the very high Damköhler number (which approaches infinity) suggests instantaneous equilibration between the mobile and immobile phases underscoring the redundancy of the MIM approach for this particular peat. Scanning electron microscope images of the peat show the typical multi-pore size distribution structures have been homogenized sufficiently by decomposition, such that physical non-equilibrium solute transport no longer governs the transport process. This result is corroborated by the fact the soil hydraulic properties were adequately described using a unimodal van Genuchten-Mualem model between saturation and a pressure head of ˜ -1000 cm of water. Hence, MIM was not the most suitable choice, and the long tailing of the Na+ breakthrough curve was caused by chemical non-equilibrium. Successful description was possible using the OSA model. To test our results for the unsaturated case, we conducted an unsaturated steady-state evaporation experiment to drive Na+ and Cl- transport. Using the parameterized transport models from the saturated experiments, we could numerically simulate the unsaturated transport using Hydrus-1-D. The simulation showed a good prediction of observed values, confirming the suitability of the parameters for use in a slightly unsaturated transport simulation. The findings improve the understanding of solute redistribution in the constructed fen and imply that MIM should not be automatically assumed for solute transport in peat but rather should be evidence based.

Physicochemical modeling of reactive violet 5 dye adsorption on home-made cocoa shell and commercial activated carbons using the statistical physics theory

NASA Astrophysics Data System (ADS)

Sellaoui, Lotfi; Lima, Éder Cláudio; Dotto, Guilherme Luiz; Dias, Silvio L. P.; Ben Lamine, Abdelmottaleb

Two equilibrium models based on statistical physics, i.e., monolayer model with single energy and multilayer model with saturation, were developed and employed to access the steric and energetic aspects in the adsorption of reactive violet 5 dye (RV-5) on cocoa shell activated carbon (AC) and commercial activated carbon (CAC), at different temperatures (from 298 to 323 K). The results showed that the multilayer model with saturation was able to represent the adsorption system. This model assumes that the adsorption occurs by a formation of certain number of layers. The n values ranged from 1.10 to 2.98, indicating that the adsorbate molecules interacted in an inclined position on the adsorbent surface and aggregate in solution. The study of the total number of the formed layers (1 + L2) showed that the steric hindrance is the dominant factor. The description of the adsorbate-adsorbent interactions by calculation of the adsorption energy indicated that the process occurred by physisorption in nature, since the values were lower than 40 kJ mol-1.

Hanging an Airplane: A Case Study in Static Equilibrium

ERIC Educational Resources Information Center

Katz, Debora M.

2009-01-01

Our classrooms are filled with engineering majors who take a semester-long course in static equilibrium. Many students find this class too challenging and drop their engineering major. In our introductory physics class, we often breeze through static equilibrium; to physicists equilibrium is just a special case of Newton's second law. While it is…

PREFACE Turbulent Mixing and Beyond

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Gauthier, Serge; Niemela, Joseph J.

2010-12-01

The goals of the International Conference 'Turbulent Mixing and Beyond', TMB-2009, are to expose the generic problem of non-equilibrium turbulent processes to a broad scientific community, to promote the development of new ideas in tackling the fundamental aspects of the problem, to assist in the application of novel approaches in a broad range of phenomena, where the turbulent processes occur, and to have a potential impact on technology. The Conference provides the opportunity to bring together researchers from different areas, which include but are not limited to fluid dynamics, plasmas, high energy density physics, astrophysics, material science, combustion, atmospheric and Earth sciences, nonlinear and statistical physics, applied mathematics, probability and statistics, data processing and computations, optics and telecommunications, and to have their attention focused on the long-standing formidable task of non-equilibrium processes. Non-equilibrium turbulent processes play a key role in a broad variety of phenomena spanning astrophysical to atomistic scales and high or low energy density regimes. Inertial confinement and magnetic fusion, light-matter interaction and non-equilibrium heat transfer, strong shocks and explosions, material transformation under high strain rate, supernovae and accretion disks, stellar non-Boussinesq and magneto-convection, planetary interiors and mantle-lithosphere tectonics, premixed and non-premixed combustion, non-canonical wall-bounded flows, hypersonic and supersonic boundary layers, dynamics of atmosphere and oceanography, are just a few examples. A grip on non-equilibrium turbulent processes is crucial for cutting-edge technology such as laser micro-machining, nano-electronics, free-space optical telecommunications, and for industrial applications in the areas of aeronautics and aerodynamics. Non-equilibrium turbulent processes are anisotropic, non-local, multi-scale and multi-phase, and often are driven by shocks or acceleration. Their scaling, spectral and invariant properties differ substantially from those of classical Kolmogorov turbulence. At atomistic and meso-scales, the non-equilibrium dynamics depart dramatically from a standard scenario given by the Gibbs statistic ensemble average and quasi-static Boltzmann equation. The singular aspect and the similarity of the non-equilibrium dynamics at macroscopic scales are interplayed with the fundamental properties of the Euler and compressible Navier-Stokes equations and with the problem sensitivity to the boundary conditions at discontinuities. The state-of-the-art numerical simulations of multi-phase flows suggest new methods for predictive modeling of the multi-scale non-equilibrium dynamics in fluids and plasmas, up to peta-scale level, for error estimate and uncertainty quantification, as well as for novel data assimilation techniques. The Second International Conference and Advanced School 'Turbulent Mixing and Beyond', TMB-2009, was held on 27 July-7 August 2009 at the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy. This was a highly informative and exciting meeting, and it strengthened and reaffirmed the success of TMB-2007. TMB-2009 brought together over 180 participants from five continents, ranging from students to members of National Academies of Sciences and Engineering and including researchers at experienced and early stages of their carriers from leading scientific institutions in academia, national laboratories, corporations and industry, from developed and developing countries. The success of TMB-2009 came from the successful work of all the participants, who were responsible professionals caring for the quality of their research and sharing their scientific vision. The level of presentations was high; about 170 presentations included over 60 invited lectures and 15 tutorials (4500 minutes of talks in total), about 40 posters and two Round Tables. TMB-2009 covered 17 different topics, maintaining the scope and the interdisciplinary character of the meeting while keeping the focus on a fundamental scientific problem of non-equilibrium processes and on the Conference objectives. The abstracts of the 194 accepted presentations of more than 400 authors were published in the Book of Abstracts of the Second International Conference and Advanced School 'Turbulent Mixing and Beyond', 27 July-7 August 2009 , Copyright © 2009, the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy (ISBN 92095003-41-1). This Topical Issue consists of 70 articles accepted for publication in the Conference Proceedings and represents a substantial part of the Conference contributions. The articles are in a broad variety of TMB-2009 themes and are sorted alphabetically by the last name of the first author within each of the following topics: Canonical turbulence and turbulent mixing: invariant, scaling, spectral properties, scalar transports, convection; Wall-bounded flows: structure and fundamentals, non-canonical turbulent boundary layers, including unsteady and transitional flows, supersonic and hypersonic flows, shock-boundary layer interactions; Non-equilibrium processes: unsteady, multiphase and shock-driven turbulent flows, anisotropic non-local dynamics, connection of continuous description at macro-scales to kinetic processes at atomistic scales; Interfacial dynamics: instabilities of Rayleigh-Taylor, Kelvin-Helmholtz, Richtmyer-Meshkov, Landau-Darrieus, Saffman-Taylor High energy density physics: inertial confinement and heavy-ion fusion, Z-pinches, light-matter and laser-plasma interactions, non-equilibrium heat transfer; Material science: material transformation under high strain rates, equation of state, impact dynamics, mixing at nano- and micro-scales; Astrophysics: supernovae, interstellar medium, star formation, stellar interiors, early Universe, cosmic-microwave background, accretion disks; Magneto-hydrodynamics: magnetic fusion and magnetically confined plasmas, magneto-convection, magneto-rotational instability, dynamo; Canonical plasmas: coupled plasmas, anomalous resistance, ionosphere; Physics of atmosphere: environmental fluid dynamics, weather forecasting, turbulent flows in stratified media and atmosphere, non-Boussinesq convection; Geophysics and Earth science: mantle-lithosphere tectonics, oceanography, turbulent convection under rotation, planetary interiors; Combustion: dynamics of flames and fires, deflagration-to-detonation transition, blast waves and explosions, flows with chemical reactions, flows in jet engines; Mathematical aspects of non-equilibrium dynamics: vortex dynamics, singularities, discontinuities, asymptotic dynamics, weak solutions, well- and ill-posedness, continuous transports out of thermodynamic equilibrium; Stochastic processes and probabilistic description: long-tail distributions and anomalous diffusion, data assimilation and processing methodologies, error estimate and uncertainty quantification, statistically unsteady processes; Advanced numerical simulations: continuous DNS/LES/RANS, molecular dynamics, Monte-Carlo, predictive modeling, validation and verification of numerical models; Experimental diagnostics: model experiments in high energy density and low energy density regimes, plasma diagnostics, fluid flow visualizations and control, opto-fluidics, novel optical methods, holography, advanced technologies. TMB-2009 was organized by the following members of the Organizing Committee: Snezhana I Abarzhi (chairperson, Chicago, USA) Malcolm J Andrews (Los Alamos National Laboratory, USA) Sergei I Anisimov (Landau Institute for Theoretical Physics, Russia) Hiroshi Azechi (Institute of Laser Engineering, Osaka, Japan) Serge Gauthier (Commissariat à l'Energie Atomique, France) Christopher J Keane (Lawrence Livermore National Laboratory, USA) Robert Rosner (Argonne National Laboratory, USA) Katepalli R Sreenivasan (International Centre for Theoretical Physics, Italy) Alexander L Velikovich (Naval Research Laboratory, USA) and the Local Organizing Committee at the International Centre for Theoretical Physics, Italy Joseph J Niemela Katepalli R Sreenivasan with the assistance of Suzie Radosic (administrator and assistant, ICTP) Daniil Ilyin (web-master, University of Chicago Laboratory Schools, Chicago, USA) The Conference and the School were sponsored by several Agencies and Institutions in the USA, Europe and Japan. The Organizing Committee of TMB-2009 gratefully acknowledges the support of International Centre for Theoretical Physics (ICTP), Italy National Science Foundation (NSF), USA Programs: Plasma Physics; Astronomy and Astrophysics; Computational Mathematics; Applied Mathematics; Fluid Dynamics; Combustion, Fire and Plasma Systems; Cyber-Physical Systems; Computer and Network Systems Air Force Office of Scientific Research (AFOSR), US Programs: Hypersonics and Turbulence; Flow Control and Aeroelasticity European Office of Aerospace Research and Development (EOARD) of the AFOSR, UK Programs: Aeronautical Sciences Department of Energy (DOE), USA, DOE Office of Science US Department of Energy Lawrence Livermore National Laboratory (LLNL), USA Programs: National Ignition Facility; Fusion Energy US Department of Energy Los Alamos National Laboratory (LANL), USA US Department of Energy Argonne National Laboratory (ANL), USA Commissariat à l'Energie Atomique (CEA), France Institute for Laser Engineering (ILE), Japan The University of Chicago, USA ASC Alliance Center for Astrophysical Thermonuclear Flashes, USA Photron (Europe) Ltd, UK and thank them for making this event possible. We express our gratitude for the help with the Conference Program to the members of the Scientific Advisory Committee: S I Abarzhi (University of Chicago, USA) Y Aglitskiy (Science Applications International Corporation, USA) H Azechi (Institute for Laser Engineering, Osaka, Japan) M J Andrews (Los Alamos National Laboratory, USA) S I Anisimov (Landau Institute for Theoretical Physics, Russia) E Bodenschatz (Max Plank Institute for Dynamics and Self-Organization, Germany) F Cattaneo (University of Chicago, USA) P Cvitanović (Georgia Institute of Technology, USA) S Cowley (Imperial College, UK) S Dalziel (DAMTP, University of Cambridge, UK) W S Don (Brown University, USA) R Ecke (Los Alamos National Laboratory, USA) H J Fernando (Arizona State University, USA) I Foster (University of Chicago, USA) S Gauthier (Commissariat à l'Energie Atomique, France) G A Glatzmaier (University of California at Santa Cruz, USA) J Glimm (State University of New York at Stony Brook, USA) W A Goddard III (California Institute of Technology, USA) J Jimenez (Universidad Politecnica de Madrid, Spain) L P Kadanoff (The University of Chicago, USA) D Q Lamb (The University of Chicago, USA) D P Lathrop (University of Maryland, USA) S Lebedev (Imperial College, UK) P Manneville (École Polytechnique, France) D I Meiron (California Institute of Technology, USA) P Moin (Stanford University, USA) A Nepomnyashchy (Technion, Israel) J Niemela (International Center for Theoretical Physics, Italy) K Nishihara (Institute for Laser Engineering, Osaka, Japan) S S Orlov (Stanford University, USA) S A Orszag (Yale University, USA) E Ott (University of Maryland, USA) N Peters (RWTH Aachen University, Germany) S B Pope (Cornell, USA) A Pouquet (University Corporation for Atmospheric Research, USA) B A Remington (Lawrence Livermore National Laboratory, USA) R Rosner (Argonne National Laboratory and University of Chicago, USA) A J Schmitt (Naval Research Laboratory, USA) C -W Shu (Brown University, USA) K R Sreenivasan (International Centre for Theoretical Physics, Italy) E Tadmor (University of Maryland, USA) Y C F Thio (US Department of Energy) A L Velikovich (Naval Research Laboratory, USA) V Yakhot (Boston University, USA) P K Yeung (Georgia Institute of Technology, USA) F A Williams (University of California at San Diego, USA) E Zweibel (University of Wisconsin, USA). We deeply appreciate the work of the Selection Committee for applications for the Advanced School: S Gauthier (Commissariat à l'Energie Atomique, France) C J Keane (Lawrence Livermore National Laboratory, USA) J Niemela (International Center for Theoretical Physics, Italy) S S Orlov (Stanford University, USA) A L Velikovich (Naval Research Laboratory, USA) and thank the members of the Committee for the award 'Turbulent Mixing and Beyond for Youth': S I Abarzhi (University of Chicago, USA) M J Andrews (Los Alamos National Laboratory, USA) P Cvitanović (Georgia Institute of Technology, USA) S Gauthier (Commissariat à l'Energie Atomique, France) C J Keane (Lawrence Livermore National Laboratory, USA) S Lebedev (Imperial College, UK) J Niemela (International Center for Theoretical Physics, Italy) S S Orlov (Stanford University, USA) A Pouquet (University Corporation for Atmospheric Research, USA) K R Sreenivasan (International Centre for Theoretical Physics, Italy) A L Velikovich (Naval Research Laboratory, USA) We would like to thank all the authors and the referees for their contributions to this Topical Issue and for offering their expertise, time and effort. The readers are cordially invited to take a look at this Topical Issue for information on the frontiers of theoretical, numerical and experimental research, and state-of-the-art technology. The Organizing Committee hopes the TMB Conference will serve to advance the state-of-the-art in understanding of fundamental physical properties of non-equilibrium turbulent processes and will have an impact on predictive modeling capabilities, physical description and, ultimately, control of these complex processes. Welcome to the Topical Issue 'Turbulent Mixing and Beyond', TMB-2009.

Entropy production in mesoscopic stochastic thermodynamics: nonequilibrium kinetic cycles driven by chemical potentials, temperatures, and mechanical forces

NASA Astrophysics Data System (ADS)

Qian, Hong; Kjelstrup, Signe; Kolomeisky, Anatoly B.; Bedeaux, Dick

2016-04-01

Nonequilibrium thermodynamics (NET) investigates processes in systems out of global equilibrium. On a mesoscopic level, it provides a statistical dynamic description of various complex phenomena such as chemical reactions, ion transport, diffusion, thermochemical, thermomechanical and mechanochemical fluxes. In the present review, we introduce a mesoscopic stochastic formulation of NET by analyzing entropy production in several simple examples. The fundamental role of nonequilibrium steady-state cycle kinetics is emphasized. The statistical mechanics of Onsager’s reciprocal relations in this context is elucidated. Chemomechanical, thermomechanical, and enzyme-catalyzed thermochemical energy transduction processes are discussed. It is argued that mesoscopic stochastic NET in phase space provides a rigorous mathematical basis of fundamental concepts needed for understanding complex processes in chemistry, physics and biology. This theory is also relevant for nanoscale technological advances.

Koszul information geometry and Souriau Lie group thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant bymore » their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].« less

General response formula and application to topological insulator in quantum open system.

PubMed

Shen, H Z; Qin, M; Shao, X Q; Yi, X X

2015-11-01

It is well-known that the quantum linear response theory is based on the first-order perturbation theory for a system in thermal equilibrium. Hence, this theory breaks down when the system is in a steady state far from thermal equilibrium and the response up to higher order in perturbation is not negligible. In this paper, we develop a nonlinear response theory for such quantum open system. We first formulate this theory in terms of general susceptibility, after which we apply it to the derivation of Hall conductance for open system at finite temperature. As an example, the Hall conductance of the two-band model is derived. Then we calculate the Hall conductance for a two-dimensional ferromagnetic electron gas and a two-dimensional lattice model. The calculations show that the transition points of topological phase are robust against the environment. Our results provide a promising platform for the coherent manipulation of the nonlinear response in quantum open system, which has potential applications for quantum information processing and statistical physics.

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials

NASA Astrophysics Data System (ADS)

Hyeon, Changbong; Hwang, Wonseok

2017-07-01

Using Brownian motion in periodic potentials V (x ) tilted by a force f , we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q , and in order to limit the output fluctuation within a relative uncertainty ɛ , at least 2 kBT /ɛ2 of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f ≪V'(x ) ] but also at far-from-equilibrium [f ≫V'(x ) ] , more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σq2) increases with its mean (μq), and it cannot be smaller than 2 kBT μq .

Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials.

PubMed

Hyeon, Changbong; Hwang, Wonseok

2017-07-01

Using Brownian motion in periodic potentials V(x) tilted by a force f, we provide physical insight into the thermodynamic uncertainty relation, a recently conjectured principle for statistical errors and irreversible heat dissipation in nonequilibrium steady states. According to the relation, nonequilibrium output generated from dissipative processes necessarily incurs an energetic cost or heat dissipation q, and in order to limit the output fluctuation within a relative uncertainty ε, at least 2k_{B}T/ε^{2} of heat must be dissipated. Our model shows that this bound is attained not only at near-equilibrium [f≪V^{'}(x)] but also at far-from-equilibrium [f≫V^{'}(x)], more generally when the dissipated heat is normally distributed. Furthermore, the energetic cost is maximized near the critical force when the barrier separating the potential wells is about to vanish and the fluctuation of Brownian particles is maximized. These findings indicate that the deviation of heat distribution from Gaussianity gives rise to the inequality of the uncertainty relation, further clarifying the meaning of the uncertainty relation. Our derivation of the uncertainty relation also recognizes a bound of nonequilibrium fluctuations that the variance of dissipated heat (σ_{q}^{2}) increases with its mean (μ_{q}), and it cannot be smaller than 2k_{B}Tμ_{q}.

Exact results in nonequilibrium statistical mechanics: Formalism and applications in chemical kinetics and single-molecule free energy estimation

NASA Astrophysics Data System (ADS)

Adib, Artur B.

In the last two decades or so, a collection of results in nonequilibrium statistical mechanics that departs from the traditional near-equilibrium framework introduced by Lars Onsager in 1931 has been derived, yielding new fundamental insights into far-from-equilibrium processes in general. Apart from offering a more quantitative statement of the second law of thermodynamics, some of these results---typified by the so-called "Jarzynski equality"---have also offered novel means of estimating equilibrium quantities from nonequilibrium processes, such as free energy differences from single-molecule "pulling" experiments. This thesis contributes to such efforts by offering three novel results in nonequilibrium statistical mechanics: (a) The entropic analog of the Jarzynski equality; (b) A methodology for estimating free energies from "clamp-and-release" nonequilibrium processes; and (c) A directly measurable symmetry relation in chemical kinetics similar to (but more general than) chemical detailed balance. These results share in common the feature of remaining valid outside Onsager's near-equilibrium regime, and bear direct applicability in protein folding kinetics as well as in single-molecule free energy estimation.

On information, negentropy and H-theorem

NASA Astrophysics Data System (ADS)

Chakrabarti, C. G.; Sarker, N. G.

1983-09-01

The paper deals with the imprtance of the Kullback descrimination information in the statistical characterization of negentropy of non-equilibrium state and the irreversibility of a classical dynamical system. The theory based on the Kullback discrimination information as the H-function gives new insight into the interrelation between the concepts of coarse-graining and the principle of sufficiency leading to important statistical characterization of thermal equilibrium of a closed system.

Statistical mechanics framework for static granular matter.

PubMed

Henkes, Silke; Chakraborty, Bulbul

2009-06-01

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by Wyart and others.

Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions.

PubMed

Chavanis, Pierre-Henri

2004-06-01

We discuss the statistical mechanics of a system of self-gravitating fermions in a space of dimension D. We plot the caloric curves of the self-gravitating Fermi gas giving the temperature as a function of energy and investigate the nature of phase transitions as a function of the dimension of space. We consider stable states (global entropy maxima) as well as metastable states (local entropy maxima). We show that for D> or =4, there exists a critical temperature (for sufficiently large systems) and a critical energy below which the system cannot be found in statistical equilibrium. Therefore, for D> or =4, quantum mechanics cannot stabilize matter against gravitational collapse. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulomb forces. This makes the dimension D=3 of our Universe very particular with possible implications regarding the anthropic principle. Our study joins a long tradition of scientific and philosophical papers that examined how the dimension of space affects the laws of physics.

On the statistical mechanics of species abundance distributions.

PubMed

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.

SkyNet: A Modular Nuclear Reaction Network Library

NASA Astrophysics Data System (ADS)

Lippuner, Jonas; Roberts, Luke F.

2017-12-01

Almost all of the elements heavier than hydrogen that are present in our solar system were produced by nuclear burning processes either in the early universe or at some point in the life cycle of stars. In all of these environments, there are dozens to thousands of nuclear species that interact with each other to produce successively heavier elements. In this paper, we present SkyNet, a new general-purpose nuclear reaction network that evolves the abundances of nuclear species under the influence of nuclear reactions. SkyNet can be used to compute the nucleosynthesis evolution in all astrophysical scenarios where nucleosynthesis occurs. SkyNet is free and open source, and aims to be easy to use and flexible. Any list of isotopes can be evolved, and SkyNet supports different types of nuclear reactions. SkyNet is modular so that new or existing physics, like nuclear reactions or equations of state, can easily be added or modified. Here, we present in detail the physics implemented in SkyNet with a focus on a self-consistent transition to and from nuclear statistical equilibrium to non-equilibrium nuclear burning, our implementation of electron screening, and coupling of the network to an equation of state. We also present comprehensive code tests and comparisons with existing nuclear reaction networks. We find that SkyNet agrees with published results and other codes to an accuracy of a few percent. Discrepancies, where they exist, can be traced to differences in the physics implementations.

Reversible first-order transition in Pauli percolation

NASA Astrophysics Data System (ADS)

Maksymenko, Mykola; Moessner, Roderich; Shtengel, Kirill

2015-06-01

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyze a new percolation problem in which the first-order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight W (n )=n +1 for a cluster of size n . This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle and their reach in practice.

A study of some non-equilibrium driven models and their contribution to the understanding of molecular motors

NASA Astrophysics Data System (ADS)

Mazilu, Irina; Gonzalez, Joshua

2008-03-01

From the point of view of a physicist, a bio-molecular motor represents an interesting non-equilibrium system and it is directly amenable to an analysis using standard methods of non-equilibrium statistical physics. We conduct a rigorous Monte Carlo study of three different driven lattice gas models that retain the basic behavior of three types of cytoskeletal molecular motors. Our models incorporate novel features such as realistic dynamics rules and complex motor-motor interactions. We are interested to have a deeper understanding of how various parameters influence the macroscopic behavior of these systems, what is the density profile and if the system undergoes a phase transition. On the analytical front, we computed the steady-state probability distributions exactly for the one of the models using the matrix method that was established in 1993 by B. Derrida et al. We also explored the possibilities offered by the ``Bethe ansatz'' method by mapping some well studied spin models into asymmetric simple exclusion models (already analyzed using computer simulations), and to use the results obtained for the spin models in finding an exact solution for our problem. We have exhaustive computational studies of the kinesin and dynein molecular motor models that prove to be very useful in checking our analytical work.

LeChâtelier's Principle in the Sciences

NASA Astrophysics Data System (ADS)

Thomsen, Volker B. E.

2000-02-01

LeChâtelier's principle of chemical equilibrium is actually a very general statement about systems in equilibrium and their behavior when subjected to external force or stress. Although one almost never finds mention of his name or law in other sciences, analogous principles and concepts do exist. In this note we examine some of the similar forms taken by this chemical principle in the fields of physics, geology, biology, and economics. Lenz's law in physics is an example of electromagnetic equilibrium and the geological principle of isostatic uplift concerns mechanical equilibrium. Both are strictly consequences of conservation of energy. LeChâtelier's principle deals with thermodynamic equilibrium and involves both the first and second laws of thermodynamics. The concept of homeostasis in biology and the economic law of supply and demand are both equilibrium-like principles, but involve systems in the steady state. However, all these principles involve the stability of the system under consideration and the analogies presented may be useful in the teaching of LeChâtelier's principle.

Departures from LTE Populations Versus Anomalous Abundances: the Effects of Heating

NASA Technical Reports Server (NTRS)

Underhill, A. B.

1985-01-01

The deposit of nonradiative heat and momentum in the mantle of a hot star affects the interpretation of the stellar spectrum in two ways. First, a superheated and moving plasma should be considered when doing the analysis, and second, a model atom which is appropriate for the physical state of the line forming regions. Some examples are presented for H and He showing how the changes in the electron temperature affect the solution of the equations of statistical equilibrium. The observed spectra of the Wolf-Raynet stars HD 191765, HD 192103, and HD 192163 are compatible with a normal H/He abundance ratio.

Non-equilibrium thermionic electron emission for metals at high temperatures

NASA Astrophysics Data System (ADS)

Domenech-Garret, J. L.; Tierno, S. P.; Conde, L.

2015-08-01

Stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non-equilibrium quantum kappa energy distribution for the electrons. The latter depends on the temperature decreasing parameter κ ( T ) , which decreases with increasing temperature and can be estimated from raw experimental data and characterizes the departure of the electron energy spectrum from equilibrium Fermi-Dirac statistics. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges. The Richardson-Dushman law governs electron emission for large values of kappa or equivalently, moderate metal temperatures. The high energy tail in the electron energy distribution function that develops at higher temperatures or lower kappa values increases the emission currents well over the predictions of the classical expression. This also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.

Thermodynamics of Biological Processes

PubMed Central

Garcia, Hernan G.; Kondev, Jane; Orme, Nigel; Theriot, Julie A.; Phillips, Rob

2012-01-01

There is a long and rich tradition of using ideas from both equilibrium thermodynamics and its microscopic partner theory of equilibrium statistical mechanics. In this chapter, we provide some background on the origins of the seemingly unreasonable effectiveness of ideas from both thermodynamics and statistical mechanics in biology. After making a description of these foundational issues, we turn to a series of case studies primarily focused on binding that are intended to illustrate the broad biological reach of equilibrium thinking in biology. These case studies include ligand-gated ion channels, thermodynamic models of transcription, and recent applications to the problem of bacterial chemotaxis. As part of the description of these case studies, we explore a number of different uses of the famed Monod–Wyman–Changeux (MWC) model as a generic tool for providing a mathematical characterization of two-state systems. These case studies should provide a template for tailoring equilibrium ideas to other problems of biological interest. PMID:21333788

Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems

NASA Astrophysics Data System (ADS)

Cazalilla, M. A.; Rigol, M.

2010-05-01

The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose-Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1⁄2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Michael Moeckel and Stefan Kehrein Quantum quenches in integrable field theories Davide Fioretto and Giuseppe Mussardo Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point A Bermudez, L Amico and M A Martin-Delgado Thermometry with spin-dependent lattices D McKay and B DeMarco Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy Martin Eckstein and Marcus Kollar Sudden change of the thermal contact between two quantum systems J Restrepo and S Camalet Reflection of a Lieb-Liniger wave packet from the hard-wall potential D Jukić and H Buljan Probing interaction-induced ferromagnetism in optical superlattices J von Stecher, E Demler, M D Lukin and A M Rey Sudden interaction quench in the quantum sine-Gordon model Javier Sabio and Stefan Kehrein Dynamics of an inhomogeneous quantum phase transition Jacek Dziarmaga and Marek M Rams

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

NASA Astrophysics Data System (ADS)

Yuan, Ruoshi; Tang, Ying; Ao, Ping

2017-12-01

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochastic differential equation (SDE) into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the α-type interpretation for multidimensional systems. The potential landscape serves as a Hamiltonian-like function in nonequilibrium processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel framework. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

Exploring parameter space effects on structure-property relationships of surfactants at liquid-liquid interfaces.

PubMed

Emborsky, Christopher P; Cox, Kenneth R; Chapman, Walter G

2011-08-28

The ubiquitous use of surfactants in commercial and industrial applications has led to many experimental, theoretical, and simulation based studies. These efforts seek to provide a molecular level understanding of the effects on structuring behavior and the corresponding impacts on observable properties (e.g., interfacial tension). With such physical detail, targeted system design can be improved over typical techniques of observational trends and phenomenological correlations by taking advantage of predictive system response. This research provides a systematic study of part of the broad parameter space effects on equilibrium microstructure and interfacial properties of amphiphiles at a liquid-liquid interface using the interfacial statistical associating fluid theory density functional theory as a molecular model for the system from the bulk to the interface. Insights into the molecular level physics and thermodynamics governing the system behavior are discussed as they relate to both predictions qualitatively consistent with experimental observations and extensions beyond currently available studies. © 2011 American Institute of Physics

Utilization of a Microcomputer for the Study of an Iodine Oxidation and Equilibrium Reaction: A Physical Chemistry Experiment.

ERIC Educational Resources Information Center

Julien, L. M.

1984-01-01

Describes a physical chemistry experiment which incorporates the use of a microcomputer to enhance understanding of combined kinetic and equilibrium phenomena, to increase experimental capabilities when working with large numbers of students and limited equipment, and for the student to develop a better understanding of experimental design. (JN)

Plasma Equilibrium Control in Nuclear Fusion Devices 2. Plasma Control in Magnetic Confinement Devices 2.1 Plasma Control in Tokamaks

NASA Astrophysics Data System (ADS)

Fukuda, Takeshi

The plasma control technique for use in large tokamak devices has made great developmental strides in the last decade, concomitantly with progress in the understanding of tokamak physics and in part facilitated by the substantial advancement in the computing environment. Equilibrium control procedures have thereby been established, and it has been pervasively recognized in recent years that the real-time feedback control of physical quantities is indispensable for the improvement and sustainment of plasma performance in a quasi-steady-state. Further development is presently undertaken to realize the “advanced plasma control” concept, where integrated fusion performance is achieved by the simultaneous feedback control of multiple physical quantities, combined with equilibrium control.

Performance Modeling of Experimental Laser Lightcrafts

NASA Technical Reports Server (NTRS)

Wang, Ten-See; Chen, Yen-Sen; Liu, Jiwen; Myrabo, Leik N.; Mead, Franklin B., Jr.; Turner, Jim (Technical Monitor)

2001-01-01

A computational plasma aerodynamics model is developed to study the performance of a laser propelled Lightcraft. The computational methodology is based on a time-accurate, three-dimensional, finite-difference, chemically reacting, unstructured grid, pressure-based formulation. The underlying physics are added and tested systematically using a building-block approach. The physics modeled include non-equilibrium thermodynamics, non-equilibrium air-plasma finite-rate kinetics, specular ray tracing, laser beam energy absorption and refraction by plasma, non-equilibrium plasma radiation, and plasma resonance. A series of transient computations are performed at several laser pulse energy levels and the simulated physics are discussed and compared with those of tests and literatures. The predicted coupling coefficients for the Lightcraft compared reasonably well with those of tests conducted on a pendulum apparatus.

Creation and protection of entanglement in systems out of thermal equilibrium

NASA Astrophysics Data System (ADS)

Bellomo, Bruno; Antezza, Mauro

2013-11-01

We investigate the creation of entanglement between two quantum emitters interacting with a realistic common stationary electromagnetic field out of thermal equilibrium. In the case of two qubits we show that the absence of equilibrium allows the generation of steady entangled states, which is inaccessible at thermal equilibrium and is realized without any further external action on the two qubits. We first give a simple physical interpretation of the phenomenon in a specific case and then we report a detailed investigation on the dependence of the entanglement dynamics on the various physical parameters involved. Sub- and super-radiant effects are discussed, and qualitative differences in the dynamics concerning both creation and protection of entanglement according to the initial two-qubit state are pointed out.

The non-equilibrium allele frequency spectrum in a Poisson random field framework.

PubMed

Kaj, Ingemar; Mugal, Carina F

2016-10-01

In population genetic studies, the allele frequency spectrum (AFS) efficiently summarizes genome-wide polymorphism data and shapes a variety of allele frequency-based summary statistics. While existing theory typically features equilibrium conditions, emerging methodology requires an analytical understanding of the build-up of the allele frequencies over time. In this work, we use the framework of Poisson random fields to derive new representations of the non-equilibrium AFS for the case of a Wright-Fisher population model with selection. In our approach, the AFS is a scaling-limit of the expectation of a Poisson stochastic integral and the representation of the non-equilibrium AFS arises in terms of a fixation time probability distribution. The known duality between the Wright-Fisher diffusion process and a birth and death process generalizing Kingman's coalescent yields an additional representation. The results carry over to the setting of a random sample drawn from the population and provide the non-equilibrium behavior of sample statistics. Our findings are consistent with and extend a previous approach where the non-equilibrium AFS solves a partial differential forward equation with a non-traditional boundary condition. Moreover, we provide a bridge to previous coalescent-based work, and hence tie several frameworks together. Since frequency-based summary statistics are widely used in population genetics, for example, to identify candidate loci of adaptive evolution, to infer the demographic history of a population, or to improve our understanding of the underlying mechanics of speciation events, the presented results are potentially useful for a broad range of topics. Copyright © 2016 Elsevier Inc. All rights reserved.

Turbulence as a Problem in Non-equilibrium Statistical Mechanics

NASA Astrophysics Data System (ADS)

Goldenfeld, Nigel; Shih, Hong-Yan

2017-05-01

The transitional and well-developed regimes of turbulent shear flows exhibit a variety of remarkable scaling laws that are only now beginning to be systematically studied and understood. In the first part of this article, we summarize recent progress in understanding the friction factor of turbulent flows in rough pipes and quasi-two-dimensional soap films, showing how the data obey a two-parameter scaling law known as roughness-induced criticality, and exhibit power-law scaling of friction factor with Reynolds number that depends on the precise form of the nature of the turbulent cascade. These results hint at a non-equilibrium fluctuation-dissipation relation that applies to turbulent flows. The second part of this article concerns the lifetime statistics in smooth pipes around the transition, showing how the remarkable super-exponential scaling with Reynolds number reflects deep connections between large deviation theory, extreme value statistics, directed percolation and the onset of coexistence in predator-prey ecosystems. Both these phenomena reflect the way in which turbulence can be fruitfully approached as a problem in non-equilibrium statistical mechanics.

Investigating Student Understanding for a Statistical Analysis of Two Thermally Interacting Solids

NASA Astrophysics Data System (ADS)

Loverude, Michael E.

2010-10-01

As part of an ongoing research and curriculum development project for upper-division courses in thermal physics, we have developed a sequence of tutorials in which students apply statistical methods to examine the behavior of two interacting Einstein solids. In the sequence, students begin with simple results from probability and develop a means for counting the states in a single Einstein solid. The students then consider the thermal interaction of two solids, and observe that the classical equilibrium state corresponds to the most probable distribution of energy between the two solids. As part of the development of the tutorial sequence, we have developed several assessment questions to probe student understanding of various aspects of this system. In this paper, we describe the strengths and weaknesses of student reasoning, both qualitative and quantitative, to assess the readiness of students for one tutorial in the sequence.

The efficiency of driving chemical reactions by a physical non-equilibrium is kinetically controlled.

PubMed

Göppel, Tobias; Palyulin, Vladimir V; Gerland, Ulrich

2016-07-27

An out-of-equilibrium physical environment can drive chemical reactions into thermodynamically unfavorable regimes. Under prebiotic conditions such a coupling between physical and chemical non-equilibria may have enabled the spontaneous emergence of primitive evolutionary processes. Here, we study the coupling efficiency within a theoretical model that is inspired by recent laboratory experiments, but focuses on generic effects arising whenever reactant and product molecules have different transport coefficients in a flow-through system. In our model, the physical non-equilibrium is represented by a drift-diffusion process, which is a valid coarse-grained description for the interplay between thermophoresis and convection, as well as for many other molecular transport processes. As a simple chemical reaction, we consider a reversible dimerization process, which is coupled to the transport process by different drift velocities for monomers and dimers. Within this minimal model, the coupling efficiency between the non-equilibrium transport process and the chemical reaction can be analyzed in all parameter regimes. The analysis shows that the efficiency depends strongly on the Damköhler number, a parameter that measures the relative timescales associated with the transport and reaction kinetics. Our model and results will be useful for a better understanding of the conditions for which non-equilibrium environments can provide a significant driving force for chemical reactions in a prebiotic setting.

Pasta Nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

Caplan, Matthew; Horowitz, Charles; da Silva Schneider, Andre; Berry, Donald

2014-09-01

We simulate the decompression of cold dense nuclear matter, near the nuclear saturation density, in order to study the role of nuclear pasta in r-process nucleosynthesis in neutron star mergers. Our simulations are performed using a classical molecular dynamics model with 51 200 and 409 600 nucleons, and are run on GPUs. We expand our simulation region to decompress systems from initial densities of 0.080 fm-3 down to 0.00125 fm-3. We study proton fractions of YP = 0.05, 0.10, 0.20, 0.30, and 0.40 at T = 0.5, 0.75, and 1 MeV. We calculate the composition of the resulting systems using a cluster algorithm. This composition is in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than YP = 0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

Thermal Equilibrium in Plastic and Glass Microscale Containers

ERIC Educational Resources Information Center

Curbelo, Estela; Cerda, Maria F.; Mendez, Eduardo

2007-01-01

The study describes the various thermal equilibrium conditions, which should be taken care for while designing or selecting the plastic and glass microscale containers for physical chemistry experiments. The results show that the thermal equilibrium completely depends on the material of the container for the same volume and thickness.

Metric of two balancing Kerr particles in physical parametrization

NASA Astrophysics Data System (ADS)

Manko, V. S.; Ruiz, E.

2015-11-01

The present paper aims at elaborating a completely physical representation for the general 4-parameter family of the extended double-Kerr spacetimes describing two spinning sources in gravitational equilibrium. This involved problem is solved in a concise analytical form by using the individual Komar masses and angular momenta as arbitrary parameters, and the simplest equatorially symmetric specialization of the general expressions obtained by us yields the physical representation for the well-known Dietz-Hoenselaers superextreme case of two balancing identical Kerr constituents. The existence of the physically meaningful "black-hole-superextreme-object" equilibrium configurations permitted by the general solution may be considered as a clear indication that the spin-spin repulsion force might actually be by far stronger than expected earlier, when only the balance between two superextreme Kerr sources was thought possible. We also present the explicit analytical formulas relating the equilibrium states in the double-Kerr and double-Reissner-Nordström configurations.

Equilibrium Fluctuation Relations for Voltage Coupling in Membrane Proteins

PubMed Central

Kim, Ilsoo; Warshel, Arieh

2015-01-01

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the reaction coordinate of “voltage coupling”, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference at zero membrane potential (i.e., between the two “non-equilibrium” conformational states) is shown to be equivalent to the free energy difference between the two “equilibrium” conformational states along the one-dimensional reaction coordinate of voltage coupling. Furthermore, the requirement that the application of linear response approximation to the free energy functions (free energies) of voltage coupling should satisfy the general free energy relations, yields a novel expression for the gating charge in terms of other experimentally measurable quantities. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the movement of a unit charge within the membrane under the influence of an external potential, using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus–type voltage dependent free energy parabolas for the two conformational states, which allow for quantitative estimations of an equilibrium free energy difference, a free energy of barrier, and the voltage dependency of channel activation (Q-V curve) for the unit charge movement. In addition, our analysis offers a quantitative rationale for the correlation between the free energy landscapes (parabolas) and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as a reaction coordinate of energy gab, the present theory offers a firm physical foundation from the equilibrium theory of statistical mechanics for the thermodynamic models of voltage activation in voltage-sensitive membrane proteins. This formulation also provides a powerful bridge between the CG model and the conventional macroscopic treatments, offering an intuitive and quantitative framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. PMID:26290960

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

Universality of clone dynamics during tissue development

NASA Astrophysics Data System (ADS)

Rulands, Steffen; Lescroart, Fabienne; Chabab, Samira; Hindley, Christopher J.; Prior, Nicole; Sznurkowska, Magdalena K.; Huch, Meritxell; Philpott, Anna; Blanpain, Cedric; Simons, Benjamin D.

2018-05-01

The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time evolution of their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease1,2. But what can be learnt from clonal dynamics in development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as a laboratory to study non-equilibrium statistical physics.

Statistical Physics of Electron Temperature of Low-Pressure Discharge Nitrogen Plasma with Non-Maxwellian EEDF

NASA Astrophysics Data System (ADS)

Akatsuka, Hiroshi; Tanaka, Yoshinori

2016-09-01

We reconsider electron temperature of non-equilibrium plasmas on the basis of thermodynamics and statistical physics. Following our previous study on the oxygen plasma in GEC 2015, we discuss the common issue for the nitrogen plasma. First, we solve the Boltzmann equation to obtain the electron energy distribution function (EEDF) F(ɛ) of the nitrogen plasma as a function of the reduced electric field E / N . We also simultaneously solve the chemical kinetic equations of some essential excite species of nitrogen molecules and atoms, including vibrational distribution function (VDF). Next, we calculate the electron mean energy as U = < ɛ > =∫0∞ɛF(ɛ) dɛ and entropy S = - k∫0∞F(ɛ) ln [ F(ɛ) ] dɛ for each value of E / N . Then, we can obtain the electron temperature as Testat =[ ∂S / ∂U ] - 1 . After that, we discuss the difference between Testat and the kinetic temperature Tekin ≡(2 / 3) < ɛ > , as well as the temperature given as a slope of the calculated EEDF for each value of E / N . We found Testat is close to the slope at ɛ 4 eV in the EEPF.

On the role of fluctuations in the modeling of complex systems.

NASA Astrophysics Data System (ADS)

Droz, Michel; Pekalski, Andrzej

2016-09-01

The study of models is ubiquitous in sciences like physics, chemistry, ecology, biology or sociology. Models are used to explain experimental facts or to make new predictions. For any system, one can distinguish several levels of description. In the simplest mean-field like description the dynamics is described in terms of spatially averaged quantities while in a microscopic approach local properties are taken into account and local fluctuations for the relevant variables are present. The properties predicted by these two different approaches may be drastically different. In a large body of research literature concerning complex systems this problem is often overlooked and simple mean-field like approximation are used without asking the question of the robustness of the corresponding predictions. The goal of this paper is twofold, first to illustrate the importance of the fluctuations in a self-contained and pedagogical way, by revisiting two different classes of problems where thorough investigations have been conducted (equilibrium and non-equilibrium statistical physics). Second, we present our original research on the dynamics of population of annual plants which are competing among themselves for just one resource (water) through a stochastic dynamics. Depending on the observable considered, the mean-field like and microscopic approaches agree or totally disagree. There is not a general criterion allowing to decide a priori when the two approaches will agree.

Mechanics: Statics; A Syllabus.

ERIC Educational Resources Information Center

Compo, Louis

The instructor's guide presents material for structuring an engineering fundamentals course covering the basic laws of statistics as part of a mechanical technology program. Detailed behavioral objectives are described for the following five areas of course content: principles of mechanics, two-dimensional equilibrium, equilibrium of internal…

Reversible and Irreversible Behavior of Glass-forming Materials from the Standpoint of Hierarchical Dynamical Facilitation

NASA Astrophysics Data System (ADS)

Keys, Aaron

2013-03-01

Using molecular simulation and coarse-grained lattice models, we study the dynamics of glass-forming liquids above and below the glass transition temperature. In the supercooled regime, we study the structure, statistics, and dynamics of excitations responsible for structural relaxation for several atomistic models of glass-formers. Excitations (or soft spots) are detected in terms of persistent particle displacements. At supercooled conditions, we find that excitations are associated with correlated particle motions that are sparse and localized, and the statistics and dynamics of these excitations are facilitated and hierarchical. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. Excitation-energy scales grow logarithmically with the characteristic size of the excitation, giving structural-relaxation times that can be predicted quantitatively from dynamics at short time scales. We demonstrate that these same physical principles govern the dynamics of glass-forming systems driven out-of-equilibrium by time-dependent protocols. For a system cooled and re-heated through the glass transition, non-equilibrium response functions, such as heat capacities, are notably asymmetric in time, and the response to melting a glass depends markedly on the cooling protocol by which the glass was formed. We introduce a quantitative description of this behavior based on the East model, with parameters determined from reversible transport data, that agrees well with irreversible differential scanning calorimetry. We find that the observed hysteresis and asymmetric response is a signature of an underlying dynamical transition between equilibrium melts with no trivial spatial correlations and non-equilibrium glasses with correlation lengths that are both large and dependent upon the rate at which the glass is prepared. The correlation length corresponds to the size of amorphous domains bounded by excitations that remain frozen on the observation time scale, thus forming stripes when viewed in space and time. We elucidate properties of the striped phase and show that glasses of this type, traditionally prepared through cooling, can be considered a finite-size realization of the inactive phase formed by the s-ensemble in the space-time thermodynamic limit.

Statistical thermodynamics of quantum Brownian motion: Construction of perpetuum mobile of the second kind

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Th. M.; Allahverdyan, A. E.

2002-09-01

The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale ħ/kBT is larger than or comparable to other time scales of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics. The known agreements occur only due to the weak coupling limit, which does not pertain to low temperatures. Experimental setups for testing the effects are discussed.

Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind.

PubMed

Nieuwenhuizen, Th M; Allahverdyan, A E

2002-09-01

The Brownian motion of a quantum particle in a harmonic confining potential and coupled to harmonic quantum thermal bath is exactly solvable. Though this system presents at high temperatures a pedagogic example to explain the laws of thermodynamics, it is shown that at low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. In physical terms, this happens when the cloud of bath modes around the particle starts to play a nontrivial role, namely, when the bath temperature T is smaller than the coupling energy. Indeed, equilibrium thermodynamics of the total system, particle plus bath, does not imply standard equilibrium thermodynamics for the particle itself at low T. Various formulations of the second law are found to be invalid at low T. First, the Clausius inequality can be violated, because heat can be extracted from the zero point energy of the cloud of bath modes. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the entropy production is partly negative. In this process the energy put on the particle does not relax monotonically, but oscillates between particle and bath, even in the limit of strong damping. Third, for nonadiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobility of the second kind, having one or several work extraction cycles, enter the realm of condensed matter physics. Fourth, it follows that the equivalence between different formulations of the second law (e.g., those by Clausius and Thomson) can be violated at low temperatures. These effects are the consequence of quantum entanglement in the presence of the slightly off-equilibrium nature of the thermal bath, and become important when the characteristic quantum time scale variant Planck's over 2pi /k(B)T is larger than or comparable to other time scales of the system. They show that there is no general consensus between standard thermodynamics and quantum mechanics. The known agreements occur only due to the weak coupling limit, which does not pertain to low temperatures. Experimental setups for testing the effects are discussed.

Diffusion-weighted magnetic resonance imaging of extraocular muscles in patients with Grave's ophthalmopathy using turbo field echo with diffusion-sensitized driven-equilibrium preparation.

PubMed

Hiwatashi, A; Togao, O; Yamashita, K; Kikuchi, K; Momosaka, D; Honda, H

2018-03-20

The purpose of this study was to correlate diffusivity of extraocular muscles, measured by three-dimensional turbo field echo (3DTFE) magnetic resonance (MR) imaging using diffusion-sensitized driven-equilibrium preparation, with their size and activity in patients with Grave's ophthalmopathy. Twenty-three patients with Grave's ophthalmopathy were included. There were 17 women and 6 men with a mean age of 55.8±12.6 (SD) years (range: 26-83 years). 3DTFE with diffusion-sensitized driven-equilibrium MR images were obtained with b-values of 0 and 500s/mm 2 . The apparent diffusion coefficient (ADC) of extraocular muscles was measured on coronal reformatted MR images. Signal intensities of extraocular muscles on conventional MR images were compared to those of normal-appearing white matter, and cross-sectional areas of the muscles were also measured. The clinical activity score was also evaluated. Statistical analyses were performed with Pearson correlation and Mann-Whitney U tests. On 3DTFE with diffusion-sensitized driven-equilibrium preparation, the mean ADC of the extraocular muscles was 2.23±0.37 (SD)×10 -3 mm2/s (range: 1.70×10 -3 -3.11×10 -3 mm 2 /s). There was a statistically significant moderate correlation between ADC and the size of the muscles (r=0.61). There were no statistically significant correlations between ADC and signal intensity on conventional MR and the clinical activity score. 3DTFE with diffusion-sensitized driven-equilibrium preparation technique allows quantifying diffusivity of extraocular muscles in patients with Grave's ophthalmopathy. The diffusivity of the extraocular muscles on 3DTFE with diffusion-sensitized driven-equilibrium preparation MR images moderately correlates with their size. Copyright © 2018. Published by Elsevier Masson SAS.

Equilibrium time correlation functions and the dynamics of fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luban, Marshall; Luscombe, James H.

1999-12-01

Equilibrium time correlation functions are of great importance because they probe the equilibrium dynamical response to external perturbations. We discuss the properties of time correlation functions for several systems that are simple enough to illustrate the calculational steps involved. The discussion underscores the need for avoiding language which misleadingly suggests that thermal equilibrium is associated with a quiescent or moribund state of the system. (c) 1999 American Association of Physics Teachers.

Research in Theoretical High Energy Nuclear Physics at the University of Arizona

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rafelski, Johann

In the past decade (2004-2015) we addressed the quest for the understanding of how quark confinement works, how it can be dissolved in a limited space-time domain, and what this means: i) for the paradigm of the laws of physics of present day; and, ii) for our understanding of cosmology. The focus of our in laboratory matter formation work has been centered on the understanding of the less frequently produced hadronic particles (e.g. strange antibaryons, charmed and beauty hadrons, massive resonances, charmonium, B c). We have developed a public analysis tool, SHARE (Statistical HAdronization with REsonances) which allows a precisemore » model description of experimental particle yield and fluctuation data. We have developed a charm recombination model to allow for off-equilibrium rate of charmonium production. We have developed methods and techniques which allowed us to study the hadron resonance yield evolution by kinetic theory. We explored entropy, strangeness and charm as signature of QGP addressing the wide range of reaction energy for AGS, SPS, RHIC and LHC energy range. In analysis of experimental data, we obtained both statistical parameters as well as physical properties of the hadron source. The following pages present listings of our primary writing on these questions. The abstracts are included in lieu of more detailed discussion of our research accomplishments in each of the publications.« less

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. V. The two-term atom

NASA Astrophysics Data System (ADS)

Bommier, Véronique

2017-11-01

Context. In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). Aims: This paper provides theoretical expressions of the redistribution function for the two-term atom. This redistribution function includes both coherent (RII) and incoherent (RIII) scattering contributions with their branching ratios. Methods: The expressions were derived by applying the formalism outlined above. The statistical equilibrium equation for the atomic density matrix is first formally solved in the case of the two-term atom with unpolarized and infinitely sharp lower levels. Then the redistribution function is derived by substituting this solution for the expression of the emissivity. Results: Expressions are provided for both magnetic and non-magnetic cases. Atomic fine structure is taken into account. Expressions are also separately provided under zero and non-zero hyperfine structure. Conclusions: Redistribution functions are widely used in radiative transfer codes. In our formulation, collisional transitions between Zeeman sublevels within an atomic level (depolarizing collisions effect) are taken into account when possible (I.e., in the non-magnetic case). However, the need for a formal solution of the statistical equilibrium as a preliminary step prevents us from taking into account collisional transfers between the levels of the upper term. Accounting for these collisional transfers could be done via a numerical solution of the statistical equilibrium equation system.

The dimerization equilibrium of a ClC Cl−/H+ antiporter in lipid bilayers

PubMed Central

Chadda, Rahul; Krishnamani, Venkatramanan; Mersch, Kacey; Wong, Jason; Brimberry, Marley; Chadda, Ankita; Kolmakova-Partensky, Ludmila; Friedman, Larry J; Gelles, Jeff; Robertson, Janice L

2016-01-01

Interactions between membrane protein interfaces in lipid bilayers play an important role in membrane protein folding but quantification of the strength of these interactions has been challenging. Studying dimerization of ClC-type transporters offers a new approach to the problem, as individual subunits adopt a stable and functionally verifiable fold that constrains the system to two states – monomer or dimer. Here, we use single-molecule photobleaching analysis to measure the probability of ClC-ec1 subunit capture into liposomes during extrusion of large, multilamellar membranes. The capture statistics describe a monomer to dimer transition that is dependent on the subunit/lipid mole fraction density and follows an equilibrium dimerization isotherm. This allows for the measurement of the free energy of ClC-ec1 dimerization in lipid bilayers, revealing that it is one of the strongest membrane protein complexes measured so far, and introduces it as new type of dimerization model to investigate the physical forces that drive membrane protein association in membranes. DOI: http://dx.doi.org/10.7554/eLife.17438.001 PMID:27484630

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Social cycling and conditional responses in the Rock-Paper-Scissors game

PubMed Central

Wang, Zhijian; Xu, Bin; Zhou, Hai-Jun

2014-01-01

How humans make decisions in non-cooperative strategic interactions is a big question. For the fundamental Rock-Paper-Scissors (RPS) model game system, classic Nash equilibrium (NE) theory predicts that players randomize completely their action choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially in finite populations. However as empirical studies have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision-making of human subjects. Here we observe population-level persistent cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. This collective behavior contradicts with the NE theory but is quantitatively explained, without any adjustable parameter, by a microscopic model of win-lose-tie conditional response. Theoretical calculations suggest that if all players adopt the same optimized conditional response strategy, their accumulated payoff will be much higher than the reference value of the NE mixed strategy. Our work demonstrates the feasibility of understanding human competition behaviors from the angle of non-equilibrium statistical physics. PMID:25060115

Statistical approach to partial equilibrium analysis

NASA Astrophysics Data System (ADS)

Wang, Yougui; Stanley, H. E.

2009-04-01

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.

Simulating Metabolism with Statistical Thermodynamics

PubMed Central

Cannon, William R.

2014-01-01

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD+:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed. PMID:25089525

Simulating metabolism with statistical thermodynamics.

PubMed

Cannon, William R

2014-01-01

New methods are needed for large scale modeling of metabolism that predict metabolite levels and characterize the thermodynamics of individual reactions and pathways. Current approaches use either kinetic simulations, which are difficult to extend to large networks of reactions because of the need for rate constants, or flux-based methods, which have a large number of feasible solutions because they are unconstrained by the law of mass action. This report presents an alternative modeling approach based on statistical thermodynamics. The principles of this approach are demonstrated using a simple set of coupled reactions, and then the system is characterized with respect to the changes in energy, entropy, free energy, and entropy production. Finally, the physical and biochemical insights that this approach can provide for metabolism are demonstrated by application to the tricarboxylic acid (TCA) cycle of Escherichia coli. The reaction and pathway thermodynamics are evaluated and predictions are made regarding changes in concentration of TCA cycle intermediates due to 10- and 100-fold changes in the ratio of NAD+:NADH concentrations. Finally, the assumptions and caveats regarding the use of statistical thermodynamics to model non-equilibrium reactions are discussed.

Chemical potentials and thermodynamic characteristics of ideal Bose- and Fermi-gases in the region of quantum degeneracy

NASA Astrophysics Data System (ADS)

Sotnikov, A. G.; Sereda, K. V.; Slyusarenko, Yu. V.

2017-01-01

Calculations of chemical potentials for ideal monatomic gases with Bose-Einstein and Fermi-Dirac statistics as functions of temperature, across the temperature region that is typical for the collective quantum degeneracy effect, are presented. Numerical calculations are performed without any additional approximations, and explicit dependences of the chemical potentials on temperature are constructed at a fixed density of gas particles. Approximate polynomial dependences of chemical potentials on temperature are obtained that allow for the results to be used in further studies without re-applying the involved numerical methods. The ease of using the obtained representations is demonstrated on examples of deformation of distribution for a population of energy states at low temperatures, and on the impact of quantum statistics (exchange interaction) on the equations of state for ideal gases and some of the thermodynamic properties thereof. The results of this study essentially unify two opposite limiting cases in an intermediate region that are used to describe the equilibrium states of ideal gases, which are well known from university courses on statistical physics, thus adding value from an educational point of view.

Hanging an Airplane: A Case Study in Static Equilibrium

NASA Astrophysics Data System (ADS)

Katz, Debora M.

2009-11-01

Our classrooms are filled with engineering majors who take a semester-long course in static equilibrium. Many students find this class too challenging and drop their engineering major. In our introductory physics class, we often breeze through static equilibrium; to physicists equilibrium is just a special case of Newton's second law. While it is difficult to find more time in the syllabus for any one topic, a hands-on case study may help students to develop their physical intuition about static equilibrium and may help them to succeed in their subsequent classes. This article describes a hands-on case study that you may wish to use in your classroom. (You may also wish to check a case study involving a boat published in this journal in the 1990s. ) The hands-on case study presented here can be easily modified to work at the high school or introductory college level. There are three major components: I) planning, II) doing, and III) calculating.

Correspondence between nonrelativistic anti-de Sitter space and conformal field theory, and aging-gravity duality.

PubMed

Minic, Djordje; Pleimling, Michel

2008-12-01

We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent z=2 and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

Remarkable nanoconfinement effects on chemical equilibrium manifested in nucleotide dimerization and H-D exchange reactions.

PubMed

Polak, Micha; Rubinovich, Leonid

2011-10-06

Nanoconfinement entropic effects on chemical equilibrium involving a small number of molecules, which we term NCECE, are revealed by two widely diverse types of reactions. Employing statistical-mechanical principles, we show how the NCECE effect stabilizes nucleotide dimerization observed within self-assembled molecular cages. Furthermore, the effect provides the basis for dimerization even under an aqueous environment inside the nanocage. Likewise, the NCECE effect is pertinent to a longstanding issue in astrochemistry, namely the extra deuteration commonly observed for molecules reacting on interstellar dust grain surfaces. The origin of the NCECE effect is elucidated by means of the probability distributions of the reaction extent and related variations in the reactant-product mixing entropy. Theoretical modelling beyond our previous preliminary work highlights the role of the nanospace size in addition to that of the nanosystem size, namely the limited amount of molecules in the reaction mixture. Furthermore, the NCECE effect can depend also on the reaction mechanism, and on deviations from stoichiometry. The NCECE effect, leading to enhanced, greatly variable equilibrium "constants", constitutes a unique physical-chemical phenomenon, distinguished from the usual thermodynamical properties of macroscopically large systems. Being significant particularly for weakly exothermic reactions, the effects should stabilize products in other closed nanoscale structures, and thus can have notable implications for the growing nanotechnological utilization of chemical syntheses conducted within confined nanoreactors.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces.

PubMed

Spezia, Riccardo; Martínez-Nuñez, Emilio; Vazquez, Saulo; Hase, William L

2017-04-28

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'. © 2017 The Author(s).

Analysis of basic clustering algorithms for numerical estimation of statistical averages in biomolecules.

PubMed

Anandakrishnan, Ramu; Onufriev, Alexey

2008-03-01

In statistical mechanics, the equilibrium properties of a physical system of particles can be calculated as the statistical average over accessible microstates of the system. In general, these calculations are computationally intractable since they involve summations over an exponentially large number of microstates. Clustering algorithms are one of the methods used to numerically approximate these sums. The most basic clustering algorithms first sub-divide the system into a set of smaller subsets (clusters). Then, interactions between particles within each cluster are treated exactly, while all interactions between different clusters are ignored. These smaller clusters have far fewer microstates, making the summation over these microstates, tractable. These algorithms have been previously used for biomolecular computations, but remain relatively unexplored in this context. Presented here, is a theoretical analysis of the error and computational complexity for the two most basic clustering algorithms that were previously applied in the context of biomolecular electrostatics. We derive a tight, computationally inexpensive, error bound for the equilibrium state of a particle computed via these clustering algorithms. For some practical applications, it is the root mean square error, which can be significantly lower than the error bound, that may be more important. We how that there is a strong empirical relationship between error bound and root mean square error, suggesting that the error bound could be used as a computationally inexpensive metric for predicting the accuracy of clustering algorithms for practical applications. An example of error analysis for such an application-computation of average charge of ionizable amino-acids in proteins-is given, demonstrating that the clustering algorithm can be accurate enough for practical purposes.

Transport Coefficients from Large Deviation Functions

NASA Astrophysics Data System (ADS)

Gao, Chloe; Limmer, David

2017-10-01

We describe a method for computing transport coefficients from the direct evaluation of large deviation function. This method is general, relying on only equilibrium fluctuations, and is statistically efficient, employing trajectory based importance sampling. Equilibrium fluctuations of molecular currents are characterized by their large deviation functions, which is a scaled cumulant generating function analogous to the free energy. A diffusion Monte Carlo algorithm is used to evaluate the large deviation functions, from which arbitrary transport coefficients are derivable. We find significant statistical improvement over traditional Green-Kubo based calculations. The systematic and statistical errors of this method are analyzed in the context of specific transport coefficient calculations, including the shear viscosity, interfacial friction coefficient, and thermal conductivity.

Universal laws of human society's income distribution

NASA Astrophysics Data System (ADS)

Tao, Yong

2015-10-01

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will provide a powerful support for the hypothesis of equal probability, then the principle of maximum entropy is available in a just and equilibrium economy so that an income distribution will occur spontaneously (with the largest probability). Remarkably, some scholars have observed such an income distribution in some democratic countries, e.g. USA. This result implies that the hypothesis of equal probability may be only suitable for some "fair" systems (economic or physical systems). From this meaning, the non-equilibrium systems may be "unfair" so that the hypothesis of equal probability is unavailable.

Graphical tests for Hardy-Weinberg equilibrium based on the ternary plot.

PubMed

Graffelman, Jan; Camarena, Jair Morales

2008-01-01

We design a graphical test for Hardy-Weinberg equilibrium. This can circumvent the calculation of p values and the statistical (non)significance of a large number of bi-allelic markers can be inferred from their position in a graph. By rewriting expressions for the chi(2) statistic (with and without continuity correction) in terms of the heterozygote frequency an acceptance region for Hardy-Weinberg equilibrium is obtained that can be depicted in a ternary plot. We obtain equations for curves in the ternary plot that separate markers that are out of Hardy-Weinberg equilibrium from those that are in equilibrium. The curves depend on the chosen significance level, the sample size and on a continuity correction parameter. Some examples of graphical tests using a set of 106 SNPs on the long arm of human chromosome 22 are described. Significant markers and poor markers with a lot of missing values are easily identified in the proposed plots. R software for making the diagrams is provided. The proposed graphs can be used as control charts for spotting problematic markers in large scale genotyping studies, and constitute an excellent tool for the graphical exploration of bi-allelic marker data. (c) 2007 S. Karger AG, Basel.

Topologically protected modes in non-equilibrium stochastic systems.

PubMed

Murugan, Arvind; Vaikuntanathan, Suriyanarayanan

2017-01-10

Non-equilibrium driving of biophysical processes is believed to enable their robust functioning despite the presence of thermal fluctuations and other sources of disorder. Such robust functions include sensory adaptation, enhanced enzymatic specificity and maintenance of coherent oscillations. Elucidating the relation between energy consumption and organization remains an important and open question in non-equilibrium statistical mechanics. Here we report that steady states of systems with non-equilibrium fluxes can support topologically protected boundary modes that resemble similar modes in electronic and mechanical systems. Akin to their electronic and mechanical counterparts, topological-protected boundary steady states in non-equilibrium systems are robust and are largely insensitive to local perturbations. We argue that our work provides a framework for how biophysical systems can use non-equilibrium driving to achieve robust function.

Thermodynamic equilibrium with acceleration and the Unruh effect

NASA Astrophysics Data System (ADS)

Becattini, F.

2018-04-01

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature TU=A /2 π where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.

Trapped ion system for sympathetic cooling and non-equilibrium dynamics

NASA Astrophysics Data System (ADS)

Doret, Charlie; Jubin, Sierra; Stevenson, Sarah

2017-04-01

Atomic systems are superbly suited to the study of non-equilibrium dynamics. These systems' exquisite isolation from environmental perturbations leads to long relaxation times that enable exploration of far-from-equilibrium phenomena. We present progress towards trapping chains of multiple co-trapped calcium isotopes geared towards measuring thermal equilibration and sympathetic cooling rates. We also discuss plans for future experiments in non-equilibrium statistical mechanics, including exploration of the quantum-to-classical crossover between ballistic transport and diffusive, Fourier's Law conduction. This work is supported by Cottrell College Science Award from the Research Corporation for Science Advancement and by Williams College.

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

NASA Astrophysics Data System (ADS)

Nandkishore, Rahul; Huse, David A.

2015-03-01

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.

Thermodynamic evolution far from equilibrium

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.

2018-05-01

The presented model of thermodynamic evolution of an open system far from equilibrium is based on the modern results of nonequilibrium statistical mechanics, the nonlocal theory of nonequilibrium transport developed by the author and the Speed Gradient principle introduced in the theory of adaptive control. Transition to a description of the system internal structure evolution at the mesoscopic level allows a new insight at the stability problem of non-equilibrium processes. The new model is used in a number of specific tasks.

Large fluctuations of the macroscopic current in diffusive systems: a numerical test of the additivity principle.

PubMed

Hurtado, Pablo I; Garrido, Pedro L

2010-04-01

Most systems, when pushed out of equilibrium, respond by building up currents of locally conserved observables. Understanding how microscopic dynamics determines the averages and fluctuations of these currents is one of the main open problems in nonequilibrium statistical physics. The additivity principle is a theoretical proposal that allows to compute the current distribution in many one-dimensional nonequilibrium systems. Using simulations, we validate this conjecture in a simple and general model of energy transport, both in the presence of a temperature gradient and in canonical equilibrium. In particular, we show that the current distribution displays a Gaussian regime for small current fluctuations, as prescribed by the central limit theorem, and non-Gaussian (exponential) tails for large current deviations, obeying in all cases the Gallavotti-Cohen fluctuation theorem. In order to facilitate a given current fluctuation, the system adopts a well-defined temperature profile different from that of the steady state and in accordance with the additivity hypothesis predictions. System statistics during a large current fluctuation is independent of the sign of the current, which implies that the optimal profile (as well as higher-order profiles and spatial correlations) are invariant upon current inversion. We also demonstrate that finite-time joint fluctuations of the current and the profile are well described by the additivity functional. These results suggest the additivity hypothesis as a general and powerful tool to compute current distributions in many nonequilibrium systems.

Technical note: Evaluation of the simultaneous measurements of mesospheric OH, HO2, and O3 under a photochemical equilibrium assumption - a statistical approach

NASA Astrophysics Data System (ADS)

Kulikov, Mikhail Y.; Nechaev, Anton A.; Belikovich, Mikhail V.; Ermakova, Tatiana S.; Feigin, Alexander M.

2018-05-01

This Technical Note presents a statistical approach to evaluating simultaneous measurements of several atmospheric components under the assumption of photochemical equilibrium. We consider simultaneous measurements of OH, HO2, and O3 at the altitudes of the mesosphere as a specific example and their daytime photochemical equilibrium as an evaluating relationship. A simplified algebraic equation relating local concentrations of these components in the 50-100 km altitude range has been derived. The parameters of the equation are temperature, neutral density, local zenith angle, and the rates of eight reactions. We have performed a one-year simulation of the mesosphere and lower thermosphere using a 3-D chemical-transport model. The simulation shows that the discrepancy between the calculated evolution of the components and the equilibrium value given by the equation does not exceed 3-4 % in the full range of altitudes independent of season or latitude. We have developed a statistical Bayesian evaluation technique for simultaneous measurements of OH, HO2, and O3 based on the equilibrium equation taking into account the measurement error. The first results of the application of the technique to MLS/Aura data (Microwave Limb Sounder) are presented in this Technical Note. It has been found that the satellite data of the HO2 distribution regularly demonstrate lower altitudes of this component's mesospheric maximum. This has also been confirmed by model HO2 distributions and comparison with offline retrieval of HO2 from the daily zonal means MLS radiance.

A physical-based gas-surface interaction model for rarefied gas flow simulation

NASA Astrophysics Data System (ADS)

Liang, Tengfei; Li, Qi; Ye, Wenjing

2018-01-01

Empirical gas-surface interaction models, such as the Maxwell model and the Cercignani-Lampis model, are widely used as the boundary condition in rarefied gas flow simulations. The accuracy of these models in the prediction of macroscopic behavior of rarefied gas flows is less satisfactory in some cases especially the highly non-equilibrium ones. Molecular dynamics simulation can accurately resolve the gas-surface interaction process at atomic scale, and hence can predict accurate macroscopic behavior. They are however too computationally expensive to be applied in real problems. In this work, a statistical physical-based gas-surface interaction model, which complies with the basic relations of boundary condition, is developed based on the framework of the washboard model. In virtue of its physical basis, this new model is capable of capturing some important relations/trends for which the classic empirical models fail to model correctly. As such, the new model is much more accurate than the classic models, and in the meantime is more efficient than MD simulations. Therefore, it can serve as a more accurate and efficient boundary condition for rarefied gas flow simulations.

New phenomena in non-equilibrium quantum physics

NASA Astrophysics Data System (ADS)

Kitagawa, Takuya

From its beginning in the early 20th century, quantum theory has become progressively more important especially due to its contributions to the development of technologies. Quantum mechanics is crucial for current technology such as semiconductors, and also holds promise for future technologies such as superconductors and quantum computing. Despite of the success of quantum theory, its applications have been mostly limited to equilibrium or static systems due to 1. lack of experimental controllability of non-equilibrium quantum systems 2. lack of theoretical frameworks to understand non-equilibrium dynamics. Consequently, physicists have not yet discovered too many interesting phenomena in non-equilibrium quantum systems from both theoretical and experimental point of view and thus, non-equilibrium quantum physics did not attract too much attentions. The situation has recently changed due to the rapid development of experimental techniques in condensed matter as well as cold atom systems, which now enables a better control of non-equilibrium quantum systems. Motivated by this experimental progress, we constructed theoretical frameworks to study three different non-equilibrium regimes of transient dynamics, steady states and periodically drives. These frameworks provide new perspectives for dynamical quantum process, and help to discover new phenomena in these systems. In this thesis, we describe these frameworks through explicit examples and demonstrate their versatility. Some of these theoretical proposals have been realized in experiments, confirming the applicability of the theories to realistic experimental situations. These studies have led to not only the improved fundamental understanding of non-equilibrium processes in quantum systems, but also suggested entirely different venues for developing quantum technologies.

The Physics of Life and Quantum Complex Matter: A Case of Cross-Fertilization

PubMed Central

Poccia, Nicola; Bianconi, Antonio

2011-01-01

Progress in the science of complexity, from the Big Bang to the coming of humankind, from chemistry and biology to geosciences and medicine, and from materials engineering to energy sciences, is leading to a shift of paradigm in the physical sciences. The focus is on the understanding of the non-equilibrium process in fine tuned systems. Quantum complex materials such as high temperature superconductors and living matter are both non-equilibrium and fine tuned systems. These topics have been subbjects of scientific discussion in the Rome Symposium on the “Quantum Physics of Living Matter”. PMID:26791661

Equilibrium and Non-Equilibrium Condensation Phenomena in Tuneable 3D and 2D Bose Gases

DTIC Science & Technology

2016-04-01

condensed gas " which remains condensed above the expected critical temperature, and performed one of the first studies of the strongly-interacting "unitary...34 Bose gas . With the 2d harmonic trap we showed how the interaction-driven BKT phase is connected with purely statistical theory, and with the 3d...box trap we created the world’s first atomic BEC in a quasi-uniform potential. 15. SUBJECT TERMS EOARD, Bose gas , ultracold, condensation, equilibrium

Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers

NASA Astrophysics Data System (ADS)

Kawai, Soshi; Larsson, Johan

2013-01-01

A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on equilibrium boundary layers and a non-equilibrium shock/boundary-layer interaction problem. The proposed method builds on the prior non-equilibrium wall-models of Balaras et al. [AIAA J. 34, 1111-1119 (1996)], 10.2514/3.13200 and Wang and Moin [Phys. Fluids 14, 2043-2051 (2002)], 10.1063/1.1476668: the failure of these wall-models to accurately predict the skin friction in equilibrium boundary layers is shown and analyzed, and an improved wall-model that solves this issue is proposed. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer, the grid resolution, and the resolution-characteristics of numerical methods. The proposed model yields accurate resolved turbulence, both in terms of structure and statistics for both the equilibrium and non-equilibrium flows without the use of ad hoc corrections. Crucially, the model accurately predicts the skin friction, something that existing non-equilibrium wall-models fail to do robustly.

Had We But World Enough, and Time... But We Don't!: Justifying the Thermodynamic and Infinite-Time Limits in Statistical Mechanics

NASA Astrophysics Data System (ADS)

Palacios, Patricia

2018-05-01

In this paper, I compare the use of the thermodynamic limit in the theory of phase transitions with the infinite-time limit in the explanation of equilibrium statistical mechanics. In the case of phase transitions, I will argue that the thermodynamic limit can be justified pragmatically since the limit behavior (i) also arises before we get to the limit and (ii) for values of N that are physically significant. However, I will contend that the justification of the infinite-time limit is less straightforward. In fact, I will point out that even in cases where one can recover the limit behavior for finite t, i.e. before we get to the limit, one cannot recover this behavior for realistic time scales. I will claim that this leads us to reconsider the role that the rate of convergence plays in the justification of infinite limits and calls for a revision of the so-called Butterfield's principle.

Had We But World Enough, and Time... But We Don't!: Justifying the Thermodynamic and Infinite-Time Limits in Statistical Mechanics

NASA Astrophysics Data System (ADS)

Palacios, Patricia

2018-04-01

In this paper, I compare the use of the thermodynamic limit in the theory of phase transitions with the infinite-time limit in the explanation of equilibrium statistical mechanics. In the case of phase transitions, I will argue that the thermodynamic limit can be justified pragmatically since the limit behavior (i) also arises before we get to the limit and (ii) for values of N that are physically significant. However, I will contend that the justification of the infinite-time limit is less straightforward. In fact, I will point out that even in cases where one can recover the limit behavior for finite t, i.e. before we get to the limit, one cannot recover this behavior for realistic time scales. I will claim that this leads us to reconsider the role that the rate of convergence plays in the justification of infinite limits and calls for a revision of the so-called Butterfield's principle.

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Moore, Joel E.

2016-06-01

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.

Molecular dynamics study of CO2 hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis.

PubMed

English, Niall J; Clarke, Elaine T

2013-09-07

Equilibrium and non-equilibrium molecular dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar CO2 hydrate interfaces in liquid water at 300-320 K. Different guest compositions, at 85%, 95%, and 100% of maximum theoretical occupation, led to statistically-significant differences in the observed initial dissociation rates. The melting temperatures of each interface were estimated, and dissociation rates were observed to be strongly dependent on temperature, with higher dissociation rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model developed previously was applied to fit the observed dissociation profiles, and this helps to identify clearly two distinct régimes of break-up; a second well-defined region is essentially independent of composition and temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. From equilibrium MD of the two-phase systems at their melting point, the relaxation times of the auto-correlation functions of fluctuations in number of enclathrated guest molecules were used as a basis for comparison of the variation in the underlying, non-equilibrium, thermal-driven dissociation rates via Onsager's hypothesis, and statistically significant differences were found, confirming the value of a fluctuation-dissipation approach in this case.

Statistical physics and physiology: monofractal and multifractal approaches

NASA Technical Reports Server (NTRS)

Stanley, H. E.; Amaral, L. A.; Goldberger, A. L.; Havlin, S.; Peng, C. K.

1999-01-01

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

Quantum statistical mechanics of dense partially ionized hydrogen

NASA Technical Reports Server (NTRS)

Dewitt, H. E.; Rogers, F. J.

1972-01-01

The theory of dense hydrogen plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. The statistical mechanical calculation of the plasma equation of state is intended for stellar interiors. The general approach is extended to the calculation of the equation of state of the outer layers of large planets.

Thermal equilibrium and statistical thermometers in special relativity.

PubMed

Cubero, David; Casado-Pascual, Jesús; Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-10-26

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Jüttner function as well as modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Jüttner distribution. Moreover, our simulations illustrate that the concept of "thermal equilibrium" extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that "temperature" can be statistically defined and measured in an observer frame independent way.

Thermodynamics of the Rhodamine B Lactone--Zwitterion Equilibrium.

ERIC Educational Resources Information Center

Hinckley, Daniel A.; Seybold, Paul G.

1987-01-01

Discusses the benefits of thermochromic transformations for studying thermodynamic properties. Describes an experiment that uses a commercially available dye, attains equilibrium rapidly, employs a simple, single-beam spectrophotometer, and is suitable for both physical chemistry and introductory chemistry laboratories. (TW)

Impact of (α, n) reactions on weak r-process in neutrino-driven winds

NASA Astrophysics Data System (ADS)

Bliss, J.; Arcones, A.; Montes, F.; Pereira, J.

2017-05-01

After a successful core-collapse supernova, a neutrino-driven wind develops where it is possible to synthesize lighter heavy elements (30 < Z < 45). In the early galaxy, the origin of these elements is associated with the r-process and to an additional process. Here we assume that the additional process corresponds to the weak r-process (sometimes referred to as alpha-process) taking place in neutrino-driven winds. Based on a trajectory obtained from hydrodynamical simulations we study the astrophysics and nuclear physics uncertainties of a weak r-process with our main focus on the (α, n) reactions. These reactions are critical to redistribute the matter and allow it to move from light to heavy elements after nuclear statistical equilibrium freezes out. In this first sensitivity study, we vary all (α, n) reactions by given constant factors which are justified based on the uncertainties of the statistical model and its nuclear physics input, mainly alpha optical potentials for weak r-process conditions. Our results show that (α, n) rate uncertainties are indeed crucial to predict abundances. Therefore, further studies will follow to identify individual critical reactions. Since the nucleosynthesis path is close to stability, these reactions can be measured in the near future. Since much of the other nuclear data for the weak r-process are known, the reduction in nuclear physics uncertainties provided by these experiments will allow astronomical observations to directly constrain the astronomical conditions in the wind.

Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

NASA Technical Reports Server (NTRS)

Peng, C. K.; Havlin, S.; Hausdorff, J. M.; Mietus, J. E.; Stanley, H. E.; Goldberger, A. L.

1995-01-01

Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

Optimal Protocols and Optimal Transport in Stochastic Thermodynamics

NASA Astrophysics Data System (ADS)

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-01

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Optimal protocols and optimal transport in stochastic thermodynamics.

PubMed

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-24

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Eigenstate Thermalization for Degenerate Observables

NASA Astrophysics Data System (ADS)

Anza, Fabio; Gogolin, Christian; Huber, Marcus

2018-04-01

Under unitary time evolution, expectation values of physically reasonable observables often evolve towards the predictions of equilibrium statistical mechanics. The eigenstate thermalization hypothesis (ETH) states that this is also true already for individual energy eigenstates. Here we aim at elucidating the emergence of the ETH for observables that can realistically be measured due to their high degeneracy, such as local, extensive, or macroscopic observables. We bisect this problem into two parts, a condition on the relative overlaps and one on the relative phases between the eigenbases of the observable and Hamiltonian. We show that the relative overlaps are unbiased for highly degenerate observables and demonstrate that unless relative phases conspire to cumulative effects, this makes such observables verify the ETH. Through this we elucidate potential pathways towards proofs of thermalization.

Studying non-equilibrium many-body dynamics using one-dimensional Bose gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langen, Tim; Gring, Michael; Kuhnert, Maximilian

2014-12-04

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

Comment on "Out-of-plane equilibrium points in the restricted three-body problem with oblateness (Research Note)"

NASA Astrophysics Data System (ADS)

Wu, Nan; Wang, Xuefeng; Zhou, Li-Yong

2018-06-01

Douskos & Markellos (2006, A&A, 446, 357) first reported the existence of the out-of-plane equilibrium points in restricted three-body problem with oblateness. This result deviates significantly from the intuitive physical point of view that there is no other force that can balance the combined gravitation in Z direction. In fact, the out-of-plane equilibrium in that model is illusory and we prove here that such equilibrium points arise from the improper application of the potential function.

Dynamical coupling between magnetic equilibrium and transport in tokamak scenario modelling, with application to current ramps

NASA Astrophysics Data System (ADS)

Fable, E.; Angioni, C.; Ivanov, A. A.; Lackner, K.; Maj, O.; Medvedev, S. Yu; Pautasso, G.; Pereverzev, G. V.; Treutterer, W.; the ASDEX Upgrade Team

2013-07-01

The modelling of tokamak scenarios requires the simultaneous solution of both the time evolution of the plasma kinetic profiles and of the magnetic equilibrium. Their dynamical coupling involves additional complications, which are not present when the two physical problems are solved separately. Difficulties arise in maintaining consistency in the time evolution among quantities which appear in both the transport and the Grad-Shafranov equations, specifically the poloidal and toroidal magnetic fluxes as a function of each other and of the geometry. The required consistency can be obtained by means of iteration cycles, which are performed outside the equilibrium code and which can have different convergence properties depending on the chosen numerical scheme. When these external iterations are performed, the stability of the coupled system becomes a concern. In contrast, if these iterations are not performed, the coupled system is numerically stable, but can become physically inconsistent. By employing a novel scheme (Fable E et al 2012 Nucl. Fusion submitted), which ensures stability and physical consistency among the same quantities that appear in both the transport and magnetic equilibrium equations, a newly developed version of the ASTRA transport code (Pereverzev G V et al 1991 IPP Report 5/42), which is coupled to the SPIDER equilibrium code (Ivanov A A et al 2005 32nd EPS Conf. on Plasma Physics (Tarragona, 27 June-1 July) vol 29C (ECA) P-5.063), in both prescribed- and free-boundary modes is presented here for the first time. The ASTRA-SPIDER coupled system is then applied to the specific study of the modelling of controlled current ramp-up in ASDEX Upgrade discharges.

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis.

PubMed

Ghaani, Mohammad Reza; English, Niall J

2018-03-21

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis

NASA Astrophysics Data System (ADS)

Ghaani, Mohammad Reza; English, Niall J.

2018-03-01

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

The effect of a senior jazz dance class on static balance in healthy women over 50 years of age: a pilot study.

PubMed

Wallmann, Harvey W; Gillis, Carrie B; Alpert, Patricia T; Miller, Sally K

2009-01-01

The purpose of this pilot study is to assess the impact of a senior jazz dance class on static balance for healthy women over 50 years of age using the NeuroCom Smart Balance Master System (Balance Master). A total of 12 healthy women aged 54-88 years completed a 15-week jazz dance class which they attended 1 time per week for 90 min per class. Balance data were collected using the Sensory Organization Test (SOT) at baseline (pre), at 7 weeks (mid), and after 15 weeks (post). An equilibrium score measuring postural sway was calculated for each of six different conditions. The composite equilibrium score (all six conditions integrated to 1 score) was used as an overall measure of balance. Repeated measures analyses of variance (ANOVAs) were used to compare the means of each participant's SOT composite equilibrium score in addition to the equilibrium score for each individual condition (1-6) across the 3 time points (pre, mid, post). There was a statistically significant difference among the means, p < .0005. Pairwise (Bonferroni) post hoc analyses revealed the following statistically significant findings for SOT composite equilibrium scores for the pre (67.33 + 10.43), mid (75.25 + 6.97), and post (79.00 + 4.97) measurements: premid (p = .008); prepost (p < .0005); midpost (p = .033). In addition, correlational statistics were used to determine any relationship between SOT scores and age. Results indicated that administration of a 15-week jazz dance class 1 time per week was beneficial in improving static balance as measured by the Balance Master SOT.

Information-theoretic equilibrium and observable thermalization

NASA Astrophysics Data System (ADS)

Anzà, F.; Vedral, V.

2017-03-01

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.

Information-theoretic equilibrium and observable thermalization

PubMed Central

Anzà, F.; Vedral, V.

2017-01-01

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light. PMID:28266646

Information-theoretic equilibrium and observable thermalization.

PubMed

Anzà, F; Vedral, V

2017-03-07

A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.

The non-equilibrium and energetic cost of sensory adaptation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lan, G.; Sartori, Pablo; Tu, Y.

2011-03-24

Biological sensory systems respond to external signals in short time and adapt to permanent environmental changes over a longer timescale to maintain high sensitivity in widely varying environments. In this work we have shown how all adaptation dynamics are intrinsically non-equilibrium and free energy is dissipated. We show that the dissipated energy is utilized to maintain adaptation accuracy. A universal relation between the energy dissipation and the optimum adaptation accuracy is established by both a general continuum model and a discrete model i n the specific case of the well-known E. coli chemo-sensory adaptation. Our study suggests that cellular levelmore » adaptations are fueled by hydrolysis of high energy biomolecules, such as ATP. The relevance of this work lies on linking the functionality of a biological system (sensory adaptation) with a concept rooted in statistical physics (energy dissipation), by a mathematical law. This has been made possible by identifying a general sensory system with a non-equilibrium steady state (a stationary state in which the probability current is not zero, but its divergence is, see figure), and then numerically and analytically solving the Fokker-Planck and Master Equations which describe the sensory adaptive system. The application of our general results to the case of E. Coli has shed light on why this system uses the high energy SAM molecule to perform adaptation, since using the more common ATP would not suffice to obtain the required adaptation accuracy.« less

Far from Equilibrium Percolation, Stochastic and Shape Resonances in the Physics of Life

PubMed Central

Poccia, Nicola; Ansuini, Alessio; Bianconi, Antonio

2011-01-01

Key physical concepts, relevant for the cross-fertilization between condensed matter physics and the physics of life seen as a collective phenomenon in a system out-of-equilibrium, are discussed. The onset of life can be driven by: (a) the critical fluctuations at the protonic percolation threshold in membrane transport; (b) the stochastic resonance in biological systems, a mechanism that can exploit external and self-generated noise in order to gain efficiency in signal processing; and (c) the shape resonance (or Fano resonance or Feshbach resonance) in the association and dissociation processes of bio-molecules (a quantum mechanism that could play a key role to establish a macroscopic quantum coherence in the cell). PMID:22072921

Evolutionary potential games on lattices

NASA Astrophysics Data System (ADS)

Szabó, György; Borsos, István

2016-04-01

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

A probable probability distribution of a series nonequilibrium states in a simple system out of equilibrium

NASA Astrophysics Data System (ADS)

Gao, Haixia; Li, Ting; Xiao, Changming

2016-05-01

When a simple system is in its nonequilibrium state, it will shift to its equilibrium state. Obviously, in this process, there are a series of nonequilibrium states. With the assistance of Bayesian statistics and hyperensemble, a probable probability distribution of these nonequilibrium states can be determined by maximizing the hyperensemble entropy. It is known that the largest probability is the equilibrium state, and the far a nonequilibrium state is away from the equilibrium one, the smaller the probability will be, and the same conclusion can also be obtained in the multi-state space. Furthermore, if the probability stands for the relative time the corresponding nonequilibrium state can stay, then the velocity of a nonequilibrium state returning back to its equilibrium can also be determined through the reciprocal of the derivative of this probability. It tells us that the far away the state from the equilibrium is, the faster the returning velocity will be; if the system is near to its equilibrium state, the velocity will tend to be smaller and smaller, and finally tends to 0 when it gets the equilibrium state.

The Intuitive Physics of the Equilibrium of the Lever and of the Hydraulic Pressures: Implications for the Teaching of Elementary Physics

ERIC Educational Resources Information Center

Masin, Sergio Cesare; Crivellaro, Francesco; Varotto, Diego

2014-01-01

The research field of intuitive physics focuses on discrepancies between theoretical and intuitive physical knowledge. Consideration of these discrepancies can help in the teaching of elementary physics. However, evidence shows that theoretical and intuitive physical knowledge may also be congruent. Physics teaching could further benefit from…

Relations between heat exchange and Rényi divergences

NASA Astrophysics Data System (ADS)

Wei, Bo-Bo

2018-04-01

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the Rényi divergences between the initial thermodynamic equilibrium state and the final nonequilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final nonequilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final nonequilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.

Relations between heat exchange and Rényi divergences.

PubMed

Wei, Bo-Bo

2018-04-01

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the Rényi divergences between the initial thermodynamic equilibrium state and the final nonequilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final nonequilibrium state of the global system. In particular the average heat exchange is quantified by the relative entropy between the initial equilibrium state and the final nonequilibrium state of the global system. The relation is applicable to both finite classical systems and finite quantum systems.

Relation between the Surface Friction of Plates and their Statistical Microgeometry

DTIC Science & Technology

1980-01-01

3-6 and 𔃽-7. Calibration-- are taken for each of the Uicr~r unit exponent values and best fit li;nes by least squares fitted through each"n set of...parameter, [ = 1.de (2-43) (Clauser 1954, 1956). Data from near equilibrium flows (Coles & Hurst 1968) was plotted along with some typical non-equilibrium...too bad a fit even for the non equilibrium flows. Coles and Hurst (1968) recommended that the fit of the law of the wake to velocity profiles should be

Failure of Local Thermal Equilibrium in Quantum Friction

NASA Astrophysics Data System (ADS)

Intravaia, F.; Behunin, R. O.; Henkel, C.; Busch, K.; Dalvit, D. A. R.

2016-09-01

Recent progress in manipulating atomic and condensed matter systems has instigated a surge of interest in nonequilibrium physics, including many-body dynamics of trapped ultracold atoms and ions, near-field radiative heat transfer, and quantum friction. Under most circumstances the complexity of such nonequilibrium systems requires a number of approximations to make theoretical descriptions tractable. In particular, it is often assumed that spatially separated components of a system thermalize with their immediate surroundings, although the global state of the system is out of equilibrium. This powerful assumption reduces the complexity of nonequilibrium systems to the local application of well-founded equilibrium concepts. While this technique appears to be consistent for the description of some phenomena, we show that it fails for quantum friction by underestimating by approximately 80% the magnitude of the drag force. Our results show that the correlations among the components of driven, but steady-state, quantum systems invalidate the assumption of local thermal equilibrium, calling for a critical reexamination of this approach for describing the physics of nonequilibrium systems.

Reactive solute transport in streams: 1. Development of an equilibrium- based model

USGS Publications Warehouse

Runkel, Robert L.; Bencala, Kenneth E.; Broshears, Robert E.; Chapra, Steven C.

1996-01-01

An equilibrium-based solute transport model is developed for the simulation of trace metal fate and transport in streams. The model is formed by coupling a solute transport model with a chemical equilibrium submodel based on MINTEQ. The solute transport model considers the physical processes of advection, dispersion, lateral inflow, and transient storage, while the equilibrium submodel considers the speciation and complexation of aqueous species, precipitation/dissolution and sorption. Within the model, reactions in the water column may result in the formation of solid phases (precipitates and sorbed species) that are subject to downstream transport and settling processes. Solid phases on the streambed may also interact with the water column through dissolution and sorption/desorption reactions. Consideration of both mobile (water-borne) and immobile (streambed) solid phases requires a unique set of governing differential equations and solution techniques that are developed herein. The partial differential equations describing physical transport and the algebraic equations describing chemical equilibria are coupled using the sequential iteration approach.

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Bounded energy states in homogeneous turbulent shear flow: An alternative view

NASA Technical Reports Server (NTRS)

Bernard, Peter S.; Speziale, Charles G.

1990-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.

Role of excited state solvent fluctuations on time-dependent fluorescence Stokes shift

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tanping, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu; Kumar, Revati, E-mail: tanping@lsu.edu, E-mail: revatik@lsu.edu

2015-11-07

We explore the connection between the solvation dynamics of a chromophore upon photon excitation and equilibrium fluctuations of the solvent. Using molecular dynamics simulations, fluorescence Stokes shift for the tryptophan in Staphylococcus nuclease was examined using both nonequilibrium calculations and linear response theory. When the perturbed and unperturbed surfaces exhibit different solvent equilibrium fluctuations, the linear response approach on the former surface shows agreement with the nonequilibrium process. This agreement is excellent when the perturbed surface exhibits Gaussian statistics and qualitative in the case of an isomerization induced non-Gaussian statistics. However, the linear response theory on the unperturbed surface breaksmore » down even in the presence of Gaussian fluctuations. Experiments also provide evidence of the connection between the excited state solvent fluctuations and the total fluorescence shift. These observations indicate that the equilibrium statistics on the excited state surface characterize the relaxation dynamics of the fluorescence Stokes shift. Our studies specifically analyze the Gaussian fluctuations of the solvent in the complex protein environment and further confirm the role of solvent fluctuations on the excited state surface. The results are consistent with previous investigations, found in the literature, of solutes dissolved in liquids.« less

Comparison between different adsorption-desorption kinetics schemes in two dimensional lattice gas

NASA Astrophysics Data System (ADS)

Huespe, V. J.; Belardinelli, R. E.; Pereyra, V. D.; Manzi, S. J.

2017-12-01

Monte Carlo simulation is used to study the adsorption-desorption kinetics in the framework of the kinetic lattice-gas model. Three schemes of the so-called hard dynamics and five schemes of the so called soft dynamics were used for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and non-equilibrium observable, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and non-equilibrium observables have several problems.

Trouble with diffusion: Reassessing hillslope erosion laws with a particle-based model

NASA Astrophysics Data System (ADS)

Tucker, Gregory E.; Bradley, D. Nathan

2010-03-01

Many geomorphic systems involve a broad distribution of grain motion length scales, ranging from a few particle diameters to the length of an entire hillslope or stream. Studies of analogous physical systems have revealed that such broad motion distributions can have a significant impact on macroscale dynamics and can violate the assumptions behind standard, local gradient flux laws. Here, a simple particle-based model of sediment transport on a hillslope is used to study the relationship between grain motion statistics and macroscopic landform evolution. Surface grains are dislodged by random disturbance events with probabilities and distances that depend on local microtopography. Despite its simplicity, the particle model reproduces a surprisingly broad range of slope forms, including asymmetric degrading scarps and cinder cone profiles. At low slope angles the dynamics are diffusion like, with a short-range, thin-tailed hop length distribution, a parabolic, convex upward equilibrium slope form, and a linear relationship between transport rate and gradient. As slope angle steepens, the characteristic grain motion length scale begins to approach the length of the slope, leading to planar equilibrium forms that show a strongly nonlinear correlation between transport rate and gradient. These high-probability, long-distance motions violate the locality assumption embedded in many common gradient-based geomorphic transport laws. The example of a degrading scarp illustrates the potential for grain motion dynamics to vary in space and time as topography evolves. This characteristic renders models based on independent, stationary statistics inapplicable. An accompanying analytical framework based on treating grain motion as a survival process is briefly outlined.

Feedback Controlled Colloidal Assembly at Fluid Interfaces

NASA Astrophysics Data System (ADS)

Bevan, Michael

The autonomous and reversible assembly of colloidal nano- and micro- scale components into ordered configurations is often suggested as a scalable process capable of manufacturing meta-materials with exotic electromagnetic properties. As a result, there is strong interest in understanding how thermal motion, particle interactions, patterned surfaces, and external fields can be optimally coupled to robustly control the assembly of colloidal components into hierarchically structured functional meta-materials. We approach this problem by directly relating equilibrium and dynamic colloidal microstructures to kT-scale energy landscapes mediated by colloidal forces, physically and chemically patterned surfaces, multiphase fluid interfaces, and electromagnetic fields. 3D colloidal trajectories are measured in real-space and real-time with nanometer resolution using an integrated suite of evanescent wave, video, and confocal microscopy methods. Equilibrium structures are connected to energy landscapes via statistical mechanical models. The dynamic evolution of initially disordered colloidal fluid configurations into colloidal crystals in the presence of tunable interactions (electromagnetic field mediated interactions, particle-interface interactions) is modeled using a novel approach based on fitting the Fokker-Planck equation to experimental microscopy and computer simulated assembly trajectories. This approach is based on the use of reaction coordinates that capture important microstructural features of crystallization processes and quantify both statistical mechanical (free energy) and fluid mechanical (hydrodynamic) contributions. Ultimately, we demonstrate real-time control of assembly, disassembly, and repair of colloidal crystals using both open loop and closed loop control to produce perfectly ordered colloidal microstructures. This approach is demonstrated for close packed colloidal crystals of spherical particles at fluid-solid interfaces and is being extended to anisotropic particles and multiphase fluid interfaces.

Dynamics of Galaxies

NASA Astrophysics Data System (ADS)

Bertin, Giuseppe

2000-08-01

Part I. Basic Phenomenology: 1. Scales; 2. Observational windows; 3. Classifications; 4. Photometry, kinematics, dark matter; 5. Basic questions, semi-empirical approach, dynamical window; Part II. Physical Models: 6. Self-gravity and relation with plasma physics; 7. Relaxation times, absence of thermodynamical equilibrium; 8. Models; 9. Equilibrium and stability: symmetry and symmetry breaking; 10. Classical ellipsoids; 11. Introduction to dispersive waves; 12. Jeans instability; Part III. Spiral Galaxies: 13. Orbits; 14. The basic state: vertical and horizontal equilibrium in the disk; 15. Density waves; 16. Role of gas; 17. Global spiral modes; 18. Spiral structure in galaxies; 19. Bending waves; 20. Dark matter in spiral galaxies; Part IV. Elliptical Galaxies: 21. Orbits; 22. Stellar dynamical approach; 23. Stability; 24. Dark matter in elliptical galaxies; Part V. In Perspective: 25. Selected aspects of formation and evolution; Notes; Index.

Statistical Physics of Colloidal Dispersions.

NASA Astrophysics Data System (ADS)

Canessa, E.

Available from UMI in association with The British Library. Requires signed TDF. This thesis is concerned with the equilibrium statistical mechanics of colloidal dispersions which represent useful model systems for the study of condensed matter physics; namely, charge stabilized colloidal dispersions and polymer stabilized colloidal dispersions. A one-component macroparticle approach is adopted in order to treat the macroscopic and microscopic properties of these systems in a simple and comprehensive manner. The thesis opens with the description of the nature of the colloidal state before reviewing some basic definitions and theory in Chapter II. In Chapter III a variational theory of phase equilibria based on the Gibbs-Bogolyobov inequality is applied to sterically stabilized colloidal dispersions. Hard spheres are chosen as the reference system for the disordered phases while an Einstein model is used for the ordered phases. The new choice of pair potential, taken for mathematical convenience, is a superposition of two Yukawa functions. By matching a double Yukawa potential to the van der Waals attractive potential at different temperatures and introducing a purely temperature dependent coefficient to the repulsive part, a rich variety of observed phase separation phenomena is qualitatively described. The behaviour of the potential is found to be consistent with a small decrease of the polymer layer thickness with increasing temperature. Using the same concept of a collapse transition the non-monotonic second virial coefficient is also explained and quantified. It is shown that a reduction of the effective macroparticle diameter with increasing temperature can only be partially examined from the point of view of a (binary-) polymer solution theory. This chapter concludes with the description of the observed, reversible, depletion flocculation behaviour. This is accomplished by using the variational formalism and by invoking the double Yukawa potential to allow changes of the depletion attraction with free polymer concentration. Chapter IV deals with the contributions of pairwise additive and volume dependent forces to the free energy of charge stabilized colloidal dispersions. To a first approximation the extra volume dependent contributions due to the chemical equilibrium and counterion-macroion coupling are treated in a one-component plasma approach. Added salt is treated as an ionized gas within the Debye-Huckel theory of electrolytes. In order to set this approach on a quantitative basis the existence of an equilibrium lattice with a small shear modulus is examined. Structural phase transitions in these systems are also analysed theoretically as a function of added electrolyte.

The Diagnostic Potential of Fe Lines Applied to Protostellar Jets

NASA Astrophysics Data System (ADS)

Giannini, T.; Nisini, B.; Antoniucci, S.; Alcalá, J. M.; Bacciotti, F.; Bonito, R.; Podio, L.; Stelzer, B.; Whelan, E. T.

2013-11-01

We investigate the diagnostic capabilities of iron lines for tracing the physical conditions of shock-excited gas in jets driven by pre-main sequence stars. We have analyzed the 3000-25000 Å, X-shooter spectra of two jets driven by the pre-main sequence stars ESO-Hα 574 and Par-Lup 3-4. Both spectra are very rich in [Fe II] lines over the whole spectral range; in addition, lines from [Fe III] are detected in the ESO-Hα 574 spectrum. Non-local thermal equilibrium codes solving the equations of the statistical equilibrium along with codes for the ionization equilibrium are used to derive the gas excitation conditions of electron temperature and density and fractional ionization. An estimate of the iron gas-phase abundance is provided by comparing the iron lines emissivity with that of neutral oxygen at 6300 Å. The [Fe II] line analysis indicates that the jet driven by ESO-Hα 574 is, on average, colder (T e ~ 9000 K), less dense (n e ~ 2 × 104 cm-3), and more ionized (x e ~ 0.7) than the Par-Lup 3-4 jet (T e ~ 13,000 K, n e ~ 6 × 104 cm-3, x e < 0.4), even if the existence of a higher density component (n e ~ 2 × 105 cm-3) is probed by the [Fe III] and [Fe II] ultra-violet lines. The physical conditions derived from the iron lines are compared with shock models suggesting that the shock at work in ESO-Hα 574 is faster and likely more energetic than the Par-Lup 3-4 shock. This latter feature is confirmed by the high percentage of gas-phase iron measured in ESO-Hα 574 (50%-60% of its solar abundance in comparison with less than 30% in Par-Lup 3-4), which testifies that the ESO-Hα 574 shock is powerful enough to partially destroy the dust present inside the jet. This work demonstrates that a multiline Fe analysis can be effectively used to probe the excitation and ionization conditions of the gas in a jet without any assumption on ionic abundances. The main limitation on the diagnostics resides in the large uncertainties of the atomic data, which, however, can be overcome through a statistical approach involving many lines. Based on observations collected with X-shooter at the Very Large Telescope on Cerro Paranal (Chile), operated by the European Southern Observatory (ESO). Program ID: 085.C-0238(A).

A Progression of Static Equilibrium Laboratory Exercises

ERIC Educational Resources Information Center

Kutzner, Mickey; Kutzner, Andrew

2013-01-01

Although simple architectural structures like bridges, catwalks, cantilevers, and Stonehenge have been integral in human societies for millennia, as have levers and other simple tools, modern students of introductory physics continue to grapple with Newton's conditions for static equilibrium. As formulated in typical introductory physics…

Student Understanding of Liquid-Vapor Phase Equilibrium

ERIC Educational Resources Information Center

Boudreaux, Andrew; Campbell, Craig

2012-01-01

Student understanding of the equilibrium coexistence of a liquid and its vapor was the subject of an extended investigation. Written assessment questions were administered to undergraduates enrolled in introductory physics and chemistry courses. Responses have been analyzed to document conceptual and reasoning difficulties in sufficient detail to…

Influence of condensed species on thermo-physical properties of LTE and non-LTE SF6-Cu mixture

NASA Astrophysics Data System (ADS)

Chen, Zhexin; Wu, Yi; Yang, Fei; Sun, Hao; Rong, Mingzhe; Wang, Chunlin

2017-10-01

SF6-Cu mixture is frequently formed in high-voltage circuit breakers due to the electrode erosion and metal vapor diffusion. During the interruption process, the multiphase effect and deviation from local thermal equilibrium (non-LTE assumption) can both affect the thermo-physical of the arc plasma and further influence the performance of circuit breaker. In this paper, thermo-physical properties, namely composition, thermodynamic properties and transport coefficients are calculated for multiphase SF6-Cu mixture with and without LTE assumption. The composition is confirmed by combining classical two-temperature mass action law with phase equilibrium condition deduced from second law of thermodynamics. The thermodynamic properties and transport coefficients are calculated using the multiphase composition result. The influence of condensed species on thermo-physical properties is discussed at different temperature, pressure (0.1-10 atm), non-equilibrium degrees (1-10), and copper molar proportions (0-50%). It is found that the multiphase effect has significant influence on specific enthalpy, specific heat and heavy species thermal conductivity in both LTE and non-LTE SF6-Cu system. This paper provides a more accurate database for computational fluid dynamic calculation.

Understanding Thermal Equilibrium through Activities

ERIC Educational Resources Information Center

Pathare, Shirish; Huli, Saurabhee; Nachane, Madhura; Ladage, Savita; Pradhan, Hemachandra

2015-01-01

Thermal equilibrium is a basic concept in thermodynamics. In India, this concept is generally introduced at the first year of undergraduate education in physics and chemistry. In our earlier studies (Pathare and Pradhan 2011 "Proc. episteme-4 Int. Conf. to Review Research on Science Technology and Mathematics Education" pp 169-72) we…

All Things Being Equal

ERIC Educational Resources Information Center

Putti, Alice

2012-01-01

This guided inquiry activity was developed to help students "view" an equilibrium system from the particulate level and make connections to their macroscopic observations. Part I helps students observe a physical equilibrium system in which water is transferred between two larger containers. In Part II, students examine what happens to a chemical…

Slope-Velocity-Equilibrium and evolution of surface roughness on a stony hillslope

USDA-ARS?s Scientific Manuscript database

Slope-velocity equilibrium is hypothesized as a state that evolves naturally over time due to the interaction between overland flow and bed morphology, wherein steeper areas develop a relative increase in physical and hydraulic roughness such that flow velocity is a unique function of overland flow ...

Computer program determines chemical composition of physical system at equilibrium

NASA Technical Reports Server (NTRS)

Kwong, S. S.

1966-01-01

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Control of Chemical Equilibrium by Solvent: A Basis for Teaching Physical Chemistry of Solutions

ERIC Educational Resources Information Center

Prezhdo, Oleg V.; Craig, Colleen F.; Fialkov, Yuriy; Prezhdo, Victor V.

2007-01-01

The study demonstrates that the solvent present in a system can highly alter and control the chemical equilibrium of a system. The results show that the dipole moment and polarizibility of a system can be highly altered by using different mixed solvents.

Budget Allocation in a Competitive Communication Spectrum Economy

NASA Astrophysics Data System (ADS)

Lin, Ming-Hua; Tsai, Jung-Fa; Ye, Yinyu

2009-12-01

This study discusses how to adjust "monetary budget" to meet each user's physical power demand, or balance all individual utilities in a competitive "spectrum market" of a communication system. In the market, multiple users share a common frequency or tone band and each of them uses the budget to purchase its own transmit power spectra (taking others as given) in maximizing its Shannon utility or pay-off function that includes the effect of interferences. A market equilibrium is a budget allocation, price spectrum, and tone power distribution that independently and simultaneously maximizes each user's utility. The equilibrium conditions of the market are formulated and analyzed, and the existence of an equilibrium is proved. Computational results and comparisons between the competitive equilibrium and Nash equilibrium solutions are also presented, which show that the competitive market equilibrium solution often provides more efficient power distribution.

Linearised and non-linearised isotherm models optimization analysis by error functions and statistical means

PubMed Central

2014-01-01

In adsorption study, to describe sorption process and evaluation of best-fitting isotherm model is a key analysis to investigate the theoretical hypothesis. Hence, numerous statistically analysis have been extensively used to estimate validity of the experimental equilibrium adsorption values with the predicted equilibrium values. Several statistical error analysis were carried out. In the present study, the following statistical analysis were carried out to evaluate the adsorption isotherm model fitness, like the Pearson correlation, the coefficient of determination and the Chi-square test, have been used. The ANOVA test was carried out for evaluating significance of various error functions and also coefficient of dispersion were evaluated for linearised and non-linearised models. The adsorption of phenol onto natural soil (Local name Kalathur soil) was carried out, in batch mode at 30 ± 20 C. For estimating the isotherm parameters, to get a holistic view of the analysis the models were compared between linear and non-linear isotherm models. The result reveled that, among above mentioned error functions and statistical functions were designed to determine the best fitting isotherm. PMID:25018878

Hyperdiffusive dynamics in Newtonian nanoparticle fluids [Hyperdiffusive dynamics in equilibrated nanoparticle fluids

DOE PAGES

Srivastava, Samanvaya; Agarwal, Praveen; Mangal, Rahul; ...

2015-09-24

Hyperdiffusive relaxations in soft glassy materials are typically associated with out-of-equilibrium states, and non-equilibrium physics and aging are often invoked in explaining their origins. Here, we report on hyperdiffusive motion in a model, equilibrium soft material comprised of single-component polymer-tethered-nanoparticles. In these materials, polymer mediated interactions lead to strong nanoparticle correlations, hyperdiffusive relaxations, and unusual variations of properties with temperature. Our experimental observations complement the current hypothesis that hyperdiffusive relaxations in soft materials require the material to exist in out–of–equilibrium states capable of driving structural rearrangements. Lastly, we propose alternatively that hyperdiffusive relaxations in our materials can arise naturally frommore » volume fluctuations brought about by equilibrium thermal forces.« less

SHAREv2: fluctuations and a comprehensive treatment of decay feed-down

NASA Astrophysics Data System (ADS)

Torrieri, G.; Jeon, S.; Letessier, J.; Rafelski, J.

2006-11-01

This the user's manual for SHARE version 2. SHARE [G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J. Letessier, J. Rafelski, Comput. Phys. Comm. 167 (2005) 229] (Statistical Hadronization with Resonances) is a collection of programs designed for the statistical analysis of particle production in relativistic heavy-ion collisions. While the structure of the program remains similar to v1.x, v2 provides several new features such as evaluation of statistical fluctuations of particle yields, and a greater versatility, in particular regarding decay feed-down and input/output structure. This article describes all the new features, with emphasis on statistical fluctuations. Program summaryTitle of program:SHAREv2 Catalogue identifier:ADVD_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVD_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:PC, Pentium III, 512 MB RAM not hardware dependent Operating system:Linux: RedHat 6.1, 7.2, FEDORA, etc. not system dependent Programming language:FORTRAN77 Size of the package:167 KB directory, without libraries (see http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/minmain.html, http://wwwasd.web.cern.ch/wwwasd/cernlib.html for details on library requirements) Number of lines in distributed program, including test data, etc.:26 101 Number of bytes in distributed program, including test data, etc.:170 346 Distribution format:tar.gzip file Computer:Any computer with an f77 compiler Nature of the physical problem:Event-by-event fluctuations have been recognized to be the physical observable capable to constrain particle production models. Therefore, consideration of event-by-event fluctuations is required for a decisive falsification or constraining of (variants of) particle production models based on (grand-, micro-) canonical statistical mechanics phase space, the so called statistical hadronization models (SHM). As in the case of particle yields, to properly compare model calculations to data it is necessary to consistently take into account resonance decays. However, event-by-event fluctuations are more sensitive than particle yields to experimental acceptance issues, and a range of techniques needs to be implemented to extract 'physical' fluctuations from an experimental event-by-event measurement. Method of solving the problem:The techniques used within the SHARE suite of programs [G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J. Letessier, J. Rafelski, Comput. Phys. Comm. 167 (2005) 229; SHAREv1] are updated and extended to fluctuations. A full particle data-table, decay tree, and set of experimental feed-down coefficients are provided. Unlike SHAREv1.x, experimental acceptance feed-down coefficients can be entered for any resonance decay. SHAREv2 can calculate yields, fluctuations, and bulk properties of the fireball from provided thermal parameters; alternatively, parameters can be obtained from fits to experimental data, via the MINUIT fitting algorithm [F. James, M. Roos, Comput. Phys. Comm. 10 (1975) 343]. Fits can also be analyzed for significance, parameter and data point sensitivity. Averages and fluctuations at freeze-out of both the stable particles and the hadronic resonances are set according to a statistical prescription, calculated via a series of Bessel functions, using CERN library programs. We also have the option of including finite particle widths of the resonances. A χ minimization algorithm, also from the CERN library programs, is used to perform and analyze the fit. Please see SHAREv1 for more details on these. Purpose:The vast amount of high quality soft hadron production data, from experiments running at the SPS, RHIC, in past at the AGS, and in the near future at the LHC, offers the opportunity for statistical particle production model falsification. This task has turned out to be difficult when considering solely particle yields addressed in the context of SHAREv1.x. For this reason physical conditions at freeze-out remain contested. Inclusion in the analysis of event-by-event fluctuations appears to resolve this issue. Similarly, a thorough analysis including both fluctuations and average multiplicities gives a way to explore the presence and strength of interactions following hadronization (when hadrons form), ending with thermal freeze-out (when all interactions cease). SHAREv2 with fluctuations will also help determine which statistical ensemble (if any), e.g., canonical or grand-canonical, is more physically appropriate for analyzing a given system. Together with resonances, fluctuations can also be used for a direct estimate of the extent the system re-interacts between chemical and thermal freeze-out. We hope and expect that SHAREv2 will contribute to decide if any of the statistical hadronization model variants has a genuine physical connection to hadron particle production. Computation time survey:We encounter, in the FORTRAN version computation, times up to seconds for evaluation of particle yields. These rise by up to a factor of 300 in the process of minimization and a further factor of a few when χ/N profiles and contours with chemical non-equilibrium are requested. Summary of new features (w.r.t. SHAREv1.x)Fluctuations:In addition to particle yields, ratios and bulk quantities SHAREv2 can calculate, fit and analyze statistical fluctuations of particles and particle ratios Decays:SHAREv2 has the flexibility to account for any experimental method of allowing for decay feed-downs to the particle yields Charm flavor:Charmed particles have been added to the decay tree, allowing as an option study of statistical hadronization of J/ψ, χ, D, etc. Quark chemistry:Chemical non-equilibrium yields for both u and d flavors, as opposed to generically light quarks q, are considered; η- η mixing, etc., are properly dealt with, and chemical non-equilibrium can be studied for each flavor separately Misc:Many new commands and features have been introduced and added to the basic user interface. For example, it is possible to study combinations of particles and their ratios. It is also possible to combine all the input files into one file. SHARE compatibility and manual:This write-up is an update and extension of SHAREv1. The user should consult SHAREv1 regarding the principles of user interface and for all particle yield related physics and program instructions, other than the parameter additions and minor changes described here. SHAREv2 is downward compatible for the changes of the user interface, offering the user of SHAREv1 a computer generated revised input files compatible with SHAREv2.

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Thermodynamics of adaptive molecular resolution

NASA Astrophysics Data System (ADS)

Delgado-Buscalioni, R.

2016-11-01

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ=U(1)-U(0). The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al., J. Chem. Phys. 142, 064115, 2015 (doi:10.1063/1.4907006)) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as `real' thermodynamic variables. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

From cell extracts to fish schools to granular layers: the universal hydrodynamics of self-driven systems

NASA Astrophysics Data System (ADS)

Ramaswamy, Sriram

2007-03-01

Collections of self-driven or ``active'' particles are now recognised as a distinct kind of nonequilibrium matter, and an understanding of their phases, hydrodynamics, mechanical response, and correlations is a vital and rapidly developing part of the statistical physics of soft-matter systems far from equilibrium. My talk will review our recent results, from theory, simulation and experiment, on order, fluctuations, and flow instabilities in collections of active particles, in suspension or on a solid surface. Our work, which began by adapting theories of flocking to include the hydrodynamics of the ambient fluid, provides the theoretical framework for understanding active matter in all its diversity: contractile filaments in cell extracts, crawling or dividing cells, collectively swimming bacteria, fish schools, and agitated monolayers of orientable granular particles.

Measurement and Statistics of Application Business in Complex Internet

NASA Astrophysics Data System (ADS)

Wang, Lei; Li, Yang; Li, Yipeng; Wu, Shuhang; Song, Shiji; Ren, Yong

Owing to independent topologies and autonomic routing mechanism, the logical networks formed by Internet application business behavior cause the significant influence on the physical networks. In this paper, the backbone traffic of TUNET (Tsinghua University Networks) is measured, further more, the two most important application business: HTTP and P2P are analyzed at IP-packet level. It is shown that uplink HTTP and P2P packets behavior presents spatio-temporal power-law characteristics with exponents 1.25 and 1.53 respectively. Downlink HTTP packets behavior also presents power-law characteristics, but has more little exponents γ = 0.82 which differs from traditional complex networks research result. Moreover, downlink P2P packets distribution presents an approximate power-law which means that flow equilibrium profits little from distributed peer-to peer mechanism actually.

Transition probability, dynamic regimes, and the critical point of financial crisis

NASA Astrophysics Data System (ADS)

Tang, Yinan; Chen, Ping

2015-07-01

An empirical and theoretical analysis of financial crises is conducted based on statistical mechanics in non-equilibrium physics. The transition probability provides a new tool for diagnosing a changing market. Both calm and turbulent markets can be described by the birth-death process for price movements driven by identical agents. The transition probability in a time window can be estimated from stock market indexes. Positive and negative feedback trading behaviors can be revealed by the upper and lower curves in transition probability. Three dynamic regimes are discovered from two time periods including linear, quasi-linear, and nonlinear patterns. There is a clear link between liberalization policy and market nonlinearity. Numerical estimation of a market turning point is close to the historical event of the US 2008 financial crisis.

Online Tools for Astronomy and Cosmochemistry

NASA Technical Reports Server (NTRS)

Meyer, B. S.

2005-01-01

Over the past year, the Webnucleo Group at Clemson University has been developing a web site with a number of interactive online tools for astronomy and cosmochemistry applications. The site uses SHP (Simplified Hypertext Preprocessor), which, because of its flexibility, allows us to embed almost any computer language into our web pages. For a description of SHP, please see http://www.joeldenny.com/ At our web site, an internet user may mine large and complex data sets, such as our stellar evolution models, and make graphs or tables of the results. The user may also run some of our detailed nuclear physics and astrophysics codes, such as our nuclear statistical equilibrium code, which is written in fortran and C. Again, the user may make graphs and tables and download the results.

Novel physical constraints on implementation of computational processes

NASA Astrophysics Data System (ADS)

Wolpert, David; Kolchinsky, Artemy

Non-equilibrium statistical physics permits us to analyze computational processes, i.e., ways to drive a physical system such that its coarse-grained dynamics implements some desired map. It is now known how to implement any such desired computation without dissipating work, and what the minimal (dissipationless) work is that such a computation will require (the so-called generalized Landauer bound\\x9D). We consider how these analyses change if we impose realistic constraints on the computational process. First, we analyze how many degrees of freedom of the system must be controlled, in addition to the ones specifying the information-bearing degrees of freedom, in order to avoid dissipating work during a given computation, when local detailed balance holds. We analyze this issue for deterministic computations, deriving a state-space vs. speed trade-off, and use our results to motivate a measure of the complexity of a computation. Second, we consider computations that are implemented with logic circuits, in which only a small numbers of degrees of freedom are coupled at a time. We show that the way a computation is implemented using circuits affects its minimal work requirements, and relate these minimal work requirements to information-theoretic measures of complexity.

Ionization and excitation in cool giant stars. I - Hydrogen and helium

NASA Technical Reports Server (NTRS)

Luttermoser, Donald G.; Johnson, Hollis R.

1992-01-01

The influence that non-LTE radiative transfer has on the electron density, ionization equilibrium, and excitation equilibrium in model atmospheres representative of both oxygen-rich and carbon-rich red giant stars is demonstrated. The radiative transfer and statistical equilibrium equations are solved self-consistently for H, H(-), H2, He I, C I, C II, Na I, Mg I, Mg II, Ca I, and Ca II in a plane-parallel static medium. Calculations are made for both radiative-equilibrium model photospheres alone and model photospheres with attached chromospheric models as determined semiempirically with IUE spectra of g Her (M6 III) and TX Psc (C6, 2). The excitation and ionization results for hydrogen and helium are reported.

Direct measurement of the Einstein relation in a macroscopic, non-equilibrium system of chaotic surface waves

NASA Astrophysics Data System (ADS)

Welch, Kyle; Liebman-Pelaez, Alexander; Corwin, Eric

Equilibrium statistical mechanics is traditionally limited to thermal systems. Can it be applied to athermal, non-equilibrium systems that nonetheless satisfy the basic criteria of steady-state chaos and isotropy? We answer this question using a macroscopic system of chaotic surface waves which is, by all measures, non-equilibrium. The waves are generated in a dish of water that is vertically oscillated above a critical amplitude. We have constructed a rheometer that actively measures the drag imparted by the waves on a buoyant particle, a quantity entirely divorced in origin from the drag imparted by the fluid in which the particle floats. We also perform a separate, passive measurement, extracting a diffusion constant and effective temperature. Having directly measured all three properties (temperature, diffusion constant, and drag coefficient) we go on to show that our macroscopic, non-equilibrium case is wholly consistent with the Einstein relation, a classic result for equilibrium thermal systems.

Effects of aircraft noise on the equilibrium of airport residents: Testing and utilization of a new methodology

NASA Technical Reports Server (NTRS)

Francois, J.

1981-01-01

The focus of the investigation is centered around two main themes: an analysis of the effects of aircraft noise on the psychological and physiological equilibrium of airport residents; and an analysis of the sources of variability of sensitivity to noise. The methodology used is presented. Nine statistical tables are included, along with a set of conclusions.

Pre-equilibrium Longitudinal Flow in the IP-Glasma Framework for Pb+Pb Collisions at the LHC

NASA Astrophysics Data System (ADS)

McDonald, Scott; Shen, Chun; Fillion-Gourdeau, François; Jeon, Sangyong; Gale, Charles

2017-08-01

In this work, we debut a new implementation of IP-Glasma and quantify the pre-equilibrium longitudinal flow in the IP-Glasma framework. The saturation physics based IP-Glasma model naturally provides a non-zero initial longitudinal flow through its pre-equilibrium Yang-Mills evolution. A hybrid IP-Glasma+MUSIC+UrQMD frame-work is employed to test this new implementation against experimental data and to make further predictions about hadronic flow observables in Pb+Pb collisions at 5.02 TeV. Finally, the non-zero pre-equilibrium longitudinal flow of the IP-Glasma model is quantified, and its origin is briefly discussed.

Towards Non-Equilibrium Dynamics with Trapped Ions

NASA Astrophysics Data System (ADS)

Silbert, Ariel; Jubin, Sierra; Doret, Charlie

2016-05-01

Atomic systems are superbly suited to the study of non-equilibrium dynamics. These systems' exquisite isolation from environmental perturbations leads to long relaxation times that enable exploration of far-from-equilibrium phenomena. One example of particular relevance to experiments in trapped ion quantum information processing, metrology, and precision spectroscopy is the approach to thermal equilibrium of sympathetically cooled linear ion chains. Suitable manipulation of experimental parameters permits exploration of the quantum-to-classical crossover between ballistic transport and diffusive, Fourier's Law conduction, a topic of interest not only to the trapped ion community but also for the development of microelectronic devices and other nanoscale structures. We present progress towards trapping chains of multiple co-trapped calcium isotopes geared towards measuring thermal equilibration and discuss plans for future experiments in non-equilibrium statistical mechanics. This work is supported by Cottrell College Science Award from the Research Corporation for Science Advancement and by Williams College.

An Information Theory Approach to Nonlinear, Nonequilibrium Thermodynamics

NASA Astrophysics Data System (ADS)

Rogers, David M.; Beck, Thomas L.; Rempe, Susan B.

2011-10-01

Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complex thermodynamic models by successively adding physical information. We present a new formulation of information algebra that generalizes methods of both information theory and statistical mechanics. From this foundation we derive a theory for ion channel kinetics, identifying a nonequilibrium `process' free energy functional in addition to the well-known integrated work functionals. The Gibbs-Maxwell relation for the free energy functional is a Green-Kubo relation, applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient thermal and mechanical driving forces. Comparing the physical significance of the Lagrange multipliers to the canonical ensemble suggests definitions of nonequilibrium ensembles at constant capacitance or inductance in addition to constant resistance. Our result is that statistical mechanical descriptions derived from a few primitive algebraic operations on information can be used to create experimentally-relevant and computable models. By construction, these models may use information from more detailed atomistic simulations. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a direct analogue of the second law for thermodynamic entropy production is found by considering information loss in stochastic processes. The information loss identifies a novel contribution from the instantaneous information entropy that ensures non-negative loss.

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

NASA Astrophysics Data System (ADS)

Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea

2016-10-01

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables {w_{ij}} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.

Physics Meets Art in the General Education Core

ERIC Educational Resources Information Center

Dark, Marta L.; Hylton, Derrick J.

2018-01-01

This article describes a general education course offering, Physics and the Arts. During the development of this course, physics and arts faculty collaborated closely. We cover the usual physics phenomena for such a course--light, color, and sound--in addition to gravity, equilibrium, and spacetime. Goals of the course are to increase students'…

An experimental study of the Online Information Paradox: Does en-route information improve road network performance?

PubMed

Wijayaratna, Kasun P; Dixit, Vinayak V; Denant-Boemont, Laurent; Waller, S Travis

2017-01-01

This study investigates the empirical presence of a theoretical transportation paradox, defined as the "Online Information Paradox" (OIP). The paradox suggests that, for certain road networks, the provision of online information deteriorate travel conditions for all users of that network relative to the situation where no online information is provided to users. The analytical presence of the paradox was derived for a specific network structure by using two equilibrium models, the first being the Expected User Equilibrium (EUE) solution (no information scenario) and the other being the User Equilibrium with Recourse (UER) solution (with information scenario). An incentivised computerised route choice game was designed using the concepts of experimental economics and administered in a controlled laboratory environment to investigate the physical presence of the paradox. Aggregate statistics of path flows and Total System Travel Costs (TSTC) were used to compare the experimental results with the theoretical findings. A total of 12 groups of 12 participants completed the experiment and the OIP and the occurrence of the OIP being significant was observed in 11 of the 12 cases. Though information increased travel costs for users on average, it reduced the volatility of travel costs experienced in the no information scenario indicating that information can achieve a more reliable system. Further replications of similar experiments and more importantly field based identification of the phenomena will force transport professionals to be aware of the emergence of the paradox. In addition, studies such as this emphasise the need for the adoption of adaptive traffic assignment techniques to appropriately model the acquisition of information on a road network.

An equilibrium-preserving discretization for the nonlinear Rosenbluth-Fokker-Planck operator in arbitrary multi-dimensional geometry

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.

2017-06-01

The Fokker-Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas [1,2], photonics in high temperature environment [3,4], biological [5], and even social systems [6]. For plasmas in the continuum, the Fokker-Planck collision operator supports such important physical properties as conservation of number, momentum, and energy, as well as positivity. It also obeys the Boltzmann's H-theorem [7-11], i.e., the operator increases the system entropy while simultaneously driving the distribution function towards a Maxwellian. In the discrete, when these properties are not ensured, numerical simulations can either fail catastrophically or suffer from significant numerical pollution [12,13]. There is strong emphasis in the literature on developing numerical techniques to solve the Fokker-Planck equation while preserving these properties [12-24]. In this short note, we focus on the analytical equilibrium preserving property, meaning that the Fokker-Planck collision operator vanishes when acting on an analytical Maxwellian distribution function. The equilibrium preservation property is especially important, for example, when one is attempting to capture subtle transport physics. Since transport arises from small O (ɛ) corrections to the equilibrium [25] (where ɛ is a small expansion parameter), numerical truncation error present in the equilibrium solution may dominate, overwhelming transport dynamics.

Failure of local thermal equilibrium in quantum friction

DOE PAGES

Intravaia, Francesco; Behunin, Ryan; Henkel, Carsten; ...

2016-09-01

Recent progress in manipulating atomic and condensed matter systems has instigated a surge of interest in nonequilibrium physics, including many-body dynamics of trapped ultracold atoms and ions, near-field radiative heat transfer, and quantum friction. Under most circumstances the complexity of such nonequilibrium systems requires a number of approximations to make theoretical descriptions tractable. In particular, it is often assumed that spatially separated components of a system thermalize with their immediate surroundings, although the global state of the system is out of equilibrium. This powerful assumption reduces the complexity of nonequilibrium systems to the local application of well-founded equilibrium concepts. Whilemore » this technique appears to be consistent for the description of some phenomena, we show that it fails for quantum friction by underestimating by approximately 80% the magnitude of the drag force. Here, our results show that the correlations among the components of driven, but steady-state, quantum systems invalidate the assumption of local thermal equilibrium, calling for a critical reexamination of this approach for describing the physics of nonequilibrium systems.« less

A game-theoretic method for cross-layer stochastic resilient control design in CPS

NASA Astrophysics Data System (ADS)

Shen, Jiajun; Feng, Dongqin

2018-03-01

In this paper, the cross-layer security problem of cyber-physical system (CPS) is investigated from the game-theoretic perspective. Physical dynamics of plant is captured by stochastic differential game with cyber-physical influence being considered. The sufficient and necessary condition for the existence of state-feedback equilibrium strategies is given. The attack-defence cyber interactions are formulated by a Stackelberg game intertwined with stochastic differential game in physical layer. The condition such that the Stackelberg equilibrium being unique and the corresponding analytical solutions are both provided. An algorithm is proposed for obtaining hierarchical security strategy by solving coupled games, which ensures the operational normalcy and cyber security of CPS subject to uncertain disturbance and unexpected cyberattacks. Simulation results are given to show the effectiveness and performance of the proposed algorithm.

13C 18O clumping in speleothems: Observations from natural caves and precipitation experiments

NASA Astrophysics Data System (ADS)

Daëron, M.; Guo, W.; Eiler, J.; Genty, D.; Blamart, D.; Boch, R.; Drysdale, R.; Maire, R.; Wainer, K.; Zanchetta, G.

2011-06-01

The oxygen isotope composition of speleothems is an important proxy of continental paleoenvironments, because of its sensitivity to variations in cave temperature and drip water δ 18O. Interpreting speleothem δ 18O records in terms of absolute paleotemperatures and δ 18O values of paleo-precipitation requires quantitative separation of the effects of these two parameters, and correcting for possible kinetic isotope fractionation associated with precipitation of calcite out of thermodynamic equilibrium. Carbonate clumped-isotope thermometry, based on measurements of Δ47 (a geochemical variable reflecting the statistical overabundance of 13C 18O bonds in CO 2 evolved from phosphoric acid digestion of carbonate minerals), potentially provides a method for absolute speleothem paleotemperature reconstructions independent of drip water composition. Application of this new technique to karst records is currently limited by the scarcity of published clumped-isotope studies of modern speleothems. The only modern stalagmite reported so far in the literature yielded a lower Δ47 value than expected for equilibrium precipitation, possibly due to kinetic isotope fractionation. Here we report Δ47 values measured in natural speleothems from various cave settings, in carbonate produced by cave precipitation experiments, and in synthetic stalagmite analogs precipitated in controlled laboratory conditions designed to mimic natural cave processes. All samples yield lower Δ47 and heavier δ 18O values than predicted by experimental calibrations of thermodynamic equilibrium in inorganic calcite. The amplitudes of these isotopic disequilibria vary between samples, but there is clear correlation between the amount of Δ47 disequilibrium and that of δ 18O. Even pool carbonates believed to offer excellent conditions for equilibrium precipitation of calcite display out-of-equilibrium δ 18O and Δ47 values, probably inherited from prior degassing within the cave system. In addition to these modern observations, clumped-isotope analyses of a flowstone from Villars cave (France) offer evidence that the amount of disequilibrium affecting Δ47 in a single speleothem can experience large variations at time scales of 10 kyr. Application of clumped-isotope thermometry to speleothem records calls for an improved physical understanding of DIC fractionation processes in karst waters, and for the resolution of important issues regarding equilibrium calibration of Δ47 in inorganic carbonates.

Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: a canonical-dissipative approach.

PubMed

Dotov, D G; Kim, S; Frank, T D

2015-02-01

We derive explicit expressions for the non-equilibrium thermodynamical variables of a canonical-dissipative limit cycle oscillator describing rhythmic motion patterns of active systems. These variables are statistical entropy, non-equilibrium internal energy, and non-equilibrium free energy. In particular, the expression for the non-equilibrium free energy is derived as a function of a suitable control parameter. The control parameter determines the Hopf bifurcation point of the deterministic active system and describes the effective pumping of the oscillator. In analogy to the equilibrium free energy of the Landau theory, it is shown that the non-equilibrium free energy decays as a function of the control parameter. In doing so, a similarity between certain equilibrium and non-equilibrium phase transitions is pointed out. Data from an experiment on human rhythmic movements is presented. Estimates for pumping intensity as well as the thermodynamical variables are reported. It is shown that in the experiment the non-equilibrium free energy decayed when pumping intensity was increased, which is consistent with the theory. Moreover, pumping intensities close to zero could be observed at relatively slow intended rhythmic movements. In view of the Hopf bifurcation underlying the limit cycle oscillator model, this observation suggests that the intended limit cycle movements were actually more similar to trajectories of a randomly perturbed stable focus. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Establishment and Assessment of Plasma Disruption and Warning Databases from EAST

NASA Astrophysics Data System (ADS)

Wang, Bo; Robert, Granetz; Xiao, Bingjia; Li, Jiangang; Yang, Fei; Li, Junjun; Chen, Dalong

2016-12-01

Disruption database and disruption warning database of the EAST tokamak had been established by a disruption research group. The disruption database, based on Structured Query Language (SQL), comprises 41 disruption parameters, which include current quench characteristics, EFIT equilibrium characteristics, kinetic parameters, halo currents, and vertical motion. Presently most disruption databases are based on plasma experiments of non-superconducting tokamak devices. The purposes of the EAST database are to find disruption characteristics and disruption statistics to the fully superconducting tokamak EAST, to elucidate the physics underlying tokamak disruptions, to explore the influence of disruption on superconducting magnets and to extrapolate toward future burning plasma devices. In order to quantitatively assess the usefulness of various plasma parameters for predicting disruptions, a similar SQL database to Alcator C-Mod for EAST has been created by compiling values for a number of proposed disruption-relevant parameters sampled from all plasma discharges in the 2015 campaign. The detailed statistic results and analysis of two databases on the EAST tokamak are presented. supported by the National Magnetic Confinement Fusion Science Program of China (No. 2014GB103000)

Dynamic scaling in natural swarms

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Conti, Daniele; Creato, Chiara; Del Castello, Lorenzo; Giardina, Irene; Grigera, Tomas S.; Melillo, Stefania; Parisi, Leonardo; Viale, Massimiliano

2017-09-01

Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ~ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ~ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

Statistical Mechanics of the Human Placenta: A Stationary State of a Near-Equilibrium System in a Linear Regime.

PubMed

Lecarpentier, Yves; Claes, Victor; Hébert, Jean-Louis; Krokidis, Xénophon; Blanc, François-Xavier; Michel, Francine; Timbely, Oumar

2015-01-01

All near-equilibrium systems under linear regime evolve to stationary states in which there is constant entropy production rate. In an open chemical system that exchanges matter and energy with the exterior, we can identify both the energy and entropy flows associated with the exchange of matter and energy. This can be achieved by applying statistical mechanics (SM), which links the microscopic properties of a system to its bulk properties. In the case of contractile tissues such as human placenta, Huxley's equations offer a phenomenological formalism for applying SM. SM was investigated in human placental stem villi (PSV) (n = 40). PSV were stimulated by means of KCl exposure (n = 20) and tetanic electrical stimulation (n = 20). This made it possible to determine statistical entropy (S), internal energy (E), affinity (A), thermodynamic force (A / T) (T: temperature), thermodynamic flow (v) and entropy production rate (A / T x v). We found that PSV operated near equilibrium, i.e., A ≺≺ 2500 J/mol and in a stationary linear regime, i.e., (A / T) varied linearly with v. As v was dramatically low, entropy production rate which quantified irreversibility of chemical processes appeared to be the lowest ever observed in any contractile system.

Network Polymers Formed Under Nonideal Conditions.

DTIC Science & Technology

1986-12-01

the system or the limited ability of the statistical model to account for stochastic correlations. The viscosity of the reacting system was measured as...based on competing reactions (ring, chain) and employs equilibrium chain statistics . The work thus far has been limited to single cycle growth on an...polymerizations, because a large number of differential equations must be solved. The Makovian approach (sometimes referred to as the statistical or

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

NASA Astrophysics Data System (ADS)

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

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Toward a Multi-scale Phase Transition Kinetics Methodology: From Non-Equilibrium Statistical Mechanics to Hydrodynamics

NASA Astrophysics Data System (ADS)

Belof, Jonathan; Orlikowski, Daniel; Wu, Christine; McLaughlin, Keith

2013-06-01

Shock and ramp compression experiments are allowing us to probe condensed matter under extreme conditions where phase transitions and other non-equilibrium aspects can now be directly observed, but first principles simulation of kinetics remains a challenge. A multi-scale approach is presented here, with non-equilibrium statistical mechanical quantities calculated by molecular dynamics (MD) and then leveraged to inform a classical nucleation and growth kinetics model at the hydrodynamic scale. Of central interest is the free energy barrier for the formation of a critical nucleus, with direct NEMD presenting the challenge of relatively long timescales necessary to resolve nucleation. Rather than attempt to resolve the time-dependent nucleation sequence directly, the methodology derived here is built upon the non-equilibrium work theorem in order to bias the formation of a critical nucleus and thus construct the nucleation and growth rates. Having determined these kinetic terms from MD, a hydrodynamics implementation of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics and metastabilty is applied to the dynamic compressive freezing of water and compared with recent ramp compression experiments [Dolan et al., Nature (2007)] Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.

Parallel equilibrium current effect on existence of reversed shear Alfvén eigenmodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Hua-sheng, E-mail: huashengxie@gmail.com; Xiao, Yong, E-mail: yxiao@zju.edu.cn

2015-02-15

A new fast global eigenvalue code, where the terms are segregated according to their physics contents, is developed to study Alfvén modes in tokamak plasmas, particularly, the reversed shear Alfvén eigenmode (RSAE). Numerical calculations show that the parallel equilibrium current corresponding to the kink term is strongly unfavorable for the existence of the RSAE. An improved criterion for the RSAE existence is given for with and without the parallel equilibrium current. In the limits of ideal magnetohydrodynamics (MHD) and zero-pressure, the toroidicity effect is the main possible favorable factor for the existence of the RSAE, which is however usually small.more » This suggests that it is necessary to include additional physics such as kinetic term in the MHD model to overcome the strong unfavorable effect of the parallel current in order to enable the existence of RSAE.« less

Economic analysis of gradual "social exhaustion" of waste management capacity.

PubMed

Koide, Hideo; Nakayama, Hirofumi

2013-12-01

This article proposes to analyze the quantitative effects of a gradual physical and "social" exhaustion of a landfill site on an equilibrium waste management service. A gradual social exhaustion of a landfill is defined here as an upward shift of a "subjective factor" associated with the amount of waste, based on the plausible hypothesis that an individual will not accept excessive presence of landfilled waste. Physical exhaustion occurs when the absolute capacity of a landfill site decreases. The paper shows some numerical examples using specific functions and parameters, and proposes appropriate directions for three policy objectives: to decrease the equilibrium waste disposal, to increase the economic surplus of the individual and/or the waste management firm, and to lower the equilibrium collection fee. Copyright © 2013 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Statistics of the Work done in a Quantum Quench

NASA Astrophysics Data System (ADS)

Silva, Alessandro

2009-03-01

The quantum quench, i.e. a rapid change in time of a control parameter of a quantum system, is the simplest paradigm of non-equilibrium process, completely analogous to a standard thermodynamic transformation. The dynamics following a quantum quench is particularly interesting in strongly correlated quantum systems, most prominently when the quench in performed across a quantum critical point. In this talk I will present a way to characterize the physics of quantum quenches by looking at the statistics of a basic thermodynamic variable: the work done on the system by changing its parameters [1]. I will first elucidate the relation between the probability distribution of the work, quantum Jarzynski equalities, and the Loschmidt echo, a quantity that emerges usually in the context of dephasing. Using this connection, I will then characterize the statistics of the work done on a Quantum Ising chain by quenching locally or globally the transverse field. I will then show that for global quenches the presence of a quantum critical point results in singularities of the moments of the distribution, while, for local quenches starting at criticality, the probability distribution itself displays an interesting edge singularity. The results of a similar analysis for other systems will be discussed. [4pt] [1] A. Silva, Phys. Rev. Lett. 101, 120603 (2008).

Science Notes.

ERIC Educational Resources Information Center

School Science Review, 1989

1989-01-01

Twenty-two activities are presented. Topics include: acid rain, microcomputers, fish farming, school-industry research projects, enzymes, equilibrium, assessment, science equipment, logic, Archimedes principle, electronics, optics, and statistics. (CW)

Anatomy of particle diffusion

NASA Astrophysics Data System (ADS)

Bringuier, E.

2009-11-01

The paper analyses particle diffusion from a thermodynamic standpoint. The main goal of the paper is to highlight the conceptual connection between particle diffusion, which belongs to non-equilibrium statistical physics, and mechanics, which deals with particle motion, at the level of third-year university courses. We start out from the fact that, near equilibrium, particle transport should occur down the gradient of the chemical potential. This yields Fick's law with two additional advantages. First, splitting the chemical potential into 'mechanical' and 'chemical' contributions shows how transport and mechanics are linked through the diffusivity-mobility relationship. Second, splitting the chemical potential into entropic and energetic contributions discloses the respective roles of entropy maximization and energy minimization in driving diffusion. The paper addresses first unary diffusion, where there is only one mobile species in an immobile medium, and next turns to binary diffusion, where two species are mobile with respect to each other in a fluid medium. The interrelationship between unary and binary diffusivities is brought out and it is shown how binary diffusion reduces to unary diffusion in the limit of high dilution of one species amidst the other one. Self- and mutual diffusion are considered and contrasted within the thermodynamic framework; self-diffusion is a time-dependent manifestation of the Gibbs paradox of mixing.

Exploring the Clapeyron Equation and the Phase Rule Using a Mechanical Drawing Toy

ERIC Educational Resources Information Center

Darvesh, Katherine V.

2013-01-01

The equilibrium between phases is a key concept from the introductory physical chemistry curriculum. Phase diagrams display which phase is the most stable at a given temperature and pressure. If more than one phase has the lowest Gibbs energy, then those phases are in equilibrium under those conditions. An activity designed to demonstrate the…

A Counterintuitive Toy: The Bird That Never Falls Down.

ERIC Educational Resources Information Center

Fort, J.; Llebot, J. E.; Saurina, J.; Sunol, J. J.

1998-01-01

Describes a toy shaped like a bird that has an intuitively astonishing property: no matter how far away from equilibrium it is moved, it oscillates back to equilibrium. The behavior of this physical system is explained and is used to illustrate the concept of mechanical stability and the usefulness of making simple, idealized models for describing…

A Simple Method to Calculate the Temperature Dependence of the Gibbs Energy and Chemical Equilibrium Constants

ERIC Educational Resources Information Center

Vargas, Francisco M.

2014-01-01

The temperature dependence of the Gibbs energy and important quantities such as Henry's law constants, activity coefficients, and chemical equilibrium constants is usually calculated by using the Gibbs-Helmholtz equation. Although, this is a well-known approach and traditionally covered as part of any physical chemistry course, the required…

Thermodynamics of energy, charge, and spin currents in a thermoelectric quantum-dot spin valve

NASA Astrophysics Data System (ADS)

Tang, Gaomin; Thingna, Juzar; Wang, Jian

2018-04-01

We provide a thermodynamically consistent description of energy, charge, and spin transfers in a thermoelectric quantum-dot spin valve in the collinear configuration based on nonequilibrium Green's function and full counting statistics. We use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials, arbitrary far from equilibrium. Close to equilibrium, we recover the Onsager reciprocal relations and the connection to linear response notions of performance such as the figure of merit. We also identify regimes where work extraction is more efficient far then close from equilibrium.

Foundations of statistical mechanics from symmetries of entanglement

DOE PAGES

Deffner, Sebastian; Zurek, Wojciech H.

2016-06-09

Envariance—entanglement assisted invariance—is a recently discovered symmetry of composite quantum systems. Here, we show that thermodynamic equilibrium states are fully characterized by their envariance. In particular, the microcanonical equilibrium of a systemmore » $${ \\mathcal S }$$ with Hamiltonian $${H}_{{ \\mathcal S }}$$ is a fully energetically degenerate quantum state envariant under every unitary transformation. A representation of the canonical equilibrium then follows from simply counting degenerate energy states. Finally, our conceptually novel approach is free of mathematically ambiguous notions such as ensemble, randomness, etc., and, while it does not even rely on probability, it helps to understand its role in the quantum world.« less

Polylogarithmic equilibrium treatment of molecular aggregation and critical concentrations.

PubMed

Michel, Denis; Ruelle, Philippe

2017-02-15

A full equilibrium treatment of molecular aggregation is presented for prototypes of 1D and 3D aggregates, with and without nucleation. By skipping complex kinetic parameters like aggregate size-dependent diffusion, the equilibrium treatment allows us to predict directly time-independent quantities such as critical concentrations. The relationships between the macroscopic equilibrium constants for different paths are first established by statistical corrections and so as to comply with the detailed balance constraints imposed by nucleation, and the composition of the mixture resulting from homogeneous aggregation is then analyzed using a polylogarithmic function. Several critical concentrations are distinguished: the residual monomer concentration at equilibrium (RMC) and the critical nucleation concentration (CNC), which is the threshold concentration of total subunits necessary for initiating aggregation. When increasing the concentration of total subunits, the RMC converges more strongly to its asymptotic value, the equilibrium constant of depolymerization, for 3D aggregates and in the case of nucleation. The CNC moderately depends on the number of subunits in the nucleus, but sharply increases with the difference between the equilibrium constants of polymerization and nucleation. As the RMC and CNC can be numerically but not analytically determined, ansatz equations connecting them to thermodynamic parameters are proposed.

Overview of Aro Program on Network Science for Human Decision Making

NASA Astrophysics Data System (ADS)

West, Bruce J.

This program brings together researchers from disparate disciplines to work on a complex research problem that defies confinement within any single discipline. Consequently, not only are new and rewarding solutions sought and obtained for a problem of importance to society and the Army, that is, the human dimension of complex networks, but, in addition, collaborations are established that would not otherwise have formed given the traditional disciplinary compartmentalization of research. This program develops the basic research foundation of a science of networks supporting the linkage between the physical and human (cognitive and social) domains as they relate to human decision making. The strategy is to extend the recent methods of non-equilibrium statistical physics to non-stationary, renewal stochastic processes that appear to be characteristic of the interactions among nodes in complex networks. We also pursue understanding of the phenomenon of synchronization, whose mathematical formulation has recently provided insight into how complex networks reach accommodation and cooperation. The theoretical analyses of complex networks, although mathematically rigorous, often elude analytic solutions and require computer simulation and computation to analyze the underlying dynamic process.

NON-EQUILIBRIUM HELIUM IONIZATION IN AN MHD SIMULATION OF THE SOLAR ATMOSPHERE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golding, Thomas Peter; Carlsson, Mats; Leenaarts, Jorrit, E-mail: thomas.golding@astro.uio.no, E-mail: mats.carlsson@astro.uio.no, E-mail: jorrit.leenaarts@astro.su.se

The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilibrium hydrogen ionization by performing a 2D radiation-magnetohydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyα and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with local thermodynamicmore » equilibrium (LTE) ionization shows that non-equilibrium helium ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behavior with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11–18 kK, compared to models with LTE helium ionization. We conclude that non-equilibrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region. It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed.« less

Statistical errors in molecular dynamics averages

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schiferl, S.K.; Wallace, D.C.

1985-11-15

A molecular dynamics calculation produces a time-dependent fluctuating signal whose average is a thermodynamic quantity of interest. The average of the kinetic energy, for example, is proportional to the temperature. A procedure is described for determining when the molecular dynamics system is in equilibrium with respect to a given variable, according to the condition that the mean and the bandwidth of the signal should be sensibly constant in time. Confidence limits for the mean are obtained from an analysis of a finite length of the equilibrium signal. The role of serial correlation in this analysis is discussed. The occurence ofmore » unstable behavior in molecular dynamics data is noted, and a statistical test for a level shift is described.« less

[The improvement of the abilities to maintain motor coordination and equilibrium in the students presenting with the functional disorders of the musculoskeletal system by introducing the elements of therapeutic physical training into the structure of academic schedule of physical education].

PubMed

Kapilevich, L V; Davlet'yarova, K V; Ovchinnikova, N A

The problem of deterioration of the health status in the university students at present remains as topical as it was before being a major cause of impaired working capacity, disability and/or poor social adaptation of the large number of graduates. It has been proposed to introduce a class of therapeutic physical training (TPT) into the schedule of physical education for the students. The objective of the present study was to evaluate the effectiveness of the formation of the skills needed to maintain motor coordination and equilibrium in the students presenting with the functional disorders of the musculoskeletal system (MSS) including scoliosis by the introduction of the elements of therapeutic physical training into their academic schedules. The main study group was comprised of 32 students (men) at the age of 18-19 years presenting with the disorders of the musculoskeletal system (type III scoliosis, osteochondropathy, and osteochondrosis). The students of this group received a curriculum aimed at improving their motor skills with the emphasis laid on the selected elements of therapeutic physical training. The control group was composed of 17 students without disorders of the musculoskeletal system who attended the physical education classes following the traditional program. The coordination abilities and balance skills were evaluated based on the analysis with the use of the Stabilan-1 stabilographic apparatus. In addition, the stability test and the Romberg test with open and closed eyes were performed. The results of the study give evidence that the introduction of the elements of therapeutic physical training into the structure of academic schedule of physical education for the students suffering from diseases of the musculoskeletal system has beneficial effect on the parameters of stability and the general ability to maintain the posture and balance. Specifically, in the beginning of the academic year, the students of the main study group presenting with the locomotor problems (the scatter of the manifest disorders in the frontal and sagittal planes, the mean amplitude and velocity of fluctuations of the center of pressure, the area of the projection of the center of pressure displacements as well as the quality of the equilibrium function that characterizes the ability to maintain the posture) were significantly different from the respective characteristics in the control group (p<0,05). After the course of therapeutic physical training given during the academic year, the scatter of the manifestations in the frontal and sagittal planes as well as the role of the visual control in the maintenance of balance decreased significantly. The present study has demonstrated that the introduction of the elements of therapeutic physical training into the structure of academic schedule of physical education for the students presenting with the functional disorders of the locomotor apparatus exerts the positive influence on the parameters characterizing stability and the ability to maintain the posture as well as equilibrium at large. Such beneficial effect is apparent in the form of reduction of the amplitude and velocity of fluctuations of the centre of pressure, the decrease in the area of projection of its displacements, and the improvement of the quality of the equilibrium function that characterizes the ability to maintain the posture. Moreover, the ratio of spreading in the frontal and sagittal planes decreases, and the role of the visual control in the maintenance of equilibrium becomes diminished. The results of the study give grounds for recommending the introduction of the elements of therapeutic physical training into the learning process of students presenting with diseases of the musculoskeletal system.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

With this thesis, we want to shed some light into the darkness of our understanding of simply defined statistical mechanics systems and the surprisingly complex dynamical behavior they exhibit. We will do so by presenting in turn one equilibrium and then one non-equilibrium system with evolutionary dynamics. In part 1, we will present the seceder-model, a newly developed system that cannot equilibrate. We will then study several properties of the system and obtain an idea of the richness of the dynamics of the seceder model, which is particular impressive given the minimal amount of modeling necessary in its setup. In part 2, we will present extensions to the directed polymer in random media problem on a hypercube and its connection to the Eigen model of evolution. Our main interest will be the influence of time-dependent and time-independent changes in the fitness landscape viewed by an evolving population. This part contains the equilibrium dynamics. The stochastic models and the topic of evolution and non-equilibrium in general will allow us to point out similarities to the various lines of thought in game theory.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Verification and rectification of the physical analogy of simulated annealing for the solution of the traveling salesman problem.

PubMed

Hasegawa, M

2011-03-01

The aim of the present study is to elucidate how simulated annealing (SA) works in its finite-time implementation by starting from the verification of its conventional optimization scenario based on equilibrium statistical mechanics. Two and one supplementary experiments, the design of which is inspired by concepts and methods developed for studies on liquid and glass, are performed on two types of random traveling salesman problems. In the first experiment, a newly parameterized temperature schedule is introduced to simulate a quasistatic process along the scenario and a parametric study is conducted to investigate the optimization characteristics of this adaptive cooling. In the second experiment, the search trajectory of the Metropolis algorithm (constant-temperature SA) is analyzed in the landscape paradigm in the hope of drawing a precise physical analogy by comparison with the corresponding dynamics of glass-forming molecular systems. These two experiments indicate that the effectiveness of finite-time SA comes not from equilibrium sampling at low temperature but from downward interbasin dynamics occurring before equilibrium. These dynamics work most effectively at an intermediate temperature varying with the total search time and thus this effective temperature is identified using the Deborah number. To test directly the role of these relaxation dynamics in the process of cooling, a supplementary experiment is performed using another parameterized temperature schedule with a piecewise variable cooling rate and the effect of this biased cooling is examined systematically. The results show that the optimization performance is not only dependent on but also sensitive to cooling in the vicinity of the above effec-tive temperature and that this feature is interpreted as a consequence of the presence or absence of the workable interbasin dynamics. It is confirmed for the present instances that the effectiveness of finite-time SA derives from the glassy relaxation dynamics occurring in the "landscape-influenced" temperature regime and that its naive optimization scenario should be rectified by considering the analogy with vitrification phenomena. A comprehensive guideline for the design of finite-time SA and SA-related algorithms is discussed on the basis of this rectified analogy.

Electron-impact excitation heating rates in the atmosphere of Titan

NASA Astrophysics Data System (ADS)

Campbell, L.; Kato, H.; Brunger, M. J.; Bradshaw, M. D.

2010-09-01

A previous study of various heating rates in the atmosphere of Titan included electron-impact excitation of molecular nitrogen as one component. This work examines this component in more detail, using a statistical equilibrium calculation to avoid approximations made in the earlier work. The sensitivity of the results to different cross-section sets is investigated. It is found that using recent and more physical cross sections for vibrational excitation produces a significant increase in the heating rate. On the other hand, using more accurate cross sections for the electronic states had little apparent effect on the heating rates when used within the approximations made in the previous model. However, the inclusion of more transitions in this study produces a significant increase in the electronic state heating rates, as states that were originally neglected are now accounted for here.

Thermodynamics of adaptive molecular resolution.

PubMed

Delgado-Buscalioni, R

2016-11-13

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ=U (1) -U (0) The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al, J. Chem. Phys. 142, 064115, 2015 (doi:10.1063/1.4907006)) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as 'real' thermodynamic variablesThis article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'. © 2016 The Author(s).

Minimum relative entropy distributions with a large mean are Gaussian

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2016-12-01

Entropy optimization principles are versatile tools with wide-ranging applications from statistical physics to engineering to ecology. Here we consider the following constrained problem: Given a prior probability distribution q , find the posterior distribution p minimizing the relative entropy (also known as the Kullback-Leibler divergence) with respect to q under the constraint that mean (p ) is fixed and large. We show that solutions to this problem are approximately Gaussian. We discuss two applications of this result. In the context of dissipative dynamics, the equilibrium distribution of a Brownian particle confined in a strong external field is independent of the shape of the confining potential. We also derive an H -type theorem for evolutionary dynamics: The entropy of the (standardized) distribution of fitness of a population evolving under natural selection is eventually increasing in time.

Mechanical Metamaterials with Negative Compressibility Transitions

NASA Astrophysics Data System (ADS)

Motter, Adilson

2015-03-01

When tensioned, ordinary materials expand along the direction of the applied force. In this presentation, I will explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which the material undergoes contraction when tensioned (or expansion when pressured). Such transitions, which are forbidden in thermodynamic equilibrium, are possible during the decay of metastable, super-strained states. I will introduce a statistical physics theory for negative compressibility transitions, derive a first-principles model to predict these transitions, and present a validation of the model using molecular dynamics simulations. Aside from its immediate mechanical implications, our theory points to a wealth of analogous inverted responses, such as inverted susceptibility or heat-capacity transitions, allowed when considering realistic scales. This research was done in collaboration with Zachary Nicolaou, and was supported by the National Science Foundation and the Alfred P. Sloan Foundation.

A thick cloud of Neptune Trojans and their colors.

PubMed

Sheppard, Scott S; Trujillo, Chadwick A

2006-07-28

The dynamical and physical properties of asteroids offer one of the few constraints on the formation, evolution, and migration of the giant planets. Trojan asteroids share a planet's semimajor axis but lead or follow it by about 60 degrees near the two triangular Lagrangian points of gravitational equilibrium. Here we report the discovery of a high-inclination Neptune Trojan, 2005 TN(53). This discovery demonstrates that the Neptune Trojan population occupies a thick disk, which is indicative of "freeze-in" capture instead of in situ or collisional formation. The Neptune Trojans appear to have a population that is several times larger than the Jupiter Trojans. Our color measurements show that Neptune Trojans have statistically indistinguishable slightly red colors, which suggests that they had a common formation and evolutionary history and are distinct from the classical Kuiper Belt objects.

Modeling stock return distributions with a quantum harmonic oscillator

NASA Astrophysics Data System (ADS)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Seeing believes: Watching entangled sculpted branched DNA in real time

NASA Astrophysics Data System (ADS)

Jee, Ah-Young; Guan, Juan; Chen, Kejia; Granick, Steve

2015-03-01

The importance of branching in polymer physics is universally accepted but the details are disputed. We have sculpted DNA to various degrees of branching and used single-molecule tracking to image its diffusion in real time when entangled. By ligating three identical or varying length DNA segments, we construct symmetric and asymmetric ?Y? branches from elements of lambda-DNA with 16 um contour length, allowing for single-molecule visualization of equilibrium dynamics. Using home-written software, a full statistical distribution based on at least hundreds of trajectories is quantified with focus on discriminating arm-retraction from branch point motion. Some part of our observations is consistent with the anticipated ?relaxation through arm retraction? mechanism but other observations do not appear to be anticipated theoretically. Currently working as a researcher in Institute for Basic Science.

Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium.

PubMed

Green, Jason R; Costa, Anthony B; Grzybowski, Bartosz A; Szleifer, Igal

2013-10-08

Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov-Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov-Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes.

Relationship between dynamical entropy and energy dissipation far from thermodynamic equilibrium

PubMed Central

Green, Jason R.; Costa, Anthony B.; Grzybowski, Bartosz A.; Szleifer, Igal

2013-01-01

Connections between microscopic dynamical observables and macroscopic nonequilibrium (NE) properties have been pursued in statistical physics since Boltzmann, Gibbs, and Maxwell. The simulations we describe here establish a relationship between the Kolmogorov–Sinai entropy and the energy dissipated as heat from a NE system to its environment. First, we show that the Kolmogorov–Sinai or dynamical entropy can be separated into system and bath components and that the entropy of the system characterizes the dynamics of energy dissipation. Second, we find that the average change in the system dynamical entropy is linearly related to the average change in the energy dissipated to the bath. The constant energy and time scales of the bath fix the dynamical relationship between these two quantities. These results provide a link between microscopic dynamical variables and the macroscopic energetics of NE processes. PMID:24065832

Traffic Flow of Interacting Self-Driven Particles: Rails and Trails, Vehicles and Vesicles

NASA Astrophysics Data System (ADS)

Chowdhury, Debashish

One common feature of a vehicle, an ant and a kinesin motor is that they all convert chemical energy, derived from fuel or food, into mechanical energy required for their forward movement; such objects have been modelled in recent years as self-driven particles. Cytoskeletal filaments, e.g., microtubules, form a rail network for intra-cellular transport of vesicular cargo by molecular motors like, for example, kinesins. Similarly, ants move along trails while vehicles move along lanes. Therefore, the traffic of vehicles and organisms as well as that of molecular motors can be modelled as systems of interacting self-driven particles; these are of current interest in non-equilibrium statistical mechanics. In this paper we point out the common features of these model systems and emphasize the crucial differences in their physical properties.

Atomistic mechanisms of ReRAM cell operation and reliability

NASA Astrophysics Data System (ADS)

Pandey, Sumeet C.

2018-01-01

We present results from first-principles-based modeling that captures functionally important physical phenomena critical to cell materials selection, operation, and reliability for resistance-switching memory technologies. An atomic-scale description of retention, the low- and high-resistance states (RS), and the sources of intrinsic cell-level variability in ReRAM is discussed. Through the results obtained from density functional theory, non-equilibrium Green’s function, molecular dynamics, and kinetic Monte Carlo simulations; the role of variable-charge vacancy defects and metal impurities in determining the RS, the LRS-stability, and electron-conduction in such RS is reported. Although, the statistical electrical characteristics of the oxygen-vacancy (Ox-ReRAM) and conductive-bridging RAM (M-ReRAM) are notably different, the underlying similar electrochemical phenomena describing retention and formation/dissolution of RS are being discussed.

Nicholas Metropolis Award for Outstanding Doctoral Thesis Work in Computational Physics Lecture: The Janus computer, a new window into spin-glass physics

NASA Astrophysics Data System (ADS)

Yllanes, David

2013-03-01

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. They enjoy a privileged status in this context, as they provide the simplest model system both for theoretical and experimental studies of glassy dynamics. However, in spite of forty years of intensive investigation, spin glasses still pose a formidable challenge to theoretical, computational and experimental physics. The main difficulty lies in their incredibly slow dynamics. A recent breakthrough has been made possible by our custom-built computer, Janus, designed and built in a collaboration formed by five universities in Spain and Italy. By employing a purpose-driven architecture, capable of fully exploiting the parallelization possibilities intrinsic to these simulations, Janus outperforms conventional computers by several orders of magnitude. After a brief introduction to spin glasses, the talk will focus on the new physics unearthed by Janus. In particular, we recall our numerical study of the nonequilibrium dynamics of the Edwards-Anderson Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. seconds). We have also studied the equilibrium properties of the spin-glass phase, with an emphasis on the quantitative matching between non-equilibrium and equilibrium correlation functions, through a time-length dictionary. Last but not least, we have clarified the existence of a glass transition in the presence of a magnetic field for a finite-range spin glass (the so-called de Almeida-Thouless line). We will finally mention some of the currently ongoing work of the collaboration, such as the characterization of the non-equilibrium dynamics in a magnetic field and the existence of a statics-dynamics dictionary in these conditions.

Nonequilibrium quantum field dynamics from the two-particle-irreducible effective action

NASA Astrophysics Data System (ADS)

Laurie, Nathan S.

The two-particle-irreducible effective action offers a powerful approach to the study of quantum field dynamics far from equilibrium. Recent and upcoming heavy ion collision experiments motivate the study of such nonequilibrium dynamics in an expanding space-time background. For the O(N) model I derive exact, causal evolution equations for the statistical and spectral functions in a longitudinally expanding system. It is followed by an investigation into how the expansion affects the prospect of the system reaching equilibrium. Results are obtained in 1+1 dimensions at next-to- leading order in loop- and 1/N-expansions of the 2PI effective action. I focus on the evolution of the statistical function from highly nonequilibrium initial conditions, presenting a detailed analysis of early, intermediate and late-time dynamics. It is found that dynamics at very early times is attracted by a nonthermal fixed point of the mean field equations, after which interactions attempt to drive the system to equilibrium. The competition between the interactions and the expansion is eventually won by the expansion, with so-called freeze-out emerging naturally in this description. In order to investigate the convergence of the 2PI-1/N expansion in the 0(N) model, I compare results obtained numerically in 1+1 dimensions at leading, next- to-leading and next-to-next-to-leading order in 1/N. Convergence with increasing N, and also with decreasing coupling are discussed. A comparison is also made in the classical statistical field theory limit, where exact numerical results are available. I focus on early-time dynamics and quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling strength.

Evaluating equilibrium and non-equilibrium transport of bromide and isoproturon in disturbed and undisturbed soil columns.

PubMed

Dousset, S; Thevenot, M; Pot, V; Simunek, J; Andreux, F

2007-12-07

In this study, displacement experiments of isoproturon were conducted in disturbed and undisturbed columns of a silty clay loam soil under similar rainfall intensities. Solute transport occurred under saturated conditions in the undisturbed soil and under unsaturated conditions in the sieved soil because of a greater bulk density of the compacted undisturbed soil compared to the sieved soil. The objective of this work was to determine transport characteristics of isoproturon relative to bromide tracer. Triplicate column experiments were performed with sieved (structure partially destroyed to simulate conventional tillage) and undisturbed (structure preserved) soils. Bromide experimental breakthrough curves were analyzed using convective-dispersive and dual-permeability (DP) models (HYDRUS-1D). Isoproturon breakthrough curves (BTCs) were analyzed using the DP model that considered either chemical equilibrium or non-equilibrium transport. The DP model described the bromide elution curves of the sieved soil columns well, whereas it overestimated the tailing of the bromide BTCs of the undisturbed soil columns. A higher degree of physical non-equilibrium was found in the undisturbed soil, where 56% of total water was contained in the slow-flow matrix, compared to 26% in the sieved soil. Isoproturon BTCs were best described in both sieved and undisturbed soil columns using the DP model combined with the chemical non-equilibrium. Higher degradation rates were obtained in the transport experiments than in batch studies, for both soils. This was likely caused by hysteresis in sorption of isoproturon. However, it cannot be ruled out that higher degradation rates were due, at least in part, to the adopted first-order model. Results showed that for similar rainfall intensity, physical and chemical non-equilibrium were greater in the saturated undisturbed soil than in the unsaturated sieved soil. Results also suggested faster transport of isoproturon in the undisturbed soil due to higher preferential flow and lower fraction of equilibrium sorption sites.

Evaluating equilibrium and non-equilibrium transport of bromide and isoproturon in disturbed and undisturbed soil columns

NASA Astrophysics Data System (ADS)

Dousset, S.; Thevenot, M.; Pot, V.; Šimunek, J.; Andreux, F.

2007-12-01

In this study, displacement experiments of isoproturon were conducted in disturbed and undisturbed columns of a silty clay loam soil under similar rainfall intensities. Solute transport occurred under saturated conditions in the undisturbed soil and under unsaturated conditions in the sieved soil because of a greater bulk density of the compacted undisturbed soil compared to the sieved soil. The objective of this work was to determine transport characteristics of isoproturon relative to bromide tracer. Triplicate column experiments were performed with sieved (structure partially destroyed to simulate conventional tillage) and undisturbed (structure preserved) soils. Bromide experimental breakthrough curves were analyzed using convective-dispersive and dual-permeability (DP) models (HYDRUS-1D). Isoproturon breakthrough curves (BTCs) were analyzed using the DP model that considered either chemical equilibrium or non-equilibrium transport. The DP model described the bromide elution curves of the sieved soil columns well, whereas it overestimated the tailing of the bromide BTCs of the undisturbed soil columns. A higher degree of physical non-equilibrium was found in the undisturbed soil, where 56% of total water was contained in the slow-flow matrix, compared to 26% in the sieved soil. Isoproturon BTCs were best described in both sieved and undisturbed soil columns using the DP model combined with the chemical non-equilibrium. Higher degradation rates were obtained in the transport experiments than in batch studies, for both soils. This was likely caused by hysteresis in sorption of isoproturon. However, it cannot be ruled out that higher degradation rates were due, at least in part, to the adopted first-order model. Results showed that for similar rainfall intensity, physical and chemical non-equilibrium were greater in the saturated undisturbed soil than in the unsaturated sieved soil. Results also suggested faster transport of isoproturon in the undisturbed soil due to higher preferential flow and lower fraction of equilibrium sorption sites.

Performance Modeling of an Experimental Laser Propelled Lightcraft

NASA Technical Reports Server (NTRS)

Wang, Ten-See; Chen, Yen-Sen; Liu, Jiwen; Myrabo, Leik N.; Mead, Franklin B., Jr.

2000-01-01

A computational plasma aerodynamics model is developed to study the performance of an experimental laser propelled lightcraft. The computational methodology is based on a time-accurate, three-dimensional, finite-difference, chemically reacting, unstructured grid, pressure- based formulation. The underlying physics are added and tested systematically using a building-block approach. The physics modeled include non-equilibn'um thermodynamics, non-equilibrium air-plasma finite-rate kinetics, specular ray tracing, laser beam energy absorption and equi refraction by plasma, non-equilibrium plasma radiation, and plasma resonance. A series of transient computations are performed at several laser pulse energy levels and the simulated physics are discussed and compared with those of tests and literature. The predicted coupling coefficients for the lightcraft compared reasonably well with those of tests conducted on a pendulum apparatus.

Non-equilibrium coherence dynamics in one-dimensional Bose gases.

PubMed

Hofferberth, S; Lesanovsky, I; Fischer, B; Schumm, T; Schmiedmayer, J

2007-09-20

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Impact of rainfall intensity on the transport of two herbicides in undisturbed grassed filter strip soil cores

NASA Astrophysics Data System (ADS)

Pot, V.; Šimůnek, J.; Benoit, P.; Coquet, Y.; Yra, A.; Martínez-Cordón, M.-J.

2005-12-01

Two series of displacement experiments with isoproturon and metribuzin herbicides were performed on two undisturbed grassed filter strip soil cores, under unsaturated steady-state flow conditions. Several rainfall intensities (0.070, 0.147, 0.161, 0.308 and 0.326 cm h - 1 ) were used. A water tracer (bromide) was simultaneously injected in each displacement experiment. A descriptive analysis of experimental breakthrough curves of bromide and herbicides combined with a modeling analysis showed an impact of rainfall intensity on the solute transport. Two contrasting physical non-equilibrium transport processes occurred. Multiple (three) porosity domains contributed to flow at the highest rainfall intensities, including preferential flow through macropore pathways. Macropores were not active any longer at intermediate and lowest velocities, and the observed preferential transport was described using dual-porosity-type models with a zero or low flow in the matrix domain. Chemical non-equilibrium transport of herbicides was found at all rainfall intensities. Significantly higher estimated values of degradation rate parameters as compared to batch data were correlated with the degree of non-equilibrium sorption. Experimental breakthrough curves were analyzed using different physical and chemical equilibrium and non-equilibrium transport models: convective-dispersive model (CDE), dual-porosity model (MIM), dual-permeability model (DP), triple-porosity, dual permeability model (DP-MIM); each combined with both chemical instantaneous and kinetic sorption.

Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamba, Irene M.; Tharkabhushanam, Sri Harsha

We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibilitymore » (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ()]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously cooling and heated granular fluids, Granular Matter 1(57) (1998); M.H. Ernst, R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, Journal of Statistical Physics 109 (2002) 407-432; S.J. Moon, M.D. Shattuck, J. Swift, Velocity distributions and correlations in homogeneously heated granular media, Physical Review E 64 (2001) 031303; I.M. Gamba, S. Rjasanow, W. Wagner, Direct simulation of the uniformly heated granular Boltzmann equation, Mathematical and Computer Modelling 42 (2005) 683-700] and rigorously proven in Gamba et al. [I.M. Gamba, V. Panferov, C. Villani, On the Boltzmann equation for diffusively excited granular media, Communications in Mathematical Physics 246 (2004) 503-541(39)] and [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions, Journal of Statistical Physics 116 (2004) 1651-1682].« less

Plasma Equilibrium in a Magnetic Field with Stochastic Regions

DOE Office of Scientific and Technical Information (OSTI.GOV)

J.A. Krommes and Allan H. Reiman

The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schluter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect onmore » the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch-Schluter currents. Implications for the numerical calculation of 3D equilibria are discussed« less

CALL FOR PAPERS: Progress in Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

2003-11-01

This is a call for contributions to a Special Issue of Journal of Physics A: Mathematical and General entitled `Statistical Physics of Disordered Systems: from Real Materials to Optimization and Codes'. This issue should be a place for high quality original work. We stress the fact that we are interested in having the topic interpreted broadly: we would like to have contributions ranging from equilibrium and dynamical studies of spin glasses, glassy behaviour in amorphous materials, and low temperature physics, to applications in non-conventional areas such as error correcting codes, image analysis and reconstruction, optimization, and algorithms based on statistical mechanical ideas. We believe that we have arrived at a very exciting moment for the development of this multidisciplinary approach, and that this issue will be of a high standard and prove to be a very useful tool in the future. The Editorial Board has invited E Marinari, H Nishimori and F Ricci-Tersenghi to serve as Guest Editors for the Special Issue. Their criteria for acceptance of contributions are the following: bullet The subject of the paper should relate to the statistical physics of disordered systems. bullet Contributions will be refereed and processed according to the usual procedures of the journal. bullet Papers should be original (they should not be simply reviews of authors' own work that is already published elsewhere). bullet Review articles will be considered for inclusion in the Special Issue only in very special cases. The editors will analyse potential proposals of reviews, and if needed they will ask for some review contributions. The guidelines for the preparation of contributions are the following: bullet The deadline for submission of contributions is 31 March 2003. This deadline will allow the Special Issue to appear in about October 2003. bullet There is a nominal page limit of 15 printed pages (approximately 9000 words) per research contribution. The contributions that have been approved by the Guest Editors as review articles will have a limit of 30 printed pages (18000 words). Papers exceeding these limits may be accepted at the discretion of the Guest Editors. Further advice on publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. bullet Contributions to the Special Issue should if possible be submitted electronically at www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'. Submissions should ideally be in either standard LaTeX form or Microsoft Word. Please see the web site for further information on electronic submissions. bullet Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue -- Statistical Physics of Disordered Systems'. bullet All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This Special Issue will be published in both paper and online editions of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue in addition to the usual 25 free offprints of their article. E Marinari, H Nishimori and F Ricci-Tersenghi Guest Editors

MAGNETAR GIANT FLARES-FLUX ROPE ERUPTIONS IN MULTIPOLAR MAGNETOSPHERIC MAGNETIC FIELDS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Cong, E-mail: cyu@ynao.ac.cn

2012-09-20

We address a primary question regarding the physical mechanism that triggers the energy release and initiates the onset of eruptions in the magnetar magnetosphere. Self-consistent stationary, axisymmetric models of the magnetosphere are constructed based on force-free magnetic field configurations that contain a helically twisted force-free flux rope. Depending on the surface magnetic field polarity, there exist two kinds of magnetic field configurations, inverse and normal. For these two kinds of configurations, variations of the flux rope equilibrium height in response to gradual surface physical processes, such as flux injections and crust motions, are carefully examined. We find that equilibrium curvesmore » contain two branches: one represents a stable equilibrium branch, and the other an unstable equilibrium branch. As a result, the evolution of the system shows a catastrophic behavior: when the magnetar surface magnetic field evolves slowly, the height of the flux rope would gradually reach a critical value beyond which stable equilibriums can no longer be maintained. Subsequently, the flux rope would lose equilibrium and the gradual quasi-static evolution of the magnetosphere will be replaced by a fast dynamical evolution. In addition to flux injections, the relative motion of active regions would give rise to the catastrophic behavior and lead to magnetic eruptions as well. We propose that a gradual process could lead to a sudden release of magnetosphere energy on a very short dynamical timescale, without being initiated by a sudden fracture in the crust of the magnetar. Some implications of our model are also discussed.« less

Transient probabilities for queues with applications to hospital waiting list management.

PubMed

Joy, Mark; Jones, Simon

2005-08-01

In this paper we study queuing systems within the NHS. Recently imposed government performance targets lead NHS executives to investigate and instigate alternative management strategies, thereby imposing structural changes on the queues. Under such circumstances, it is most unlikely that such systems are in equilibrium. It is crucial, in our opinion, to recognise this state of affairs in order to make a balanced assessment of the role of queue management in the modern NHS. From a mathematical perspective it should be emphasised that measures of the state of a queue based upon the assumption of statistical equilibrium (a pervasive methodology in the study of queues) are simply wrong in the above scenario. To base strategic decisions around such ideas is therefore highly questionable and it is one of the purposes of this paper to offer alternatives: we present some (recent) research whose results generate performance measures and measures of risk, for example, of waiting-times growing unacceptably large; we emphasise that these results concern the transient behaviour of the queueing model-there is no asssumption of statistical equilibrium. We also demonstrate that our results are computationally tractable.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

PubMed

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.; Shalymov, Dmitry S.

2017-03-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.

Non-equilibrium phase transitions in a driven-dissipative system of interacting bosons

NASA Astrophysics Data System (ADS)

Young, Jeremy T.; Foss-Feig, Michael; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-04-01

Atomic, molecular, and optical systems provide unique opportunities to study simple models of driven-dissipative many-body quantum systems. Typically, one is interested in the resultant steady state, but the non-equilibrium nature of the physics involved presents several problems in understanding its behavior theoretically. Recently, it has been shown that in many of these models, it is possible to map the steady-state phase transitions onto classical equilibrium phase transitions. In the language of Keldysh field theory, this relation typically only becomes apparent after integrating out massive fields near the critical point, leaving behind a single massless field undergoing near-equilibrium dynamics. In this talk, we study a driven-dissipative XXZ bosonic model and discover critical points at which two fields become gapless. Each critical point separates three different possible phases: a uniform phase, an anti-ferromagnetic phase, and a limit cycle phase. Furthermore, a description in terms of an equilibrium phase transition does not seem possible, so the associated phase transitions appear to be inherently non-equilibrium.

Use of JANAF Tables in Equilibrium Calculations and Partition Function Calculations for an Undergraduate Physical Chemistry Course

ERIC Educational Resources Information Center

Cleary, David A.

2014-01-01

The usefulness of the JANAF tables is demonstrated with specific equilibrium calculations. An emphasis is placed on the nature of standard chemical potential calculations. Also, the use of the JANAF tables for calculating partition functions is examined. In the partition function calculations, the importance of the zero of energy is highlighted.

Investigating the Magnetic Interaction with Geomag and Tracker Video Analysis: Static Equilibrium and Anharmonic Dynamics

ERIC Educational Resources Information Center

Onorato, P.; Mascheretti, P.; DeAmbrosis, A.

2012-01-01

In this paper, we describe how simple experiments realizable by using easily found and low-cost materials allow students to explore quantitatively the magnetic interaction thanks to the help of an Open Source Physics tool, the Tracker Video Analysis software. The static equilibrium of a "column" of permanents magnets is carefully investigated by…

The Universal Statistical Distributions of the Affinity, Equilibrium Constants, Kinetics and Specificity in Biomolecular Recognition

PubMed Central

Zheng, Xiliang; Wang, Jin

2015-01-01

We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics. PMID:25885453

Why Non-Equilibrium is Different

NASA Astrophysics Data System (ADS)

Dorfman, J. Robert; Kirkpatrick, Theodore R.; Sengers, Jan V.

The 1970 paper, "Decay of the Velocity Correlation Function" [Phys. Rev. A1, 18 (1970), see also Phys. Rev. Lett. 18, 988, (1967)] by Berni Alder and Tom Wainwright, demonstrated, by means of computer simulations, that the velocity autocorrelation function for a particle moving diffusively in a gas of hard disks decays algebraically in time as t-1, and as t-3/2 for a gas of hard spheres. These decays appear in non-equilibrium fluids and have no counterpart in fluids in thermodynamic equilibrium. The work of Alder and Wainwright stimulated theorists to find explanations for these "long time tails" using kinetic theory or a mesoscopic mode-coupling theory. This paper has had a profound influence on our understanding of the non-equilibrium properties of fluid systems. Here we discuss the kinetic origins of the long time tails, the microscopic foundations of modecoupling theory, and the implications of these results for the physics of fluids. We also mention applications of the long time tails and mode-coupling theory to other, seemingly unrelated, fields of physics. We are honored to dedicate this short review to Berni Alder on the occasion of his 90th birthday!

Physics of Magnetospheric Variability

NASA Astrophysics Data System (ADS)

Vasyliūnas, Vytenis M.

2011-01-01

Many widely used methods for describing and understanding the magnetosphere are based on balance conditions for quasi-static equilibrium (this is particularly true of the classical theory of magnetosphere/ionosphere coupling, which in addition presupposes the equilibrium to be stable); they may therefore be of limited applicability for dealing with time-variable phenomena as well as for determining cause-effect relations. The large-scale variability of the magnetosphere can be produced both by changing external (solar-wind) conditions and by non-equilibrium internal dynamics. Its developments are governed by the basic equations of physics, especially Maxwell's equations combined with the unique constraints of large-scale plasma; the requirement of charge quasi-neutrality constrains the electric field to be determined by plasma dynamics (generalized Ohm's law) and the electric current to match the existing curl of the magnetic field. The structure and dynamics of the ionosphere/magnetosphere/solar-wind system can then be described in terms of three interrelated processes: (1) stress equilibrium and disequilibrium, (2) magnetic flux transport, (3) energy conversion and dissipation. This provides a framework for a unified formulation of settled as well as of controversial issues concerning, e.g., magnetospheric substorms and magnetic storms.

The quasi-equilibrium response of MOS structures: Quasi-static factor

NASA Astrophysics Data System (ADS)

Okeke, M.; Balland, B.

1984-07-01

The dynamic response of a MOS structure driven into a non-equilibrium behaviour by a voltage ramp is presented. In contrast to Khun's quasi-static technique it is shown that any ramp-driven MOS structure has some degree of non-equilibrium. A quasi staticity factor μAK which serves as a measure of the degree of quasi-equilibrium, has been introduced for the first time. The mathematical model presented in the paper allows a better explanation of the experimental recordings. It is shown that this model could be used to analyse the various features of the response of the structure and that such physical parameters as the generation-rate, trap activation energy, and the effective capture constants could be obtained.

Coupling of phytoplankton uptake and air-water exchange of persistent organic pollutants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dachs, J.; Eisenreich, S.J.; Baker, J.E.

1999-10-15

A dynamic model that couples air-water exchange and phytoplankton uptake of persistent organic pollutants has been developed and then applied to PCB data from a small experimental lake. A sensitivity analysis of the model, taking into account the influence of physical environmental conditions such as temperature, wind speed, and mixing depth as well as plankton-related parameters such as biomass and growth rate was carried out for a number of PCBs with different physical-chemical properties. The results indicate that air-water exchange dynamics are influenced not only by physical parameters but also by phytoplankton biomass and growth rate. New phytoplankton production resultsmore » in substantially longer times to reach equilibrium. Phytoplankton uptake-induced depletion of the dissolved phase concentration maintains air and water phases out of equilibrium. Furthermore, PCBs in phytoplankton also take longer times to reach equilibrium with the dissolved water phase when the latter is supported by diffusive air-water exchange. However, both model analysis and model application to the Experimental Lakes Area of northwestern Ontario (Canada) suggest that the gas phase supports the concentrations of persistent organic pollutants, such as PCBs, in atmospherically driven aquatic environments.« less

Evaluating measurement uncertainty in fluid phase equilibrium calculations

NASA Astrophysics Data System (ADS)

van der Veen, Adriaan M. H.

2018-04-01

The evaluation of measurement uncertainty in accordance with the ‘Guide to the expression of uncertainty in measurement’ (GUM) has not yet become widespread in physical chemistry. With only the law of the propagation of uncertainty from the GUM, many of these uncertainty evaluations would be cumbersome, as models are often non-linear and require iterative calculations. The methods from GUM supplements 1 and 2 enable the propagation of uncertainties under most circumstances. Experimental data in physical chemistry are used, for example, to derive reference property data and support trade—all applications where measurement uncertainty plays an important role. This paper aims to outline how the methods for evaluating and propagating uncertainty can be applied to some specific cases with a wide impact: deriving reference data from vapour pressure data, a flash calculation, and the use of an equation-of-state to predict the properties of both phases in a vapour-liquid equilibrium. The three uncertainty evaluations demonstrate that the methods of GUM and its supplements are a versatile toolbox that enable us to evaluate the measurement uncertainty of physical chemical measurements, including the derivation of reference data, such as the equilibrium thermodynamical properties of fluids.

BOOK REVIEW: Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

NASA Astrophysics Data System (ADS)

Franz, S.

2004-10-01

Since the discovery of the renormalization group theory in statistical physics, the realm of applications of the concepts of scale invariance and criticality has pervaded several fields of natural and social sciences. This is the leitmotiv of Didier Sornette's book, who in Critical Phenomena in Natural Sciences reviews three decades of developments and applications of the concepts of criticality, scale invariance and power law behaviour from statistical physics, to earthquake prediction, ruptures, plate tectonics, modelling biological and economic systems and so on. This strongly interdisciplinary book addresses students and researchers in disciplines where concepts of criticality and scale invariance are appropriate: mainly geology from which most of the examples are taken, but also engineering, biology, medicine, economics, etc. A good preparation in quantitative science is assumed but the presentation of statistical physics principles, tools and models is self-contained, so that little background in this field is needed. The book is written in a simple informal style encouraging intuitive comprehension rather than stressing formal derivations. Together with the discussion of the main conceptual results of the discipline, great effort is devoted to providing applied scientists with the tools of data analysis and modelling necessary to analyse, understand, make predictions and simulate systems undergoing complex collective behaviour. The book starts from a purely descriptive approach, explaining basic probabilistic and geometrical tools to characterize power law behaviour and scale invariant sets. Probability theory is introduced by a detailed discussion of interpretative issues warning the reader on the use and misuse of probabilistic concepts when the emphasis is on prediction of low probability rare---and often catastrophic---events. Then, concepts that have proved useful in risk evaluation, extreme value statistics, large limit theorems for sums of independent variables with power law distribution, random walks, fractals and multifractal formalisms, etc, are discussed in an immediate and direct way so as to provide ready-to-use tools for analysing and representing power law behaviour in natural phenomena. The exposition then continues discussing the main developments, allowing the reader to understand theoretically and model strongly correlated behaviour. After a concise, but useful, introduction to the fundamentals of statistical physics a discussion of equilibrium critical phenomena and the renormalization group is proposed to the reader. With the centrality of the problem of non-equilibrium behaviour in mind, a discussion is devoted to tentative applications of the concept of temperature in the off-equilibrium context. Particular emphasis is given to the development of long range correlation and of precursors of phase transitions, and their role in the prediction of catastrophic events. Then, basic models such as percolation and rupture models are described. A central position in the book is occupied by a chapter on mechanisms for power laws and a subsequent one on self-organized criticality as a general paradigm for critical behaviour as proposed by P Bak and collaborators. The book concludes with a chapter on the prediction of fields generated by a random distribution of sources. The book maintains the promise of the title of providing concepts and tools to tackle criticality and self-organization. The second edition, while retaining the structure of the first edition, considerably extends the scope with new examples and applications of a research field which is constantly growing. Any scientific book has to solve the dichotomy between the depth of discussion, the pedagogical character of exposition and the quantity of material discussed. In general the book, which evolved from a graduate student course, favours these last two aspects at the expense of the first one. This makes the book very readable and means that, while complicated concepts are always explained by means of simple examples, important results are often mentioned but not derived or discussed in depth. Most of the time this style of exposition manages to successfully convey the essential information, other times unfortunately, e.g. in the case of the chapter on disordered systems, the presentation appears rather superficial. This is the price we pay for a book covering an impressively vast subject area and the huge bibliography (more than 1000 references) furnishes a necessary guide for acquiring the working knowledge of the subject covered. I would recommend it to teachers planning introductory courses on the field of complex systems and to researchers wanting to learn about an area of great contemporary interest.

Statistical mechanics of shell models for two-dimensional turbulence

NASA Astrophysics Data System (ADS)

Aurell, E.; Boffetta, G.; Crisanti, A.; Frick, P.; Paladin, G.; Vulpiani, A.

1994-12-01

We study shell models that conserve the analogs of energy and enstrophy and hence are designed to mimic fluid turbulence in two-dimensions (2D). The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous to the approach to two-dimensional ideal hydrodynamics of Onsager [Nuovo Cimento Suppl. 6, 279 (1949)], Hopf [J. Rat. Mech. Anal. 1, 87 (1952)], and Lee [Q. Appl. Math. 10, 69 (1952)]. In the presence of forcing and dissipation we observe a forward flux of enstrophy and a backward flux of energy. These fluxes can be understood as mean diffusive drifts from a source to two sinks in a system which is close to local equilibrium with Lagrange multipliers (``shell temperatures'') changing slowly with scale. This is clear evidence that the simplest shell models are not adequate to reproduce the main features of two-dimensional turbulence. The dimensional predictions on the power spectra from a supposed forward cascade of enstrophy and from one branch of the formal statistical equilibrium coincide in these shell models in contrast to the corresponding predictions for the Navier-Stokes and Euler equations in 2D. This coincidence has previously led to the mistaken conclusion that shell models exhibit a forward cascade of enstrophy. We also study the dynamical properties of the models and the growth of perturbations.

Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

Caplan, M. E.; Schneider, A. S.; Horowitz, C. J.; Berry, D. K.

2015-06-01

Background: Exotic nonspherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short-range nuclear attraction and long-range Coulomb repulsion. Purpose: We explore the impact nuclear pasta may have on nucleosynthesis during neutron star mergers when cold dense nuclear matter is ejected and decompressed. Methods: We use a hybrid CPU/GPU molecular dynamics (MD) code to perform decompression simulations of cold dense matter with 51 200 and 409 600 nucleons from 0.080 fm-3 down to 0.00125 fm-3 . Simulations are run for proton fractions YP= 0.05, 0.10, 0.20, 0.30, and 0.40 at temperatures T = 0.5, 0.75, and 1.0 MeV. The final composition of each simulation is obtained using a cluster algorithm and compared to a constant density run. Results: Size of nuclei in the final state of decompression runs are in good agreement with nuclear statistical equilibrium (NSE) models for temperatures of 1 MeV while constant density runs produce nuclei smaller than the ones obtained with NSE. Our MD simulations produces unphysical results with large rod-like nuclei in the final state of T =0.5 MeV runs. Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

The Physics of Toys.

ERIC Educational Resources Information Center

Levinstein, Henry

1982-01-01

Outlines a course in which toys are used to demonstrate physics concepts, stressing available or easily constructed toys. A recent lecture sequence included toys demonstrating equilibrium, force/torque, linear/angular momentum conservation, energy conservation/storage, flying, vibrations, programed music, and others. Illustrations of selected toys…

Non-equilibrium synergistic effects in atmospheric pressure plasmas.

PubMed

Guo, Heng; Zhang, Xiao-Ning; Chen, Jian; Li, He-Ping; Ostrikov, Kostya Ken

2018-03-19

Non-equilibrium is one of the important features of an atmospheric gas discharge plasma. It involves complicated physical-chemical processes and plays a key role in various actual plasma processing. In this report, a novel complete non-equilibrium model is developed to reveal the non-equilibrium synergistic effects for the atmospheric-pressure low-temperature plasmas (AP-LTPs). It combines a thermal-chemical non-equilibrium fluid model for the quasi-neutral plasma region and a simplified sheath model for the electrode sheath region. The free-burning argon arc is selected as a model system because both the electrical-thermal-chemical equilibrium and non-equilibrium regions are involved simultaneously in this arc plasma system. The modeling results indicate for the first time that it is the strong and synergistic interactions among the mass, momentum and energy transfer processes that determine the self-consistent non-equilibrium characteristics of the AP-LTPs. An energy transfer process related to the non-uniform spatial distributions of the electron-to-heavy-particle temperature ratio has also been discovered for the first time. It has a significant influence for self-consistently predicting the transition region between the "hot" and "cold" equilibrium regions of an AP-LTP system. The modeling results would provide an instructive guidance for predicting and possibly controlling the non-equilibrium particle-energy transportation process in various AP-LTPs in future.

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Revealing missing charges with generalised quantum fluctuation relations.

PubMed

Mur-Petit, J; Relaño, A; Molina, R A; Jaksch, D

2018-05-22

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

Foundations of atmospheric pressure non-equilibrium plasmas

NASA Astrophysics Data System (ADS)

Bruggeman, Peter J.; Iza, Felipe; Brandenburg, Ronny

2017-12-01

Non-equilibrium plasmas have been intensively studied over the past century in the context of material processing, environmental remediation, ozone generation, excimer lamps and plasma display panels. Research on atmospheric pressure non-equilibrium plasmas intensified over the last two decades leading to a large variety of plasma sources that have been developed for an extended application range including chemical conversion, medicine, chemical analysis and disinfection. The fundamental understanding of these discharges is emerging but there remain a lot of unexplained phenomena in these intrinsically complex plasmas. The properties of non-equilibrium plasmas at atmospheric pressure span over a huge range of electron densities as well as heavy particle and electron temperatures. This paper provides an overview of the key underlying processes that are important for the generation and stabilization of atmospheric pressure non-equilibrium plasmas. The unique physical and chemical properties of theses discharges are also summarized.

An experimental study of the Online Information Paradox: Does en-route information improve road network performance?

PubMed Central

2017-01-01

This study investigates the empirical presence of a theoretical transportation paradox, defined as the “Online Information Paradox” (OIP). The paradox suggests that, for certain road networks, the provision of online information deteriorate travel conditions for all users of that network relative to the situation where no online information is provided to users. The analytical presence of the paradox was derived for a specific network structure by using two equilibrium models, the first being the Expected User Equilibrium (EUE) solution (no information scenario) and the other being the User Equilibrium with Recourse (UER) solution (with information scenario). An incentivised computerised route choice game was designed using the concepts of experimental economics and administered in a controlled laboratory environment to investigate the physical presence of the paradox. Aggregate statistics of path flows and Total System Travel Costs (TSTC) were used to compare the experimental results with the theoretical findings. A total of 12 groups of 12 participants completed the experiment and the OIP and the occurrence of the OIP being significant was observed in 11 of the 12 cases. Though information increased travel costs for users on average, it reduced the volatility of travel costs experienced in the no information scenario indicating that information can achieve a more reliable system. Further replications of similar experiments and more importantly field based identification of the phenomena will force transport professionals to be aware of the emergence of the paradox. In addition, studies such as this emphasise the need for the adoption of adaptive traffic assignment techniques to appropriately model the acquisition of information on a road network. PMID:28902854

Quantum theory of multiscale coarse-graining.

PubMed

Han, Yining; Jin, Jaehyeok; Wagner, Jacob W; Voth, Gregory A

2018-03-14

Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.

Absolute Equilibrium Entropy

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1997-01-01

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magneto-fluid turbulence is discussed and the three-dimensional fluid case is examined in detail. A sigma-function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions sigma and phase functions H (associated with the development of various H-theorems of ideal turbulence). It is shown that the two approaches are complimentary though conceptually different: H-theorems show that an isolated system tends to equilibrium while sigma-functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.

Against the grain: The physical properties of anisotropic partially molten rocks

NASA Astrophysics Data System (ADS)

Ghanbarzadeh, S.; Hesse, M. A.; Prodanovic, M.

2014-12-01

Partially molten rocks commonly develop textures that appear close to textural equilibrium, where the melt network evolves to minimize the energy of the melt-solid interfaces, while maintaining the dihedral angle θ at solid-solid-melt contact lines. Textural equilibrium provides a powerful model for the melt distribution that controls the petro-physical properties of partially molten rocks, e.g., permeability, elastic moduli, and electrical resistivity. We present the first level-set computations of three-dimensional texturally equilibrated melt networks in rocks with an anisotropic fabric. Our results show that anisotropy induces wetting of smaller grain boundary faces for θ > 0 at realistic porosities ϕ < 3%. This was previously not thought to be possible at textural equilibrium and reconciles the theory with experimental observations. Wetting of the grain boundary faces leads to a dramatic redistribution of the melt from the edges to the faces that introduces strong anisotropy in the petro-physical properties such as permeability, effective electrical conductivity and mechanical properties. Figure, on left, shows that smaller grain boundaries become wetted at relatively low melt fractions of 3% in stretched polyhedral grains with elongation factor 1.5. Right plot represents the ratio of melt electrical conductivity to effective conductivity of medium (known as formation factor) as an example of anisotropy in physical properties. The plot shows that even slight anisotropy in grains induces considerable anisotropy in electrical properties.

Random walk to a nonergodic equilibrium concept

NASA Astrophysics Data System (ADS)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

Monte Carlo Simulation of the Rapid Crystallization of Bismuth-Doped Silicon

NASA Technical Reports Server (NTRS)

Jackson, Kenneth A.; Gilmer, George H.; Temkin, Dmitri E.

1995-01-01

In this Letter we report Ising model simulations of the growth of alloys which predict quite different behavior near and far from equilibrium. Our simulations reproduce the phenomenon which has been termed 'solute trapping,' where concentrations of solute, which are far in excess of the equilibrium concentrations, are observed in the crystal after rapid crystallization. This phenomenon plays an important role in many processes which involve first order phase changes which take place under conditions far from equilibrium. The underlying physical basis for it has not been understood, but these Monte Carlo simulations provide a powerful means for investigating it.

Chance and time: Cutting the Gordian knot

NASA Astrophysics Data System (ADS)

Hagar, Amit

One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous approach away from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions---monstrous Schrodinger cats---and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. A well-known explanatory framework due to Ludwig Boltzmann traces the rarity of "abnormal" thermodynamic phenomena to the scarcity of the initial conditions that lead to it. After all, physical laws are no more than algorithms and these are expected to generate different results according to different initial conditions, hence Boltzmann's insight that violations of thermodynamic laws are possible but highly improbable. Yet Boltzmann introduces probabilities into this explanatory scheme, and since the latter is couched in terms of classical mechanics, these probabilities must be interpreted as a result of ignorance of the exact state the system is in. Quantum mechanics has taught us otherwise. Here the attempts to explain why we never observe macroscopic superpositions have led to different interpretations of the formalism and to different solutions to the quantum measurement problem. These solutions introduce additional interpretations to the meaning of probability over and above ignorance of the definite state of the physical system: quantum probabilities may result from pure chance. Notwithstanding the success of the Boltzmannian framework in explaining the thermodynamic arrow in time it leaves us with a foundational puzzle: how can ignorance play a role in scientific explanation of objective reality? In turns out that two opposing solutions to the quantum measurement problem in which probabilities arise from the stochastic character of the underlying dynamics may scratch this explanatory itch. By offering a dynamical justification to the probabilities employed in classical statistical mechanics these two interpretations complete the Boltzmannian explanatory scheme and allow us to exorcize ignorance from scientific explanations of unobserved phenomena. In this thesis I argue that the puzzle of the thermodynamic arrow in time is closely related to the problem of interpreting quantum mechanics, i.e., to the measurement problem. We may solve one by fiat and thus solve the other, but it seems unwise to try solving them independently. I substantiate this claim by presenting two possible interpretations to non-relativistic quantum mechanics. Differing as they do on the meaning of the probabilities they introduce into the otherwise deterministic dynamics, these interpretations offer alternative explanatory schemes to the standard Boltzmannian statistical mechanical explanation of thermodynamic approach to equilibrium. I then show how notwithstanding their current empirical equivalence, the two approaches diverge at the continental divide between scientific realism and anti-realism.

An extensive study of Bose-Einstein condensation in liquid helium using Tsallis statistics

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-05-01

Realistic scenario can be represented by general canonical ensemble way better than the ideal one, with proper parameter sets involved. We study the Bose-Einstein condensation phenomena of liquid helium within the framework of Tsallis statistics. With a comparatively high value of the deformation parameter q(∼ 1 . 4) , the theoretically calculated value of the critical temperature (Tc) of the phase transition of liquid helium is found to agree with the experimentally determined value (Tc = 2 . 17 K), although they differs from each other for q = 1 (undeformed scenario). This throws a light on the understanding of the phenomenon and connects temperature fluctuation(non-equilibrium conditions) with the interactions between atoms qualitatively. More interactions between atoms give rise to more non-equilibrium conditions which is as expected.

Wash-out in N{sub 2}-dominated leptogenesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hahn-Woernle, F., E-mail: fhahnwo@mppmu.mpg.de

2010-08-01

We study the wash-out of a cosmological baryon asymmetry produced via leptogenesis by subsequent interactions. Therefore we focus on a scenario in which a lepton asymmetry is established in the out-of-equilibrium decays of the next-to-lightest right-handed neutrino. We apply the full classical Boltzmann equations without the assumption of kinetic equilibrium and including all quantum statistical factors to calculate the wash-out of the lepton asymmetry by interactions of the lightest right-handed state. We include scattering processes with top quarks in our analysis. This is of particular interest since the wash-out is enhanced by scatterings and the use of mode equations withmore » quantum statistical distribution functions. In this way we provide a restriction on the parameter space for this scenario.« less

Generalized gas-solid adsorption modeling: Single-component equilibria

DOE PAGES

Ladshaw, Austin; Yiacoumi, Sotira; Tsouris, Costas; ...

2015-01-07

Over the last several decades, modeling of gas–solid adsorption at equilibrium has generally been accomplished through the use of isotherms such as the Freundlich, Langmuir, Tóth, and other similar models. While these models are relatively easy to adapt for describing experimental data, their simplicity limits their generality to be used with many different sets of data. This limitation forces engineers and scientists to test each different model in order to evaluate which one can best describe their data. Additionally, the parameters of these models all have a different physical interpretation, which may have an effect on how they can bemore » further extended into kinetic, thermodynamic, and/or mass transfer models for engineering applications. Therefore, it is paramount to adopt not only a more general isotherm model, but also a concise methodology to reliably optimize for and obtain the parameters of that model. A model of particular interest is the Generalized Statistical Thermodynamic Adsorption (GSTA) isotherm. The GSTA isotherm has enormous flexibility, which could potentially be used to describe a variety of different adsorption systems, but utilizing this model can be fairly difficult due to that flexibility. To circumvent this complication, a comprehensive methodology and computer code has been developed that can perform a full equilibrium analysis of adsorption data for any gas-solid system using the GSTA model. The code has been developed in C/C++ and utilizes a Levenberg–Marquardt’s algorithm to handle the non-linear optimization of the model parameters. Since the GSTA model has an adjustable number of parameters, the code iteratively goes through all number of plausible parameters for each data set and then returns the best solution based on a set of scrutiny criteria. Data sets at different temperatures are analyzed serially and then linear correlations with temperature are made for the parameters of the model. The end result is a full set of optimal GSTA parameters, both dimensional and non-dimensional, as well as the corresponding thermodynamic parameters necessary to predict the behavior of the system at temperatures for which data were not available. It will be shown that this code, utilizing the GSTA model, was able to describe a wide variety of gas-solid adsorption systems at equilibrium.In addition, a physical interpretation of these results will be provided, as well as an alternate derivation of the GSTA model, which intends to reaffirm the physical meaning.« less

Parametric Symmetry Breaking in a Nonlinear Resonator

NASA Astrophysics Data System (ADS)

Leuch, Anina; Papariello, Luca; Zilberberg, Oded; Degen, Christian L.; Chitra, R.; Eichler, Alexander

2016-11-01

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

Fluids by design using chaotic surface waves to create a metafluid that is Newtonian, thermal, and entirely tunable

PubMed Central

Welch, Kyle J.; Liebman-Peláez, Alexander; Corwin, Eric I.

2016-01-01

In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties. PMID:27621467

DREAM3D simulations of inner-belt dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cunningham, Gregory Scott

2015-05-26

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of themore » problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.« less

Evolution of a terrestrial magma ocean: Thermodynamics, kinetics, rheology, convection, differentiation

NASA Technical Reports Server (NTRS)

Solomatov, V. S.; Stevenson, D. J.

1992-01-01

The evolution of an initially totally molten magma ocean is constrained on the basis of analysis of various physical problems in the magma ocean. First of all an equilibrium thermodynamics of the magma ocean is developed in the melting temperature range. The equilibrium thermodynamical parameters are found as functions only of temperature and pressure and are used in the subsequent models of kinetics and convection. Kinematic processes determine the crystal size and also determine a non-equilibrium thermodynamics of the system. Rheology controls all dynamical regimes of the magma ocean. The thermal convection models for different rheological laws are developed for both the laminar convection and for turbulent convection in the case of equilibrium thermodynamics of the multiphase system. The evolution is estimated on the basis of all the above analysis.

Statistical effects related to low numbers of reacting molecules analyzed for a reversible association reaction A + B = C in ideally dispersed systems: An apparent violation of the law of mass action

DOE Office of Scientific and Technical Information (OSTI.GOV)

Szymanski, R., E-mail: rszymans@cbmm.lodz.pl; Sosnowski, S.; Maślanka, Ł.

2016-03-28

Theoretical analysis and computer simulations (Monte Carlo and numerical integration of differential equations) show that the statistical effect of a small number of reacting molecules depends on a way the molecules are distributed among the small volume nano-reactors (droplets in this study). A simple reversible association A + B = C was chosen as a model reaction, enabling to observe both thermodynamic (apparent equilibrium constant) and kinetic effects of a small number of reactant molecules. When substrates are distributed uniformly among droplets, all containing the same equal number of substrate molecules, the apparent equilibrium constant of the association is highermore » than the chemical one (observed in a macroscopic—large volume system). The average rate of the association, being initially independent of the numbers of molecules, becomes (at higher conversions) higher than that in a macroscopic system: the lower the number of substrate molecules in a droplet, the higher is the rate. This results in the correspondingly higher apparent equilibrium constant. A quite opposite behavior is observed when reactant molecules are distributed randomly among droplets: the apparent association rate and equilibrium constants are lower than those observed in large volume systems, being the lower, the lower is the average number of reacting molecules in a droplet. The random distribution of reactant molecules corresponds to ideal (equal sizes of droplets) dispersing of a reaction mixture. Our simulations have shown that when the equilibrated large volume system is dispersed, the resulting droplet system is already at equilibrium and no changes of proportions of droplets differing in reactant compositions can be observed upon prolongation of the reaction time.« less

Kinetics and thermodynamics of living copolymerization processes.

PubMed

Gaspard, Pierre

2016-11-13

Theoretical advances are reported on the kinetics and thermodynamics of free and template-directed living copolymerizations. Until recently, the kinetic theory of these processes had only been established in the fully irreversible regime, in which the attachment rates are only considered. However, the entropy production is infinite in this regime and the approach to thermodynamic equilibrium cannot be investigated. For this purpose, the detachment rates should also be included. Inspite of this complication, the kinetics can be exactly solved in the regimes of steady growth and depolymerization. In this way, analytical expressions are obtained for the mean growth velocity, the statistical properties of the copolymer sequences, as well as the thermodynamic entropy production. The results apply to DNA replication, transcription and translation, allowing us to understand important aspects of molecular evolution.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'. © 2016 The Author(s).

Dynamics and Emergent Structures in Active Fluids

NASA Astrophysics Data System (ADS)

Baskaran, Aparna

2014-03-01

In this talk, we consider an active fluid of colloidal sized particles, with the primary manifestation of activity being a self-replenishing velocity along one body axis of the particle. This is a minimal model for varied systems such as bacterial colonies, cytoskeletal filament motility assays vibrated granular particles and self propelled diffusophoretic colloids, depending on the nature of interaction among the particles. Using microscopic Brownian dynamics simulations, coarse-graining using the tools of non-equilibrium statistical mechanics and analysis of macroscopic hydrodynamic theories, we characterize emergent structures seen in these systems, which are determined by the symmetry of the interactions among the active units, such as propagating density waves, dense stationary bands, asters and phase separated isotropic clusters. We identify a universal mechanism, termed ``self-regulation,'' as the underlying physics that leads to these structures in diverse systems. Support from NSF through DMR-1149266 and DMR-0820492.

On the Boltzmann-Grad Limit for Smooth Hard-Sphere Systems

NASA Astrophysics Data System (ADS)

Tessarotto, Massimo; Cremaschini, Claudio; Mond, Michael; Asci, Claudio; Soranzo, Alessandro; Tironi, Gino

2018-03-01

The problem is posed of the prescription of the so-called Boltzmann-Grad limit operator (L_{BG}) for the N-body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. It is proved, that, despite the non-commutative property of the operator L_{BG}, the Boltzmann equation can nevertheless be uniquely determined. In particular, consistent with the claim of Uffink and Valente (Found Phys 45:404, 2015) that there is "no time-asymmetric ingredient" in its derivation, the Boltzmann equation is shown to be time-reversal symmetric. The proof is couched on the "ab initio" axiomatic approach to the classical statistical mechanics recently developed (Tessarotto et al. in Eur Phys J Plus 128:32, 2013). Implications relevant for the physical interpretation of the Boltzmann H-theorem and the phenomenon of decay to kinetic equilibrium are pointed out.

A probabilistic approach to radiative energy loss calculations for optically thick atmospheres - Hydrogen lines and continua

NASA Technical Reports Server (NTRS)

Canfield, R. C.; Ricchiazzi, P. J.

1980-01-01

An approximate probabilistic radiative transfer equation and the statistical equilibrium equations are simultaneously solved for a model hydrogen atom consisting of three bound levels and ionization continuum. The transfer equation for L-alpha, L-beta, H-alpha, and the Lyman continuum is explicitly solved assuming complete redistribution. The accuracy of this approach is tested by comparing source functions and radiative loss rates to values obtained with a method that solves the exact transfer equation. Two recent model solar-flare chromospheres are used for this test. It is shown that for the test atmospheres the probabilistic method gives values of the radiative loss rate that are characteristically good to a factor of 2. The advantage of this probabilistic approach is that it retains a description of the dominant physical processes of radiative transfer in the complete redistribution case, yet it achieves a major reduction in computational requirements.

Continuity equation for probability as a requirement of inference over paths

NASA Astrophysics Data System (ADS)

González, Diego; Díaz, Daniela; Davis, Sergio

2016-09-01

Local conservation of probability, expressed as the continuity equation, is a central feature of non-equilibrium Statistical Mechanics. In the existing literature, the continuity equation is always motivated by heuristic arguments with no derivation from first principles. In this work we show that the continuity equation is a logical consequence of the laws of probability and the application of the formalism of inference over paths for dynamical systems. That is, the simple postulate that a system moves continuously through time following paths implies the continuity equation. The translation between the language of dynamical paths to the usual representation in terms of probability densities of states is performed by means of an identity derived from Bayes' theorem. The formalism presented here is valid independently of the nature of the system studied: it is applicable to physical systems and also to more abstract dynamics such as financial indicators, population dynamics in ecology among others.

Low-frequency Carbon Radio Recombination Lines. I. Calculations of Departure Coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salgado, F.; Morabito, L. K.; Oonk, J. B. R.

In the first paper of this series, we study the level population problem of recombining carbon ions. We focus our study on high quantum numbers, anticipating observations of carbon radio recombination lines to be carried out by the Low Frequency Array. We solve the level population equation including angular momentum levels with updated collision rates up to high principal quantum numbers. We derive departure coefficients by solving the level population equation in the hydrogenic approximation and including low-temperature dielectronic capture effects. Our results in the hydrogenic approximation agree well with those of previous works. When comparing our results including dielectronicmore » capture, we find differences that we ascribe to updates in the atomic physics (e.g., collision rates) and to the approximate solution method of the statistical equilibrium equations adopted in previous studies. A comparison with observations is discussed in an accompanying article, as radiative transfer effects need to be considered.« less

Kinetics and thermodynamics of living copolymerization processes

NASA Astrophysics Data System (ADS)

Gaspard, Pierre

2016-11-01

Theoretical advances are reported on the kinetics and thermodynamics of free and template-directed living copolymerizations. Until recently, the kinetic theory of these processes had only been established in the fully irreversible regime, in which the attachment rates are only considered. However, the entropy production is infinite in this regime and the approach to thermodynamic equilibrium cannot be investigated. For this purpose, the detachment rates should also be included. Inspite of this complication, the kinetics can be exactly solved in the regimes of steady growth and depolymerization. In this way, analytical expressions are obtained for the mean growth velocity, the statistical properties of the copolymer sequences, as well as the thermodynamic entropy production. The results apply to DNA replication, transcription and translation, allowing us to understand important aspects of molecular evolution. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Kinetics from Replica Exchange Molecular Dynamics Simulations.

PubMed

Stelzl, Lukas S; Hummer, Gerhard

2017-08-08

Transitions between metastable states govern many fundamental processes in physics, chemistry and biology, from nucleation events in phase transitions to the folding of proteins. The free energy surfaces underlying these processes can be obtained from simulations using enhanced sampling methods. However, their altered dynamics makes kinetic and mechanistic information difficult or impossible to extract. Here, we show that, with replica exchange molecular dynamics (REMD), one can not only sample equilibrium properties but also extract kinetic information. For systems that strictly obey first-order kinetics, the procedure to extract rates is rigorous. For actual molecular systems whose long-time dynamics are captured by kinetic rate models, accurate rate coefficients can be determined from the statistics of the transitions between the metastable states at each replica temperature. We demonstrate the practical applicability of the procedure by constructing master equation (Markov state) models of peptide and RNA folding from REMD simulations.

Transfer Entropy and Transient Limits of Computation

PubMed Central

Prokopenko, Mikhail; Lizier, Joseph T.

2014-01-01

Transfer entropy is a recently introduced information-theoretic measure quantifying directed statistical coherence between spatiotemporal processes, and is widely used in diverse fields ranging from finance to neuroscience. However, its relationships to fundamental limits of computation, such as Landauer's limit, remain unknown. Here we show that in order to increase transfer entropy (predictability) by one bit, heat flow must match or exceed Landauer's limit. Importantly, we generalise Landauer's limit to bi-directional information dynamics for non-equilibrium processes, revealing that the limit applies to prediction, in addition to retrodiction (information erasure). Furthermore, the results are related to negentropy, and to Bremermann's limit and the Bekenstein bound, producing, perhaps surprisingly, lower bounds on the computational deceleration and information loss incurred during an increase in predictability about the process. The identified relationships set new computational limits in terms of fundamental physical quantities, and establish transfer entropy as a central measure connecting information theory, thermodynamics and theory of computation. PMID:24953547

An Updated Nuclear Equation of State for Neutron Stars and Supernova Simulations

NASA Astrophysics Data System (ADS)

Meixner, M. A.; Mathews, G. J.; Dalhed, H. E.; Lan, N. Q.

2011-10-01

We present an updated and improved Equation of State based upon the framework originally developed by Bowers & Wilson. The details of the EoS and improvements are described along with a description of how to access this EOS for numerical simulations. Among the improvements are an updated compressibility based upon recent measurements, the possibility of the formation of proton excess (Ye> 0.5) material and an improved treatment of the nuclear statistical equilibrium and the transition to pasta nuclei as the density approaches nuclear matter density. The possibility of a QCD chiral phase transition is also included at densities above nuclear matter density. We show comparisons of this EOS with the other two publicly available equations of state used in supernova collapse simulations. The advantages of the present EoS is that it is easily amenable to phenomenological parameterization to fit observed explosion properties and to accommodate new physical parameters.

The natural history of Halley's comet

NASA Astrophysics Data System (ADS)

McLaughlin, W. I.

1981-07-01

The 1986 apparition of Halley's comet will be the subject of numerous space probes, planned to determine the chemical nature and physical structure of comet nuclei, atmospheres, and ionospheres, as well as comet tails. The problems of cometary origin remain inconclusive, with theories ranging from a purely interstellar origin to their being ejecta from the Galilean satellites of Jupiter. Comets can be grouped into one of two classes, depending on their periodicity, and statistical mechanics of the entire Jovian family of comets can be examined under the equilibrium hypothesis. Comet anatomy estimations have been determined, and there is speculation that comet chemistry may have been a factor in the origin of life on earth. Halley's comet was first noted using Newton's dynamical methods, and Brady (1972) attempted to use the comet as a gravitational probe in search of a trans-Plutonian planet. Halley's orbit is calculated by combination of ancient observations and modern scientific methods.

Modelling the dynamics of crime and punishment. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Abou Chakra, Maria; Hilbe, Christian

2015-03-01

The causes and consequences of crime have fascinated humans for centuries. What makes people break the law, and how does crime affect societies? To approach such questions, it may seem most natural to take the viewpoint of sociology or psychology. However, starting with the pioneering work of Nobel prize laureate Gary S. Becker [1], it has been increasingly emphasized that crime does not need to be the result of insane minds. Instead, committing a crime may be quite rational, given the right circumstances. Whether we are willing to break the law depends on the environment and on the incentives at stake: What are the chances of being caught after committing a certain felony? And how severe is the punishment? From the perspective of economics, crime can often be understood as a result of conscious decisions, as an equilibrium in a strategic game.

Self Organized Criticality as a new paradigm of sleep regulation

NASA Astrophysics Data System (ADS)

Ivanov, Plamen Ch.; Bartsch, Ronny P.

2012-02-01

Humans and animals often exhibit brief awakenings from sleep (arousals), which are traditionally viewed as random disruptions of sleep caused by external stimuli or pathologic perturbations. However, our recent findings show that arousals exhibit complex temporal organization and scale-invariant behavior, characterized by a power-law probability distribution for their durations, while sleep stage durations exhibit exponential behavior. The co-existence of both scale-invariant and exponential processes generated by a single regulatory mechanism has not been observed in physiological systems until now. Such co-existence resembles the dynamical features of non-equilibrium systems exhibiting self-organized criticality (SOC). Our empirical analysis and modeling approaches based on modern concepts from statistical physics indicate that arousals are an integral part of sleep regulation and may be necessary to maintain and regulate healthy sleep by releasing accumulated excitations in the regulatory neuronal networks, following a SOC-type temporal organization.

Active matter logic for autonomous microfluidics

NASA Astrophysics Data System (ADS)

Woodhouse, Francis G.; Dunkel, Jörn

2017-04-01

Chemically or optically powered active matter plays an increasingly important role in materials design, but its computational potential has yet to be explored systematically. The competition between energy consumption and dissipation imposes stringent physical constraints on the information transport in active flow networks, facilitating global optimization strategies that are not well understood. Here, we combine insights from recent microbial experiments with concepts from lattice-field theory and non-equilibrium statistical mechanics to introduce a generic theoretical framework for active matter logic. Highlighting conceptual differences with classical and quantum computation, we demonstrate how the inherent non-locality of incompressible active flow networks can be utilized to construct universal logical operations, Fredkin gates and memory storage in set-reset latches through the synchronized self-organization of many individual network components. Our work lays the conceptual foundation for developing autonomous microfluidic transport devices driven by bacterial fluids, active liquid crystals or chemically engineered motile colloids.

Equilibrium, quasi-equilibrium, and nonequilibrium freezing of mammalian embryos.

PubMed

Mazur, P

1990-08-01

The first successful freezing of early embryos to -196 degrees C in 1972 required that they be cooled slowly at approximately 1 degree C/min to about -70 degrees C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to -70 degrees C, the results is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.

Profiles of equilibrium constants for self-association of aromatic molecules

NASA Astrophysics Data System (ADS)

Beshnova, Daria A.; Lantushenko, Anastasia O.; Davies, David B.; Evstigneev, Maxim P.

2009-04-01

Analysis of the noncovalent, noncooperative self-association of identical aromatic molecules assumes that the equilibrium self-association constants are either independent of the number of molecules (the EK-model) or change progressively with increasing aggregation (the AK-model). The dependence of the self-association constant on the number of molecules in the aggregate (i.e., the profile of the equilibrium constant) was empirically derived in the AK-model but, in order to provide some physical understanding of the profile, it is proposed that the sources for attenuation of the equilibrium constant are the loss of translational and rotational degrees of freedom, the ordering of molecules in the aggregates and the electrostatic contribution (for charged units). Expressions are derived for the profiles of the equilibrium constants for both neutral and charged molecules. Although the EK-model has been widely used in the analysis of experimental data, it is shown in this work that the derived equilibrium constant, KEK, depends on the concentration range used and hence, on the experimental method employed. The relationship has also been demonstrated between the equilibrium constant KEK and the real dimerization constant, KD, which shows that the value of KEK is always lower than KD.

Correspondence between spanning trees and the Ising model on a square lattice

NASA Astrophysics Data System (ADS)

Viswanathan, G. M.

2017-06-01

An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function T (z ) gives the spanning tree constant when evaluated at z =1 , while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function Z (K ) of the Ising model evaluated at the critical temperature K =Kc is related to T (1 ) . Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K ) s e c h 2 K ] 2=k exp[T (k )] , where k =2 tanh(2 K )s e c h (2 K ) . The identical Mahler measure connects the two seemingly disparate quantities T (z ) and Z (K ) . In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.

Fluctuation-dissipation theory of input-output interindustrial relations

NASA Astrophysics Data System (ADS)

Iyetomi, Hiroshi; Nakayama, Yasuhiro; Aoyama, Hideaki; Fujiwara, Yoshi; Ikeda, Yuichi; Souma, Wataru

2011-01-01

In this study, the fluctuation-dissipation theory is invoked to shed light on input-output interindustrial relations at a macroscopic level by its application to indices of industrial production (IIP) data for Japan. Statistical noise arising from finiteness of the time series data is carefully removed by making use of the random matrix theory in an eigenvalue analysis of the correlation matrix; as a result, two dominant eigenmodes are detected. Our previous study successfully used these two modes to demonstrate the existence of intrinsic business cycles. Here a correlation matrix constructed from the two modes describes genuine interindustrial correlations in a statistically meaningful way. Furthermore, it enables us to quantitatively discuss the relationship between shipments of final demand goods and production of intermediate goods in a linear response framework. We also investigate distinctive external stimuli for the Japanese economy exerted by the current global economic crisis. These stimuli are derived from residuals of moving-average fluctuations of the IIP remaining after subtracting the long-period components arising from inherent business cycles. The observation reveals that the fluctuation-dissipation theory is applicable to an economic system that is supposed to be far from physical equilibrium.

Modeling Stochastic Kinetics of Molecular Machines at Multiple Levels: From Molecules to Modules

PubMed Central

Chowdhury, Debashish

2013-01-01

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here. PMID:23746505

Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth

PubMed Central

Sornette, Didier

2002-01-01

We propose that catastrophic events are “outliers” with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. We describe a unifying approach for modeling and predicting these catastrophic events or “ruptures,” that is, sudden transitions from a quiescent state to a crisis. Such ruptures involve interactions between structures at many different scales. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence, and abrupt changes of weather regimes, financial crashes, and human parturition (birth). Future improvements will involve combining ideas and tools from statistical physics and artificial/computational intelligence, to identify and classify possible universal structures that occur at different scales, and to develop application-specific methodologies to use these structures for prediction of the “crises” known to arise in each application of interest. We live on a planet and in a society with intermittent dynamics rather than a state of equilibrium, and so there is a growing and urgent need to sensitize students and citizens to the importance and impacts of ruptures in their multiple forms. PMID:11875205

Towards a statistical mechanical theory of active fluids.

PubMed

Marini Bettolo Marconi, Umberto; Maggi, Claudio

2015-12-07

We present a stochastic description of a model of N mutually interacting active particles in the presence of external fields and characterize its steady state behavior in the absence of currents. To reproduce the effects of the experimentally observed persistence of the trajectories of the active particles we consider a Gaussian force having a non-vanishing correlation time τ, whose finiteness is a measure of the activity of the system. With these ingredients we show that it is possible to develop a statistical mechanical approach similar to the one employed in the study of equilibrium liquids and to obtain the explicit form of the many-particle distribution function by means of the multidimensional unified colored noise approximation. Such a distribution plays a role analogous to the Gibbs distribution in equilibrium statistical mechanics and provides complete information about the microscopic state of the system. From here we develop a method to determine the one- and two-particle distribution functions in the spirit of the Born-Green-Yvon (BGY) equations of equilibrium statistical mechanics. The resulting equations which contain extra-correlations induced by the activity allow us to determine the stationary density profiles in the presence of external fields, the pair correlations and the pressure of active fluids. In the low density regime we obtained the effective pair potential ϕ(r) acting between two isolated particles separated by a distance, r, showing the existence of an effective attraction between them induced by activity. Based on these results, in the second half of the paper we propose a mean field theory as an approach simpler than the BGY hierarchy and use it to derive a van der Waals expression of the equation of state.

Teaching an Old Dog an Old Trick: FREE-FIX and Free-Boundary Axisymmetric MHD Equilibrium

NASA Astrophysics Data System (ADS)

Guazzotto, Luca

2015-11-01

A common task in plasma physics research is the calculation of an axisymmetric equilibrium for tokamak modeling. The main unknown of the problem is the magnetic poloidal flux ψ. The easiest approach is to assign the shape of the plasma and only solve the equilibrium problem in the plasma / closed-field-lines region (the ``fixed-boundary approach''). Often, one may also need the vacuum fields, i.e. the equilibrium in the open-field-lines region, requiring either coil currents or ψ on some closed curve outside the plasma to be assigned (the ``free-boundary approach''). Going from one approach to the other is a textbook problem, involving the calculation of Green's functions and surface integrals in the plasma. However, no tools are readily available to perform this task. Here we present a code (FREE-FIX) to compute a boundary condition for a free-boundary equilibrium given only the corresponding fixed-boundary equilibrium. An improvement to the standard solution method, allowing for much faster calculations, is presented. Applications are discussed. PPPL fund 245139 and DOE grant G00009102.

Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium.

PubMed

Ceccato, Alessandro; Frezzato, Diego

2018-02-14

The chemical Langevin equation and the associated chemical Fokker-Planck equation are well-known continuous approximations of the discrete stochastic evolution of reaction networks. In this work, we show that these approximations suffer from a physical inconsistency, namely, the presence of nonphysical probability currents at the thermal equilibrium even for closed and fully detailed-balanced kinetic schemes. An illustration is given for a model case.

Maya Healers' Conception of Cancer as Revealed by Comparison With Western Medicine

PubMed Central

Gharzouzi, Eduardo; Renner, Christoph

2016-01-01

Purpose Cultural diversity in clinical encounters is common, yet mental constructions regarding cancer that influence expected treatment are poorly studied for indigenous people. We explored Maya healers' conceptions, diagnosis, and treatment of cancer to remedy this problem. Methods In-depth structured interviews with 67 traditional Maya healers in Guatemala across Kaqchikel, Kiche', Mam, Mopan, and Q'eqchi' ethnolinguistic groups were conducted by using a transdisciplinary format. Analysis of qualitative data in categorized matrixes allowed for statistical examination of tendencies and the results were complemented by validation workshops with Maya representatives. Results Maya classification of diseases has broad categories of malignant diseases including cancer. Specific Maya terms might equate to particular cancer types, which would open new avenues for research. Notions of malignancy and metastasis were expressed by healers as core characteristics of cancer, a disease believed to be both material and spiritual. Resolution of and/or treatment for cancer is based on restoring physical, mental, emotional, and spiritual equilibrium of the patient and extending that equilibrium to his larger social circle. Conclusion Maya conceptions of cancer determine how traditional diagnostic tools are used and dictate treatment options that include the patient's social-spiritual support system. Official health care providers' understanding of these principles can improve implementation of culturally appropriate protocols that increase indigenous patients' compliance and reduce rates of treatment abandonment. PMID:28717684

Equilibrium and diffusion studies of metal-hydrogen systems

NASA Astrophysics Data System (ADS)

Maroevic, Petar

Several new methods and models have been developed pertaining to equilibrium properties of hydrogen in random binary substitutional alloys at room and lower temperatures, describing both statistics and kinetics of hydrogen in them. They represent a solution to the problem of the complete Fermi-Dirac description which is physically appropriate for these systems. Hydrogen diffusion which proceeds via lattice assisted quantum tunneling at room and lower temperatures requires a new and different description from the one based on the thermal hopping picture, which pertains only to relatively high temperatures. It is also shown that the analogs of the solution to the Fermi-Dirac problem of hydrogen can be successfully applied to the description of vacancies in a hydrogenated system, a phenomena known to occur due to high hydrogen-vacancy binding energies and the creation of hydrogen-vacancy clusters. The solution based on this model applies to much lower temperatures and higher concentrations than the tradition alone. This methodology has also been applied to the surface problem where very large vacancy and hydrogen concentrations occur. This is of special importance since mechanical properties are known to be greatly affected by the surface. As another consequence of hydrogen induced vacancies, hydrogen induced lattice migration (HILM) occurs. This has been demonstrated in our electrical resistivity study of palladium wires where recrystallization and annealing effects were observed upon hydrogen-heat-treatment (HHT).

Emergent inequality and self-organized social classes in a network of power and frustration

DOE PAGES

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

2017-02-17

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution ofmore » wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.« less

Emergent inequality and self-organized social classes in a network of power and frustration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution ofmore » wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.« less

Emergent inequality and self-organized social classes in a network of power and frustration

PubMed Central

Mahault, Benoit; Saxena, Avadh

2017-01-01

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes. PMID:28212440

Emergent inequality and self-organized social classes in a network of power and frustration.

PubMed

Mahault, Benoit; Saxena, Avadh; Nisoli, Cristiano

2017-01-01

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.

Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas.

PubMed

Brey, J Javier; Maynar, Pablo; García de Soria, M I

2016-10-01

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle diameters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function S(t) is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, S(t) increases monotonically in time, until the system reaches a stationary inhomogeneous state, when S becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and molecular dynamics simulations are used to verify some of the theoretical predictions.

Tidal Heating in Enceladus

NASA Astrophysics Data System (ADS)

Meyer, Jennifer; Wisdom, J.

2007-07-01

The heating in Enceladus in an equilibrium resonant configuration with other saturnian satellites can be estimated independently of the physical properties of Enceladus. Our results update the values obtained for the equilibrium tidal heating found by Lissauer et al. (1984) and Peale (2003). We find that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus, and current heating rates are even less for conventional estimates of the Love number for Enceladus. Even allowing for a much larger dynamic Love number, as can occur in viscoelastic models (Ross and Schubert, 1989), the equilibrium tidal heating is less than the heat observed to be coming from Enceladus. One resolution is that the tidal equilibrium is unstable and that the system oscillates about equilibrium. Yoder (1981) suggested that Enceladus might oscillate about equilibrium if the Q of Enceladus is stress dependent. An alternate suggestion was made by Ojakangas and Stevenson (1986), who emphasized the possible temperature dependence of Q. In these models Enceladus would now be releasing heat stored during a recent high eccentricity phase. However, we have shown that the Ojakangas and Stevenson model does not produce oscillations for parameters appropriate for Enceladus. Other low-order resonance configurations are possible for the saturnian satellites in the past. These include the 3:2 Mimas-Enceladus and the 3:4 Enceladus-Tethys resonances. The latter resonance has no equilibrium because the orbits are diverging, and the former has an equilibrium heating rate of only 0.48 GW. So equilibrium heating at past resonances is no more successful at explaining past resurfacing events than equilibrium heating is at explaining the present activity.

Probability distributions of molecular observables computed from Markov models. II. Uncertainties in observables and their time-evolution

NASA Astrophysics Data System (ADS)

Chodera, John D.; Noé, Frank

2010-09-01

Discrete-state Markov (or master equation) models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic (such as the correlation function) of the equilibrium dynamics of a single molecule. Without meaningful error bars (which arise from both approximation and statistical error), there is no way to determine whether the deviations between model and experiment are statistically meaningful. Previous work has demonstrated that a Bayesian method that enforces microscopic reversibility can be used to characterize the statistical component of correlated uncertainties in state-to-state transition probabilities (and functions thereof) for a model inferred from molecular simulation data. Here, we extend this approach to include the uncertainty in observables that are functions of molecular conformation (such as surrogate spectroscopic signals) characterizing each state, permitting the full statistical uncertainty in computed spectroscopic experiments to be assessed. We test the approach in a simple model system to demonstrate that the computed uncertainties provide a useful indicator of statistical variation, and then apply it to the computation of the fluorescence autocorrelation function measured for a dye-labeled peptide previously studied by both experiment and simulation.

Ergodicity in natural earthquake fault networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tiampo, K. F.; Rundle, J. B.; Holliday, J.

2007-06-15

Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C. D. Ferguson, W. Klein, and J. B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibriumlike systems with statistically stationary dynamics over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system, by means of the Thirumalai-Mountain (TM) fluctuation metric developed in the study of diffusive systems [K. F.more » Tiampo, J. B. Rundle, W. Klein, J. S. Sa Martins, and C. D. Ferguson, Phys. Rev. Lett. 91, 238501 (2003)]. We analyze the seismicity of three naturally occurring earthquake fault networks from a variety of tectonic settings in an attempt to investigate the range of applicability of effective ergodicity, using the TM metric and other related statistics. Results suggest that, once variations in the catalog data resulting from technical and network issues are accounted for, all of these natural earthquake systems display stationary periods of metastable equilibrium and effective ergodicity that are disrupted by large events. We conclude that a constant rate of events is an important prerequisite for these periods of punctuated ergodicity and that, while the level of temporal variability in the spatial statistics is the controlling factor in the ergodic behavior of seismic networks, no single statistic is sufficient to ensure quantification of ergodicity. Ergodicity in this application not only requires that the system be stationary for these networks at the applicable spatial and temporal scales, but also implies that they are in a state of metastable equilibrium, one in which the ensemble averages can be substituted for temporal averages in studying their spatiotemporal evolution.« less

Bounded energy states in homogeneous turbulent shear flow - An alternative view

NASA Technical Reports Server (NTRS)

Bernard, P. S.; Speziale, C. G.

1992-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.

Vapor-Liquid Equilibrium in the Mixture 1,1-Difluoroethane C2H4F2 + C4H8 2-Methylpropene (EVLM1131, LB5730_E)

NASA Astrophysics Data System (ADS)

Cibulka, I.; Fontaine, J.-C.; Sosnkowska-Kehiaian, K.; Kehiaian, H. V.

This document is part of Subvolume A 'Binary Liquid Systems of Nonelectrolytes I' of Volume 26 'Heats of Mixing, Vapor-Liquid Equilibrium, and Volumetric Properties of Mixtures and Solutions' of Landolt-Börnstein Group IV 'Physical Chemistry'. It contains the Chapter 'Vapor-Liquid Equilibrium in the Mixture 1,1-Difluoroethane C2H4F2 + C4H8 2-Methylpropene (EVLM1131, LB5730_E)' providing data from direct measurement of pressure and mole fraction in vapor phase at variable mole fraction in liquid phase and constant temperature.

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

NASA Technical Reports Server (NTRS)

Lerche, I.; Low, B. C.

1980-01-01

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

Condensate statistics in interacting and ideal dilute bose gases

PubMed

Kocharovsky; Kocharovsky; Scully

2000-03-13

We obtain analytical formulas for the statistics, in particular, for the characteristic function and all cumulants, of the Bose-Einstein condensate in dilute weakly interacting and ideal equilibrium gases in the canonical ensemble via the particle-number-conserving operator formalism of Girardeau and Arnowitt. We prove that the ground-state occupation statistics is not Gaussian even in the thermodynamic limit. We calculate the effect of Bogoliubov coupling on suppression of ground-state occupation fluctuations and show that they are governed by a pair-correlation, squeezing mechanism.

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

NASA Astrophysics Data System (ADS)

van Lith, Janneke

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 averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

Random bursts determine dynamics of active filaments.

PubMed

Weber, Christoph A; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S; Bausch, Andreas R; Frey, Erwin

2015-08-25

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model.

Random bursts determine dynamics of active filaments

PubMed Central

Weber, Christoph A.; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S.; Bausch, Andreas R.; Frey, Erwin

2015-01-01

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system’s dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. PMID:26261319

A new equation of state Based on Nuclear Statistical Equilibrium for Core-Collapse Simulations

NASA Astrophysics Data System (ADS)

Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki

2012-09-01

We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simunovic, Srdjan; Piro, Markus H.A.

Thermochimica is a software library that determines a unique combination of phases and their compositions at thermochemical equilibrium. Thermochimica can be used for stand-alone calculations or it can be directly coupled to other codes. This release of the software does not have a graphical user interface (GUI) and it can be executed from the command line or from an Application Programming Interface (API). Also, it is not intended for thermodynamic model development or for constructing phase diagrams. The main purpose of the software is to be directly coupled with a multi-physics code to provide material properties and boundary conditions formore » various physical phenomena. Significant research efforts have been dedicated to enhance computational performance through advanced algorithm development, such as improved estimation techniques and non-linear solvers. Various useful parameters can be provided as output from Thermochimica, such as: determination of which phases are stable at equilibrium, the mass of solution species and phases at equilibrium, mole fractions of solution phase constituents, thermochemical activities (which are related to partial pressures for gaseous species), chemical potentials of solution species and phases, and integral Gibbs energy (referenced relative to standard state). The overall goal is to provide an open source computational tool to enhance the predictive capability of multi-physics codes without significantly impeding computational performance.« less

Theoretical models of non-Maxwellian equilibria for one-dimensional collisionless plasmas

NASA Astrophysics Data System (ADS)

Allanson, O.; Neukirch, T.; Wilson, F.; Troscheit, S.

2016-12-01

It is ideal to use exact equilibrium solutions of the steady state Vlasov-Maxwell system to intialise collsionless simulations. However, exact equilibrium distribution functions (DFs) for a given macroscopic configuration are typically unknown, and it is common to resort to using `flow-shifted' Maxwellian DFs in their stead. These DFs may be consistent with a macrosopic system with the target number density and current density, but could well have inaccurate higher order moments. We present recent theoretical work on the `inverse problem in Vlasov-Maxwell equilibria', namely calculating an exact solution of the Vlasov equation for a specific given magnetic field. In particular, we focus on one-dimensional geometries in Cartesian (current sheets) coordinates.1. From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials: (O. Allanson, T. Neukirch, S. Troscheit and F. Wilson, Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )2. An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta: (O. Allanson, T. Neukirch, F. Wilson and S. Troscheit, Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])3. Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field (O. Allanson, F. Wilson and T. Neukirch, (2016)) (accepted, Physics of Plasmas)

Final Report on DTRA Basic Research Project #BRCALL08-Per3-C-2-0006 "High-Z Non-Equilibrium Physics and Bright X-ray Sources with New Laser Targets"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colvin, Jeffrey D.

This project had two major goals. Final Goal: obtain spectrally resolved, absolutely calibrated x-ray emission data from uniquely uniform mm-scale near-critical-density high-Z plasmas not in local thermodynamic equilibrium (LTE) to benchmark modern detailed atomic physics models. Scientific significance: advance understanding of non-LTE atomic physics. Intermediate Goal: develop new nano-fabrication techniques to make suitable laser targets that form the required highly uniform non-LTE plasmas when illuminated by high-intensity laser light. Scientific significance: advance understanding of nano-science. The new knowledge will allow us to make x-ray sources that are bright at the photon energies of most interest for testing radiation hardening technologies,more » the spectral energy range where current x-ray sources are weak. All project goals were met.« less

Stress-induced electric current fluctuations in rocks: a superstatistical model

NASA Astrophysics Data System (ADS)

Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter

2017-04-01

We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local equilibrium processes whose variance fluctuates over time. The appearance of q-Gaussian statistics are caused by the fluctuating β parameter, which effectively models the fluctuating energy dissipation rate in the system. This concept is known as superstatistics and is physically relevant for modelling driven non-equilibrium systems where the environmental conditions fluctuate on a large scale. The idea is that the environmental variable, such as temperature or pressure, changes so slowly that a rapidly fluctuating variable within that environment has time to relax back to equilibrium between each change in the environment. The application of superstatistical techniques to our experimental electric current fluctuations show that they can indeed be described, to good approximation, by the superposition of local Gaussian processes with fluctuating variance. We conclude, then, that the measured electric current fluctuates in response to intermittent energy dissipation and is driven to varying temporary local equilibria during deformation by the variations in stress intensity. The advantage of this technique is that, once the model has been established to be a good description of the system in question, the average β parameter (a measure of the average energy dissipation rate) for the system can be obtained simply from the macroscopic q-Gaussian distribution parameters.

"Non-equilibrium" block copolymer micelles with glassy cores: a predictive approach based on theory of equilibrium micelles.

PubMed

Nagarajan, Ramanathan

2015-07-01

Micelles generated in water from most amphiphilic block copolymers are widely recognized to be non-equilibrium structures. Typically, the micelles are prepared by a kinetic process, first allowing molecular scale dissolution of the block copolymer in a common solvent that likes both the blocks and then gradually replacing the common solvent by water to promote the hydrophobic blocks to aggregate and create the micelles. The non-equilibrium nature of the micelle originates from the fact that dynamic exchange between the block copolymer molecules in the micelle and the singly dispersed block copolymer molecules in water is suppressed, because of the glassy nature of the core forming polymer block and/or its very large hydrophobicity. Although most amphiphilic block copolymers generate such non-equilibrium micelles, no theoretical approach to a priori predict the micelle characteristics currently exists. In this work, we propose a predictive approach for non-equilibrium micelles with glassy cores by applying the equilibrium theory of micelles in two steps. In the first, we calculate the properties of micelles formed in the mixed solvent while true equilibrium prevails, until the micelle core becomes glassy. In the second step, we freeze the micelle aggregation number at this glassy state and calculate the corona dimension from the equilibrium theory of micelles. The condition when the micelle core becomes glassy is independently determined from a statistical thermodynamic treatment of diluent effect on polymer glass transition temperature. The predictions based on this "non-equilibrium" model compare reasonably well with experimental data for polystyrene-polyethylene oxide diblock copolymer, which is the most extensively studied system in the literature. In contrast, the application of the equilibrium model to describe such a system significantly overpredicts the micelle core and corona dimensions and the aggregation number. The non-equilibrium model suggests ways to obtain different micelle sizes for the same block copolymer, by the choices we can make of the common solvent and the mode of solvent substitution. Published by Elsevier Inc.

Determination and theoretical aspects of the equilibrium between dissolved organic matter and hydrophobic organic micropollutants in water (Kdoc).

PubMed

Krop, H B; van Noort, P C; Govers, H A

2001-01-01

Literature on the equilibrium constant for distribution between dissolved organic carbon (DOC) (Kdoc) data of strongly hydrophobic organic contaminants were collected and critically analyzed. About 900 Kdoc entries for experimental values were retrieved and tabulated, including those factors that can influence them. In addition, quantitative structure-activity relationship (QSAR) prediction equations were retrieved and tabulated. Whether a partition or association process between the contaminant and DOC takes place could not be fully established, but indications toward an association process are strong in several cases. Equilibrium between a contaminant and DOC in solution was shown to be achieved within a minute. When the equilibrium shifts in time, this was caused by either a physical or chemical change of the DOC, affecting the lighter fractions most. Adsorption isotherms turned out to be linear in the contaminant concentration for the relevant DOC concentration up to 100 mg of C/L. Eighteen experimental methods have been developed for the determination of the pertinent distribution constant. Experimental Kdoc values revealed the expected high correlation with partition coefficients over n-octanol and water (Kow) for all experimental methods, except for the HPLC and apparent solubility (AS) method. Only fluorescence quenching (FQ) and solid-phase microextraction (SPME) methods could quantify fast equilibration. Only 21% of the experimental values had a 95% confidence interval, which was statistically significantly different from zero. Variation in Kdoc values was shown to be high, caused mainly by the large variation of DOC in water samples. Even DOC from one sample gave different equilibrium constants for different DOC fractions. Measured Kdoc values should, therefore, be regarded as average values. Kdoc was shown to increase on increasing molecular mass, indicating that the molecular mass distribution is a proper normalization function for the average Kdoc at the current state of knowledge. The weakly bound fraction could easily be desorbed when other adsorbing media, such as a SepPak column or living organism, are present. The amount that moves from the DOC to the other medium will depend, among other reasons, on the size of the labile DOC fraction and the equilibrium constant of the other medium. Variation of Kdoc with temperature turned out to be small, probably caused by a small enthalpy of transfer from water to DOC. Ionic strength turned out to be more important, leading to changes of a factor of 2-5. The direction of this effect depends on the type of ion. With respect to QSAR relationships between Kdoc and macroscopic or molecular descriptors, it was concluded that only a small number of equations are available in the literature, for apolar compounds only, and with poor statistics and predictive power. Therefore, a first requirement is the improvement of the availability and quality of experimental data. Along with this, theoretical (mechanistic) models for the relationship between DOC plus contaminant descriptors on the one side and Kdoc on the other should be further developed. Correlations between Kdoc and Kow and those between the soil-water partition constant (Koc) and Kow were significantly different only in the case of natural aquatic DOC, pointing at substantial differences between these two types of organic material and at a high correspondence for other types of commercial and natural DOC.

Is “morphodynamic equilibrium” an oxymoron?

USGS Publications Warehouse

Zhou, Zeng; Coco, Giovanni; Townend, Ian; Olabarrieta, Maitane; van der Wegen, Mick; Gong, Zheng; D'Alpaos, Andrea; Gao, Shu; Jaffe, Bruce E.; Gelfenbaum, Guy R.; He, Qing; Wang, Yaping; Lanzoni, Stefano; Wang, Zhengbing; Winterwerp, Han; Zhang, Changkuan

2017-01-01

Morphodynamic equilibrium is a widely adopted yet elusive concept in the field of geomorphology of coasts, rivers and estuaries. Based on the Exner equation, an expression of mass conservation of sediment, we distinguish three types of equilibrium defined as static and dynamic, of which two different types exist. Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use. The choice of a temporal scale is imperative to analyse the type of equilibrium. We discuss the difference between morphodynamic equilibrium in the “real world” (nature) and the “virtual world” (model). Modelling studies rely on simplifications of the real world and lead to understanding of process interactions. A variety of factors affect the use of virtual-world predictions in the real world (e.g., variability in environmental drivers and variability in the setting) so that the concept of morphodynamic equilibrium should be mathematically unequivocal in the virtual world and interpreted over the appropriate spatial and temporal scale in the real world. We draw examples from estuarine settings which are subject to various governing factors which broadly include hydrodynamics, sedimentology and landscape setting. Following the traditional “tide-wave-river” ternary diagram, we summarize studies to date that explore the “virtual world”, discuss the type of equilibrium reached and how it relates to the real world.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

NASA Astrophysics Data System (ADS)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory physics with a bio focus. Supported by NSF DUE.

Physics of base-pairing dynamics in DNA

NASA Astrophysics Data System (ADS)

Manghi, Manoel; Destainville, Nicolas

2016-05-01

As a key molecule of life, Deoxyribo-Nucleic Acid (DNA) is the focus of numbers of investigations with the help of biological, chemical and physical techniques. From a physical point of view, both experimental and theoretical works have brought quantitative insights into DNA base-pairing dynamics that we review in this Report, putting emphasis on theoretical developments. We discuss the dynamics at the base-pair scale and its pivotal coupling with the polymer one, with a polymerization index running from a few nucleotides to tens of kilo-bases. This includes opening and closure of short hairpins and oligomers as well as zipping and unwinding of long macromolecules. We review how different physical mechanisms are either used by Nature or utilized in biotechnological processes to separate the two intertwined DNA strands, by insisting on quantitative results. They go from thermally-assisted denaturation bubble nucleation to force- or torque-driven mechanisms. We show that the helical character of the molecule, possibly supercoiled, can play a key role in many denaturation and renaturation processes. We categorize the mechanisms according to the relative timescales associated with base-pairing and chain orientational degrees of freedom such as bending and torsional elastic ones. In some specific situations, these chain orientational degrees of freedom can be integrated out, and the quasi-static approximation is valid. The complex dynamics then reduces to the diffusion in a low-dimensional free-energy landscape. In contrast, some important cases of experimental interest necessarily appeal to far-from-equilibrium statistical mechanics and hydrodynamics.

An accurate symplectic calculation of the inboard magnetic footprint from statistical topological noise and field errors in the DIII-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Punjabi, Alkesh; Ali, Halima

2011-02-15

Any canonical transformation of Hamiltonian equations is symplectic, and any area-preserving transformation in 2D is a symplectomorphism. Based on these, a discrete symplectic map and its continuous symplectic analog are derived for forward magnetic field line trajectories in natural canonical coordinates. The unperturbed axisymmetric Hamiltonian for magnetic field lines is constructed from the experimental data in the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The equilibrium Hamiltonian is a highly accurate, analytic, and realistic representation of the magnetic geometry of the DIII-D. These symplectic mathematical maps are used to calculate the magnetic footprint onmore » the inboard collector plate in the DIII-D. Internal statistical topological noise and field errors are irreducible and ubiquitous in magnetic confinement schemes for fusion. It is important to know the stochasticity and magnetic footprint from noise and error fields. The estimates of the spectrum and mode amplitudes of the spatial topological noise and magnetic errors in the DIII-D are used as magnetic perturbation. The discrete and continuous symplectic maps are used to calculate the magnetic footprint on the inboard collector plate of the DIII-D by inverting the natural coordinates to physical coordinates. The combination of highly accurate equilibrium generating function, natural canonical coordinates, symplecticity, and small step-size together gives a very accurate calculation of magnetic footprint. Radial variation of magnetic perturbation and the response of plasma to perturbation are not included. The inboard footprint from noise and errors are dominated by m=3, n=1 mode. The footprint is in the form of a toroidally winding helical strip. The width of stochastic layer scales as (1/2) power of amplitude. The area of footprint scales as first power of amplitude. The physical parameters such as toroidal angle, length, and poloidal angle covered before striking, and the safety factor all have fractal structure. The average field diffusion near the X-point for lines that strike and that do not strike differs by about three to four orders of magnitude. The magnetic footprint gives the maximal bounds on size and heat flux density on collector plate.« less

Implementation of Radiation, Ablation, and Free Energy Minimization Modules for Coupled Simulations of Hypersonic Flow

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; Johnston, Christopher O.; Thompson, Richard A.

2009-01-01

A description of models and boundary conditions required for coupling radiation and ablation physics to a hypersonic flow simulation is provided. Chemical equilibrium routines for varying elemental mass fraction are required in the flow solver to integrate with the equilibrium chemistry assumption employed in the ablation models. The capability also enables an equilibrium catalytic wall boundary condition in the non-ablating case. The paper focuses on numerical implementation issues using FIRE II, Mars return, and Apollo 4 applications to provide context for discussion. Variable relaxation factors applied to the Jacobian elements of partial equilibrium relations required for convergence are defined. Challenges of strong radiation coupling in a shock capturing algorithm are addressed. Results are presented to show how the current suite of models responds to a wide variety of conditions involving coupled radiation and ablation.

Effect of a Perturbation on the Chemical Equilibrium: Comparison with Le Châtelier's Principle

NASA Astrophysics Data System (ADS)

Martínez Torres, Emilio

2007-03-01

This article develops a general thermodynamic treatment to predict the direction of shift in a chemical equilibrium when it is subjected to a stress. This treatment gives an inequality that relates the change in the perturbed variable and the change that the equilibrium shift produces in the conjugated variable. To illustrate the generality of this approach, it has been applied to predict the direction of shift caused by changes of pressure, volume, and amount of substance. In this last case, the well-known unexpected shift in the ammonia synthesis equilibrium upon addition of nitrogen is easily explained. From the above referred inequality and the stability criteria of thermodynamics some conclusions have been obtained about the direction of shift in terms of extensive and extensive variables. This article is suitable for physical chemistry courses.

Statistical investigation of simulated intestinal fluid composition on the equilibrium solubility of biopharmaceutics classification system class II drugs.

PubMed

Khadra, Ibrahim; Zhou, Zhou; Dunn, Claire; Wilson, Clive G; Halbert, Gavin

2015-01-25

A drug's solubility and dissolution behaviour within the gastrointestinal tract is a key property for successful administration by the oral route and one of the key factors in the biopharmaceutics classification system. This property can be determined by investigating drug solubility in human intestinal fluid (HIF) but this is difficult to obtain and highly variable, which has led to the development of multiple simulated intestinal fluid (SIF) recipes. Using a statistical design of experiment (DoE) technique this paper has investigated the effects and interactions on equilibrium drug solubility of seven typical SIF components (sodium taurocholate, lecithin, sodium phosphate, sodium chloride, pH, pancreatin and sodium oleate) within concentration ranges relevant to human intestinal fluid values. A range of poorly soluble drugs with acidic (naproxen, indomethacin, phenytoin, and piroxicam), basic (aprepitant, carvedilol, zafirlukast, tadalafil) or neutral (fenofibrate, griseofulvin, felodipine and probucol) properties have been investigated. The equilibrium solubility results determined are comparable with literature studies of the drugs in either HIF or SIF indicating that the DoE is operating in the correct space. With the exception of pancreatin, all of the factors individually had a statistically significant influence on equilibrium solubility with variations in magnitude of effect between the acidic and basic or neutral compounds and drug specific interactions were evident. Interestingly for the neutral compounds pH was the factor with the second largest solubility effect. Around one third of all the possible factor combinations showed a significant influence on equilibrium solubility with variations in interaction significance and magnitude of effect between the acidic and basic or neutral compounds. The least number of significant media component interactions were noted for the acidic compounds with three and the greatest for the neutral compounds at seven, with again drug specific effects evident. This indicates that a drug's equilibrium solubility in SIF is influenced depending upon drug type by between eight to fourteen individual or combinations of media components with some of these drug specific. This illustrates the complex nature of these fluids and provides for individual drugs a visualisation of the possible solubility envelope within the gastrointestinal tract, which may be of importance for modelling in vivo behaviour. In addition the results indicate that the design of experiment approach can be employed to provide greater detail of drug solubility behaviour, possible drug specific interactions and influence of variations in gastrointestinal media components due to disease. The approach is also feasible and amenable to adaptation for high throughput screening of drug candidates. Copyright © 2014 Elsevier B.V. All rights reserved.

Statistical mechanics and combinatorics of some discrete lattice models

NASA Astrophysics Data System (ADS)

Ayyer, Arvind

Many problems in statistical physics involve enumeration of certain objects. In this thesis, we apply ideas from combinatorics and statistical physics to understand three different lattice models. (I) We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites and second class particles constrained to lie the system. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. We show in a conceptually simple way how pinned and unpinned (fat) shocks determine the general structure of the phase diagram. We also point out some unexpected features in the microscopic structure of the NESS both for finite L and in the limit L → infinity. In the latter case the local distribution of second class particles is given by an equilibrium pressure ensemble with a pair potential between neighboring particles which grows logarithmically with distance. (II) We model a long linear polymer constrained between two plates as a walk on a two-dimensional lattice constrained to lie between two lines, x = y and x = y+w, which interacts with these lines via contact parameters s and t. The atomic steps of the walk can be taken to be from an arbitrary but fixed set S with the only condition being that the first coordinate of every element in S is strictly positive. For any such S and any w, we prescribe general algorithms (fully implemented in Maple) for the automated calculation of several mathematical and physical quantities of interest. (III) Ferrers (or Young) diagrams are very classical objects in representation theory, whose half-perimeter generating function of Ferrers diagrams is a straightforward rational function. We construct two new classes of Ferrers diagrams, which we call wicketed and gated Ferrers diagrams, which have internal voids in the shape of Ferrers diagrams, and calculate their half-perimeter generating functions, one of which is closely related to the generating function of the Catalan numbers, using a more abstract version of the usual transfer matrix method.

The photon gas formulation of thermal radiation

NASA Technical Reports Server (NTRS)

Ried, R. C., Jr.

1975-01-01

A statistical consideration of the energy, the linear momentum, and the angular momentum of the photons that make up a thermal radiation field was presented. A general nonequilibrium statistical thermodynamics approach toward a macroscopic description of thermal radiation transport was developed and then applied to the restricted equilibrium statistical thermostatics derivation of the energy, linear momentum, and intrinsic angular momentum equations for an isotropic photon gas. A brief treatment of a nonisotropic photon gas, as an example of the results produced by the nonequilibrium statistical thermodynamics approach, was given. The relativistic variation of temperature and the invariance of entropy were illustrated.

A Printed Equilibrium Dialysis Device with Integrated Membranes for Improved Binding Affinity Measurements.

PubMed

Pinger, Cody W; Heller, Andrew A; Spence, Dana M

2017-07-18

Equilibrium dialysis is a simple and effective technique used for investigating the binding of small molecules and ions to proteins. A three-dimensional (3D) printer was used to create a device capable of measuring binding constants between a protein and a small ion based on equilibrium dialysis. Specifically, the technology described here enables the user to customize an equilibrium dialysis device to fit their own experiments by choosing membranes of various material and molecular-weight cutoff values. The device has dimensions similar to that of a standard 96-well plate, thus being amenable to automated sample handlers and multichannel pipettes. The device consists of a printed base that hosts multiple windows containing a porous regenerated-cellulose membrane with a molecular-weight cutoff of ∼3500 Da. A key step in the fabrication process is a print-pause-print approach for integrating membranes directly into the windows subsequently inserted into the base. The integrated membranes display no leaking upon placement into the base. After characterizing the system's requirements for reaching equilibrium, the device was used to successfully measure an equilibrium dissociation constant for Zn 2+ and human serum albumin (K d = (5.62 ± 0.93) × 10 -7 M) under physiological conditions that is statistically equal to the constants reported in the literature.

Fundamentals of Physics, Part 2 (Chapters 12-20)

NASA Astrophysics Data System (ADS)

Halliday, David; Resnick, Robert; Walker, Jearl

2003-12-01

Chapter 12 Equilibrium and Elasticity. What injury can occur to a rock climber hanging by a crimp hold? 12-1 What Is Physics? 12-2 Equilibrium. 12-3 The Requirements of Equilibrium. 12-4 The Center of Gravity. 12-5 Some Examples of Static Equilibrium. 12-6 Indeterminate Structures. 12-7 Elasticity. Review & Summary Questions Problems. Chapter 13 Gravitation. What lies at the center of our Milky Way galaxy? 13-1 What Is Physics? 13-2 Newton's Law of Gravitation. 13-3 Gravitation and the Principle of Superposition. 13-4 Gravitation Near Earth's Surface. 13-5 Gravitation Inside Earth. 13-6 Gravitational Potential Energy. 13-7 Planets and Satellites: Kepler's Laws. 13-8 Satellites: Orbits and Energy. 13-9 Einstein and Gravitation. Review & Summary Questions Problems. Chapter 14 Fluids. What causes ground effect in race car driving? 14-1 What Is Physics? 14-2 What Is a Fluid? 14-3 Density and Pressure. 14-4 Fluids at Rest. 14-5 Measuring Pressure. 14-6 Pascal's Principle. 14-7 Archimedes' Principle. 14-8 Ideal Fluids in Motion. 14-9 The Equation of Continuity. 14-10 Bernoulli's Equation. Review & SummaryQuestionsProblems. Chapter 15 Oscillations. What is the "secret" of a skilled diver's high catapult in springboard diving? 15-1 What Is Physics? 15-2 Simple Harmonic Motion. 15-3 The Force Law for Simple Harmonic Motion. 15-4 Energy in Simple Harmonic Motion. 15-5 An Angular Simple Harmonic Oscillator. 15-6 Pendulums. 15-7 Simple Harmonic Motion and Uniform Circular Motion. 15-8 Damped Simple Harmonic Motion. 15-9 Forced Oscillations and Resonance. Review & Summary Questions Problems. Chapter 16 Waves--I. How can a submarine wreck be located by distant seismic stations? 16-1 What Is Physics? 16-2 Types of Waves. 16-3 Transverse and Longitudinal Waves. 16-4 Wavelength and Frequency. 16-5 The Speed of a Traveling Wave. 16-6 Wave Speed on a Stretched String. 16-7 Energy and Power of a Wave Traveling Along a String. 16-8 The Wave Equation. 16-9 The Principle of Superposition for Waves. 16-10 Interference of Waves. 16-11 Phasors. 16-12 Standing Waves. 16-13 Standing Waves and Resonance. Review & Summary Questions Problems. Chapter 17 Waves--II. How can an emperor penguin .nd its mate among thousands of huddled penguins? 17-1 What Is Physics? 17-2 Sound Waves. 17-3 The Speed of Sound. 17-4 Traveling Sound Waves. 17-5 Interference. 17-6 Intensity and Sound Level. 17-7 Sources of Musical Sound. 17-8 Beats. 17-9 The Doppler Effect. 17-10 Supersonic Speeds, Shock Waves. Review & Summary Questions Problems. Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. How can a dead rattlesnake detect and strike a reaching hand? 18-1 What Is Physics?. 18-2 Temperature. 18-3 The Zeroth Law of Thermodynamics. 18-4 Measuring Temperature. 18-5 The Celsius and Fahrenheit Scales. 18-6 Thermal Expansion. 18-7 Temperature and Heat. 18-8 The Absorption of Heat by Solids and Liquids. 18-9 A Closer Look at Heat and Work. 18-10 The First Law of Thermodynamics. 18-11 Some Special Cases of the First Law of Thermodynamics. 18-12 Heat Transfer Mechanisms. Review & Summary Questions Problems. Chapter 19 The Kinetic Theory of Gases. How can cooling steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary Questions Problems. Chapter 20 Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary Questions Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.

Effects of mass variation on structures of differentially rotating polytropic stars

NASA Astrophysics Data System (ADS)

Kumar, Sunil; Saini, Seema; Singh, Kamal Krishan

2018-07-01

A method is proposed for determining equilibrium structures and various physical parameters of differentially rotating polytropic models of stars, taking into account the effect of mass variation inside the star and on its equipotential surfaces. The law of differential rotation has been assumed to be the form of ω2(s) =b1 +b2s2 +b3s4 . The proposed method utilizes the averaging approach of Kippenhahn and Thomas and concepts of Roche-equipotential to incorporate the effects of differential rotation on the equilibrium structures of polytropic stellar models. Mathematical expressions of determining the equipotential surfaces, volume, surface area and other physical parameters are also obtained under the effects of mass variation inside the stars. Some significant conclusions are also drawn.

Entropy in Collisionless Self-gravitating Systems

NASA Astrophysics Data System (ADS)

Barnes, Eric; Williams, L.

2010-01-01

Collisionless systems, like simulated dark matter halos or gas-less elliptical galaxies, often times have properties suggesting that a common physical principle controls their evolution. For example, N-body simulations of dark matter halos present nearly scale-free density/velocity-cubed profiles. In an attempt to understand the origins of such relationships, we adopt a thermodynamics approach. While it is well-known that self-gravitating systems do not have physically realizable thermal equilibrium configurations, we are interested in the behavior of entropy as mechanical equilibrium is acheived. We will discuss entropy production in these systems from a kinetic theory point of view. This material is based upon work supported by the National Aeronautics and Space Administration under grant NNX07AG86G issued through the Science Mission Directorate.

Balancing Newtonian gravity and spin to create localized structures

NASA Astrophysics Data System (ADS)

Bush, Michael; Lindner, John

2015-03-01

Using geometry and Newtonian physics, we design localized structures that do not require electromagnetic or other forces to resist implosion or explosion. In two-dimensional Euclidean space, we find an equilibrium configuration of a rotating ring of massive dust whose inward gravity is the centripetal force that spins it. We find similar solutions in three-dimensional Euclidean and hyperbolic spaces, but only in the limit of vanishing mass. Finally, in three-dimensional Euclidean space, we generalize the two-dimensional result by finding an equilibrium configuration of a spherical shell of massive dust that supports itself against gravitational collapse by spinning isoclinically in four dimensions so its three-dimensional acceleration is everywhere inward. These Newtonian ``atoms'' illuminate classical physics and geometry.

Non-equilibrium mechanisms of light in the microwave region

NASA Astrophysics Data System (ADS)

Mortenson, Juliana H. J.

2011-09-01

Quantum mechanics and quantum chemistry have taught for more than 100 years that "photons" associated with microwaves cannot exert photochemical effects because their "photon energies" are smaller than chemical bond energies. Those quantum theories have been strongly contradicted within the last few decades by physical experiments demonstrating non-equilibrium, photochemical and photomaterial activity by microwaves. Reactions among scientists to these real physical models and proofs have varied from disbelief and denial, to acceptance of the real physical phenomena and demands for revisions to quantum theory. At the previous "Nature of Light" meeting, an advance in the foundations of quantum mechanics was presented. Those discoveries have revealed the source of these conflicts between quantum theory and microwave experiments. Critical variables and constants were missing from quantum theory due to a minor mathematical inadvertence in Planck's original quantum work. As a result, erroneous concepts were formed nearly a century ago regarding the energetics and mechanisms of lower frequency light, such as in the microwave region. The new discoveries have revealed that the traditional concept of "photons" mistakenly attributed elementary particle status to what is actually an arbitrarily time-based collection of sub-photonic, elementary particles. In a mathematical dimensional sense, those time-based energy measurements cannot be mathematically equivalent to bond energies as historically believed. Only an "isolated quantity of energy", as De Broglie referred to it, can be equivalent to bond energy. With the aid of the new variables and constants, the non-equilibrium mechanisms of light in the microwave region can now be described. They include resonant absorption, splitting frequency stimulation leading to electronic excitation, and resonant acoustic transduction. Numerous practical engineering applications can be envisioned for non-equilibrium microwaves.

Nonequilibrium self-energy functional theory

NASA Astrophysics Data System (ADS)

Hofmann, Felix; Eckstein, Martin; Arrigoni, Enrico; Potthoff, Michael

2013-10-01

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by starting from a reformulation of the original equilibrium theory in terms of double-time Green's functions on the Keldysh-Matsubara contour. With the help of a generalized Luttinger-Ward functional, we construct a functional Ω̂[Σ] which is stationary at the physical (nonequilibrium) self-energy Σ and which yields the grand potential of the initial thermal state Ω at the physical point. Nonperturbative approximations can be defined by specifying a reference system that serves to generate trial self-energies. These self-energies are varied by varying the reference system's one-particle parameters on the Keldysh-Matsubara contour. In the case of thermal equilibrium, this approach reduces to the conventional SFT. Contrary to the equilibrium theory, however, “unphysical” variations, i.e., variations that are different on the upper and the lower branches of the Keldysh contour, must be considered to fix the time dependence of the optimal physical parameters via the variational principle. Functional derivatives in the nonequilibrium SFT Euler equation are carried out analytically to derive conditional equations for the variational parameters that are accessible to a numerical evaluation via a time-propagation scheme. Approximations constructed by means of the nonequilibrium SFT are shown to be inherently causal, internally consistent, and to respect macroscopic conservation laws resulting from gauge symmetries of the Hamiltonian. This comprises the nonequilibrium dynamical mean-field theory but also dynamical-impurity and variational-cluster approximations that are specified by reference systems with a finite number of degrees of freedom. In this way, nonperturbative and consistent approximations can be set up, the numerical evaluation of which is accessible to an exact-diagonalization approach.

Approaches to the Treatment of Equilibrium Perturbations

NASA Astrophysics Data System (ADS)

Canagaratna, Sebastian G.

2003-10-01

Perturbations from equilibrium are treated in the textbooks by a combination of Le Châtelier's principle, the comparison of the equilibrium constant K with the reaction quotient Q,and the kinetic approach. Each of these methods is briefly reviewed. This is followed by derivations of the variation of the equilibrium value of the extent of reaction, ξeq, with various parameters on which it depends. Near equilibrium this relationship can be represented by a straight line. The equilibrium system can be regarded as moving on this line as the parameter is varied. The slope of the line depends on quantities like enthalpy of reaction, volume of reaction and so forth. The derivation shows that these quantities pertain to the equilibrium system, not the standard state. Also, the derivation makes clear what kind of assumptions underlie our conclusions. The derivation of these relations involves knowledge of thermodynamics that is well within the grasp of junior level physical chemistry students. The conclusions that follow from the derived relations are given as subsidiary rules in the form of the slope of ξeq, with T, p, et cetera. The rules are used to develop a visual way of predicting the direction of shift of a perturbed system. This method can be used to supplement one of the other methods even at the introductory level.

Controlling species richness in spin-glass model ecosystems

NASA Astrophysics Data System (ADS)

Poderoso, Fábio C.; Fontanari, José F.

2006-11-01

Within the framework of the random replicator model of ecosystems, we use equilibrium statistical mechanics tools to study the effect of manipulating the ecosystem so as to guarantee that a fixed fraction of the surviving species at equilibrium display a predefined set of characters (e.g., characters of economic value). Provided that the intraspecies competition is not too weak, we find that the consequence of such intervention on the ecosystem composition is a significant increase on the number of species that become extinct, and so the impoverishment of the ecosystem.

On thermalization of electron-positron-photon plasma

NASA Astrophysics Data System (ADS)

Siutsou, I. A.; Aksenov, A. G.; Vereshchagin, G. V.

2015-12-01

Recently a progress has been made in understanding thermalization mechanism of relativistic plasma starting from a non-equilibrium state. Relativistic Boltzmann equations were solved numerically for homogeneous isotropic plasma with collision integrals for two- and three-particle interactions calculated from the first principles by means of QED matrix elements. All particles were assumed to fulfill Boltzmann statistics. In this work we follow plasma thermalization by accounting for Bose enhancement and Pauli blocking in particle interactions. Our results show that particle in equilibrium reach Bose-Einstein distribution for photons, and Fermi-Dirac one for electrons, respectively.

Galactic Abundance Gradients fro IR Fine Strucuture LInes in Compact H II regions

NASA Technical Reports Server (NTRS)

Afflerbach, A.; Churchwell, E.; Werner, M. W.

1996-01-01

We present observations of the [S III]19(micro)m, [O III]52 and 88(micro)m, and [N III]57(micro)m lines toward 18 compact and ultracompact (UC) H II regions. These data were combined with data from the literature and high-resolution radio continuum maps to construct detailed statistical equilibrium and ionization equilibrium models of 34 compact H II regions located at galactocentric distances (Dg)0-12kpc. Our models simultaneously fit the observed IR fine-structure lines and high-resolution radio continuum maps.

Entropic Description of Gas Hydrate Ice-Liquid Equilibrium via Enhanced Sampling of Coexisting Phases

NASA Astrophysics Data System (ADS)

Małolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-05-01

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid-liquid equilibrium is of interest. However, aqueous crystal-liquid transitions are very difficult to simulate. A new molecular dynamics algorithm generates trajectories in a generalized N P T ensemble and equilibrates states of coexisting phases with a selectable enthalpy. With replicas spanning the range between β ice and liquid water, we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Systems with a constant heat flux with applications to radiative heat transport across nanoscale gaps and layers

NASA Astrophysics Data System (ADS)

Budaev, Bair V.; Bogy, David B.

2018-06-01

We extend the statistical analysis of equilibrium systems to systems with a constant heat flux. This extension leads to natural generalizations of Maxwell-Boltzmann's and Planck's equilibrium energy distributions to energy distributions of systems with a net heat flux. This development provides a long needed foundation for addressing problems of nanoscale heat transport by a systematic method based on a few fundamental principles. As an example, we consider the computation of the radiative heat flux between narrowly spaced half-spaces maintained at different temperatures.

Entropic description of gas hydrate ice/liquid equilibrium via enhanced sampling of coexisting phases

DOE PAGES

Malolepsza, Edyta; Kim, Jaegil; Keyes, Tom

2015-04-28

Metastable β ice holds small guest molecules in stable gas hydrates, so its solid/liquid equilibrium is of interest. However, aqueous crystal/liquid transitions are very difficult to simulate. A new MD algorithm generates trajectories in a generalized NPT ensemble and equilibrates states of coexisting phases with a selectable enthalpy. Furthermore, with replicas spanning the range between β ice and liquid water we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Supernova Driving. IV. The Star-formation Rate of Molecular Clouds

NASA Astrophysics Data System (ADS)

Padoan, Paolo; Haugbølle, Troels; Nordlund, Åke; Frimann, Søren

2017-05-01

We compute the star-formation rate (SFR) in molecular clouds (MCs) that originate ab initio in a new, higher-resolution simulation of supernova-driven turbulence. Because of the large number of well-resolved clouds with self-consistent boundary and initial conditions, we obtain a large range of cloud physical parameters with realistic statistical distributions, which is an unprecedented sample of star-forming regions to test SFR models and to interpret observational surveys. We confirm the dependence of the SFR per free-fall time, SFRff, on the virial parameter, α vir, found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, { M }, gas to magnetic pressure ratio, β, and compressive to solenoidal power ratio, χ at fixed α vir are not well constrained, because of random scatter due to time and cloud-to-cloud variations in SFRff. We find that SFRff in MCs can take any value in the range of 0 ≤ SFRff ≲ 0.2, and its probability distribution peaks at a value of SFRff ≈ 0.025, consistent with observations. The values of SFRff and the scatter in the SFRff-α vir relation are consistent with recent measurements in nearby MCs and in clouds near the Galactic center. Although not explicitly modeled by the theory, the scatter is consistent with the physical assumptions of our revised model and may also result in part from a lack of statistical equilibrium of the turbulence, due to the transient nature of MCs.

Photoinduced nanobubble-driven superfast diffusion of nanoparticles imaged by 4D electron microscopy

PubMed Central

Fu, Xuewen; Chen, Bin; Tang, Jau; Zewail, Ahmed H.

2017-01-01

Dynamics of active or propulsive Brownian particles in nonequilibrium status have recently attracted great interest in many fields including artificial micro/nanoscopic motors and biological entities. Understanding of their dynamics can provide insight into the statistical properties of physical and biological systems far from equilibrium. We report the translational dynamics of photon-activated gold nanoparticles (NPs) in water imaged by liquid-cell four-dimensional electron microscopy (4D-EM) with high spatiotemporal resolution. Under excitation of femtosecond laser pulses, we observed that those NPs exhibit superfast diffusive translation with a diffusion constant four to five orders of magnitude greater than that in the absence of laser excitation. The measured diffusion constant follows a power-law dependence on the laser fluence and a linear increase with the laser repetition rate, respectively. This superfast diffusion of the NPs is induced by a strong random driving force arising from the photoinduced steam nanobubbles (NBs) near the NP surface. In contrast, the NPs exhibit a superfast ballistic translation at a short time scale down to nanoseconds. Combining with a physical model simulation, this study reveals a photoinduced NB propulsion mechanism for propulsive motion, providing physical insights into better design of light-activated artificial micro/nanomotors. The liquid-cell 4D-EM also provides the potential of studying other numerical dynamical behaviors in their native environments. PMID:28875170

Perspective: Maximum caliber is a general variational principle for dynamical systems

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

2018-01-01

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

On the testing of Hardy-Weinberg proportions and equality of allele frequencies in males and females at biallelic genetic markers.

PubMed

Graffelman, Jan; Weir, Bruce S

2018-02-01

Standard statistical tests for equality of allele frequencies in males and females and tests for Hardy-Weinberg equilibrium are tightly linked by their assumptions. Tests for equality of allele frequencies assume Hardy-Weinberg equilibrium, whereas the usual chi-square or exact test for Hardy-Weinberg equilibrium assume equality of allele frequencies in the sexes. In this paper, we propose ways to break this interdependence in assumptions of the two tests by proposing an omnibus exact test that can test both hypotheses jointly, as well as a likelihood ratio approach that permits these phenomena to be tested both jointly and separately. The tests are illustrated with data from the 1000 Genomes project. © 2017 The Authors Genetic Epidemiology Published by Wiley Periodicals, Inc.

Observation of a discrete time crystal

NASA Astrophysics Data System (ADS)

Zhang, J.; Hess, P. W.; Kyprianidis, A.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potirniche, I.-D.; Potter, A. C.; Vishwanath, A.; Yao, N. Y.; Monroe, C.

2017-03-01

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a ‘time crystal’ was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a ‘discrete time crystal’. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Observation of a discrete time crystal.

PubMed

Zhang, J; Hess, P W; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I-D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C

2017-03-08

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a 'time crystal' was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a 'discrete time crystal'. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

Extension of the quantum-kinetic model to lunar and Mars return physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liechty, D. S.; Lewis, M. J.

The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high-mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. A recently introduced molecular-level chemistry model, the quantum-kinetic, or Q-K, model that predicts reaction rates for gases in thermal equilibrium and non-equilibrium using only kinetic theory and fundamental molecular properties, is extended in the current work to include electronic energy level transitions and reactions involving charged particles. Like the Q-K procedures for neutral species chemical reactions, these new models are phenomenological procedures that aimmore » to reproduce the reaction/transition rates but do not necessarily capture the exact physics. These engineering models are necessarily efficient due to the requirement to compute billions of simulated collisions in direct simulation Monte Carlo (DSMC) simulations. The new models are shown to generally agree within the spread of reported transition and reaction rates from the literature for near equilibrium conditions.« less

Cooling of Accretion-Heated Neutron Stars

NASA Astrophysics Data System (ADS)

Wijnands, Rudy; Degenaar, Nathalie; Page, Dany

2017-09-01

We present a brief, observational review about the study of the cooling behaviour of accretion-heated neutron stars and the inferences about the neutron-star crust and core that have been obtained from these studies. Accretion of matter during outbursts can heat the crust out of thermal equilibrium with the core and after the accretion episodes are over, the crust will cool down until crust-core equilibrium is restored. We discuss the observed properties of the crust cooling sources and what has been learned about the physics of neutron-star crusts. We also briefly discuss those systems that have been observed long after their outbursts were over, i.e, during times when the crust and core are expected to be in thermal equilibrium. The surface temperature is then a direct probe for the core temperature. By comparing the expected temperatures based on estimates of the accretion history of the targets with the observed ones, the physics of neutron-star cores can be investigated. Finally, we discuss similar studies performed for strongly magnetized neutron stars in which the magnetic field might play an important role in the heating and cooling of the neutron stars.

Why Tsallis statistics?

NASA Astrophysics Data System (ADS)

Baranger, Michel

2002-03-01

It is a remarkable fact that the traditional teaching of thermodynamics, as reflected in the textbooks and including the long developments about ensembles and thermodynamic functions, is almost entirely about systems in equilibrium. The time variable does not enter. There is one exception, however. The single most important item, the flagship of the thermodynamic navy, the second law, is about the irreversibility of the time evolution of systems out of equilibrium. This is a bizarre situation, to say the least; a glaring case of the drunk man looking for his key under the lamp-post, when he knows that he lost it in the dark part of the street. The moment has come for us to go looking in the dark part, the behavior of systems as a function of time. We have been given a powerful new flashlight, chaos theory. We should use it. There, on the formerly dark pavement, we can find Tsallis statistics.

Stochastic cycle selection in active flow networks

NASA Astrophysics Data System (ADS)

Woodhouse, Francis; Forrow, Aden; Fawcett, Joanna; Dunkel, Jorn

2016-11-01

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. By connecting concepts from lattice field theory, graph theory and transition rate theory, we show how topology controls dynamics in a generic model for actively driven flow on a network. Through theoretical and numerical analysis we identify symmetry-based rules to classify and predict the selection statistics of complex flow cycles from the network topology. Our conceptual framework is applicable to a broad class of biological and non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models.

Deviations from LTE in a stellar atmosphere

NASA Technical Reports Server (NTRS)

Kalkofen, W.; Klein, R. I.; Stein, R. F.

1979-01-01

Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.

Coronal emission-line polarization from the statistical equilibrium of magnetic sublevels. II. Fe XIV 5303 A

DOE Office of Scientific and Technical Information (OSTI.GOV)

House, L.L.; Querfeld, C.W.; Rees, D.E.

1982-04-15

Coronal magnetic fields influence in the intensity and linear polarization of light scattered by coronal Fe XIV ions. To interpret polarization measurements of Fe XIV 5303 A coronal emission requires a detailed understanding of the dependence of the emitted Stokes vector on coronal magnetic field direction, electron density, and temperature and on height of origin. The required dependence is included in the solutions of statistical equilibrium for the ion which are solved explicitly for 34 magnetic sublevels in both the ground and four excited terms. The full solutions are reduced to equivalent simple analytic forms which clearly show the requiredmore » dependence on coronal conditions. The analytic forms of the reduced solutions are suitable for routine analysis of 5303 green line polarimetric data obtained at Pic du Midi and from the Solar Maximum Mission Coronagraph/Polarimeter.« less

An experiment on radioactive equilibrium and its modelling using the ‘radioactive dice’ approach

NASA Astrophysics Data System (ADS)

Santostasi, Davide; Malgieri, Massimiliano; Montagna, Paolo; Vitulo, Paolo

2017-07-01

In this article we describe an educational activity on radioactive equilibrium we performed with secondary school students (17-18 years old) in the context of a vocational guidance stage for talented students at the Department of Physics of the University of Pavia. Radioactive equilibrium is investigated experimentally by having students measure the activity of 214Bi from two different samples, obtained using different preparation procedures from an uraniferous rock. Students are guided in understanding the mathematical structure of radioactive equilibrium through a modelling activity in two parts. Before the lab measurements, a dice game, which extends the traditional ‘radioactive dice’ activity to the case of a chain of two decaying nuclides, is performed by students divided into small groups. At the end of the laboratory work, students design and run a simple spreadsheet simulation modelling the same basic radioactive chain with user defined decay constants. By setting the constants to realistic values corresponding to nuclides of the uranium decay chain, students can deepen their understanding of the meaning of the experimental data, and also explore the difference between cases of non-equilibrium, transient and secular equilibrium.

Physics transforming the life sciences.

PubMed

Onuchic, José N

2014-10-08

Biological physics is clearly becoming one of the leading sciences of the 21st century. This field involves the cross-fertilization of ideas and methods from biology and biochemistry on the one hand and the physics of complex and far from equilibrium systems on the other. Here I want to discuss how biological physics is a new area of physics and not simply applications of known physics to biological problems. I will focus in particular on the new advances in theoretical physics that are already flourishing today. They will become central pieces in the creation of this new frontier of science.

Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs' statistical mechanics.

PubMed

Plastino, A; Rocca, M C

2017-06-01

Appealing to the 1902 Gibbs formalism for classical statistical mechanics (SM)-the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics-we show that already at the classical level there is a strong correlation between Renyi's exponent α and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.

Long-ranged Fermi-Pasta-Ulam systems in thermal contact: Crossover from q-statistics to Boltzmann-Gibbs statistics

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee; Tsallis, Constantino

2017-04-01

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.

Fugacity of H2O from 0° to 350°C at the liquid-vapor equilibrium and at 1 atmosphere

USGS Publications Warehouse

Hass, John L.

1970-01-01

The fugacity and fugacity coefficient of H2O at the liquid-vapor equilibrium, the fugacity and the Gibbs free energy of formation of H2O at 1 atm (1.01325 bars) total pressure have been calculated from published data on the physical and thermodynamic properties of H2O and are presented at ten-degree intervals from 0° to 350°C.

Strongly-Perturbed Non-Equilibrium Gas Physics Model for the Paraxial Diode Transport Cell

DTIC Science & Technology

2003-06-01

species and energy flow is critical to the plasma chemistry . The new model’s slight underestimate of the electron density may be a consequence of the...beam physics and plasma chemistry allows the modeling of intense charged-particle beam transport environments such as the paraxial diode gas cell

ATMOSPHERIC CHEMISTRY FOR ASTROPHYSICISTS: A SELF-CONSISTENT FORMALISM AND ANALYTICAL SOLUTIONS FOR ARBITRARY C/O

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heng, Kevin; Tsai, Shang-Min; Lyons, James R., E-mail: kevin.heng@csh.unibe.ch

2016-01-10

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equatemore » to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.« less

Atmospheric Chemistry for Astrophysicists: A Self-consistent Formalism and Analytical Solutions for Arbitrary C/O

NASA Astrophysics Data System (ADS)

Heng, Kevin; Lyons, James R.; Tsai, Shang-Min

2016-01-01

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

Non-equilibrium Transport in Carbon based Adsorbate Systems

NASA Astrophysics Data System (ADS)

Fürst, Joachim; Brandbyge, Mads; Stokbro, Kurt; Jauho, Antti-Pekka

2007-03-01

We have used the Atomistix Tool Kit(ATK) and TranSIESTA[1] packages to investigate adsorption of iron atoms on a graphene sheet. The technique of both codes is based on density functional theory using local basis sets[2], and non-equilibrium Green's functions (NEGF) to calculate the charge distribution under external bias. Spin dependent electronic structure calculations are performed for different iron coverages. These reveal adsorption site dependent charge transfer from iron to graphene leading to screening effects. Transport calculations show spin dependent scattering of the transmission which is analysed obtaining the transmission eigenchannels for each spin type. The phenomena of electromigration of iron in these systems at finite bias will be discussed, estimating the so-called wind force from the reflection[3]. [1] M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, and K. Stokbro. Physical Review B (Condensed Matter and Materials Physics), 65(16):165401/11-7, 2002. [2] Jose M. Soler, Emilio Artacho, Julian D. Gale, Alberto Garcia, Javier Junquera, Pablo Ordejon, and Daniel Sanchez-Portal. Journal of Physics Condensed Matter, 14(11):2745-2779, 2002. [3] Sorbello. Theory of electromigration. Solid State Physics, 1997.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Solid/liquid extraction equilibria of phenolic compounds with trioctylphosphine oxide impregnated in polymeric membranes.

PubMed

Praveen, Prashant; Loh, Kai-Chee

2016-06-01

Trioctylphosphine oxide based extractant impregnated membranes (EIM) were used for extraction of phenol and its methyl, hydroxyl and chloride substituted derivatives. The distribution coefficients of the phenols varied from 2 to 234, in the order of 1-napthol > p-chlorophenol > m-cresol > p-cresol > o-cresol > phenol > catechol > pyrogallol > hydroquinone, when initial phenols loadings was varied in 100-2000 mg/L. An extraction model, based on the law of mass action, was formulated to predict the equilibrium distribution of the phenols. The model was in excellent agreement (R(2) > 0.97) with the experimental results at low phenols concentrations (<800 mg/L). At higher phenols loadings though, Langmuir isotherm was better suited for equilibrium prediction (R(2) > 0.95), which signified high mass transfer resistance in the EIMs. Examination of the effects of ring substitution on equilibrium, and bivariate statistical analysis between the amounts of phenols extracted into the EIMs and factors affecting phenols interaction with TOPO, indicated the dominant role of hydrophobicity in equilibrium determination. These results improve understanding of the solid/liquid equilibrium process between phenols and the EIMs, and these will be useful in designing phenol recovery process from wastewater. Copyright © 2016 Elsevier Ltd. All rights reserved.

Conformal field theory out of equilibrium: a review

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2016-06-01

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

Study Modules for Calculus-Based General Physics. [Includes Modules 11-14: Collisions; Equilibrium of Rigid Bodies; Rotational Dynamics; and Fluid Mechanics].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Equilibrium sampling of environmental pollutants in fish: comparison with lipid-normalized concentrations and homogenization effects on chemical activity.

PubMed

Jahnke, Annika; Mayer, Philipp; Adolfsson-Erici, Margaretha; McLachlan, Michael S

2011-07-01

Equilibrium sampling of organic pollutants into the silicone polydimethylsiloxane (PDMS) has recently been applied in biological tissues including fish. Pollutant concentrations in PDMS can then be multiplied with lipid/PDMS distribution coefficients (D(Lipid,PDMS) ) to obtain concentrations in fish lipids. In the present study, PDMS thin films were used for equilibrium sampling of polychlorinated biphenyls (PCBs) in intact tissue of two eels and one salmon. A classical exhaustive extraction technique to determine lipid-normalized PCB concentrations, which assigns the body burden of the chemical to the lipid fraction of the fish, was additionally applied. Lipid-based PCB concentrations obtained by equilibrium sampling were 85 to 106% (Norwegian Atlantic salmon), 108 to 128% (Baltic Sea eel), and 51 to 83% (Finnish lake eel) of those determined using total extraction. This supports the validity of the equilibrium sampling technique, while at the same time confirming that the fugacity capacity of these lipid-rich tissues for PCBs was dominated by the lipid fraction. Equilibrium sampling was also applied to homogenates of the same fish tissues. The PCB concentrations in the PDMS were 1.2 to 2.0 times higher in the homogenates (statistically significant in 18 of 21 cases, p < 0.05), indicating that homogenization increased the chemical activity of the PCBs and decreased the fugacity capacity of the tissue. This observation has implications for equilibrium sampling and partition coefficients determined using tissue homogenates. Copyright © 2011 SETAC.

A note on the theory of fast money flow dynamics

NASA Astrophysics Data System (ADS)

Sokolov, A.; Kieu, T.; Melatos, A.

2010-08-01

The gauge theory of arbitrage was introduced by Ilinski in [K. Ilinski, preprint arXiv:hep-th/9710148 (1997)] and applied to fast money flows in [A. Ilinskaia, K. Ilinski, preprint arXiv:cond-mat/9902044 (1999); K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)]. The theory of fast money flow dynamics attempts to model the evolution of currency exchange rates and stock prices on short, e.g. intra-day, time scales. It has been used to explain some of the heuristic trading rules, known as technical analysis, that are used by professional traders in the equity and foreign exchange markets. A critique of some of the underlying assumptions of the gauge theory of arbitrage was presented by Sornette in [D. Sornette, Int. J. Mod. Phys. C 9, 505 (1998)]. In this paper, we present a critique of the theory of fast money flow dynamics, which was not examined by Sornette. We demonstrate that the choice of the input parameters used in [K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)] results in sinusoidal oscillations of the exchange rate, in conflict with the results presented in [K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)]. We also find that the dynamics predicted by the theory are generally unstable in most realistic situations, with the exchange rate tending to zero or infinity exponentially.

Single molecule RNA folding studied with optical trapping

NASA Astrophysics Data System (ADS)

Vieregg, Jeffrey Robert

The RNA folding problem (predicting the equilibrium structure and folding pathway of an RNA molecule from its sequence) is one of the classic problems of biophysics. Recent discoveries of many new functions for RNA have increased its importance, and new instrumental techniques have provided new ways to characterize molecular behavior. In particular, optical trapping (optical tweezers) allows controlled mechanical force to be applied to single RNA molecules while their end-to-end extension is monitored in real time. This enables characterization of RNA folding dynamics at a level unreachable by traditional bulk methods. Furthermore, recent advances in statistical mechanics make it possible to recover equilibrium quantities such as free energy from reactions which occur away from equilibrium. This dissertation describes the application of optical trapping and non-equilibrium statistical mechanics to quantitatively characterize folding of RNA secondary structures. By measuring the folding free energy of several specially designed hairpins in solutions containing various amounts of sodium and potassium, we were able to determine that RNA secondary structure thermodynamics depends not only on monovalent cation concentration but also surprisingly, on species. We also investigated the temperature dependence of hairpin folding thermodynamics and kinetics, which provided a direct measurement of enthalpy and entropy for RNA folding at physiological temperatures. We found that the folding pathway was quite sensitive to both salt and temperature, as measured by the folding success rate of a biologically important hairpin from the HIV-1 viral genome. Finally, I discuss modeling of force-induced RNA folding and unfolding, as well as a series of efforts which have dramatically improved the performance of our optical trapping instrument.

Linear theory for filtering nonlinear multiscale systems with model error

PubMed Central

Berry, Tyrus; Harlim, John

2014-01-01

In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online, as part of a filtering procedure, simultaneously produce accurate filtering and equilibrium statistical prediction. In contrast, an offline estimation technique based on a linear regression, which fits the parameters to a training dataset without using the filter, yields filter estimates which are worse than the observations or even divergent when the slow variables are not fully observed. This finding does not imply that all offline methods are inherently inferior to the online method for nonlinear estimation problems, it only suggests that an ideal estimation technique should estimate all parameters simultaneously whether it is online or offline. PMID:25002829

Extracting Aggregation Free Energies of Mixed Clusters from Simulations of Small Systems: Application to Ionic Surfactant Micelles.

PubMed

Zhang, X; Patel, L A; Beckwith, O; Schneider, R; Weeden, C J; Kindt, J T

2017-11-14

Micelle cluster distributions from molecular dynamics simulations of a solvent-free coarse-grained model of sodium octyl sulfate (SOS) were analyzed using an improved method to extract equilibrium association constants from small-system simulations containing one or two micelle clusters at equilibrium with free surfactants and counterions. The statistical-thermodynamic and mathematical foundations of this partition-enabled analysis of cluster histograms (PEACH) approach are presented. A dramatic reduction in computational time for analysis was achieved through a strategy similar to the selector variable method to circumvent the need for exhaustive enumeration of the possible partitions of surfactants and counterions into clusters. Using statistics from a set of small-system (up to 60 SOS molecules) simulations as input, equilibrium association constants for micelle clusters were obtained as a function of both number of surfactants and number of associated counterions through a global fitting procedure. The resulting free energies were able to accurately predict micelle size and charge distributions in a large (560 molecule) system. The evolution of micelle size and charge with SOS concentration as predicted by the PEACH-derived free energies and by a phenomenological four-parameter model fit, along with the sensitivity of these predictions to variations in cluster definitions, are analyzed and discussed.

3rd International Conference on Turbulent Mixing and Beyond

NASA Astrophysics Data System (ADS)

Abarzhi, Snezhana I.; Gauthier, Serge; Keane, Christopher J.; Niemela, Joseph J.

2013-07-01

1. Introduction 'Turbulent Mixing and Beyond' (TMB) is the programme established for scientists, by scientists. It is merit-based, and is shaped by requirements of academic credentials, and novelty and quality of information. The goals of this programme are to expose the generic problem of non-equilibrium turbulent processes to a wide scientific community, to promote the development of new ideas in tackling the fundamental aspects of the problem, to assist in application of novel approaches in a broad range of phenomena, in which the turbulent processes occur, and to have a potential impact on technology. The programme was founded in 2007 with the support of the international scientific community and of the US National Science Foundation, the US Air Force Office of the Scientific Research and its European Office for Research and Development in the UK, the UNESCO-IAEA International Centre for Theoretical Physics in Italy, the Commissariat l'Energie Atomique in France, the US Department of Energy and the Department of Energy National Laboratories, the Institute for Laser Engineering in Japan, and the University of Chicago in the USA. The International Conference on Turbulent Mixing and Beyond provides opportunities to bring together researchers from the areas, which include but are not limited to, fluid dynamics, plasmas, high energy density physics, astrophysics, material science, combustion, atmospheric and earth sciences, nonlinear and statistical physics, applied mathematics, probability and statistics, data processing and computations, optics and communications, and to have their attention focused on the long-standing formidable task of non-equilibrium turbulent processes. 2. Non-equilibrium turbulent processes Non-equilibrium turbulent processes play a key role in a wide variety of phenomena, ranging from astrophysical to atomistic scales, under either high or low energy density conditions. Inertial confinement and magnetic fusion, light-matter interaction and non-equilibrium heat transfer, strong shocks and explosions, material transformation under high strain rate, supernovae and accretion discs, stellar non-Boussinesq and magneto-convection, planetary interiors and mantle-lithosphere tectonics, premixed and non-premixed combustion, non-canonical wall-bounded flows, hypersonic and supersonic boundary layers, dynamics of atmosphere and oceanography, are just a few examples to list. A grip on non-equilibrium turbulent processes is crucial for cutting-edge technology such as laser micro-machining, nano-electronics, free-space optical telecommunications and for industrial applications in the areas of aeronautics and aerodynamics. Non-equilibrium turbulent processes are anisotropic, non-local, multi-scale and multi-phase, and often are driven by shocks or acceleration. Their scaling, spectral and invariant properties differ substantially from those of classical Kolmogorov turbulence. At atomistic and meso-scales, the non-equilibrium dynamics depart dramatically from a standard scenario given by Gibbs statistic ensemble average and quasi-static Boltzmann equation. The singular aspect and the similarity of the non-equilibrium dynamics at macroscopic scales are interplayed with the fundamental properties of the Euler and compressible Navier-Stokes equations and with the problem sensitivity to the boundary conditions at discontinuities. The state-of-the-art numerical simulations of multi-phase flows suggest new methods for predictive modelling of the multi-scale non-equilibrium dynamics in fluids and plasmas, for error estimates and uncertainty quantifications, as well as for novel data assimilation techniques. 3. International Conference 'Turbulent Mixing and Beyond' The First and Second International Conferences on Turbulent Mixing and Beyond found that: (i) TMB-related problems have in common a set of outstanding research issues; (ii) their solution has a potential to significantly advance a variety of disciplines in science, technology and mathematics; (iii) TMB participants conduct highly innovative research and their interactions strengthen the community's might. Based on the success of the first and second conferences and on the recommendations of the conference round table discussions, and in response to the inquiry of the community, the Third International Conference on Turbulent Mixing and Beyond was organized. The Third International Conference on Turbulent Mixing and Beyond, TMB-2011, was held on 21-28 August 2011 at the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy. This was a highly informative and exciting meeting, and it strengthened and reaffirmed the success of TMB-2009 and 2007. The objectives of the Third International Conference on Turbulent Mixing and Beyond were to: (i) focus the integration of theory, experiments, large-scale numerical simulations and state-of-the-art technologies on the exploration of physical mechanisms of non-equilibrium dynamics, from micro to macro-scales, in both high and low energy density regimes; (ii) foster the application of innovative approaches for tackling the fundamental aspects of turbulent mixing problems and for understanding and further extending the range of applicability of canonical considerations; (iii) encourage the development of new approaches and stimulate the application of advanced data analysis techniques for unified characterization of experimental and numerical data sets, for estimation of their quality and information capacity, and for transforming data to knowledge; (iv) further develop the 'Turbulent Mixing and Beyond' community via organizing a positive and constructive collaborative environment, maintaining the quality of information flux in the community and sharing research methodologies, tools and data among the community members. The objectives were accomplished at TMB-2011. 4. Programme of TMB-2011 TMB-2011 brought together 150 participants, ranging from students to members of National Academies of Sciences and Engineering, and including researchers at experienced and early stages of their careers from leading scientific institutions in academia, national laboratories, corporations and industry, from developed and developing countries across five continents. The success of TMB-2011 consisted from the successful work of the conference participants, who were responsible professionals caring for the quality of their research and sharing their scientific vision. The level of presentations was high, and 205 presentations included about 50 invited lectures, nearly 70 oral talks (3500 min of talks in total), some 90 posters and one round table. The special course on 'Turbulence and Waves' was organized at TMB-2011 with the support of the US Office of Naval Research Global, and included nearly 40 lectures and talks (960 minutes of talks in total). TMB-2011 covered 16 different topics, maintaining the scope and the interdisciplinary character of the meeting and at the same time keeping the focus on a fundamental scientific problem of non-equilibrium processes and on the conference objectives. The topics included: • Canonical turbulent and turbulent mixing: invariant, scaling, spectral properties, scalar transports, convection. • Wall-bounded flows: structure and fundamentals, non-canonical turbulent boundary layers, including unsteady and transitional flows, supersonic and hypersonic flows, shock-boundary layer interactions. • Non-equilibrium processes: unsteady, multiphase and shock-driven turbulent flows, anisotropic non-local dynamics, connection of continuous description at macro-scales to kinetic processes at atomistic scales. • Interfacial dynamics: the instabilities of Rayleigh-Taylor, Kelvin-Helmholtz, Richtmyer-Meshkov, Landau-Darrieus, Saffmann-Taylor. • High energy density physics: inertial confinement and heavy-ion fusion, Z-pinches, light-material and laser-plasma interaction, non-equilibrium heat transfer. • Material science: material transformation under high strain rates, equation of state, impact dynamics, mixing at nano- and micro-scales. • Astrophysics: supernovae, interstellar medium, star formation, stellar interiors, early Universe, cosmic-microwave background, accretion discs. • Magneto-hydrodynamics: magnetic fusion and magnetically confined plasmas, magneto-convection, magneto-rotational instability, dynamo. • Canonical plasmas: coupled plasmas, anomalous resistance, ionosphere. • Physics of atmosphere: environmental fluid dynamics, forecasting, turbulent flows in stratified media and atmosphere. • Geophysics and Earth science: mantle-lithosphere tectonics, oceanography, turbulent convection under rotation, planetary interiors. • Combustion: dynamics of flames and fires, deflagration-to-detonation transition, blast waves and explosions, flows with chemical reactions, reactive flows in jet engines. • Theoretical aspects of non-equilibrium dynamics: vortex dynamics, singularities, discontinuities, asymptotic dynamics, weak solutions, well- and ill-posedness, continuous transports out of thermodynamic equilibrium. • Stochastic processes and probabilistic description: long-tail distributions and anomalous diffusion, data assimilation and processing methodologies, error estimate and uncertainty quantification, statistically unsteady processes. • Advanced numerical simulations: continuous DNS/LES/RANS, molecular dynamics, Monte-Carlo, predictive modelling, validation and verification of numerical models. • Experiments and experimental diagnostics: model experiments in high energy density and low energy density regimes, plasma diagnostics, fluid flow visualizations and control, opto-fluidics, novel optical method, holography, advanced technologies. The abstracts of the 207 accepted presentations of 443 authors were published in Proceedings. Abstracts. The Third International Conference 'Turbulent Mixing and Beyond', 21 -28 August 2011. Copyright (ISBN 92-95003-45-4). All the accepted contributions have been reviewed by the international team of 27 members of the Scientific Committee, with every contribution considered by four to eleven experts. In the majority of cases, the opinions of referees with diverse backgrounds and expertise converged. In 2011, the award 'Turbulent Mixing and Beyond for Youth' was issued to Gregory P Bewley (Max Plank Institute for Dynamics and Self-Organization, Germany) and Robert Zimmermann (Ecole Normale Superieure de Lyon, France) in recognition of their contributions to TMB-related scientific problems. The Best Poster Award was issued by Physica Scripta to Michael Winkler (University of Potsdam, Germany) in recognition of their poster presentation at TMB-2011. 5. Organization and acknowledgments The Third International Conference on Turbulent Mixing and Beyond was organized by the following members of the Organizing Committee: • Snezhana I Abarzhi (Chairperson, University of Chicago, USA) • Malcolm J Andrews (Los Alamos National Laboratory, USA) • Hiroshi Azechi (Institute for Laser Engineering, Osaka, Japan) • Vladimir E Fortov (Institute for High Energy Density, Russia) • Boris Galperin (Organizer of the Special Course, University of South Florida, USA) • Serge Gauthier (Commissariat à l'Energie Atomique, France) • Christopher J Keane (Lawrence Livermore National Laboratory, USA) • Joseph J Niemela (Local Organizer, International Centre for Theoretical Physics, Italy) • Katepalli R Sreenivasan (New York University, USA) The conference and course were sponsored by several agencies and institutions in the USA, Europe, Russia and Japan. The Organizing Committee of the TMB-2011 gratefully acknowledges support of the: • National Science Foundation (NSF), USA. Programmes: Plasma Physics; Physics Education and Interdisciplinary Research; Astronomy and Astrophysics; Applied Mathematics; Particulate and Multiphase Processes; Combustion, Fire and Plasma Systems • European Office of Aerospace Research and Development (EOARD), UK, of the Air Force Office of Scientific Research (AFOSR), USA • Office of Naval Research Global, UK • Department of Energy, Office of Science, USA • US Department of Energy Lawrence Livermore National Laboratory (LLNL), USA. Programme: National Ignition Facility (NIF) • US Department of Energy Argonne National Laboratory (ANL), USA • US Department of Energy Los Alamos National Laboratory (LANL), USA • The UNESCO- IAEA International Centre for Theoretical Physics (ICTP), Italy • Commissariat à l'Énergie Atomique et aux énergies Alternatives (CEA), France • The University of Chicago, USA • Institute for Laser Engineering (ILE), Japan • Joint Institute for High Temperatures (JIHT) of the Academy of Sciences, Russia • Institute of Physics Publishing (IOP), UK • Physica Scripta , the journal of the Royal Swedish Academy of Sciences for the Science Academies and the Physical Societies of the Nordic Countries and thank them for making this event possible. We express our gratitude to the members of the Scientific Advisory Committee: • S I Abarzhi (University of Chicago, USA) • Y Aglitskiy (Science Applications International Corporation, USA) • H Azechi (Institute for Laser Engineering, Osaka, Japan) • M J Andrews (Los Alamos National Laboratory, USA) • S I Anisimov (Landau Institute for Theoretical Physics, Russia) • E Bodenschatz (Max Plank Institute, Germany) • F Cattaneo (University of Chicago, USA) • P Cvitanović (Georgia Institute of Technology, USA) • S Cowley (Imperial College, UK) • S Dalziel (DAMTP, Cambridge, UK) • R Ecke (Los Alamos National Laboratory, USA) • H J Fernando (University of Notre Dame, USA) • Y Fukumoto (Kyushu University, Japan) • B Galperin (University of South Floorida, USA) • S Gauthier (Commissariat à l'Energie Atomique, France) • W Gekelman (University of California, Los Angeles, USA) • G A Glatzmaier (University of California at Santa Cruz, USA) • J Glimm (State University of New York at Stony Brook, USA) • W A Goddard III (California Institute of Technology, USA) • F Grinstein (Los Alamos National Laboratory, USA) • J Jimenez (Universidad Politecnica de Madrid, Spain) • L P Kadanoff (The University of Chicago, USA) • D Q Lamb (The University of Chicago, USA) • D P Lathrop (University of Maryland, USA) • S Lebedev (Imperial College, UK) • P Manneville (Ecole Polytechnique, France) • D I Meiron (California Institute of Technology, USA) • P Moin (Stanford University, USA) • A Nepomnyashchy (Technion, Israel) • J Niemela (International Center for Theoretical Physics, Italy) • K Nishihara (Institute for Laser Engineering, Osaka, Japan) • S S Orlov (Physical Optics Corporation, USA) • N Peters (RWTS, Aachen, Germany) • S B Pope (Cornell, USA) • A Pouquet (University Corporation for Atmospheric Research, USA) • B A Remington (Lawrence Livermore National Laboratory, USA) • R R Rosales (Massachusetts Institute of Technology, USA) • R Rosner (Argonne National Laboratory and University of Chicago, USA) • A J Schmitt (Naval Research Laboratory, USA) • C-W Shu (Brown University, USA) • K R Sreenivasan (New York University, USA) • E Tadmor (University of Maryland, USA) • A L Velikovich (Naval Research Laboratory, USA) • V Yakhot (Boston University, USA) • P K Yeung (Georgia Institute of Technology, USA) • F A Williams (University of California at San Diego, USA) • E Zweibel (University of Wisconsin, USA) We deeply appreciate the work of the Members of Steering Committee for Financial Support: • Snezhana I Abarzhi (University of Chicago, USA) • Serge Gauthier (Commissariat à l'Energie Atomique, France) • Joseph J Niemela (International Centre for Theoretical Physics, Italy) • Walter Gekelman (University of California, Los Angeles, USA) We thank the members of the Committee for the award 'Turbulent Mixing and Beyond for Youth': • Boris Galperin (University of South Florida, USA) • Serge Gauthier (Commissariat à l'Energie Atomique, France) • Joseph J Niemela (International Centre for Theoretical Physics, Italy) • Katsunobu Nishihara (Institute for Laser Engineering, Osaka, Japan) • Katepalli R Sreenivasan (New York University, USA) We greatly acknowledge the effort and dedication of the members of the Committee for Best Poster Award: • Serge Gauthier (Commissariat à l'Energie Atomique, France) • Katsunobu Nishihara (Institute for Laser Engineering, Osaka, Japan) • Annick Pouquet (National Center for Atmospheric Research, USA) • Walter Gekelman (University of California, Los Angeles, USA) • Graeme Watt (Institute of Physics, UK) We greatly appreciate the work of conference web-master Daniil V Ilyin (University of Chicago, USA). We thank for technical support: • Bhanesh Akula (Texas A & M University, USA) • Ahmad Qamar (University of Chicago, USA) We warmly acknowledge the logistics assistance of the offices and officers of the Abdus Salam International Centre for Theoretical Physics: • Conference Support Office, and Ms Katrina Danforth and Ms Daniela Giombi • Financial Office, and Mr Andrej Michelcich and Ms Alessandra Ricci • Visa Office, and Mr Erich Jost and Mr Adriano Maggio • Housing Office, and Ms Tiziana Bottazzi and Ms Dora Photiou • Publications Office, and Mr Guido Comar and Mr Raffaele Corona • Computer Office, and Dr Johannes Grassberger • Science Dissemination Unit, and Dr Enrique Canessa, Dr. Carlo Fonda and Dr Marco Zennaro We gratefully appreciate the support of the members of the Programme Coordination Board: • Snezhana I Abarzhi (University of Chicago, USA) • Malcolm J Andrews (Los Alamos National Laboratory, USA) • Sergei I Anisimov (Landau Institute for Theoretical Physics, Russia) • Hiroshi Azechi (Institute for Laser Engineering, Osaka, Japan) • Vladimir E Fortov (Institute for High Energy Density, Russia) • Serge Gauthier (Commissariat à l'Energie Atomique, France) • Christopher J Keane (Lawrence Livermore National Laboratory, USA) • Joseph J Niemela (International Centre for Theoretical Physics, Italy) • Katsunobu Nishihara (Institute for Laser Engineering, Osaka, Japan) • Sergei S Orlov (Physical Optics Corporation, USA) • Bruce Remington (Lawrence Livermore National Laboratory, USA) • Robert Rosner (University of Chicago, USA) • Katepalli R Sreenivasan (New York University, USA) • Alexander L Velikovich (Naval Research Laboratory, USA) 6. The Topical Issue This Topical Issue consists of over 70 articles accepted for publication and represents a substantial part of the Conference contributions, including research papers, research briefs and review papers. The papers are in a broad variety of TMB-2011 themes and are sorted alphabetically by the last name of the first author within each topic. The review papers are published as 'Comments' articles in Physica Scripta . We thank all the authors and the referees for their contributions to this Topical Issue and for offering their expertise, time and effort. To conclude, the TMB programme was organized to serve to advance the state-of-the-art in understanding of fundamental physical properties of non-equilibrium turbulent processes and to have an impact on predictive modelling capabilities, physical description and, ultimately, control of these complex processes. The readers are cordially invited to take a look at this Topical Issue for information on the frontiers of theoretical, numerical and experimental research, and state-of-the-art technology. Welcome to 'Turbulent Mixing and Beyond'.

Non-equilibrium Quasi-Chemical Nucleation Model

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy E.

2018-04-01

Quasi-chemical model, which is widely used for nucleation description, is revised on the basis of recent results in studying of non-equilibrium effects in reacting gas mixtures (Kolesnichenko and Gorbachev in Appl Math Model 34:3778-3790, 2010; Shock Waves 23:635-648, 2013; Shock Waves 27:333-374, 2017). Non-equilibrium effects in chemical reactions are caused by the chemical reactions themselves and therefore these contributions should be taken into account in the corresponding expressions for reaction rates. Corrections to quasi-equilibrium reaction rates are of two types: (a) spatially homogeneous (caused by physical-chemical processes) and (b) spatially inhomogeneous (caused by gas expansion/compression processes and proportional to the velocity divergency). Both of these processes play an important role during the nucleation and are included into the proposed model. The method developed for solving the generalized Boltzmann equation for chemically reactive gases is applied for solving the set of equations of the revised quasi-chemical model. It is shown that non-equilibrium processes lead to essential deviation of the quasi-stationary distribution and therefore the nucleation rate from its traditional form.

Chemical Principls Exemplified

ERIC Educational Resources Information Center

Plumb, Robert C.

1973-01-01

Two topics are discussed: (1) Stomach Upset Caused by Aspirin, illustrating principles of acid-base equilibrium and solubility; (2) Physical Chemistry of the Drinking Duck, illustrating principles of phase equilibria and thermodynamics. (DF)

Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle.

PubMed

Kobayashi, Michikazu; Cugliandolo, Leticia F

2016-12-01

We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.

Chemistry of vaporization of refractory materials

NASA Technical Reports Server (NTRS)

Gilles, P. W.

1975-01-01

A discussion is given of the principles of physical chemistry important in vaporization studies, notably the concepts of equilibrium, phase behavior, thermodynamics, solid solution, and kinetics. The important factors influencing equilibrium vaporization phenomena are discussed and illustrated. A proper course of a vaporization study consisting of 9 stages is proposed. The important experimental techniques of Knudsen effusion, Langmuir vaporization and mass spectrometry are discussed. The principles, the factors, the course of a study and the experimental techniques and procedures are illustrated by recent work on the Ti-O system.

Non-equilibrium Numerical Analysis of Microwave-supported Detonation Threshold Propagating through Diatomic Gas

NASA Astrophysics Data System (ADS)

Shiraishi, Hiroyuki

2015-09-01

Microwave-supported Detonation (MSD), one type of Microwave-supported Plasma (MSP), is considered as one of the most important phenomena because it can generate high pressure and high temperature for beam-powered space propulsion systems. In this study, I numerically simulate MSD waves propagating through a diatomic gas. In order to evaluate the threshold of beam intensity, I use the physical-fluid dynamics scheme, which has been developed for simulating unsteady and non-equilibrium LSD waves propagating through a hydrogen gas.

Observation of a Discrete Time Crystal

NASA Astrophysics Data System (ADS)

Kyprianidis, A.; Zhang, J.; Hess, P.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potter, A.; Vishwanath, A.; Potirniche, I.-D.; Yao, N.; Monroe, C.

2017-04-01

Spontaneous symmetry breaking is a key concept in the understanding of many physical phenomena, such as the formation of spatial crystals and the phase transition from paramagnetism to magnetic order. While the breaking of time translation symmetry is forbidden in equilibrium systems, it is possible for non-equilibrium Floquet driven systems to break a discrete time translation symmetry, and we present clear signatures of the formation of such a discrete time crystal. We apply a time periodic Hamiltonian to a chain of interacting spins under many-body localization conditions and observe the system's sub-harmonic response at twice that period. This spontaneous doubling of the periodicity is robust to external perturbations. We represent the spins with a linear chain of trapped 171Yb+ ions in an rf Paul trap, generate spin-spin interactions through spin-dependent optical dipole forces, and measure each spin using state-dependent fluorescence. This work is supported by the ARO Atomic Physics Program, the AFOSR MURI on Quantum Measurement and Verification, and the NSF Physics Frontier Center at JQI.

Innovative Interactive Lecture Demonstrations Using Wireless Force Sensors and Accelerometers for Introductory Physics Courses

NASA Astrophysics Data System (ADS)

Yoder, G.; Cook, J.

2010-12-01

Interactive lecture demonstrations1-6 (ILDs) are a powerful tool designed to help instructors bring state-of-the-art teaching pedagogies into the college-level introductory physics classroom. ILDs have been shown to improve students' conceptual understanding, and many examples have been created and published by Sokoloff and Thornton.6 We have used the new technology of Vernier's Wireless Dynamics Sensor System (WDSS)7 to develop three new ILDs for the first-semester introductory physics (calculus-based or algebra-based) classroom. These three are the Force Board, to demonstrate the vector nature of forces, addition of vectors, and the first condition of equilibrium; the Torque Board, to demonstrate torque and the second condition for equilibrium; and the Circular Motion Board, to discover the nature of the acceleration an object exhibiting uniform circular motion. With the WDSS, all three of these ILDs are easy to set up and use in any classroom or laboratory situation, and allow more instructors to utilize the technique of interactive lecture demonstrations.

Selective gas capture via kinetic trapping

DOE PAGES

Kundu, Joyjit; Pascal, Tod; Prendergast, David; ...

2016-07-13

Conventional approaches to the capture of CO 2 by metal-organic frameworks focus on equilibrium conditions, and frameworks that contain little CO 2 in equilibrium are often rejected as carbon-capture materials. Here we use a statistical mechanical model, parameterized by quantum mechanical data, to suggest that metal-organic frameworks can be used to separate CO 2 from a typical flue gas mixture when used under nonequilibrium conditions. The origin of this selectivity is an emergent gas-separation mechanism that results from the acquisition by different gas types of different mobilities within a crowded framework. The resulting distribution of gas types within the frameworkmore » is in general spatially and dynamically heterogeneous. Our results suggest that relaxing the requirement of equilibrium can substantially increase the parameter space of conditions and materials for which selective gas capture can be effected.« less

Equilibrium statistical mechanics of self-consistent wave-particle system

NASA Astrophysics Data System (ADS)

Elskens, Yves

2005-10-01

The equilibrium distribution of N particles and M waves (e.g. Langmuir) is analysed in the weak-coupling limit for the self-consistent hamiltonian model H = ∑rpr^2 /(2m) + ∑jφjIj+ ɛ∑r,j(βj/ kj) (kjxr- θj) [1]. In the canonical ensemble, with temperature T and reservoir velocity v < jφj/kj, the wave intensities are almost independent and exponentially distributed, with expectation = kBT / (φj- kjv). These equilibrium predictions are in agreement with Monte Carlo samplings [2] and with direct simulations of the dynamics, indicating equivalence between canonical and microcanonical ensembles. [1] Y. Elskens and D.F. Escande, Microscopic dynamics of plasmas and chaos (IoP publishing, Bristol, 2003). [2] M-C. Firpo and F. Leyvraz, 30th EPS conf. contr. fusion and plasma phys., P-2.8 (2003).

Comparison of Methods for Characterizing Nonideal Solute Self-Association by Sedimentation Equilibrium

PubMed Central

Scott, David J.; Winzor, Donald J.

2009-01-01

Abstract We have examined in detail analytical solutions of expressions for sedimentation equilibrium in the analytical ultracentrifuge to describe self-association under nonideal conditions. We find that those containing the radial dependence of total solute concentration that incorporate the Adams-Fujita assumption for composition-dependence of activity coefficients reveal potential shortcomings for characterizing such systems. Similar deficiencies are shown in the use of the NONLIN software incorporating the same assumption about the interrelationship between activity coefficients for monomer and polymer species. These difficulties can be overcome by iterative analyses incorporating expressions for the composition-dependence of activity coefficients predicted by excluded volume considerations. A recommendation is therefore made for the replacement of current software packages by programs that incorporate rigorous statistical-mechanical allowance for thermodynamic nonideality in sedimentation equilibrium distributions reflecting solute self-association. PMID:19651047

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

NASA Technical Reports Server (NTRS)

Jayaraman, Vegnesh; Liu, Yen; Panesi, Marco

2017-01-01

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

Description of intraoral pressures on sub-palatal space in young adult patients with normal occlusion.

PubMed

Fuentes, Ramón; Engelke, Wilfried; Flores, Tania; Navarro, Pablo; Borie, Eduardo; Curiqueo, Aldo; Salamanca, Carlos

2015-01-01

Under normal conditions, the oral cavity presents a perfect system of equilibrium between teeth, soft tissues and tongue. The equilibrium of soft tissues forms a closed capsular matrix, generating differences with the atmospheric environment. This difference is known as intraoral pressure. Negative intraoral pressure is fundamental to the stabilization of the soft palate and tongue, reducing neuromuscular activity for the permeability of the respiratory tract. Thus, the aim of this study was to describe the variations of intraoral pressure of the sub-palatal space (SPS) under different physiological conditions and biofunctional phases. A case series was conducted with 20 individuals aged between 18 and 25. The intraoral pressures were measured through a system of cannulae connected to a digital pressure meter in the SPS during seven biofunctional phases. Descriptive statistics were used based on the mean and standard deviation. The data recorded pressure variations under physiological conditions, reaching 65 mbar as the intraoral peak in forced inspiration. In the swallowing phase, peaks reached -91.9 mbar. No pressure variations were recorded in terms of atmospheric changes with the mouth open and semi-open. The data obtained during the swallowing and forced inspiration phases indicated forced lingual activity. In the swallowing phase, the adequate position of the tongue creates negative intraoral pressure, which represents a fundamental mechanism for the physical stabilization of the soft palate. This information could contribute to subsequent research into the treatment of primary roncopathies.

Comments on "The Sensitivity Study of Radiative-Convective Equilibrium in the Tropics with a Convective Resolving Model"

NASA Technical Reports Server (NTRS)

Tao, W.-K.; Shie, C.-L.; Simpson, J.

2000-01-01

In general, there are two broad scientific objectives when using cloud resolving models (CRMs or cloud ensemble models-CEMs) to study tropical convection. The first one is to use them as a physics resolving models to understand the dynamic and microphysical processes associated with the tropical water and energy cycles and their role in the climate system. The second approach is to use the CRMs to improve the representation of moist processes and their interaction with radiation in large-scale models. In order to improve the credibility of the CRMs and achieve the above goals, CRMs using identical initial conditions and large-scale influences need to produce very similar results. Two CRMs produced different statistical equilibrium (SE) states even though both used the same initial thermodynamic and wind conditions. Sensitivity tests to identify the major physical processes that determine the SE states for the different CRM simulations were performed. Their results indicated that atmospheric horizontal wind is treated quite differently in these two CRMs. The model that had stronger surface winds and consequently larger latent and sensible heat fluxes from the ocean produced a warmer and more humid modeled thermodynamic SE state. In addition, the domain mean thermodynamic state is more unstable for those experiments that produced a warmer and more humid SE state. Their simulated wet (warm and humid) SE states are thermally more stable in the lower troposphere (from the surface to 4-5 km in altitude). The large-scale horizontal advective effects on temperature and water vapor mixing ratio are needed when using CRMs to perform long-term integrations to study convective feedback under specified large-scale environments. In addition, it is suggested that the dry and cold SE state simulated was caused by enhanced precipitation but not enough surface evaporation. We find some problems with the interpretation of these three phenomena.

Nuclear-level densities in the {sup 49}V and {sup 57}Co nuclei on the basis of evaporated-neutron spectra in (p, n) and (d, n) reactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhuravlev, B. V., E-mail: zhurav@ippe.ru; Titarenko, N. N.

The spectra of neutrons from the reactions {sup 49}Ti(p, n){sup 49}V and {sup 57}Fe (p, n){sup 57}Co were measured in the range of proton energies between 8 and 11 MeV along with their counterparts from the reactions {sup 48}Ti(d, n){sup 49}V and {sup 56}Fe (d, n){sup 57}Co at the deuteron energies of 2.7 and 3.8 MeV. These measurements were conducted with the aid of a time-of-flight fast-neutron spectrometer on the basis of the EGP-15 pulsed tandem accelerator of the Institute for Physics and Power Engineering (IPPE, Obninsk). An analysis of measured data was performed within the statistical equilibrium and preequilibriummore » models of nuclear reactions. The respective calculations based on the Hauser–Feshbach formalism of statistical theory were carried out with nuclear-level densities given by the generalized superfluid model of the nucleus, the backshifted Fermi-gas model, and the Gilbert–Cameron composite formula. The nuclear-level densities of {sup 49}V and {sup 57}Co and their energy dependences were determined. The results were discussed together with available experimental data and data recommended by model systematics.« less

Isotropic Inelastic Collisions in a Multiterm Atom with Hyperfine Structure

NASA Astrophysics Data System (ADS)

Belluzzi, Luca; Landi Degl'Innocenti, Egidio; Trujillo Bueno, Javier

2015-10-01

A correct modeling of the scattering polarization profiles observed in some spectral lines of diagnostic interest, the sodium doublet being one of the most important examples, requires taking hyperfine structure (HFS) and quantum interference between different J-levels into account. An atomic model suitable for taking these physical ingredients into account is the so-called multiterm atom with HFS. In this work, we introduce and study the transfer and relaxation rates due to isotropic inelastic collisions with electrons, which enter the statistical equilibrium equations (SEE) for the atomic density matrix of this atomic model. Under the hypothesis that the electron-atom interaction is described by a dipolar operator, we provide useful relations between the rates describing the transfer and relaxation of quantum interference between different levels (whose numerical values are in most cases unknown) and the usual rates for the atomic level populations, for which experimental data and/or approximate theoretical expressions are generally available. For the particular case of a two-term atom with HFS, we present an analytical solution of the SEE for the spherical statistical tensors of the upper term, including both radiative and collisional processes, and we derive the expression of the emission coefficient in the four Stokes parameters. Finally, an illustrative application to the Na i D1 and D2 lines is presented.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules.

PubMed

Chowdhury, Debashish

2013-06-04

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.