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

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

PGT: A Statistical Approach to Prediction and Mechanism Design

NASA Astrophysics Data System (ADS)

Wolpert, David H.; Bono, James W.

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

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

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

Ionization and thermal equilibrium models for O star winds based on time-independent radiation-driven wind theory

NASA Technical Reports Server (NTRS)

Drew, J. E.

1989-01-01

Ab initio ionization and thermal equilibrium models are calculated for the winds of O stars using the results of steady state radiation-driven wind theory to determine the input parameters. Self-consistent methods are used for the roles of H, He, and the most abundant heavy elements in both the statistical and the thermal equilibrium. The model grid was chosen to encompass all O spectral subtypes and the full range of luminosity classes. Results of earlier modeling of O star winds by Klein and Castor (1978) are reproduced and used to motivate improvements in the treatment of the hydrogen equilibrium. The wind temperature profile is revealed to be sensitive to gross changes in the heavy element abundances, but insensitive to other factors considered such as the mass-loss rate and velocity law. The reduced wind temperatures obtained in observing the luminosity dependence of the Si IV lambda 1397 wind absorption profile are shown to eliminate any prospect of explaining the observed O VI lambda 1036 line profiles in terms of time-independent radiation-driven wind theory.

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.

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.

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.

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.

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.

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.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng

2015-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

Equation of state of detonation products based on statistical mechanical theory

NASA Astrophysics Data System (ADS)

Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng; Iapcm Team

2013-06-01

The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.

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.

"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.

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…

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.

Perspective: chemical dynamics simulations of non-statistical reaction dynamics

PubMed Central

Ma, Xinyou; Hase, William L.

2017-01-01

Non-statistical chemical dynamics are exemplified by disagreements with the transition state (TS), RRKM and phase space theories of chemical kinetics and dynamics. The intrinsic reaction coordinate (IRC) is often used for the former two theories, and non-statistical dynamics arising from non-IRC dynamics are often important. In this perspective, non-statistical dynamics are discussed for chemical reactions, with results primarily obtained from chemical dynamics simulations and to a lesser extent from experiment. The non-statistical dynamical properties discussed are: post-TS dynamics, including potential energy surface bifurcations, product energy partitioning in unimolecular dissociation and avoiding exit-channel potential energy minima; non-RRKM unimolecular decomposition; non-IRC dynamics; direct mechanisms for bimolecular reactions with pre- and/or post-reaction potential energy minima; non-TS theory barrier recrossings; and roaming dynamics. 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’. PMID:28320906

Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states)

NASA Astrophysics Data System (ADS)

Dubin, Daniel H.; O'neil, T. M.

1999-01-01

Plasmas consisting exclusively of particles with a single sign of charge (e.g., pure electron plasmas and pure ion plasmas) can be confined by static electric and magnetic fields (in a Penning trap) and also be in a state of global thermal equilibrium. This important property distinguishes these totally unneutralized plasmas from neutral and quasineutral plasmas. This paper reviews the conditions for, and the structure of, the thermal equilibrium states. Both theory and experiment are discussed, but the emphasis is decidedly on theory. It is a huge advantage to be able to use thermal equilibrium statistical mechanics to describe the plasma state. Such a description is easily obtained and complete, including for example the details of the plasma shape and microscopic order. Pure electron and pure ion plasmas are routinely confined for hours and even days, and thermal equilibrium states are observed. These plasmas can be cooled to the cryogenic temperature range, where liquid and crystal-like states are realized. The authors discuss the structure of the correlated states separately for three plasma sizes: large plasmas, in which the free energy is dominated by the bulk plasma; mesoscale plasmas, in which the free energy is strongly influenced by the surface; and Coulomb clusters, in which the number of particles is so small that the canonical ensemble is not a good approximation for the microcanonical ensemble. All three cases have been studied through numerical simulations, analytic theory, and experiment. In addition to describing the structure of the thermal equilibrium states, the authors develop a thermodynamic theory of the trapped plasma system. Thermodynamic inequalities and Maxwell relations provide useful bounds on and general relationships between partial derivatives of the various thermodynamic variables.

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.

Evolutionary dynamics of group interactions on structured populations: a review

PubMed Central

Perc, Matjaž; Gómez-Gardeñes, Jesús; Szolnoki, Attila; Floría, Luis M.; Moreno, Yamir

2013-01-01

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory. PMID:23303223

Bond-equilibrium theory of liquid Se-Te alloys. II. Effect of singly attached ring molecules

NASA Astrophysics Data System (ADS)

Cutler, Melvin; Bez, Wolfgang G.

1981-06-01

A statistical-mechanical theory for bond equilibrium of chain polymers containing threefold (3F) and onefold (1F) bond defects is extended to include the effects of free ring molecules and ring molecules attached to chains by a single 3F atom. Positively charged singly attached rings are shown to play a key role in bond equilibrium in liquid Sex Te1-x by permitting the formation of ion pairs in which both constituents are effectively chain terminators, thus decreasing the average polymer size. The theory is applied to explain the behavior of the paramagnetic susceptibility, χp, and electronic transport as affected by the Fermi energy EF. It is found that the increase in χp with the concentration of Te is primarily the result of the smaller energy for breaking Te bonds. In addition, attached rings play an important role in determining the effect of temperature on χp. At x<~0.5, the concentrations of both free and attached rings becomes small at high T because of the high concentration of bond defects.

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.

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).

Statistical physics of the spatial Prisoner's Dilemma with memory-aware agents

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto

2016-02-01

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner's Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner's Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner's Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.

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.

Analyzing the equilibrium states of a quasi-neutral spatially inhomogeneous system of charges above a liquid dielectric film based on the first principles of quantum statistics

NASA Astrophysics Data System (ADS)

Lytvynenko, D. M.; Slyusarenko, Yu V.

2017-08-01

A theory of quasi-neutral equilibrium states of charges above a liquid dielectric surface is developed. This theory is based on the first principles of quantum statistics for systems comprising many identical particles. The proposed approach involves applying the variational principle, modified for the considered systems, and the Thomas-Fermi model. In the terms of the developed theory self-consistency equations are obtained. These equations provide the relation between the main parameters describing the system: the potential of the static electric field, the distribution function of charges and the surface profile of the liquid dielectric. The equations are used to study the phase transition in the system to a spatially periodic state. The proposed method can be applied in analyzing the properties of the phase transition in the system in relation to the spatially periodic states of wave type. Using the analytical and numerical methods, we perform a detailed study of the dependence of the critical parameters of such a phase transition on the thickness of the liquid dielectric film. Some stability criteria for the new asymmetric phase of the studied system are discussed.

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.

{Phi}{sup 4} kinks: Statistical mechanics

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

Habib, S.

1995-12-31

Some recent investigations of the thermal equilibrium properties of kinks in a 1+1-dimensional, classical {phi}{sup 4} field theory are reviewed. The distribution function, kink density, correlation function, and certain thermodynamic quantities were studied both theoretically and via large scale simulations. A simple double Gaussian variational approach within the transfer operator formalism was shown to give good results in the intermediate temperature range where the dilute gas theory is known to fail.

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.

Protein Condensation

NASA Astrophysics Data System (ADS)

Gunton, James D.; Shiryayev, Andrey; Pagan, Daniel L.

2007-09-01

Preface; 1. Introduction; 2. Globular protein structure; 3. Experimental methods; 4. Thermodynamics and statistical mechanics; 5. Protein-protein interactions; 6. Theoretical studies of equilibrium; 7. Nucleation theory; 8. Experimental studies of nucleation; 9. Lysozyme; 10. Some other globular proteins; 11. Membrane proteins; 12. Crystallins and cataracts; 13. Sickle hemoglobin and sickle cell anemia; 14, Alzheimer's disease; Index.

Protein Condensation

NASA Astrophysics Data System (ADS)

Gunton, James D.; Shiryayev, Andrey; Pagan, Daniel L.

2014-07-01

Preface; 1. Introduction; 2. Globular protein structure; 3. Experimental methods; 4. Thermodynamics and statistical mechanics; 5. Protein-protein interactions; 6. Theoretical studies of equilibrium; 7. Nucleation theory; 8. Experimental studies of nucleation; 9. Lysozyme; 10. Some other globular proteins; 11. Membrane proteins; 12. Crystallins and cataracts; 13. Sickle hemoglobin and sickle cell anemia; 14, Alzheimer's disease; Index.

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.

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.

Sir Fred Hoyle and the theory of the synthesis of the elements

NASA Astrophysics Data System (ADS)

Arnett, David

Some of Fred Hoyle's pioneering ideas about the site and the nature of the synthesis of the elements are examined in a modern context of theory, experiment and observations. Hoyle's ideas concerning the nucleosynthesis cycle of stellar birth and death, rotational instability of supernovae, the onion-skin model of presupernovae, neutronization, nuclear statistical equilibrium and core collapse, thermonuclear supernovae, nucleosynthesis processes and freeze-out are discussed. The history of the clash of theory and experiment on the second excited state of 8Be and helium ignition in red giants is reviewed.

Computing molecular fluctuations in biochemical reaction systems based on a mechanistic, statistical theory of irreversible processes.

PubMed

Kulasiri, Don

2011-01-01

We discuss the quantification of molecular fluctuations in the biochemical reaction systems within the context of intracellular processes associated with gene expression. We take the molecular reactions pertaining to circadian rhythms to develop models of molecular fluctuations in this chapter. There are a significant number of studies on stochastic fluctuations in intracellular genetic regulatory networks based on single cell-level experiments. In order to understand the fluctuations associated with the gene expression in circadian rhythm networks, it is important to model the interactions of transcriptional factors with the E-boxes in the promoter regions of some of the genes. The pertinent aspects of a near-equilibrium theory that would integrate the thermodynamical and particle dynamic characteristics of intracellular molecular fluctuations would be discussed, and the theory is extended by using the theory of stochastic differential equations. We then model the fluctuations associated with the promoter regions using general mathematical settings. We implemented ubiquitous Gillespie's algorithms, which are used to simulate stochasticity in biochemical networks, for each of the motifs. Both the theory and the Gillespie's algorithms gave the same results in terms of the time evolution of means and variances of molecular numbers. As biochemical reactions occur far away from equilibrium-hence the use of the Gillespie algorithm-these results suggest that the near-equilibrium theory should be a good approximation for some of the biochemical reactions. © 2011 Elsevier Inc. All rights reserved.

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.

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 hydrogenic 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. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

NASA Astrophysics Data System (ADS)

Pusev, R. S.

2010-10-01

We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.

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.

Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

NASA Astrophysics Data System (ADS)

Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.

2010-01-01

We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.

Statistical Teleodynamics: Toward a Theory of Emergence.

PubMed

Venkatasubramanian, Venkat

2017-10-24

The central scientific challenge of the 21st century is developing a mathematical theory of emergence that can explain and predict phenomena such as consciousness and self-awareness. The most successful research program of the 20th century, reductionism, which goes from the whole to parts, seems unable to address this challenge. This is because addressing this challenge inherently requires an opposite approach, going from parts to the whole. In addition, reductionism, by the very nature of its inquiry, typically does not concern itself with teleology or purposeful behavior. Modeling emergence, in contrast, requires the addressing of teleology. Together, these two requirements present a formidable challenge in developing a successful mathematical theory of emergence. In this article, I describe a new theory of emergence, called statistical teleodynamics, that addresses certain aspects of the general problem. Statistical teleodynamics is a mathematical framework that unifies three seemingly disparate domains-purpose-free entities in statistical mechanics, human engineered teleological systems in systems engineering, and nature-evolved teleological systems in biology and sociology-within the same conceptual formalism. This theory rests on several key conceptual insights, the most important one being the recognition that entropy mathematically models the concept of fairness in economics and philosophy and, equivalently, the concept of robustness in systems engineering. These insights help prove that the fairest inequality of income is a log-normal distribution, which will emerge naturally at equilibrium in an ideal free market society. Similarly, the theory predicts the emergence of the three classes of network organization-exponential, scale-free, and Poisson-seen widely in a variety of domains. Statistical teleodynamics is the natural generalization of statistical thermodynamics, the most successful parts-to-whole systems theory to date, but this generalization is only a modest step toward a more comprehensive mathematical theory of emergence.

Nucleon matter equation of state, particle number fluctuations, and shear viscosity within UrQMD box calculations

NASA Astrophysics Data System (ADS)

Motornenko, A.; Bravina, L.; Gorenstein, M. I.; Magner, A. G.; Zabrodin, E.

2018-03-01

Properties of equilibrated nucleon system are studied within the ultra-relativistic quantum molecular dynamics (UrQMD) transport model. The UrQMD calculations are done within a finite box with periodic boundary conditions. The system achieves thermal equilibrium due to nucleon-nucleon elastic scattering. For the UrQMD-equilibrium state, nucleon energy spectra, equation of state, particle number fluctuations, and shear viscosity η are calculated. The UrQMD results are compared with both, statistical mechanics and Chapman-Enskog kinetic theory, for a classical system of nucleons with hard-core repulsion.

The influence of processor focus on speckle correlation statistics for a Shuttle imaging radar scene of Hurricane Josephine

NASA Technical Reports Server (NTRS)

Tilley, David G.

1988-01-01

The surface wave field produced by Hurricane Josephine was imaged by the L-band SAR aboard the Challenger on October 12, 1984. Exponential trends found in the two-dimensional autocorrelations of speckled image data support an equilibrium theory model of sea surface hydrodynamics. The notions of correlated specular reflection, surface coherence, optimal Doppler parameterization and spatial resolution are discussed within the context of a Poisson-Rayleigh statistical model of the SAR imaging process.

The physician-patient relationship as a game of strategic information transmission.

PubMed

De Jaegher, K; Jegers, M

2001-10-01

We show that the intuition underlying the supplier-induced demand (SID) hypothesis is reflected in the cheap-talk literature from game theory, and in the credence-good literature from the economics of information. Applying these theories, we conclude that a neoclassical version of the SID hypothesis is only relevant for treatment decisions involving an expensive treatment that is equally effective in curing several states, but efficient in curing only some of these states (in that a cheaper treatment is efficient otherwise). For a simple game involving such a treatment decision, we show that a Nash equilibrium exists where the patient is able to constrain the physician in inducing demand, without the market for the potentially induced treatment failing. This equilibrium allows us to derive comparative statistics and welfare results. Copyright 2001 John Wiley & Sons, Ltd.

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study.

PubMed

Malijevský, Alexandr; Archer, Andrew J

2013-10-14

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

Theory of hydromagnetic turbulence

NASA Technical Reports Server (NTRS)

Montgomery, D.

1983-01-01

The present state of MHD turbulence theory as a possible solar wind research tool is surveyed. The theory is statistical, and does not make statements about individual events. The ensembles considered typically have individual realizations which differ qualitatively, unlike equilibrium statistical mechanics. Most of the theory deals with highly symmetric situations; most of these symmetries have yet to be tested in the solar wind. The applicability of MHD itself to solar wind parameters is highly questionable; yet it has no competitors, as a potentially comprehensive dynamical description. The purpose of solar wind research require sharper articulation. If they are to understand radial turbulent plasma flows from spheres, laboratory experiments and numerical solution of equations of motion may be cheap alternative to spacecraft. If "real life" information is demanded, multiple spacecraft with variable separation may be necessary to go further. The principal emphasis in the theory so far has been on spectral behavior for spatial covariances in wave number space. There is no respectable theory of these for highly anisotropic situations. A rather slow development of theory acts as a brake on justifiable measurement, at this point.

Statistical theory and applications of lock-in carrierographic image pixel brightness dependence on multi-crystalline Si solar cell efficiency and photovoltage

NASA Astrophysics Data System (ADS)

Mandelis, Andreas; Zhang, Yu; Melnikov, Alexander

2012-09-01

A solar cell lock-in carrierographic image generation theory based on the concept of non-equilibrium radiation chemical potential was developed. An optoelectronic diode expression was derived linking the emitted radiative recombination photon flux (current density), the solar conversion efficiency, and the external load resistance via the closed- and/or open-circuit photovoltage. The expression was shown to be of a structure similar to the conventional electrical photovoltaic I-V equation, thereby allowing the carrierographic image to be used in a quantitative statistical pixel brightness distribution analysis with outcome being the non-contacting measurement of mean values of these important parameters averaged over the entire illuminated solar cell surface. This is the optoelectronic equivalent of the electrical (contacting) measurement method using an external resistor circuit and the outputs of the solar cell electrode grid, the latter acting as an averaging distribution network over the surface. The statistical theory was confirmed using multi-crystalline Si solar cells.

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.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion.

PubMed

Freed, Karl F

2014-10-14

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

NASA Astrophysics Data System (ADS)

Freed, Karl F.

2014-10-01

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.

Communication: Towards first principles theory of relaxation in supercooled liquids formulated in terms of cooperative motion

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

Freed, Karl F., E-mail: freed@uchicago.edu

A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition” [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic naturemore » of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.« less

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.

Theory of Quasi-Equilibrium Nucleosynthesis and Applications to Matter Expanding from High Temperature and Density

NASA Astrophysics Data System (ADS)

Meyer, Bradley S.; Krishnan, Tracy D.; Clayton, Donald D.

1998-05-01

Our first purpose is construction of a formal theory of quasi-equilibrium. We define quasi-equilibrium, in its simplest form, as statistical equilibrium in the face of an extra constraint on the nuclear populations. We show that the extra constraint introduces a uniform translation of the chemical potentials for the heavy nuclei and derive the abundances in terms of it. We then generalize this theory to accommodate any number of constraints. For nucleosynthesis, the most important constraint occurs when the total number of heavy nuclei Yh within a system of nuclei differs from the number that would exist in nuclear statistical equilibrium (NSE) under the same conditions of density and temperature. Three situations of high relevance are (1) silicon burning, wherein the total number of nuclei exceeds but asymptotically approaches the NSE number; (2) alpha-rich freezeout expansions of high entropy, wherein Yh is less than the NSE number; and (3) expansions from high temperature of low-entropy matter, in which Yh exceeds the NSE number. These are of importance, respectively, within (1) supernova shells, (2) Type II supernova cores modestly outside the mass cut, and (3) Type Ia supernova cores in near-Chandrasekhar-mass events. Our next goal is the detailed analysis of situation (2), the high-entropy alpha-rich neutron-rich freezeout. We employ a nuclear reaction network, which we integrate, to compare the actual abundances with those obtained at the same thermal conditions by the quasi-equilibrium (QSE) theory and by the NSE theory. For this detailed comparison, we choose a high-entropy photon-to-nucleon ratio φ = 6.8, for which we conduct expansions at initial bulk neutron excess η0 = 0.10. We demonstrate that the abundance populations, as they begin expansion and cooling from temperature 10 × 109 K, are characterized by three distinct phases: (1) NSE, (2) QSE having Yh smaller than the NSE value, and (3) final reaction rate-dependent freezeout modifications of the QSE. We demonstrate that the true final abundances are well approximated by the QSE distribution near the freezeout temperature T9f = 4.0. During the expansion, the QSE distribution changes shape continuously in ways that are independent of the reaction cross sections of the heavy nuclei with free light particles. It is this changing shape, rather than ``nuclear flows,'' that establish the abundance pattern. The abundance pattern is actually determined by the parameter Yh and the degree to which it differs from the NSE value owing to the slowness with which light particles can be assembled into heavy nuclei (A >= 12). We also detail the nature and magnitude of the freezeout corrections to the QSE distribution. The entire distribution depends less upon the values of heavy-element cross sections than has been heretofore thought. Our third goal is to survey the alpha-rich freezeout. We do this by less complete analysis of nine different expansions determined by the matrix of three distinct entropies (φ = 1.7, 6.8, and 17) and three distinct initial neutron excesses (η0 = 0.003, 0.10, and 0.1667). The trends are easily comprehended in terms of the concept of quasi-equilibrium, whereas they are not understandable in terms of either NSE or in terms of reaction rates. This secures for the QSE concept a major diagnostic capability within nucleosynthesis theory. We delineate the key trends and also remark on the ways that order arises from disorder in this complex system. We conclude with a discussion of how such systems assemble heavy nuclei.

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.

Testing for detailed balance in a financial market

NASA Astrophysics Data System (ADS)

Fiebig, H. R.; Musgrove, D. P.

2015-06-01

We test a historical price-time series in a financial market (the NASDAQ 100 index) for a statistical property known as detailed balance. The presence of detailed balance would imply that the market can be modeled by a stochastic process based on a Markov chain, thus leading to equilibrium. In economic terms, a positive outcome of the test would support the efficient market hypothesis, a cornerstone of neo-classical economic theory. In contrast to the usage in prevalent economic theory the term equilibrium here is tied to the returns, rather than the price-time series. The test is based on an action functional S constructed from the elements of the detailed balance condition and the historical data set, and then analyzing S by means of simulated annealing. Checks are performed to verify the validity of the analysis method. We discuss the outcome of this analysis.

Stochastic cycle selection in active flow networks.

PubMed

Woodhouse, Francis G; Forrow, Aden; Fawcett, Joanna B; Dunkel, Jörn

2016-07-19

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 nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models.

Stochastic cycle selection in active flow networks

PubMed Central

Woodhouse, Francis G.; Forrow, Aden; Fawcett, Joanna B.; Dunkel, Jörn

2016-01-01

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 nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models. PMID:27382186

Punctuated equilibrium dynamics in human communications

NASA Astrophysics Data System (ADS)

Peng, Dan; Han, Xiao-Pu; Wei, Zong-Wen; Wang, Bing-Hong

2015-10-01

A minimal model based on network incorporating individual interactions is proposed to study the non-Poisson statistical properties of human behavior: individuals in system interact with their neighbors, the probability of an individual acting correlates to its activity, and all the individuals involved in action will change their activities randomly. The model reproduces varieties of spatial-temporal patterns observed in empirical studies of human daily communications, providing insight into various human activities and embracing a range of realistic social interacting systems, particularly, intriguing bimodal phenomenon. This model bridges priority queueing theory and punctuated equilibrium dynamics, and our modeling and analysis is likely to shed light on non-Poisson phenomena in many complex systems.

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.

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.

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.

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.

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

A Conditional Curie-Weiss Model for Stylized Multi-group Binary Choice with Social Interaction

NASA Astrophysics Data System (ADS)

Opoku, Alex Akwasi; Edusei, Kwame Owusu; Ansah, Richard Kwame

2018-04-01

This paper proposes a conditional Curie-Weiss model as a model for decision making in a stylized society made up of binary decision makers that face a particular dichotomous choice between two options. Following Brock and Durlauf (Discrete choice with social interaction I: theory, 1955), we set-up both socio-economic and statistical mechanical models for the choice problem. We point out when both the socio-economic and statistical mechanical models give rise to the same self-consistent equilibrium mean choice level(s). Phase diagram of the associated statistical mechanical model and its socio-economic implications are discussed.

Statistical Ring Catenation under Thermodynamic Control: Should the Jacobson-Stockmayer Cyclization Theory Take into Account Catenane Formation?

PubMed

Di Stefano, Stefano; Ercolani, Gianfranco

2017-01-26

An extension of the Jacobson-Stockmayer theory is presented to include the reversible formation of [2]catenanes in a ring-chain system under thermodynamic control. The extended theory is based on the molar catenation constant, measuring the ease of catenation of two ring oligomers, whose expression was obtained in a previous work. Two scenarios have been considered: that of "thick" (hydrocarbon-like) chains and that of "thin" (DNA-like) chains. In the case of "thick" chains, the formation of catenanes can be neglected, unless in the unlikely case of a very large value of the equilibrium constant for linear propagation (K ≈ 10 8 mol -1 L, or larger). For K tending to infinity, the system becomes a chain-free system where only ring-catenane equilibria occur. Under this condition, there is a critical concentration below which only rings are present at equilibrium and above which the ring fraction remains constant, and the excess monomer is converted only into catenanes. In the case of "thin" chains, the formation of catenanes cannot be neglected even for values of K as low as 10 2 mol -1 L, thus justifying the use of the extended theory.

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.

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

Studies in Non-Equilibrium Statistical Mechanics.

DTIC Science & Technology

1982-09-01

in the formalism, and this is used to simulate the effects of rotational states and collisions. At each stochastic step the energy changes in the...uses of this method. 10. A Scaling Theoretical Analysis of Vibrational Relaxation Experiments: Rotational Effects and Long-Range Collisions 0...in- elude rotational effects through the rotational energy gaps and the rotational distributions. The variables in this theory are a fundamental set

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

Free energy landscape theory of glass transition

NASA Astrophysics Data System (ADS)

Odagaki, Takashi

2010-03-01

I first present a free energy landscape (FEL) description of statistical mechanics, which is an exact reformulation of statistical mechanics and can be applied to non-equilibrium systems. Then, I discuss thermodynamic and dynamic properties of the vitrification process on the basis of the FEL formalism. I show that thermodynamic and dynamic anomalies at the glass transition, including the cooling rate dependence, can be understood in a unified manner which has not been achieved by any other theories of the glass transition. Namely, I show that the vitrification is a transition from annealed to quenched averages in the FEL and that the fast beta, the JG and the slow alpha relaxations are attributed to stochastic dynamics within a basin of FEL, jumping motion among locally connected basins and diffusive dynamics over barriers of the FEL.

Equilibrium theory of island biogeography: A review

Treesearch

Angela D. Yu; Simon A. Lei

2001-01-01

The topography, climatic pattern, location, and origin of islands generate unique patterns of species distribution. The equilibrium theory of island biogeography creates a general framework in which the study of taxon distribution and broad island trends may be conducted. Critical components of the equilibrium theory include the species-area relationship, island-...

A Holistic Equilibrium Theory of Organization Development

ERIC Educational Resources Information Center

Yang, Baiyin; Zheng, Wei

2005-01-01

This paper proposes a holistic equilibrium theory of organizational development (OD). The theory states that there are three driving forces in organizational change and development--rationality, reality, and liberty. OD can be viewed as a planned process of change in an organization so as to establish equilibrium among these three interacting…

Theory for solubility in static systems

NASA Astrophysics Data System (ADS)

Gusev, Andrei A.; Suter, Ulrich W.

1991-06-01

A theory for the solubility of small particles in static structures has been developed. The distribution function of the solute in a frozen solid has been derived in analytical form for the quantum and the quasiclassical cases. The solubility at infinitesimal gas pressure (Henry's constant) as well as the pressure dependence of the solute concentration at elevated pressures has been found from the statistical equilibrium between the solute in the static matrix and the ideal-gas phase. The distribution function of a solute containing different particles has been evaluated in closed form. An application of the theory to the sorption of methane in the computed structures of glassy polycarbonate has resulted in a satisfactory agreement with experimental data.

Elasticity and Fluctuations of Frustrated Nanoribbons

NASA Astrophysics Data System (ADS)

Grossman, Doron; Sharon, Eran; Diamant, Haim

2016-06-01

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes nonmonotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of nonfrustrated fluctuating filaments.

Statistical prescission point model of fission fragment angular distributions

NASA Astrophysics Data System (ADS)

John, Bency; Kataria, S. K.

1998-03-01

In light of recent developments in fission studies such as slow saddle to scission motion and spin equilibration near the scission point, the theory of fission fragment angular distribution is examined and a new statistical prescission point model is developed. The conditional equilibrium of the collective angular bearing modes at the prescission point, which is guided mainly by their relaxation times and population probabilities, is taken into account in the present model. The present model gives a consistent description of the fragment angular and spin distributions for a wide variety of heavy and light ion induced fission reactions.

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.

Statistical Mechanics of Coherent Ising Machine — The Case of Ferromagnetic and Finite-Loading Hopfield Models —

NASA Astrophysics Data System (ADS)

Aonishi, Toru; Mimura, Kazushi; Utsunomiya, Shoko; Okada, Masato; Yamamoto, Yoshihisa

2017-10-01

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large scale optimization problems because of its scalability and high-speed computational ability. However, it is difficult to implement the Ising computation in the CIM because the theories and techniques of classical thermodynamic equilibrium Ising spin systems cannot be directly applied to the CIM. This means we have to adapt these theories and techniques to the CIM. Here we focus on a ferromagnetic model and a finite loading Hopfield model, which are canonical models sharing a common mathematical structure with almost all other Ising models. We derive macroscopic equations to capture nonequilibrium phase transitions in these models. The statistical mechanical methods developed here constitute a basis for constructing evaluation methods for other Ising computation models.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

PubMed Central

Aquilanti, Vincenzo; Coutinho, Nayara Dantas

2017-01-01

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto–Tsallis statistical weights: these generalize the Boltzmann–Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature. 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’. PMID:28320904

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions.

PubMed

Aquilanti, Vincenzo; Coutinho, Nayara Dantas; Carvalho-Silva, Valter Henrique

2017-04-28

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d  < 0, to those where d  > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d  = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d  > 0 or for a negative binomial distribution if d  < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super -Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub -Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti -Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.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).

Ecological optimality in water-limited natural soil-vegetation systems. I - Theory and hypothesis

NASA Technical Reports Server (NTRS)

Eagleson, P. S.

1982-01-01

The solution space of an approximate statistical-dynamic model of the average annual water balance is explored with respect to the hydrologic parameters of both soil and vegetation. Within the accuracy of this model it is shown that water-limited natural vegetation systems are in stable equilibrium with their climatic and pedologic environments when the canopy density and species act to minimize average water demand stress. Theory shows a climatic limit to this equilibrium above which it is hypothesized that ecological pressure is toward maximization of biomass productivity. It is further hypothesized that natural soil-vegetation systems will develop gradually and synergistically, through vegetation-induced changes in soil structure, toward a set of hydraulic soil properties for which the minimum stress canopy density of a given species is maximum in a given climate. Using these hypotheses, only the soil effective porosity need be known to determine the optimum soil and vegetation parameters in a given climate.

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.

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.

COLLABORATIVE RESEARCH AND DEVELOPMENT (CR&D) Delivery Order 0059: Molecular Dynamics Modeling Support

DTIC Science & Technology

2008-03-01

Molecular Dynamics Simulations 5 Theory: Equilibrium Molecular Dynamics Simulations 6 Theory: Non...Equilibrium Molecular Dynamics Simulations 8 Carbon Nanotube Simulations : Approach and results from equilibrium and non-equilibrium molecular dynamics ...touched from the perspective of molecular dynamics simulations . However, ordered systems such as “Carbon Nanotubes” have been investigated in terms

Analytical approach for collective diffusion: One-dimensional lattice with the nearest neighbor and the next nearest neighbor lateral interactions

NASA Astrophysics Data System (ADS)

Tarasenko, Alexander

2018-01-01

Diffusion of particles adsorbed on a homogeneous one-dimensional lattice is investigated using a theoretical approach and MC simulations. The analytical dependencies calculated in the framework of approach are tested using the numerical data. The perfect coincidence of the data obtained by these different methods demonstrates that the correctness of the approach based on the theory of the non-equilibrium statistical operator.

Dipole Alignment in Rotating MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.; Fu, Terry; Morin, Lee

2012-01-01

We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.

Effective convergence of the two-particle irreducible 1/N expansion for nonequilibrium quantum fields

NASA Astrophysics Data System (ADS)

Aarts, Gert; Laurie, Nathan; Tranberg, Anders

2008-12-01

The 1/N expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the 1/N expansion in the O(N) model by comparing results obtained numerically in 1+1 dimensions at leading, next-to-leading and next-to-next-to-leading order in 1/N as well as in the weak coupling limit. A comparison in classical statistical field theory, where exact numerical results are available, is made as well. We focus on early-time dynamics and quasiparticle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling.

Resolving Discrepancies in the Measurements of the Interfacial Tension for the CO2 + H2O Mixture by Computer Simulation.

PubMed

Müller, Erich A; Mejía, Andrés

2014-04-03

Literature values regarding the pressure dependence of the interfacial tension of the system of carbon dioxide (CO2) + water (H2O) show an unexplained divergence and scatter at the transition between low-pressure gas-liquid equilibrium and the high-pressure liquid-liquid equilibrium. We employ the Statistical Associating Fluid Theory (SAFT) and canonical molecular dynamics simulations based on the corresponding coarse grained force field to map out the phase diagram of the mixture and the interfacial tension for this system. We showcase how at ambient temperatures a triple point (gas-liquid-liquid) is expected and detail the implications that the appearance of the third phase has on the interfacial tensions of the system.

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.

Magnetospheric equilibrium configurations and slow adiabatic convection

NASA Technical Reports Server (NTRS)

Voigt, Gerd-Hannes

1986-01-01

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.

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.

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.

Relativistic Fluid Dynamics Far From Local Equilibrium

NASA Astrophysics Data System (ADS)

Romatschke, Paul

2018-01-01

Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N =4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.

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

Soft active matter: a contemporary example of Edwardsian statistical mechanics

NASA Astrophysics Data System (ADS)

Liverpool, Tanniemola

Colonies of swimming bacteria, algae or spermatozoa are examples of active systems composed of interacting units that consume energy and collectively generate motion and mechanical stresses. Due to the anisotropy of their interactions, these active particles can exhibit orientational order at high concentrations and have been called ``living liquid crystals''. Biology at the cellular and multicellular scale provides numerous examples of these active systems. They provide a novel class of experimentally accessible system far from equilibrium. Their rich collective behaviour includes non-equilibrium phase transitions and pattern formation on mesoscopic scales. Interestingly however, some of the theoretical insights gained from field theories applied to equilibrium soft matter systems can be used to explain aspects of their behaviour, but with a number of surprising new twists. I will describe and summarise recent theoretical results characterising the behaviour of such soft active systems highlighting in particular the effects of their internal dynamics on their macroscopic behaviour. With support of the EPSRC Grant No. EP/G026440/1.

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

Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges

PubMed Central

Yunger Halpern, Nicole; Faist, Philippe; Oppenheim, Jonathan; Winter, Andreas

2016-01-01

The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented by operators that fail to commute. Whether such a system thermalizes and what form the thermal state has are questions about truly quantum thermodynamics. Here we investigate this thermal state from three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system-and-bath composite, tracing out the bath yields the system's thermal state. This state is expected to be the equilibrium point, we argue, of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity—the inability to extract work from equilibrium states—implies the thermal state's form, too. Our work opens new avenues into equilibrium in the presence of quantum noncommutation. PMID:27384494

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.

Thermodynamics and proton activities of protic ionic liquids with quantum cluster equilibrium theory

NASA Astrophysics Data System (ADS)

Ingenmey, Johannes; von Domaros, Michael; Perlt, Eva; Verevkin, Sergey P.; Kirchner, Barbara

2018-05-01

We applied the binary Quantum Cluster Equilibrium (bQCE) method to a number of alkylammonium-based protic ionic liquids in order to predict boiling points, vaporization enthalpies, and proton activities. The theory combines statistical thermodynamics of van-der-Waals-type clusters with ab initio quantum chemistry and yields the partition functions (and associated thermodynamic potentials) of binary mixtures over a wide range of thermodynamic phase points. Unlike conventional cluster approaches that are limited to the prediction of thermodynamic properties, dissociation reactions can be effortlessly included into the bQCE formalism, giving access to ionicities, as well. The method is open to quantum chemical methods at any level of theory, but combination with low-cost composite density functional theory methods and the proposed systematic approach to generate cluster sets provides a computationally inexpensive and mostly parameter-free way to predict such properties at good-to-excellent accuracy. Boiling points can be predicted within an accuracy of 50 K, reaching excellent accuracy for ethylammonium nitrate. Vaporization enthalpies are predicted within an accuracy of 20 kJ mol-1 and can be systematically interpreted on a molecular level. We present the first theoretical approach to predict proton activities in protic ionic liquids, with results fitting well into the experimentally observed correlation. Furthermore, enthalpies of vaporization were measured experimentally for some alkylammonium nitrates and an excellent linear correlation with vaporization enthalpies of their respective parent amines is observed.

The economics of motion perception and invariants of visual sensitivity.

PubMed

Gepshtein, Sergei; Tyukin, Ivan; Kubovy, Michael

2007-06-21

Neural systems face the challenge of optimizing their performance with limited resources, just as economic systems do. Here, we use tools of neoclassical economic theory to explore how a frugal visual system should use a limited number of neurons to optimize perception of motion. The theory prescribes that vision should allocate its resources to different conditions of stimulation according to the degree of balance between measurement uncertainties and stimulus uncertainties. We find that human vision approximately follows the optimal prescription. The equilibrium theory explains why human visual sensitivity is distributed the way it is and why qualitatively different regimes of apparent motion are observed at different speeds. The theory offers a new normative framework for understanding the mechanisms of visual sensitivity at the threshold of visibility and above the threshold and predicts large-scale changes in visual sensitivity in response to changes in the statistics of stimulation and system goals.

Analysis of Static Spacecraft Floating Potential at Low Earth Orbit (LEO)

NASA Technical Reports Server (NTRS)

Herr, Joel L.; Hwang, K. S.; Wu, S. T.

1995-01-01

Spacecraft floating potential is the charge on the external surfaces of orbiting spacecraft relative to the space. Charging is caused by unequal negative and positive currents to spacecraft surfaces. The charging process continues until the accelerated particles can be collected rapidly enough to balance the currents at which point the spacecraft has reached its equilibrium or floating potential. In low inclination. Low Earth Orbit (LEO), the collection of positive ion and negative electrons. in a particular direction. are typically not equal. The level of charging required for equilibrium to be established is influenced by the characteristics of the ambient plasma environment. by the spacecraft motion, and by the geometry of the spacecraft. Using the kinetic theory, a statistical approach for studying the interaction is developed. The approach used to study the spacecraft floating potential depends on which phenomena are being applied. and on the properties of the plasma. especially the density and temperature. The results from kinetic theory derivation are applied to determine the charging level and the electric potential distribution at an infinite flat plate perpendicular to a streaming plasma using finite-difference scheme.

Energy Current Cumulants in One-Dimensional Systems in Equilibrium

NASA Astrophysics Data System (ADS)

Dhar, Abhishek; Saito, Keiji; Roy, Anjan

2018-06-01

A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

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.

Statistical mechanics of simple models of protein folding and design.

PubMed Central

Pande, V S; Grosberg, A Y; Tanaka, T

1997-01-01

It is now believed that the primary equilibrium aspects of simple models of protein folding are understood theoretically. However, current theories often resort to rather heavy mathematics to overcome some technical difficulties inherent in the problem or start from a phenomenological model. To this end, we take a new approach in this pedagogical review of the statistical mechanics of protein folding. The benefit of our approach is a drastic mathematical simplification of the theory, without resort to any new approximations or phenomenological prescriptions. Indeed, the results we obtain agree precisely with previous calculations. Because of this simplification, we are able to present here a thorough and self contained treatment of the problem. Topics discussed include the statistical mechanics of the random energy model (REM), tests of the validity of REM as a model for heteropolymer freezing, freezing transition of random sequences, phase diagram of designed ("minimally frustrated") sequences, and the degree to which errors in the interactions employed in simulations of either folding and design can still lead to correct folding behavior. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 6 PMID:9414231

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Invariant criteria for bound states, degree of ionization, and plasma phase transition

NASA Technical Reports Server (NTRS)

Girardeau, M. D.

1990-01-01

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.

The Distributive Issue in Latin America.

ERIC Educational Resources Information Center

Figueroa, Adolfo

1996-01-01

Presents the central features of an economic theory of social equilibrium based on the theory of distributive equilibrium. Uses the situation in Latin America in the 1980s and 1990s to test the validity of the theory. Argues that excessive inequality cripples sustained growth and democratic movements. (MJP)

The Nash equilibrium: A perspective

PubMed Central

Holt, Charles A.; Roth, Alvin E.

2004-01-01

In 1950, John Nash contributed a remarkable one-page PNAS article that defined and characterized a notion of equilibrium for n- person games. This notion, now called the “Nash equilibrium,” has been widely applied and adapted in economics and other behavioral sciences. Indeed, game theory, with the Nash equilibrium as its centerpiece, is becoming the most prominent unifying theory of social science. In this perspective, we summarize the historical context and subsequent impact of Nash's contribution. PMID:15024100

Competitive Abilities in Experimental Microcosms Are Accurately Predicted by a Demographic Index for R*

PubMed Central

Murrell, Ebony G.; Juliano, Steven A.

2012-01-01

Resource competition theory predicts that R*, the equilibrium resource amount yielding zero growth of a consumer population, should predict species' competitive abilities for that resource. This concept has been supported for unicellular organisms, but has not been well-tested for metazoans, probably due to the difficulty of raising experimental populations to equilibrium and measuring population growth rates for species with long or complex life cycles. We developed an index (Rindex) of R* based on demography of one insect cohort, growing from egg to adult in a non-equilibrium setting, and tested whether Rindex yielded accurate predictions of competitive abilities using mosquitoes as a model system. We estimated finite rate of increase (λ′) from demographic data for cohorts of three mosquito species raised with different detritus amounts, and estimated each species' Rindex using nonlinear regressions of λ′ vs. initial detritus amount. All three species' Rindex differed significantly, and accurately predicted competitive hierarchy of the species determined in simultaneous pairwise competition experiments. Our Rindex could provide estimates and rigorous statistical comparisons of competitive ability for organisms for which typical chemostat methods and equilibrium population conditions are impractical. PMID:22970128

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.

Ensemble theory for slightly deformable granular matter.

PubMed

Tejada, Ignacio G

2014-09-01

Given a granular system of slightly deformable particles, it is possible to obtain different static and jammed packings subjected to the same macroscopic constraints. These microstates can be compared in a mathematical space defined by the components of the force-moment tensor (i.e. the product of the equivalent stress by the volume of the Voronoi cell). In order to explain the statistical distributions observed there, an athermal ensemble theory can be used. This work proposes a formalism (based on developments of the original theory of Edwards and collaborators) that considers both the internal and the external constraints of the problem. The former give the density of states of the points of this space, and the latter give their statistical weight. The internal constraints are those caused by the intrinsic features of the system (e.g. size distribution, friction, cohesion). They, together with the force-balance condition, determine which the possible local states of equilibrium of a particle are. Under the principle of equal a priori probabilities, and when no other constraints are imposed, it can be assumed that particles are equally likely to be found in any one of these local states of equilibrium. Then a flat sampling over all these local states turns into a non-uniform distribution in the force-moment space that can be represented with density of states functions. Although these functions can be measured, some of their features are explored in this paper. The external constraints are those macroscopic quantities that define the ensemble and are fixed by the protocol. The force-moment, the volume, the elastic potential energy and the stress are some examples of quantities that can be expressed as functions of the force-moment. The associated ensembles are included in the formalism presented here.

The Lack of Chemical Equilibrium does not Preclude the Use of the Classical Nucleation Theory in Circumstellar Outflows

NASA Technical Reports Server (NTRS)

Paquette, John A.; Nuth, Joseph A., III

2011-01-01

Classical nucleation theory has been used in models of dust nucleation in circumstellar outflows around oxygen-rich asymptotic giant branch stars. One objection to the application of classical nucleation theory (CNT) to astrophysical systems of this sort is that an equilibrium distribution of clusters (assumed by CNT) is unlikely to exist in such conditions due to a low collision rate of condensable species. A model of silicate grain nucleation and growth was modified to evaluate the effect of a nucleation flux orders of magnitUde below the equilibrium value. The results show that a lack of chemical equilibrium has only a small effect on the ultimate grain distribution.

A Thermodynamic Theory of Solid Viscoelasticity. Part II:; Nonlinear Thermo-viscoelasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

This paper, second in the series of three papers, develops a general, nonlinear, non-isothermal, compressible theory for finite rubber viscoelasticity and specifies it in a form convenient for solving problems important to the rubber, tire, automobile, and air-space industries, among others. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory of differential type has been developed for arbitrary non-isothermal deformations of viscoelastic solids. In this theory, the constitutive equations were presented as the sum of a rubber elastic (equilibrium) and a liquid type viscoelastic (non-equilibrium) terms. These equations have then been simplified using several modeling and simplicity arguments.

Effects of rotational symmetry breaking in polymer-coated nanopores

NASA Astrophysics Data System (ADS)

Osmanović, D.; Kerr-Winter, M.; Eccleston, R. C.; Hoogenboom, B. W.; Ford, I. J.

2015-01-01

The statistical theory of polymers tethered around the inner surface of a cylindrical channel has traditionally employed the assumption that the equilibrium density of the polymers is independent of the azimuthal coordinate. However, simulations have shown that this rotational symmetry can be broken when there are attractive interactions between the polymers. We investigate the phases that emerge in these circumstances, and we quantify the effect of the symmetry assumption on the phase behavior of the system. In the absence of this assumption, one can observe large differences in the equilibrium densities between the rotationally symmetric case and the non-rotationally symmetric case. A simple analytical model is developed that illustrates the driving thermodynamic forces responsible for this symmetry breaking. Our results have implications for the current understanding of the behavior of polymers in cylindrical nanopores.

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.

Effects of rotational symmetry breaking in polymer-coated nanopores

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

Osmanović, D.; Hoogenboom, B. W.; Ford, I. J.

2015-01-21

The statistical theory of polymers tethered around the inner surface of a cylindrical channel has traditionally employed the assumption that the equilibrium density of the polymers is independent of the azimuthal coordinate. However, simulations have shown that this rotational symmetry can be broken when there are attractive interactions between the polymers. We investigate the phases that emerge in these circumstances, and we quantify the effect of the symmetry assumption on the phase behavior of the system. In the absence of this assumption, one can observe large differences in the equilibrium densities between the rotationally symmetric case and the non-rotationally symmetricmore » case. A simple analytical model is developed that illustrates the driving thermodynamic forces responsible for this symmetry breaking. Our results have implications for the current understanding of the behavior of polymers in cylindrical nanopores.« less

Current Trends in Modeling Research for Turbulent Aerodynamic Flows

NASA Technical Reports Server (NTRS)

Gatski, Thomas B.; Rumsey, Christopher L.; Manceau, Remi

2007-01-01

The engineering tools of choice for the computation of practical engineering flows have begun to migrate from those based on the traditional Reynolds-averaged Navier-Stokes approach to methodologies capable, in theory if not in practice, of accurately predicting some instantaneous scales of motion in the flow. The migration has largely been driven by both the success of Reynolds-averaged methods over a wide variety of flows as well as the inherent limitations of the method itself. Practitioners, emboldened by their ability to predict a wide-variety of statistically steady, equilibrium turbulent flows, have now turned their attention to flow control and non-equilibrium flows, that is, separation control. This review gives some current priorities in traditional Reynolds-averaged modeling research as well as some methodologies being applied to a new class of turbulent flow control problems.

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.

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 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.

Chimpanzee choice rates in competitive games match equilibrium game theory predictions.

PubMed

Martin, Christopher Flynn; Bhui, Rahul; Bossaerts, Peter; Matsuzawa, Tetsuro; Camerer, Colin

2014-06-05

The capacity for strategic thinking about the payoff-relevant actions of conspecifics is not well understood across species. We use game theory to make predictions about choices and temporal dynamics in three abstract competitive situations with chimpanzee participants. Frequencies of chimpanzee choices are extremely close to equilibrium (accurate-guessing) predictions, and shift as payoffs change, just as equilibrium theory predicts. The chimpanzee choices are also closer to the equilibrium prediction, and more responsive to past history and payoff changes, than two samples of human choices from experiments in which humans were also initially uninformed about opponent payoffs and could not communicate verbally. The results are consistent with a tentative interpretation of game theory as explaining evolved behavior, with the additional hypothesis that chimpanzees may retain or practice a specialized capacity to adjust strategy choice during competition to perform at least as well as, or better than, humans have.

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.

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.

Deformation in Metallic Glass: Connecting Atoms to Continua

NASA Astrophysics Data System (ADS)

Hinkle, Adam R.; Falk, Michael L.; Rycroft, Chris H.; Shields, Michael D.

Metallic glasses like other amorphous solids experience strain localization as the primary mode of failure. However, the development of continuum constitutive laws which provide a quantitative description of disorder and mechanical deformation remains an open challenge. Recent progress has shown the necessity of accurately capturing fluctuations in material structure, in particular the statistical changes in potential energy of the atomic constituents during the non-equilibrium process of applied shear. Here we directly cross-compare molecular dynamics shear simulations of a ZrCu glass with continuum shear transformation zone (STZ) theory representations. We present preliminary results for a methodology to coarse-grain detailed molecular dynamics data with the goal of initializing a continuum representation in the STZ theory. NSF Grants Awards 1107838, 1408685, and 0801471.

Microeconomics, Socialization, and Norms. Program Report No. 79-B22.

ERIC Educational Resources Information Center

Field, Alexander J.

Microeconomic theory encompasses two basic theoretical concepts. First is the theory of general competitive equilibrium in a market economy, which holds that the actions of any one agent cannot affect prices or quantities for the system as a whole. The second is that when the conditions of competitive equilibrium do not apply, theories of games…

Studies on the formulation of thermodynamics and stochastic theory for systems far from equilibrium

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

Ross, J.

We have been working for some time on the formulation of thermodynamics and the theory of fluctuations in systems far from equilibrium and progress in several aspects of that development are reported here.

Self-Consistency of the Theory of Elementary Stage Rates of Reversible Processes and the Equilibrium Distribution of Reaction Mixture Components

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-06-01

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.

Weak turbulence theory for beam-plasma interaction

NASA Astrophysics Data System (ADS)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

A statistical formulation of one-dimensional electron fluid turbulence

NASA Technical Reports Server (NTRS)

Fyfe, D.; Montgomery, D.

1977-01-01

A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.

Kinetic field theory: exact free evolution of Gaussian phase-space correlations

NASA Astrophysics Data System (ADS)

Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias

2018-04-01

In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

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.

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

NASA Astrophysics Data System (ADS)

Dahmen, David; Bos, Hannah; Helias, Moritz

2016-07-01

Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics. The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings. However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks. Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections. The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units. The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.

Theory and simulations of adhesion receptor dimerization on membrane surfaces.

PubMed

Wu, Yinghao; Honig, Barry; Ben-Shaul, Avinoam

2013-03-19

The equilibrium constants of trans and cis dimerization of membrane bound (2D) and freely moving (3D) adhesion receptors are expressed and compared using elementary statistical-thermodynamics. Both processes are mediated by the binding of extracellular subdomains whose range of motion in the 2D environment is reduced upon dimerization, defining a thin reaction shell where dimer formation and dissociation take place. We show that the ratio between the 2D and 3D equilibrium constants can be expressed as a product of individual factors describing, respectively, the spatial ranges of motions of the adhesive domains, and their rotational freedom within the reaction shell. The results predicted by the theory are compared to those obtained from a novel, to our knowledge, dynamical simulations methodology, whereby pairs of receptors perform realistic translational, internal, and rotational motions in 2D and 3D. We use cadherins as our model system. The theory and simulations explain how the strength of cis and trans interactions of adhesive receptors are affected both by their presence in the constrained intermembrane space and by the 2D environment of membrane surfaces. Our work provides fundamental insights as to the mechanism of lateral clustering of adhesion receptors after cell-cell contact and, more generally, to the formation of lateral microclusters of proteins on cell surfaces. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Non-Equilibrium Turbulence and Two-Equation Modeling

NASA Technical Reports Server (NTRS)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Applicability of Donnan equilibrium theory at nanochannel-reservoir interfaces.

PubMed

Tian, Huanhuan; Zhang, Li; Wang, Moran

2015-08-15

Understanding ionic transport in nanochannels has attracted broad attention from various areas in energy and environmental fields. In most pervious research, Donnan equilibrium has been applied widely to nanofluidic systems to obtain ionic concentration and electrical potential at channel-reservoir interfaces; however, as well known that Donnan equilibrium is derived from classical thermodynamic theories with equilibrium assumptions. Therefore the applicability of the Donnan equilibrium may be questionable when the transport at nanochannel-reservoir interface is strongly non-equilibrium. In this work, the Poisson-Nernst-Planck model for ion transport is numerically solved to obtain the exact distributions of ionic concentration and electrical potential. The numerical results are quantitatively compared with the Donnan equilibrium predictions. The applicability of Donnan equilibrium is therefore justified by changing channel length, reservoir ionic concentration, surface charge density and channel height. The results indicate that the Donnan equilibrium is not applicable for short nanochannels, large concentration difference and wide openings. A non-dimensional parameter, Q factor, is proposed to measure the non-equilibrium extent and the relation between Q and the working conditions is studied in detail. Copyright © 2015 Elsevier Inc. All rights reserved.

Mode-selective control of thermal Brownian vibration of micro-resonator (Generation of a thermal no-equilibrium state by mechanical feedback control)

NASA Astrophysics Data System (ADS)

Kawamura, Y.; Kanegae, R.

2017-09-01

Recently, there have been various attempts to dampen the vibration amplitude of the Brownian motion of a microresonator below the thermal vibration amplitude, with the goal of reaching the quantum ground vibration level. To further develop the approach of reaching the quantum ground state, it is essential to clarify whether or not coupling exists between the different vibration modes of the resonator. In this paper, the mode-selective control of thermal Brownian vibration is shown. The first and the second vibration modes of a micro-cantilever moved by a random Brownian motion are cooled selectively and independently below the thermal vibration amplitude, as determined by the statistical thermodynamic theory, using a mechanical feedback control method. This experimental result shows that the thermal no-equilibrium condition was generated by mechanical feedback control.

The physicist's companion to current fluctuations: one-dimensional bulk-driven lattice gases

NASA Astrophysics Data System (ADS)

Lazarescu, Alexandre

2015-12-01

One of the main features of statistical systems out of equilibrium is the currents they exhibit in their stationary state: microscopic currents of probability between configurations, which translate into macroscopic currents of mass, charge, etc. Understanding the general behaviour of these currents is an important step towards building a universal framework for non-equilibrium steady states akin to the Gibbs-Boltzmann distribution for equilibrium systems. In this review, we consider one-dimensional bulk-driven particle gases, and in particular the asymmetric simple exclusion process (ASEP) with open boundaries, which is one of the most popular models of one-dimensional transport. We focus, in particular, on the current of particles flowing through the system in its steady state, and on its fluctuations. We show how one can obtain the complete statistics of that current, through its large deviation function, by combining results from various methods: exact calculation of the cumulants of the current, using the integrability of the model; direct diagonalization of a biased process in the limits of very high or low current; hydrodynamic description of the model in the continuous limit using the macroscopic fluctuation theory. We give a pedagogical account of these techniques, starting with a quick introduction to the necessary mathematical tools, as well as a short overview of the existing works relating to the ASEP. We conclude by drawing the complete dynamical phase diagram of the current. We also remark on a few possible generalizations of these results.

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.

Anomaly on Superspace of Time Series Data

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Pincak, Richard; Kanjamapornkul, Kabin

2017-11-01

We apply the G-theory and anomaly of ghost and antighost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide proof of the existence of a general equilibrium point over 14 extradimensions of the new G-theory compared with the M-theory of the 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into two topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14th Batalin-Vilkovisky cohomology group with the negative dimensions underlying 14 major hidden factors influencing the market is zero.

Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries

NASA Astrophysics Data System (ADS)

Esler, J. G.

2017-12-01

A theory (Esler and Ashbee in J Fluid Mech 779:275-308, 2015) describing the statistics of N freely-evolving point vortices in a bounded two-dimensional domain is extended. First, the case of a non-neutral vortex gas is addressed, and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non-central chi-squared random variables, the details of which depend only on the shape of the domain. Equations for the equilibrium energy spectrum and other statistical quantities follow, the validity of which are verified against direct numerical simulations of the equations of motion. Second, domains with additional conserved quantities associated with a symmetry (e.g., circle, periodic channel) are investigated, and it is shown that the treatment of the non-neutral case can be modified to account for the additional constraint.

An Evolutionary Comparison of the Handicap Principle and Hybrid Equilibrium Theories of Signaling.

PubMed

Kane, Patrick; Zollman, Kevin J S

2015-01-01

The handicap principle has come under significant challenge both from empirical studies and from theoretical work. As a result, a number of alternative explanations for honest signaling have been proposed. This paper compares the evolutionary plausibility of one such alternative, the "hybrid equilibrium," to the handicap principle. We utilize computer simulations to compare these two theories as they are instantiated in Maynard Smith's Sir Philip Sidney game. We conclude that, when both types of communication are possible, evolution is unlikely to lead to handicap signaling and is far more likely to result in the partially honest signaling predicted by hybrid equilibrium theory.

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Economic order quantity (EOQ) by game theory approach in probabilistic supply chain system under service level constraint for items with imperfect quality

NASA Astrophysics Data System (ADS)

Setiawan, R.

2018-03-01

In this paper, Economic Order Quantity (EOQ) of probabilistic two-level supply – chain system for items with imperfect quality has been analyzed under service level constraint. A firm applies an active service level constraint to avoid unpredictable shortage terms in the objective function. Mathematical analysis of optimal result is delivered using two equilibrium scheme concept in game theory approach. Stackelberg’s equilibrium for cooperative strategy and Stackelberg’s Equilibrium for noncooperative strategy. This is a new approach to game theory result in inventory system whether service level constraint is applied by a firm in his moves.

Maximum entropy approach to H -theory: Statistical mechanics of hierarchical systems

NASA Astrophysics Data System (ADS)

Vasconcelos, Giovani L.; Salazar, Domingos S. P.; Macêdo, A. M. S.

2018-02-01

A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem—representing the region where the measurements are made—in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017), 10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.

A statistical mechanics approach to Granovetter theory

NASA Astrophysics Data System (ADS)

Barra, Adriano; Agliari, Elena

2012-05-01

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

Statistical theory of light nucleus reactions with 1p-shell light nuclei

NASA Astrophysics Data System (ADS)

Xiaojun, Sun; Jingshang, Zhang

2017-09-01

The 1p-shell light elements (Li, Be, B, C, N, and O) had long been selected as the most important materials for improving neutron economy in thermal and fast fission reactors and in the design of accelerator-driven spallation neutron sources. A statistical theory of light nucleus reactions (STLN) is proposed to describe the double-differential cross sections for both neutron and light charged particle induced nuclear reactions with 1p-shell light nuclei. The dynamics of STLN is described by the unified Hauser-Feshbach and exciton model, in which the angular momentum and parity conservations are strictly considered in equilibrium and pre-equilibrium processes. The Coulomb barriers of the incoming and outgoing charged particles, which significantly influence the open channels of the reaction, can be reasonably considered in incident channel and different outgoing channels. In kinematics, the recoiling effects in various emission processes are strictly taken into account. The analytical energy and angular spectra of the reaction products in sequential and simultaneous emission processes are obtained in terms of the new integral formula proposed in our recent paper. Taking 12C(n, xn), 9Be(n, xn), 16O(n, xn), and 9Be(p,xn) reactions as examples, we had calculated the double-differential cross sections of outgoing neutrons and compared with the experimental data. In addition, we had also calculated the partition and total kerma coefficients for 12C(n, xn) and 16O(n, xn) reactions, respectively. The existing experimental data can be remarkably well reproduced by STLN, which had been used to set up file-6 in CENDL database.

Master equation theory applied to the redistribution of polarized radiation in the weak radiation field limit. III. Theory for the multilevel atom

NASA Astrophysics Data System (ADS)

Bommier, Véronique

2016-06-01

Context. We discuss the case of lines formed by scattering, which comprises both coherent and incoherent scattering. Both processes contribute to form the line profiles in the so-called second solar spectrum, which is the spectrum of the linear polarization of such lines observed close to the solar limb. However, most of the lines cannot be simply modeled with a two-level or two-term atom model, and we present a generalized formalism for this purpose. Aims: The aim is to obtain a formalism that is able to describe scattering in line centers (resonant scattering or incoherent scattering) and in far wings (Rayleigh/Raman scattering or coherent scattering) for a multilevel and multiline atom. Methods: The method is designed to overcome the Markov approximation, which is often performed in the atom-photon interaction description. The method was already presented in the two first papers of this series, but the final equations of those papers were for a two-level atom. Results: We present here the final equations generalized for the multilevel and multiline atom. We describe the main steps of the theoretical development, and, in particular, how we performed the series development to overcome the Markov approximation. Conclusions: The statistical equilibrium equations for the atomic density matrix and the radiative transfer equation coefficients are obtained with line profiles. The Doppler redistribution is also taken into account because we show that the statistical equilibrium equations must be solved for each atomic velocity class.

Maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems.

PubMed

Vasconcelos, Giovani L; Salazar, Domingos S P; Macêdo, A M S

2018-02-01

A formalism, called H-theory, is applied to the problem of statistical equilibrium of a hierarchical complex system with multiple time and length scales. In this approach, the system is formally treated as being composed of a small subsystem-representing the region where the measurements are made-in contact with a set of "nested heat reservoirs" corresponding to the hierarchical structure of the system, where the temperatures of the reservoirs are allowed to fluctuate owing to the complex interactions between degrees of freedom at different scales. The probability distribution function (pdf) of the temperature of the reservoir at a given scale, conditioned on the temperature of the reservoir at the next largest scale in the hierarchy, is determined from a maximum entropy principle subject to appropriate constraints that describe the thermal equilibrium properties of the system. The marginal temperature distribution of the innermost reservoir is obtained by integrating over the conditional distributions of all larger scales, and the resulting pdf is written in analytical form in terms of certain special transcendental functions, known as the Fox H functions. The distribution of states of the small subsystem is then computed by averaging the quasiequilibrium Boltzmann distribution over the temperature of the innermost reservoir. This distribution can also be written in terms of H functions. The general family of distributions reported here recovers, as particular cases, the stationary distributions recently obtained by Macêdo et al. [Phys. Rev. E 95, 032315 (2017)10.1103/PhysRevE.95.032315] from a stochastic dynamical approach to the problem.

Statistics of Macroturbulence from Flow Equations

NASA Astrophysics Data System (ADS)

Marston, Brad; Iadecola, Thomas; Qi, Wanming

2012-02-01

Probability distribution functions of stochastically-driven and frictionally-damped fluids are governed by a linear framework that resembles quantum many-body theory. Besides the Fokker-Planck approach, there is a closely related Hopf functional methodfootnotetextOokie Ma and J. B. Marston, J. Stat. Phys. Th. Exp. P10007 (2005).; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we generalize the flow equation approachfootnotetextF. Wegner, Ann. Phys. 3, 77 (1994). (also known as the method of continuous unitary transformationsfootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994).) to find the zero mode. We test the approach using a prototypical model of geophysical and astrophysical flows on a rotating sphere that spontaneously organizes into a coherent jet. Good agreement is found with low-order equal-time statistics accumulated by direct numerical simulation, the traditional method. Different choices for the generators of the continuous transformations, and for closure approximations of the operator algebra, are discussed.

Theory of competitive solvation of polymers by two solvents and entropy-enthalpy compensation in the solvation free energy upon dilution with the second solvent.

PubMed

Dudowicz, Jacek; Freed, Karl F; Douglas, Jack F

2015-06-07

We develop a statistical mechanical lattice theory for polymer solvation by a pair of relatively low molar mass solvents that compete for binding to the polymer backbone. A theory for the equilibrium mixture of solvated polymer clusters {AiBCj} and free unassociated molecules A, B, and C is formulated in the spirit of Flory-Huggins mean-field approximation. This theoretical framework enables us to derive expressions for the boundaries for phase stability (spinodals) and other basic properties of these polymer solutions: the internal energy U, entropy S, specific heat CV, extent of solvation Φsolv, average degree of solvation 〈Nsolv〉, and second osmotic virial coefficient B2 as functions of temperature and the composition of the mixture. Our theory predicts many new phenomena, but the current paper applies the theory to describe the entropy-enthalpy compensation in the free energy of polymer solvation, a phenomenon observed for many years without theoretical explanation and with significant relevance to liquid chromatography and other polymer separation methods.

General theory for calculating disorder-averaged Green's function correlators within the coherent potential approximation

NASA Astrophysics Data System (ADS)

Zhou, Chenyi; Guo, Hong

2017-01-01

We report a diagrammatic method to solve the general problem of calculating configurationally averaged Green's function correlators that appear in quantum transport theory for nanostructures containing disorder. The theory treats both equilibrium and nonequilibrium quantum statistics on an equal footing. Since random impurity scattering is a problem that cannot be solved exactly in a perturbative approach, we combine our diagrammatic method with the coherent potential approximation (CPA) so that a reliable closed-form solution can be obtained. Our theory not only ensures the internal consistency of the diagrams derived at different levels of the correlators but also satisfies a set of Ward-like identities that corroborate the conserving consistency of transport calculations within the formalism. The theory is applied to calculate the quantum transport properties such as average ac conductance and transmission moments of a disordered tight-binding model, and results are numerically verified to high precision by comparing to the exact solutions obtained from enumerating all possible disorder configurations. Our formalism can be employed to predict transport properties of a wide variety of physical systems where disorder scattering is important.

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.

Life history theory predicts fish assemblage response to hydrologic regimes.

PubMed

Mims, Meryl C; Olden, Julian D

2012-01-01

The hydrologic regime is regarded as the primary driver of freshwater ecosystems, structuring the physical habitat template, providing connectivity, framing biotic interactions, and ultimately selecting for specific life histories of aquatic organisms. In the present study, we tested ecological theory predicting directional relationships between major dimensions of the flow regime and life history composition of fish assemblages in perennial free-flowing rivers throughout the continental United States. Using long-term discharge records and fish trait and survey data for 109 stream locations, we found that 11 out of 18 relationships (61%) tested between the three life history strategies (opportunistic, periodic, and equilibrium) and six hydrologic metrics (two each describing flow variability, predictability, and seasonality) were statistically significant (P < or = 0.05) according to quantile regression. Our results largely support a priori hypotheses of relationships between specific flow indices and relative prevalence of fish life history strategies, with 82% of all significant relationships observed supporting predictions from life history theory. Specifically, we found that (1) opportunistic strategists were positively related to measures of flow variability and negatively related to predictability and seasonality, (2) periodic strategists were positively related to high flow seasonality and negatively related to variability, and (3) the equilibrium strategists were negatively related to flow variability and positively related to predictability. Our study provides important empirical evidence illustrating the value of using life history theory to understand both the patterns and processes by which fish assemblage structure is shaped by adaptation to natural regimes of variability, predictability, and seasonality of critical flow events over broad biogeographic scales.

I. Dissociation free energies of drug-receptor systems via non-equilibrium alchemical simulations: a theoretical framework.

PubMed

Procacci, Piero

2016-06-01

In this contribution I critically revise the alchemical reversible approach in the context of the statistical mechanics theory of non-covalent bonding in drug-receptor systems. I show that most of the pitfalls and entanglements for the binding free energy evaluation in computer simulations are rooted in the equilibrium assumption that is implicit in the reversible method. These critical issues can be resolved by using a non-equilibrium variant of the alchemical method in molecular dynamics simulations, relying on the production of many independent trajectories with a continuous dynamical evolution of an externally driven alchemical coordinate, completing the decoupling of the ligand in a matter of a few tens of picoseconds rather than nanoseconds. The absolute binding free energy can be recovered from the annihilation work distributions by applying an unbiased unidirectional free energy estimate, on the assumption that any observed work distribution is given by a mixture of normal distributions, whose components are identical in either direction of the non-equilibrium process, with weights regulated by the Crooks theorem. I finally show that the inherent reliability and accuracy of the unidirectional estimate of the decoupling free energies, based on the production of a few hundreds of non-equilibrium independent sub-nanosecond unrestrained alchemical annihilation processes, is a direct consequence of the funnel-like shape of the free energy surface in molecular recognition. An application of the technique to a real drug-receptor system is presented in the companion paper.

Thermodynamics and Kinetics of Chemical Equilibrium in Solution.

ERIC Educational Resources Information Center

Leenson, I. A.

1986-01-01

Discusses theory of thermodynamics of the equilibrium in solution and dissociation-dimerization kinetics. Describes experimental procedure including determination of molar absorptivity and equilibrium constant, reaction enthalpy, and kinetics of the dissociation-dimerization reaction. (JM)

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Asymptotic stability estimates near an equilibrium point

NASA Astrophysics Data System (ADS)

Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia

2017-07-01

We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.

Statistical Mechanics and Applications in Condensed Matter

NASA Astrophysics Data System (ADS)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

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

An Evolutionary Comparison of the Handicap Principle and Hybrid Equilibrium Theories of Signaling

PubMed Central

Kane, Patrick; Zollman, Kevin J. S.

2015-01-01

The handicap principle has come under significant challenge both from empirical studies and from theoretical work. As a result, a number of alternative explanations for honest signaling have been proposed. This paper compares the evolutionary plausibility of one such alternative, the “hybrid equilibrium,” to the handicap principle. We utilize computer simulations to compare these two theories as they are instantiated in Maynard Smith’s Sir Philip Sidney game. We conclude that, when both types of communication are possible, evolution is unlikely to lead to handicap signaling and is far more likely to result in the partially honest signaling predicted by hybrid equilibrium theory. PMID:26348617

Non-equilibrium phase transition in mesoscopic biochemical systems: from stochastic to nonlinear dynamics and beyond

PubMed Central

Ge, Hao; Qian, Hong

2011-01-01

A theory for an non-equilibrium phase transition in a driven biochemical network is presented. The theory is based on the chemical master equation (CME) formulation of mesoscopic biochemical reactions and the mathematical method of large deviations. The large deviations theory provides an analytical tool connecting the macroscopic multi-stability of an open chemical system with the multi-scale dynamics of its mesoscopic counterpart. It shows a corresponding non-equilibrium phase transition among multiple stochastic attractors. As an example, in the canonical phosphorylation–dephosphorylation system with feedback that exhibits bistability, we show that the non-equilibrium steady-state (NESS) phase transition has all the characteristics of classic equilibrium phase transition: Maxwell construction, a discontinuous first-derivative of the ‘free energy function’, Lee–Yang's zero for a generating function and a critical point that matches the cusp in nonlinear bifurcation theory. To the biochemical system, the mathematical analysis suggests three distinct timescales and needed levels of description. They are (i) molecular signalling, (ii) biochemical network nonlinear dynamics, and (iii) cellular evolution. For finite mesoscopic systems such as a cell, motions associated with (i) and (iii) are stochastic while that with (ii) is deterministic. Both (ii) and (iii) are emergent properties of a dynamic biochemical network. PMID:20466813

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

Meso-scale turbulence in living fluids

NASA Astrophysics Data System (ADS)

Dunkel, Jorn; Wensink, Rik; Heidenreich, Sebastian; Drescher, Knut; Goldstein, Ray; Loewen, Hartmut; Yeomans, Julia

2012-11-01

The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which generalizations of the Navier-Stokes equations are able to describe them adequately. We combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence. Supported by the ERC, EPSRC and DFG.

Theoretical study of gas hydrate decomposition kinetics--model development.

PubMed

Windmeier, Christoph; Oellrich, Lothar R

2013-10-10

In order to provide an estimate of the order of magnitude of intrinsic gas hydrate dissolution and dissociation kinetics, the "Consecutive Desorption and Melting Model" (CDM) is developed by applying only theoretical considerations. The process of gas hydrate decomposition is assumed to comprise two consecutive and repetitive quasi chemical reaction steps. These are desorption of the guest molecule followed by local solid body melting. The individual kinetic steps are modeled according to the "Statistical Rate Theory of Interfacial Transport" and the Wilson-Frenkel approach. All missing required model parameters are directly linked to geometric considerations and a thermodynamic gas hydrate equilibrium model.

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.

From atoms to steps: The microscopic origins of crystal evolution

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Einstein, T. L.; Margetis, Dionisios

2014-07-01

The Burton-Cabrera-Frank (BCF) theory of crystal growth has been successful in describing a wide range of phenomena in surface physics. Typical crystal surfaces are slightly misoriented with respect to a facet plane; thus, the BCF theory views such systems as composed of staircase-like structures of steps separating terraces. Adsorbed atoms (adatoms), which are represented by a continuous density, diffuse on terraces, and steps move by absorbing or emitting these adatoms. Here we shed light on the microscopic origins of the BCF theory by deriving a simple, one-dimensional (1D) version of the theory from an atomistic, kinetic restricted solid-on-solid (KRSOS) model without external material deposition. We define the time-dependent adatom density and step position as appropriate ensemble averages in the KRSOS model, thereby exposing the non-equilibrium statistical mechanics origins of the BCF theory. Our analysis reveals that the BCF theory is valid in a low adatom-density regime, much in the same way that an ideal gas approximation applies to dilute gasses. We find conditions under which the surface remains in a low-density regime and discuss the microscopic origin of corrections to the BCF model.

Statistical mechanics of monatomic liquids

NASA Astrophysics Data System (ADS)

Wallace, Duane C.

1997-10-01

Two key experimental properties of elemental liquids, together with an analysis of the condensed-system potential-energy surface, lead us logically to the dynamical theory of monatomic liquids. Experimentally, the ion motional specific heat is approximately 3Nk for N ions, implying the normal modes of motion are approximately 3N independent harmonic oscillators. This implies the potential surface contains nearly harmonic valleys. The equilibrium configuration at the bottom of each valley is a ``structure.'' Structures are crystalline or amorphous, and amorphous structures can have a remnant of local crystal symmetry, or can be random. The random structures are by far the most numerous, and hence dominate the statistical mechanics of the liquid state, and their macroscopic properties are uniform over the structure class, for large-N systems. The Hamiltonian for any structural valley is the static structure potential, a sum of harmonic normal modes, and an anharmonic correction. Again from experiment, the constant-density entropy of melting contains a universal disordering contribution of NkΔ, suggesting the random structural valleys are of universal number wN, where lnw=Δ. Our experimental estimate for Δ is 0.80. In quasiharmonic approximation, the liquid theory for entropy agrees with experiment, for all currently analyzable experimental data at elevated temperatures, to within 1-2% of the total entropy. Further testable predictions of the theory are mentioned.

Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments.

PubMed

Bowler, Michael G; Bowler, David R; Bowler, Matthew W

2017-04-01

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F 68 , 111-114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult's law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult's law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult's law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample.

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.

Integrable structure in discrete shell membrane theory

PubMed Central

Schief, W. K.

2014-01-01

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755

Integrable structure in discrete shell membrane theory.

PubMed

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Predicting RNA folding thermodynamics with a reduced chain representation model

PubMed Central

CAO, SONG; CHEN, SHI-JIE

2005-01-01

Based on the virtual bond representation for the nucleotide backbone, we develop a reduced conformational model for RNA. We use the experimentally measured atomic coordinates to model the helices and use the self-avoiding walks in a diamond lattice to model the loop conformations. The atomic coordinates of the helices and the lattice representation for the loops are matched at the loop–helix junction, where steric viability is accounted for. Unlike the previous simplified lattice-based models, the present virtual bond model can account for the atomic details of realistic three-dimensional RNA structures. Based on the model, we develop a statistical mechanical theory for RNA folding energy landscapes and folding thermodynamics. Tests against experiments show that the theory can give much more improved predictions for the native structures, the thermal denaturation curves, and the equilibrium folding/unfolding pathways than the previous models. The application of the model to the P5abc region of Tetrahymena group I ribozyme reveals the misfolded intermediates as well as the native-like intermediates in the equilibrium folding process. Moreover, based on the free energy landscape analysis for each and every loop mutation, the model predicts five lethal mutations that can completely alter the free energy landscape and the folding stability of the molecule. PMID:16251382

Quantum gambling based on Nash-equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Pei; Zhou, Xiao-Qi; Wang, Yun-Long; Liu, Bi-Heng; Shadbolt, Pete; Zhang, Yong-Sheng; Gao, Hong; Li, Fu-Li; O'Brien, Jeremy L.

2017-06-01

The problem of establishing a fair bet between spatially separated gambler and casino can only be solved in the classical regime by relying on a trusted third party. By combining Nash-equilibrium theory with quantum game theory, we show that a secure, remote, two-party game can be played using a quantum gambling machine which has no classical counterpart. Specifically, by modifying the Nash-equilibrium point we can construct games with arbitrary amount of bias, including a game that is demonstrably fair to both parties. We also report a proof-of-principle experimental demonstration using linear optics.

Derivation of the chemical-equilibrium rate coefficient using scattering theory

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1977-01-01

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Understanding how biodiversity unfolds through time under neutral theory.

PubMed

Missa, Olivier; Dytham, Calvin; Morlon, Hélène

2016-04-05

Theoretical predictions for biodiversity patterns are typically derived under the assumption that ecological systems have reached a dynamic equilibrium. Yet, there is increasing evidence that various aspects of ecological systems, including (but not limited to) species richness, are not at equilibrium. Here, we use simulations to analyse how biodiversity patterns unfold through time. In particular, we focus on the relative time required for various biodiversity patterns (macroecological or phylogenetic) to reach equilibrium. We simulate spatially explicit metacommunities according to the Neutral Theory of Biodiversity (NTB) under three modes of speciation, which differ in how evenly a parent species is split between its two daughter species. We find that species richness stabilizes first, followed by species area relationships (SAR) and finally species abundance distributions (SAD). The difference in timing of equilibrium between these different macroecological patterns is the largest when the split of individuals between sibling species at speciation is the most uneven. Phylogenetic patterns of biodiversity take even longer to stabilize (tens to hundreds of times longer than species richness) so that equilibrium predictions from neutral theory for these patterns are unlikely to be relevant. Our results suggest that it may be unwise to assume that biodiversity patterns are at equilibrium and provide a first step in studying how these patterns unfold through time. © 2016 The Author(s).

Understanding how biodiversity unfolds through time under neutral theory

PubMed Central

2016-01-01

Theoretical predictions for biodiversity patterns are typically derived under the assumption that ecological systems have reached a dynamic equilibrium. Yet, there is increasing evidence that various aspects of ecological systems, including (but not limited to) species richness, are not at equilibrium. Here, we use simulations to analyse how biodiversity patterns unfold through time. In particular, we focus on the relative time required for various biodiversity patterns (macroecological or phylogenetic) to reach equilibrium. We simulate spatially explicit metacommunities according to the Neutral Theory of Biodiversity (NTB) under three modes of speciation, which differ in how evenly a parent species is split between its two daughter species. We find that species richness stabilizes first, followed by species area relationships (SAR) and finally species abundance distributions (SAD). The difference in timing of equilibrium between these different macroecological patterns is the largest when the split of individuals between sibling species at speciation is the most uneven. Phylogenetic patterns of biodiversity take even longer to stabilize (tens to hundreds of times longer than species richness) so that equilibrium predictions from neutral theory for these patterns are unlikely to be relevant. Our results suggest that it may be unwise to assume that biodiversity patterns are at equilibrium and provide a first step in studying how these patterns unfold through time. PMID:26977066

Group entropies, correlation laws, and zeta functions.

PubMed

Tempesta, Piergiulio

2011-08-01

The notion of group entropy is proposed. It enables the unification and generaliztion of many different definitions of entropy known in the literature, such as those of Boltzmann-Gibbs, Tsallis, Abe, and Kaniadakis. Other entropic functionals are introduced, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.

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.

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

PubMed Central

Wu, Jiang Hao; Sun, Mao

2012-01-01

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed. PMID:22491980

A Bayesian perspective on Markovian dynamics and the fluctuation theorem

NASA Astrophysics Data System (ADS)

Virgo, Nathaniel

2013-08-01

One of E. T. Jaynes' most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of the fluctuation theorem that I will discuss applies to discrete, stochastic systems that begin in a non-equilibrium state and relax toward equilibrium. I will show that for such systems the fluctuation theorem can be seen as a consequence of the fact that the equilibrium distribution must obey the property of detailed balance. Although the principle of detailed balance applies only to equilibrium ensembles, it puts constraints on the form of non-equilibrium trajectories. This will be made clear by taking a novel kind of Bayesian perspective, in which the equilibrium distribution is seen as a prior over the system's set of possible trajectories. Non-equilibrium ensembles are calculated from this prior using Bayes' theorem, with the initial conditions playing the role of the data. I will also comment on the implications of this perspective for the question of how to derive the second law.

Applicability of Markets to Global Scheduling in Grids: Critical Examination of General Equilibrium Theory and Market Folklore

NASA Technical Reports Server (NTRS)

Nakai, Junko; VanDerWijngaart, Rob F.

2003-01-01

Markets are often considered superior to other global scheduling mechanisms for distributed computing systems. This claim is supported by: a casual observation from our every-day life that markets successfully equilibrate supply and demand, and the features of markets which originate in the general equilibrium theory, e.g., efficiency and the lack of necessity of 2 central controller. This paper describes why such beliefs in markets are not warranted. It does so by examining the general equilibrium theory, in terms of scope, abstraction, and interpretation. Not only does the general equilibrium theory fail to provide a satisfactory explanation of actual economies, including a computing-resource economy, it also falls short of supplying theoretical foundations for commonly held views of market desirability. This paper also points out that the argument for the desirability of markets involves circular reasoning and that the desirability can be established only vis-a-vis a scheduling goal. Finally, recasting the conclusion of Arrow's Impossibility Theorem as that for global scheduling, we conclude that there exists no market-based scheduler that is rational (in the sense defined in microeconomic theory), takes into account utility of more than one user, and yet yields a Pareto-optimal outcome for arbitrary user utility functions.

[60 years of the equilibrium theory of insular biogeography: problems of testing, results of the field studies, applied importance].

PubMed

Akatov, V V

2012-01-01

A review is presented of publications dealing with analysis of species richness of island biological communities and habitat islands based on the equilibrium theory of insular biogeography by MacArthur and Wilson (1963). Principal points of the theory are considered along with its shortcomings, problems and results of its testing. Also, possibilities are appraised for using recommendations elaborated on the base of the theory in nature conservation practice. The results of island and habitat island biota studies indicate that in many cases data corroborate the equilibrium theory while in many other cases they do not. In particular, for cenoses fragmented 50-250 years ago, especially for the ones formed by long living species, there have been no conspicuous effects of species relaxation detected. At that, the theory prediction of substantial reduction in species richness of fragmented communities in the long run is hardly disputed. The results of studies conducted in the field of insular biogeography are taken as a basis for recommendations on the long-term conservation of isolated communities integrity, although mostly they are of qualitative nature.

Universal self-similar dynamics of relativistic and nonrelativistic field theories near nonthermal fixed points

NASA Astrophysics Data System (ADS)

Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen

2015-07-01

We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

Thermodynamic analogies in economics and finance: instability of markets

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2003-11-01

Interest in thermodynamic analogies in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper, we go further and use a standard strategy from trading theory to pinpoint why thermodynamic analogies necessarily fail to describe financial markets, in spite of the presence of liquidity as the underlying basis for market entropy. Market liquidity of frequently traded assets does play the role of the ‘heat bath‘, as anticipated by von Neumann, but we are able to identify the no-arbitrage condition geometrically as an assumption of translational and rotational invariance rather than (as finance theorists would claim) an equilibrium condition. We then use the empirical market distribution to introduce an asset's entropy and discuss the underlying reason why real financial markets cannot behave thermodynamically: financial markets are unstable, they do not approach statistical equilibrium, nor are there any available topological invariants on which to base a purely formal statistical mechanics. After discussing financial markets, we finally generalize our result by proposing that the idea of Adam Smith's Invisible Hand is a falsifiable proposition: we suggest how to test nonfinancial markets empirically for the stabilizing action of The Invisible Hand.

A gravitational potential finding for rotating cosmological body in the context of proto-planetary dynamics problem solving

NASA Astrophysics Data System (ADS)

Krot, Alexander M.

2008-09-01

The statistical theory for a cosmological body forming (so-called the spheroidal body model) has been proposed in [1]-[9]. Within the framework of this theory, bodies have fuzzy outlines and are represented by means of spheroidal forms [1],[2]. In the work [3], it has been investigated a slowly evolving in time process of a gravitational compression of a spheroidal body close to an unstable equilibrium state. In the papers [4],[5], the equation of motion of particles inside the weakly gravitating spheroidal body modeled by means of an ideal liquid has been obtained. Using Schwarzschild's and Kerr's metrics a consistency of the proposed statistical model with the general relativity has been shown in [6]. The proposed theory follows from the conception for forming a spheroidal body from protoplanetary nebula [7],[8]; it permits to derive the form of distribution functions for an immovable [1]-[5] and rotating spheroidal body [6]-[8] as well as their density masses and also the distribution function of specific angular momentum of the rotating uniformly spheroidal body [7],[8]. It is well-known there is not a statistical equilibrium in a gas-dust proto-planetary cloud because of long relaxation time for proto-planets formation in own gravitational field. This proto-planetary system behavior can be described by Jeans' equation in partial derivations relative to a distribution function [9]. The problem for finding a general solution of Jeans' equation is connected directly with an analytical expression for potential of gravitational field. Thus, the determination of gravitational potential is the main problem of statistical dynamics for proto-planetary system [9]. This work shows this task of proto-planetary dynamics can be solved on the basis of spheroidal bodies theory. The proposed theory permits to derive the form of gravitational potential for a rotating spheroidal body at a long distance from its center. Using the obtained analytical expression for potential of gravitational field, the gravitational strength (as well as angular momentum space function) in a remote zone of a slowly gravitational compressed rotating spheroidal body is obtained. As a result, a distribution function describing mechanical state of proto-planetary system can be found from the Jeans' equation. References: [1] Krot AM. The statistical model of gravitational interaction of particles. Uspekhi Sovremennoï Radioelektroniki (special issue "Cosmic Radiophysics", Moscow) 1996; 8: 66-81 (in Russian). [2] Krot AM. Use of the statistical model of gravity for analysis of nonhomogeneity in earth surface. Proc. SPIE's 13th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 5-9, 1999; 3710: 1248-1259. [3] Krot AM. Statistical description of gravitational field: a new approach. Proc. SPIE's 14th Annual Intern.Symposium "AeroSense", Orlando, Florida, USA, April 24-28, 2000; 4038: 1318-1329. [4] Krot AM. Gravidynamical equations for a weakly gravitating spheroidal body. Proc. SPIE's 15th Annual Intern. Symposium "AeroSense", Orlando, Florida, USA, April 16-20, 2001; 4394: 1271-1282. [5] Krot AM. Development of gravidynamical equations for a weakly gravitating body in the vicinity of absolute zero temperature. Proc. 53rd Intern. Astronautical Congress (IAC) - The 2nd World Space Congress-2002, Houston, Texas, USA, October 10-19, 2002; Preprint IAC-02-J.P.01: 1-11. [6] Krot AM. The statistical model of rotating and gravitating spheroidal body with the point of view of general relativity. Proc. 35th COSPAR Scientific Assembly, Paris, France, July 18-25, 2004; Abstract-Nr. COSPAR 04-A- 00162. [7] Krot A. The statistical approach to exploring formation of Solar system. Proc. European Geoscinces Union (EGU) General Assembly, Vienna, Austria, April 02-07, 2006; Geophysical Research Abstracts, vol. 8: EGU06-A- 00216, SRef-ID: 1607-7962/gra/. [8] Krot AM. The statistical model of original and evolution planets of Solar system and planetary satellities. Proc. European Planetary Science Congress, Berlin, Germany, September 18-22, 2006; Planetary Research Abstracts, ESPC2006-A-00014. [9] Krot A. On the principal difficulties and ways to their solution in the theory of gravitational condensation of infinitely distributed dust substance. Proc. XXIV IUGG General Assembly, Perugia, Italy, July 2-13, 2007; GS002 Symposium "Gravity Field", Abstract GS002-3598: 143-144.

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.

Equilibrium Structures and Absorption Spectra for SixOy-nH2O Molecular Clusters using Density Functional Theory

DTIC Science & Technology

2017-05-04

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6390--17-9723 Equilibrium Structures and Absorption Spectra for SixOy-nH2O Molecular...Absorption Spectra for SixOy-nH2O Molecular Clusters using Density Functional Theory L. Huang, S.G. Lambrakos, and L. Massa1 Naval Research Laboratory, Code...and time-dependent density functional theory (TD-DFT). The size of the clusters considered is relatively large compared to those considered in

Generalized non-equilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

In realistic nanoelectronics, disordered impurities/defects are inevitable and play important roles in electron transport. However, due to the lack of effective quantum transport method, the important effects of disorders remain poorly understood. Here, we report a generalized non-equilibrium vertex correction (NVC) method with coherent potential approximation to treat the disorder effects in quantum transport simulation. With this generalized NVC method, any averaged product of two single-particle Green's functions can be obtained by solving a set of simple linear equations. As a result, the averaged non-equilibrium density matrix and various important transport properties, including averaged current, disordered induced current fluctuation and the averaged shot noise, can all be efficiently computed in a unified scheme. Moreover, a generalized form of conditionally averaged non-equilibrium Green's function is derived to incorporate with density functional theory to enable first-principles simulation. We prove the non-equilibrium coherent potential equals the non-equilibrium vertex correction. Our approach provides a unified, efficient and self-consistent method for simulating non-equilibrium quantum transport through disorder nanoelectronics. Shanghaitech start-up fund.

The Oxygen Equilibrium of Mammalian Hemoglobin

PubMed Central

Roughton, F. J. W.

1965-01-01

The three chief physicochemical theories of the oxygen-hemoglobin equilibrium in vogue 40 years ago still influence current thought on the problem. Although the Hill theory lost its fundamental basis some 40 years ago, the famous empiric equation to which it gave rise is still much used, as a useful phenomenological expression, only involving two disposable constants. The Haldane theory, of which a difference in aggregation of oxygenated and deoxygenated hemoglobin was a fundamental feature, lay for many years dormant but has recently had an astonishing reawakening through the work on lamprey hemoglobin, which clearly reveals such differences in aggregation. Lamprey hemoglobin might thus be called a "Haldane type" hemoglobin. Adair's four-stage intermediate compound theory still seems applicable in the case of hemoglobins such as those of sheep, whose tetramer molecules do not tend to dissociate into dimers, and which might therefore be called "Adair type" hemoglobins. Horse and human hemoglobins appear to reveal both "Haldane" and "Adair" behaviour. The effects of pH, temperature, and protein concentration on the oxygen-equilibrium of sheep hemoglobin are summarised, and it is shown that, although the equilibrium curves are often isomorphous over their middle range, intensive work at the top and bottom of the curves reveals considerable differences in the relative effects of these factors on the several equilibrium constants of Adair's four intermediate equations. In the last section an account is given of preliminary experimental attempts to interpret the oxygen- and carbon monoxide—equilibrium curves of whole human blood, under physiological conditions in terms of the Adair intermediate compound hypothesis. PMID:5859923

Radiative heat transfer and nonequilibrium Casimir-Lifshitz force in many-body systems with planar geometry

NASA Astrophysics Data System (ADS)

Latella, Ivan; Ben-Abdallah, Philippe; Biehs, Svend-Age; Antezza, Mauro; Messina, Riccardo

2017-05-01

A general theory of photon-mediated energy and momentum transfer in N -body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equilibrium temperatures in such systems. An analogous formulation is introduced to quantify momentum transfer coefficients describing Casimir-Lifshitz forces out of thermal equilibrium. Forces at thermal equilibrium are readily obtained as a particular case. As an illustration of this general theoretical framework, we show on three-body systems how the presence of a fourth slab can impact equilibrium temperatures in heat-transfer problems and equilibrium positions resulting from the forces acting on the system.

Product Distribution Theory for Control of Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Lee, Chia Fan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties.

PubMed

Wilhelmsen, Øivind; Trinh, Thuat T; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Temperature anisotropy at equilibrium reveals nonlocal entropic contributions to interfacial properties

NASA Astrophysics Data System (ADS)

Wilhelmsen, Øivind; Trinh, Thuat T.; Lervik, Anders

2018-01-01

Density gradient theory for fluids has played a key role in the study of interfacial phenomena for a century. In this work, we revisit its fundamentals by examining the vapor-liquid interface of argon, represented by the cut and shifted Lennard-Jones fluid. The starting point has traditionally been a Helmholtz energy functional using mass densities as arguments. By using rather the internal energy as starting point and including the entropy density as an additional argument, following thereby the phenomenological approach from classical thermodynamics, the extended theory suggests that the configurational part of the temperature has different contributions from the parallel and perpendicular directions at the interface, even at equilibrium. We find a similar anisotropy by examining the configurational temperature in molecular dynamics simulations and obtain a qualitative agreement between theory and simulations. The extended theory shows that the temperature anisotropy originates in nonlocal entropic contributions, which are currently missing from the classical theory. The nonlocal entropic contributions discussed in this work are likely to play a role in the description of both equilibrium and nonequilibrium properties of interfaces. At equilibrium, they influence the temperature- and curvature-dependence of the surface tension. Across the vapor-liquid interface of the Lennard Jones fluid, we find that the maximum in the temperature anisotropy coincides precisely with the maximum in the thermal resistivity relative to the equimolar surface, where the integral of the thermal resistivity gives the Kapitza resistance. This links the temperature anisotropy at equilibrium to the Kapitza resistance of the vapor-liquid interface at nonequilibrium.

Near-equilibrium dumb-bell-shaped figures for cohesionless small bodies

NASA Astrophysics Data System (ADS)

Descamps, Pascal

2016-02-01

In a previous paper (Descamps, P. [2015]. Icarus 245, 64-79), we developed a specific method aimed to retrieve the main physical characteristics (shape, density, surface scattering properties) of highly elongated bodies from their rotational lightcurves through the use of dumb-bell-shaped equilibrium figures. The present work is a test of this method. For that purpose we introduce near-equilibrium dumb-bell-shaped figures which are base dumb-bell equilibrium shapes modulated by lognormal statistics. Such synthetic irregular models are used to generate lightcurves from which our method is successfully applied. Shape statistical parameters of such near-equilibrium dumb-bell-shaped objects are in good agreement with those calculated for example for the Asteroid (216) Kleopatra from its dog-bone radar model. It may suggest that such bilobed and elongated asteroids can be approached by equilibrium figures perturbed be the interplay with a substantial internal friction modeled by a Gaussian random sphere.

A statistical mechanics approach to computing rare transitions in multi-stable turbulent geophysical flows

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.

2012-04-01

Many turbulent flows undergo sporadic random transitions, after long periods of apparent statistical stationarity. For instance, paths of the Kuroshio [1], the Earth's magnetic field reversal, atmospheric flows [2], MHD experiments [3], 2D turbulence experiments [4,5], 3D flows [6] show this kind of behavior. The understanding of this phenomena is extremely difficult due to the complexity, the large number of degrees of freedom, and the non-equilibrium nature of these turbulent flows. It is however a key issue for many geophysical problems. A straightforward study of these transitions, through a direct numerical simulation of the governing equations, is nearly always impracticable. This is mainly a complexity problem, due to the large number of degrees of freedom involved for genuine turbulent flows, and the extremely long time between two transitions. In this talk, we consider two-dimensional and geostrophic turbulent models, with stochastic forces. We consider regimes where two or more attractors coexist. As an alternative to direct numerical simulation, we propose a non-equilibrium statistical mechanics approach to the computation of this phenomenon. Our strategy is based on large deviation theory [7], derived from a path integral representation of the stochastic process. Among the trajectories connecting two non-equilibrium attractors, we determine the most probable one. Moreover, we also determine the transition rates, and in which cases this most probable trajectory is a typical one. Interestingly, we prove that in the class of models we consider, a mechanism exists for diffusion over sets of connected attractors. For the type of stochastic forces that allows this diffusion, the transition between attractors is not a rare event. It is then very difficult to characterize the flow as bistable. However for another class of stochastic forces, this diffusion mechanism is prevented, and genuine bistability or multi-stability is observed. We discuss how these results are probably connected to the long debated existence of multi-stability in the atmosphere and oceans.

A philosophy of rivers: Equilibrium states, channel evolution, teleomatic change and least action principle

NASA Astrophysics Data System (ADS)

Nanson, Gerald C.; Huang, He Qing

2018-02-01

Until recently no universal agreement as to a philosophical or scientific methodological framework has been proposed to guide the study of fluvial geomorphology. An understanding of river form and process requires an understanding of the principles that govern the behaviour and evolution of alluvial rivers at the most fundamental level. To date, the investigations of such principles have followed four approaches: develop qualitative unifying theories that are usually untested; collect and examine data visually and statistically to define semi-quantitative relationships among variables; apply Newtonian theoretical and empirical mechanics in a reductionist manner; resolve the primary flow equations theoretically by assuming maximum or minimum outputs. Here we recommend not a fifth but an overarching philosophy to embrace all four: clarifying and formalising an understanding of the evolution of river channels and iterative directional changes in the context of least action principle (LAP), the theoretical basis of variational mechanics. LAP is exemplified in rivers in the form of maximum flow efficiency (MFE). A sophisticated understanding of evolution in its broadest sense is essential to understand how rivers adjust towards an optimum state rather than towards some other. Because rivers, as dynamic contemporary systems, flow in valleys that are commonly historical landforms and often tectonically determined, we propose that most of the world's alluvial rivers are over-powered for the work they must do. To remain stable they commonly evolve to expend surplus energy via a variety of dynamic equilibrium forms that will further adjust, where possible, to maximise their stability as much less common MFE forms in stationary equilibrium. This paper: 1. Shows that the theory of evolution is derived from, and applicable to, both the physical and biological sciences; 2. Focusses the development of theory in geomorphology on the development of equilibrium theory; 3. Proposes that river channels, like organisms, evolve teleomatically (progression towards an end-state by following natural laws) and iteratively (one stage forming the basis for the next) towards an optimal end-state; 4. Describes LAP as the methodological basis for understanding the self-adjustment alluvial channels towards MFE. 5. Acknowledges that whereas river channels that form within their unmodified alluvium evolve into optimal minimum-energy systems, exogenic variables, such as riparian or aquatic vegetation, can cause significant variations in resultant river-styles. We specifically attempt to address Luna Leopold's lament in 1994 that no clearly expressed philosophy explains the remarkable self-adjustment of alluvial channels.

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!

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.

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.

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Marston, J. B.; Hastings, M. B.

2005-03-01

The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.

On the theory of time dilation in chemical kinetics

NASA Astrophysics Data System (ADS)

Baig, Mirza Wasif

2017-10-01

The rates of chemical reactions are not absolute but their magnitude depends upon the relative speeds of the moving observers. This has been proved by unifying basic theories of chemical kinetics, which are transition state theory, collision theory, RRKM and Marcus theory, with the special theory of relativity. Boltzmann constant and energy spacing between permitted quantum levels of molecules are quantum mechanically proved to be Lorentz variant. The relativistic statistical thermodynamics has been developed to explain quasi-equilibrium existing between reactants and activated complex. The newly formulated Lorentz transformation of the rate constant from Arrhenius equation, of the collision frequency and of the Eyring and Marcus equations renders the rate of reaction to be Lorentz variant. For a moving observer moving at fractions of the speed of light along the reaction coordinate, the transition state possess less kinetic energy to sweep translation over it. This results in the slower transformation of reactants into products and in a stretched time frame for the chemical reaction to complete. Lorentz transformation of the half-life equation explains time dilation of the half-life period of chemical reactions and proves special theory of relativity and presents theory in accord with each other. To demonstrate the effectiveness of the present theory, the enzymatic reaction of methylamine dehydrogenase and radioactive disintegration of Astatine into Bismuth are considered as numerical examples.

Non-equilibrium magnetic interactions in strongly correlated systems

NASA Astrophysics Data System (ADS)

Secchi, A.; Brener, S.; Lichtenstein, A. I.; Katsnelson, M. I.

2013-06-01

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

DNA viewed as an out-of-equilibrium structure

NASA Astrophysics Data System (ADS)

Provata, A.; Nicolis, C.; Nicolis, G.

2014-05-01

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ2 tests shows that DNA can not be described as a low order Markov chain of order up to r =6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

DNA viewed as an out-of-equilibrium structure.

PubMed

Provata, A; Nicolis, C; Nicolis, G

2014-05-01

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory, and information theory. A collection of statistical analyses is performed on the DNA data and the results are compared with sequences derived from different stochastic processes. The use of χ^{2} tests shows that DNA can not be described as a low order Markov chain of order up to r=6. Although detailed balance seems to hold at the level of a binary alphabet, it fails when all four base pairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long-range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain, we study the exit distances from a specific symbol, the distribution of recurrence distances, and the Hurst exponent, all of which show power law tails and long-range characteristics. These results suggest that human DNA can be viewed as a nonequilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method, we construct a model DNA sequence. This method allows us to keep both long- and short-range statistical characteristics of the native DNA data. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture spatial correlations and point-to-point details.

Several comparison result of two types of equilibrium (Pareto Schemes and Stackelberg Scheme) of game theory approach in probabilistic vendor – buyer supply chain system with imperfect quality

NASA Astrophysics Data System (ADS)

Setiawan, R.

2018-05-01

In this paper, Economic Order Quantity (EOQ) of the vendor-buyer supply-chain model under a probabilistic condition with imperfect quality items has been analysed. The analysis is delivered using two concepts in game theory approach, which is Stackelberg equilibrium and Pareto Optimal, under non-cooperative and cooperative games, respectively. Another result is getting acomparison of theoptimal result between integrated scheme and game theory approach based on analytical and numerical result using appropriate simulation data.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

How to Compute Electron Ionization Mass Spectra from First Principles.

PubMed

Bauer, Christoph Alexander; Grimme, Stefan

2016-06-02

The prediction of electron ionization (EI) mass spectra (MS) from first principles has been a major challenge for quantum chemistry (QC). The unimolecular reaction space grows rapidly with increasing molecular size. On the one hand, statistical models like Eyring's quasi-equilibrium theory and Rice-Ramsperger-Kassel-Marcus theory have provided valuable insight, and some predictions and quantitative results can be obtained from such calculations. On the other hand, molecular dynamics-based methods are able to explore automatically the energetically available regions of phase space and thus yield reaction paths in an unbiased way. We describe in this feature article the status of both methodologies in relation to mass spectrometry for small to medium sized molecules. We further present results obtained with the QCEIMS program developed in our laboratory. Our method, which incorporates stochastic and dynamic elements, has been a significant step toward the reliable routine calculation of EI mass spectra.

Self-Consistent Field Lattice Model for Polymer Networks.

PubMed

Tito, Nicholas B; Storm, Cornelis; Ellenbroek, Wouter G

2017-12-26

A lattice model based on polymer self-consistent field theory is developed to predict the equilibrium statistics of arbitrary polymer networks. For a given network topology, our approach uses moment propagators on a lattice to self-consistently construct the ensemble of polymer conformations and cross-link spatial probability distributions. Remarkably, the calculation can be performed "in the dark", without any prior knowledge on preferred chain conformations or cross-link positions. Numerical results from the model for a test network exhibit close agreement with molecular dynamics simulations, including when the network is strongly sheared. Our model captures nonaffine deformation, mean-field monomer interactions, cross-link fluctuations, and finite extensibility of chains, yielding predictions that differ markedly from classical rubber elasticity theory for polymer networks. By examining polymer networks with different degrees of interconnectivity, we gain insight into cross-link entropy, an important quantity in the macroscopic behavior of gels and self-healing materials as they are deformed.

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

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

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.

Dynamic Self-Consistent Field Theories for Polymer Blends and Block Copolymers

NASA Astrophysics Data System (ADS)

Kawakatsu, Toshihiro

Understanding the behavior of the phase separated domain structures and rheological properties of multi-component polymeric systems require detailed information on the dynamics of domains and that of conformations of constituent polymer chains. Self-consistent field (SCF) theory is a useful tool to treat such a problem because the conformation entropy of polymer chains in inhomogeneous systems can be evaluated quantitatively using this theory. However, when we turn our attention to the dynamic properties in a non-equilibrium state, the basic assumption of the SCF theory, i.e. the assumption of equilibrium chain conformation, breaks down. In order to avoid such a difficulty, dynamic SCF theories were developed. In this chapter, we give a brief review of the recent developments of dynamic SCF theories, and discuss where the cutting-edge of this theory is.

Stochastic and equilibrium pictures of the ultracold Fano-Feshbach-resonance molecular conversion rate

NASA Astrophysics Data System (ADS)

Yamakoshi, Tomotake; Watanabe, Shinichi; Zhang, Chen; Greene, Chris H.

2013-05-01

The ultracold molecular conversion rate occurring in an adiabatic ramp through a Fano-Feshbach resonance is studied and compared in two statistical models. One model, the so-called stochastic phase-space sampling (SPSS) [Hodby , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.94.120402 94, 120402 (2005)] evaluates the overlap of two atomic distributions in phase space by sampling atomic pairs according to a phase-space criterion. The other model, the chemical equilibrium theory (ChET) [Watabe and Nikuni, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.77.013616 77, 013616 (2008)] considers atomic and molecular distributions in the limit of the chemical and thermal equilibrium. The present study applies SPSS and ChET to a prototypical system of K+K→ K2 in all the symmetry combinations, namely Fermi-Fermi, Bose-Bose, and Bose-Fermi cases. To examine implications of the phase-space criterion for SPSS, the behavior of molecular conversion is analyzed using four distinct geometrical constraints. Our comparison of the results of SPSS with those of ChET shows that while they appear similar in most situations, the two models give rise to rather dissimilar behaviors when the presence of a Bose-Einstein condensate strongly affects the molecule formation.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment.

PubMed

Astumian, R D

2018-01-11

In the absence of input energy, a chemical reaction in a closed system ineluctably relaxes toward an equilibrium state governed by a Boltzmann distribution. The addition of a catalyst to the system provides a way for more rapid equilibration toward this distribution, but the catalyst can never, in and of itself, drive the system away from equilibrium. In the presence of external fluctuations, however, a macromolecular catalyst (e.g., an enzyme) can absorb energy and drive the formation of a steady state between reactant and product that is not determined solely by their relative energies. Due to the ubiquity of non-equilibrium steady states in living systems, the development of a theory for the effects of external fluctuations on chemical systems has been a longstanding focus of non-equilibrium thermodynamics. The theory of stochastic pumping has provided insight into how a non-equilibrium steady-state can be formed and maintained in the presence of dissipation and kinetic asymmetry. This effort has been greatly enhanced by a confluence of experimental and theoretical work on synthetic molecular machines designed explicitly to harness external energy to drive non-equilibrium transport and self-assembly.

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory.

PubMed

Weikl, Thomas R; Hu, Jinglei; Xu, Guang-Kui; Lipowsky, Reinhard

2016-09-02

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

PubMed Central

Weikl, Thomas R.; Hu, Jinglei; Xu, Guang-Kui; Lipowsky, Reinhard

2016-01-01

ABSTRACT The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between K2D and the binding constant K3D of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D). PMID:27294442

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

NASA Astrophysics Data System (ADS)

Sukhorukov, Eugene V.

2016-08-01

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga-Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.

Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

NASA Astrophysics Data System (ADS)

Sukhorukov, Eugene V.

2016-03-01

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga-Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

NASA Astrophysics Data System (ADS)

Seibt, Joachim; Mančal, Tomáš

2017-05-01

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

Thermostatistical description of gas mixtures from space partitions

NASA Astrophysics Data System (ADS)

Rohrmann, R. D.; Zorec, J.

2006-10-01

The new mathematical framework based on the free energy of pure classical fluids presented by Rohrmann [Physica A 347, 221 (2005)] is extended to multicomponent systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on D -dimensional mixtures in the low-density limit (packing factor η<0.01 ). The formalism combines the free-energy minimization technique with space partitions that assign an available volume v to each particle. v is related to the closeness of the nearest neighbor and provides a useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials μil , conjugate variable of the populations Nil of particles class i with the nearest neighbors of class l are defined and their relationships with the usual chemical potentials μi are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to Kac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.

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.

Neutron-induced fission: properties of prompt neutron and γ rays as a function of incident energy

NASA Astrophysics Data System (ADS)

Stetcu, I.; Talou, P.; Kawano, T.

2016-06-01

We have applied the Hauser-Feshbach statistical theory, in a Monte-Carlo implementation, to the de-excitation of fission fragments, obtaining a reasonable description of the characteristics of neutrons and gamma rays emitted before beta decays toward stability. Originally implemented for the spontaneous fission of 252Cf and the neutroninduced fission of 235U and 239Pu at thermal neutron energy, in this contribution we discuss the extension of the formalism to incident neutron energies up to 20 MeV. For the emission of pre-fission neutrons, at incident energies beyond second-chance fission, we take into account both the pre-equilibrium and statistical pre-fission components. Phenomenological parameterizations of mass, charge and TKE yields are used to obtain the initial conditions for the fission fragments that subsequently decay via neutron and emissions. We illustrate this approach for 239Pu(n,f).

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

NASA Astrophysics Data System (ADS)

Kretchmer, Joshua S.; Chan, Garnet Kin-Lic

2018-02-01

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics.

PubMed

Kretchmer, Joshua S; Chan, Garnet Kin-Lic

2018-02-07

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory.

PubMed

Ng, Yee-Hong; Bettens, Ryan P A

2016-03-03

Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

Beyond temperature: Clumped isotope signatures in dissolved inorganic carbon species and the influence of solution chemistry on carbonate mineral composition

NASA Astrophysics Data System (ADS)

Tripati, Aradhna K.; Hill, Pamela S.; Eagle, Robert A.; Mosenfelder, Jed L.; Tang, Jianwu; Schauble, Edwin A.; Eiler, John M.; Zeebe, Richard E.; Uchikawa, Joji; Coplen, Tyler B.; Ries, Justin B.; Henry, Drew

2015-10-01

;Clumped-isotope; thermometry is an emerging tool to probe the temperature history of surface and subsurface environments based on measurements of the proportion of 13C and 18O isotopes bound to each other within carbonate minerals in 13C18O16O22- groups (heavy isotope ;clumps;). Although most clumped isotope geothermometry implicitly presumes carbonate crystals have attained lattice equilibrium (i.e., thermodynamic equilibrium for a mineral, which is independent of solution chemistry), several factors other than temperature, including dissolved inorganic carbon (DIC) speciation may influence mineral isotopic signatures. Therefore we used a combination of approaches to understand the potential influence of different variables on the clumped isotope (and oxygen isotope) composition of minerals. We conducted witherite precipitation experiments at a single temperature and at varied pH to empirically determine 13C-18O bond ordering (Δ47) and δ18O of CO32- and HCO3- molecules at a 25 °C equilibrium. Ab initio cluster models based on density functional theory were used to predict equilibrium 13C-18O bond abundances and δ18O of different DIC species and minerals as a function of temperature. Experiments and theory indicate Δ47 and δ18O compositions of CO32- and HCO3- ions are significantly different from each other. Experiments constrain the Δ47-δ18O slope for a pH effect (0.011 ± 0.001; 12 ⩾ pH ⩾ 7). Rapidly-growing temperate corals exhibit disequilibrium mineral isotopic signatures with a Δ47-δ18O slope of 0.011 ± 0.003, consistent with a pH effect. Our theoretical calculations for carbonate minerals indicate equilibrium lattice calcite values for Δ47 and δ18O are intermediate between HCO3- and CO32-. We analyzed synthetic calcites grown at temperatures ranging from 0.5 to 50 °C with and without the enzyme carbonic anhydrase present. This enzyme catalyzes oxygen isotopic exchange between DIC species and is present in many natural systems. The two types of experiments yielded statistically indistinguishable results, and these measurements yield a calibration that overlaps with our theoretical predictions for calcite at equilibrium. The slow-growing Devils Hole calcite exhibits Δ47 and δ18O values consistent with lattice equilibrium. Factors influencing DIC speciation (pH, salinity) and the timescale for DIC equilibration, as well as reactions at the mineral-solution interface, have the potential to influence clumped-isotope signatures and the δ18O of carbonate minerals. In fast-growing carbonate minerals, solution chemistry may be an important factor, particularly over extremes of pH and salinity. If a crystal grows too rapidly to reach an internal equilibrium (i.e., achieve the value for the temperature-dependent mineral lattice equilibrium), it may record the clumped-isotope signature of a DIC species (e.g., the temperature-dependent equilibrium of HCO3-) or a mixture of DIC species, and hence record a disequilibrium mineral composition. For extremely slow-growing crystals, and for rapidly-grown samples grown at a pH where HCO3- dominates the DIC pool at equilibrium, effects of solution chemistry are likely to be relatively small or negligible. In summary, growth environment, solution chemistry, surface equilibria, and precipitation rate may all play a role in dictating whether a crystal achieves equilibrium or disequilibrium clumped-isotope signatures.

Beyond temperature: Clumped isotope signatures in dissolved inorganic carbon species and the influence of solution chemistry on carbonate mineral composition

USGS Publications Warehouse

Tripati, Aradhna K.; Hill, Pamela S.; Eagle, Robert A.; Mosenfelder, Jed L.; Tang, Jianwu; Schauble, Edwin A.; Eiler, John M.; Zeebe, Richard E.; Uchikawa, Joji; Coplen, Tyler B.; Ries, Justin B.; Henry, Drew

2015-01-01

“Clumped-isotope” thermometry is an emerging tool to probe the temperature history of surface and subsurface environments based on measurements of the proportion of 13C and 18O isotopes bound to each other within carbonate minerals in 13C18O16O22- groups (heavy isotope “clumps”). Although most clumped isotope geothermometry implicitly presumes carbonate crystals have attained lattice equilibrium (i.e., thermodynamic equilibrium for a mineral, which is independent of solution chemistry), several factors other than temperature, including dissolved inorganic carbon (DIC) speciation may influence mineral isotopic signatures. Therefore we used a combination of approaches to understand the potential influence of different variables on the clumped isotope (and oxygen isotope) composition of minerals.We conducted witherite precipitation experiments at a single temperature and at varied pH to empirically determine 13C-18O bond ordering (Δ47) and δ18O of CO32- and HCO3- molecules at a 25 °C equilibrium. Ab initio cluster models based on density functional theory were used to predict equilibrium 13C-18O bond abundances and δ18O of different DIC species and minerals as a function of temperature. Experiments and theory indicate Δ47 and δ18O compositions of CO32- and HCO3- ions are significantly different from each other. Experiments constrain the Δ47-δ18O slope for a pH effect (0.011 ± 0.001; 12 ⩾ pH ⩾ 7). Rapidly-growing temperate corals exhibit disequilibrium mineral isotopic signatures with a Δ47-δ18O slope of 0.011 ± 0.003, consistent with a pH effect.Our theoretical calculations for carbonate minerals indicate equilibrium lattice calcite values for Δ47 and δ18O are intermediate between HCO3− and CO32−. We analyzed synthetic calcites grown at temperatures ranging from 0.5 to 50 °C with and without the enzyme carbonic anhydrase present. This enzyme catalyzes oxygen isotopic exchange between DIC species and is present in many natural systems. The two types of experiments yielded statistically indistinguishable results, and these measurements yield a calibration that overlaps with our theoretical predictions for calcite at equilibrium. The slow-growing Devils Hole calcite exhibits Δ47 and δ18O values consistent with lattice equilibrium.Factors influencing DIC speciation (pH, salinity) and the timescale for DIC equilibration, as well as reactions at the mineral–solution interface, have the potential to influence clumped-isotope signatures and the δ18O of carbonate minerals. In fast-growing carbonate minerals, solution chemistry may be an important factor, particularly over extremes of pH and salinity. If a crystal grows too rapidly to reach an internal equilibrium (i.e., achieve the value for the temperature-dependent mineral lattice equilibrium), it may record the clumped-isotope signature of a DIC species (e.g., the temperature-dependent equilibrium of HCO3−) or a mixture of DIC species, and hence record a disequilibrium mineral composition. For extremely slow-growing crystals, and for rapidly-grown samples grown at a pH where HCO3- dominates the DIC pool at equilibrium, effects of solution chemistry are likely to be relatively small or negligible. In summary, growth environment, solution chemistry, surface equilibria, and precipitation rate may all play a role in dictating whether a crystal achieves equilibrium or disequilibrium clumped-isotope signatures.

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

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

Ivanov, A. A., E-mail: aai@a5.kiam.ru; Martynov, A. A., E-mail: martynov@a5.kiam.ru; Medvedev, S. Yu., E-mail: medvedev@a5.kiam.ru

In the MHD tokamak plasma theory, the plasma pressure is usually assumed to be isotropic. However, plasma heating by neutral beam injection and RF heating can lead to a strong anisotropy of plasma parameters and rotation of the plasma. The development of MHD equilibrium theory taking into account the plasma inertia and anisotropic pressure began a long time ago, but until now it has not been consistently applied in computational codes for engineering calculations of the plasma equilibrium and evolution in tokamak. This paper contains a detailed derivation of the axisymmetric plasma equilibrium equation in the most general form (withmore » arbitrary rotation and anisotropic pressure) and description of the specialized version of the SPIDER code. The original method of calculation of the equilibrium with an anisotropic pressure and a prescribed rotational transform profile is proposed. Examples of calculations and discussion of the results are also presented.« less

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.

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

NASA Astrophysics Data System (ADS)

Verkley, Wim; Severijns, Camiel

2014-05-01

Lorenz [1] has devised a dynamical system that has proved to be very useful as a benchmark system in geophysical fluid dynamics. The system in its simplest form consists of a periodic array of variables that can be associated with an atmospheric field on a latitude circle. The system is driven by a constant forcing, is damped by linear friction and has a simple advection term that causes the model to behave chaotically if the forcing is large enough. Our aim is to predict the statistics of Lorenz' model on the basis of a given average value of its total energy - obtained from a numerical integration - and the assumption of statistical stationarity. Our method is the principle of maximum entropy [2] which in this case reads: the information entropy of the system's probability density function shall be maximal under the constraints of normalization, a given value of the average total energy and statistical stationarity. Statistical stationarity is incorporated approximately by using `stationarity constraints', i.e., by requiring that the average first and possibly higher-order time-derivatives of the energy are zero in the maximization of entropy. The analysis [3] reveals that, if the first stationarity constraint is used, the resulting probability density function rather accurately reproduces the statistics of the individual variables. If the second stationarity constraint is used as well, the correlations between the variables are also reproduced quite adequately. The method can be generalized straightforwardly and holds the promise of a viable non-equilibrium statistical mechanics of the forced-dissipative systems of geophysical fluid dynamics. [1] E.N. Lorenz, 1996: Predictability - A problem partly solved, in Proc. Seminar on Predictability (ECMWF, Reading, Berkshire, UK), Vol. 1, pp. 1-18. [2] E.T. Jaynes, 2003: Probability Theory - The Logic of Science (Cambridge University Press, Cambridge). [3] W.T.M. Verkley and C.A. Severijns, 2014: The maximum entropy principle applied to a dynamical system proposed by Lorenz, Eur. Phys. J. B, 87:7, http://dx.doi.org/10.1140/epjb/e2013-40681-2 (open access).

Significance of vapor phase chemical reactions on CVD rates predicted by chemically frozen and local thermochemical equilibrium boundary layer theories

NASA Technical Reports Server (NTRS)

Gokoglu, Suleyman A.

1988-01-01

This paper investigates the role played by vapor-phase chemical reactions on CVD rates by comparing the results of two extreme theories developed to predict CVD mass transport rates in the absence of interfacial kinetic barrier: one based on chemically frozen boundary layer and the other based on local thermochemical equilibrium. Both theories consider laminar convective-diffusion boundary layers at high Reynolds numbers and include thermal (Soret) diffusion and variable property effects. As an example, Na2SO4 deposition was studied. It was found that gas phase reactions have no important role on Na2SO4 deposition rates and on the predictions of the theories. The implications of the predictions of the two theories to other CVD systems are discussed.

Transport processes in magnetically confined plasmas in the nonlinear regime.

PubMed

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

The development of spheroidal bodies theory for proto-planetary dynamics problem solving

NASA Astrophysics Data System (ADS)

Krot, A. M.

2007-08-01

There is not a full statistical equilibrium in a gas-dust proto-planetary cloud because of long relaxation time for proto-planet formation in own gravitational field. This protoplanetary system behavior can be described by Jeans equation in partial derivations relatively a distribution function. The problem for finding a general solution of Jeans equation is connected directly with an analytical expression for potential of gravitational field. Thus, the determination of gravitational potential is the main problem of statistical dynamics for proto-planetary system. The work shows this task of protoplanetary dynamics can be solved on the basis of spheroidal bodies theory [1]-[4]. Within the framework of this theory, cosmological bodies have fuzzy outlines and are represented by means of spheroidal forms. The proposed theory follows from the conception for forming a spheroidal body as a proto-planet from dust-like nebula; it permits to derive the form of distribution functions for an immovable spheroidal body [1],[2] and rotating one [3],[4] as well as their density masses (gravitational potentials and strengths) and also to find the distribution function of specific angular momentum for the rotating spheroidal body [4]. References: [1] A.M.Krot, Achievement in Modern Radioelectronics, 1996, no.8, pp.66-81 (in Russian). [2] A.M.Krot, Proc. SPIE's 13thAnnual Intern.Symp. "AeroSense", Orlando, Florida, USA, 1999, vol.3710, pp.1248-1259. [3] A.M.Krot, Proc. 35th COSPAR Scientific Assembly, Paris, France, 2004, Abstract A-00162. [4] A.Krot, Proc. EGU General Assembly, Vienna, Austria, 2006, Geophys. Res. Abstracts, vol.8, A-00216; SRef-ID: 1607-7962/gra/.

Characterization and Detection of ϵ-Berge-Zhukovskii Equilibria

PubMed Central

Lung, Rodica Ioana; Suciu, Mihai; Gaskó, Noémi; Dumitrescu, D.

2015-01-01

The Berge-Zhukovskii equilibrium is an alternate solution concept in non-cooperative game theory that formalizes cooperation in a noncooperative setting. In this paper, the ϵ-Berge-Zhukovskii equilibrium is introduced and characterized by using a generative relation. The generative relation also provides a solution to the problem of computing the ϵ-Berge-Zhukovskii equilibrium for large games, by using evolutionary algorithms. Numerical examples illustrate the approach and provide a possible application for this equilibrium concept. PMID:26177217

Electron Impact Excitation of the Electronic States of Water

NASA Astrophysics Data System (ADS)

Thorn, Penny; Diakomichalis, N.; Brunger, M. J.; Campbell, L.; Teubner, P. J. O.; Kato, H.; Makochekanwa, C.; Hoshino, M.; Tanaka, H.

2006-10-01

We report differential and integral cross sections for excitation of the lowest lying ^3B1, ^1B1, ^3A1 and ^1A1 electronic states of water. The energy range of these measurements is 15-50eV and the angular range of the DCS measurements is 10-90^o. From these DCS the corresponding ICS is calculated using a molecular phase shift analysis technique. Where possible, comparison is made to the results of available theory. One of the main objectives of this study is to perform statistical equilibrium calculations to determine if the origin of the OH Meinel bands in our atmosphere are due to electron driven processes.

Synchronization behaviors of coupled systems composed of hidden attractors

NASA Astrophysics Data System (ADS)

Zhang, Ge; Wu, Fuqiang; Wang, Chunni; Ma, Jun

2017-10-01

Based on a class of chaotic system composed of hidden attractors, in which the equilibrium points are described by a circular function, complete synchronization between two identical systems, pattern formation and synchronization of network is investigated, respectively. A statistical factor of synchronization is defined and calculated by using the mean field theory, the dependence of synchronization on bifurcation parameters discussed in numerical way. By setting a chain network, which local kinetic is described by hidden attractors, synchronization approach is investigated. It is found that the synchronization and pattern formation are dependent on the coupling intensity and also the selection of coupling variables. In the end, open problems are proposed for readers’ extensive guidance and investigation.

On determining absolute entropy without quantum theory or the third law of thermodynamics

NASA Astrophysics Data System (ADS)

Steane, Andrew M.

2016-04-01

We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

Coagulation-Fragmentation Model for Animal Group-Size Statistics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.

2017-04-01

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent -2/3 for small size to -3/2 for large size, with an exponential cutoff.

Answer Sets in a Fuzzy Equilibrium Logic

NASA Astrophysics Data System (ADS)

Schockaert, Steven; Janssen, Jeroen; Vermeir, Dirk; de Cock, Martine

Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general “classical” approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.

Grain formation in astronomical systems: A critical review of condensation processes

NASA Technical Reports Server (NTRS)

Donn, B.

1978-01-01

An analysis is presented of the assumption and the applicability of the three theoretical methods for calculating condensations in cosmic clouds where no pre-existing nuclei exist. The three procedures are: thermodynamic equilibrium calculations, nucleation theory, and a kinetic treatment which would take into account the characteristics of each individual collision. Thermodynamics provide detailed results on the composition temperature and composition of the condensate provided the system attains equilibrium. Because of the cosmic abundance mixture of elements, large supersaturations in some cases and low pressures, equilibrium is not expected in astronomical clouds. Nucleation theory, a combination of thermodynamics and kinetics, has the limitations of each scheme. Kinetics, not requiring equilibrium, avoids nearly all the thermodynamics difficulties but requires detailed knowledge of many reactions which thermodynamics avoids. It appears to be the only valid way to treat grain formation in space. A review of experimental studies is given.

Efficient steady-state solver for hierarchical quantum master equations

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2017-07-01

Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching.

PubMed

Glowacki, David R; Rodgers, W J; Shannon, Robin; Robertson, Struan H; Harvey, Jeremy N

2017-04-28

The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH 3 does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of systems.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 Authors.

Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching

PubMed Central

Rodgers, W. J.; Shannon, Robin; Robertson, Struan H.; Harvey, Jeremy N.

2017-01-01

The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at ‘hotspots’ that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH3 does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of systems. 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’. PMID:28320908

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Equilibrium figures in geodesy and geophysics.

NASA Astrophysics Data System (ADS)

Moritz, H.

There is an enormous literature on geodetic equilibrium figures, but the various works have not always been interrelated, also for linguistic reasons (English, French, German, Italian, Russian). The author attempts to systematize the various approaches and to use the standard second-order theory for a study of the deviation of the actual earth and of the equipotential reference ellipsoid from an equilibrium figure.

The Speed Reading Is in Disrepute: Advantages of Slow Reading for the Information Equilibrium

ERIC Educational Resources Information Center

Tsvetkova, Milena I.

2017-01-01

The study is dedicated to the impact of the speed and the acceleration on the preservation of the information equilibrium and the ability for critical thinking in the active person. The methods about the fast reading training are subjected to a critical analysis. On the grounds of the theory for the information equilibrium and the philosophy of…

Adaptive Multi-Agent Systems for Constrained Optimization

NASA Technical Reports Server (NTRS)

Macready, William; Bieniawski, Stefan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

Coherent Structures and Chaos Control in High-Power Microwave and Charged-Particle Beam Devices

DTIC Science & Technology

2009-01-31

34Equilibrium Theory of an Intense Elliptic Beam for High - Power Ribbon-Beam Klystron Applications," Proc. 2007 Part. Accel. Conf. p. 2316. Courant...34Equilibrium Theory of an Intense Elliptic Beam for High - Power Ribbon-Beam Klystron Applications," C. Chen and J. Zhou, Proc. 2007 Part. Accel. Conf. (2007...accelerator focusing systems. Over 600 high - power , high -efficiency klystrons , for example, may be needed to provide rf power for the acceleration

Thermodynamics of enzyme-catalyzed esterifications: II. Levulinic acid esterification with short-chain alcohols.

PubMed

Altuntepe, Emrah; Emel'yanenko, Vladimir N; Forster-Rotgers, Maximilian; Sadowski, Gabriele; Verevkin, Sergey P; Held, Christoph

2017-10-01

Levulinic acid was esterified with methanol, ethanol, and 1-butanol with the final goal to predict the maximum yield of these equilibrium-limited reactions as function of medium composition. In a first step, standard reaction data (standard Gibbs energy of reaction Δ R g 0 ) were determined from experimental formation properties. Unexpectedly, these Δ R g 0 values strongly deviated from data obtained with classical group contribution methods that are typically used if experimental standard data is not available. In a second step, reaction equilibrium concentrations obtained from esterification catalyzed by Novozym 435 at 323.15 K were measured, and the corresponding activity coefficients of the reacting agents were predicted with perturbed-chain statistical associating fluid theory (PC-SAFT). The so-obtained thermodynamic activities were used to determine Δ R g 0 at 323.15 K. These results could be used to cross-validate Δ R g 0 from experimental formation data. In a third step, reaction-equilibrium experiments showed that equilibrium position of the reactions under consideration depends strongly on the concentration of water and on the ratio of levulinic acid: alcohol in the initial reaction mixtures. The maximum yield of the esters was calculated using Δ R g 0 data from this work and activity coefficients of the reacting agents predicted with PC-SAFT for varying feed composition of the reaction mixtures. The use of the new Δ R g 0 data combined with PC-SAFT allowed good agreement to the measured yields, while predictions based on Δ R g 0 values obtained with group contribution methods showed high deviations to experimental yields.

Stellar equilibrium configurations of white dwarfs in the f( R, T) gravity

NASA Astrophysics Data System (ADS)

Carvalho, G. A.; Lobato, R. V.; Moraes, P. H. R. S.; Arbañil, José D. V.; Otoniel, E.; Marinho, R. M.; Malheiro, M.

2017-12-01

In this work we investigate the equilibrium configurations of white dwarfs in a modified gravity theory, namely, f( R, T) gravity, for which R and T stand for the Ricci scalar and trace of the energy-momentum tensor, respectively. Considering the functional form f(R,T)=R+2λ T, with λ being a constant, we obtain the hydrostatic equilibrium equation for the theory. Some physical properties of white dwarfs, such as: mass, radius, pressure and energy density, as well as their dependence on the parameter λ are derived. More massive and larger white dwarfs are found for negative values of λ when it decreases. The equilibrium configurations predict a maximum mass limit for white dwarfs slightly above the Chandrasekhar limit, with larger radii and lower central densities when compared to standard gravity outcomes. The most important effect of f( R, T) theory for massive white dwarfs is the increase of the radius in comparison with GR and also f( R) results. By comparing our results with some observational data of massive white dwarfs we also find a lower limit for λ , namely, λ >- 3× 10^{-4}.

The Unquiet State of Violent Relaxation

NASA Astrophysics Data System (ADS)

Henriksen, Richard

2005-08-01

In 1967 Lynden-Bell presented a statistical mechanical theory for the relaxation of collisionless systems. Since then this theory has been studied numerically and theoretically by many authors. Nakamura in 2000 gave an alternate theory that differed from that of Lynden- Bell by predicting a Gaussian equilibrium distribution function rather than Fermi-Dirac. More recently Henriksen in 2004 has used a coarsegraining technique on cosmological infall systems that also predicts a Gaussian equilibrium distribution function. These relaxed states are thought to occur from the centre of the system outwards. Simulations of cosmological cold dark-matter halos however persist in finding central density cusps (the NFWprofile), which are inconsistent with the predicted distribution functions and perhaps with the observations of some galaxies. Some numerical studies (e.g.Merrall & Henriksen 2003) that attempt to measure the distribution function of dark matter do find Gaussian functions, provided that the initial asymmetry is not too great. Moreover recent work at Queen's reported here by MacMillan, suggests that it is the growth of asymmetry during the infall that produces the cusped behaviour. So put briefly, the essential physics of dark-matter relaxation remains "obscure" as does the validity of the theoretical predictions. "Violent virialization" occurs rapidly, well before subscale relaxation, but the scale at which the relaxation stops (and why) remains unclear. I will present some results that argue for wave-particle relaxation (Landau damping as frequently suggested by Kandrup) and in addition I will suggest that the evolution of isolated systems is very different from that of systems constantly disturbed by infall. Isolated systems may become trapped in an unrelaxed state by the development or existence of multipolar internal structure. Nevertheless a suitable coarse graining of the system may restore the predicted distribution functions.

Thermostatistically approaching living systems: Boltzmann Gibbs or nonextensive statistical mechanics?

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2006-03-01

Boltzmann-Gibbs ( BG) statistical mechanics is, since well over one century, successfully used for many nonlinear dynamical systems which, in one way or another, exhibit strong chaos. A typical case is a classical many-body short-range-interacting Hamiltonian system (e.g., the Lennard-Jones model for a real gas at moderately high temperature). Its Lyapunov spectrum (which characterizes the sensitivity to initial conditions) includes positive values. This leads to ergodicity, the stationary state being thermal equilibrium, hence standard applicability of the BG theory is verified. The situation appears to be of a different nature for various phenomena occurring in living organisms. Indeed, such systems exhibit a complexity which does not really accommodate with this standard dynamical behavior. Life appears to emerge and evolve in a kind of delicate situation, at the frontier between large order (low adaptability and long memory; typically characterized by regular dynamics, hence only nonpositive Lyapunov exponents) and large disorder (high adaptability and short memory; typically characterized by strong chaos, hence at least one positive Lyapunov exponent). Along this frontier, the maximal relevant Lyapunov exponents are either zero or close to that, characterizing what is currently referred to as weak chaos. This type of situation is shared by a great variety of similar complex phenomena in economics, linguistics, to cite but a few. BG statistical mechanics is built upon the entropy S=-k∑plnp. A generalization of this form, S=k(1-∑piq)/(q-1) (with S=S), has been proposed in 1988 as a basis for formulating what is nowadays currently called nonextensive statistical mechanics. This theory appears to be particularly adapted for nonlinear dynamical systems exhibiting, precisely, weak chaos. Here, we briefly review the theory, its dynamical foundation, its applications in a variety of disciplines (with special emphasis to living systems), and its connections with the ubiquitous scale-free networks.

Continuum theory of phase separation kinetics for active Brownian particles.

PubMed

Stenhammar, Joakim; Tiribocchi, Adriano; Allen, Rosalind J; Marenduzzo, Davide; Cates, Michael E

2013-10-04

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

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.

Paths to equilibrium in non-conformal collisions

NASA Astrophysics Data System (ADS)

Attems, Maximilian; Bea, Yago; Casalderrey-Solana, Jorge; Mateos, David; Santos-Oliván, Daniel; Sopuerta, Carlos F.; Triana, Miquel; Zilhão, Miguel

2018-03-01

Ever since fast hydrodynamization has been observed in heavy ion collisions the understanding of the hot early out-of-equilibrium stage of such collisions has been a topic of intense research. We use the gauge/gravity duality to model the creation of a strongly coupled Quark-Gluon plasma in a non-conformal gauge theory. This numerical relativity study is the first non-conformal holographic simulation of a heavy ion collision and reveals the existence of new relaxation channels due to the presence of non-vanishing bulk viscosity. We study shock wave collisions at different energies in gauge theories with different degrees of non-conformality and compare three relaxation times which can occur in different orderings: the hydrodynamization time (when hydrodynamics becomes applicable), the EoSization time (when the average pressure approaches its equilibrium value) and the condensate relaxation time (when the expectation value of a scalar operator approaches its equilibrium value). We find that these processes can occur in several different orderings. In particular, the condensate can remain far from equilibrium even long after the plasma has hydrodynamized and EoSized.

Entropy is in Flux V3.4

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2017-05-01

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. Since thermodynamics does not define entropy out of equilibrium, pure thermodynamics cannot follow the details of how this increase occurs. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed kinetic entropy to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann's insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau's theory of the Fermi liquid thereby giving the kinetic entropy within that theory. The dynamics of many condensed matter systems including Fermi liquids, low temperature superfluids, and ordinary metals lend themselves to the definition of kinetic entropy. In fact, entropy has been defined and used for a wide variety of situations in which a condensed matter system has been allowed to relax for a sufficient period so that the very most rapid fluctuations have been ironed out. One of the broadest applications of non-equilibrium analysis considers quantum degenerate systems using Martin-Schwinger Green's functions (Phys Rev 115:1342-1373, 1959) as generalized Wigner functions, g^<({p},ω ,{R},T) and g^>({p},ω ,{R},T). This paper describes once again how the quantum kinetic equations for these functions give locally defined conservation laws for mass momentum and energy. In local thermodynamic equilibrium, this kinetic theory enables a reasonable definition of the density of kinetic entropy. However, when the system is outside of local equilibrium, this definition fails. It is speculated that quantum entanglement is the source of this failure.

Extension of a Kinetic-Theory Approach for Computing Chemical-Reaction Rates to Reactions with Charged Particles

NASA Technical Reports Server (NTRS)

Liechty, Derek S.; Lewis, Mark J.

2010-01-01

Recently introduced molecular-level chemistry models that predict equilibrium and nonequilibrium reaction rates using only kinetic theory and fundamental molecular properties (i.e., no macroscopic reaction rate information) are extended to include reactions involving charged particles and electronic energy levels. The proposed extensions include ionization reactions, exothermic associative ionization reactions, endothermic and exothermic charge exchange reactions, and other exchange reactions involving ionized species. The extensions are shown to agree favorably with the measured Arrhenius rates for near-equilibrium conditions.

Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide

NASA Technical Reports Server (NTRS)

Zahn, J.-P.

1989-01-01

The theory of the equilibrium tide in stars that possess a convective envelope is reexamined critically, taking recent developments into account and treating thermal convection in the most consistent way within the mixing-length approach. The weak points are identified and discussed, in particular, the reduction of the turbulent viscosity when the tidal period becomes shorter than the convective turnover time. An improved version is derived for the secular equations governing the dynamical evolution of close binaries of such type.

Counting relative equilibrium configurations of the full two-body problem

NASA Astrophysics Data System (ADS)

Moeckel, Richard

2018-02-01

Consider a system of two rigid, massive bodies interacting according to their mutual gravitational attraction. In a relative equilibrium motion, the bodies rotate rigidly and uniformly about a fixed axis in R^3. This is possible only for special positions and orientations of the bodies. After fixing the angular momentum, these relative equilibrium configurations can be characterized as critical points of a smooth function on configuration space. The goal of this paper is to use Morse theory and Lusternik-Schnirelmann category theory to give lower bounds for the number of critical points when the angular momentum is sufficiently large. In addition, the exact number of critical points and their Morse indices are found in the limit as the angular momentum tends to infinity.

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.

Children's Working Theories: Invoking Disequilibrium

ERIC Educational Resources Information Center

Lovatt, Daniel; Hedges, Helen

2015-01-01

One of the outcomes of the New Zealand early childhood curriculum, "Te Whariki", is "working theories". Prior research on this concept has primarily utilised sociocultural theoretical underpinnings and neglected Piagetian constructivist theories. This paper explores ways the Piagetian concepts of equilibrium and disequilibrium…

Spectacular phenomena and limits to rationality in genetic and cultural evolution.

PubMed Central

Enquist, Magnus; Arak, Anthony; Ghirlanda, Stefano; Wachtmeister, Carl-Adam

2002-01-01

In studies of both animal and human behaviour, game theory is used as a tool for understanding strategies that appear in interactions between individuals. Game theory focuses on adaptive behaviour, which can be attained only at evolutionary equilibrium. We suggest that behaviour appearing during interactions is often outside the scope of such analysis. In many types of interaction, conflicts of interest exist between players, fuelling the evolution of manipulative strategies. Such strategies evolve out of equilibrium, commonly appearing as spectacular morphology or behaviour with obscure meaning, to which other players may react in non-adaptive, irrational ways. We present a simple model to show some limitations of the game-theory approach, and outline the conditions in which evolutionary equilibria cannot be maintained. Evidence from studies of biological interactions seems to support the view that behaviour is often not at equilibrium. This also appears to be the case for many human cultural traits, which have spread rapidly despite the fact that they have a negative influence on reproduction. PMID:12495515

Spectacular phenomena and limits to rationality in genetic and cultural evolution.

PubMed

Enquist, Magnus; Arak, Anthony; Ghirlanda, Stefano; Wachtmeister, Carl-Adam

2002-11-29

In studies of both animal and human behaviour, game theory is used as a tool for understanding strategies that appear in interactions between individuals. Game theory focuses on adaptive behaviour, which can be attained only at evolutionary equilibrium. We suggest that behaviour appearing during interactions is often outside the scope of such analysis. In many types of interaction, conflicts of interest exist between players, fuelling the evolution of manipulative strategies. Such strategies evolve out of equilibrium, commonly appearing as spectacular morphology or behaviour with obscure meaning, to which other players may react in non-adaptive, irrational ways. We present a simple model to show some limitations of the game-theory approach, and outline the conditions in which evolutionary equilibria cannot be maintained. Evidence from studies of biological interactions seems to support the view that behaviour is often not at equilibrium. This also appears to be the case for many human cultural traits, which have spread rapidly despite the fact that they have a negative influence on reproduction.

Cooperativity in self-limiting equilibrium self-associating systems

NASA Astrophysics Data System (ADS)

Freed, Karl F.

2012-11-01

A wide variety of highly cooperative self-assembly processes in biological and synthetic systems involve the assembly of a large number (m) of units into clusters, with m narrowly peaked about a large size m0 ≫ 1 and with a second peak centered about the m = 1 unassembled monomers. While very specific models have been proposed for the assembly of, for example, viral capsids and core-shell micelles of ß-casein, no available theory describes a thermodynamically general mechanism for this double peaked, highly cooperative equilibrium assembly process. This study provides a general mechanism for these cooperative processes by developing a minimal Flory-Huggins type theory. Beginning from the simplest non-cooperative, free association model in which the equilibrium constant for addition of a monomer to a cluster is independent of cluster size, the new model merely allows more favorable growth for clusters of intermediate sizes. The theory is illustrated by computing the phase diagram for cases of self-assembly on cooling or heating and for the mass distribution of the two phases.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

Habitat islands and the equilibrium theory of island biogeography: testing some predictions

USGS Publications Warehouse

Brown, M.; Dinsmore, J.J.

1988-01-01

Species-area data from a study of marsh birds are used to test five predictions generated by the equilibrium theory of island biogeography. Three predictions are supported: we found a significant species-area relationship, a non-zero level of turnover, and a variance-mean ratio of 0.5. One prediction is rejected: the extinction rates were not greater on small islands. The results of one test are equivocal: the number of species on each island was not always the same. As Gilbert (1980) suggests, a strong species-area relationship alone does not validate the theory. The avian communities we studied were on habitat islands, not true islands, and underwent complete extinction annually. Thus caution must be used before applying the theory to these and other habitat islands.

Evolutionary games on graphs

NASA Astrophysics Data System (ADS)

Szabó, György; Fáth, Gábor

2007-07-01

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

Specificity Switching Pathways in Thermal and Mass Evaporation of Multicomponent Hydrocarbon Droplets: A Mesoscopic Observation.

PubMed

Nasiri, Rasoul; Luo, Kai H

2017-07-10

For well over one century, the Hertz-Knudsen equation has established the relationship between thermal - mass transfer coefficients through a liquid - vapour interface and evaporation rate. These coefficients, however, have been often separately estimated for one-component equilibrium systems and their simultaneous influences on evaporation rate of fuel droplets in multicomponent systems have yet to be investigated at the atomic level. Here we first apply atomistic simulation techniques and quantum/statistical mechanics methods to understand how thermal and mass evaporation effects are controlled kinetically/thermodynamically. We then present a new development of a hybrid method of quantum transition state theory/improved kinetic gas theory, for multicomponent hydrocarbon systems to investigate how concerted-distinct conformational changes of hydrocarbons at the interface affect the evaporation rate. The results of this work provide an important physical concept in fundamental understanding of atomistic pathways in topological interface transitions of chain molecules, resolving an open problem in kinetics of fuel droplets evaporation.

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

Statistical mechanics of light elements at high pressure. VI - Liquid-state calculations with Thomas-Fermi-Dirac theory

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.

1984-01-01

A model free energy is developed for hydrogen-helium mixtures based on solid-state Thomas-Fermi-Dirac calculations at pressures relevant to the interiors of giant planets. Using a model potential similar to that for a two-component plasma, effective charges for the nuclei (which are in general smaller than the actual charges because of screening effects) are parameterized, being constrained by calculations at a number of densities, compositions, and lattice structures. These model potentials are then used to compute the equilibrium properties of H-He fluids using a charged hard-sphere model. The results find critical temperatures of about 0 K, 500 K, and 1500 K, for pressures of 10, 100, and 1000 Mbar, respectively. These phase separation temperatures are considerably lower (approximately 6,000-10,000 K) than those found from calculations using free electron perturbation theory, and suggest that H-He solutions should be stable against phase separation in the metallic zones of Jupiter and Saturn.

Quantum and Ecosystem Entropies

NASA Astrophysics Data System (ADS)

Kirwan, A. D.

2008-06-01

Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than Planck’s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.

Truly work-like work extraction via a single-shot analysis.

PubMed

Aberg, Johan

2013-01-01

The work content of non-equilibrium systems in relation to a heat bath is often analysed in terms of expectation values of an underlying random work variable. However, when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se, in which case the extracted energy is unpredictable, thus intuitively more heat-like than work-like. This raises the question of the 'truly' work-like energy that can be extracted. Here we consider an alternative that corresponds to an essentially fluctuation-free extraction. We show that this quantity can be expressed in terms of a one-shot relative entropy measure introduced in information theory. This suggests that the relations between information theory and statistical mechanics, as illustrated by concepts like Maxwell's demon, Szilard engines and Landauer's principle, extends to the single-shot regime.

Step-wise pulling protocols for non-equilibrium dynamics

NASA Astrophysics Data System (ADS)

Ngo, Van Anh

The fundamental laws of thermodynamics and statistical mechanics, and the deeper understandings of quantum mechanics have been rebuilt in recent years. It is partly because of the increasing power of computing resources nowadays, that allow shedding direct insights into the connections among the thermodynamics laws, statistical nature of our world, and the concepts of quantum mechanics, which have not yet been understood. But mostly, the most important reason, also the ultimate goal, is to understand the mechanisms, statistics and dynamics of biological systems, whose prevailing non-equilibrium processes violate the fundamental laws of thermodynamics, deviate from statistical mechanics, and finally complicate quantum effects. I believe that investigations of the fundamental laws of non-equilibrium dynamics will be a frontier research for at least several more decades. One of the fundamental laws was first discovered in 1997 by Jarzynski, so-called Jarzynski's Equality. Since then, different proofs, alternative descriptions of Jarzynski's Equality, and its further developments and applications have been quickly accumulated. My understandings, developments and applications of an alternative theory on Jarzynski's Equality form the bulk of this dissertation. The core of my theory is based on stepwise pulling protocols, which provide deeper insight into how fluctuations of reaction coordinates contribute to free-energy changes along a reaction pathway. We find that the most optimal pathways, having the largest contribution to free-energy changes, follow the principle of detailed balance. This is a glimpse of why the principle of detailed balance appears so powerful for sampling the most probable statistics of events. In a further development on Jarzynski's Equality, I have been trying to use it in the formalism of diagonal entropy to propose a way to extract useful thermodynamic quantities such temperature, work and free-energy profiles from far-from-equilibrium ensembles, which can be used to characterize non-equilibrium dynamics. Furthermore, we have applied the stepwise pulling protocols and Jarzynski's Equality to investigate the ion selectivity of potassium channels via molecular dynamics simulations. The mechanism of the potassium ion selectivity has remained poorly understood for over fifty years, although a Nobel Prize was awarded to the discovery of the molecular structure of a potassium-selective channel in 2003. In one year of performing simulations, we were able to reproduce the major results of ion selectivity accumulated in fifty years. We have been even boldly going further to propose a new model for ion selectivity based on the structural rearrangement of the selectivity filter of potassium-selective KcsA channels. This structural rearrangement has never been shown to play such a pivotal role in selecting and conducting potassium ions, but effectively rejecting sodium ions. Using the stepwise pulling protocols, we are also able to estimate conductance for ion channels, which remains elusive by using other methods. In the light of ion channels, we have also investigated how a synthetic channel of telemeric G-quadruplex conducts different types of ions. These two studies on ion selectivity not only constitute an interesting part of this dissertation, but also will enable us to further explore a new set of ion-selectivity principles. Beside the focus of my dissertation, I used million-atom molecular dynamics simulations to investigate the mechanical properties of body-centered-cubic (BCCS) and face-centered-cubic (FCCS) supercrystals of DNA-functionalized gold nanoparticles. These properties are valuable for examining whether these supercrystals can be used in gene delivery and gene therapy. The formation of such ordered supercrystals is useful to protect DNAs or RNAs from being attacked and destroyed by enzymes in cells. I also performed all-atom molecular dynamics simulations to study a pure oleic acid (OA) membrane in water that results into a triple-layer structure. The simulations show that the trans-membrane movement of water and OAs is cooperative and correlated, and agrees with experimentally measured absorption rates. The simulation results support the idea that OA flip-flop is more favorable than transport by means of functional proteins. This study might provide further insight into how primitive cell membranes work, and how the interplay and correlation between water and fatty acids may occur.

Finite temperature grand canonical ensemble study of the minimum electrophilicity principle.

PubMed

Miranda-Quintana, Ramón Alain; Chattaraj, Pratim K; Ayers, Paul W

2017-09-28

We analyze the minimum electrophilicity principle of conceptual density functional theory using the framework of the finite temperature grand canonical ensemble. We provide support for this principle, both for the cases of systems evolving from a non-equilibrium to an equilibrium state and for the change from one equilibrium state to another. In doing so, we clearly delineate the cases where this principle can, or cannot, be used.

Finite-deformation phase-field chemomechanics for multiphase, multicomponent solids

NASA Astrophysics Data System (ADS)

Svendsen, Bob; Shanthraj, Pratheek; Raabe, Dierk

2018-03-01

The purpose of this work is the development of a framework for the formulation of geometrically non-linear inelastic chemomechanical models for a mixture of multiple chemical components diffusing among multiple transforming solid phases. The focus here is on general model formulation. No specific model or application is pursued in this work. To this end, basic balance and constitutive relations from non-equilibrium thermodynamics and continuum mixture theory are combined with a phase-field-based description of multicomponent solid phases and their interfaces. Solid phase modeling is based in particular on a chemomechanical free energy and stress relaxation via the evolution of phase-specific concentration fields, order-parameter fields (e.g., related to chemical ordering, structural ordering, or defects), and local internal variables. At the mixture level, differences or contrasts in phase composition and phase local deformation in phase interface regions are treated as mixture internal variables. In this context, various phase interface models are considered. In the equilibrium limit, phase contrasts in composition and local deformation in the phase interface region are determined via bulk energy minimization. On the chemical side, the equilibrium limit of the current model formulation reduces to a multicomponent, multiphase, generalization of existing two-phase binary alloy interface equilibrium conditions (e.g., KKS). On the mechanical side, the equilibrium limit of one interface model considered represents a multiphase generalization of Reuss-Sachs conditions from mechanical homogenization theory. Analogously, other interface models considered represent generalizations of interface equilibrium conditions consistent with laminate and sharp-interface theory. In the last part of the work, selected existing models are formulated within the current framework as special cases and discussed in detail.

An equilibrium method for prediction of transverse shear stresses in a thick laminated plate

NASA Technical Reports Server (NTRS)

Chaudhuri, R. Z.

1986-01-01

First two equations of equilibrium are utilized to compute the transverse shear stress variation through thickness of a thick laminated plate after in-plane stresses have been computed using an assumed quadratic displacement triangular element based on transverse inextensibility and layerwise constant shear angle theory (LCST). Centroid of the triangle is the point of exceptional accuracy for transverse shear stresses. Numerical results indicate close agreement with elasticity theory. An interesting comparison between the present theory and that based on assumed stress hybrid finite element approach suggests that the latter does not satisfy the condition of free normal traction at the edge. Comparison with numerical results obtained by using constant shear angle theory suggests that LCST is close to the elasticity solution while the CST is closer to classical (CLT) solution. It is also demonstrated that the reduced integration gives faster convergence when the present theory is applied to a thin plate.

Computing Models of M-type Host Stars and their Panchromatic Spectral Output

NASA Astrophysics Data System (ADS)

Linsky, Jeffrey; Tilipman, Dennis; France, Kevin

2018-06-01

We have begun a program of computing state-of-the-art model atmospheres from the photospheres to the coronae of M stars that are the host stars of known exoplanets. For each model we are computing the emergent radiation at all wavelengths that are critical for assessingphotochemistry and mass-loss from exoplanet atmospheres. In particular, we are computing the stellar extreme ultraviolet radiation that drives hydrodynamic mass loss from exoplanet atmospheres and is essential for determing whether an exoplanet is habitable. The model atmospheres are computed with the SSRPM radiative transfer/statistical equilibrium code developed by Dr. Juan Fontenla. The code solves for the non-LTE statistical equilibrium populations of 18,538 levels of 52 atomic and ion species and computes the radiation from all species (435,986 spectral lines) and about 20,000,000 spectral lines of 20 diatomic species.The first model computed in this program was for the modestly active M1.5 V star GJ 832 by Fontenla et al. (ApJ 830, 152 (2016)). We will report on a preliminary model for the more active M5 V star GJ 876 and compare this model and its emergent spectrum with GJ 832. In the future, we will compute and intercompare semi-empirical models and spectra for all of the stars observed with the HST MUSCLES Treasury Survey, the Mega-MUSCLES Treasury Survey, and additional stars including Proxima Cen and Trappist-1.This multiyear theory program is supported by a grant from the Space Telescope Science Institute.

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.

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.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators.

PubMed

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H-S; Ahn, Jaewook

2018-05-04

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

NASA Astrophysics Data System (ADS)

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H.-S.; Ahn, Jaewook

2018-05-01

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Critical parameters of hard-core Yukawa fluids within the structural theory

NASA Astrophysics Data System (ADS)

Bahaa Khedr, M.; Osman, S. M.

2012-10-01

A purely statistical mechanical approach is proposed to account for the liquid-vapor critical point based on the mean density approximation (MDA) of the direct correlation function. The application to hard-core Yukawa (HCY) fluids facilitates the use of the series mean spherical approximation (SMSA). The location of the critical parameters for HCY fluid with variable intermolecular range is accurately calculated. Good agreement is observed with computer simulation results and with the inverse temperature expansion (ITE) predictions. The influence of the potential range on the critical parameters is demonstrated and the universality of the critical compressibility ratio is discussed. The behavior of the isochoric and isobaric heat capacities along the equilibrium line and the near vicinity of the critical point is discussed in details.

Making baryons dark: the quantum prediction of the variation of photon-particle scattering cross section with the approach to equilibrium in deep gravity wells

NASA Astrophysics Data System (ADS)

Ernest, Alllan David; Collins, Matthew P.

2015-08-01

Analysis of astrophysical phenomena relies on knowledge of cross sections. These cross sections are measured in scattering experiments, or calculated using theoretical techniques such as partial wave analysis. It has been recently shown [1,2,3] however that photon scattering cross sections depend also on the degree of localization of the target particle, and that particles in large-scale, deep-gravity wells can exhibit lower cross sections than those measured in lab-based experiments where particles are implicitly localized. This purely quantum effect arises as a consequence of differences in the gravitational eigenspectral distribution of a particle’s wavefunction in different situations, and is in addition to the obvious notion that delocalized particle scattering is less likely simply because the target particles are ‘in a bigger box’.In this presentation we consider the quantum equilibrium statistics of particles in gravitational potentials corresponding to dark matter density profiles. We show that as galactic halos approach equilibrium, the dark eigenstates of the eigenspectral ensemble are favoured and baryons exhibit lower photon scattering cross sections, rendering halos less visible than expected from currently accepted cross sections. Traditional quantum theory thus predicts that baryons that have not coalesced into self-bound macroscopic structures such as stars, can essentially behave as dark matter simply by equilibrating within a deep gravity well. We will discuss this effect and the consequences for microwave anisotropy analysis and primordial nucleosynthesis.[1] Ernest, A. D., and Collins, M. P., 2014, Australian Institute of Physics, AIP Congress, Canberra, December, 2014.[2] Ernest, A. D., 2009, J. Phys. A: Math. Theor., 42, 115207, 115208.[3] Ernest, A. D., 2012, In Prof. Ion Cotaescu (Ed) Advances in Quantum Theory (pp 221-248). Rijeka: InTech. ISBN 978-953-51-0087-4

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.

Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy

NASA Astrophysics Data System (ADS)

Ausloos, M.

2000-09-01

Recent observations have indicated that the traditional equilibrium market hypothesis (EMH; also known as Efficient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-field approximations like a Gaussian distribution of price fluctuations. A kinetic theory for prices can be simply derived, considering in a first approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium (isothermal) equation for the price (taken as the order parameter) of a stock as a function of the volume of money available are obtained.

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.

PubMed

Kleidon, Axel

2010-01-13

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society

Long-range correlations, geometrical structure, and transport properties of macromolecular solutions. The equivalence of configurational statistics and geometrodynamics of large molecules.

PubMed

Mezzasalma, Stefano A

2007-12-04

A special theory of Brownian relativity was previously proposed to describe the universal picture arising in ideal polymer solutions. In brief, it redefines a Gaussian macromolecule in a 4-dimensional diffusive spacetime, establishing a (weak) Lorentz-Poincaré invariance between liquid and polymer Einstein's laws for Brownian movement. Here, aimed at inquiring into the effect of correlations, we deepen the extension of the special theory to a general formulation. The previous statistical equivalence, for dynamic trajectories of liquid molecules and static configurations of macromolecules, and rather obvious in uncorrelated systems, is enlarged by a more general principle of equivalence, for configurational statistics and geometrodynamics. Accordingly, the three geodesic motion, continuity, and field equations could be rewritten, and a number of scaling behaviors were recovered in a spacetime endowed with general static isotropic metric (i.e., for equilibrium polymer solutions). We also dealt with universality in the volume fraction and, unexpectedly, found that a hyperscaling relation of the form, (average size) x (diffusivity) x (viscosity)1/2 ~f(N0, phi0) is fulfilled in several regimes, both in the chain monomer number (N) and polymer volume fraction (phi). Entangled macromolecular dynamics was treated as a geodesic light deflection, entaglements acting in close analogy to the field generated by a spherically symmetric mass source, where length fluctuations of the chain primitive path behave as azimuth fluctuations of its shape. Finally, the general transformation rule for translational and diffusive frames gives a coordinate gauge invariance, suggesting a widened Lorentz-Poincaré symmetry for Brownian statistics. We expect this approach to find effective applications to solutions of arbitrarily large molecules displaying a variety of structures, where the effect of geometry is more explicit and significant in itself (e.g., surfactants, lipids, proteins).

Progress in understanding heavy-ion stopping

NASA Astrophysics Data System (ADS)

Sigmund, P.; Schinner, A.

2016-09-01

We report some highlights of our work with heavy-ion stopping in the energy range where Bethe stopping theory breaks down. Main tools are our binary stopping theory (PASS code), the reciprocity principle, and Paul's data base. Comparisons are made between PASS and three alternative theoretical schemes (CasP, HISTOP and SLPA). In addition to equilibrium stopping we discuss frozen-charge stopping, deviations from linear velocity dependence below the Bragg peak, application of the reciprocity principle in low-velocity stopping, modeling of equilibrium charges, and the significance of the so-called effective charge.

Equilibrium paths analysis of materials with rheological properties by using the chaos theory

NASA Astrophysics Data System (ADS)

Bednarek, Paweł; Rządkowski, Jan

2018-01-01

The numerical equilibrium path analysis of the material with random rheological properties by using standard procedures and specialist computer programs was not successful. The proper solution for the analysed heuristic model of the material was obtained on the base of chaos theory elements and neural networks. The paper deals with mathematical reasons of used computer programs and also are elaborated the properties of the attractor used in analysis. There are presented results of conducted numerical analysis both in a numerical and in graphical form for the used procedures.

Stock markets as Minority Games: cognitive heterogeneity and equilibrium emergence

NASA Astrophysics Data System (ADS)

Brandouy, O.

2005-04-01

Standard finance theory generally assumes homogeneous agents relatively to their preferences, heuristics and investment strategies. We propose to study, in an agent-based simulation, the emergence of equilibrium under various heterogeneous conditions. Market interaction is stylized with the Minority Game representation. It is shown that inductive rational equilibrium emerges even though agents do not share the same representations of the value. This may lead to consider again the roots of EMH and REH.

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.

Equilibrium fluctuation relations for voltage coupling in membrane proteins.

PubMed

Kim, Ilsoo; Warshel, Arieh

2015-11-01

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 "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done 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 response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a 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. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments. Copyright © 2015 Elsevier B.V. All rights reserved.

Examination of the gamma equilibrium point hypothesis when applied to single degree of freedom movements performed with different inertial loads.

PubMed

Bellomo, A; Inbar, G

1997-01-01

One of the theories of human motor control is the gamma Equilibrium Point Hypothesis. It is an attractive theory since it offers an easy control scheme where the planned trajectory shifts monotionically from an initial to a final equilibrium state. The feasibility of this model was tested by reconstructing the virtual trajectory and the stiffness profiles for movements performed with different inertial loads and examining them. Three types of movements were tested: passive movements, targeted movements, and repetitive movements. Each of the movements was performed with five different inertial loads. Plausible virtual trajectories and stiffness profiles were reconstructed based on the gamma Equilibrium Point Hypothesis for the three different types of movements performed with different inertial loads. However, the simple control strategy supported by the model, where the planned trajectory shifts monotonically from an initial to a final equilibrium state, could not be supported for targeted movements performed with added inertial load. To test the feasibility of the model further we must examine the probability that the human motor control system would choose a trajectory more complicated than the actual trajectory to control.

Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

Application of Equilibrium Partitioning Theory to Soil PAH Contamination (External Review Draft)

EPA Science Inventory

In March 2004, ORD's Ecological Risk Assessment Support Center (ERASC) received a request from the Ecological Risk Assessment Forum (ERAF) to provide insight into the issue of whether equilibrium partitioning (EqP) techniques can be used to predict the toxicity of polycyclic arom...

Problem Solving and Chemical Equilibrium: Successful versus Unsuccessful Performance.

ERIC Educational Resources Information Center

Camacho, Moises; Good, Ron

1989-01-01

Describes the problem-solving behaviors of experts and novices engaged in solving seven chemical equilibrium problems. Lists 27 behavioral tendencies of successful and unsuccessful problem solvers. Discusses several implications for a problem solving theory, think-aloud techniques, adequacy of the chemistry domain, and chemistry instruction.…

Equilibrium statistical-thermal models in high-energy physics

NASA Astrophysics Data System (ADS)

Tawfik, Abdel Nasser

2014-05-01

We review some recent highlights from the applications of statistical-thermal models to different experimental measurements and lattice QCD thermodynamics that have been made during the last decade. We start with a short review of the historical milestones on the path of constructing statistical-thermal models for heavy-ion physics. We discovered that Heinz Koppe formulated in 1948, an almost complete recipe for the statistical-thermal models. In 1950, Enrico Fermi generalized this statistical approach, in which he started with a general cross-section formula and inserted into it, the simplifying assumptions about the matrix element of the interaction process that likely reflects many features of the high-energy reactions dominated by density in the phase space of final states. In 1964, Hagedorn systematically analyzed the high-energy phenomena using all tools of statistical physics and introduced the concept of limiting temperature based on the statistical bootstrap model. It turns to be quite often that many-particle systems can be studied with the help of statistical-thermal methods. The analysis of yield multiplicities in high-energy collisions gives an overwhelming evidence for the chemical equilibrium in the final state. The strange particles might be an exception, as they are suppressed at lower beam energies. However, their relative yields fulfill statistical equilibrium, as well. We review the equilibrium statistical-thermal models for particle production, fluctuations and collective flow in heavy-ion experiments. We also review their reproduction of the lattice QCD thermodynamics at vanishing and finite chemical potential. During the last decade, five conditions have been suggested to describe the universal behavior of the chemical freeze-out parameters. The higher order moments of multiplicity have been discussed. They offer deep insights about particle production and to critical fluctuations. Therefore, we use them to describe the freeze-out parameters and suggest the location of the QCD critical endpoint. Various extensions have been proposed in order to take into consideration the possible deviations of the ideal hadron gas. We highlight various types of interactions, dissipative properties and location-dependences (spatial rapidity). Furthermore, we review three models combining hadronic with partonic phases; quasi-particle model, linear sigma model with Polyakov potentials and compressible bag model.

Quantum Sensors for the Generating Functional of Interacting Quantum Field Theories

NASA Astrophysics Data System (ADS)

Bermudez, A.; Aarts, G.; Müller, M.

2017-10-01

Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in- or out-of-equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories.

Relaxation of vacuum energy in q-theory

NASA Astrophysics Data System (ADS)

Klinkhamer, F. R.; Savelainen, M.; Volovik, G. E.

2017-08-01

The q-theory formalism aims to describe the thermodynamics and dynamics of the deep quantum vacuum. The thermodynamics leads to an exact cancellation of the quantum-field zero-point-energies in equilibrium, which partly solves the main cosmological constant problem. But, with reversible dynamics, the spatially flat Friedmann-Robertson-Walker universe asymptotically approaches the Minkowski vacuum only if the Big Bang already started out in an initial equilibrium state. Here, we extend q-theory by introducing dissipation from irreversible processes. Neglecting the possible instability of a de-Sitter vacuum, we obtain different scenarios with either a de-Sitter asymptote or collapse to a final singularity. The Minkowski asymptote still requires fine-tuning of the initial conditions. This suggests that, within the q-theory approach, the decay of the de-Sitter vacuum is a necessary condition for the dynamical solution of the cosmological constant problem.

Testing Neoclassical Competitive Theory in Multilateral Decentralized Markets

ERIC Educational Resources Information Center

List, John A.

2004-01-01

Walrasian tatonnement has been a fundamental assumption in economics ever since Walras' general equilibrium theory was introduced in 1874. Nearly a century after its introduction, Vernon Smith relaxed the Walrasian tatonnement assumption by showing that neoclassical competitive market theory explains the equilibrating forces in "double-auction"…

Future disability projections could be improved by connecting to the theory of a dynamic equilibrium.

PubMed

Klijs, Bart; Mackenbach, Johan P; Kunst, Anton E

2011-04-01

Projections of future trends in the burden of disability could be guided by models linking disability to life expectancy, such as the dynamic equilibrium theory. This article tests the key assumption of this theory that severe disability is associated with proximity to death, whereas mild disability is not. Using data from the GLOBE study (Gezondheid en Levensomstandigheden Bevolking Eindhoven en omstreken), the association of three levels of self-reported disabilities in activities of daily living with age and proximity to death was studied using logistic regression models. Regression estimates were used to estimate the number of life years with disability for life spans of 75 and 85 years. Odds ratios of 0.976 (not significant) for mild disability, 1.137 for moderate disability, and 1.231 for severe disability showed a stronger effect of proximity to death for more severe levels of disability. A 10-year increase of life span was estimated to result in a substantial expansion of mild disability (4.6 years) compared with a small expansion of moderate (0.7 years) and severe (0.9 years) disability. These findings support the theory of a dynamic equilibrium. Projections of the future burden of disability could be substantially improved by connecting to this theory and incorporating information on proximity to death. Copyright © 2011 Elsevier Inc. All rights reserved.

Adaptive, Distributed Control of Constrained Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Bieniawski, Stefan; Wolpert, David H.

2004-01-01

Product Distribution (PO) theory was recently developed as a broad framework for analyzing and optimizing distributed systems. Here we demonstrate its use for adaptive distributed control of Multi-Agent Systems (MASS), i.e., for distributed stochastic optimization using MAS s. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (Probability dist&&on on the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. One common way to find that equilibrium is to have each agent run a Reinforcement Learning (E) algorithm. PD theory reveals this to be a particular type of search algorithm for minimizing the Lagrangian. Typically that algorithm i s quite inefficient. A more principled alternative is to use a variant of Newton's method to minimize the Lagrangian. Here we compare this alternative to RL-based search in three sets of computer experiments. These are the N Queen s problem and bin-packing problem from the optimization literature, and the Bar problem from the distributed RL literature. Our results confirm that the PD-theory-based approach outperforms the RL-based scheme in all three domains.

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.

A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums

NASA Astrophysics Data System (ADS)

Dantsev, Danylo

In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.

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.

Hawking radiation and nonequilibrium quantum critical current noise.

PubMed

Sonner, Julian; Green, A G

2012-08-31

The dynamical scaling of quantum critical systems in thermal equilibrium may be inherited in the driven steady state, leading to universal out-of-equilibrium behavior. This attractive notion has been demonstrated in just a few cases. We demonstrate how holography-a mapping between the quantum critical system and a gravity dual-provides an illuminating perspective and new results. Nontrivial out-of-equilibrium universality is particularly apparent in current noise, which is dual to Hawking radiation in the gravitational system. We calculate this in a two-dimensional system driven by a strong in-plane electric field and deduce a universal scaling function interpolating between previously established equilibrium and far-from-equilibrium current noise. Since this applies at all fields, out-of-equilibrium experiments no longer require very high fields for comparison with theory.

Stochastic game theory: for playing games, not just for doing theory.

PubMed

Goeree, J K; Holt, C A

1999-09-14

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Evolution and Punctuation of Theories of Educational Expenditure and Student Outcomes.

ERIC Educational Resources Information Center

Marion, Russ; Flanigan, Jack

2001-01-01

Examines whether school-expenditure theory can be described in terms of Thomas Kuhn's punctuated-equilibrium model: long periods of theoretical stasis interspersed with brief periods of revolutionary change. Current researchers, influenced by organizational behavior theories, believe that finding a global money/student outcome relationship is an…

Kinetic theory of two-temperature polyatomic plasmas

NASA Astrophysics Data System (ADS)

Orlac'h, Jean-Maxime; Giovangigli, Vincent; Novikova, Tatiana; Roca i Cabarrocas, Pere

2018-03-01

We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

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.

An experimental and theoretical method for determination of standard electrode potential for the redox couple diphenyl sulfone/diphenyl sulfide

NASA Astrophysics Data System (ADS)

Song, Y. Z.; Wei, K. X.; Lv, J. S.

2013-12-01

DFT calculations were performed for diphenyl sulfide and diphenyl sulfone. The electrochemistry of diphenyl sulfide on the gold electrode was investigated by cyclic voltammety and the results show that standard electrode potential for redox couple diphenyl sulfone/diphenyl sulfide is 1.058 V, which is consistent with that of 1.057 calculated at B3LYP/6-31++G( d, p)-IEFPCM level. The front orbit theory and Mulliken charges of molecular explain well on the oxidation of diphenyl sulfide in oxidative desulfurization. According to equilibrium theory the experimental equilibrium constant in the oxidative desulfurization of H2O2, is 1.17 × 1048, which is consistent with the theoretical equilibrium constant is 2.18 × 1048 at B3LYP/6-31++G( d, p)-IEFPCM level.

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids.

PubMed

Kowalczyk, Piotr; MacElroy, J M D

2006-08-03

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.

Instability of quantum equilibrium in Bohm's dynamics

PubMed Central

Colin, Samuel; Valentini, Antony

2014-01-01

We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for ‘extended’ non-equilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended non-equilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis, we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics, there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation. PMID:25383020

Folding thermodynamics of pseudoknotted chain conformations

PubMed Central

Kopeikin, Zoia; Chen, Shi-Jie

2008-01-01

We develop a statistical mechanical framework for the folding thermodynamics of pseudoknotted structures. As applications of the theory, we investigate the folding stability and the free energy landscapes for both the thermal and the mechanical unfolding of pseudoknotted chains. For the mechanical unfolding process, we predict the force-extension curves, from which we can obtain the information about structural transitions in the unfolding process. In general, a pseudoknotted structure unfolds through multiple structural transitions. The interplay between the helix stems and the loops plays an important role in the folding stability of pseudoknots. For instance, variations in loop sizes can lead to the destabilization of some intermediate states and change the (equilibrium) folding pathways (e.g., two helix stems unfold either cooperatively or sequentially). In both thermal and mechanical unfolding, depending on the nucleotide sequence, misfolded intermediate states can emerge in the folding process. In addition, thermal and mechanical unfoldings often have different (equilibrium) pathways. For example, for certain sequences, the misfolded intermediates, which generally have longer tails, can fold, unfold, and refold again in the pulling process, which means that these intermediates can switch between two different average end-end extensions. PMID:16674261

Dynamics of an optically confined nanoparticle diffusing normal to a surface.

PubMed

Schein, Perry; O'Dell, Dakota; Erickson, David

2016-06-01

Here we measure the hindered diffusion of an optically confined nanoparticle in the direction normal to a surface, and we use this to determine the particle-surface interaction profile in terms of the absolute height. These studies are performed using the evanescent field of an optically excited single-mode silicon nitride waveguide, where the particle is confined in a height-dependent potential energy well generated from the balance of optical gradient and surface forces. Using a high-speed cmos camera, we demonstrate the ability to capture the short time-scale diffusion dominated motion for 800-nm-diam polystyrene particles, with measurement times of only a few seconds per particle. Using established theory, we show how this information can be used to estimate the equilibrium separation of the particle from the surface. As this measurement can be made simultaneously with equilibrium statistical mechanical measurements of the particle-surface interaction energy landscape, we demonstrate the ability to determine these in terms of the absolute rather than relative separation height. This enables the comparison of potential energy landscapes of particle-surface interactions measured under different experimental conditions, enhancing the utility of this technique.

Computerized optimization of radioimmunoassays for hCG and estradiol: an experimental evaluation

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

Yanagishita, M.; Rodbard, D.

1978-07-15

The mathematical and statistical theory of radioimmunoassays (RIAs) has been used to develop a series of computer programs to optimize sensitivity or precision at any desired dose level for either equilibrium or nonequilibrium assays. These computer programs provide for the calculation of the equilibrium constants of association and binding capacities for antisera (parameters of Scatchard plots), the association and dissociation rate constants, and prediction of optimum concentration of labeled ligand and antibody and optimum incubation times for the assay. This paper presents an experimental evaluation of the use of these computer programs applied to RIAs for human chorionic gonadotropin (hCG)more » and estradiol. The experimental results are in reasonable semiquantitative agreement with the predictions of the computer simulations (usually within a factor of two) and thus partially validate the use of computer techniques to optimize RIAs that are reasonably well behaved, as in the case of the hCG and estradiol RIAs. Further, these programs can provide insights into the nature of the RIA system, e.g., the general nature of the sensitivity and precision surfaces. This facilitates empirical optimization of conditions.« less

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.

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

NASA Astrophysics Data System (ADS)

Wang, Wan-Yong; Pei, Li-Jun

2011-04-01

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluctuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratio-dependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.

Equilibrium E × B Flows in Nonlinear Gyrofluid Flux-Tube Simulations

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

2000-10-01

Comparisons of theory with experiment often indicate levels of sheared E × B flow large enough to significantly suppress turbulence, especially when local transport barriers are formed. We extend our previous simulations by including equilibrium scale sheared E × B flow directly, by introducing a coordinate transformation which shears the simulation domain with the equilibrium E × B flow, while preserving smooth statistical periodicity across the radial domain. This method was used linearly in our previous comparisons with JET [Beer, Budny, Challis, et al., EPS (1999)] and is now applied to nonlinear simulations. This method makes use of some tricks suggested for this problem by Dimits [Int. Conf. on Numerical Simulation of Plasmas (1994)] based on special properties of discrete Fourier transforms. A similar coordinate transformation was previously used successfully by Waltz, et al. [Phys. Plasmas 5, 1784 (1998)], and we confirm their finding that the turbulence is suppressed when the shearing rate, ω_E, is comparable to the maximum linear growth rate in the absence of sheared flow, γ_lin. This is often significantly different than the threshold for linear suppression. With this extension, our simulations are able to address transport barriers from a more rigorous footing. Of particular interest will be the investigation of the expansion or propagation of barriers, where E × B shear suppression is by definition at the marginal point. In addition, our formulation uses general magnetic geometry, so we can rigorously investigate various geometrical effects (e.g. hats, Δ', κ) on the threshold for suppression.

The deconfining phase transition in and out of equilibrium

NASA Astrophysics Data System (ADS)

Bazavov, Oleksiy

Recent experiments carried out at the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory provide strong evidence that a matter can be driven from a confined, low-temperature phase, observed in our every day world into a deconfined high-temperature phase of liberated quarks and gluons. The equilibrium and dynamical properties of the deconfining phase transition are thus of great theoretical interest, since they also provide an information about the first femtoseconds of the evolution of our Universe, when the hot primordial soup while cooling has undergone a chain of phase transitions. The aspects of the deconfining phase transition studied in this work include: the dynamics of the SU(3) gauge theory after the heating quench (which models rapid heating in the heavy-ion collisions), equilibrium properties of the phase transition in the SU(3) gauge theory with boundaries at low temperature (small volumes at RHIC suggest that boundary effects cannot be neglected and periodic boundary conditions normally used in lattice simulations do not correspond to the experimental situation), and a study of the order of the transition in U(1) gauge theory.

Dynamics and Statistical Mechanics of Rotating and non-Rotating Vortical Flows

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

Lim, Chjan

Three projects were analyzed with the overall aim of developing a computational/analytical model for estimating values of the energy, angular momentum, enstrophy and total variation of fluid height at phase transitions between disordered and self-organized flow states in planetary atmospheres. It is believed that these transitions in equilibrium statistical mechanics models play a role in the construction of large-scale, stable structures including super-rotation in the Venusian atmosphere and the formation of the Great Red Spot on Jupiter. Exact solutions of the spherical energy-enstrophy models for rotating planetary atmospheres by Kac's method of steepest descent predicted phase transitions to super-rotating solid-bodymore » flows at high energy to enstrophy ratio for all planetary spins and to sub-rotating modes if the planetary spin is large enough. These canonical statistical ensembles are well-defined for the long-range energy interactions that arise from 2D fluid flows on compact oriented manifolds such as the surface of the sphere and torus. This is because in Fourier space available through Hodge theory, the energy terms are exactly diagonalizable and hence has zero range, leading to well-defined heat baths.« less

Elasticity and Fluctuations of Incompatible Nanoribbons

NASA Astrophysics Data System (ADS)

Grossman, Doron; Sharon, Eran; Diamant, Haim

Geometrically incompatible ribbons are ubiquitous in nature, from the growing of biological tissues, to self assemblies of peptides and lipids. These exhibit unusual characteristics such shape bifurcations, and abnormal mechanical properties. When considering nano and micro ribbons, thermal fluctuations convert these properties into nontrivial statistics. We derive a reduced quasi-one-dimensional theory, which describes a wide range of incompatible elastic ribbons, and can be integrated into statistical mechanics formalism. Using it, we compute equilibrium configurations and statistical properties of two types of incompatible ribbons, with experimental significance: ribbons with positive spontaneous curvature, and ribbons with negative spontaneous curvature. The former, above a critical width, has a continuous family of degenerate configurations. In turn this causes the ribbons to behave as a random coils. The latter, however, exhibits a twisted-to-helical transition at a critical width, and behaves as an abnormal coil. It's persistence length is non-monotonic in the ribbon width and vanishes at a critical width, with principal modes of deformation different than compatible ribbons. Measurements of twisted ribbons made of chiral peptides, confirm some predictions of the model. European Research Council SoftGrowth project and The Harvey M. Kruger Family Center of Nanoscience and Nanotechnology.

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…

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.

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.

Dynamic equilibrium behaviour observed on two contrasting tidal flats from daily monitoring of bed-level changes

NASA Astrophysics Data System (ADS)

Hu, Zhan; van der Wal, Daphne; Cai, Huayang; van Belzen, Jim; Bouma, Tjeerd J.

2018-06-01

Dynamic equilibrium theory (DET) has been applied to tidal flats to systematically explain intertidal morphological responses to various distributions of bed shear stress (BSS). However, it is difficult to verify this theory with field observations because of the discrepancy between the idealized conceptions of theory and the complex reality of intertidal dynamics. The core relation between intertidal morphodynamics and BSS distribution can be easily masked by noise in complex datasets, leading to conclusions of insufficient field evidence to support DET. In the current study, hydrodynamic and morphodynamic data were monitored daily for one year on two tidal flats with contrasting wave exposures. BSS distribution was obtained by validated numerical models. Tidal flat dynamic equilibrium behaviour and BSS were linked via Empirical Orthogonal Function (EOF) analysis. We show that the principal morphodynamic modes corresponded well with the respective modes of BSS found at both sites. Tide-induced BSS was the dominant force at both sites, regardless of the level of wave exposure. The overall erosional and steepening trend found at the two flats can be attributed to the prevailing action of tidal forcing and reduced sediment supply. Hence, EOF analysis confirmed that tidal flat morphodynamics are consistent with DET, providing both field and model evidence to support this theory.

Hydrostatic figure of the earth: Theory and results

NASA Technical Reports Server (NTRS)

Khan, M. A.

1973-01-01

The complete development of the mathematical theory of hydrostatic equilibrium for the earth is recounted. Modifications of the first order theory are given along with the subsequent extension to the second order. In addition, the equations are presented which resulted from a revision of the second order theory to suit the new applications and data types of the post-artificial earth satellite era.

Geometry and symmetry in non-equilibrium thermodynamic systems

NASA Astrophysics Data System (ADS)

Sonnino, Giorgio

2017-06-01

The ultimate aim of this series of works is to establish the closure equations, valid for thermodynamic systems out from the Onsager region, and to describe the geometry and symmetry in thermodynamic systems far from equilibrium. Geometry of a non-equilibrium thermodynamic system is constructed by taking into account the second law of thermodynamics and by imposing the validity of the Glansdorff-Prigogine Universal Criterion of Evolution. These two constraints allow introducing the metrics and the affine connection of the Space of the Thermodynamic Forces, respectively. The Lie group associated to the nonlinear Thermodynamic Coordinate Transformations (TCT) leaving invariant both the entropy production σ and the Glansdorff-Prigogine dissipative quantity P, is also described. The invariance under TCT leads to the formulation of the Thermodynamic Covariance Principle (TCP): The nonlinear closure equations, i.e. the flux-force relations, must be covariant under TCT. In other terms, the fundamental laws of thermodynamics should be manifestly covariant under transformations between the admissible thermodynamic forces (i.e. under TCT). The symmetry properties of a physical system are intimately related to the conservation laws characterizing the thermodynamic system. Noether's theorem gives a precise description of this relation. The macroscopic theory for closure relations, based on this geometrical description and subject to the TCP, is referred to as the Thermodynamic Field Theory (TFT). This theory ensures the validity of the fundamental theorems for systems far from equilibrium.

Explicit Computations of Instantons and Large Deviations in Beta-Plane Turbulence

NASA Astrophysics Data System (ADS)

Laurie, J.; Bouchet, F.; Zaboronski, O.

2012-12-01

We use a path integral formalism and instanton theory in order to make explicit analytical predictions about large deviations and rare events in beta-plane turbulence. The path integral formalism is a concise way to get large deviation results in dynamical systems forced by random noise. In the most simple cases, it leads to the same results as the Freidlin-Wentzell theory, but it has a wider range of applicability. This approach is however usually extremely limited, due to the complexity of the theoretical problems. As a consequence it provides explicit results in a fairly limited number of models, often extremely simple ones with only a few degrees of freedom. Few exception exist outside the realm of equilibrium statistical physics. We will show that the barotropic model of beta-plane turbulence is one of these non-equilibrium exceptions. We describe sets of explicit solutions to the instanton equation, and precise derivations of the action functional (or large deviation rate function). The reason why such exact computations are possible is related to the existence of hidden symmetries and conservation laws for the instanton dynamics. We outline several applications of this apporach. For instance, we compute explicitly the very low probability to observe flows with an energy much larger or smaller than the typical one. Moreover, we consider regimes for which the system has multiple attractors (corresponding to different numbers of alternating jets), and discuss the computation of transition probabilities between two such attractors. These extremely rare events are of the utmost importance as the dynamics undergo qualitative macroscopic changes during such transitions.

Treatment of Chemical Equilibrium without Using Thermodynamics or Statistical Mechanics.

ERIC Educational Resources Information Center

Nelson, P. G.

1986-01-01

Discusses the conventional approaches to teaching about chemical equilibrium in advanced physical chemistry courses. Presents an alternative approach to the treatment of this concept by using Boltzmann's distribution law. Lists five advantages to using this method as compared with the other approaches. (TW)

Integral Equation for the Equilibrium State of Colliding Electron Beams

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

Warnock, Robert L.

2002-11-11

We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.

Experiential Learning of the Efficient Market Hypothesis: Two Trading Games

ERIC Educational Resources Information Center

Park, Andreas

2010-01-01

In goods markets, an equilibrium price balances demand and supply. In a financial market, an equilibrium price also aggregates people's information to reveal the true value of a financial security. Although the underlying idea of informationally efficient markets is one of the centerpieces of capital market theory, students often have difficulties…

Drop-tower experiments for capillary surfaces in an exotic container

NASA Technical Reports Server (NTRS)

Concus, Paul; Finn, Robert; Weislogel, Mark

1991-01-01

Low-gravity drop-tower experiments are carried out for an 'exotic' rotationally-symmetric container, which admits an entire continuum of distinct equilibrium symmetric capillary free surfaces. It is found that an initial equilibrium planer interface, a member of the continuum, will reorient toward a non-symmetric interface, as predicted by recent mathematical theory.

DEVELOPMENT AND AVAILABILITY OF EQUILIBRIUM PARTITIONING SEDIMENT GUIDELINES (ESGS) FOR NONIONIC ORGANIC CONTAMINANTS, METALS MIXTURES, AND POLYCYCLIC AROMATIC HYDROCARBON (PAH) MIXTURES

EPA Science Inventory

Collaborative efforts between EPA's Office of Water and Office of Research and Development have resulted in the development of sediment guidelines based on equilibrium partitioning theory (EqP). The guidance available includes a technical support document, describing the derivat...

Out-of-equilibrium chiral magnetic effect from chiral kinetic theory

NASA Astrophysics Data System (ADS)

Huang, Anping; Jiang, Yin; Shi, Shuzhe; Liao, Jinfeng; Zhuang, Pengfei

2018-02-01

Recently there has been significant interest in the macroscopic manifestation of chiral anomaly in many-body systems of chiral fermions. A notable example is the Chiral Magnetic Effect (CME). Enthusiastic efforts have been made to search for the CME in the quark-gluon plasma created in heavy ion collisions. A crucial challenge is that the extremely strong magnetic field in such collisions may last only for a brief moment and the CME current may have to occur at so early a stage that the quark-gluon matter is still far from thermal equilibrium. This thus requires modeling of the CME in an out-of-equilibrium setting. With the recently developed theoretical tool of chiral kinetic theory, we make a first phenomenological study of the CME-induced charge separation during the pre-thermal stage in heavy ion collisions. The effect is found to be very sensitive to the time dependence of the magnetic field and also influenced by the initial quark momentum spectrum as well as the relaxation time of the system evolution toward thermal equilibrium. Within the present approach, such pre-thermal charge separation is found to be modest.

Information management in DNA replication modeled by directional, stochastic chains with memory

NASA Astrophysics Data System (ADS)

Arias-Gonzalez, J. Ricardo

2016-11-01

Stochastic chains represent a key variety of phenomena in many branches of science within the context of information theory and thermodynamics. They are typically approached by a sequence of independent events or by a memoryless Markov process. Stochastic chains are of special significance to molecular biology, where genes are conveyed by linear polymers made up of molecular subunits and transferred from DNA to proteins by specialized molecular motors in the presence of errors. Here, we demonstrate that when memory is introduced, the statistics of the chain depends on the mechanism by which objects or symbols are assembled, even in the slow dynamics limit wherein friction can be neglected. To analyze these systems, we introduce a sequence-dependent partition function, investigate its properties, and compare it to the standard normalization defined by the statistical physics of ensembles. We then apply this theory to characterize the enzyme-mediated information transfer involved in DNA replication under the real, non-equilibrium conditions, reproducing measured error rates and explaining the typical 100-fold increase in fidelity that is experimentally found when proofreading and edition take place. Our model further predicts that approximately 1 kT has to be consumed to elevate fidelity in one order of magnitude. We anticipate that our results are necessary to interpret configurational order and information management in many molecular systems within biophysics, materials science, communication, and engineering.

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

A Short Note on Haroutunian's View of Piaget's Biological Conception of Knowledge.

ERIC Educational Resources Information Center

Doll, William E., Jr.

1981-01-01

The author discusses major premises of a paper, by Sophie Haroutunian (Educational Theory, v30 n3), that relates Jean Piaget's conception of knowledge to his biological theory of equilibrium. Doll argues that Piaget's theory of equilibration (striving for control over the environment) is not sufficiently appreciated by Haroutunian. (PP)

Advanced classical thermodynamics

NASA Astrophysics Data System (ADS)

Emanuel, George

The theoretical and mathematical foundations of thermodynamics are presented in an advanced text intended for graduate engineering students. Chapters are devoted to definitions and postulates, the fundamental equation, equilibrium, the application of Jacobian theory to thermodynamics, the Maxwell equations, stability, the theory of real gases, critical-point theory, and chemical thermodynamics. Diagrams, graphs, tables, and sample problems are provided.

Double Scaling in the Relaxation Time in the β -Fermi-Pasta-Ulam-Tsingou Model

NASA Astrophysics Data System (ADS)

Lvov, Yuri V.; Onorato, Miguel

2018-04-01

We consider the original β -Fermi-Pasta-Ulam-Tsingou system; numerical simulations and theoretical arguments suggest that, for a finite number of masses, a statistical equilibrium state is reached independently of the initial energy of the system. Using ensemble averages over initial conditions characterized by different Fourier random phases, we numerically estimate the time scale of equipartition and we find that for very small nonlinearity it matches the prediction based on exact wave-wave resonant interaction theory. We derive a simple formula for the nonlinear frequency broadening and show that when the phenomenon of overlap of frequencies takes place, a different scaling for the thermalization time scale is observed. Our result supports the idea that the Chirikov overlap criterion identifies a transition region between two different relaxation time scalings.

Trade-off between information and disturbance in qubit thermometry

NASA Astrophysics Data System (ADS)

Seveso, Luigi; Paris, Matteo G. A.

2018-03-01

We address the trade-off between information and disturbance in qubit thermometry from the perspective of quantum estimation theory. Given a quantum measurement, we quantify information via the Fisher information of the measurement and disturbance via four different figures of merit, which capture different aspects (statistical, thermodynamical, geometrical) of the trade-off. For each disturbance measure, the efficient measurements, i.e., the measurements that introduce a disturbance not greater than any other measurement extracting the same amount of information, are determined explicitly. The family of efficient measurements varies with the choice of the disturbance measure. On the other hand, commutativity between the elements of the probability operator-valued measure (POVM) and the equilibrium state of the thermometer is a necessary condition for efficiency with respect to any figure of disturbance.

Stochastic arbitrage return and its implication for option pricing

NASA Astrophysics Data System (ADS)

Fedotov, Sergei; Panayides, Stephanos

2005-01-01

The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility “smile” can also be explained in terms of random arbitrage opportunities.

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

Good-enough linguistic representations and online cognitive equilibrium in language processing.

PubMed

Karimi, Hossein; Ferreira, Fernanda

2016-01-01

We review previous research showing that representations formed during language processing are sometimes just "good enough" for the task at hand and propose the "online cognitive equilibrium" hypothesis as the driving force behind the formation of good-enough representations in language processing. Based on this view, we assume that the language comprehension system by default prefers to achieve as early as possible and remain as long as possible in a state of cognitive equilibrium where linguistic representations are successfully incorporated with existing knowledge structures (i.e., schemata) so that a meaningful and coherent overall representation is formed, and uncertainty is resolved or at least minimized. We also argue that the online equilibrium hypothesis is consistent with current theories of language processing, which maintain that linguistic representations are formed through a complex interplay between simple heuristics and deep syntactic algorithms and also theories that hold that linguistic representations are often incomplete and lacking in detail. We also propose a model of language processing that makes use of both heuristic and algorithmic processing, is sensitive to online cognitive equilibrium, and, we argue, is capable of explaining the formation of underspecified representations. We review previous findings providing evidence for underspecification in relation to this hypothesis and the associated language processing model and argue that most of these findings are compatible with them.

MHD waves and instabilities for gravitating, magnetized configurations in motion

NASA Astrophysics Data System (ADS)

Keppens, Rony; Goedbloed, Hans J. P.

Seismic probing of equilibrium configurations is of course well-known from geophysics, but has also been succesfully used to determine the internal structure of the Sun to an amazing accuracy. The results of helioseismology are quite impressive, although they only exploit an equilibrium structure where inward gravity is balanced by a pressure gradient in a 1D radial fashion. In principle, one can do the same for stationary, gravitating, magnetized plasma equilibria, as needed to perform MHD seismology in astrophysical jets or accretion disks. The introduction of (sheared) differential rotation does require the important switch from diagnosing static to stationary equilibrium configurations. The theory to describe all linear waves and instabilities in ideal MHD, given an exact stationary, gravitating, magnetized plasma equilibrium, in any dimensionality (1D, 2D, 3D) has been known since 1960, and is governed by the Frieman-Rotenberg equation. The full (mathematical) power of spectral theory governing physical eigenmode determination comes into play when using the Frieman-Rotenberg equation for moving equilibria, as applicable to astrophysical jets, accretion disks, but also solar flux ropes with stationary flow patterns. I will review exemplary seismic studies of flowing equilibrium configurations, covering solar to astrophysical configurations in motion. In that case, even essentially 1D configurations require quantification of the spectral web of eigenmodes, organizing the complex eigenfrequency plane.

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.

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.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

We point out that the quantum Grad's 13-moment system (Yano in Physica A 416:231-241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001-2023, 2015) and Fan et al. (J Stat Phys 162(2):457-486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.

Nonequilibrium Entropy in a Shock

DOE PAGES

Margolin, Len G.

2017-07-19

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

Chemical reactions simulated by ground-water-quality models

USGS Publications Warehouse

Grove, David B.; Stollenwerk, Kenneth G.

1987-01-01

Recent literature concerning the modeling of chemical reactions during transport in ground water is examined with emphasis on sorption reactions. The theory of transport and reactions in porous media has been well documented. Numerous equations have been developed from this theory, to provide both continuous and sequential or multistep models, with the water phase considered for both mobile and immobile phases. Chemical reactions can be either equilibrium or non-equilibrium, and can be quantified in linear or non-linear mathematical forms. Non-equilibrium reactions can be separated into kinetic and diffusional rate-limiting mechanisms. Solutions to the equations are available by either analytical expressions or numerical techniques. Saturated and unsaturated batch, column, and field studies are discussed with one-dimensional, laboratory-column experiments predominating. A summary table is presented that references the various kinds of models studied and their applications in predicting chemical concentrations in ground waters.

Nonequilibrium Entropy in a Shock

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

Margolin, Len G.

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibrium (LTE). However, gas kinetic theory provides a perfectly general formulation of a nonequilibrium entropy in terms of the probability distribution function (PDF) solutions of the Boltzmann equation. In this paper I will evaluate the Boltzmann entropy for the PDF that underlies themore » Navier–Stokes equations and also for the PDF of the Mott–Smith shock solution. I will show that both monotonically increase in the shock. As a result, I will propose a new nonequilibrium thermodynamic entropy and show that it is also monotone and closely approximates the Boltzmann entropy.« less

A geometrically nonlinear theory of elastic plates

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Atilgan, Ali R.; Danielson, D. A.

1992-01-01

A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

PubMed Central

Zhuang, Qian; Di, Zengru; Wu, Jinshan

2014-01-01

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs. PMID:25157502

Access point selection game with mobile users using correlated equilibrium.

PubMed

Sohn, Insoo

2015-01-01

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation.

Access Point Selection Game with Mobile Users Using Correlated Equilibrium

PubMed Central

Sohn, Insoo

2015-01-01

One of the most important issues in wireless local area network (WLAN) systems with multiple access points (APs) is the AP selection problem. Game theory is a mathematical tool used to analyze the interactions in multiplayer systems and has been applied to various problems in wireless networks. Correlated equilibrium (CE) is one of the powerful game theory solution concepts, which is more general than the Nash equilibrium for analyzing the interactions in multiplayer mixed strategy games. A game-theoretic formulation of the AP selection problem with mobile users is presented using a novel scheme based on a regret-based learning procedure. Through convergence analysis, we show that the joint actions based on the proposed algorithm achieve CE. Simulation results illustrate that the proposed algorithm is effective in a realistic WLAN environment with user mobility and achieves maximum system throughput based on the game-theoretic formulation. PMID:25785726

Non-equilibrium price theories

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Kern, Daniel

2000-11-01

We propose two theories for the formation of stock prices under the condition that the number of available stocks is fixed. Both theories consider the balance equations for cash and several kinds of stocks. They also take into account interest rates, dividends, and transaction costs. The proposed theories have the advantage that they do not require iterative procedures to determine the price, which would be inefficient for simulations with many agents.

What Can Reinforcement Learning Teach Us About Non-Equilibrium Quantum Dynamics

NASA Astrophysics Data System (ADS)

Bukov, Marin; Day, Alexandre; Sels, Dries; Weinberg, Phillip; Polkovnikov, Anatoli; Mehta, Pankaj

Equilibrium thermodynamics and statistical physics are the building blocks of modern science and technology. Yet, our understanding of thermodynamic processes away from equilibrium is largely missing. In this talk, I will reveal the potential of what artificial intelligence can teach us about the complex behaviour of non-equilibrium systems. Specifically, I will discuss the problem of finding optimal drive protocols to prepare a desired target state in quantum mechanical systems by applying ideas from Reinforcement Learning [one can think of Reinforcement Learning as the study of how an agent (e.g. a robot) can learn and perfect a given policy through interactions with an environment.]. The driving protocols learnt by our agent suggest that the non-equilibrium world features possibilities easily defying intuition based on equilibrium physics.

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.

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.

Should the Equilibrium Point Hypothesis (EPH) be Considered a Scientific Theory?

PubMed Central

Sainburg, Robert L.

2017-01-01

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature. PMID:25386681

Should the Equilibrium Point Hypothesis (EPH) be Considered a Scientific Theory?

PubMed

Sainburg, Robert L

2015-04-01

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature.

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.

Accelerating Multiagent Reinforcement Learning by Equilibrium Transfer.

PubMed

Hu, Yujing; Gao, Yang; An, Bo

2015-07-01

An important approach in multiagent reinforcement learning (MARL) is equilibrium-based MARL, which adopts equilibrium solution concepts in game theory and requires agents to play equilibrium strategies at each state. However, most existing equilibrium-based MARL algorithms cannot scale due to a large number of computationally expensive equilibrium computations (e.g., computing Nash equilibria is PPAD-hard) during learning. For the first time, this paper finds that during the learning process of equilibrium-based MARL, the one-shot games corresponding to each state's successive visits often have the same or similar equilibria (for some states more than 90% of games corresponding to successive visits have similar equilibria). Inspired by this observation, this paper proposes to use equilibrium transfer to accelerate equilibrium-based MARL. The key idea of equilibrium transfer is to reuse previously computed equilibria when each agent has a small incentive to deviate. By introducing transfer loss and transfer condition, a novel framework called equilibrium transfer-based MARL is proposed. We prove that although equilibrium transfer brings transfer loss, equilibrium-based MARL algorithms can still converge to an equilibrium policy under certain assumptions. Experimental results in widely used benchmarks (e.g., grid world game, soccer game, and wall game) show that the proposed framework: 1) not only significantly accelerates equilibrium-based MARL (up to 96.7% reduction in learning time), but also achieves higher average rewards than algorithms without equilibrium transfer and 2) scales significantly better than algorithms without equilibrium transfer when the state/action space grows and the number of agents increases.

How much inequality in income is fair? A microeconomic game theoretic perspective

NASA Astrophysics Data System (ADS)

Venkatasubramanian, Venkat; Luo, Yu; Sethuraman, Jay

2015-10-01

The increasing inequality in income and wealth in recent years, and the associated excessive pay packages of CEOs in the US and elsewhere, is of growing concern among policy makers as well as the common person. However, there seems to be no satisfactory answer, in conventional economic theories and models, to the fundamental questions of what kind of income distribution we ought to see, at least under ideal conditions, in a free market environment, and whether this distribution is fair. We propose a novel microeconomic game theoretic framework that addresses these questions and proves that the lognormal distribution is the fairest inequality of pay in an organization comprising of homogeneous agents, under ideal free market conditions at equilibrium. We also show that for a population of two different classes of agents, the equilibrium distribution is a combination of two different lognormal distributions where one of them, corresponding to the top ˜3-5% of the population, can be misidentified as a Pareto distribution. We compare our predictions with empirical data on global income inequality trends provided by Piketty and others. Our analysis suggests that the Scandinavian countries, and to a lesser extent Switzerland, Netherlands and Australia, have managed to get close to the ideal distribution for the bottom ˜99% of the population, while the US and UK remain less fair at the other extreme. Other European countries such as France and Germany, and Japan and Canada, are in the middle. Our theory also shows the deep and direct connection between potential game theory and statistical mechanics through entropy, which we identify as a measure of fairness in a distribution. This leads us to propose the fair market hypothesis, that the self-organizing dynamics of the ideal free market, i.e., Adam Smith's "invisible hand", not only promotes efficiency but also maximizes fairness under the given constraints.

USING INFORMATION THEORY TO DEFINE A SUSTAINABILITY INDEX

EPA Science Inventory

Information theory has many applications in Ecology and Environmental science, such as a biodiversity indicator, as a measure of evolution, a measure of distance from thermodynamic equilibrium, and as a measure of system organization. Fisher Information, in particular, provides a...

Balancing Eggs

ERIC Educational Resources Information Center

Mills, Allan

2014-01-01

Theory predicts that an egg-shaped body should rest in stable equilibrium when on its side, balance vertically in metastable equilibrium on its broad end and be completely unstable on its narrow end. A homogeneous solid egg made from wood, clay or plastic behaves in this way, but a real egg will not stand on either end. It is shown that this…

Some Considerations on the Fundamentals of Chemical Kinetics: Steady State, Quasi-Equilibrium, and Transition State Theory

ERIC Educational Resources Information Center

Perez-Benito, Joaquin F.

2017-01-01

The elementary reaction sequence A ? I ? Products is the simplest mechanism for which the steady-state and quasi-equilibrium kinetic approximations can be applied. The exact integrated solutions for this chemical system allow inferring the conditions that must fulfill the rate constants for the different approximations to hold. A graphical…

An Application of Variational Theory to an Integrated Walrasian Model of Exchange, Consumption and Production

NASA Astrophysics Data System (ADS)

Donato, M. B.; Milasi, M.; Vitanza, C.

2010-09-01

An existence result of a Walrasian equilibrium for an integrated model of exchange, consumption and production is obtained. The equilibrium model is characterized in terms of a suitable generalized quasi-variational inequality; so the existence result comes from an original technique which takes into account tools of convex and set-valued analysis.

Dynamics of two-phase interfaces and surface tensions: A density-functional theory perspective

NASA Astrophysics Data System (ADS)

Yatsyshin, Petr; Sibley, David N.; Duran-Olivencia, Miguel A.; Kalliadasis, Serafim

2016-11-01

Classical density functional theory (DFT) is a statistical mechanical framework for the description of fluids at the nanoscale, where the inhomogeneity of the fluid structure needs to be carefully accounted for. By expressing the grand free-energy of the fluid as a functional of the one-body density, DFT offers a theoretically consistent and computationally accessible way to obtain two-phase interfaces and respective interfacial tensions in a ternary solid-liquid-gas system. The dynamic version of DFT (DDFT) can be rigorously derived from the Smoluchowsky picture of the dynamics of colloidal particles in a solvent. It is generally agreed that DDFT can capture the diffusion-driven evolution of many soft-matter systems. In this context, we use DDFT to investigate the dynamic behaviour of two-phase interfaces in both equilibrium and dynamic wetting and discuss the possibility of defining a time-dependent surface tension, which still remains in debate. We acknowledge financial support from the European Research Council via Advanced Grant No. 247031 and from the Engineering and Physical Sciences Research Council of the UK via Grants No. EP/L027186 and EP/L020564.

Temperature lapse rates at restricted thermodynamic equilibrium. Part II: Saturated air and further discussions

NASA Astrophysics Data System (ADS)

Björnbom, Pehr

2016-03-01

In the first part of this work equilibrium temperature profiles in fluid columns with ideal gas or ideal liquid were obtained by numerically minimizing the column energy at constant entropy, equivalent to maximizing column entropy at constant energy. A minimum in internal plus potential energy for an isothermal temperature profile was obtained in line with Gibbs' classical equilibrium criterion. However, a minimum in internal energy alone for adiabatic temperature profiles was also obtained. This led to a hypothesis that the adiabatic lapse rate corresponds to a restricted equilibrium state, a type of state in fact discussed already by Gibbs. In this paper similar numerical results for a fluid column with saturated air suggest that also the saturated adiabatic lapse rate corresponds to a restricted equilibrium state. The proposed hypothesis is further discussed and amended based on the previous and the present numerical results and a theoretical analysis based on Gibbs' equilibrium theory.

Stability and bifurcation analysis on a ratio-dependent predator-prey model with time delay

NASA Astrophysics Data System (ADS)

Xu, Rui; Gan, Qintao; Ma, Zhien

2009-08-01

A ratio-dependent predator-prey model with time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and a semi-trivial boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semi-trivial equilibrium is also addressed. Numerical simulations are carried out to illustrate the main results.

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.

Nonlinear response from transport theory and quantum field theory at finite temperature

NASA Astrophysics Data System (ADS)

Carrington, M. E.; Defu, Hou; Kobes, R.

2001-07-01

We study the nonlinear response in weakly coupled hot φ4 theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is done by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By performing a Chapman-Enskog expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of the expanded distribution function. To do the response theory calculation we use Zubarev's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded Green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theory to show that this three-point function can be calculated by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams. The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function. We conclude that calculating the quadratic shear viscous response using transport theory and keeping terms that are quadratic in the gradient of the velocity field in the Chapman-Enskog expansion of the Boltzmann equation is equivalent to calculating the quadratic shear viscous response from response theory using the next-to-linear response Kubo formula, with a vertex given by an infinite resummation of ladder and extended-ladder diagrams.

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

NASA Technical Reports Server (NTRS)

Medvedev, A. S.

1987-01-01

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

NASA Astrophysics Data System (ADS)

Medvedev, A. S.

1987-08-01

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.

Structural design using equilibrium programming formulations

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

1995-01-01

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Children's strategic theory of mind.

PubMed

Sher, Itai; Koenig, Melissa; Rustichini, Aldo

2014-09-16

Human strategic interaction requires reasoning about other people's behavior and mental states, combined with an understanding of their incentives. However, the ontogenic development of strategic reasoning is not well understood: At what age do we show a capacity for sophisticated play in social interactions? Several lines of inquiry suggest an important role for recursive thinking (RT) and theory of mind (ToM), but these capacities leave out the strategic element. We posit a strategic theory of mind (SToM) integrating ToM and RT with reasoning about incentives of all players. We investigated SToM in 3- to 9-y-old children and adults in two games that represent prevalent aspects of social interaction. Children anticipate deceptive and competitive moves from the other player and play both games in a strategically sophisticated manner by 7 y of age. One game has a pure strategy Nash equilibrium: In this game, children achieve equilibrium play by the age of 7 y on the first move. In the other game, with a single mixed-strategy equilibrium, children's behavior moved toward the equilibrium with experience. These two results also correspond to two ways in which children's behavior resembles adult behavior in the same games. In both games, children's behavior becomes more strategically sophisticated with age on the first move. Beyond the age of 7 y, children begin to think about strategic interaction not myopically, but in a farsighted way, possibly with a view to cooperating and capitalizing on mutual gains in long-run relationships.

Children’s strategic theory of mind

PubMed Central

Sher, Itai; Koenig, Melissa; Rustichini, Aldo

2014-01-01

Human strategic interaction requires reasoning about other people’s behavior and mental states, combined with an understanding of their incentives. However, the ontogenic development of strategic reasoning is not well understood: At what age do we show a capacity for sophisticated play in social interactions? Several lines of inquiry suggest an important role for recursive thinking (RT) and theory of mind (ToM), but these capacities leave out the strategic element. We posit a strategic theory of mind (SToM) integrating ToM and RT with reasoning about incentives of all players. We investigated SToM in 3- to 9-y-old children and adults in two games that represent prevalent aspects of social interaction. Children anticipate deceptive and competitive moves from the other player and play both games in a strategically sophisticated manner by 7 y of age. One game has a pure strategy Nash equilibrium: In this game, children achieve equilibrium play by the age of 7 y on the first move. In the other game, with a single mixed-strategy equilibrium, children’s behavior moved toward the equilibrium with experience. These two results also correspond to two ways in which children’s behavior resembles adult behavior in the same games. In both games, children’s behavior becomes more strategically sophisticated with age on the first move. Beyond the age of 7 y, children begin to think about strategic interaction not myopically, but in a farsighted way, possibly with a view to cooperating and capitalizing on mutual gains in long-run relationships. PMID:25197065

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Aggregation of 2-aminobenzimidazole--a combined experimental and theoretical investigation.

PubMed

Angelova, Silvia E; Spassova, Milena I; Deneva, Vera V; Rogojerov, Marin I; Antonov, Liudmil M

2011-06-20

An investigation of 2-aminobenzimidazole was carried out by calculations at HF, MP2, and DFT levels of theory and also by UV and IR spectroscopy. The quantum chemical calculations predict a full shift of the equilibrium towards the amino form, but the absorption spectra in different solvents distinctly show a two-component equilibrium system. Examination of possible equilibria in solution shows that an equilibrium between two dimeric forms of the amino tautomer of 2-aminobenzimidazole explains the spectral observations. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Electron transfer across a thermal gradient

PubMed Central

Craven, Galen T.

2016-01-01

Charge transfer is a fundamental process that underlies a multitude of phenomena in chemistry and biology. Recent advances in observing and manipulating charge and heat transport at the nanoscale, and recently developed techniques for monitoring temperature at high temporal and spatial resolution, imply the need for considering electron transfer across thermal gradients. Here, a theory is developed for the rate of electron transfer and the associated heat transport between donor–acceptor pairs located at sites of different temperatures. To this end, through application of a generalized multidimensional transition state theory, the traditional Arrhenius picture of activation energy as a single point on a free energy surface is replaced with a bithermal property that is derived from statistical weighting over all configurations where the reactant and product states are equienergetic. The flow of energy associated with the electron transfer process is also examined, leading to relations between the rate of heat exchange among the donor and acceptor sites as functions of the temperature difference and the electronic driving bias. In particular, we find that an open electron transfer channel contributes to enhanced heat transport between sites even when they are in electronic equilibrium. The presented results provide a unified theory for charge transport and the associated heat conduction between sites at different temperatures. PMID:27450086

Non-equilibrium Properties of a Pumped-Decaying Bose-Condensed Electron–Hole Gas in the BCS–BEC Crossover Region

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

Hanai, R.; Littlewood, P. B.; Ohashi, Y.

2016-03-01

We theoretically investigate a Bose-condensed exciton gas out of equilibrium. Within the framework of the combined BCS-Leggett strong-coupling theory with the non-equilibrium Keldysh formalism, we show how the Bose-Einstein condensation (BEC) of excitons is suppressed to eventually disappear, when the system is in the non-equilibrium steady state. The supply of electrons and holes from the bath is shown to induce quasi-particle excitations, leading to the partial occupation of the upper branch of Bogoliubov single-particle excitation spectrum. We also discuss how this quasi-particle induction is related to the suppression of exciton BEC, as well as the stability of the steady state.

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

Liapunov stability analysis of hybrid dynamical systems in the neighborhood of nontrivial equilibrium

NASA Technical Reports Server (NTRS)

Meirovitch, L.

1973-01-01

This paper is concerned with the stability of a hybrid dynamical system in the neighborhood of a nontrivial equilibrium, where the system consists of one rigid part and n elastic members. The body moves in a central-force field with its mass center describing a circular orbit. The nontrivial equilibrium is defined by steady rotation of the system at an angular velocity equal to the orbital velocity, with the elastic members being in deformed state. A Liapunov stability analysis is performed by assuming small perturbations about the nontrivial equilibrium, where the latter is generally defined by nonlinear differential equations. The theory is applied to a gravity-gradient stabilized satellite with flexible appendages.

Dynamics of traffic flow with real-time traffic information

NASA Astrophysics Data System (ADS)

Yokoya, Yasushi

2004-01-01

We studied dynamics of traffic flow with real-time information provided. Provision of the real-time traffic information based on advancements in telecommunication technology is expected to facilitate the efficient utilization of available road capacity. This system has a potentiality of not only engineering for road usage but also the science of complexity series. In the system, the information plays a role of feedback connecting microscopic and macroscopic phenomena beyond the hierarchical structure of statistical physics. In this paper, we tried to clarify how the information works in a network of traffic flow from the perspective of statistical physics. The dynamical feature of the traffic flow is abstracted by a contrastive study between the nonequilibrium statistical physics and a computer simulation based on cellular automaton. We found that the information disrupts the local equilibrium of traffic flow by a characteristic dissipation process due to interaction between the information and individual vehicles. The dissipative structure was observed in the time evolution of traffic flow driven far from equilibrium as a consequence of the breakdown of the local-equilibrium hypothesis.

Irreversible Processes in Ionized Gases

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

Balescu, R.

1960-01-01

The general theory of irreversible processes, developed by Prigogine and Balescu, is applied to the case of long range interactions in ionized gases. A similar diagram technique permits the systematic selection of all the contributions to the evolution of the distribution function, a an order of approximation equivalent to Debye's equilibrium theory. The infinite series which appear in this way can be summed exactly. The resulting evolution equations have a clear physical significance: they describe interactions of "quasi particles," which are electrons or ions "dressed" by their polarization clouds. These clouds are not a permanent feature, as in equilibrium theory,more » but have a nonequilibrium, changing shape, distorted by the motions of the particles. From the mathematical point of view, these equations exhibit a new type of nonlinearity, which is very directly related to the collective nature of the interactions.« less

Kinetic theory for DNA melting with vibrational entropy

NASA Astrophysics Data System (ADS)

Sensale, Sebastian; Peng, Zhangli; Chang, Hsueh-Chia

2017-10-01

By treating DNA as a vibrating nonlinear lattice, an activated kinetic theory for DNA melting is developed to capture the breakage of the hydrogen bonds and subsequent softening of torsional and bending vibration modes. With a coarse-grained lattice model, we identify a key bending mode with GHz frequency that replaces the hydrogen vibration modes as the dominant out-of-phase phonon vibration at the transition state. By associating its bending modulus to a universal in-phase bending vibration modulus at equilibrium, we can hence estimate the entropic change in the out-of-phase vibration from near-equilibrium all-atom simulations. This and estimates of torsional and bending entropy changes lead to the first predictive and sequence-dependent theory with good quantitative agreement with experimental data for the activation energy of melting of short DNA molecules without intermediate hairpin structures.

On the Fluctuations that Order and Frustrate Liquid Water

NASA Astrophysics Data System (ADS)

Limmer, David Tyler

At ambient conditions, water sits close to phase coexistence with its crystal. More so than in many other materials, this fact is manifested in the fluctuations that maintain a large degree of local order in the liquid. These fluctuations and how they result in long-ranged order, or its absence, are emergent features of many interacting molecules. Their study therefore requires using the tools of statistical mechanics for their their systematic understanding. In this dissertation we develop such an understanding. In particular, we focus on collective behavior that emerges in liquid and solid water. At room temperatures, the thermophysical properties of water are quantified and rationalized with simple molecular models. A key feature of these models is the correct characterization of the competition between entropic forces of packing and the energetic preference for tetrahedral order. At cold temperatures, the properties of ice surfaces are studied with statistical field theory. The theory we develop for the long wavelength features of ice interfaces allows us to explain the existence of a premelting layer on the surface of ice and the stability of ice in confinement. In between these extremes, the dynamics of supercooled water are considered. A detailed theory for the early stages of coarsening is developed and used to explain the peculiar observation of a transient second liquid state of water. When coarsening dynamics are arrested, the result is the formation of a glassy states of water. We show that out-of-equilibrium the phase diagram for supercooled water exhibits a rich amount of structure, including a triple point between two glass phases of water and the liquid. At the end, we explore possible technological implications for the interplay between ordering and frustration in studies of water at metal interfaces.

Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics

NASA Astrophysics Data System (ADS)

Zaripov, R. G.

2018-05-01

On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.

Learning dynamics in social dilemmas

PubMed Central

Macy, Michael W.; Flache, Andreas

2002-01-01

The Nash equilibrium, the main solution concept in analytical game theory, cannot make precise predictions about the outcome of repeated mixed-motive games. Nor can it tell us much about the dynamics by which a population of players moves from one equilibrium to another. These limitations, along with concerns about the cognitive demands of forward-looking rationality, have motivated efforts to explore backward-looking alternatives to analytical game theory. Most of the effort has been invested in evolutionary models of population dynamics. We shift attention to a learning-theoretic alternative. Computational experiments with adaptive agents identify a fundamental solution concept for social dilemmas–−stochastic collusion–−based on a random walk from a self-limiting noncooperative equilibrium into a self-reinforcing cooperative equilibrium. However, we show that this solution is viable only within a narrow range of aspiration levels. Below the lower threshold, agents are pulled into a deficient equilibrium that is a stronger attractor than mutual cooperation. Above the upper threshold, agents are dissatisfied with mutual cooperation. Aspirations that adapt with experience (producing habituation to stimuli) do not gravitate into the window of viability; rather, they are the worst of both worlds. Habituation destabilizes cooperation and stabilizes defection. Results from the two-person problem suggest that applications to multiplex and embedded relationships will yield unexpected insights into the global dynamics of cooperation in social dilemmas. PMID:12011402

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.

Are Equity and Efficiency Irreconcilable Goals in Education? A General Equilibrium Analysis of Basic Education Finance in China

ERIC Educational Resources Information Center

Ding, Weili; Lu, Ming

2007-01-01

Lacking guidance of general equilibrium (GE) theories in public economics and the corresponding proper mechanisms, China has not surprisingly witnessed an inequality in educational expenditures across regions as well as insufficiency of funds for education in poor areas. It is wrongly thought that what happens is due to the decentralized financing…

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory.

PubMed

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M; Dean, David S

2018-02-28

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory

NASA Astrophysics Data System (ADS)

Krüger, Matthias; Solon, Alexandre; Démery, Vincent; Rohwer, Christian M.; Dean, David S.

2018-02-01

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles and show that its average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces due to external potentials and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in generic, non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. Subsequently, we give a general form for the stress tensor which is valid for a large variety of energy functionals and which reproduces the two mentioned cases. We then use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we compute to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute to the Green-Kubo relation for the viscosity.

Individual-based models for adaptive diversification in high-dimensional phenotype spaces.

PubMed

Ispolatov, Iaroslav; Madhok, Vaibhav; Doebeli, Michael

2016-02-07

Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state before diversification occurs, as exemplified by the concept of evolutionary branching points in adaptive dynamics theory. Recent results indicate that adaptive dynamics may often not converge to equilibrium points and instead generate complicated trajectories if evolution takes place in high-dimensional phenotype spaces. Even though some analytical results on diversification in complex phenotype spaces are available, to study this problem in general we need to reconstruct individual-based models from the adaptive dynamics generating the non-equilibrium dynamics. Here we first provide a method to construct individual-based models such that they faithfully reproduce the given adaptive dynamics attractor without diversification. We then show that a propensity to diversify can be introduced by adding Gaussian competition terms that generate frequency dependence while still preserving the same adaptive dynamics. For sufficiently strong competition, the disruptive selection generated by frequency-dependence overcomes the directional evolution along the selection gradient and leads to diversification in phenotypic directions that are orthogonal to the selection gradient. Copyright © 2015 Elsevier Ltd. All rights reserved.

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Halford, Gary R.

2004-01-01

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

Analytical gradients for subsystem density functional theory within the slater-function-based amsterdam density functional program.

PubMed

Schlüns, Danny; Franchini, Mirko; Götz, Andreas W; Neugebauer, Johannes; Jacob, Christoph R; Visscher, Lucas

2017-02-05

We present a new implementation of analytical gradients for subsystem density-functional theory (sDFT) and frozen-density embedding (FDE) into the Amsterdam Density Functional program (ADF). The underlying theory and necessary expressions for the implementation are derived and discussed in detail for various FDE and sDFT setups. The parallel implementation is numerically verified and geometry optimizations with different functional combinations (LDA/TF and PW91/PW91K) are conducted and compared to reference data. Our results confirm that sDFT-LDA/TF yields good equilibrium distances for the systems studied here (mean absolute deviation: 0.09 Å) compared to reference wave-function theory results. However, sDFT-PW91/PW91k quite consistently yields smaller equilibrium distances (mean absolute deviation: 0.23 Å). The flexibility of our new implementation is demonstrated for an HCN-trimer test system, for which several different setups are applied. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

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.

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.

Equilibrium properties of DNA and other semiflexible polymers confined in nanochannels

NASA Astrophysics Data System (ADS)

Muralidhar, Abhiram

Recent developments in next-generation sequencing (NGS) techniques have opened the door for low-cost, high-throughput sequencing of genomes. However, these developments have also exposed the inability of NGS to track large scale genomic information, which are extremely important to understand the relationship between genotype and phenotype. Genome mapping offers a reliable way to obtain information about large-scale structural variations in a given genome. A promising variant of genome mapping involves confining single DNA molecules in nanochannels whose cross-sectional dimensions are approximately 50 nm. Despite the development and commercialization of nanochannel-based genome mapping technology, the polymer physics of DNA in confinement is only beginning to be understood. Apart from its biological relevance, DNA is also used as a model polymer in experiments by polymer physicists. Indeed, the seminal experiments by Reisner et al. (2005) of DNA confined in nanochannels of different widths revealed discrepancies with the classical theories of Odijk and de Gennes for polymer confinement. Picking up from the conclusions of the dissertation of Tree (2014), this dissertation addresses a number of key outstanding problems in the area of nanoconfined DNA. Adopting a Monte Carlo chain growth technique known as the pruned-enriched Rosenbluth method, we examine the equilibrium and near-equilibrium properties of DNA and other semiflexible polymers in nanochannel confinement. We begin by analyzing the dependence of molecular weight on various thermodynamic properties of confined semiflexible polymers. This allows us to point out the finite size effects that can occur when using low molecular weight DNA in experiments. We then analyze the statistics of backfolding and hairpin formation in the context of existing theories and discuss how our results can be used to engineer better conditions for genome mapping. Finally, we elucidate the diffusion behavior of confined semiflexible polymers by comparing and contrasting our results for asymptotically long chains with other similar studies in the literature. We expect our findings to be not only beneficial to the design of better genome mapping devices, but also to the fundamental understanding of semiflexible polymers in confinement.

Investigation of the hydrochlorination of SiCl4

NASA Technical Reports Server (NTRS)

Mui, J. Y. P.

1983-01-01

A basic, experimental study on the hydrochlorination of silicon tetrachloride and metallurgical grade silicon with hydrogen gas to form trichlorosilane was carried out to greatly expand the range of reaction conditions. The equilibrium constant, K sub p, for the hydrochlorination reaction was measured as a function of temperature, pressure and concentration. The variation of the equilibrium constant as a function of temperature provided the measurement on the heat of reaction, delta H, by the Second Law Method. The value of delta H was measured to give 10.6 Kcal/mole. The equilibrium constant was also studied as a function of concentration. In agreement with the theory, the equilibrium constant remained constant with respect to the varying H2/SiCl4 feed ratios. On the other hand, the effect of pressure on the equilibrium constant was found to be more complex.

Calculation of individual isotope equilibrium constants for implementation in geochemical models

USGS Publications Warehouse

Thorstenson, Donald C.; Parkhurst, David L.

2002-01-01

Theory is derived from the work of Urey to calculate equilibrium constants commonly used in geochemical equilibrium and reaction-transport models for reactions of individual isotopic species. Urey showed that equilibrium constants of isotope exchange reactions for molecules that contain two or more atoms of the same element in equivalent positions are related to isotope fractionation factors by , where is n the number of atoms exchanged. This relation is extended to include species containing multiple isotopes, for example and , and to include the effects of nonideality. The equilibrium constants of the isotope exchange reactions provide a basis for calculating the individual isotope equilibrium constants for the geochemical modeling reactions. The temperature dependence of the individual isotope equilibrium constants can be calculated from the temperature dependence of the fractionation factors. Equilibrium constants are calculated for all species that can be formed from and selected species containing , in the molecules and the ion pairs with where the subscripts g, aq, l, and s refer to gas, aqueous, liquid, and solid, respectively. These equilibrium constants are used in the geochemical model PHREEQC to produce an equilibrium and reaction-transport model that includes these isotopic species. Methods are presented for calculation of the individual isotope equilibrium constants for the asymmetric bicarbonate ion. An example calculates the equilibrium of multiple isotopes among multiple species and phases.

Advanced Tokamak Stability Theory

NASA Astrophysics Data System (ADS)

Zheng, Linjin

2015-03-01

The intention of this book is to introduce advanced tokamak stability theory. We start with the derivation of the Grad-Shafranov equation and the construction of various toroidal flux coordinates. An analytical tokamak equilibrium theory is presented to demonstrate the Shafranov shift and how the toroidal hoop force can be balanced by the application of a vertical magnetic field in tokamaks. In addition to advanced theories, this book also discusses the intuitive physics pictures for various experimentally observed phenomena.

Global dynamics of non-equilibrium gliding in animals.

PubMed

Yeaton, Isaac J; Socha, John J; Ross, Shane D

2017-03-17

Gliding flight-moving horizontally downward through the air without power-has evolved in a broad diversity of taxa and serves numerous ecologically relevant functions such as predator escape, expanding foraging locations, and finding mates, and has been suggested as an evolutionary pathway to powered flight. Historically, gliding has been conceptualized using the idealized conditions of equilibrium, in which the net aerodynamic force on the glider balances its weight. While this assumption is appealing for its simplicity, recent studies of glide trajectories have shown that equilibrium gliding is not the norm for most species. Furthermore, equilibrium theory neglects the aerodynamic differences between species, as well as how a glider can modify its glide path using control. To investigate non-equilibrium glide behavior, we developed a reduced-order model of gliding that accounts for self-similarity in the equations of motion, such that the lift and drag characteristics alone determine the glide trajectory. From analysis of velocity polar diagrams of horizontal and vertical velocity from several gliding species, we find that pitch angle, the angle between the horizontal and chord line, is a control parameter that can be exploited to modulate glide angle and glide speed. Varying pitch results in changing locations of equilibrium glide configurations in the velocity polar diagram that govern passive glide dynamics. Such analyses provide a new mechanism of interspecies comparison and tools to understand experimentally-measured kinematics data and theory. In addition, this analysis suggests that the lift and drag characteristics of aerial and aquatic autonomous gliders can be engineered to passively alter glide trajectories with minimal control effort.

Equilibrium Bird Species Diversity in Atlantic Islands.

PubMed

Valente, Luis; Illera, Juan Carlos; Havenstein, Katja; Pallien, Tamara; Etienne, Rampal S; Tiedemann, Ralph

2017-06-05

Half a century ago, MacArthur and Wilson proposed that the number of species on islands tends toward a dynamic equilibrium diversity around which species richness fluctuates [1]. The current prevailing view in island biogeography accepts the fundamentals of MacArthur and Wilson's theory [2] but questions whether their prediction of equilibrium can be fulfilled over evolutionary timescales, given the unpredictable and ever-changing nature of island geological and biotic features [3-7]. Here we conduct a complete molecular phylogenetic survey of the terrestrial bird species from four oceanic archipelagos that make up the diverse Macaronesian bioregion-the Azores, the Canary Islands, Cape Verde, and Madeira [8, 9]. We estimate the times at which birds colonized and speciated in the four archipelagos, including many previously unsampled endemic and non-endemic taxa and their closest continental relatives. We develop and fit a new multi-archipelago dynamic stochastic model to these data, explicitly incorporating information from 91 taxa, both extant and extinct. Remarkably, we find that all four archipelagos have independently achieved and maintained a dynamic equilibrium over millions of years. Biogeographical rates are homogeneous across archipelagos, except for the Canary Islands, which exhibit higher speciation and colonization. Our finding that the avian communities of the four Macaronesian archipelagos display an equilibrium diversity pattern indicates that a diversity plateau may be rapidly achieved on islands where rates of in situ radiation are low and extinction is high. This study reveals that equilibrium processes may be more prevalent than recently proposed, supporting MacArthur and Wilson's 50-year-old theory. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

Statistical mechanics of the international trade network.

PubMed

Fronczak, Agata; Fronczak, Piotr

2012-05-01

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e., a quasistatic process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills a fluctuation-response theorem, which states that the average relative change in imports (exports) between two countries is a sum of the relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.

Statistical mechanics of the international trade network

NASA Astrophysics Data System (ADS)

Fronczak, Agata; Fronczak, Piotr

2012-05-01

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e., a quasistatic process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills a fluctuation-response theorem, which states that the average relative change in imports (exports) between two countries is a sum of the relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.

Voltage-Gated Lipid Ion Channels

PubMed Central

Blicher, Andreas; Heimburg, Thomas

2013-01-01

Synthetic lipid membranes can display channel-like ion conduction events even in the absence of proteins. We show here that these events are voltage-gated with a quadratic voltage dependence as expected from electrostatic theory of capacitors. To this end, we recorded channel traces and current histograms in patch-experiments on lipid membranes. We derived a theoretical current-voltage relationship for pores in lipid membranes that describes the experimental data very well when assuming an asymmetric membrane. We determined the equilibrium constant between closed and open state and the open probability as a function of voltage. The voltage-dependence of the lipid pores is found comparable to that of protein channels. Lifetime distributions of open and closed events indicate that the channel open distribution does not follow exponential statistics but rather power law behavior for long open times. PMID:23823188

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.

Principle of minimal work fluctuations.

PubMed

Xiao, Gaoyang; Gong, Jiangbin

2015-08-01

Understanding and manipulating work fluctuations in microscale and nanoscale systems are of both fundamental and practical interest. For example, in considering the Jarzynski equality 〈e-βW〉=e-βΔF, a change in the fluctuations of e-βW may impact how rapidly the statistical average of e-βW converges towards the theoretical value e-βΔF, where W is the work, β is the inverse temperature, and ΔF is the free energy difference between two equilibrium states. Motivated by our previous study aiming at the suppression of work fluctuations, here we obtain a principle of minimal work fluctuations. In brief, adiabatic processes as treated in quantum and classical adiabatic theorems yield the minimal fluctuations in e-βW. In the quantum domain, if a system initially prepared at thermal equilibrium is subjected to a work protocol but isolated from a bath during the time evolution, then a quantum adiabatic process without energy level crossing (or an assisted adiabatic process reaching the same final states as in a conventional adiabatic process) yields the minimal fluctuations in e-βW, where W is the quantum work defined by two energy measurements at the beginning and at the end of the process. In the classical domain where the classical work protocol is realizable by an adiabatic process, then the classical adiabatic process also yields the minimal fluctuations in e-βW. Numerical experiments based on a Landau-Zener process confirm our theory in the quantum domain, and our theory in the classical domain explains our previous numerical findings regarding the suppression of classical work fluctuations [G. Y. Xiao and J. B. Gong, Phys. Rev. E 90, 052132 (2014)].

Half-Heusler Alloys as Promising Thermoelectric Materials

NASA Astrophysics Data System (ADS)

Page, Alexander A.

This thesis describes Ph.D. research on the half-Heusler class of thermoelectric materials. Half-Heusler alloys are a versatile class of materials that have been studied for use in photovoltaics, phase change memory, and thermoelectric power generation. With respect to thermoelectric power generation, new approaches were recently developed in order to improve the thermoelectric figure of merit, ZT, of half-Heusler alloys. Two of the strategies discussed in this work are adding excess Ni within MNiSn (M = Ti, Zr, or Hf) compounds to form full-Heusler nanostructures and using isoelectronic substitution of Ti, Zr, and Hf in MNiSn compounds to create microscale grain boundaries. This work uses computational simulations based on density functional theory, combined with the cluster expansion method, to predict the stable phases of pseudo-binary and pseudo-ternary composition systems. Statistical mechanics methods were used to calculate temperature-composition phase diagrams that relate the equilibrium phases. It is shown that full-Heusler nanostructures are predicted to remain stable even at high temperatures, and the microscale grain boundaries observed in (Ti,Zr,Hf)NiSn materials are found to be thermodynamically unstable at equilibrium. A new strategy of combining MNiSn materials with ZrNiPb has also recently emerged, and theoretical and experimental work show that a solid solution of the two materials is stable.

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

DOE PAGES

Miloshevich, George; Lingam, Manasvi; Morrison, Philip J.

2017-01-16

Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHDmore » inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. Finally, the consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.« less

Applying Chaos Theory to Careers: Attraction and Attractors

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim E. H.

2007-01-01

This article presents the Chaos Theory of Careers with particular reference to the concepts of "attraction" and "attractors". Attractors are defined in terms of characteristic trajectories, feedback mechanisms, end states, ordered boundedness, reality visions and equilibrium and fluctuation. The identified types of attractors (point, pendulum,…

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.

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.

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.

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.

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

PubMed Central

Putz, Mihai V.

2009-01-01

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

PubMed

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics

NASA Astrophysics Data System (ADS)

Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco

2014-06-01

The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in the investigated system.

Observations and Thermochemical Calculations for Hot-Jupiter Atmospheres

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver; Cubillos, Patricio; Stemm, Madison

2015-01-01

I present Spitzer eclipse observations for WASP-14b and WASP-43b, an open source tool for thermochemical equilibrium calculations, and components of an open source tool for atmospheric parameter retrieval from spectroscopic data. WASP-14b is a planet that receives high irradiation from its host star, yet, although theory does not predict it, the planet hosts a thermal inversion. The WASP-43b eclipses have signal-to-noise ratios of ~25, one of the largest among exoplanets. To assess these planets' atmospheric composition and thermal structure, we developed an open-source Bayesian Atmospheric Radiative Transfer (BART) code. My dissertation tasks included developing a Thermochemical Equilibrium Abundances (TEA) code, implementing the eclipse geometry calculation in BART's radiative transfer module, and generating parameterized pressure and temperature profiles so the radiative-transfer module can be driven by the statistical module.To initialize the radiative-transfer calculation in BART, TEA calculates the equilibrium abundances of gaseous molecular species at a given temperature and pressure. It uses the Gibbs-free-energy minimization method with an iterative Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. The code is tested against the original method developed by White at al. (1958), the analytic method developed by Burrows and Sharp (1999), and the Newton-Raphson method implemented in the open-source Chemical Equilibrium with Applications (CEA) code. TEA, written in Python, is modular, documented, and available to the community via the open-source development site GitHub.com.Support for this work was provided by NASA Headquarters under the NASA Earth and Space Science Fellowship Program, grant NNX12AL83H, by NASA through an award issued by JPL/Caltech, and through the Science Mission Directorate's Planetary Atmospheres Program, grant NNX12AI69G.

Knowledge Management through the Equilibrium Pattern Model for Learning

NASA Astrophysics Data System (ADS)

Sarirete, Akila; Noble, Elizabeth; Chikh, Azeddine

Contemporary students are characterized by having very applied learning styles and methods of acquiring knowledge. This behavior is consistent with the constructivist models where students are co-partners in the learning process. In the present work the authors developed a new model of learning based on the constructivist theory coupled with the cognitive development theory of Piaget. The model considers the level of learning based on several stages and the move from one stage to another requires learners' challenge. At each time a new concept is introduced creates a disequilibrium that needs to be worked out to return back to its equilibrium stage. This process of "disequilibrium/equilibrium" has been analyzed and validated using a course in computer networking as part of Cisco Networking Academy Program at Effat College, a women college in Saudi Arabia. The model provides a theoretical foundation for teaching especially in a complex knowledge domain such as engineering and can be used in a knowledge economy.

Longitudinal magnetization dynamics in Heisenberg magnets: Spin Green functions approach (Review Article)

NASA Astrophysics Data System (ADS)

Krivoruchko, V. N.

2017-11-01

In spite of the fact that dynamical properties of magnets have been extensively studied over the past years, the longitudinal magnetization dynamics is still much less understood than transverse one even in the equilibrium state of a system. In this paper, we give a review of existing, based on quantum-mechanical approach, theoretical descriptions of the longitudinal magnetization dynamics for ferro-, ferri- and antiferromagnetic dielectrics. The aim is to reveal specific features of this type of magnetization vibrations under description a system within the framework of one of the basic model theory of magnetism—the Heisenberg model. Related experimental investigations as well as open questions are also briefly discussed. We hope that understanding of the longitudinal magnetization dynamics distinctive features in the equilibrium state have to be a reference point for a theory uncovering the physical mechanisms that govern ultrafast spin dynamics after femtosecond laser pulse demagnetization when a system is far beyond an equilibrium state.

Transport and equilibrium in field-reversed mirrors

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

Boyd, J.K.

Two plasma models relevant to compact torus research have been developed to study transport and equilibrium in field reversed mirrors. In the first model for small Larmor radius and large collision frequency, the plasma is described as an adiabatic hydromagnetic fluid. In the second model for large Larmor radius and small collision frequency, a kinetic theory description has been developed. Various aspects of the two models have been studied in five computer codes ADB, AV, NEO, OHK, RES. The ADB code computes two dimensional equilibrium and one dimensional transport in a flux coordinate. The AV code calculates orbit average integralsmore » in a harmonic oscillator potential. The NEO code follows particle trajectories in a Hill's vortex magnetic field to study stochasticity, invariants of the motion, and orbit average formulas. The OHK code displays analytic psi(r), B/sub Z/(r), phi(r), E/sub r/(r) formulas developed for the kinetic theory description. The RES code calculates resonance curves to consider overlap regions relevant to stochastic orbit behavior.« less

Revisiting kinetic boundary conditions at the surface of fuel droplet hydrocarbons: An atomistic computational fluid dynamics simulation

PubMed Central

Nasiri, Rasoul

2016-01-01

The role of boundary conditions at the interface for both Boltzmann equation and the set of Navier-Stokes equations have been suggested to be important for studying of multiphase flows such as evaporation/condensation process which doesn’t always obey the equilibrium conditions. Here we present aspects of transition-state theory (TST) alongside with kinetic gas theory (KGT) relevant to the study of quasi-equilibrium interfacial phenomena and the equilibrium gas phase processes, respectively. A two-state mathematical model for long-chain hydrocarbons which have multi-structural specifications is introduced to clarify how kinetics and thermodynamics affect evaporation/condensation process at the surface of fuel droplet, liquid and gas phases and then show how experimental observations for a number of n-alkane may be reproduced using a hybrid framework TST and KGT with physically reasonable parameters controlling the interface, gas and liquid phases. The importance of internal activation dynamics at the surface of n-alkane droplets is established during the evaporation/condensation process. PMID:27215897

Many-Body Spectral Functions from Steady State Density Functional Theory.

PubMed

Jacob, David; Kurth, Stefan

2018-03-14

We propose a scheme to extract the many-body spectral function of an interacting many-electron system from an equilibrium density functional theory (DFT) calculation. To this end we devise an ideal scanning tunneling microscope (STM) setup and employ the recently proposed steady-state DFT formalism (i-DFT) which allows one to calculate the steady current through a nanoscopic region coupled to two biased electrodes. In our setup, one of the electrodes serves as a probe ("STM tip"), which is weakly coupled to the system we want to measure. In the ideal STM limit of vanishing coupling to the tip, the system is restored to quasi-equilibrium and the normalized differential conductance yields the exact equilibrium many-body spectral function. Calculating this quantity from i-DFT, we derive an exact relation expressing the interacting spectral function in terms of the Kohn-Sham one. As illustrative examples, we apply our scheme to calculate the spectral functions of two nontrivial model systems, namely the single Anderson impurity model and the Constant Interaction Model.

Statistical physics and economic fluctuations: do outliers exist?

NASA Astrophysics Data System (ADS)

Stanley, H. Eugene

2003-02-01

We present an overview of recent research applying ideas of statistical physics to try to better understand puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, phenomena that lie outside of patterns of statistical regularity. We review evidence consistent with the possibility that such outliers may not exist. This possibility is supported by recent analysis by Plerou et al. of a database containing the bid, ask, and sale price of each trade of every stock. Further, the data support the picture of economic fluctuations, due to Plerou et al., in which a financial market alternates between being in an “equilibrium phase” where market behavior is split roughly equally between buying and selling, and an “out-of-equilibrium phase” where the market is mainly either buying or selling.

Study on the Electronic Transport Properties of Zigzag GaN Nanotubes

NASA Astrophysics Data System (ADS)

Li, Enling; Wang, Xiqiang; Hou, Liping; Zhao, Danna; Dai, Yuanbin; Wang, Xuewen

2011-02-01

The electronic transport properties of zigzag GaN nanotubes (n, 0) (4 <= n <= 9) have been calculated using the density functional theory and non-equilibrium Green's functions method. Firstly, the density functional theory (DFT) is used to optimize and calculate the electronic structure of GaNNTs (n, 0) (4<=n<=9). Secondly, DFT and non-equilibrium Green function (NEGF) method are also used to predict the electronic transport properties of GaNNTs two-probe system. The results showed: there is a corresponding relation between the electronic transport properties and the valley of state density of each GaNNT. In addition, the volt-ampere curve of GaNNT is approximately linear.

Kinetics of polyelectrolyte adsorption

NASA Astrophysics Data System (ADS)

Cohen Stuart, M. A.; Hoogendam, C. W.; de Keizer, A.

1997-09-01

The kinetics of polyelectrolyte adsorption has been investigated theoretically. In analogy with Kramers' rate theory for chemical reactions we present a model which is based on the assumption that a polyelectrolyte encounters a barrier in its motion towards an adsorbing surface. The height of the barrier, which is of electrostatic origin, is calculated with a self-consistent-field (SCF) model. The salt concentration strongly affects the height of the barrier. At moderate salt concentrations (0953-8984/9/37/009/img1) equilibrium in the adsorption is attained; at low salt concentration (0953-8984/9/37/009/img2) equilibrium is not reached on the time scale of experiments. The attachment process shows resemblances to the classical DLVO theory.

Derivation of the Second Law of Thermodynamics from Boltzmann's Distribution Law.

ERIC Educational Resources Information Center

Nelson, P. G.

1988-01-01

Shows how the thermodynamic condition for equilibrium in an isolated system can be derived by the application of Boltzmann's law to a simple physical system. States that this derivation could be included in an introductory course on chemical equilibrium to help prepare students for a statistical mechanical treatment presented in the curriculum.…

Universality far from equilibrium: From superfluid Bose gases to heavy-ion collisions

DOE PAGES

Schlichting, S.; Venugopalan, R.; Berges, J.; ...

2015-02-10

Isolated quantum systems in extreme conditions can exhibit unusually large occupancies per mode. In addition, this over-population gives rise to new universality classes of many-body systems far from equilibrium. We present theoretical evidence that important aspects of non-Abelian plasmas in the ultra-relativistic limit admit a dual description in terms of a Bose condensed scalar field theory.

BINARY CORRELATIONS IN IONIZED GASES

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

Balescu, R.; Taylor, H.S.

1961-01-01

An equation of evolution for the binary distribution function in a classical homogeneous, nonequilibrium plasma was derived. It is shown that the asymptotic (long-time) solution of this equation is the Debye distribution, thus providing a rigorous dynamical derivation of the equilibrium distribution. This proof is free from the fundamental conceptual difficulties of conventional equilibrium derivations. Out of equilibrium, a closed formula was obtained for the long living correlations, in terms of the momentum distribution function. These results should form an appropriate starting point for a rigorous theory of transport phenomena in plasmas, including the effect of molecular correlations. (auth)

On magnetoelectric coupling at equilibrium in continua with microstructure

NASA Astrophysics Data System (ADS)

Romeo, Maurizio

2017-10-01

A theory of micromorphic continua, applied to electromagnetic solids, is exploited to study magnetoelectric effects at equilibrium. Microcurrents are modeled by the microgyration tensor of stationary micromotions, compatibly with the balance equations for null microdeformation. The equilibrium of the continuum subject to electric and magnetic fields is reformulated accounting for electric multipoles which are related to microdeformation by evolution equations. Polarization and magnetization are derived for uniform fields under the micropolar reduction in terms of microstrain and octupole structural parameters. Nonlinear dependance on the electromagnetic fields is evidenced, compatibly with known theoretical and experimental results on magnetoelectric coupling.

Distributed Nash Equilibrium Seeking for Generalized Convex Games with Shared Constraints

NASA Astrophysics Data System (ADS)

Sun, Chao; Hu, Guoqiang

2018-05-01

In this paper, we deal with the problem of finding a Nash equilibrium for a generalized convex game. Each player is associated with a convex cost function and multiple shared constraints. Supposing that each player can exchange information with its neighbors via a connected undirected graph, the objective of this paper is to design a Nash equilibrium seeking law such that each agent minimizes its objective function in a distributed way. Consensus and singular perturbation theories are used to prove the stability of the system. A numerical example is given to show the effectiveness of the proposed algorithms.

Students' Understanding of Acids/Bases in Organic Chemistry Contexts

ERIC Educational Resources Information Center

Cartrette, David P.; Mayo, Provi M.

2011-01-01

Understanding key foundational principles is vital to learning chemistry across different contexts. One such foundational principle is the acid/base behavior of molecules. In the general chemistry sequence, the Bronsted-Lowry theory is stressed, because it lends itself well to studying equilibrium and kinetics. However, the Lewis theory of…

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

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.

Non-equilibrium reactive flux: A unified framework for slow and fast reaction kinetics.

PubMed

Bose, Amartya; Makri, Nancy

2017-10-21

The flux formulation of reaction rate theory is recast in terms of the expectation value of the reactive flux with an initial condition that corresponds to a non-equilibrium, factorized reactant density. In the common case of slow reactive processes, the non-equilibrium expression reaches the plateau regime only slightly slower than the equilibrium flux form. When the reactants are described by a single quantum state, as in the case of electron transfer reactions, the factorized reactant density describes the true initial condition of the reactive process. In such cases, the time integral of the non-equilibrium flux expression yields the reactant population as a function of time, allowing characterization of the dynamics in cases where there is no clear separation of time scales and thus a plateau regime cannot be identified. The non-equilibrium flux offers a unified approach to the kinetics of slow and fast chemical reactions and is ideally suited to mixed quantum-classical methods.

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.

Kinetic theory for strongly coupled Coulomb systems

NASA Astrophysics Data System (ADS)

Dufty, James; Wrighton, Jeffrey

2018-01-01

The calculation of dynamical properties for matter under extreme conditions is a challenging task. The popular Kubo-Greenwood model exploits elements from equilibrium density-functional theory (DFT) that allow a detailed treatment of electron correlations, but its origin is largely phenomenological; traditional kinetic theories have a more secure foundation but are limited to weak ion-electron interactions. The objective here is to show how a combination of the two evolves naturally from the short-time limit for the generator of the effective single-electron dynamics governing time correlation functions without such limitations. This provides a theoretical context for the current DFT-related approach, the Kubo-Greenwood model, while showing the nature of its corrections. The method is to calculate the short-time dynamics in the single-electron subspace for a given configuration of the ions. This differs from the usual kinetic theory approach in which an average over the ions is performed as well. In this way the effective ion-electron interaction includes strong Coulomb coupling and is shown to be determined from DFT. The correlation functions have the form of the random-phase approximation for an inhomogeneous system but with renormalized ion-electron and electron-electron potentials. The dynamic structure function, density response function, and electrical conductivity are calculated as examples. The static local field corrections in the dielectric function are identified in this way. The current analysis is limited to semiclassical electrons (quantum statistical potentials), so important quantum conditions are excluded. However, a quantization of the kinetic theory is identified for broader application while awaiting its detailed derivation.

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.

A Van der Waals-like theory of plasma double layers

NASA Technical Reports Server (NTRS)

Katz, Ira; Davis, V. A.

1989-01-01

A theory describing plasma double layers in terms of multiple roots of the charge density expression is presented. The theory presented uses the fact that equilibrium plasmas shield small potential perturbations linearly; for high potentials, the shielding decreases. The approach is analogous to Van der Waals' theory of simple fluids in which inclusion of approximate expressions for both excluded volume and long range attractive forces sufficiently describes the first-order liquid-gas phase transition.

String Theory Methods for Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Nastase, Horatiu

2017-09-01

Preface; Acknowledgments; Introduction; Part I. Condensed Matter Models and Problems: 1. Lightning review of statistical mechanics, thermodynamics, phases and phase transitions; 2. Magnetism in solids; 3. Electrons in solids: Fermi gas vs. Fermi liquid; 4. Bosonic quasi-particles: phonons and plasmons; 5. Spin-charge separation in 1+1 dimensional solids: spinons and holons; 6. The Ising model and the Heisenberg spin chain; 7. Spin chains and integrable systems; 8. The thermodynamic Bethe ansatz; 9. Conformal field theories and quantum phase transitions; 10. Classical vs. quantum Hall effect; 11. Superconductivity: Landau-Ginzburg, London and BCS; 12. Topology and statistics: Berry and Chern-Simons, anyons and nonabelions; 13. Insulators; 14. The Kondo effect and the Kondo problem; 15. Hydrodynamics and transport properties: from Boltzmann to Navier-Stokes; Part II. Elements of General Relativity and String Theory: 16. The Einstein equation and the Schwarzschild solution; 17. The Reissner-Nordstrom and Kerr-Newman solutions and thermodynamic properties of black holes; 18. Extra dimensions and Kaluza-Klein; 19. Electromagnetism and gravity in various dimensions. Consistent truncations; 20. Gravity plus matter: black holes and p-branes in various dimensions; 21. Weak/strong coupling dualities in 1+1, 2+1, 3+1 and d+1 dimensions; 22. The relativistic point particle and the relativistic string; 23. Lightcone strings and quantization; 24. D-branes and gauge fields; 25. Electromagnetic fields on D-branes. Supersymmetry and N = 4 SYM. T-duality of closed strings; 26. Dualities and M theory; 27. The AdS/CFT correspondence: definition and motivation; Part III. Applying String Theory to Condensed Matter Problems: 28. The pp wave correspondence: string Hamiltonian from N = 4 SYM; 29. Spin chains from N = 4 SYM; 30. The Bethe ansatz: Bethe strings from classical strings in AdS; 31. Integrability and AdS/CFT; 32. AdS/CFT phenomenology: Lifshitz, Galilean and Schrodinger symmetries and their gravity duals; 33. Finite temperature and black holes; 34. Hot plasma equilibrium thermodynamics: entropy, charge density and chemical potential of strongly coupled theories; 35. Spectral functions and transport properties; 36. Dynamic and nonequilibrium properties of plasmas: electric transport, Langevin diffusion and thermalization via black hole quasi-normal modes; 37. The holographic superconductor; 38. The fluid-gravity correspondence: conformal relativistic fluids from black hole horizons; 39. Nonrelativistic fluids: from Einstein to Navier-Stokes and back; Part IV. Advanced Applications: 40. Fermi gas and liquid in AdS/CFT; 41. Quantum Hall effect from string theory; 42. Quantum critical systems and AdS/CFT; 43. Particle-vortex duality and ABJM vs. AdS4 X CP3 duality; 44. Topology and non-standard statistics from AdS/CFT; 45. DBI scalar model for QGP/black hole hydro- and thermo-dynamics; 46. Holographic entanglement entropy in condensed matter; 47. Holographic insulators; 48. Holographic strange metals and the Kondo problem; References; Index.

Quantum Rényi relative entropies affirm universality of thermodynamics.

PubMed

Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A K

2015-10-01

We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.

Stellar equilibrium configurations of compact stars in f ( R , T ) theory of gravity

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

Moraes, P.H.R.S.; Arbañil, José D.V.; Malheiro, M., E-mail: moraes.phrs@gmail.com, E-mail: arbanil@ita.br, E-mail: malheiro@ita.br

In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p =ωρ{sup 5/3} and p =0.28(ρ−4B), respectively, with ω and B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f ( R , T ) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrievedmore » for a certain limit of the theory. For the f ( R , T )= R +2λ T functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f ( R , T ) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.« less

Stellar equilibrium configurations of compact stars in f(R,T) theory of gravity

NASA Astrophysics Data System (ADS)

Moraes, P. H. R. S.; Arbañil, José D. V.; Malheiro, M.

2016-06-01

In this article we study the hydrostatic equilibrium configuration of neutron stars and strange stars, whose fluid pressure is computed from the equations of state p=ωρ5/3 and p=0.28(ρ-4Script B), respectively, with ω and Script B being constants and ρ the energy density of the fluid. We start by deriving the hydrostatic equilibrium equation for the f(R,T) theory of gravity, with R and T standing for the Ricci scalar and trace of the energy-momentum tensor, respectively. Such an equation is a generalization of the one obtained from general relativity, and the latter can be retrieved for a certain limit of the theory. For the f(R,T)=R+2λ T functional form, with λ being a constant, we find that some physical properties of the stars, such as pressure, energy density, mass and radius, are affected when λ is changed. We show that for a fixed central star energy density, the mass of neutron and strange stars can increase with λ. Concerning the star radius, it increases for neutron stars and it decreases for strange stars with the increment of λ. Thus, in f(R,T) theory of gravity we can push the maximum mass above the observational limits. This implies that the equation of state cannot be eliminated if the maximum mass within General Relativity lies below the limit given by observed pulsars.

Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking

PubMed Central

Iosa, Marco; Morone, Giovanni; Paolucci, Stefano

2017-01-01

Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability. Many different computational approaches have been used to explain human walking mechanisms, from pendular model to fractal approaches. A new perspective can be gained from using the principles developed in the field of Optimization theory and in particularly the branch of Game Theory. In particular we provide a new insight into human walking showing as the trade-off between advancement and equilibrium managed during walking has the same solution of the Ultimatum game, one of the most famous paradigms of game theory, and this solution is the golden ratio. The golden ratio is an irrational number that was found in many biological and natural systems self-organized in a harmonic, asymmetric, and fractal structure. Recently, the golden ratio has also been found as the equilibrium point between two players involved into the Ultimatum Game. It has been suggested that this result can be due to the fact that the golden ratio is perceived as the fairest asymmetric solution by the two players. The golden ratio is also the most common proportion between stance and swing phase of human walking. This approach may explain the importance of harmony in human walking, and provide new perspectives for developing quantitative assessment of human walking, efficient humanoid robotic walkers, and effective neurorobots for rehabilitation. PMID:29311890

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

Systems Models for Transportation Problems : Volume 1. Introducing a Systems Science for Transportation Planning.

DOT National Transportation Integrated Search

1976-03-01

This introductory portion of a system science for tranportation planning, which is based on the statistical physics of ensembles, a foundations laid on how statistical mechanics, equilibrium thermodynamics, and near equilbrium thermodynamics can be u...

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

Amorphous ices explained in terms of nonequilibrium phase transitions in supercooled water

NASA Astrophysics Data System (ADS)

Limmer, David; Chandler, David

2013-03-01

We analyze the phase diagram of supercooled water out-of-equilibrium using concepts from space-time thermodynamics and the dynamic facilitation theory of the glass transition, together with molecular dynamics simulations. We find that when water is driven out-of-equilibrium, it can exist in multiple amorphous states. In contrast, we find that when water is at equilibrium, it can exist in only one liquid state. The amorphous non-equilibrium states are solids, distinguished from the liquid by their lack of mobility, and distinguished from each other by their different densities and local structure. This finding explains the experimentally observed polyamorphism of water as a class of nonequilibrium phenomena involving glasses of different densities. While the amorphous solids can be long lived, they are thermodynamically unstable. When allowed to relax to equilibrium, they crystallize with pathways that pass first through liquid state configurations and then to ordered ice.

Testing Modified Gravity Theories via Wide Binaries and GAIA

NASA Astrophysics Data System (ADS)

Pittordis, Charalambos; Sutherland, Will

2018-06-01

The standard ΛCDM model based on General Relativity (GR) including cold dark matter (CDM) is very successful at fitting cosmological observations, but recent non-detections of candidate dark matter (DM) particles mean that various modified-gravity theories remain of significant interest. The latter generally involve modifications to GR below a critical acceleration scale ˜10-10 m s-2. Wide-binary (WB) star systems with separations ≳ 5 kAU provide an interesting test for modified gravity, due to being in or near the low-acceleration regime and presumably containing negligible DM. Here, we explore the prospects for new observations pending from the GAIA spacecraft to provide tests of GR against MOND or TeVes-like theories in a regime only partially explored to date. In particular, we find that a histogram of (3D) binary relative velocities, relative to equilibrium circular velocity predicted from the (2D) projected separation predicts a rather sharp feature in this distribution for standard gravity, with an 80th (90th) percentile value close to 1.025 (1.14) with rather weak dependence on the eccentricity distribution. However, MOND/TeVeS theories produce a shifted distribution, with a significant increase in these upper percentiles. In MOND-like theories without an external field effect, there are large shifts of order unity. With the external field effect included, the shifts are considerably reduced to ˜0.04 - 0.08, but are still potentially detectable statistically given reasonably large samples and good control of contaminants. In principle, followup of GAIA-selected wide binaries with ground-based radial velocities accurate to ≲ 0.03 { km s^{-1}} should be able to produce an interesting new constraint on modified-gravity theories.

On the universal stellar law

NASA Astrophysics Data System (ADS)

Krot, Alexander

In this work, we consider a statistical theory of gravitating spheroidal bodies to derive and develop the universal stellar law for extrasolar systems. Previously, the statistical theory for a cosmogonic body forming (so-called spheroidal body)has been proposed [1-3]. This theory starts from the conception for forming a spheroidal body inside a gas-dust protoplanetary nebula; it permits us to derive the form of distribution functions, mass density, gravitational potentials and strengths both for immovable and rotating spheroidal bodies as well as to find the distribution function of specific angular momentum[1-3]. If we start from the conception for forming a spheroidal body as a protostar (in particular, proto-Sun) inside a prestellar (presolar) nebula then the derived distribution functions of particle (as well as the mass density of an immovable spheroidal body) characterizes the first stage of evolution: from a prestellar molecular cloud (the presolar nebula) to the forming core of protostar (the proto-Sun) together with its shell as a stellar nebula (the solar nebula). This work derives the equation of state of an ideal stellar substance based on conception of gravitating spheroidal body. Using this equation, we obtain the universal stellar law (USL) for the planetary systems connecting temperature, size and mass of each of stars. This work also considers the Solar corona in the connection with USL. Then it is accounting under calculation of the ratio of temperature of the Solar corona to effective temperature of the Sun’ surfaceand modification of USL. To test justice of the modified USLfor different types of stars, the temperature of stellar corona is estimated. The prediction of parameters of stars is carrying out by means of the modified USL,as well as the Hertzsprung-Russell’s dependence [5-7]is derivedby means of USL directly. This paper also shows that knowledge of some characteristics for multi-planet extrasolar systems refines own parameters of stars. In this connection, comparison with estimations of temperatures using of the regression dependences for multi-planet extrasolar systems [8] testifies the obtained results entirely. References 1. Krot, A.M.:2009, A statistical approach to investigate the formation of the solar system. Chaos, Solitons and Fractals41(3), 1481-1500. 2. Krot, A.M.:2012, A models of forming planets and distribution of planetary distances and orbits in the solar system based on the statistical theory of spheroidal bodies. In:Solar System: Structure, Formation and Exploration, ch.9 (Ed. by Matteo de Rossi). New York, Nova Science Publishers, pp. 201-264. - ISBN: 978-1-62100-057-0. 3. Krot, A. M.:2012, A statistical theory of formation of gravitating cosmogonicbodies. Minsk,Bel. Navuka, 4. 448 p. - ISBN 978-985-08-1442-5 [monograph in Russian]. 5. Eddington, A.S.: 1916,On the radiative equilibrium of the stars.Mon. Not. Roy. Astron. Soc.84 (7), 525-528. 6. Jeans, J.: 1929, Astronomy and cosmogony. Cambridge, University Press. 7. Chandrasekhar, S.:1939, An introduction to the study of stellar structure.Cambridge, University Press. 8. Pintr, P., Peřinová, V., Lukš, A., Pathak, A.:2013, Statistical and regression analyses of detected extrasolar systems. Planetary and Space Science, 75(1), 37-45.

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.

Emergent dynamic structures and statistical law in spherical lattice gas automata.

PubMed

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Emergent dynamic structures and statistical law in spherical lattice gas automata

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Statistical Physics of Adaptation

DTIC Science & Technology

2016-08-23

Statistical Physics of Adaptation Nikolay Perunov, Robert A. Marsland, and Jeremy L. England Department of Physics , Physics of Living Systems Group...Subject Areas: Biological Physics , Complex Systems, Statistical Physics I. INTRODUCTION It has long been understood that nonequilibrium driving can...equilibrium may appear to have been specially selected for physical properties connected to their ability to absorb work from the particular driving environment

Topics in Non-Equilibrium Dynamics and the Emergence of Spacetime

NASA Astrophysics Data System (ADS)

Engelhardt, Dalit

The Anti-de Sitter / Conformal Field Theory (AdS/CFT) correspondence that arises in string theory has had implications for the study of phenomena across a range of subfields in physics, from spacetime geometry to the behavior of condensed matter systems. Two major themes that have featured prominently in these investigations have been the behavior of systems out of equilibrium, and the emergence of spacetime. In this thesis, aspects of these themes are considered and analyzed. The question of equilibration and thermalization in 2D conformal field theories is addressed and refined via a number of observations about local versus global thermalization in such systems, the validity of particular diagnostics of thermalization, the dependence of the equilibration behavior of a conformal field theory on its operator spectrum, and the holographic dual of the generalized Gibbs ensemble that is of interest in studies of equilibration in systems with a large number of conserved quantities. A formalism for analyzing the non-equilibrium dynamics of 1+1-dimensional conformal field theories is discussed, and its physical relevance is motivated with an example connecting such a system to an experimental system that exhibited unusual equilibration behavior. Qualitative agreement is demonstrated between the CFT picture and the experimental observations. The emergence of spacetime geometry from quantum entanglement, while largely a byproduct of considerations from holographic dualities, has also been proposed to have a direct, non-holographic manifestation. Here a particular realization of such a direct emergence is presented through a demonstration that, in the presence of quantum entanglement alone, certain observations of electric fields in the entangled system appear qualitatively the same as the corresponding observations in a physically-connected geometric spacetime, so that the entanglement effectively mimics particular features associated with geometric connectivity.

Effects of Equilibrium Toroidal Flow on Locked Mode and Plasma Response in a Tokamak

NASA Astrophysics Data System (ADS)

Zhu, Ping; Huang, Wenlong; Yan, Xingting

2016-10-01

It is widely believed that plasma flow plays significant roles in regulating the processes of mode locking and plasma response in a tokamak in presence of external resonant magnetic perturbations (RMPs). Recently a common analytic relation for both locked mode and plasma response has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance. The analytic relation predicts the size of the magnetic island of a locked mode or a static nonlinear plasma response for a given RMP amplitude, and rigorously proves a screening effect of the equilibrium toroidal flow. To test the theory, we solve for the locked mode and the nonlinear plasma response in presence of RMP for a circular-shaped limiter tokamak equilibrium with constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. The comparison between the simulation results and the theory prediction, in terms of the quantitative screening effects of equilibrium toroidal flow, will be reported and discussed. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.