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.

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.

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...

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

NASA Technical Reports Server (NTRS)

Jayaraman, Vegnesh; Liu, Yen; Panesi, Marco

2017-01-01

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

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.

Physics-based statistical learning approach to mesoscopic model selection.

PubMed

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

2015-11-01

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

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.

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

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

NASA Astrophysics Data System (ADS)

Chodera, John D.; Noé, Frank

2010-09-01

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

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.

Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Particle Sorting and Motility Out of Equilibrium

NASA Astrophysics Data System (ADS)

Sandford, Cato

The theory of equilibrium statistical physics, formulated over a century ago, provides an excellent description of physical systems which have reached a static, relaxed state. Such systems can be loosely thought of as maximally disordered, in keeping with the Second Law of Thermodynamics which states that a thermal system in equilibrium has reached a state of highest entropy. However, many entities in the world around us maintain themselves in an remarkably ordered and dynamic state, and must pay for this by producing entropy in their surroundings. Organisms, for example, convert chemical energy (food) into heat, which is then dumped into the environment, raising its entropy. Systems which produce entropy through any mechanism must be described by theories of non-equilibrium statistical physics, for which there currently exists no unified framework or ontology. Here we examine two specific cases of non-equilibrium phenomena from a theoretical perspective. First, we explore the behaviour of microscopic particles which continually dissipate energy to propel themselves through their environment. Second, we consider how devices which distinguish between different types of particles can exploit non-equilibrium processes to enhance their performance. For the case of self-propelled particles, we consider a theoretical model where the particle's propulsion force has "memory"--it is a random process whose instantaneous value depends on its past evolution. This introduces a persistence in the particle's motion, and requires the dissipation of energy into its surroundings. These particles are found to exhibit a variety of behaviours forbidden in equilibrium systems: for instance they may cluster around barriers, exert unbalanced forces, and sustain steady flows through space. We develop the understanding of these particles' dynamics through a combination of explicit calculations, approximations and numerical simulation which characterise and quantify their non-equilibrium behaviour. The second situation investigated concerns the physics of particle-sorting, which is fundamental to biological systems. We introduce a number of model devices designed to distinguish between and segregate two species of particles, and analyse how the quality and speed of their operation may be influenced by providing them with an energy source which pushes them out of equilibrium. We identify different physical regimes, where our devices may consume energy to deliver better results or deliver them faster or both; and we furthermore connect the broader theory of particle sorting to the fundamental theoretical framework of statistical physics.

Strongly magnetized classical plasma models

NASA Technical Reports Server (NTRS)

Montgomery, D. C.

1972-01-01

The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.

The non-equilibrium nature of culinary evolution

NASA Astrophysics Data System (ADS)

Kinouchi, Osame; Diez-Garcia, Rosa W.; Holanda, Adriano J.; Zambianchi, Pedro; Roque, Antonio C.

2008-07-01

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

Network Polymers Formed Under Nonideal Conditions.

DTIC Science & Technology

1986-12-01

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

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.

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.

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.

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

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

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

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

Analysis of non-equilibrium phenomena in inductively coupled plasma generators

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Mixed-order phase transition in a minimal, diffusion-based spin model.

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

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.

Controlling species richness in spin-glass model ecosystems

NASA Astrophysics Data System (ADS)

Poderoso, Fábio C.; Fontanari, José F.

2006-11-01

Within the framework of the random replicator model of ecosystems, we use equilibrium statistical mechanics tools to study the effect of manipulating the ecosystem so as to guarantee that a fixed fraction of the surviving species at equilibrium display a predefined set of characters (e.g., characters of economic value). Provided that the intraspecies competition is not too weak, we find that the consequence of such intervention on the ecosystem composition is a significant increase on the number of species that become extinct, and so the impoverishment of the ecosystem.

Galactic Abundance Gradients fro IR Fine Strucuture LInes in Compact H II regions

NASA Technical Reports Server (NTRS)

Afflerbach, A.; Churchwell, E.; Werner, M. W.

1996-01-01

We present observations of the [S III]19(micro)m, [O III]52 and 88(micro)m, and [N III]57(micro)m lines toward 18 compact and ultracompact (UC) H II regions. These data were combined with data from the literature and high-resolution radio continuum maps to construct detailed statistical equilibrium and ionization equilibrium models of 34 compact H II regions located at galactocentric distances (Dg)0-12kpc. Our models simultaneously fit the observed IR fine-structure lines and high-resolution radio continuum maps.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

Probability of identity by descent in metapopulations.

PubMed Central

Kaj, I; Lascoux, M

1999-01-01

Equilibrium probabilities of identity by descent (IBD), for pairs of genes within individuals, for genes between individuals within subpopulations, and for genes between subpopulations are calculated in metapopulation models with fixed or varying colony sizes. A continuous-time analog to the Moran model was used in either case. For fixed-colony size both propagule and migrant pool models were considered. The varying population size model is based on a birth-death-immigration (BDI) process, to which migration between colonies is added. Wright's F statistics are calculated and compared to previous results. Adding between-island migration to the BDI model can have an important effect on the equilibrium probabilities of IBD and on Wright's index. PMID:10388835

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.

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

NASA Astrophysics Data System (ADS)

Goldsworthy, M. J.

2012-10-01

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

Random bursts determine dynamics of active filaments.

PubMed

Weber, Christoph A; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S; Bausch, Andreas R; Frey, Erwin

2015-08-25

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model.

Random bursts determine dynamics of active filaments

PubMed Central

Weber, Christoph A.; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S.; Bausch, Andreas R.; Frey, Erwin

2015-01-01

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system’s dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. PMID:26261319

Data Needs and Modeling of the Upper Atmosphere

NASA Astrophysics Data System (ADS)

Brunger, M. J.; Campbell, L.

2007-04-01

We present results from our enhanced statistical equilibrium and time-step codes for atmospheric modeling. In particular we use these results to illustrate the role of electron-driven processes in atmospheric phenomena and the sensitivity of the model results to data inputs such as integral cross sections, dissociative recombination rates and chemical reaction rates.

Statistical mechanics explanation for the structure of ocean eddies and currents

NASA Astrophysics Data System (ADS)

Venaille, A.; Bouchet, F.

2010-12-01

The equilibrium statistical mechanics of two dimensional and geostrophic flows predicts the outcome for the large scales of the flow, resulting from the turbulent mixing. This theory has been successfully applied to describe detailed properties of Jupiter's Great Red Spot. We discuss the range of applicability of this theory to ocean dynamics. It is able to reproduce mesoscale structures like ocean rings. It explains, from statistical mechanics, the westward drift of rings at the speed of non dispersive baroclinic waves, and the recently observed (Chelton and col.) slower northward drift of cyclonic eddies and southward drift of anticyclonic eddies. We also uncover relations between strong eastward mid-basin inertial jets, like the Kuroshio extension and the Gulf Stream, and statistical equilibria. We explain under which conditions such strong mid-basin jets can be understood as statistical equilibria. We claim that these results are complementary to the classical Sverdrup-Munk theory: they explain the inertial part basin dynamics, the jets structure and location, using very simple theoretical arguments. References: A. VENAILLE and F. BOUCHET, Ocean rings and jets as statistical equilibrium states, submitted to JPO F. BOUCHET and A. VENAILLE, Statistical mechanics of two-dimensional and geophysical flows, arxiv ...., submitted to Physics Reports P. BERLOFF, A. M. HOGG, W. DEWAR, The Turbulent Oscillator: A Mechanism of Low- Frequency Variability of the Wind-Driven Ocean Gyres, Journal of Physical Oceanography 37 (2007) 2363-+. D. B. CHELTON, M. G. SCHLAX, R. M. SAMELSON, R. A. de SZOEKE, Global observations of large oceanic eddies, Geo. Res. Lett.34 (2007) 15606-+ b) and c) are snapshots of streamfunction and potential vorticity (red: positive values; blue: negative values) in the upper layer of a three layer quasi-geostrophic model of a mid-latitude ocean basin (from Berloff and co.). a) Streamfunction predicted by statistical mechanics. Even in an out-equilibrium situation like this one, equilibrium statistical mechanics predicts remarkably the overall qualitative flow structure. Observation of westward drift of ocean eddies and of slower northward drift of cyclones and southward drift of anticyclones by Chelton and co. We explain these observations from statistical mechanics.

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.

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.

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.

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.

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

NASA Astrophysics Data System (ADS)

Dettmer, Simon L.; Berg, Johannes

2018-02-01

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

Stochastic cycle selection in active flow networks

NASA Astrophysics Data System (ADS)

Woodhouse, Francis; Forrow, Aden; Fawcett, Joanna; Dunkel, Jorn

2016-11-01

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. By connecting concepts from lattice field theory, graph theory and transition rate theory, we show how topology controls dynamics in a generic model for actively driven flow on a network. Through theoretical and numerical analysis we identify symmetry-based rules to classify and predict the selection statistics of complex flow cycles from the network topology. Our conceptual framework is applicable to a broad class of biological and non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models.

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.

"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.

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.

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.

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.

Combustion Technology for Incinerating Wastes from Air Force Industrial Processes.

DTIC Science & Technology

1984-02-01

The assumption of equilibrium between environmental compartments. * The statistical extrapolations yielding "safe" doses of various constituents...would be contacted to identify the assumptions and data requirements needed to design, construct and implement the model. The model’s primary objective...Recovery Planning Model (RRPLAN) is described. This section of the paper summarizes the model’s assumptions , major components and modes of operation

Is “morphodynamic equilibrium” an oxymoron?

USGS Publications Warehouse

Zhou, Zeng; Coco, Giovanni; Townend, Ian; Olabarrieta, Maitane; van der Wegen, Mick; Gong, Zheng; D'Alpaos, Andrea; Gao, Shu; Jaffe, Bruce E.; Gelfenbaum, Guy R.; He, Qing; Wang, Yaping; Lanzoni, Stefano; Wang, Zhengbing; Winterwerp, Han; Zhang, Changkuan

2017-01-01

Morphodynamic equilibrium is a widely adopted yet elusive concept in the field of geomorphology of coasts, rivers and estuaries. Based on the Exner equation, an expression of mass conservation of sediment, we distinguish three types of equilibrium defined as static and dynamic, of which two different types exist. Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use. The choice of a temporal scale is imperative to analyse the type of equilibrium. We discuss the difference between morphodynamic equilibrium in the “real world” (nature) and the “virtual world” (model). Modelling studies rely on simplifications of the real world and lead to understanding of process interactions. A variety of factors affect the use of virtual-world predictions in the real world (e.g., variability in environmental drivers and variability in the setting) so that the concept of morphodynamic equilibrium should be mathematically unequivocal in the virtual world and interpreted over the appropriate spatial and temporal scale in the real world. We draw examples from estuarine settings which are subject to various governing factors which broadly include hydrodynamics, sedimentology and landscape setting. Following the traditional “tide-wave-river” ternary diagram, we summarize studies to date that explore the “virtual world”, discuss the type of equilibrium reached and how it relates to the real world.

Energy flow in non-equilibrium conformal field theory

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2012-09-01

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

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

DOE PAGES

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

2018-01-11

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

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

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

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

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

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

Solid/liquid extraction equilibria of phenolic compounds with trioctylphosphine oxide impregnated in polymeric membranes.

PubMed

Praveen, Prashant; Loh, Kai-Chee

2016-06-01

Trioctylphosphine oxide based extractant impregnated membranes (EIM) were used for extraction of phenol and its methyl, hydroxyl and chloride substituted derivatives. The distribution coefficients of the phenols varied from 2 to 234, in the order of 1-napthol > p-chlorophenol > m-cresol > p-cresol > o-cresol > phenol > catechol > pyrogallol > hydroquinone, when initial phenols loadings was varied in 100-2000 mg/L. An extraction model, based on the law of mass action, was formulated to predict the equilibrium distribution of the phenols. The model was in excellent agreement (R(2) > 0.97) with the experimental results at low phenols concentrations (<800 mg/L). At higher phenols loadings though, Langmuir isotherm was better suited for equilibrium prediction (R(2) > 0.95), which signified high mass transfer resistance in the EIMs. Examination of the effects of ring substitution on equilibrium, and bivariate statistical analysis between the amounts of phenols extracted into the EIMs and factors affecting phenols interaction with TOPO, indicated the dominant role of hydrophobicity in equilibrium determination. These results improve understanding of the solid/liquid equilibrium process between phenols and the EIMs, and these will be useful in designing phenol recovery process from wastewater. Copyright © 2016 Elsevier Ltd. All rights reserved.

Statistical equilibrium calculations for silicon in early-type model stellar atmospheres

NASA Technical Reports Server (NTRS)

Kamp, L. W.

1976-01-01

Line profiles of 36 multiplets of silicon (Si) II, III, and IV were computed for a grid of model atmospheres covering the range from 15,000 to 35,000 K in effective temperature and 2.5 to 4.5 in log (gravity). The computations involved simultaneous solution of the steady-state statistical equilibrium equations for the populations and of the equation of radiative transfer in the lines. The variables were linearized, and successive corrections were computed until a minimal accuracy of 1/1000 in the line intensities was reached. The common assumption of local thermodynamic equilibrium (LTE) was dropped. The model atmospheres used also were computed by non-LTE methods. Some effects that were incorporated into the calculations were the depression of the continuum by free electrons, hydrogen and ionized helium line blocking, and auto-ionization and dielectronic recombination, which later were found to be insignificant. Use of radiation damping and detailed electron (quadratic Stark) damping constants had small but significant effects on the strong resonance lines of Si III and IV. For weak and intermediate-strength lines, large differences with respect to LTE computations, the results of which are also presented, were found in line shapes and strengths. For the strong lines the differences are generally small, except for the models at the hot, low-gravity extreme of our range. These computations should be useful in the interpretation of the spectra of stars in the spectral range B0-B5, luminosity classes III, IV, and V.

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.

Photocatalytic TMO-NMs adsorbent: Temperature-Time dependent Safranine degradation, sorption study validated under optimized effective equilibrium models parameter with standardized statistical analysis

PubMed Central

Wahab, Rizwan; Khan, Farheen; Kaushik, Nagendra Kumar; Musarrat, Javed; Al-Khedhairy, Abdulaziz A.

2017-01-01

In this paper, chemically synthesized copper oxide nanoparticles (CuO-NPs), were employed for two processes: one is photocatalytic degradation and second one adsorption for the sorption of safranine (SA) dye in an aqueous medium at pH = 12.01. The optimized analytes amount (nano-adsorbent = 0.10 g, conc. range of SA dye 56.13 ppm to 154.37 ppm, pH = 12.01, temperature 303 K) reached to equilibrium point in 80 min, which acquired for chemical adsorption-degradation reactions. The degredated SA dye data’s recorded by UV-visible spectroscopy for the occurrence of TMO-NMs of CuO-NPs at anticipated period of interval. The feasible performance of CuO-NPs was admirable, shows good adsorption capacity qm = 53.676 mg g−1 and most convenient to best fitted results establish by linear regression equation, corresponded for selected kinetic model (pseudo second order (R2 = 0.9981), equilibrium isotherm models (Freundlich, Langmuir, Dubnin-Radushkevich (D-R), Temkin, H-J and Halsey), and thermodynamic parameters (∆H° = 75461.909 J mol−1, ∆S° = 253.761 J mol−1, ∆G° = −1427.93 J mol−1, Ea = 185.142 J mol−1) with error analysis. The statistical study revealed that CuO-NPs was an effective adsorbent certified photocatalytic efficiency (η = 84.88%) for degradation of SA dye, exhibited more feasibility and good affinity toward adsorbate, the sorption capacity increases with increased temperature at equilibrium point. PMID:28195174

Effects of sample size, number of markers, and allelic richness on the detection of spatial genetic pattern

USGS Publications Warehouse

Landguth, Erin L.; Gedy, Bradley C.; Oyler-McCance, Sara J.; Garey, Andrew L.; Emel, Sarah L.; Mumma, Matthew; Wagner, Helene H.; Fortin, Marie-Josée; Cushman, Samuel A.

2012-01-01

The influence of study design on the ability to detect the effects of landscape pattern on gene flow is one of the most pressing methodological gaps in landscape genetic research. To investigate the effect of study design on landscape genetics inference, we used a spatially-explicit, individual-based program to simulate gene flow in a spatially continuous population inhabiting a landscape with gradual spatial changes in resistance to movement. We simulated a wide range of combinations of number of loci, number of alleles per locus and number of individuals sampled from the population. We assessed how these three aspects of study design influenced the statistical power to successfully identify the generating process among competing hypotheses of isolation-by-distance, isolation-by-barrier, and isolation-by-landscape resistance using a causal modelling approach with partial Mantel tests. We modelled the statistical power to identify the generating process as a response surface for equilibrium and non-equilibrium conditions after introduction of isolation-by-landscape resistance. All three variables (loci, alleles and sampled individuals) affect the power of causal modelling, but to different degrees. Stronger partial Mantel r correlations between landscape distances and genetic distances were found when more loci were used and when loci were more variable, which makes comparisons of effect size between studies difficult. Number of individuals did not affect the accuracy through mean equilibrium partial Mantel r, but larger samples decreased the uncertainty (increasing the precision) of equilibrium partial Mantel r estimates. We conclude that amplifying more (and more variable) loci is likely to increase the power of landscape genetic inferences more than increasing number of individuals.

Effects of sample size, number of markers, and allelic richness on the detection of spatial genetic pattern

USGS Publications Warehouse

Landguth, E.L.; Fedy, B.C.; Oyler-McCance, S.J.; Garey, A.L.; Emel, S.L.; Mumma, M.; Wagner, H.H.; Fortin, M.-J.; Cushman, S.A.

2012-01-01

The influence of study design on the ability to detect the effects of landscape pattern on gene flow is one of the most pressing methodological gaps in landscape genetic research. To investigate the effect of study design on landscape genetics inference, we used a spatially-explicit, individual-based program to simulate gene flow in a spatially continuous population inhabiting a landscape with gradual spatial changes in resistance to movement. We simulated a wide range of combinations of number of loci, number of alleles per locus and number of individuals sampled from the population. We assessed how these three aspects of study design influenced the statistical power to successfully identify the generating process among competing hypotheses of isolation-by-distance, isolation-by-barrier, and isolation-by-landscape resistance using a causal modelling approach with partial Mantel tests. We modelled the statistical power to identify the generating process as a response surface for equilibrium and non-equilibrium conditions after introduction of isolation-by-landscape resistance. All three variables (loci, alleles and sampled individuals) affect the power of causal modelling, but to different degrees. Stronger partial Mantel r correlations between landscape distances and genetic distances were found when more loci were used and when loci were more variable, which makes comparisons of effect size between studies difficult. Number of individuals did not affect the accuracy through mean equilibrium partial Mantel r, but larger samples decreased the uncertainty (increasing the precision) of equilibrium partial Mantel r estimates. We conclude that amplifying more (and more variable) loci is likely to increase the power of landscape genetic inferences more than increasing number of individuals. ?? 2011 Blackwell Publishing Ltd.

Extracting Aggregation Free Energies of Mixed Clusters from Simulations of Small Systems: Application to Ionic Surfactant Micelles.

PubMed

Zhang, X; Patel, L A; Beckwith, O; Schneider, R; Weeden, C J; Kindt, J T

2017-11-14

Micelle cluster distributions from molecular dynamics simulations of a solvent-free coarse-grained model of sodium octyl sulfate (SOS) were analyzed using an improved method to extract equilibrium association constants from small-system simulations containing one or two micelle clusters at equilibrium with free surfactants and counterions. The statistical-thermodynamic and mathematical foundations of this partition-enabled analysis of cluster histograms (PEACH) approach are presented. A dramatic reduction in computational time for analysis was achieved through a strategy similar to the selector variable method to circumvent the need for exhaustive enumeration of the possible partitions of surfactants and counterions into clusters. Using statistics from a set of small-system (up to 60 SOS molecules) simulations as input, equilibrium association constants for micelle clusters were obtained as a function of both number of surfactants and number of associated counterions through a global fitting procedure. The resulting free energies were able to accurately predict micelle size and charge distributions in a large (560 molecule) system. The evolution of micelle size and charge with SOS concentration as predicted by the PEACH-derived free energies and by a phenomenological four-parameter model fit, along with the sensitivity of these predictions to variations in cluster definitions, are analyzed and discussed.

Influence of non-local thermodynamic equilibrium and Zeeman effects on magnetic equilibrium reconstruction using spectral motional Stark effect diagnostic

NASA Astrophysics Data System (ADS)

Reimer, R.; Marchuk, O.; Geiger, B.; Mc Carthy, P. J.; Dunne, M.; Hobirk, J.; Wolf, R.; ASDEX Upgrade Team

2017-08-01

The Motional Stark Effect (MSE) diagnostic is a well established technique to infer the local internal magnetic field in fusion plasmas. In this paper, the existing forward model which describes the MSE data is extended by the Zeeman effect, fine-structure, and relativistic corrections in the interpretation of the MSE spectra for different experimental conditions at the tokamak ASDEX Upgrade. The contribution of the non-Local Thermodynamic Equilibrium (non-LTE) populations among the magnetic sub-levels and the Zeeman effect on the derived plasma parameters is different. The obtained pitch angle is changed by 3 ° … 4 ° and by 0 . 5 ° … 1 ° including the non-LTE and the Zeeman effects into the standard statistical MSE model. The total correction is about 4°. Moreover, the variation of the magnetic field strength is significantly changed by 2.2% due to the Zeeman effect only. While the data on the derived pitch angle still could not be tested against the other diagnostics, the results from an equilibrium reconstruction solver confirm the obtained values for magnetic field strength.

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

NASA Astrophysics Data System (ADS)

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

2013-06-01

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

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.

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

PubMed

Bianca, Carlo

2012-12-01

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

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

PubMed

Joy, Mark; Jones, Simon

2005-08-01

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

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

PubMed

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

2014-01-08

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

The effects of intraspecific competition and stabilizing selection on a polygenic trait.

PubMed Central

Bürger, Reinhard; Gimelfarb, Alexander

2004-01-01

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed. PMID:15280253

A first principles calculation and statistical mechanics modeling of defects in Al-H system

NASA Astrophysics Data System (ADS)

Ji, Min; Wang, Cai-Zhuang; Ho, Kai-Ming

2007-03-01

The behavior of defects and hydrogen in Al was investigated by first principles calculations and statistical mechanics modeling. The formation energy of different defects in Al+H system such as Al vacancy, H in institution and multiple H in Al vacancy were calculated by first principles method. Defect concentration in thermodynamical equilibrium was studied by total free energy calculation including configuration entropy and defect-defect interaction from low concentration limit to hydride limit. In our grand canonical ensemble model, hydrogen chemical potential under different environment plays an important role in determing the defect concentration and properties in Al-H system.

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.

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.

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.

Statistical mechanics of the Huxley-Simmons model

NASA Astrophysics Data System (ADS)

Caruel, M.; Truskinovsky, L.

2016-06-01

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971), 10.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

ON THE DYNAMICAL DERIVATION OF EQUILIBRIUM STATISTICAL MECHANICS

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

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

1960-12-01

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

Entropy in universes evolving from initial to final de Sitter eras

NASA Astrophysics Data System (ADS)

Mimoso, José P.; Pavón, Diego

2014-05-01

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

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

NASA Astrophysics Data System (ADS)

Mazilu, Irina; Gonzalez, Joshua

2008-03-01

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

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

Statistical simulation of the magnetorotational dynamo.

PubMed

Squire, J; Bhattacharjee, A

2015-02-27

Turbulence and dynamo induced by the magnetorotational instability (MRI) are analyzed using quasilinear statistical simulation methods. It is found that homogenous turbulence is unstable to a large-scale dynamo instability, which saturates to an inhomogenous equilibrium with a strong dependence on the magnetic Prandtl number (Pm). Despite its enormously reduced nonlinearity, the dependence of the angular momentum transport on Pm in the quasilinear model is qualitatively similar to that of nonlinear MRI turbulence. This demonstrates the importance of the large-scale dynamo and suggests how dramatically simplified models may be used to gain insight into the astrophysically relevant regimes of very low or high Pm.

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.

Water adsorption isotherms of carboxymethyl cellulose, guar, locust bean, tragacanth and xanthan gums.

PubMed

Torres, María D; Moreira, Ramón; Chenlo, Francisco; Vázquez, María J

2012-06-20

Water adsorption isotherms of carboxymethyl cellulose (CMC), guar gum (GG), locust bean gum (LBG), tragacanth gum (TG) and xanthan gum (XG) were determined at different temperatures (20, 35, 50, and 65°C) using a gravimetric method. Several saturated salt solutions were selected to obtain different water activities in the range from 0.09 to 0.91. Water adsorption isotherms of tested hydrocolloids were classified like type II isotherms. In all cases, equilibrium moisture content decreased with increasing temperature at each water activity value. Three-parameter Guggenheim-Anderson-de Boer (GAB) model was employed to fit the experimental data in the water activity range and statistical analysis indicated that this model gave satisfactory results. CMC and GG were the most and the least hygroscopic gums, respectively. Sorption heats decreased with increasing moisture content. Monolayer moisture content evaluated with GAB model was consistent with equilibrium conditions of maximum stability calculated from thermodynamic analysis of net integral entropy. Values of equilibrium relative humidity at 20°C are proposed to storage adequately the tested gums. Copyright © 2012 Elsevier Ltd. All rights reserved.

On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

NASA Astrophysics Data System (ADS)

Patriarchi, P.; Perinotto, M.

The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.

Spectrophotometry of comets Giacobini-Zinner and Halley

NASA Technical Reports Server (NTRS)

Tegler, Stephen C.; O'Dell, C. R.

1987-01-01

Optical window spectrophotometry was performed on comets Giacobini-Zinner and Halley over the interval 300-1000 nm. Band and band-sequence fluxes were obtained for the brightest features of OH, CN, NH, and C2, special care having been given to determinations of extinction, instrumental sensitivities, and corrections for Fraunhofer lines. C2 Swan band-sequence flux ratios were determined with unprecedented accuracy and compared with the predictions of the detailed equilibrium models of Krishna Swamy et al. (1977, 1979, 1981, and 1987). It is found that these band sequences do not agree with the predictions, which calls into question the assumptions made in deriving the model, namely resonance fluorescence statistical equilibrium. Suggestions are made as to how to resolve this discrepancy.

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.

Calculating phase equilibrium properties of plasma pseudopotential model using hybrid Gibbs statistical ensemble Monte-Carlo technique

NASA Astrophysics Data System (ADS)

Butlitsky, M. A.; Zelener, B. B.; Zelener, B. V.

2015-11-01

Earlier a two-component pseudopotential plasma model, which we called a “shelf Coulomb” model has been developed. A Monte-Carlo study of canonical NVT ensemble with periodic boundary conditions has been undertaken to calculate equations of state, pair distribution functions, internal energies and other thermodynamics properties of the model. In present work, an attempt is made to apply so-called hybrid Gibbs statistical ensemble Monte-Carlo technique to this model. First simulation results data show qualitatively similar results for critical point region for both methods. Gibbs ensemble technique let us to estimate the melting curve position and a triple point of the model (in reduced temperature and specific volume coordinates): T* ≈ 0.0476, v* ≈ 6 × 10-4.

Statistical thermodynamics of a two-dimensional relativistic gas.

PubMed

Montakhab, Afshin; Ghodrat, Malihe; Barati, Mahmood

2009-03-01

In this paper we study a fully relativistic model of a two-dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for x and y components of velocity in the rest frame (Gamma) as well as the moving frame (Gamma;{'}) . Our results confirm that Jüttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter beta for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).

Forgetfulness can help you win games.

PubMed

Burridge, James; Gao, Yu; Mao, Yong

2015-09-01

We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths can compete and coexist in a dynamical equilibrium. Our analytical formulation makes a connection to statistical urn models, and we show that temperature is mirrored by the agent's memory. Our simple model of memory may be incorporated into other game models with implications that we briefly discuss.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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

2018-01-07

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

Methods for modeling non-equilibrium degenerate statistics and quantum-confined scattering in 3D ensemble Monte Carlo transport simulations

NASA Astrophysics Data System (ADS)

Crum, Dax M.; Valsaraj, Amithraj; David, John K.; Register, Leonard F.; Banerjee, Sanjay K.

2016-12-01

Particle-based ensemble semi-classical Monte Carlo (MC) methods employ quantum corrections (QCs) to address quantum confinement and degenerate carrier populations to model tomorrow's ultra-scaled metal-oxide-semiconductor-field-effect-transistors. Here, we present the most complete treatment of quantum confinement and carrier degeneracy effects in a three-dimensional (3D) MC device simulator to date, and illustrate their significance through simulation of n-channel Si and III-V FinFETs. Original contributions include our treatment of far-from-equilibrium degenerate statistics and QC-based modeling of surface-roughness scattering, as well as considering quantum-confined phonon and ionized-impurity scattering in 3D. Typical MC simulations approximate degenerate carrier populations as Fermi distributions to model the Pauli-blocking (PB) of scattering to occupied final states. To allow for increasingly far-from-equilibrium non-Fermi carrier distributions in ultra-scaled and III-V devices, we instead generate the final-state occupation probabilities used for PB by sampling the local carrier populations as function of energy and energy valley. This process is aided by the use of fractional carriers or sub-carriers, which minimizes classical carrier-carrier scattering intrinsically incompatible with degenerate statistics. Quantum-confinement effects are addressed through quantum-correction potentials (QCPs) generated from coupled Schrödinger-Poisson solvers, as commonly done. However, we use these valley- and orientation-dependent QCPs not just to redistribute carriers in real space, or even among energy valleys, but also to calculate confinement-dependent phonon, ionized-impurity, and surface-roughness scattering rates. FinFET simulations are used to illustrate the contributions of each of these QCs. Collectively, these quantum effects can substantially reduce and even eliminate otherwise expected benefits of considered In0.53Ga0.47 As FinFETs over otherwise identical Si FinFETs despite higher thermal velocities in In0.53Ga0.47 As. It also may be possible to extend these basic uses of QCPs, however calculated, to still more computationally efficient drift-diffusion and hydrodynamic simulations, and the basic concepts even to compact device modeling.

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.

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

PubMed Central

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

2014-01-01

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

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

Selective gas capture via kinetic trapping

DOE PAGES

Kundu, Joyjit; Pascal, Tod; Prendergast, David; ...

2016-07-13

Conventional approaches to the capture of CO 2 by metal-organic frameworks focus on equilibrium conditions, and frameworks that contain little CO 2 in equilibrium are often rejected as carbon-capture materials. Here we use a statistical mechanical model, parameterized by quantum mechanical data, to suggest that metal-organic frameworks can be used to separate CO 2 from a typical flue gas mixture when used under nonequilibrium conditions. The origin of this selectivity is an emergent gas-separation mechanism that results from the acquisition by different gas types of different mobilities within a crowded framework. The resulting distribution of gas types within the frameworkmore » is in general spatially and dynamically heterogeneous. Our results suggest that relaxing the requirement of equilibrium can substantially increase the parameter space of conditions and materials for which selective gas capture can be effected.« less

Equilibrium statistical mechanics of self-consistent wave-particle system

NASA Astrophysics Data System (ADS)

Elskens, Yves

2005-10-01

The equilibrium distribution of N particles and M waves (e.g. Langmuir) is analysed in the weak-coupling limit for the self-consistent hamiltonian model H = ∑rpr^2 /(2m) + ∑jφjIj+ ɛ∑r,j(βj/ kj) (kjxr- θj) [1]. In the canonical ensemble, with temperature T and reservoir velocity v < jφj/kj, the wave intensities are almost independent and exponentially distributed, with expectation = kBT / (φj- kjv). These equilibrium predictions are in agreement with Monte Carlo samplings [2] and with direct simulations of the dynamics, indicating equivalence between canonical and microcanonical ensembles. [1] Y. Elskens and D.F. Escande, Microscopic dynamics of plasmas and chaos (IoP publishing, Bristol, 2003). [2] M-C. Firpo and F. Leyvraz, 30th EPS conf. contr. fusion and plasma phys., P-2.8 (2003).

Free Energy Minimization by Simulated Annealing with Applications to Lithospheric Slabs and Mantle Plumes

NASA Astrophysics Data System (ADS)

Bina, C. R.

An optimization algorithm based upon the method of simulated annealing is of utility in calculating equilibrium phase assemblages as functions of pressure, temperature, and chemical composi tion. Operating by analogy to the statistical mechanics of the chemical system, it is applicable both to problems of strict chemical equilibrium and to problems involving metastability. The method reproduces known phase diagrams and illustrates the expected thermal deflection of phase transitions in thermal models of subducting lithospheric slabs and buoyant mantle plumes. It reveals temperature-induced changes in phase transition sharpness and the stability of Fe-rich γ phase within an α+γ field in cold slab thermal models, and it suggests that transitions such as the possible breakdown of silicate perovskite to mixed oxides can amplify velocity anomalies.

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.

The Statistical Basis of Chemical Equilibria.

ERIC Educational Resources Information Center

Hauptmann, Siegfried; Menger, Eva

1978-01-01

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

Entropy Production and Fluctuation Theorems for Active Matter

NASA Astrophysics Data System (ADS)

Mandal, Dibyendu; Klymko, Katherine; DeWeese, Michael R.

2017-12-01

Active biological systems reside far from equilibrium, dissipating heat even in their steady state, thus requiring an extension of conventional equilibrium thermodynamics and statistical mechanics. In this Letter, we have extended the emerging framework of stochastic thermodynamics to active matter. In particular, for the active Ornstein-Uhlenbeck model, we have provided consistent definitions of thermodynamic quantities such as work, energy, heat, entropy, and entropy production at the level of single, stochastic trajectories and derived related fluctuation relations. We have developed a generalization of the Clausius inequality, which is valid even in the presence of the non-Hamiltonian dynamics underlying active matter systems. We have illustrated our results with explicit numerical studies.

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

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.

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.

VizieR Online Data Catalog: Supernova matter EOS (Buyukcizmeci+, 2014)

NASA Astrophysics Data System (ADS)

Buyukcizmeci, N.; Botvina, A. S.; Mishustin, I. N.

2017-03-01

The Statistical Model for Supernova Matter (SMSM) was developed in Botvina & Mishustin (2004, PhLB, 584, 233 ; 2010, NuPhA, 843, 98) as a direct generalization of the Statistical Multifragmentation Model (SMM; Bondorf et al. 1995, PhR, 257, 133). We treat supernova matter as a mixture of nuclear species, electrons, and photons in statistical equilibrium. The SMSM EOS tables cover the following ranges of control parameters: 1. Temperature: T = 0.2-25 MeV; for 35 T values. 2. Electron fraction Ye: 0.02-0.56; linear mesh of Ye = 0.02, giving 28 Ye values. It is equal to the total proton fraction Xp, due to charge neutrality. 3. Baryon number density fraction {rho}/{rho}0 = (10-8-0.32), giving 31 {rho}/{rho}0 values. (2 data files).

The chromospheres of late-type stars. I - Eridani as a test case of multiline modelling

NASA Technical Reports Server (NTRS)

Thatcher, John D.; Robinson, Richard D.; Rees, David E.

1991-01-01

A new model of the lower chromosphere of the dwarf K2 star Epsilon Eridani is derived by matching flux profiles of the Ca IR triplet lines 8498 and 8542 A H-alpha and H-beta lines and the Na D lines (all observed simultaneously at the AAT), and the Ca II K line. The coupled non-LTE equations of statistical equilibrium and radiative transfer are solved under the constraint of hydrostatic equilibrium using the Carlsson (1986) code. Within the framework of the model, the Na D lines are an important photospheric diagnostic, and the Ca IR triplet lines can be used to locate the temperature minimum. The computed H-alpha and H-beta depths are highly sensitive constraints on the transition zone gradients and base pressures allowing us to derive a pressure at the base of the transition zone of 0.9 dyn/cm.

Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves.

PubMed

Welch, Kyle J; Hastings-Hauss, Isaac; Parthasarathy, Raghuveer; Corwin, Eric I

2014-04-01

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

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

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

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

2016-03-28

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

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Conformal field theory out of equilibrium: a review

NASA Astrophysics Data System (ADS)

Bernard, Denis; Doyon, Benjamin

2016-06-01

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.

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.

Direct and Large Eddy Simulation of non-equilibrium wall-bounded turbulent flows

NASA Astrophysics Data System (ADS)

Park, Hee-Jun

2005-11-01

The performance of several existing SGS models in non-equilibrium wall-bounded turbulent flows is investigated through comparisons of LES and DNS. The test problem is a shear-driven three-dimensional turbulent channel flow at base Reτ˜210 established by impulsive motion of one of the channel walls in the spanwise direction with a spanwise velocity equal to 3/4 of the bulk mean velocity in the channel. The DNS and LES are performed using pseudo-spectral methods with resolutions of 128x128x129 and 32x64x65, respectively. The SGS models tested include the nonlinear Interactions Approximation model (NIA) [Haliloglu and Akhavan (2004)], the Dynamic Smagorinsky model (DSM) [Germano et al. (1991)], and the Dynamic Mixed Model (DMM) [Zang et al. (1993)]. The results show that NIA gives the best overall agreement with DNS. Both DMM and DSM over-predict the decay of the mean streamwise wall shear stress on the moving wall, while NIA gives results in close agreements with DNS. Similarly, NIA gives the best agreement with DNS in the prediction of the mean velocity, the higher-order turbulence statistics, and the lag angle between the mean shear and the turbulent shear stress. These results suggest that non-equilibrium wall-bounded turbulent flows can be accurately computed by LES with NIA as the SGS model.

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.

Long-ranged Fermi-Pasta-Ulam systems in thermal contact: Crossover from q-statistics to Boltzmann-Gibbs statistics

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee; Tsallis, Constantino

2017-04-01

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.

Uncertainty Quantification of Equilibrium Climate Sensitivity in CCSM4

NASA Astrophysics Data System (ADS)

Covey, C. C.; Lucas, D. D.; Tannahill, J.; Klein, R.

2013-12-01

Uncertainty in the global mean equilibrium surface warming due to doubled atmospheric CO2, as computed by a "slab ocean" configuration of the Community Climate System Model version 4 (CCSM4), is quantified using 1,039 perturbed-input-parameter simulations. The slab ocean configuration reduces the model's e-folding time when approaching an equilibrium state to ~5 years. This time is much less than for the full ocean configuration, consistent with the shallow depth of the upper well-mixed layer of the ocean represented by the "slab." Adoption of the slab ocean configuration requires the assumption of preset values for the convergence of ocean heat transport beneath the upper well-mixed layer. A standard procedure for choosing these values maximizes agreement with the full ocean version's simulation of the present-day climate when input parameters assume their default values. For each new set of input parameter values, we computed the change in ocean heat transport implied by a "Phase 1" model run in which sea surface temperatures and sea ice concentrations were set equal to present-day values. The resulting total ocean heat transport (= standard value + change implied by Phase 1 run) was then input into "Phase 2" slab ocean runs with varying values of atmospheric CO2. Our uncertainty estimate is based on Latin Hypercube sampling over expert-provided uncertainty ranges of N = 36 adjustable parameters in the atmosphere (CAM4) and sea ice (CICE4) components of CCSM4. Two-dimensional projections of our sampling distribution for the N(N-1)/2 possible pairs of input parameters indicate full coverage of the N-dimensional parameter space, including edges. We used a machine learning-based support vector regression (SVR) statistical model to estimate the probability density function (PDF) of equilibrium warming. This fitting procedure produces a PDF that is qualitatively consistent with the raw histogram of our CCSM4 results. Most of the values from the SVR statistical model are within ~0.1 K of the raw results, well below the inter-decile range inferred below. Independent validation of the fit indicates residual errors that are distributed about zero with a standard deviation of 0.17 K. Analysis of variance shows that the equilibrium warming in CCSM4 is mainly linear in parameter changes. Thus, in accord with the Central Limit Theorem of statistics, the PDF of the warming is approximately Gaussian, i.e. symmetric about its mean value (3.0 K). Since SVR allows for highly nonlinear fits, the symmetry is not an artifact of the fitting procedure. The 10-90 percentile range of the PDF is 2.6-3.4 K, consistent with earlier estimates from CCSM4 but narrower than estimates from other models, which sometimes produce a high-temperature asymmetric tail in the PDF. This work was performed under auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and was funded by LLNL's Uncertainty Quantification Strategic Initiative (Laboratory Directed Research and Development Project 10-SI-013).

Validation of chemistry models employed in a particle simulation method

NASA Technical Reports Server (NTRS)

Haas, Brian L.; Mcdonald, Jeffrey D.

1991-01-01

The chemistry models employed in a statistical particle simulation method, as implemented in the Intel iPSC/860 multiprocessor computer, are validated and applied. Chemical relaxation of five-species air in these reservoirs involves 34 simultaneous dissociation, recombination, and atomic-exchange reactions. The reaction rates employed in the analytic solutions are obtained from Arrhenius experimental correlations as functions of temperature for adiabatic gas reservoirs in thermal equilibrium. Favorable agreement with the analytic solutions validates the simulation when applied to relaxation of O2 toward equilibrium in reservoirs dominated by dissociation and recombination, respectively, and when applied to relaxation of air in the temperature range 5000 to 30,000 K. A flow of O2 over a circular cylinder at high Mach number is simulated to demonstrate application of the method to multidimensional reactive flows.

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.

Controlling reactivity of nanoporous catalyst materials by tuning reaction product-pore interior interactions: Statistical mechanical modeling

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

Wang, Jing; Ackerman, David M.; Lin, Victor S.-Y.

2013-04-02

Statistical mechanical modeling is performed of a catalytic conversion reaction within a functionalized nanoporous material to assess the effect of varying the reaction product-pore interior interaction from attractive to repulsive. A strong enhancement in reactivity is observed not just due to the shift in reaction equilibrium towards completion but also due to enhanced transport within the pore resulting from reduced loading. The latter effect is strongest for highly restricted transport (single-file diffusion), and applies even for irreversible reactions. The analysis is performed utilizing a generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reactionmore » and restricted transport.« less

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

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).

Long-range interacting systems in the unconstrained ensemble.

PubMed

Latella, Ivan; Pérez-Madrid, Agustín; Campa, Alessandro; Casetti, Lapo; Ruffo, Stefano

2017-01-01

Completely open systems can exchange heat, work, and matter with the environment. While energy, volume, and number of particles fluctuate under completely open conditions, the equilibrium states of the system, if they exist, can be specified using the temperature, pressure, and chemical potential as control parameters. The unconstrained ensemble is the statistical ensemble describing completely open systems and the replica energy is the appropriate free energy for these control parameters from which the thermodynamics must be derived. It turns out that macroscopic systems with short-range interactions cannot attain equilibrium configurations in the unconstrained ensemble, since temperature, pressure, and chemical potential cannot be taken as a set of independent variables in this case. In contrast, we show that systems with long-range interactions can reach states of thermodynamic equilibrium in the unconstrained ensemble. To illustrate this fact, we consider a modification of the Thirring model and compare the unconstrained ensemble with the canonical and grand-canonical ones: The more the ensemble is constrained by fixing the volume or number of particles, the larger the space of parameters defining the equilibrium configurations.

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.

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

NASA Astrophysics Data System (ADS)

Adib, Artur B.

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

On information, negentropy and H-theorem

NASA Astrophysics Data System (ADS)

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

1983-09-01

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

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.

Random dopant fluctuations and statistical variability in n-channel junctionless FETs

NASA Astrophysics Data System (ADS)

Akhavan, N. D.; Umana-Membreno, G. A.; Gu, R.; Antoszewski, J.; Faraone, L.

2018-01-01

The influence of random dopant fluctuations on the statistical variability of the electrical characteristics of n-channel silicon junctionless nanowire transistor (JNT) has been studied using three dimensional quantum simulations based on the non-equilibrium Green’s function (NEGF) formalism. Average randomly distributed body doping densities of 2 × 1019, 6 × 1019 and 1 × 1020 cm-3 have been considered employing an atomistic model for JNTs with gate lengths of 5, 10 and 15 nm. We demonstrate that by properly adjusting the doping density in the JNT, a near ideal statistical variability and electrical performance can be achieved, which can pave the way for the continuation of scaling in silicon CMOS technology.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Modelling the CO emission in southern Bok globules

NASA Astrophysics Data System (ADS)

Cecchi-Pestellini, Cesare; Casu, Silvia; Scappini, Flavio

2001-10-01

The analysis of the sample of southern globules investigated by Scappini et al. in the CO (4-3) transition has been extended using a statistical equilibrium-radiative transfer model and making use of the results of Bourke et al. and Henning & Launardt for those globules which are in common among these samples. CO column densities and excitation temperatures have been calculated and the results compared with a chemical model representative of the chemistry of a spherical dark cloud. In a number of cases the gas kinetic temperatures have been constrained.

Sample selection and spatial models of housing price indexes, and, A disequilibrium analysis of the U.S. gasoline market using panel data

NASA Astrophysics Data System (ADS)

Hu, Haixin

This dissertation consists of two parts. The first part studies the sample selection and spatial models of housing price index using transaction data on detached single-family houses of two California metropolitan areas from 1990 through 2008. House prices are often spatially correlated due to shared amenities, or when the properties are viewed as close substitutes in a housing submarket. There have been many studies that address spatial correlation in the context of housing markets. However, none has used spatial models to construct housing price indexes at zip code level for the entire time period analyzed in this dissertation to the best of my knowledge. In this paper, I study a first-order autoregressive spatial model with four different weighing matrix schemes. Four sets of housing price indexes are constructed accordingly. Gatzlaff and Haurin (1997, 1998) study the sample selection problem in housing index by using Heckman's two-step method. This method, however, is generally inefficient and can cause multicollinearity problem. Also, it requires data on unsold houses in order to carry out the first-step probit regression. Maximum likelihood (ML) method can be used to estimate a truncated incidental model which allows one to correct for sample selection based on transaction data only. However, convergence problem is very prevalent in practice. In this paper I adopt Lewbel's (2007) sample selection correction method which does not require one to model or estimate the selection model, except for some very general assumptions. I then extend this method to correct for spatial correlation. In the second part, I analyze the U.S. gasoline market with a disequilibrium model that allows lagged-latent variables, endogenous prices, and panel data with fixed effects. Most existing studies (see the survey of Espey, 1998, Energy Economics) of the gasoline market assume equilibrium. In practice, however, prices do not always adjust fast enough to clear the market. Equilibrium assumptions greatly simplify statistical inference, but are very restrictive and can produce conflicting estimates. For example, econometric models of markets that assume equilibrium often produce more elastic demand price elasticity than their disequilibrium counterparts (Holt and Johnson, 1989, Review of Economics and Statistics, Oczkowski, 1998, Economics Letters). The few studies that allow disequilibrium, however, have been limited to macroeconomic time-series data without lagged-latent variables. While time series data allows one to investigate national trends, it cannot be used to identify and analyze regional differences and the role of local markets. Exclusion of the lagged-latent variables is also undesirable because such variables capture adjustment costs and inter-temporal spillovers. Simulation methods offer tractable solutions to dynamic and panel data disequilibrium models (Lee, 1997, Journal of Econometrics), but assume normally distributed errors. This paper compares estimates of price/income elasticity and excess supply/demand across time periods, regions, and model specifications, using both equilibrium and disequilibrium methods. In the equilibrium model, I compare the within group estimator with Anderson and Hsiao's first-difference 2SLS estimator. In the disequilibrium model, I extend Amemiya's 2SLS by using Newey's efficient estimator with optimal instruments.

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.

Saturated and unsaturated salt transport in peat from a constructed fen

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Single molecule RNA folding studied with optical trapping

NASA Astrophysics Data System (ADS)

Vieregg, Jeffrey Robert

The RNA folding problem (predicting the equilibrium structure and folding pathway of an RNA molecule from its sequence) is one of the classic problems of biophysics. Recent discoveries of many new functions for RNA have increased its importance, and new instrumental techniques have provided new ways to characterize molecular behavior. In particular, optical trapping (optical tweezers) allows controlled mechanical force to be applied to single RNA molecules while their end-to-end extension is monitored in real time. This enables characterization of RNA folding dynamics at a level unreachable by traditional bulk methods. Furthermore, recent advances in statistical mechanics make it possible to recover equilibrium quantities such as free energy from reactions which occur away from equilibrium. This dissertation describes the application of optical trapping and non-equilibrium statistical mechanics to quantitatively characterize folding of RNA secondary structures. By measuring the folding free energy of several specially designed hairpins in solutions containing various amounts of sodium and potassium, we were able to determine that RNA secondary structure thermodynamics depends not only on monovalent cation concentration but also surprisingly, on species. We also investigated the temperature dependence of hairpin folding thermodynamics and kinetics, which provided a direct measurement of enthalpy and entropy for RNA folding at physiological temperatures. We found that the folding pathway was quite sensitive to both salt and temperature, as measured by the folding success rate of a biologically important hairpin from the HIV-1 viral genome. Finally, I discuss modeling of force-induced RNA folding and unfolding, as well as a series of efforts which have dramatically improved the performance of our optical trapping instrument.

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.

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

NASA Astrophysics Data System (ADS)

Keys, Aaron

2013-03-01

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

Capturing the Interaction Potential of Amyloidogenic Proteins

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

Javid, Nadeem; Vogtt, Karsten; Winter, Roland

2007-07-13

Experimentally derived static structure factors obtained for the aggregation-prone protein insulin were analyzed with a statistical mechanical model based on the Derjaguin-Landau-Verwey-Overbeek potential. The data reveal that the protein self-assembles into equilibrium clusters already at low concentrations. Furthermore, striking differences regarding interaction forces between aggregation-prone proteins such as insulin in the preaggregated regime and natively stable globular proteins are found.

Isotherms for Water Adsorption on Molecular Sieve 3A: Influence of Cation Composition

DOE PAGES

Lin, Ronghong; Ladshaw, Austin; Nan, Yue; ...

2015-06-16

This study is part of our continuing efforts to address engineering issues related to the removal of tritiated water from off-gases produced in used nuclear fuel reprocessing facilities. In the current study, adsorption equilibrium of water on molecular sieve 3A beads was investigated. Adsorption isotherms for water on the UOP molecular sieve 3A were measured by a continuous-flow adsorption system at 298, 313, 333, and 353 K. Experimental data collected were analyzed by the Generalized Statistical Thermodynamic Adsorption (GSTA) isotherm model. The K +/Na + molar ratio of this particular type of molecular sieve 3A was ~4:6. Our results showedmore » that the GSTA isotherm model worked very well to describe the equilibrium behavior of water adsorption on molecular sieve 3A. The optimum number of parameters for the current experimental data was determined to be a set of four equilibrium parameters. This result suggests that the adsorbent crystals contain four energetically distinct adsorption sites. In addition, it was found that water adsorption on molecular sieve 3A follows a three-stage adsorption process. This three-stage adsorption process confirmed different water adsorption sites in molecular sieve crystals. In addition, the second adsorption stage is significantly affected by the K +/Na + molar ratio. In this stage, the equilibrium adsorption capacity at a given water vapor pressure increases as the K +/Na + molar ratio increases.« less

A New Methodology for Open Pit Slope Design in Karst-Prone Ground Conditions Based on Integrated Stochastic-Limit Equilibrium Analysis

NASA Astrophysics Data System (ADS)

Zhang, Ke; Cao, Ping; Ma, Guowei; Fan, Wenchen; Meng, Jingjing; Li, Kaihui

2016-07-01

Using the Chengmenshan Copper Mine as a case study, a new methodology for open pit slope design in karst-prone ground conditions is presented based on integrated stochastic-limit equilibrium analysis. The numerical modeling and optimization design procedure contain a collection of drill core data, karst cave stochastic model generation, SLIDE simulation and bisection method optimization. Borehole investigations are performed, and the statistical result shows that the length of the karst cave fits a negative exponential distribution model, but the length of carbonatite does not exactly follow any standard distribution. The inverse transform method and acceptance-rejection method are used to reproduce the length of the karst cave and carbonatite, respectively. A code for karst cave stochastic model generation, named KCSMG, is developed. The stability of the rock slope with the karst cave stochastic model is analyzed by combining the KCSMG code and the SLIDE program. This approach is then applied to study the effect of the karst cave on the stability of the open pit slope, and a procedure to optimize the open pit slope angle is presented.

Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating

NASA Astrophysics Data System (ADS)

ChatÉ, H.; Manneville, P.

1992-01-01

Assessing the extent to which dynamical systems with many degrees of freedom can be described within a thermodynamics formalism is a problem that currently attracts much attention. In this context, synchronously updated regular lattices of identical, chaotic elements with local interactions are promising models for which statistical mechanics may be hoped to provide some insights. This article presents a large class of cellular automata rules and coupled map lattices of the above type in space dimensions d = 2 to 6.Such simple models can be approached by a mean-field approximation which usually reduces the dynamics to that of a map governing the evolution of some extensive density. While this approximation is exact in the d = infty limit, where macroscopic variables must display the time-dependent behavior of the mean-field map, basic intuition from equilibrium statistical mechanics rules out any such behavior in a low-dimensional systems, since it would involve the collective motion of locally disordered elements.The models studied are chosen to be as close as possible to mean-field conditions, i.e., rather high space dimension, large connectivity, and equal-weight coupling between sites. While the mean-field evolution is never observed, a new type of non-trivial collective behavior is found, at odds with the predictions of equilibrium statistical mechanics. Both in the cellular automata models and in the coupled map lattices, macroscopic variables frequently display a non-transient, time-dependent, low-dimensional dynamics emerging out of local disorder. Striking examples are period 3 cycles in two-state cellular automata and a Hopf bifurcation for a d = 5 lattice of coupled logistic maps. An extensive account of the phenomenology is given, including a catalog of behaviors, classification tables for the celular automata rules, and bifurcation diagrams for the coupled map lattices.The observed underlying dynamics is accompanied by an intrinsic quasi-Gaussian noise (stemming from the local disorder) which disappears in the infinite-size limit. The collective behaviors constitute a robust phenomenon, resisting external noise, small changes in the local dynamics, and modifications of the initial and boundary conditions. Synchronous updating, high space dimension and the regularity of connections are shown to be crucial ingredients in the subtle build-up of correlations giving rise to the collective motion. The discussion stresses the need for a theoretical understanding that neither equilibrium statistical mechanics nor higher-order mean-field approximations are able to provide.

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

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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.

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

Gyrofluid modeling and phenomenology of low-βe Alfvén wave turbulence

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.; Tassi, E.

2018-04-01

A two-field reduced gyrofluid model including electron inertia, ion finite Larmor radius corrections, and parallel magnetic field fluctuations is derived from the model of Brizard [Brizard, Phys. Fluids B 4, 1213 (1992)]. It assumes low βe, where βe indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong uniform magnetic guide field, but permits an arbitrary ion-to-electron equilibrium temperature ratio. It is shown to have a noncanonical Hamiltonian structure and provides a convenient framework for studying kinetic Alfvén wave turbulence, from magnetohydrodynamics to sub-de scales (where de holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized cross-helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range, the generalized cross-helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

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.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

Equilibration of energy in slow–fast systems

PubMed Central

Shah, Kushal; Gelfreich, Vassili; Rom-Kedar, Vered

2017-01-01

Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. However, in systems with several characteristic timescales, the ergodicity of the fast subsystem impedes the equilibration of the whole system because of the presence of an adiabatic invariant. In this paper, we show that violation of ergodicity in the fast dynamics can drive the whole system to equilibrium. To show this principle, we investigate the dynamics of springy billiards, which are mechanical systems composed of a small particle bouncing elastically in a bounded domain, where one of the boundary walls has finite mass and is attached to a linear spring. Numerical simulations show that the springy billiard systems approach equilibrium at an exponential rate. However, in the limit of vanishing particle-to-wall mass ratio, the equilibration rates remain strictly positive only when the fast particle dynamics reveal two or more ergodic components for a range of wall positions. For this case, we show that the slow dynamics of the moving wall can be modeled by a random process. Numerical simulations of the corresponding springy billiards and their random models show equilibration with similar positive rates. PMID:29183966

Primitive-path statistics of entangled polymers: mapping multi-chain simulations onto single-chain mean-field models

NASA Astrophysics Data System (ADS)

Steenbakkers, Rudi J. A.; Tzoumanekas, Christos; Li, Ying; Liu, Wing Kam; Kröger, Martin; Schieber, Jay D.

2014-01-01

We present a method to map the full equilibrium distribution of the primitive-path (PP) length, obtained from multi-chain simulations of polymer melts, onto a single-chain mean-field ‘target’ model. Most previous works used the Doi-Edwards tube model as a target. However, the average number of monomers per PP segment, obtained from multi-chain PP networks, has consistently shown a discrepancy of a factor of two with respect to tube-model estimates. Part of the problem is that the tube model neglects fluctuations in the lengths of PP segments, the number of entanglements per chain and the distribution of monomers among PP segments, while all these fluctuations are observed in multi-chain simulations. Here we use a recently proposed slip-link model, which includes fluctuations in all these variables as well as in the spatial positions of the entanglements. This turns out to be essential to obtain qualitative and quantitative agreement with the equilibrium PP-length distribution obtained from multi-chain simulations. By fitting this distribution, we are able to determine two of the three parameters of the model, which govern its equilibrium properties. This mapping is executed for four different linear polymers and for different molecular weights. The two parameters are found to depend on chemistry, but not on molecular weight. The model predicts a constant plateau modulus minus a correction inversely proportional to molecular weight. The value for well-entangled chains, with the parameters determined ab initio, lies in the range of experimental data for the materials investigated.

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.

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.

Statistical physics of vehicular traffic and some related systems

NASA Astrophysics Data System (ADS)

Chowdhury, Debashish; Santen, Ludger; Schadschneider, Andreas

2000-05-01

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

Nonequilibrium critical behavior of model statistical systems and methods for the description of its features

NASA Astrophysics Data System (ADS)

Prudnikov, V. V.; Prudnikov, P. V.; Mamonova, M. V.

2017-11-01

This paper reviews features in critical behavior of far-from-equilibrium macroscopic systems and presents current methods of describing them by referring to some model statistical systems such as the three-dimensional Ising model and the two-dimensional XY model. The paper examines the critical relaxation of homogeneous and structurally disordered systems subjected to abnormally strong fluctuation effects involved in ordering processes in solids at second-order phase transitions. Interest in such systems is due to the aging properties and fluctuation-dissipation theorem violations predicted for and observed in systems slowly evolving from a nonequilibrium initial state. It is shown that these features of nonequilibrium behavior show up in the magnetic properties of magnetic superstructures consisting of alternating nanoscale-thick magnetic and nonmagnetic layers and can be observed not only near the film’s critical ferromagnetic ordering temperature Tc, but also over the wide temperature range T ⩽ Tc.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

Statistical investigation of simulated intestinal fluid composition on the equilibrium solubility of biopharmaceutics classification system class II drugs.

PubMed

Khadra, Ibrahim; Zhou, Zhou; Dunn, Claire; Wilson, Clive G; Halbert, Gavin

2015-01-25

A drug's solubility and dissolution behaviour within the gastrointestinal tract is a key property for successful administration by the oral route and one of the key factors in the biopharmaceutics classification system. This property can be determined by investigating drug solubility in human intestinal fluid (HIF) but this is difficult to obtain and highly variable, which has led to the development of multiple simulated intestinal fluid (SIF) recipes. Using a statistical design of experiment (DoE) technique this paper has investigated the effects and interactions on equilibrium drug solubility of seven typical SIF components (sodium taurocholate, lecithin, sodium phosphate, sodium chloride, pH, pancreatin and sodium oleate) within concentration ranges relevant to human intestinal fluid values. A range of poorly soluble drugs with acidic (naproxen, indomethacin, phenytoin, and piroxicam), basic (aprepitant, carvedilol, zafirlukast, tadalafil) or neutral (fenofibrate, griseofulvin, felodipine and probucol) properties have been investigated. The equilibrium solubility results determined are comparable with literature studies of the drugs in either HIF or SIF indicating that the DoE is operating in the correct space. With the exception of pancreatin, all of the factors individually had a statistically significant influence on equilibrium solubility with variations in magnitude of effect between the acidic and basic or neutral compounds and drug specific interactions were evident. Interestingly for the neutral compounds pH was the factor with the second largest solubility effect. Around one third of all the possible factor combinations showed a significant influence on equilibrium solubility with variations in interaction significance and magnitude of effect between the acidic and basic or neutral compounds. The least number of significant media component interactions were noted for the acidic compounds with three and the greatest for the neutral compounds at seven, with again drug specific effects evident. This indicates that a drug's equilibrium solubility in SIF is influenced depending upon drug type by between eight to fourteen individual or combinations of media components with some of these drug specific. This illustrates the complex nature of these fluids and provides for individual drugs a visualisation of the possible solubility envelope within the gastrointestinal tract, which may be of importance for modelling in vivo behaviour. In addition the results indicate that the design of experiment approach can be employed to provide greater detail of drug solubility behaviour, possible drug specific interactions and influence of variations in gastrointestinal media components due to disease. The approach is also feasible and amenable to adaptation for high throughput screening of drug candidates. Copyright © 2014 Elsevier B.V. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Schmittmann, Beate

2007-03-01

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

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

The Impacts and Economic Costs of Climate Change in Agriculture and the Costs and Benefits of Adaptation

NASA Astrophysics Data System (ADS)

Iglesias, A.; Quiroga, S.; Garrote, L.; Cunningham, R.

2012-04-01

This paper provides monetary estimates of the effects of agricultural adaptation to climate change in Europe. The model computes spatial crop productivity changes as a response to climate change linking biophysical and socioeconomic components. It combines available data sets of crop productivity changes under climate change (Iglesias et al 2011, Ciscar et al 2011), statistical functions of productivity response to water and nitrogen inputs, catchment level water availability, and environmental policy scenarios. Future global change scenarios are derived from several socio-economic futures of representative concentration pathways and regional climate models. The economic valuation is conducted by using GTAP general equilibrium model. The marginal productivity changes has been used as an input for the economic general equilibrium model in order to analyse the economic impact of the agricultural changes induced by climate change in the world. The study also includes the analysis of an adaptive capacity index computed by using the socio-economic results of GTAP. The results are combined to prioritize agricultural adaptation policy needs in Europe.

Non-equilibrium diffusion combustion of a fuel droplet

NASA Astrophysics Data System (ADS)

Tyurenkova, Veronika V.

2012-06-01

A mathematical model for the non-equilibrium combustion of droplets in rocket engines is developed. This model allows to determine the divergence of combustion rate for the equilibrium and non-equilibrium model. Criterion for droplet combustion deviation from equilibrium is introduced. It grows decreasing droplet radius, accommodation coefficient, temperature and decreases on decreasing diffusion coefficient. Also divergence from equilibrium increases on reduction of droplet radius. Droplet burning time essentially increases under non-equilibrium conditions. Comparison of theoretical and experimental data shows that to have adequate solution for small droplets it is necessary to use the non-equilibrium model.

Collisional-radiative switching - A powerful technique for converging non-LTE calculations

NASA Technical Reports Server (NTRS)

Hummer, D. G.; Voels, S. A.

1988-01-01

A very simple technique has been developed to converge statistical equilibrium and model atmospheric calculations in extreme non-LTE conditions when the usual iterative methods fail to converge from an LTE starting model. The proposed technique is based on a smooth transition from a collision-dominated LTE situation to the desired non-LTE conditions in which radiation dominates, at least in the most important transitions. The proposed approach was used to successfully compute stellar models with He abundances of 0.20, 0.30, and 0.50; Teff = 30,000 K, and log g = 2.9.

Statistical Equilibrium of Copper in the Solar Atmosphere

NASA Astrophysics Data System (ADS)

Shi, J. R.; Gehren, T.; Zeng, J. L.; Mashonkina, L.; Zhao, G.

2014-02-01

Non-local thermodynamic equilibrium (NLTE) line formation for neutral copper in the one-dimensional solar atmospheres is presented for the atomic model, including 96 terms of Cu I and the ground state of Cu II. The accurate oscillator strengths for all the line transitions in model atom and photoionization cross sections were calculated using the R-matrix method in the Russell-Saunders coupling scheme. The main NLTE mechanism for Cu I is the ultraviolet overionization. We find that NLTE leads to systematically depleted total absorption in the Cu I lines and, accordingly, positive abundance corrections. Inelastic collisions with neutral hydrogen atoms produce minor effects on the statistical equilibrium of Cu I in the solar atmosphere. For the solar Cu I lines, the departures from LTE are found to be small, the mean NLTE abundance correction of ~0.01 dex. It was found that the six low-excitation lines, with excitation energy of the lower level E exc <= 1.64 eV, give a 0.14 dex lower mean solar abundance compared to that from the six E exc > 3.7 eV lines, when applying experimental gf-values of Kock & Richter. Without the two strong resonance transitions, the solar mean NLTE abundance from 10 lines of Cu I is log ɛ⊙(Cu) = 4.19 ± 0.10, which is consistent within the error bars with the meteoritic value 4.25 ± 0.05 of Lodders et al. The discrepancy between E exc = 1.39-1.64 eV and E exc > 3.7 eV lines can be removed when the calculated gf-values are adopted and a mean solar abundance of log ɛ⊙(Cu) = 4.24 ± 0.08 is derived.

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.

Local conformity induced global oscillation

NASA Astrophysics Data System (ADS)

Li, Dong; Li, Wei; Hu, Gang; Zheng, Zhigang

2009-04-01

The game ‘rock-paper-scissors’ model, with the consideration of the effect of the psychology of conformity, is investigated. The interaction between each two agents is global, but the strategy of the conformity is local for individuals. In the statistical opinion, the probability of the appearance of each strategy is uniform. The dynamical analysis of this model indicates that the equilibrium state may lose its stability at a threshold and is replaced by a globally oscillating state. The global oscillation is induced by the local conformity, which is originated from the synchronization of individual strategies.

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

Colloquium: Statistical mechanics of money, wealth, and income

NASA Astrophysics Data System (ADS)

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

2009-10-01

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

Ranking nano-enabled hybrid media for simultaneous removal of contaminants with different chemistries: Pseudo-equilibrium sorption tests versus column tests.

PubMed

Custodio, Tomas; Garcia, Jose; Markovski, Jasmina; McKay Gifford, James; Hristovski, Kiril D; Olson, Larry W

2017-12-15

The underlying hypothesis of this study was that pseudo-equilibrium and column testing conditions would provide the same sorbent ranking trends although the values of sorbents' performance descriptors (e.g. sorption capacity) may vary because of different kinetics and competition effects induced by the two testing approaches. To address this hypothesis, nano-enabled hybrid media were fabricated and its removal performances were assessed for two model contaminants under multi-point batch pseudo-equilibrium and continuous-flow conditions. Calculation of simultaneous removal capacity indices (SRC) demonstrated that the more resource demanding continuous-flow tests are able to generate the same performance rankings as the ones obtained by conducing the simpler pseudo-equilibrium tests. Furthermore, continuous overlap between the 98% confidence boundaries for each SRC index trend, not only validated the hypothesis that both testing conditions provide the same ranking trends, but also pointed that SRC indices are statistically the same for each media, regardless of employed method. In scenarios where rapid screening of new media is required to obtain the best performing synthesis formulation, use of pseudo-equilibrium tests proved to be reliable. Considering that kinetics induced effects on sorption capacity must not be neglected, more resource demanding column test could be conducted only with the top performing media that exhibit the highest sorption capacity. Copyright © 2017 Elsevier B.V. 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.

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)

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.

Edwards statistical mechanics for jammed granular matter

NASA Astrophysics Data System (ADS)

Baule, Adrian; Morone, Flaviano; Herrmann, Hans J.; Makse, Hernán A.

2018-01-01

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter—one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out-of-equilibrium matter—has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter—primarily governed by the steric interactions between the constitutive particles—a theoretical understanding based on first principles has proved exceedingly challenging. Here a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble is reviewed. The construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems, is discussed. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to nonspherical shapes such as dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse, and polydisperse particles in any dimensions is discussed providing insight into a unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards ensemble of metastable jammed states and metastability in spin glasses is established. This highlights the fact that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin glasses.

The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics

NASA Astrophysics Data System (ADS)

Benettin, G.; Christodoulidi, H.; Ponno, A.

2013-07-01

This paper is devoted to a numerical study of the familiar α+ β FPU model. Precisely, we here discuss, revisit and combine together two main ideas on the subject: (i) In the system, at small specific energy ɛ= E/ N, two well separated time-scales are present: in the former one a kind of metastable state is produced, while in the second much larger one, such an intermediate state evolves and reaches statistical equilibrium. (ii) FPU should be interpreted as a perturbed Toda model, rather than (as is typical) as a linear model perturbed by nonlinear terms. In the view we here present and support, the former time scale is the one in which FPU is essentially integrable, its dynamics being almost indistinguishable from the Toda dynamics: the Toda actions stay constant for FPU too (while the usual linear normal modes do not), the angles fill their almost invariant torus, and nothing else happens. The second time scale is instead the one in which the Toda actions significantly evolve, and statistical equilibrium is possible. We study both FPU-like initial states, in which only a few degrees of freedom are excited, and generic initial states extracted randomly from an (approximated) microcanonical distribution. The study is based on a close comparison between the behavior of FPU and Toda in various situations. The main technical novelty is the study of the correlation functions of the Toda constants of motion in the FPU dynamics; such a study allows us to provide a good definition of the equilibrium time τ, i.e. of the second time scale, for generic initial data. Our investigation shows that τ is stable in the thermodynamic limit, i.e. the limit of large N at fixed ɛ, and that by reducing ɛ (ideally, the temperature), τ approximately grows following a power law τ˜ ɛ - a , with a=5/2.

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

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).

Advances in Statistical and Deterministic Modeling of Wind-Driven Seas

DTIC Science & Technology

2011-09-30

Zakharov. Scales of nonlinear relaxation and balance of wind- driven seas. Geophysical Research Abstracts Vol. 13, EGU2011-2042, 2011. EGU General ...Dyachenko A. “On canonical equation for water waves” at General Assembly 2011 of the European Geosciences Union in Vienna, Austria, 03 – 08 April...scattering and equilibrium ranges in wind- generated waves with application to spectrometry, J. Geoph. Res., 92, 49715029, 1987. [3] Hsiao S.V. and

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.

Statistical Evaluation of CRM-Simulated Cloud and Precipitation Structures Using Multi- sensor TRMM Measurements and Retrievals

NASA Astrophysics Data System (ADS)

Posselt, D.; L'Ecuyer, T.; Matsui, T.

2009-05-01

Cloud resolving models are typically used to examine the characteristics of clouds and precipitation and their relationship to radiation and the large-scale circulation. As such, they are not required to reproduce the exact location of each observed convective system, much less each individual cloud. Some of the most relevant information about clouds and precipitation is provided by instruments located on polar-orbiting satellite platforms, but these observations are intermittent "snapshots" in time, making assessment of model performance challenging. In contrast to direct comparison, model results can be evaluated statistically. This avoids the requirement for the model to reproduce the observed systems, while returning valuable information on the performance of the model in a climate-relevant sense. The focus of this talk is a model evaluation study, in which updates to the microphysics scheme used in a three-dimensional version of the Goddard Cumulus Ensemble (GCE) model are evaluated using statistics of observed clouds, precipitation, and radiation. We present the results of multiday (non-equilibrium) simulations of organized deep convection using single- and double-moment versions of a the model's cloud microphysical scheme. Statistics of TRMM multi-sensor derived clouds, precipitation, and radiative fluxes are used to evaluate the GCE results, as are simulated TRMM measurements obtained using a sophisticated instrument simulator suite. We present advantages and disadvantages of performing model comparisons in retrieval and measurement space and conclude by motivating the use of data assimilation techniques for analyzing and improving model parameterizations.

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.

Thermodynamic modeling using BINGO-ANTIDOTE: A new strategy to investigate metamorphic rocks

NASA Astrophysics Data System (ADS)

Lanari, Pierre; Duesterhoeft, Erik

2016-04-01

BINGO-ANTIDOTE is a new program, combing the achievements of the two petrological software packages XMAPTOOLS[1] and THERIAK-DOMINO[2]. XMAPTOOLS affords information about compositional zoning in mineral and local bulk composition of domains at the thin sections scale. THERIAK-DOMINO calculates equilibrium phase assemblages from given bulk rock composition, temperature T and pressure P. Primarily BINGO-ANTIDOTE can be described as an inverse THERIAK-DOMINO, because it uses the information provided by XMAPTOOLS to calculate the probable P-T equilibrium conditions of metamorphic rocks. Consequently, the introduced program combines the strengths of forward Gibbs free energy minimization models with the intuitive output of inverse thermobarometry models. In order to get "best" P-T equilibrium conditions of a metamorphic rock sample and thus estimating the degree of agreement between the observed and calculated mineral assemblage, it is critical to define a reliable scoring strategy. BINGO uses the THERIAKD ADD-ON[3] (Duesterhoeft and de Capitani, 2013) and is a flexible model scorer with 3+1 evaluation criteria. These criteria are the statistical agreement between the observed and calculated mineral-assemblage, -proportions (vol%) and -composition (mol). Additionally, a total likelihood, consisting of the first three criteria, allows the user an evaluation of the most probable equilibrium P-T condition. ANTIDOTE is an interactive user interface, displaying the 3+1 evaluation criteria as probability P-T-maps. It can be used with and without XMAPTOOLS. As a stand-alone program, the user is able to give the program macroscopic observations (i.e., mineral names and proportions), which ANTIDOTE converts to a readable BINGO input. In this manner, the use of BINGO-ANTIDOTE opens up thermodynamics to students and people with only a basic knowledge of phase diagrams and thermodynamic modeling techniques. This presentation introduces BINGO-ANTIDOTE and includes typical examples of its functionality, such as the determination of P-T conditions of high-grade rocks. BINGO-ANTIDOTE is still under development and will soon be freely available online. References: [1] Lanari P., Vidal O., De Andrade V., Dubacq B., Lewin E., Grosch E. G. and Schwartz S. (2013) XMapTools: a MATLAB©-based program for electron microprobe X-ray image processing and geothermobarometry. Comput. Geosci. 62, 227-240. [2] de Capitani C. and Petrakakis K. (2010) The computation of equilibrium assemblage diagrams with Theriak/Domino software. Am. Mineral. 95, 1006-1016. [3] Duesterhoeft E. and de Capitani C. (2013) Theriak_D: An add-on to implement equilibrium computations in geodynamic models. Geochem. Geophys. Geosyst. 14, 4962-4967.

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.

Equilibrium Beach Profiles on the East and West U.S. Coasts

NASA Astrophysics Data System (ADS)

Ludka, B. C.; Guza, R. T.; McNinch, J. E.; O'Reilly, W.

2012-12-01

Beach elevation change observations from the United States west and east coasts are used to identify statistically the dominant cross-shore patterns in sand level fluctuations, and these changes are related to equilibrium beach profile concepts. Three to seven years of observations at four beaches in Southern California include monthly surveys of the subaerial (near MSL) beach, and quarterly surveys from the backbeach to about 8m depth. At Duck, North Carolina, observations include 31 years of monthly surveys from the dunes to about 8m depth. On the Southern California beaches, the dominant seasonal pattern is subaerial erosion in winter and accretion in summer. Seasonal fluctuations of 3m in shoreline vertical sand levels, and 50m in subaerial beach width, are not uncommon. The sand eroded from the shoreline in winter is stored in an offshore sand bar and returns to the beach face in summer. Wave conditions in Southern California also vary seasonally, with energetic waves arriving from the north in winter, and lower energy, longer period southerly swell arriving in summer. A spectral refraction model, initialized with a regional network of directional wave buoys, is used to estimate hourly wave conditions, in 10m water depth. Using an equilibrium hypothesis, that the shoreline (defined as the cross-shore location of the MSL contour) change rate depends on the wave energy and the wave energy disequilibrium, Yates (2009) modeled the time-varying shoreline location at several Southern California beaches with significant skill. The four free model parameters were calibrated to fit observations. Following Yates (2009), we extend the equilibrium shoreline model to include the horizontal displacement of other elevation contours. At the Southern California sites, the modeled contour translation depends on the incident wave energy, the present contour configuration, and observation-based estimates of the contour behavior (based on EOF spatial amplitudes). At Duck, seasonal variations of the wave field (measured immediately offshore) are large, but shoreline changes (usually <30cm) are smaller than in Southern California. Maximum vertical variations occur just seaward of the shoreline and the nearshore bathymetry is often barred. Plant (1999) show that bar crest position at Duck has equilibrium-like behavior. We will present the results of equilibrium shoreline and profile modeling at Duck. At both sites, we diagnose sources (e.g. grain size and incident waves) of the sometimes strong observed alongshore variations in sand level change patterns. Funding was provided by the US Army Corps of Engineers and the California Department of Boating and Waterways. REFERENCES Plant, N. G., R. A. Holman, M. H. Freilich, and W. A. Birkemeier (1999), A simple model for interannual sandbar behavior, J. Geophys. Res., 104(C7), 15,755-15,776. Yates, M. L., R. T. Guza, and W. C. O'Reilly (2009), Equilibrium shoreline response: Observations and modeling, J. Geophys. Res., 114, C09014.

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.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

Continuous time random walk (CTRW) models are widely used to model diffusion in condensed matter. There are two classes of such models, distinguished by the convergence or divergence of the mean waiting time. Systems with finite average sojourn time are ergodic and thus Boltzmann-Gibbs statistics can be applied. We investigate the statistical properties of CTRW models with infinite average sojourn time; in particular, the occupation time probability density function is obtained. It is shown that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point exhibits bimodal U or trimodal W shape, related to the arcsine law. The key points are as follows. (a) In a CTRW with finite or infinite mean waiting time, the distribution of the number of visits on a lattice point is determined by the probability that a member of an ensemble of particles in equilibrium occupies the lattice point. (b) The asymmetry parameter of the probability distribution function of occupation times is related to the Boltzmann probability and to the partition function. (c) The ensemble average is given by Boltzmann-Gibbs statistics for either finite or infinite mean sojourn time, when detailed balance conditions hold. (d) A non-ergodic generalization of the Boltzmann-Gibbs statistical mechanics for systems with infinite mean sojourn time is found.

Transfer Kinetics at the Aqueous/Non-Aqueous Phase Liquid Interface. A Statistical Mechanic Approach

NASA Astrophysics Data System (ADS)

Doss, S. K.; Ezzedine, S.; Ezzedine, S.; Ziagos, J. P.; Hoffman, F.; Gelinas, R. J.

2001-05-01

Many modeling efforts in the literature use a first-order, linear-driving-force model to represent the chemical dissolution process at the non-aqueous/aqueous phase liquid (NAPL/APL) interface. In other words, NAPL to APL phase flux is assumed to be equal to the difference between the solubility limit and the "bulk aqueous solution" concentrations times a mass transfer coefficient. Under such assumptions, a few questions are raised: where, in relation to a region of pure NAPL, does the "bulk aqueous solution" regime begin and how does it behave? The answers are assumed to be associated with an arbitrary, predetermined boundary layer, which separates the NAPL from the surrounding solution. The mass transfer rate is considered to be, primarily, limited by diffusion of the component through the boundary layer. In fact, compositional models of interphase mass transfer usually assume that a local equilibrium is reached between phases. Representing mass flux as a rate-limiting process is equivalent to assuming diffusion through a stationary boundary layer with an instantaneous local equilibrium and linear concentration profile. Some environmental researchers have enjoyed success explaining their data using chemical engineering-based correlations. Correlations are strongly dependent on the experimental conditions employed. A universally applicable theory for NAPL dissolution in natural systems does not exist. These correlations are usually expressed in terms of the modified Sherwood number as a function of Reynolds, Peclet, and Schmidt numbers. The Sherwood number may be interpreted as the ratio between the grain size and the thickness of the Nernst stagnant film. In the present study, we show that transfer kinetics at the NAPL/APL interface under equilibrium conditions disagree with approaches based on the Nernst stagnant film concept. It is unclear whether local equilibrium assumptions used in current models are suitable for all situations.A statistical mechanic framework has been chosen to study the transfer kinetic processes at the microscale level. The rationale for our approach is based on both the activation energy of transfer of an ion and its velocity across the NAPL/APL interface. There are four major energies controlling the interfacial NAPL dissolution kinetics: (de)solvation energy, interfacial tension energy, electrostatic energy, and thermal fluctuation energy. Transfer of an ion across the NAPL/APL interface is accelerated by the viscous forces which can be described using the averaged Langevin master equation. The resulting energies and viscous forces were combined using the Boltzmann probability distribution. Asymptotic time limits of the resulting kinetics lead to instantaneous local equilibrium conditions that contradict the Nernst equilibrium equation. The NAPL/APL interface is not an ideal one: it does not conserve energy and heat. In our case the interface is treated as a thin film or slush zone that alters the thermodynamic variables. Such added zone, between the two phases, is itself a phase, and, therefore, the equilibrium does not occur between two phases but rather three. All these findings led us to develop a new non-linearly coupled flow and transport system of equations which is able to account for specific chemical dissolution processes and precludes the need for empirical mass-transfer parameters. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

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.

Soil Moisture and the Persistence of North American Drought.

NASA Astrophysics Data System (ADS)

Oglesby, Robert J.; Erickson, David J., III

1989-11-01

We describe numerical sensitivity experiments exploring the effects of soil moisture on North American summertime climate using the NCAR CCMI, a 12-layer global atmospheric general circulation model. In particular. the hypothesis that reduced soil moisture may help induce and amplify warm, dry summers over midlatitude continental interiors is examined. Equilibrium climate statistics are computed for the perpetual July model response to imposed soil moisture anomalies over North America between 36° and 49°N. In addition, the persistence of imposed soil moisture anomalies is examined through use of the seasonal cycle mode of operation with use of various initial atmospheric states both equilibrated and nonequilibrated to the initial soil moisture anomaly.The climate statistics generated by thew model simulations resemble in a general way those of the summer of 1988, when extensive heat and drought occurred over much of North America. A reduction in soil moisture in the model leads to an increase in surface temperature, lower surface pressure, increased ridging aloft, and a northward shift of the jet stream. Low-level moisture advection from the Gulf of Mexico is important in determining where persistent soil moisture deficits can be maintained. In seasonal cycle simulations, it lock longer for an initially unequilibrated atmosphere to respond to the imposed soil moisture anomaly, via moisture transport from the Gulf of Mexico, than when initially the atmosphere was in equilibrium with the imposed anomaly., i.e., the initial state was obtained from the appropriate perpetual July simulation. The results demonstrate the important role of soil moisture in prolonging and/or amplifying North American summertime drought.

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

NASA Astrophysics Data System (ADS)

Tucker, Gregory E.; Bradley, D. Nathan

2010-03-01

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

Helium emission from model flare layers. [of outer solar atmosphere

NASA Technical Reports Server (NTRS)

Kulander, J. I.

1976-01-01

The emission of visible and UV He I and He II line radiation from a plane-parallel model flare layer characterized by electron temperatures of 10,000 to 50,000 K and electron densities of 10 to the 10th power to 10 to the 15th power per cu cm is analyzed by solving the statistical-equilibrium equations for a 30-level He I-II-III system, using parametric representations of the line and continuum radiation fields. The atomic model was chosen to provide accurate solutions for the first two resonance lines of He I and He II as well as for the D3 and 10,830-A lines of He I. Reaction rates are discussed, and sample solutions to the steady-state population equations are given for a generally optically thin gas assumed to be irradiated over 2pi sr by a blackbody spectrum at 6000 K. Specific results are examined for ionization equilibrium, level populations, approximate optical depths of a 1000-km-thick flare layer, line intensities, and upper-level population rates.

On the importance of variable soil depth and process representation in the modeling of shallow landslide initiation

NASA Astrophysics Data System (ADS)

Fatichi, S.; Burlando, P.; Anagnostopoulos, G.

2014-12-01

Sub-surface hydrology has a dominant role on the initiation of rainfall-induced landslides, since changes in the soil water potential affect soil shear strength and thus apparent cohesion. Especially on steep slopes and shallow soils, loss of shear strength can lead to failure even in unsaturated conditions. A process based model, HYDROlisthisis, characterized by high resolution in space and, time is developed to investigate the interactions between surface and subsurface hydrology and shallow landslide initiation. Specifically, 3D variably saturated flow conditions, including soil hydraulic hysteresis and preferential flow, are simulated for the subsurface flow, coupled with a surface runoff routine. Evapotranspiration and specific root water uptake are taken into account for continuous simulations of soil water content during storm and inter-storm periods. The geotechnical component of the model is based on a multidimensional limit equilibrium analysis, which takes into account the basic principles of unsaturated soil mechanics. The model is applied to a small catchment in Switzerland historically prone to rainfall-triggered landslides. A series of numerical simulations were carried out with various boundary conditions (soil depths) and using hydrological and geotechnical components of different complexity. Specifically, the sensitivity to the inclusion of preferential flow and soil hydraulic hysteresis was tested together with the replacement of the infinite slope assumption with a multi-dimensional limit equilibrium analysis. The effect of the different model components on model performance was assessed using accuracy statistics and Receiver Operating Characteristic (ROC) curve. The results show that boundary conditions play a crucial role in the model performance and that the introduced hydrological (preferential flow and soil hydraulic hysteresis) and geotechnical components (multidimensional limit equilibrium analysis) considerably improve predictive capabilities in the presented case study.

Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories

PubMed Central

Donovan, Rory M.; Tapia, Jose-Juan; Sullivan, Devin P.; Faeder, James R.; Murphy, Robert F.; Dittrich, Markus; Zuckerman, Daniel M.

2016-01-01

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation—by orders of magnitude for some observables. PMID:26845334

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.

Enhancement of low-temperature thermometry by strong coupling

NASA Astrophysics Data System (ADS)

Correa, Luis A.; Perarnau-Llobet, Martí; Hovhannisyan, Karen V.; Hernández-Santana, Senaida; Mehboudi, Mohammad; Sanpera, Anna

2017-12-01

We consider the problem of estimating the temperature T of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low T can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures—a regime which is particularly relevant to quantum technologies.

Non-LTE CO, revisited

NASA Technical Reports Server (NTRS)

Ayres, Thomas R.; Wiedemann, Gunter R.

1989-01-01

A more extensive and detailed non-LTE simulation of the Delta v = 1 bands of CO than attempted previously is reported. The equations of statistical equilibrium are formulated for a model molecule containing 10 bound vibrational levels, each split into 121 rotational substates and connected by more than 1000 radiative transitions. Solutions are obtained for self-consistent populations and radiation fields by iterative application of the 'Lambda-operator' to an initial LTE distribution. The formalism is used to illustrate models of the sun and Arcturus. For the sun, negligible departures from LTE are found in either a theoretical radiative-equilibrium photosphere with outwardly falling temperatures in its highest layers or in a semiempirical hot chromosphere that reproduces the spatially averaged emission cores of Ca II H and K. The simulations demonstrate that the puzzling 'cool cores' of the CO Delta V = 1 bands observed in limb spectra of the sun and in flux spectra of Arcturus cannot be explained simply by non-LTE scattering effects.

Galactic evolution of copper in the light of NLTE computations

NASA Astrophysics Data System (ADS)

Andrievsky, S.; Bonifacio, P.; Caffau, E.; Korotin, S.; Spite, M.; Spite, F.; Sbordone, L.; Zhukova, A. V.

2018-01-01

We have developed a model atom for Cu with which we perform statistical equilibrium computations that allow us to compute the line formation of Cu I lines in stellar atmospheres without assuming local thermodynamic equilibrium (LTE). We validate this model atom by reproducing the observed line profiles of the Sun, Procyon and 11 metal-poor stars. Our sample of stars includes both dwarfs and giants. Over a wide range of stellar parameters, we obtain excellent agreement among different Cu I lines. The 11 metal-poor stars have iron abundances in the range - 4.2 ≤ [Fe/H] ≤ -1.4, the weighted mean of the [Cu/Fe] ratios is -0.22 dex, with a scatter of -0.15 dex. This is very different from the results from LTE analysis (the difference between NLTE and LTE abundances reaches 1 dex) and in spite of the small size of our sample, it prompts for a revision of the Galactic evolution of Cu.

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.

Simulating Metabolism with Statistical Thermodynamics

PubMed Central

Cannon, William R.

2014-01-01

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

Simulating metabolism with statistical thermodynamics.

PubMed

Cannon, William R

2014-01-01

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

A two-layer composite model of the vocal fold lamina propria for fundamental frequency regulation.

PubMed

Zhang, Kai; Siegmund, Thomas; Chan, Roger W

2007-08-01

The mechanical properties of the vocal fold lamina propria, including the vocal fold cover and the vocal ligament, play an important role in regulating the fundamental frequency of human phonation. This study examines the equilibrium hyperelastic tensile deformation behavior of cover and ligament specimens isolated from excised human larynges. Ogden's hyperelastic model is used to characterize the tensile stress-stretch behaviors at equilibrium. Several statistically significant differences in the mechanical response differentiating cover and ligament, as well as gender are found. Fundamental frequencies are predicted from a string model and a beam model, both accounting for the cover and the ligament. The beam model predicts nonzero F(0) for the unstretched state of the vocal fold. It is demonstrated that bending stiffness significantly contributes to the predicted F(0), with the ligament contributing to a higher F(0), especially in females. Despite the availability of only a small data set, the model predicts an age dependence of F(0) in males in agreement with experimental findings. Accounting for two mechanisms of fundamental frequency regulation--vocal fold posturing (stretching) and extended clamping--brings predicted F(0) close to the lower bound of the human phonatory range. Advantages and limitations of the current model are discussed.

The Fermi-Pasta-Ulam System as a Model for Glasses

NASA Astrophysics Data System (ADS)

Carati, A.; Maiocchi, A.; Galgani, L.; Amati, G.

2015-12-01

We show that the standard Fermi-Pasta-Ulam system, with a suitable choice for the interparticle potential, constitutes a model for glasses, and indeed an extremely simple and manageable one. Indeed, it allows one to describe the landscape of the minima of the potential energy and to deal concretely with any one of them, determining the spectrum of frequencies and the normal modes. A relevant role is played by the harmonic energy {E} relative to a given minimum, i.e., the expansion of the Hamiltonian about the minimum up to second order. Indeed we find that there exists an energy threshold in {E} such that below it the harmonic energy {E} appears to be an approximate integral of motion for the whole observation time. Consequently, the system remains trapped near the minimum, in what may be called a vitreous or glassy state. Instead, for larger values of {E} the system rather quickly relaxes to a final equilibrium state. Moreover we find that the vitreous states present peculiar statistical behaviors, still involving the harmonic energy {E}. Indeed, the vitreous states are described by a Gibbs distribution with an effective Hamiltonian close to {E} and with a suitable effective inverse temperature. The final equilibrium state presents instead statistical properties which are in very good agreement with the Gibbs distribution relative to the full Hamiltonian of the system.

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.

Statistical analysis of experimental multifragmentation events in 64Zn+112Sn at 40 MeV/nucleon

NASA Astrophysics Data System (ADS)

Lin, W.; Zheng, H.; Ren, P.; Liu, X.; Huang, M.; Wada, R.; Chen, Z.; Wang, J.; Xiao, G. Q.; Qu, G.

2018-04-01

A statistical multifragmentation model (SMM) is applied to the experimentally observed multifragmentation events in an intermediate heavy-ion reaction. Using the temperature and symmetry energy extracted from the isobaric yield ratio (IYR) method based on the modified Fisher model (MFM), SMM is applied to the reaction 64Zn+112Sn at 40 MeV/nucleon. The experimental isotope distribution and mass distribution of the primary reconstructed fragments are compared without afterburner and they are well reproduced. The extracted temperature T and symmetry energy coefficient asym from SMM simulated events, using the IYR method, are also consistent with those from the experiment. These results strongly suggest that in the multifragmentation process there is a freezeout volume, in which the thermal and chemical equilibrium is established before or at the time of the intermediate-mass fragments emission.

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

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.

Developing QSPR model of gas/particle partition coefficients of neutral poly-/perfluoroalkyl substances

NASA Astrophysics Data System (ADS)

Yuan, Quan; Ma, Guangcai; Xu, Ting; Serge, Bakire; Yu, Haiying; Chen, Jianrong; Lin, Hongjun

2016-10-01

Poly-/perfluoroalkyl substances (PFASs) are a class of synthetic fluorinated organic substances that raise increasing concern because of their environmental persistence, bioaccumulation and widespread presence in various environment media and organisms. PFASs can be released into the atmosphere through both direct and indirect sources, and the gas/particle partition coefficient (KP) is an important parameter that helps us to understand their atmospheric behavior. In this study, we developed a temperature-dependent predictive model for log KP of PFASs and analyzed the molecular mechanism that governs their partitioning equilibrium between gas phase and particle phase. All theoretical computation was carried out at B3LYP/6-31G (d, p) level based on neutral molecular structures by Gaussian 09 program package. The regression model has a good statistical performance and robustness. The application domain has also been defined according to OECD guidance. The mechanism analysis shows that electrostatic interaction and dispersion interaction play the most important role in the partitioning equilibrium. The developed model can be used to predict log KP values of neutral fluorotelomer alcohols and perfluor sulfonamides/sulfonamidoethanols with different substitutions at nitrogen atoms, providing basic data for their ecological risk assessment.

Light clusters and pasta phases in warm and dense nuclear matter

NASA Astrophysics Data System (ADS)

Avancini, Sidney S.; Ferreira, Márcio; Pais, Helena; Providência, Constança; Röpke, Gerd

2017-04-01

The pasta phases are calculated for warm stellar matter in a framework of relativistic mean-field models, including the possibility of light cluster formation. Results from three different semiclassical approaches are compared with a quantum statistical calculation. Light clusters are considered as point-like particles, and their abundances are determined from the minimization of the free energy. The couplings of the light clusters to mesons are determined from experimental chemical equilibrium constants and many-body quantum statistical calculations. The effect of these light clusters on the chemical potentials is also discussed. It is shown that, by including heavy clusters, light clusters are present up to larger nucleonic densities, although with smaller mass fractions.

Efecto de la difusión y la velocidad en la ionización del átomo de Carbono

NASA Astrophysics Data System (ADS)

Rovira, M. G.; Fontenla, J. M.

The equations of statistical equilibrium for all ionization states of the atom are solved. The effects of diffusion and center of mass velocity are included. In order to estimate the modifications of the ionization curves, they were applied to the Carbon atom. To solve these equations, solar prominences' models obtained in a previous paper were adopted. They were extended to reach a temperature of 1.5 × 106 K and the complete model of the prominence was calculated. Ionization curves for different values of velocity, diffusion and medium models were obtained. The different models represent structures with different densities. Considerable modifications due to these effects are found.

Agent-based model to rural urban migration analysis

NASA Astrophysics Data System (ADS)

Silveira, Jaylson J.; Espíndola, Aquino L.; Penna, T. J. P.

2006-05-01

In this paper, we analyze the rural-urban migration phenomenon as it is usually observed in economies which are in the early stages of industrialization. The analysis is conducted by means of a statistical mechanics approach which builds a computational agent-based model. Agents are placed on a lattice and the connections among them are described via an Ising-like model. Simulations on this computational model show some emergent properties that are common in developing economies, such as a transitional dynamics characterized by continuous growth of urban population, followed by the equalization of expected wages between rural and urban sectors (Harris-Todaro equilibrium condition), urban concentration and increasing of per capita income.

Photoionization Modeling

NASA Technical Reports Server (NTRS)

Kallman, T.

2010-01-01

Warm absorber spectra are characterized by the many lines from partially ionized intermediate-Z elements, and iron, detected with the grating instruments on Chandra and XMM-Newton. If these ions are formed in a gas which is in photoionization equilibrium, they correspond to a broad range of ionization parameters, although there is evidence for certain preferred values. A test for any dynamical model for these outflows is to reproduce these properties, at some level of detail. In this paper we present a statistical analysis of the ionization distribution which can be applied both the observed spectra and to theoretical models. As an example, we apply it to our dynamical models for warm absorber outflows, based on evaporation from the molecular torus.

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

Nonlocal thermodynamic equilibrium processes in ozone - Implications for the energy budget of the mesosphere and lower thermosphere

NASA Technical Reports Server (NTRS)

Milynczak, Martin G.

1991-01-01

The conversion of chemical potential energy and infrared radiative energy to kinetic energy by non-LTE processes involving ozone is a potentially significant source of heat in the terrestrial upper mesosphere and lower thermosphere. Heating rates are calculated and compared using two different statistical equilibrium models previously applied in the analysis of measurements of limb emission from ozone. The calculated heating depends strongly on the assumed distribution and relaxation of energy in the quasi-nascent ozone molecule. Finally, in the absence of a detailed data base of rate coefficients it may be possible to estimate the heating rate due to non-LTE processes in ozone from appropriate satellite measurements of the ozone concentration and of the infrared emission from ozone in the 9-12 micron spectral interval.

Final excitation energy of fission fragments

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

Schmidt, Karl-Heinz; Jurado, Beatriz

We study how the excitation energy of the fully accelerated fission fragments is built up. It is stressed that only the intrinsic excitation energy available before scission can be exchanged between the fission fragments to achieve thermal equilibrium. This is in contradiction with most models used to calculate prompt neutron emission, where it is assumed that the total excitation energy of the final fragments is shared between the fragments by the condition of equal temperatures. We also study the intrinsic excitation-energy partition in statistical equilibrium for different level-density descriptions as a function of the total intrinsic excitation energy of themore » fissioning system. Excitation energies are found to be strongly enhanced in the heavy fragment, if the level density follows a constant-temperature behavior at low energies, e.g., in the composed Gilbert-Cameron description.« less

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.

Investigation of fast ion pressure effects in ASDEX Upgrade by spectral MSE measurements

NASA Astrophysics Data System (ADS)

Reimer, René; Dinklage, Andreas; Wolf, Robert; Dunne, Mike; Geiger, Benedikt; Hobirk, Jörg; Reich, Matthias; ASDEX Upgrade Team; McCarthy, Patrick J.

2017-04-01

High precision measurements of fast ion effects on the magnetic equilibrium in the ASDEX Upgrade tokamak have been conducted in a high-power (10 MW) neutral-beam injection discharge. An improved analysis of the spectral motional Stark effect data based on forward-modeling, including the Zeeman effect, fine-structure and non-statistical sub-level distribution, revealed changes in the order of 1% in |B| . The results were found to be consistent with results from the equilibrium solver CLISTE. The measurements allowed us to derive the fast ion pressure fraction to be Δ {{p}\\text{FI}}/{{p}\\text{mhd}}≈ 10 % and variations of the fast ion pressure are consistent with calculations of the transport code TRANSP. The results advance the understanding of fast ion confinement and magneto-hydrodynamic stability in the presence of fast ions.

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.

Anharmonic effects in the quantum cluster equilibrium method

NASA Astrophysics Data System (ADS)

von Domaros, Michael; Perlt, Eva

2017-03-01

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

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

Zone clearance in an infinite TASEP with a step initial condition

NASA Astrophysics Data System (ADS)

Cividini, Julien; Appert-Rolland, Cécile

2017-06-01

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

Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure.

PubMed

Campi, Gaetano; Di Gioacchino, Michael; Poccia, Nicola; Ricci, Alessandro; Burghammer, Manfred; Ciasca, Gabriele; Bianconi, Antonio

2018-01-23

Ultrastructural fluctuations at nanoscale are fundamental to assess properties and functionalities of advanced out-of-equilibrium materials. We have taken myelin as a model of supramolecular assembly in out-of-equilibrium living matter. Myelin sheath is a simple stable multilamellar structure of high relevance and impact in biomedicine. Although it is known that myelin has a quasi-crystalline ultrastructure, there is no information on its fluctuations at nanoscale in different states due to limitations of the available standard techniques. To overcome these limitations, we have used scanning micro X-ray diffraction, which is a unique non-invasive probe of both reciprocal and real space to visualize statistical fluctuations of myelin order of the sciatic nerve of Xenopus laevis. The results show that the ultrastructure period of the myelin is stabilized by large anticorrelated fluctuations at nanoscale, between hydrophobic and hydrophilic layers. The ratio between the total thickness of hydrophilic and hydrophobic layers defines the conformational parameter, which describes the different states of myelin. Our key result is that myelin in its out-of-equilibrium functional state fluctuates point-to-point between different conformations showing a correlated disorder described by a Levy distribution. As the system approaches the thermodynamic equilibrium in an aged state, the disorder loses its correlation degree and the structural fluctuation distribution changes to Gaussian. In a denatured state at low pH, it changes to a completely disordered stage. Our results aim to clarify the degradation mechanism in biological systems by associating these states with ultrastructural dynamic fluctuations at nanoscale.

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.

Earthquake nucleation in a stochastic fault model of globally coupled units with interaction delays

NASA Astrophysics Data System (ADS)

Vasović, Nebojša; Kostić, Srđan; Franović, Igor; Todorović, Kristina

2016-09-01

In present paper we analyze dynamics of fault motion by considering delayed interaction of 100 all-to-all coupled blocks with rate-dependent friction law in presence of random seismic noise. Such a model sufficiently well describes a real fault motion, whose prevailing stochastic nature is implied by surrogate data analysis of available GPS measurements of active fault movement. Interaction of blocks in an analyzed model is studied as a function of time delay, observed both for dynamics of individual faults and phenomenological models. Analyzed model is examined as a system of all-to-all coupled blocks according to typical assumption of compound faults as complex of globally coupled segments. We apply numerical methods to show that there are local bifurcations from equilibrium state to periodic oscillations, with an occurrence of irregular aperiodic behavior when initial conditions are set away from the equilibrium point. Such a behavior indicates a possible existence of a bi-stable dynamical regime, due to effect of the introduced seismic noise or the existence of global attractor. The latter assumption is additionally confirmed by analyzing the corresponding mean-field approximated model. In this bi-stable regime, distribution of event magnitudes follows Gutenberg-Richter power law with satisfying statistical accuracy, including the b-value within the real observed range.

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.

Quantum statistical mechanics of dense partially ionized hydrogen

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

Thermal equilibrium and statistical thermometers in special relativity.

PubMed

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

2007-10-26

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

Stress-induced electric current fluctuations in rocks: a superstatistical model

NASA Astrophysics Data System (ADS)

Cartwright-Taylor, Alexis; Vallianatos, Filippos; Sammonds, Peter

2017-04-01

We recorded spontaneous electric current flow in non-piezoelectric Carrara marble samples during triaxial deformation. Mechanical data, ultrasonic velocities and acoustic emissions were acquired simultaneously with electric current to constrain the relationship between electric current flow, differential stress and damage. Under strain-controlled loading, spontaneous electric current signals (nA) were generated and sustained under all conditions tested. In dry samples, a detectable electric current arises only during dilatancy and the overall signal is correlated with the damage induced by microcracking. Our results show that fracture plays a key role in the generation of electric currents in deforming rocks (Cartwright-Taylor et al., in prep). We also analysed the high-frequency fluctuations of these electric current signals and found that they are not normally distributed - they exhibit power-law tails (Cartwright-Taylor et al., 2014). We modelled these distributions with q-Gaussian statistics, derived by maximising the Tsallis entropy. This definition of entropy is particularly applicable to systems which are strongly correlated and far from equilibrium. Good agreement, at all experimental conditions, between the distributions of electric current fluctuations and the q-Gaussian function with q-values far from one, illustrates the highly correlated, fractal nature of the electric source network within the samples and provides further evidence that the source of the electric signals is the developing fractal network of cracks. It has been shown (Beck, 2001) that q-Gaussian distributions can arise from the superposition of local relaxations in the presence of a slowly varying driving force, thus providing a dynamic reason for the appearance of Tsallis statistics in systems with a fluctuating energy dissipation rate. So, the probability distribution for a dynamic variable, u under some external slow forcing, β, can be obtained as a superposition of temporary local equilibrium processes whose variance fluctuates over time. The appearance of q-Gaussian statistics are caused by the fluctuating β parameter, which effectively models the fluctuating energy dissipation rate in the system. This concept is known as superstatistics and is physically relevant for modelling driven non-equilibrium systems where the environmental conditions fluctuate on a large scale. The idea is that the environmental variable, such as temperature or pressure, changes so slowly that a rapidly fluctuating variable within that environment has time to relax back to equilibrium between each change in the environment. The application of superstatistical techniques to our experimental electric current fluctuations show that they can indeed be described, to good approximation, by the superposition of local Gaussian processes with fluctuating variance. We conclude, then, that the measured electric current fluctuates in response to intermittent energy dissipation and is driven to varying temporary local equilibria during deformation by the variations in stress intensity. The advantage of this technique is that, once the model has been established to be a good description of the system in question, the average β parameter (a measure of the average energy dissipation rate) for the system can be obtained simply from the macroscopic q-Gaussian distribution parameters.

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.

Optimal control of predator-prey mathematical model with infection and harvesting on prey

NASA Astrophysics Data System (ADS)

Diva Amalia, R. U.; Fatmawati; Windarto; Khusnul Arif, Didik

2018-03-01

This paper presents a predator-prey mathematical model with infection and harvesting on prey. The infection and harvesting only occur on the prey population and it assumed that the prey infection would not infect predator population. We analysed the mathematical model of predator-prey with infection and harvesting in prey. Optimal control, which is a prevention of the prey infection, also applied in the model and denoted as U. The purpose of the control is to increase the susceptible prey. The analytical result showed that the model has five equilibriums, namely the extinction equilibrium (E 0), the infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), the predator extinction equilibrium (E 3), and the coexistence equilibrium (E 4). The extinction equilibrium (E 0) is not stable. The infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), also the predator extinction equilibrium (E 3), are locally asymptotically stable with some certain conditions. The coexistence equilibrium (E 4) tends to be locally asymptotically stable. Afterwards, by using the Maximum Pontryagin Principle, we obtained the existence of optimal control U. From numerical simulation, we can conclude that the control could increase the population of susceptible prey and decrease the infected prey.

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

NASA Astrophysics Data System (ADS)

Cazalilla, M. A.; Rigol, M.

2010-05-01

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

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.

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.

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.

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.

Statistical mechanical models for dissociative adsorption of O2 on metal(100) surfaces with blocking, steering, and funneling

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

Evans, James W.; Liu, Da-Jiang

We develop statistical mechanical models amenable to analytic treatment for the dissociative adsorption of O2 at hollow sites on fcc(100) metal surfaces. The models incorporate exclusion of nearest-neighbor pairs of adsorbed O. However, corresponding simple site-blocking models, where adsorption requires a large ensemble of available sites, exhibit an anomalously fast initial decrease in sticking. Thus, in addition to blocking, our models also incorporate more facile adsorption via orientational steering and funneling dynamics (features supported by ab initio Molecular Dynamics studies). Behavior for equilibrated adlayers is distinct from those with finite adspecies mobility. We focus on the low-temperature limited-mobility regime wheremore » analysis of the associated master equations readily produces exact results for both short- and long-time behavior. Kinetic Monte Carlo simulation is also utilized to provide a more complete picture of behavior. These models capture both the initial decrease and the saturation of the experimentally observed sticking versus coverage, as well as features of non-equilibrium adlayer ordering as assessed by surface-sensitive diffraction.« less

Statistical mechanical models for dissociative adsorption of O{sub 2} on metal(100) surfaces with blocking, steering, and funneling

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

Evans, James W.; Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011; Liu, Da-Jiang

We develop statistical mechanical models amenable to analytic treatment for the dissociative adsorption of O{sub 2} at hollow sites on fcc(100) metal surfaces. The models incorporate exclusion of nearest-neighbor pairs of adsorbed O. However, corresponding simple site-blocking models, where adsorption requires a large ensemble of available sites, exhibit an anomalously fast initial decrease in sticking. Thus, in addition to blocking, our models also incorporate more facile adsorption via orientational steering and funneling dynamics (features supported by ab initio Molecular Dynamics studies). Behavior for equilibrated adlayers is distinct from those with finite adspecies mobility. We focus on the low-temperature limited-mobility regimemore » where analysis of the associated master equations readily produces exact results for both short- and long-time behavior. Kinetic Monte Carlo simulation is also utilized to provide a more complete picture of behavior. These models capture both the initial decrease and the saturation of the experimentally observed sticking versus coverage, as well as features of non-equilibrium adlayer ordering as assessed by surface-sensitive diffraction.« less

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

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.

Unsteady Computational Tests of a Non-Equilibrium

NASA Astrophysics Data System (ADS)

Jirasek, Adam; Hamlington, Peter; Lofthouse, Andrew; Usafa Collaboration; Cu Boulder Collaboration

2017-11-01

A non-equilibrium turbulence model is assessed on simulations of three practically-relevant unsteady test cases; oscillating channel flow, transonic flow around an oscillating airfoil, and transonic flow around the Benchmark Super-Critical Wing. The first case is related to piston-driven flows while the remaining cases are relevant to unsteady aerodynamics at high angles of attack and transonic speeds. Non-equilibrium turbulence effects arise in each of these cases in the form of a lag between the mean strain rate and Reynolds stresses, resulting in reduced kinetic energy production compared to classical equilibrium turbulence models that are based on the gradient transport (or Boussinesq) hypothesis. As a result of the improved representation of unsteady flow effects, the non-equilibrium model provides substantially better agreement with available experimental data than do classical equilibrium turbulence models. This suggests that the non-equilibrium model may be ideally suited for simulations of modern high-speed, high angle of attack aerodynamics problems.

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

The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence.

PubMed

Niu, Yuanling; Wang, Yue; Zhou, Da

2015-12-07

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In the previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples. Copyright © 2015 Elsevier Ltd. All rights reserved.

Identifiability of sorption parameters in stirred flow-through reactor experiments and their identification with a Bayesian approach.

PubMed

Nicoulaud-Gouin, V; Garcia-Sanchez, L; Giacalone, M; Attard, J C; Martin-Garin, A; Bois, F Y

2016-10-01

This paper addresses the methodological conditions -particularly experimental design and statistical inference- ensuring the identifiability of sorption parameters from breakthrough curves measured during stirred flow-through reactor experiments also known as continuous flow stirred-tank reactor (CSTR) experiments. The equilibrium-kinetic (EK) sorption model was selected as nonequilibrium parameterization embedding the K d approach. Parameter identifiability was studied formally on the equations governing outlet concentrations. It was also studied numerically on 6 simulated CSTR experiments on a soil with known equilibrium-kinetic sorption parameters. EK sorption parameters can not be identified from a single breakthrough curve of a CSTR experiment, because K d,1 and k - were diagnosed collinear. For pairs of CSTR experiments, Bayesian inference allowed to select the correct models of sorption and error among sorption alternatives. Bayesian inference was conducted with SAMCAT software (Sensitivity Analysis and Markov Chain simulations Applied to Transfer models) which launched the simulations through the embedded simulation engine GNU-MCSim, and automated their configuration and post-processing. Experimental designs consisting in varying flow rates between experiments reaching equilibrium at contamination stage were found optimal, because they simultaneously gave accurate sorption parameters and predictions. Bayesian results were comparable to maximum likehood method but they avoided convergence problems, the marginal likelihood allowed to compare all models, and credible interval gave directly the uncertainty of sorption parameters θ. Although these findings are limited to the specific conditions studied here, in particular the considered sorption model, the chosen parameter values and error structure, they help in the conception and analysis of future CSTR experiments with radionuclides whose kinetic behaviour is suspected. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Non-equilibrium synergistic effects in atmospheric pressure plasmas.

PubMed

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

2018-03-19

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

A statistical model for interpreting computerized dynamic posturography data

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.; Metter, E. Jeffrey; Paloski, William H.

2002-01-01

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

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.…

Maximum caliber inference of nonequilibrium processes

NASA Astrophysics Data System (ADS)

Otten, Moritz; Stock, Gerhard

2010-07-01

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

Understanding the drug release mechanism from a montmorillonite matrix and its binary mixture with a hydrophilic polymer using a compartmental modelling approach

NASA Astrophysics Data System (ADS)

Choiri, S.; Ainurofiq, A.

2018-03-01

Drug release from a montmorillonite (MMT) matrix is a complex mechanism controlled by swelling mechanism of MMT and an interaction of drug and MMT. The aim of this research was to explain a suitable model of the drug release mechanism from MMT and its binary mixture with a hydrophilic polymer in the controlled release formulation based on a compartmental modelling approach. Theophylline was used as a drug model and incorporated into MMT and a binary mixture with hydroxyl propyl methyl cellulose (HPMC) as a hydrophilic polymer, by a kneading method. The dissolution test was performed and the modelling of drug release was assisted by a WinSAAM software. A 2 model was purposed based on the swelling capability and basal spacing of MMT compartments. The model evaluation was carried out to goodness of fit and statistical parameters and models were validated by a cross-validation technique. The drug release from MMT matrix regulated by a burst release mechanism of unloaded drug, swelling ability, basal spacing of MMT compartment, and equilibrium between basal spacing and swelling compartments. Furthermore, the addition of HPMC in MMT system altered the presence of swelling compartment and equilibrium between swelling and basal spacing compartment systems. In addition, a hydrophilic polymer reduced the burst release mechanism of unloaded drug.

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.

Laser Raman Diagnostics in Subsonic and Supersonic Turbulent Jet Diffusion Flames.

NASA Astrophysics Data System (ADS)

Cheng, Tsarng-Sheng

1991-02-01

UV spontaneous vibrational Raman scattering combined with laser-induced predissociative fluorescence (LIPF) is developed for temperature and multi-species concentration measurements. For the first time, simultaneous measurements of temperature, major species (H_2, O_2, N_2, H_2O), and minor species (OH) concentrations are made with a "single" narrowband KrF excimer laser in subsonic and supersonic lifted turbulent hydrogen-air diffusion flames. The UV Raman system is calibrated with a flat -flame diffusion burner operated at several known equivalence ratios from fuel-lean to fuel-rich. Temperature measurements made by the ratio of Stokes/anti-Stokes signal and by the ideal gas law are compared. Single-shot uncertainties for temperature and concentration measurements are analyzed with photon statistics. Calibration constants and bandwidth factors are used in the data reduction program to arrive at temperature and species concentration measurements. UV Raman measurements in the subsonic lifted turbulent diffusion flame indicate that fuel and oxidizer are in rich, premixed, and unignited conditions in the center core of the lifted flame base. The unignited mixtures are due to rapid turbulent mixing that affects chemical reaction. Combustion occurs in an intermittent annular turbulent flame brush with strong finite-rate chemistry effects. The OH radical exists in sub-equilibrium and super-equilibrium concentrations. Major species and temperature are found with non-equilibrium values. Further downstream the super-equilibrium OH radicals decay toward equilibrium through slow three-body recombination reactions. In the supersonic lifted flame, a little reaction occurs upstream of the flame base, due to shock wave interactions and mixing with hot vitiated air. The strong turbulent mixing and total enthalpy fluctuations lead to temperature, major, and minor species concentrations with non-equilibrium values. Combustion occurs farther downstream of the lifted region. Slow three-body recombination reactions result in super-equilibrium OH concentrations that depress temperature below the equilibrium values. Near the equilibrium region, ambient air entrainment contaminates flame properties. These simultaneous measurements of temperature and multi-species concentrations allow a better understanding of the complex turbulence-chemistry interactions and provide information for the input and validation of CFD models.

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

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

Diffusion-model analysis of pPb and PbPb collisions at LHC energies

NASA Astrophysics Data System (ADS)

Schulz, P.; Wolschin, G.

2018-06-01

We present an analysis of centrality-dependent pseudorapidity distributions of produced charged hadrons in pPb and PbPb collisions at the Large Hadron Collider (LHC) energy of s NN = 5.02 TeV, and of minimum-bias pPb collisions at 8.16 TeV within the non-equilibrium-statistical relativistic diffusion model (RDM). In a three-source approach, the role of the fragmentation sources is emphasized. Together with the Jacobian transformation from rapidity to pseudorapidity and the limiting fragmentation conjecture, these are essential for modeling the centrality dependence. For central PbPb collisions, a prediction at the projected FCC energy of s NN = 39 TeV is made.

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

Jin Fengtao; Yuan Jianmin

The experimental transmission spectrum of a hot bromine plasma [J. E. Bailey et al., J. Quant. Spectrosc. Radiat. Transf. 81, 31 (2003)] has been simulated by using a detailed level accounting model (DLA). With assumption of the local thermodynamic equilibrium, the major absorption lines of the experimental spectrum are well reproduced by the present DLA calculation, and the details of the absorption line shapes are used to determine the temperature of the plasma. In contrast to the results of two former statistical models, where the temperature was determined via a global fitting to the experimental data, the present DLA diagnosesmore » the plasma temperature by the line ratios of different charge states in the 2p{yields}3d transition groups resulting in a temperature of 37 eV. It is shown that a change of 1 eV in temperature could cause perceptible changes in the simulated spectrum. It is also shown that the 2p{sub 1/2}{yields}3d{sub 3/2} absorptions have been overestimated by the statistical models.« less

Some comments on thermodynamic consistency for equilibrium mixture equations of state

DOE PAGES

Grove, John W.

2018-03-28

We investigate sufficient conditions for thermodynamic consistency for equilibrium mixtures. Such models assume that the mass fraction average of the material component equations of state, when closed by a suitable equilibrium condition, provide a composite equation of state for the mixture. Here, we show that the two common equilibrium models of component pressure/temperature equilibrium and volume/temperature equilibrium (Dalton, 1808) define thermodynamically consistent mixture equations of state and that other equilibrium conditions can be thermodynamically consistent provided appropriate values are used for the mixture specific entropy and pressure.

Exactly soluble model of the time-resolved fluorescence return to thermal equilibrium in many-particle systems after excitation

NASA Astrophysics Data System (ADS)

Czachor, Andrzej

2016-02-01

In this paper we consider the assembly of weakly interacting identical particles, where the occupation of single-particle energy-levels at thermal equilibrium is governed by statistics. The analytic form of the inter-energy-level jump matrix is derived and analytic solution of the related eigen-problem is given. It allows one to demonstrate the nature of decline in time of the energy emission (fluorescence, recombination) of such many-level system after excitation in a relatively simple and unifying way - as a multi-exponential de-excitation. For the system of L energy levels the number of the de-excitation lifetimes is L-1. The lifetimes depend on the energy level spectrum as a whole. Two- and three-level systems are considered in detail. The impact of the energy level degeneracy on the lifetimes is discussed.

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.

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

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.

PROM7: 1D modeler of solar filaments or prominences

NASA Astrophysics Data System (ADS)

Gouttebroze, P.

2018-05-01

PROM7 is an update of PROM4 (ascl:1306.004) and computes simple models of solar prominences and filaments using Partial Radiative Distribution (PRD). The models consist of plane-parallel slabs standing vertically above the solar surface. Each model is defined by 5 parameters: temperature, density, geometrical thickness, microturbulent velocity and height above the solar surface. It solves the equations of radiative transfer, statistical equilibrium, ionization and pressure equilibria, and computes electron and hydrogen level population and hydrogen line profiles. Moreover, the code treats calcium atom which is reduced to 3 ionization states (Ca I, Ca II, CA III). Ca II ion has 5 levels which are useful for computing 2 resonance lines (H and K) and infrared triplet (to 8500 A).

Economic consequences of aviation system disruptions: A reduced-form computable general equilibrium analysis

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

Chen, Zhenhua; Rose, Adam Z.; Prager, Fynnwin

The state of the art approach to economic consequence analysis (ECA) is computable general equilibrium (CGE) modeling. However, such models contain thousands of equations and cannot readily be incorporated into computerized systems used by policy analysts to yield estimates of economic impacts of various types of transportation system failures due to natural hazards, human related attacks or technological accidents. This paper presents a reduced-form approach to simplify the analytical content of CGE models to make them more transparent and enhance their utilization potential. The reduced-form CGE analysis is conducted by first running simulations one hundred times, varying key parameters, suchmore » as magnitude of the initial shock, duration, location, remediation, and resilience, according to a Latin Hypercube sampling procedure. Statistical analysis is then applied to the “synthetic data” results in the form of both ordinary least squares and quantile regression. The analysis yields linear equations that are incorporated into a computerized system and utilized along with Monte Carlo simulation methods for propagating uncertainties in economic consequences. Although our demonstration and discussion focuses on aviation system disruptions caused by terrorist attacks, the approach can be applied to a broad range of threat scenarios.« less

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

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

Free Energy Defect Model for the Cu-In-Ga-Se Tetrahedral Lattice

NASA Astrophysics Data System (ADS)

Stanbery, B. J.

2003-03-01

The most efficient thin-film photovoltaic converters of solar insolation to electrical power have recently achieved conversion efficiencies exceeding 19%, and are based on light absorbing layers containing the binary alloy (CuInSe_2)_1-X(CuGaSe_2)X of the α phases of these ternary chalcopyrite compounds. A statistical quantum mechanical model of the thermodynamic equilibrium defect structure of the tetrahedral lattice of copper, indium, and selenium with composition in the domain between that of the stoichiometric CuIn_1-XGa_XSe2 alloy and the β phase Cu(In_1-XGa_X)_3Se5 composition is presented. Compositions more copper-deficient than the latter have been reported experimentally to result in a breakdown of the tetrahedral coordination characteristic of the chalcopyrite lattice. These computations are based on a cluster expansion algorithm that minimizes the total free energy of the system using the Gibbs-Duhem equation to compute quasichemical reaction equilibria between the neutral clusters, and explicitly incorporates Fermi-Dirac statistics to determine their ionization equilibria and consequent carrier concentrations in the conduction and valence bands. The results are consistent with recent experimental evidence that the stoichiometric CuIn_1-XGa_XSe2 composition segregates in equilibrium into a two-phase mixture of a copper-deficient quaternary Cu_1-γIn_1-XGa_XSe2 composition and the binary Cu_2-δSe compound. The model predicts that the hole majority carrier (p-type) can only be achieved in the equilibrium single-phase chalcopyrite lattice with compositions that correspond to Cu_1-γIn_1-XGa_XSe_2+ɛ with γ and ɛ >0. This predicted requirement for selenium enrichment compared to the stoichiometric CuIn_1-XGa_XSe2 alloy composition for the dominance of holes over electrons as the majority carrier type is consistent with experimental evidence, and is explained in terms of a transition of the dominant lattice defect from the selenium vacancy in the stoichiometric case to the copper vacancy defect in the selenium-enriched lattice. This result is of particular importance since all CuIn_1-XGa_XSe2 thin-film solar cells utilize p-type absorber films.

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.

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

PubMed

Liu, Xinzijian; Liu, Jian

2018-03-14

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

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

NASA Astrophysics Data System (ADS)

Liu, Xinzijian; Liu, Jian

2018-03-01

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

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

Grape stalks biomass as raw material for activated carbon production: synthesis, characterization and adsorption ability

NASA Astrophysics Data System (ADS)

Hashemi Shahraki, Zahra; Sharififard, Hakimeh; Lashanizadegan, Asghar

2018-05-01

In order to produce activated carbon from grape stalks, this biomass was activated chemically with KOH. Identification methods including FTIR, BET, SEM, Boehm titration and pHzpc measurement were applied to characterize the produced carbon. The adsorption ability of produced activated carbon toward cadmium removal from aqueous solution was evaluated by using Central Composite Design methodology and the effects of process parameters were analysed, as well as, the optimum processing conditions were determined using statistical methods. In order to characterize the equilibrium behaviour of adsorption process, the equilibrium data were analysed by Langmuir, Freundlich, and R-D isotherm models. Results indicated that the adsorption process is a monolayer process and the adsorption capacity of prepared activated carbon was 140.84 mg L‑1. Analysis of kinetics data showed that the pseudo-second-order and Elovich models were well fitted with the kinetics results and this suggests the domination of chemical adsorption. The regenerability results showed that the prepared activated carbon has a reasonable adsorption capacity toward cadmium after five adsorption/desorption cycles.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Isotropic–Nematic Phase Transitions in Gravitational Systems. II. Higher Order Multipoles

NASA Astrophysics Data System (ADS)

Takács, Ádám; Kocsis, Bence

2018-04-01

The gravitational interaction among bodies orbiting in a spherical potential leads to the rapid relaxation of the orbital planes’ distribution, a process called vector resonant relaxation. We examine the statistical equilibrium of this process for a system of bodies with similar semimajor axes and eccentricities. We extend the previous model of Roupas et al. by accounting for the multipole moments beyond the quadrupole, which dominate the interaction for radially overlapping orbits. Nevertheless, we find no qualitative differences between the behavior of the system with respect to the model restricted to the quadrupole interaction. The equilibrium distribution resembles a counterrotating disk at low temperature and a spherical structure at high temperature. The system exhibits a first-order phase transition between the disk and the spherical phase in the canonical ensemble if the total angular momentum is below a critical value. We find that the phase transition erases the high-order multipoles, i.e., small-scale structure in angular momentum space, most efficiently. The system admits a maximum entropy and a maximum energy, which lead to the existence of negative temperature equilibria.

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

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms. [in early star atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Kunasz, P. B.

1978-01-01

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

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

Grove, John W.

We investigate sufficient conditions for thermodynamic consistency for equilibrium mixtures. Such models assume that the mass fraction average of the material component equations of state, when closed by a suitable equilibrium condition, provide a composite equation of state for the mixture. Here, we show that the two common equilibrium models of component pressure/temperature equilibrium and volume/temperature equilibrium (Dalton, 1808) define thermodynamically consistent mixture equations of state and that other equilibrium conditions can be thermodynamically consistent provided appropriate values are used for the mixture specific entropy and pressure.

Mathematical analysis of tuberculosis transmission model with delay

NASA Astrophysics Data System (ADS)

Lapaan, R. D.; Collera, J. A.; Addawe, J. M.

2016-11-01

In this paper, a delayed Tuberculosis infection model is formulated and investigated. We showed the existence of disease free equilibrium and endemic equilibrium points. We used La Salle-Lyapunov Invariance Principle to show that if the reproductive number R0 < 1, the disease-free equilibrium of the model is globally asymptotically stable. Numerical simulations are then performed to illustrate the existence of the disease free equilibrium and the endemic equilibrium point for a given value of R0. Thus, when R0 < 1, the disease dies out in the population.

A complex network description on traditional Chinese medicine system

NASA Astrophysics Data System (ADS)

Sun, Anzheng; Zhang, Peipei; He, Yue; Su, Beibei; He, Da-Ren

2004-03-01

Chinese traditional philosophy believes that a healthy body can adjust itself to reach a dynamic equilibrium with the environment. At an ill state the equilibrium is lost. Any single medicine can only attack one problem and cannot recover the whole equilibrium. A prescription formulation (PF) usually contains an "emperor" or principal medicine, several "minister" or assistant medicines, some accessorial medicines, and one or two inducting or harmonizing edicines. Therefore different traditional Chinese medicine (TCM) appears in different number of PFs. The whole TCM system may be viewed as a network set composed of many complete graphs (PFs). The TCMs, which have the highest node degrees in the network, serve as the "bridges" between the complete graphs for forming the network. While the TCMs, which have lowest node degrees in the network, serve as the "emperors" in each complete graph. According to this idea we have performed a manual statistical investigation on approximately 1000 PFs and computed 8 different tatistical properties of the network. The results show that TCM system is a scale-free one and has a nice clustering structure. We are suggesting a dynamical model to describe the development of TCM system.

Stability analysis of the Euler discretization for SIR epidemic model

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

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

Memcapacitor model and its application in chaotic oscillator with memristor.

PubMed

Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

2017-01-01

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

All human Na(+)-K(+)-ATPase alpha-subunit isoforms have a similar affinity for cardiac glycosides.

PubMed

Wang, J; Velotta, J B; McDonough, A A; Farley, R A

2001-10-01

Three alpha-subunit isoforms of the sodium pump, which is the receptor for cardiac glycosides, are expressed in human heart. The aim of this study was to determine whether these isoforms have distinct affinities for the cardiac glycoside ouabain. Equilibrium ouabain binding to membranes from a panel of different human tissues and cell lines derived from human tissues was compared by an F statistic to determine whether a single population of binding sites or two populations of sites with different affinities would better fit the data. For all tissues, the single-site model fit the data as well as the two-site model. The mean equilibrium dissociation constant (K(d)) for all samples calculated using the single-site model was 18 +/- 6 nM (mean +/- SD). No difference in K(d) was found between nonfailing and failing human heart samples, although the maximum number of binding sites in failing heart was only approximately 50% of the number of sites in nonfailing heart. Measurement of association rate constants and dissociation rate constants confirmed that the binding affinities of the different human alpha-isoforms are similar to each other, although calculated K(d) values were lower than those determined by equilibrium binding. These results indicate both that the affinity of all human alpha-subunit isoforms for ouabain is similar and that the increased sensitivity of failing human heart to cardiac glycosides is probably due to a reduction in the number of pumps in the heart rather than to a selective inhibition of a subset of pumps with different affinities for the drugs.

HCN production from impact ejecta on the early Earth

NASA Astrophysics Data System (ADS)

Parkos, Devon; Pikus, Aaron; Alexeenko, Alina; Melosh, H. J.

2016-11-01

Major impact events have drastically altered the evolution of life on Earth. The reentry of ejecta formed from these events can trigger widespread chemical changes to the atmosphere on a global scale. This mechanism was proposed as a source of HCN during the Late Heavy Bombardment (LHB), 4.1 to 3.8 billion years ago. Significant concentrations of HCN in surface water could directly lead to adenine formation, a precursor for RNA. This work uses the Direct Simulation Monte Carlo (DSMC) method to examine the production of CN and HCN due to the reentry of impact ejecta. We use the Statistical Modeling in Low-Density Environment (SMILE) code, which utilizes the Total Collisional Energy (TCE) model for reactions. The collisions are described by the Variable Soft Sphere (VSS) and Larsen-Borgnakke (LB) models. We compare this nonequilibrium production to equilibrium concentrations from bulk atmospheric heating. The equilibrium HCN yield for a 1023 J impact is 7.0×104 moles, corresponding to a 2.5×1014 molecules per m2 surface deposition. We find that additional CN and HCN is produced under thermochemical nonequilibrium, particularly at higher altitudes. The total nonequilibrium yield for a 1023 J impact is 1.2×106 moles of HCN, a value 17 times the equilibrium result. This corresponds to a surface deposition of 1.4×1015 molecules per m2. This increase in production indicates that thermochemical nonequilibrium effects play a strong role in HCN from impact ejecta, and must be considered when investigating impacts as a plausible mechanism for significant adenine production during the LHB.

Rates of profit as correlated sums of random variables

NASA Astrophysics Data System (ADS)

Greenblatt, R. E.

2013-10-01

Profit realization is the dominant feature of market-based economic systems, determining their dynamics to a large extent. Rather than attaining an equilibrium, profit rates vary widely across firms, and the variation persists over time. Differing definitions of profit result in differing empirical distributions. To study the statistical properties of profit rates, I used data from a publicly available database for the US Economy for 2009-2010 (Risk Management Association). For each of three profit rate measures, the sample space consists of 771 points. Each point represents aggregate data from a small number of US manufacturing firms of similar size and type (NAICS code of principal product). When comparing the empirical distributions of profit rates, significant ‘heavy tails’ were observed, corresponding principally to a number of firms with larger profit rates than would be expected from simple models. An apparently novel correlated sum of random variables statistical model was used to model the data. In the case of operating and net profit rates, a number of firms show negative profits (losses), ruling out simple gamma or lognormal distributions as complete models for these data.

Description of the General Equilibrium Model of Ecosystem Services (GEMES)

Treesearch

Travis Warziniack; David Finnoff; Jenny Apriesnig

2017-01-01

This paper serves as documentation for the General Equilibrium Model of Ecosystem Services (GEMES). GEMES is a regional computable general equilibrium model that is composed of values derived from natural capital and ecosystem services. It models households, producing sectors, and governments, linked to one another through commodity and factor markets. GEMES was...

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Technical Reports Server (NTRS)

Francois, J.

1981-01-01

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

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

NASA Astrophysics Data System (ADS)

Rudd, James Andrew, II

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

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

PubMed

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Statistical thermodynamics and the size distributions of tropical convective clouds.

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Pavlos, George

2015-04-01

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

Towards Non-Equilibrium Dynamics with Trapped Ions

NASA Astrophysics Data System (ADS)

Silbert, Ariel; Jubin, Sierra; Doret, Charlie

2016-05-01

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

Equilibrium and kinetic models for colloid release under transient solution chemistry conditions

USDA-ARS?s Scientific Manuscript database

We present continuum models to describe colloid release in the subsurface during transient physicochemical conditions. Our modeling approach relates the amount of colloid release to changes in the fraction of the solid surface area that contributes to retention. Equilibrium, kinetic, equilibrium and...

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

NASA Astrophysics Data System (ADS)

Bargigli, Leonardo; Viaggiu, Stefano; Lionetto, Andrea

2016-10-01

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

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

PubMed Central

Chowdhury, Debashish

2013-01-01

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

The assumption of equilibrium in models of migration.

PubMed

Schachter, J; Althaus, P G

1993-02-01

In recent articles Evans (1990) and Harrigan and McGregor (1993) (hereafter HM) scrutinized the equilibrium model of migration presented in a 1989 paper by Schachter and Althaus. This model used standard microeconomics to analyze gross interregional migration flows based on the assumption that gross flows are in approximate equilibrium. HM criticized the model as theoretically untenable, while Evans summoned empirical as well as theoretical objections. HM claimed that equilibrium of gross migration flows could be ruled out on theoretical grounds. They argued that the absence of net migration requires that either all regions have equal populations or that unsustainable regional migration propensities must obtain. In fact some moves are inter- and other are intraregional. It does not follow, however, that the number of interregional migrants will be larger for the more populous region. Alternatively, a country could be divided into a large number of small regions that have equal populations. With uniform propensities to move, each of these analytical regions would experience in equilibrium zero net migration. Hence, the condition that net migration equal zero is entirely consistent with unequal distributions of population across regions. The criticisms of Evans were based both on flawed reasoning and on misinterpretation of the results of a number of econometric studies. His reasoning assumed that the existence of demand shifts as found by Goldfarb and Yezer (1987) and Topel (1986) invalidated the equilibrium model. The equilibrium never really obtains exactly, but economic modeling of migration properly begins with a simple equilibrium model of the system. A careful reading of the papers Evans cited in support of his position showed that in fact they affirmed rather than denied the appropriateness of equilibrium modeling. Zero net migration together with nonzero gross migration are not theoretically incompatible with regional heterogeneity of population, wages, or amenities.

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

Lei, Huan; Baker, Nathan A.; Li, Xiantao

We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.

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

Gevorkyan, A. S., E-mail: g-ashot@sci.am; Sahakyan, V. V.

We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.

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.

Aggregation and Disaggregation of Senile Plaques in Alzheimer Disease

NASA Astrophysics Data System (ADS)

Cruz, L.; Urbanc, B.; Buldyrev, S. V.; Christie, R.; Gomez-Isla, T.; Havlin, S.; McNamara, M.; Stanley, H. E.; Hyman, B. T.

1997-07-01

We quantitatively analyzed, using laser scanning confocal microscopy, the three-dimensional structure of individual senile plaques in Alzheimer disease. We carried out the quantitative analysis using statistical methods to gain insights about the processes that govern Aβ peptide deposition. Our results show that plaques are complex porous structures with characteristic pore sizes. We interpret plaque morphology in the context of a new dynamical model based on competing aggregation and disaggregation processes in kinetic steady-state equilibrium with an additional diffusion process allowing Aβ deposits to diffuse over the surface of plaques.

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.

Collective effects in models for interacting molecular motors and motor-microtubule mixtures

NASA Astrophysics Data System (ADS)

Menon, Gautam I.

2006-12-01

Three problems in the statistical mechanics of models for an assembly of molecular motors interacting with cytoskeletal filaments are reviewed. First, a description of the hydrodynamical behaviour of density-density correlations in fluctuating ratchet models for interacting molecular motors is outlined. Numerical evidence indicates that the scaling properties of dynamical behaviour in such models belong to the KPZ universality class. Second, the generalization of such models to include boundary injection and removal of motors is provided. In common with known results for the asymmetric exclusion processes, simulations indicate that such models exhibit sharp boundary driven phase transitions in the thermodynamic limit. In the third part of this paper, recent progress towards a continuum description of pattern formation in mixtures of motors and microtubules is described, and a non-equilibrium “phase-diagram” for such systems discussed.

Economic communication model set

NASA Astrophysics Data System (ADS)

Zvereva, Olga M.; Berg, Dmitry B.

2017-06-01

This paper details findings from the research work targeted at economic communications investigation with agent-based models usage. The agent-based model set was engineered to simulate economic communications. Money in the form of internal and external currencies was introduced into the models to support exchanges in communications. Every model, being based on the general concept, has its own peculiarities in algorithm and input data set since it was engineered to solve the specific problem. Several and different origin data sets were used in experiments: theoretic sets were estimated on the basis of static Leontief's equilibrium equation and the real set was constructed on the basis of statistical data. While simulation experiments, communication process was observed in dynamics, and system macroparameters were estimated. This research approved that combination of an agent-based and mathematical model can cause a synergetic effect.

Modeling stock return distributions with a quantum harmonic oscillator

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Experimental testing of olivine-melt equilibrium models at high temperatures

NASA Astrophysics Data System (ADS)

Krasheninnikov, S. P.; Sobolev, A. V.; Batanova, V. G.; Kargaltsev, A. A.; Borisov, A. A.

2017-08-01

Data are presented on the equilibrium compositions of olivine and melts in the products of 101 experiments performed at 1300-1600°C, atmospheric pressure, and controlled oxygen fugacity by means of new equipment at the Vernadsky Institute. It was shown that the available models of the olivine-melt equilibrium describe with insufficient adequacy the natural systems at temperatures over 1400°C. The most adequate is the model by Ford et al. (1983). However, this model overestimates systematically the equilibrium temperature with underestimating by 20-40°C at 1450-1600°C. These data point to the need for developing a new, improved quantitative model of the olivine-melt equilibrium for high-temperature magnesian melts, as well as to the possibility of these studies on the basis of the equipment presented.

MINTEQA2

EPA Science Inventory

MINTEQA2 is a equilibrium speciation model that can be used to calculate the equilibrium composition of dilute aqueous solutions in the laboratory or in natural aqueous systems. The model is useful for calculating the equilibrium mass distribution among dissolved species, adsorb...

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

PubMed

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

2015-01-01

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

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

NASA Technical Reports Server (NTRS)

Tew, Roy C.; Simon, Terry; Gedeon, David; Ibrahim, Mounir; Rong, Wei

2006-01-01

The objective of this paper is to define empirical parameters for an initial thermal non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two codes currently used at Glenn Research Center for Stirling modeling are Fluent and CFD-ACE. The codes porous-media models are equilibrium models, which assume solid matrix and fluid are in thermal equilibrium. This is believed to be a poor assumption for Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, use non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location and time during the cycle. Experimentally based information was used to define: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity was also estimated. Determination of model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Converter (TDC), which uses a random-fiber regenerator matrix. Emphasis is on use of available data to define empirical parameters needed in a thermal non-equilibrium porous media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates.

The non-equilibrium and energetic cost of sensory adaptation

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

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

2011-03-24

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

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

PubMed

Bustamante, Carlos

2005-11-01

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

Dynamic Processes of Conceptual Change: Analysis of Constructing Mental Models of Chemical Equilibrium.

ERIC Educational Resources Information Center

Chiu, Mei-Hung; Chou, Chin-Cheng; Liu, Chia-Ju

2002-01-01

Investigates students' mental models of chemical equilibrium using dynamic science assessments. Reports that students at various levels have misconceptions about chemical equilibrium. Involves 10th grade students (n=30) in the study doing a series of hands-on chemical experiments. Focuses on the process of constructing mental models, dynamic…

An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Turkington, Bruce

2013-08-01

A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

NASA Technical Reports Server (NTRS)

Tew, Roy; Simon, Terry; Gedeon, David; Ibrahim, Mounir; Rong, Wei

2006-01-01

The objective of this paper is to define empirical parameters (or closwre models) for an initial thermai non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two CFD codes currently being used at Glenn Research Center (GRC) for Stirling engine modeling are Fluent and CFD-ACE. The porous-media models available in each of these codes are equilibrium models, which assmne that the solid matrix and the fluid are in thermal equilibrium at each spatial location within the porous medium. This is believed to be a poor assumption for the oscillating-flow environment within Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, we non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location end time during the cycle. A NASA regenerator research grant has been providing experimental and computational results to support definition of various empirical coefficients needed in defining a noa-equilibrium, macroscopic, porous-media model (i.e., to define "closure" relations). The grant effort is being led by Cleveland State University, with subcontractor assistance from the University of Minnesota, Gedeon Associates, and Sunpower, Inc. Friction-factor and heat-transfer correlations based on data taken with the NASAlSunpower oscillating-flow test rig also provide experimentally based correlations that are useful in defining parameters for the porous-media model; these correlations are documented in Gedeon Associates' Sage Stirling-Code Manuals. These sources of experimentally based information were used to define the following terms and parameters needed in the non-equilibrium porous-media model: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity (including themal dispersion and estimate of tortuosity effects}, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity (including the effect of tortuosity) was also estimated. Determination of the porous-media model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Convertor (TDC), which uses a random-fiber regenerator matrix. The non-equilibrium porous-media model presented is considered to be an initial, or "draft," model for possible incorporation in commercial CFD codes, with the expectation that the empirical parameters will likely need to be updated once resulting Stirling CFD model regenerator and engine results have been analyzed. The emphasis of the paper is on use of available data to define empirical parameters (and closure models) needed in a thermal non-equilibrium porous-media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates. However, it is anticipated that a thermal non-equilibrium model such as that presented here, when iacorporated in the CFD codes, will improve our ability to accurately model Stirling regenerators with CFD relative to current thermal-equilibrium porous-media models.

A Viscoelastic Constitutive Model Can Accurately Represent Entire Creep Indentation Tests of Human Patella Cartilage

PubMed Central

Pal, Saikat; Lindsey, Derek P.; Besier, Thor F.; Beaupre, Gary S.

2013-01-01

Cartilage material properties provide important insights into joint health, and cartilage material models are used in whole-joint finite element models. Although the biphasic model representing experimental creep indentation tests is commonly used to characterize cartilage, cartilage short-term response to loading is generally not characterized using the biphasic model. The purpose of this study was to determine the short-term and equilibrium material properties of human patella cartilage using a viscoelastic model representation of creep indentation tests. We performed 24 experimental creep indentation tests from 14 human patellar specimens ranging in age from 20 to 90 years (median age 61 years). We used a finite element model to reproduce the experimental tests and determined cartilage material properties from viscoelastic and biphasic representations of cartilage. The viscoelastic model consistently provided excellent representation of the short-term and equilibrium creep displacements. We determined initial elastic modulus, equilibrium elastic modulus, and equilibrium Poisson’s ratio using the viscoelastic model. The viscoelastic model can represent the short-term and equilibrium response of cartilage and may easily be implemented in whole-joint finite element models. PMID:23027200

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.

Science Notes.

ERIC Educational Resources Information Center

School Science Review, 1989

1989-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Tang, Gaomin; Thingna, Juzar; Wang, Jian

2018-04-01

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

Foundations of statistical mechanics from symmetries of entanglement

DOE PAGES

Deffner, Sebastian; Zurek, Wojciech H.

2016-06-09

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

Equilibrium of Global Amphibian Species Distributions with Climate

PubMed Central

Munguía, Mariana; Rahbek, Carsten; Rangel, Thiago F.; Diniz-Filho, Jose Alexandre F.; Araújo, Miguel B.

2012-01-01

A common assumption in bioclimatic envelope modeling is that species distributions are in equilibrium with contemporary climate. A number of studies have measured departures from equilibrium in species distributions in particular regions, but such investigations were never carried out for a complete lineage across its entire distribution. We measure departures of equilibrium with contemporary climate for the distributions of the world amphibian species. Specifically, we fitted bioclimatic envelopes for 5544 species using three presence-only models. We then measured the proportion of the modeled envelope that is currently occupied by the species, as a metric of equilibrium of species distributions with climate. The assumption was that the greater the difference between modeled bioclimatic envelope and the occupied distribution, the greater the likelihood that species distribution would not be at equilibrium with contemporary climate. On average, amphibians occupied 30% to 57% of their potential distributions. Although patterns differed across regions, there were no significant differences among lineages. Species in the Neotropic, Afrotropics, Indo-Malay, and Palaearctic occupied a smaller proportion of their potential distributions than species in the Nearctic, Madagascar, and Australasia. We acknowledge that our models underestimate non equilibrium, and discuss potential reasons for the observed patterns. From a modeling perspective our results support the view that at global scale bioclimatic envelope models might perform similarly across lineages but differently across regions. PMID:22511938

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.

Feedback Controlled Colloidal Assembly at Fluid Interfaces

NASA Astrophysics Data System (ADS)

Bevan, Michael

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

Polylogarithmic equilibrium treatment of molecular aggregation and critical concentrations.

PubMed

Michel, Denis; Ruelle, Philippe

2017-02-15

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

The Cluster Variation Method: A Primer for Neuroscientists.

PubMed

Maren, Alianna J

2016-09-30

Effective Brain-Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables , is defined in terms of a single interaction enthalpy parameter ( h ) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.

Time irreversibility in reversible shell models of turbulence.

PubMed

De Pietro, Massimo; Biferale, Luca; Boffetta, Guido; Cencini, Massimo

2018-04-06

Turbulent flows governed by the Navier-Stokes equations (NSE) generate an out-of-equilibrium time irreversible energy cascade from large to small scales. In the NSE, the energy transfer is due to the nonlinear terms that are formally symmetric under time reversal. As for the dissipative term: first, it explicitly breaks time reversibility; second, it produces a small-scale sink for the energy transfer that remains effective even in the limit of vanishing viscosity. As a result, it is not clear how to disentangle the time irreversibility originating from the non-equilibrium energy cascade from the explicit time-reversal symmetry breaking due to the viscous term. To this aim, in this paper we investigate the properties of the energy transfer in turbulent shell models by using a reversible viscous mechanism, avoiding any explicit breaking of the [Formula: see text] symmetry. We probe time irreversibility by studying the statistics of Lagrangian power, which is found to be asymmetric under time reversal also in the time-reversible model. This suggests that the turbulent dynamics converges to a strange attractor where time reversibility is spontaneously broken and whose properties are robust for what concerns purely inertial degrees of freedoms, as verified by the anomalous scaling behavior of the velocity structure functions.

The Cluster Variation Method: A Primer for Neuroscientists

PubMed Central

Maren, Alianna J.

2016-01-01

Effective Brain–Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found. PMID:27706022

Evolution of social versus individual learning in a subdivided population revisited: comparative analysis of three coexistence mechanisms using the inclusive-fitness method.

PubMed

Kobayashi, Yutaka; Ohtsuki, Hisashi

2014-03-01

Learning abilities are categorized into social (learning from others) and individual learning (learning on one's own). Despite the typically higher cost of individual learning, there are mechanisms that allow stable coexistence of both learning modes in a single population. In this paper, we investigate by means of mathematical modeling how the effect of spatial structure on evolutionary outcomes of pure social and individual learning strategies depends on the mechanisms for coexistence. We model a spatially structured population based on the infinite-island framework and consider three scenarios that differ in coexistence mechanisms. Using the inclusive-fitness method, we derive the equilibrium frequency of social learners and the genetic load of social learning (defined as average fecundity reduction caused by the presence of social learning) in terms of some summary statistics, such as relatedness, for each of the three scenarios and compare the results. This comparative analysis not only reconciles previous models that made contradictory predictions as to the effect of spatial structure on the equilibrium frequency of social learners but also derives a simple mathematical rule that determines the sign of the genetic load (i.e. whether or not social learning contributes to the mean fecundity of the population). Copyright © 2013 Elsevier Inc. All rights reserved.

Spread of Ebola disease with susceptible exposed infected isolated recovered (SEIIhR) model

NASA Astrophysics Data System (ADS)

Azizah, Afina; Widyaningsih, Purnami; Retno Sari Saputro, Dewi

2017-06-01

Ebola is a deadly infectious disease and has caused an epidemic on several countries in West Africa. Mathematical modeling to study the spread of Ebola disease has been developed, including through models susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR). Furthermore, susceptible exposed infected isolated recovered (SEIIhR) model has been derived. The aims of this research are to derive SEIIhR model for Ebola disease, to determine the patterns of its spread, to determine the equilibrium point and stability of the equilibrium point using phase plane analysis, and also to apply the SEIIhR model on Ebola epidemic in Sierra Leone in 2014. The SEIIhR model is a differential equation system. Pattern of ebola disease spread with SEIIhR model is solution of the differential equation system. The equilibrium point of SEIIhR model is unique and it is a disease-free equilibrium point that stable. Application of the model is based on the data Ebola epidemic in Sierra Leone. The free-disease equilibrium point (Se; Ee; Ie; Ihe; Re )=(5743865, 0, 0, 0, 0) is stable.

Wet scrubbing of biomass producer gas tars using vegetable oil

NASA Astrophysics Data System (ADS)

Bhoi, Prakashbhai Ramabhai

The overall aims of this research study were to generate novel design data and to develop an equilibrium stage-based thermodynamic model of a vegetable oil based wet scrubbing system for the removal of model tar compounds (benzene, toluene and ethylbenzene) found in biomass producer gas. The specific objectives were to design, fabricate and evaluate a vegetable oil based wet scrubbing system and to optimize the design and operating variables; i.e., packed bed height, vegetable oil type, solvent temperature, and solvent flow rate. The experimental wet packed bed scrubbing system includes a liquid distributor specifically designed to distribute a high viscous vegetable oil uniformly and a mixing section, which was designed to generate a desired concentration of tar compounds in a simulated air stream. A method and calibration protocol of gas chromatography/mass spectroscopy was developed to quantify tar compounds. Experimental data were analyzed statistically using analysis of variance (ANOVA) procedure. Statistical analysis showed that both soybean and canola oils are potential solvents, providing comparable removal efficiency of tar compounds. The experimental height equivalent to a theoretical plate (HETP) was determined as 0.11 m for vegetable oil based scrubbing system. Packed bed height and solvent temperature had highly significant effect (p0.05) effect on the removal of model tar compounds. The packing specific constants, Ch and CP,0, for the Billet and Schultes pressure drop correlation were determined as 2.52 and 2.93, respectively. The equilibrium stage based thermodynamic model predicted the removal efficiency of model tar compounds in the range of 1-6%, 1-4% and 1-2% of experimental data for benzene, toluene and ethylbenzene, respectively, for the solvent temperature of 30° C. The NRTL-PR property model and UNIFAC for estimating binary interaction parameters are recommended for modeling absorption of tar compounds in vegetable oils. Bench scale experimental data from the wet scrubbing system would be useful in the design and operation of a pilot scale vegetable oil based system. The process model, validated using experimental data, would be a key design tool for the design and optimization of a pilot scale vegetable oil based system.

Wall ablation of heated compound-materials into non-equilibrium discharge plasmas

NASA Astrophysics Data System (ADS)

Wang, Weizong; Kong, Linghan; Geng, Jinyue; Wei, Fuzhi; Xia, Guangqing

2017-02-01

The discharge properties of the plasma bulk flow near the surface of heated compound-materials strongly affects the kinetic layer parameters modeled and manifested in the Knudsen layer. This paper extends the widely used two-layer kinetic ablation model to the ablation controlled non-equilibrium discharge due to the fact that the local thermodynamic equilibrium (LTE) approximation is often violated as a result of the interaction between the plasma and solid walls. Modifications to the governing set of equations, to account for this effect, are derived and presented by assuming that the temperature of the electrons deviates from that of the heavy particles. The ablation characteristics of one typical material, polytetrafluoroethylene (PTFE) are calculated with this improved model. The internal degrees of freedom as well as the average particle mass and specific heat ratio of the polyatomic vapor, which strongly depends on the temperature, pressure and plasma non-equilibrium degree and plays a crucial role in the accurate determination of the ablation behavior by this model, are also taken into account. Our assessment showed the significance of including such modifications related to the non-equilibrium effect in the study of vaporization of heated compound materials in ablation controlled arcs. Additionally, a two-temperature magneto-hydrodynamic (MHD) model accounting for the thermal non-equilibrium occurring near the wall surface is developed and applied into an ablation-dominated discharge for an electro-thermal chemical launch device. Special attention is paid to the interaction between the non-equilibrium plasma and the solid propellant surface. Both the mass exchange process caused by the wall ablation and plasma species deposition as well as the associated momentum and energy exchange processes are taken into account. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The non-equilibrium results show a non-equilibrium region near the plasma-wall interaction region and this indicates the need for the consideration of the influence of the possible departure from LTE in the plasma bulk on the determination of ablation rate.

A New Statistical Model of Electroencephalogram Noise Spectra for Real-Time Brain-Computer Interfaces.

PubMed

Paris, Alan; Atia, George K; Vosoughi, Azadeh; Berman, Stephen A

2017-08-01

A characteristic of neurological signal processing is high levels of noise from subcellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model that has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 to over 30 Hz, and has approximately 1/f θ behavior in the midfrequencies without infinities. We validate this model using three approaches. First, we show how GVZM PSDs can arise in a population of ion channels at maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely used SSVEP estimators. The GVZM noise model can be a useful and reliable technique for EEG signal processing. Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces, which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.

Statistical errors in molecular dynamics averages

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

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

1985-11-15

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

cgDNAweb: a web interface to the cgDNA sequence-dependent coarse-grain model of double-stranded DNA.

PubMed

De Bruin, Lennart; Maddocks, John H

2018-06-14

The sequence-dependent statistical mechanical properties of fragments of double-stranded DNA is believed to be pertinent to its biological function at length scales from a few base pairs (or bp) to a few hundreds of bp, e.g. indirect read-out protein binding sites, nucleosome positioning sequences, phased A-tracts, etc. In turn, the equilibrium statistical mechanics behaviour of DNA depends upon its ground state configuration, or minimum free energy shape, as well as on its fluctuations as governed by its stiffness (in an appropriate sense). We here present cgDNAweb, which provides browser-based interactive visualization of the sequence-dependent ground states of double-stranded DNA molecules, as predicted by the underlying cgDNA coarse-grain rigid-base model of fragments with arbitrary sequence. The cgDNAweb interface is specifically designed to facilitate comparison between ground state shapes of different sequences. The server is freely available at cgDNAweb.epfl.ch with no login requirement.

Some Research Centers for Plasma Physics and Solid State Physics in the Netherlands and Belgium. Part II. Belgium,

DTIC Science & Technology

plasma column and observed the interesting phenomenon of plasma ejection. At FUB, Balescu and Prigogine direct a group of sixty theoreticians doing...outstanding work in statistical physics. Balescu is writing another graduate textbook on non-equilibrium statistical mechanics. He is tackling the

An Analytic Approach to Modeling Land-Atmosphere Interaction: 1. Construct and Equilibrium Behavior

NASA Astrophysics Data System (ADS)

Brubaker, Kaye L.; Entekhabi, Dara

1995-03-01

A four-variable land-atmosphere model is developed to investigate the coupled exchanges of water and energy between the land surface and atmosphere and the role of these exchanges in the statistical behavior of continental climates. The land-atmosphere system is substantially simplified and formulated as a set of ordinary differential equations that, with the addition of random noise, are suitable for analysis in the form of the multivariate Îto equation. The model treats the soil layer and the near-surface atmosphere as reservoirs with storage capacities for heat and water. The transfers between these reservoirs are regulated by four states: soil saturation, soil temperature, air specific humidity, and air potential temperature. The atmospheric reservoir is treated as a turbulently mixed boundary layer of fixed depth. Heat and moisture advection, precipitation, and layer-top air entrainment are parameterized. The system is forced externally by solar radiation and the lateral advection of air and water mass. The remaining energy and water mass exchanges are expressed in terms of the state variables. The model development and equilibrium solutions are presented. Although comparisons between observed data and steady state model results re inexact, the model appears to do a reasonable job of partitioning net radiation into sensible and latent heat flux in appropriate proportions for bare-soil midlatitude summer conditions. Subsequent work will introduce randomness into the forcing terms to investigate the effect of water-energy coupling and land-atmosphere interaction on variability and persistence in the climatic system.

Models of supply function equilibrium with applications to the electricity industry

NASA Astrophysics Data System (ADS)

Aromi, J. Daniel

Electricity market design requires tools that result in a better understanding of incentives of generators and consumers. Chapter 1 and 2 provide tools and applications of these tools to analyze incentive problems in electricity markets. In chapter 1, models of supply function equilibrium (SFE) with asymmetric bidders are studied. I prove the existence and uniqueness of equilibrium in an asymmetric SFE model. In addition, I propose a simple algorithm to calculate numerically the unique equilibrium. As an application, a model of investment decisions is considered that uses the asymmetric SFE as an input. In this model, firms can invest in different technologies, each characterized by distinct variable and fixed costs. In chapter 2, option contracts are introduced to a supply function equilibrium (SFE) model. The uniqueness of the equilibrium in the spot market is established. Comparative statics results on the effect of option contracts on the equilibrium price are presented. A multi-stage game where option contracts are traded before the spot market stage is considered. When contracts are optimally procured by a central authority, the selected profile of option contracts is such that the spot market price equals marginal cost for any load level resulting in a significant reduction in cost. If load serving entities (LSEs) are price takers, in equilibrium, there is no trade of option contracts. Even when LSEs have market power, the central authority's solution cannot be implemented in equilibrium. In chapter 3, we consider a game in which a buyer must repeatedly procure an input from a set of firms. In our model, the buyer is able to sign long term contracts that establish the likelihood with which the next period contract is awarded to an entrant or the incumbent. We find that the buyer finds it optimal to favor the incumbent, this generates more intense competition between suppliers. In a two period model we are able to completely characterize the optimal mechanism.

Modeling of uncertainties in biochemical reactions.

PubMed

Mišković, Ljubiša; Hatzimanikatis, Vassily

2011-02-01

Mathematical modeling is an indispensable tool for research and development in biotechnology and bioengineering. The formulation of kinetic models of biochemical networks depends on knowledge of the kinetic properties of the enzymes of the individual reactions. However, kinetic data acquired from experimental observations bring along uncertainties due to various experimental conditions and measurement methods. In this contribution, we propose a novel way to model the uncertainty in the enzyme kinetics and to predict quantitatively the responses of metabolic reactions to the changes in enzyme activities under uncertainty. The proposed methodology accounts explicitly for mechanistic properties of enzymes and physico-chemical and thermodynamic constraints, and is based on formalism from systems theory and metabolic control analysis. We achieve this by observing that kinetic responses of metabolic reactions depend: (i) on the distribution of the enzymes among their free form and all reactive states; (ii) on the equilibrium displacements of the overall reaction and that of the individual enzymatic steps; and (iii) on the net fluxes through the enzyme. Relying on this observation, we develop a novel, efficient Monte Carlo sampling procedure to generate all states within a metabolic reaction that satisfy imposed constrains. Thus, we derive the statistics of the expected responses of the metabolic reactions to changes in enzyme levels and activities, in the levels of metabolites, and in the values of the kinetic parameters. We present aspects of the proposed framework through an example of the fundamental three-step reversible enzymatic reaction mechanism. We demonstrate that the equilibrium displacements of the individual enzymatic steps have an important influence on kinetic responses of the enzyme. Furthermore, we derive the conditions that must be satisfied by a reversible three-step enzymatic reaction operating far away from the equilibrium in order to respond to changes in metabolite levels according to the irreversible Michelis-Menten kinetics. The efficient sampling procedure allows easy, scalable, implementation of this methodology to modeling of large-scale biochemical networks. © 2010 Wiley Periodicals, Inc.

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

Bayesian inference for the spatio-temporal invasion of alien species.

PubMed

Cook, Alex; Marion, Glenn; Butler, Adam; Gibson, Gavin

2007-08-01

In this paper we develop a Bayesian approach to parameter estimation in a stochastic spatio-temporal model of the spread of invasive species across a landscape. To date, statistical techniques, such as logistic and autologistic regression, have outstripped stochastic spatio-temporal models in their ability to handle large numbers of covariates. Here we seek to address this problem by making use of a range of covariates describing the bio-geographical features of the landscape. Relative to regression techniques, stochastic spatio-temporal models are more transparent in their representation of biological processes. They also explicitly model temporal change, and therefore do not require the assumption that the species' distribution (or other spatial pattern) has already reached equilibrium as is often the case with standard statistical approaches. In order to illustrate the use of such techniques we apply them to the analysis of data detailing the spread of an invasive plant, Heracleum mantegazzianum, across Britain in the 20th Century using geo-referenced covariate information describing local temperature, elevation and habitat type. The use of Markov chain Monte Carlo sampling within a Bayesian framework facilitates statistical assessments of differences in the suitability of different habitat classes for H. mantegazzianum, and enables predictions of future spread to account for parametric uncertainty and system variability. Our results show that ignoring such covariate information may lead to biased estimates of key processes and implausible predictions of future distributions.

Prediction of Down-Gradient Impacts of DNAPL Source Depletion Using Tracer Techniques

NASA Astrophysics Data System (ADS)

Basu, N. B.; Fure, A. D.; Jawitz, J. W.

2006-12-01

Four simplified DNAPL source depletion models that have been discussed in the literature recently are evaluated for the prediction of long-term effects of source depletion under natural gradient flow. These models are simple in form (a power function equation is an example) but are shown here to serve as mathematical analogs to complex multiphase flow and transport simulators. One of the source depletion models, the equilibrium streamtube model, is shown to be relatively easily parameterized using non-reactive and reactive tracers. Non-reactive tracers are used to characterize the aquifer heterogeneity while reactive tracers are used to describe the mean DNAPL mass and its distribution. This information is then used in a Lagrangian framework to predict source remediation performance. In a Lagrangian approach the source zone is conceptualized as a collection of non-interacting streamtubes with hydrodynamic and DNAPL heterogeneity represented by the variation of the travel time and DNAPL saturation among the streamtubes. The travel time statistics are estimated from the non-reactive tracer data while the DNAPL distribution statistics are estimated from the reactive tracer data. The combined statistics are used to define an analytical solution for contaminant dissolution under natural gradient flow. The tracer prediction technique compared favorably with results from a multiphase flow and transport simulator UTCHEM in domains with different hydrodynamic heterogeneity (variance of the log conductivity field = 0.2, 1 and 3).

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

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.

A micrometre-sized heat engine operating between bacterial reservoirs

NASA Astrophysics Data System (ADS)

Krishnamurthy, Sudeesh; Ghosh, Subho; Chatterji, Dipankar; Ganapathy, Rajesh; Sood, A. K.

2016-12-01

Artificial microscale heat engines are prototypical models to explore the mechanisms of energy transduction in a fluctuation-dominated regime. The heat engines realized so far on this scale have operated between thermal reservoirs, such that stochastic thermodynamics provides a precise framework for quantifying their performance. It remains to be seen whether these concepts readily carry over to situations where the reservoirs are out of equilibrium, a scenario of particular importance to the functioning of synthetic and biological microscale engines and motors. Here, we experimentally realize a micrometre-sized active Stirling engine by periodically cycling a colloidal particle in a time-varying optical potential across bacterial baths characterized by different degrees of activity. We find that the displacement statistics of the trapped particle becomes increasingly non-Gaussian with activity and contributes substantially to the overall power output and the efficiency. Remarkably, even for engines with the same energy input, differences in non-Gaussianity of reservoir noise results in distinct performances. At high activities, the efficiency of our engines surpasses the equilibrium saturation limit of Stirling efficiency, the maximum efficiency of a Stirling engine where the ratio of cold to hot reservoir temperatures is vanishingly small. Our experiments provide fundamental insights into the functioning of micromotors and engines operating out of equilibrium.

Thermodynamic equilibrium solubility measurements in simulated fluids by 96-well plate method in early drug discovery.

PubMed

Bharate, Sonali S; Vishwakarma, Ram A

2015-04-01

An early prediction of solubility in physiological media (PBS, SGF and SIF) is useful to predict qualitatively bioavailability and absorption of lead candidates. Despite of the availability of multiple solubility estimation methods, none of the reported method involves simplified fixed protocol for diverse set of compounds. Therefore, a simple and medium-throughput solubility estimation protocol is highly desirable during lead optimization stage. The present work introduces a rapid method for assessment of thermodynamic equilibrium solubility of compounds in aqueous media using 96-well microplate. The developed protocol is straightforward to set up and takes advantage of the sensitivity of UV spectroscopy. The compound, in stock solution in methanol, is introduced in microgram quantities into microplate wells followed by drying at an ambient temperature. Microplates were shaken upon addition of test media and the supernatant was analyzed by UV method. A plot of absorbance versus concentration of a sample provides saturation point, which is thermodynamic equilibrium solubility of a sample. The established protocol was validated using a large panel of commercially available drugs and with conventional miniaturized shake flask method (r(2)>0.84). Additionally, the statistically significant QSPR models were established using experimental solubility values of 52 compounds. Copyright © 2015 Elsevier Ltd. All rights reserved.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics

NASA Astrophysics Data System (ADS)

Czinner, Viktor G.; Iguchi, Hideo

2017-12-01

Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a Hawking-Page transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

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.

Is an intuitive convergence definition of molecular dynamics simulations solely based on the root mean square deviation possible?

PubMed

Knapp, B; Frantal, S; Cibena, M; Schreiner, W; Bauer, P

2011-08-01

Molecular dynamics is a commonly used technique in computational biology. One key issue of each molecular dynamics simulation is: When does this simulation reach equilibrium state? A widely used way to determine this is the visual and intuitive inspection of root mean square deviation (RMSD) plots of the simulation. Although this technique has been criticized several times, it is still often used. Therefore, we present a study proving that this method is not reliable at all. We conducted a survey with participants from the field in which we illustrated different RMSD plots to scientists in the field of molecular dynamics. These plots were randomized and repeated, using a statistical model and different variants of the plots. We show that there is no mutual consent about the point of equilibrium. The decisions are severely biased by different parameters. Therefore, we conclude that scientists should not discuss the equilibration of a molecular dynamics simulation on the basis of a RMSD plot.

Dynamics of Large-Scale Fluctuations in Native Proteins.

NASA Astrophysics Data System (ADS)

Erman, Burak; Erkip, Albert

2003-03-01

The fluctuations of residues of proteins about their equilibrium configurations are analyzed by Langevin dynamics. Residue pairs that are within a given cutoff distance of each other are assumed to be connected by linear springs. The action of the solvent and intramolecular interactions on each residue are treated as random noise. The correlations of fluctuations resulting from the solution of the Langevin equation are observed to be identical to those obtained by the Gaussian Network Model based on equilibrium statistical mechanics. The time delayed correlations of fluctuations, and the response of the protein to a given frequency and to a window of frequencies are determined. The fluctuations of the residues resulting from a given fixed externally applied frequency are evaluated for different modes of the system. Synchronous and asynchronous components of correlations for different modes are formulated. The results of the present study are applied to study the fluctuation dynamics of the 241 residue protein S. marcescens endonuclease (1QL0).

Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks

NASA Astrophysics Data System (ADS)

Huo, Jingjing; Zhao, Hongyong

2016-04-01

In this paper, a fractional SIR model with birth and death rates on heterogeneous complex networks is proposed. Firstly, we obtain a threshold value R0 based on the existence of endemic equilibrium point E∗, which completely determines the dynamics of the model. Secondly, by using Lyapunov function and Kirchhoff's matrix tree theorem, the globally asymptotical stability of the disease-free equilibrium point E0 and the endemic equilibrium point E∗ of the model are investigated. That is, when R0 < 1, the disease-free equilibrium point E0 is globally asymptotically stable and the disease always dies out; when R0 > 1, the disease-free equilibrium point E0 becomes unstable and in the meantime there exists a unique endemic equilibrium point E∗, which is globally asymptotically stable and the disease is uniformly persistent. Finally, the effects of various immunization schemes are studied and compared. Numerical simulations are given to demonstrate the main results.

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.

Validation of a Statistical Methodology for Extracting Vegetation Feedbacks: Focus on North African Ecosystems in the Community Earth System Model

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

Yu, Yan; Notaro, Michael; Wang, Fuyao

Generalized equilibrium feedback assessment (GEFA) is a potentially valuable multivariate statistical tool for extracting vegetation feedbacks to the atmosphere in either observations or coupled Earth system models. The reliability of GEFA at capturing the terrestrial impacts on regional climate is demonstrated in this paper using the National Center for Atmospheric Research Community Earth System Model (CESM), with focus on North Africa. The feedback is assessed statistically by applying GEFA to output from a fully coupled control run. To reduce the sampling error caused by short data records, the traditional or full GEFA is refined through stepwise GEFA by dropping unimportantmore » forcings. Two ensembles of dynamical experiments are developed for the Sahel or West African monsoon region against which GEFA-based vegetation feedbacks are evaluated. In these dynamical experiments, regional leaf area index (LAI) is modified either alone or in conjunction with soil moisture, with the latter runs motivated by strong regional soil moisture–LAI coupling. Stepwise GEFA boasts higher consistency between statistically and dynamically assessed atmospheric responses to land surface anomalies than full GEFA, especially with short data records. GEFA-based atmospheric responses are more consistent with the coupled soil moisture–LAI experiments, indicating that GEFA is assessing the combined impacts of coupled vegetation and soil moisture. Finally, both the statistical and dynamical assessments reveal a negative vegetation–rainfall feedback in the Sahel associated with an atmospheric stability mechanism in CESM versus a weaker positive feedback in the West African monsoon region associated with a moisture recycling mechanism in CESM.« less

Validation of a Statistical Methodology for Extracting Vegetation Feedbacks: Focus on North African Ecosystems in the Community Earth System Model

DOE PAGES

Yu, Yan; Notaro, Michael; Wang, Fuyao; ...

2018-02-05

Generalized equilibrium feedback assessment (GEFA) is a potentially valuable multivariate statistical tool for extracting vegetation feedbacks to the atmosphere in either observations or coupled Earth system models. The reliability of GEFA at capturing the terrestrial impacts on regional climate is demonstrated in this paper using the National Center for Atmospheric Research Community Earth System Model (CESM), with focus on North Africa. The feedback is assessed statistically by applying GEFA to output from a fully coupled control run. To reduce the sampling error caused by short data records, the traditional or full GEFA is refined through stepwise GEFA by dropping unimportantmore » forcings. Two ensembles of dynamical experiments are developed for the Sahel or West African monsoon region against which GEFA-based vegetation feedbacks are evaluated. In these dynamical experiments, regional leaf area index (LAI) is modified either alone or in conjunction with soil moisture, with the latter runs motivated by strong regional soil moisture–LAI coupling. Stepwise GEFA boasts higher consistency between statistically and dynamically assessed atmospheric responses to land surface anomalies than full GEFA, especially with short data records. GEFA-based atmospheric responses are more consistent with the coupled soil moisture–LAI experiments, indicating that GEFA is assessing the combined impacts of coupled vegetation and soil moisture. Finally, both the statistical and dynamical assessments reveal a negative vegetation–rainfall feedback in the Sahel associated with an atmospheric stability mechanism in CESM versus a weaker positive feedback in the West African monsoon region associated with a moisture recycling mechanism in CESM.« less

Particle orbits in two-dimensional equilibrium models for the magnetotail

NASA Technical Reports Server (NTRS)

Karimabadi, H.; Pritchett, P. L.; Coroniti, F. V.

1990-01-01

Assuming that there exist an equilibrium state for the magnetotail, particle orbits are investigated in two-dimensional kinetic equilibrium models for the magnetotail. Particle orbits in the equilibrium field are compared with those calculated earlier with one-dimensional models, where the main component of the magnetic field (Bx) was approximated as either a hyperbolic tangent or a linear function of z with the normal field (Bz) assumed to be a constant. It was found that the particle orbits calculated with the two types of models are significantly different, mainly due to the neglect of the variation of Bx with x in the one-dimensional fields.

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

NASA Astrophysics Data System (ADS)

Gyftopoulos, Elias P.

2008-08-01

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

IS THE SIZE DISTRIBUTION OF URBAN AEROSOLS DETERMINED BY THERMODYNAMIC EQUILIBRIUM? (R826371C005)

EPA Science Inventory

A size-resolved equilibrium model, SELIQUID, is presented and used to simulate the size–composition distribution of semi-volatile inorganic aerosol in an urban environment. The model uses the efflorescence branch of aerosol behavior to predict the equilibrium partitioni...

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

PubMed Central

Zheng, Xiliang; Wang, Jin

2015-01-01

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

Prediction of U-Mo dispersion nuclear fuels with Al-Si alloy using artificial neural network

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

Susmikanti, Mike, E-mail: mike@batan.go.id; Sulistyo, Jos, E-mail: soj@batan.go.id

2014-09-30

Dispersion nuclear fuels, consisting of U-Mo particles dispersed in an Al-Si matrix, are being developed as fuel for research reactors. The equilibrium relationship for a mixture component can be expressed in the phase diagram. It is important to analyze whether a mixture component is in equilibrium phase or another phase. The purpose of this research it is needed to built the model of the phase diagram, so the mixture component is in the stable or melting condition. Artificial neural network (ANN) is a modeling tool for processes involving multivariable non-linear relationships. The objective of the present work is to developmore » code based on artificial neural network models of system equilibrium relationship of U-Mo in Al-Si matrix. This model can be used for prediction of type of resulting mixture, and whether the point is on the equilibrium phase or in another phase region. The equilibrium model data for prediction and modeling generated from experimentally data. The artificial neural network with resilient backpropagation method was chosen to predict the dispersion of nuclear fuels U-Mo in Al-Si matrix. This developed code was built with some function in MATLAB. For simulations using ANN, the Levenberg-Marquardt method was also used for optimization. The artificial neural network is able to predict the equilibrium phase or in the phase region. The develop code based on artificial neural network models was built, for analyze equilibrium relationship of U-Mo in Al-Si matrix.« less

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.

Profiles of equilibrium constants for self-association of aromatic molecules

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Kim, Kyungsik; Lee, Dong-In; Scalas, Enrico

2008-05-01

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

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

NASA Astrophysics Data System (ADS)

Viswanathan, G. M.

2017-06-01

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

Classical molecular dynamics simulations for non-equilibrium correlated plasmas

NASA Astrophysics Data System (ADS)

Ferri, S.; Calisti, A.; Talin, B.

2017-03-01

A classical molecular dynamics model was recently extended to simulate neutral multi-component plasmas where various charge states of the same atom and electrons coexist. It is used to investigate the plasma effects on the ion charge and on the ionization potential in dense plasmas. Different simulated statistical properties will show that the concept of isolated particles is lost in such correlated plasmas. The charge equilibration is discussed for a carbon plasma at solid density and investigation on the charge distribution and on the ionization potential depression (IPD) for aluminum plasmas is discussed with reference to existing experiments.

Evolution of cosmic string networks

NASA Technical Reports Server (NTRS)

Albrecht, Andreas; Turok, Neil

1989-01-01

Results on cosmic strings are summarized including: (1) the application of non-equilibrium statistical mechanics to cosmic string evolution; (2) a simple one scale model for the long strings which has a great deal of predictive power; (3) results from large scale numerical simulations; and (4) a discussion of the observational consequences of our results. An upper bound on G mu of approximately 10(-7) emerges from the millisecond pulsar gravity wave bound. How numerical uncertainties affect this are discussed. Any changes which weaken the bound would probably also give the long strings the dominant role in producing observational consequences.

Data-driven parameterization of the generalized Langevin equation

DOE PAGES

Lei, Huan; Baker, Nathan A.; Li, Xiantao

2016-11-29

We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules.

PubMed

Chowdhury, Debashish

2013-06-04

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here. Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Biomechanical stability analysis of the lambda-model controlling one joint.

PubMed

Lan, L; Zhu, K Y

2007-06-01

Computer modeling and control of the human motor system might be helpful for understanding the mechanism of human motor system and for the diagnosis and treatment of neuromuscular disorders. In this paper, a brief view of the equilibrium point hypothesis for human motor system modeling is given, and the lambda-model derived from this hypothesis is studied. The stability of the lambda-model based on equilibrium and Jacobian matrix is investigated. The results obtained in this paper suggest that the lambda-model is stable and has a unique equilibrium point under certain conditions.

Modelling the effect of immigration on drinking behaviour.

PubMed

Xiang, Hong; Zhu, Cheng-Cheng; Huo, Hai-Feng

2017-12-01

A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region.

Insights: Simple Models for Teaching Equilibrium and Le Chatelier's Principle.

ERIC Educational Resources Information Center

Russell, Joan M.

1988-01-01

Presents three models that have been effective for teaching chemical equilibrium and Le Chatelier's principle: (1) the liquid transfer model, (2) the fish model, and (3) the teeter-totter model. Explains each model and its relation to Le Chatelier's principle. (MVL)

Thermal characterization assessment of rigid and flexible water models in a nanogap using molecular dynamics

NASA Astrophysics Data System (ADS)

Akıner, Tolga; Mason, Jeremy; Ertürk, Hakan

2017-11-01

The thermal properties of the TIP3P and TIP5P water models are investigated using equilibrium and non-equilibrium molecular dynamics techniques in the presence of solid surfaces. The performance of the non-equilibrium technique for rigid molecules is found to depend significantly on the distribution of atomic degrees of freedom. An improved approach to distribute atomic degrees of freedom is proposed for which the thermal conductivity of the TIP5P model agrees more closely with equilibrium molecular dynamics and experimental results than the existing state of the art.

Vapor-liquid equilibrium thermodynamics of N2 + CH4 - Model and Titan applications

NASA Technical Reports Server (NTRS)

Thompson, W. R.; Zollweg, John A.; Gabis, David H.

1992-01-01

A thermodynamic model is presented for vapor-liquid equilibrium in the N2 + CH4 system, which is implicated in calculations of the Titan tropospheric clouds' vapor-liquid equilibrium thermodynamics. This model imposes constraints on the consistency of experimental equilibrium data, and embodies temperature effects by encompassing enthalpy data; it readily calculates the saturation criteria, condensate composition, and latent heat for a given pressure-temperature profile of the Titan atmosphere. The N2 content of condensate is about half of that computed from Raoult's law, and about 30 percent greater than that computed from Henry's law.

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.

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

ERIC Educational Resources Information Center

Loverude, Michael

2015-01-01

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

Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material

NASA Astrophysics Data System (ADS)

Dean, David S.; Démery, Vincent; Parsegian, V. Adrian; Podgornik, Rudolf

2012-03-01

Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.

Refinements in the Los Alamos model of the prompt fission neutron spectrum

DOE PAGES

Madland, D. G.; Kahler, A. C.

2017-01-01

This paper presents a number of refinements to the original Los Alamos model of the prompt fission neutron spectrum and average prompt neutron multiplicity as derived in 1982. The four refinements are due to new measurements of the spectrum and related fission observables many of which were not available in 1982. Here, they are also due to a number of detailed studies and comparisons of the model with previous and present experimental results including not only the differential spectrum, but also integal cross sections measured in the field of the differential spectrum. The four refinements are (a) separate neutron contributionsmore » in binary fission, (b) departure from statistical equilibrium at scission, (c) fission-fragment nuclear level-density models, and (d) center-of-mass anisotropy. With these refinements, for the first time, good agreement has been obtained for both differential and integral measurements using the same Los Alamos model spectrum.« less

Eliminating the Cuspidal Temperature Profile of a Non-equilibrium Chain

NASA Astrophysics Data System (ADS)

Cândido, Michael M.; M. Morgado, Welles A.; Duarte Queirós, Sílvio M.

2017-06-01

In 1967, Z. Rieder, J. L. Lebowitz, and E. Lieb (RLL) introduced a model of heat conduction on a crystal that became a milestone problem of non-equilibrium statistical mechanics. Along with its inability to reproduce Fourier's law—which subsequent generalizations have been trying to amend—the RLL model is also characterized by awkward cusps at the ends of the non-equilibrium chain, an effect that has endured all these years without a satisfactory answer. In this paper, we first show that such trait stems from the insufficiency of pinning interactions between the chain and the substrate. Assuming the possibility of pinning the chain, the analysis of the temperature profile in the space of parameters reveals that for a proper combination of the border and bulk pinning values, the temperature profile may shift twice between the RLL cuspidal behavior and the expected monotonic local temperature evolution along the system, as a function of the pinning. At those inversions, the temperature profile along the chain is characterized by perfect plateaux: at the first threshold, the cumulants of the heat flux reach their maxima and the vanishing of the two-point velocity correlation function for all sites of the chain so that the system behaves similarly to a "phonon box." On the other hand, at the second change of the temperature profile, we still have the vanishing of the two-point correlation function but only for the bulk, which explains the emergence of the temperature plateau and thwarts the reaching of the maximal values of the cumulants of the heat flux.

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

PubMed

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

2017-01-01

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

Computational prediction of kink properties of helices in membrane proteins

NASA Astrophysics Data System (ADS)

Mai, T.-L.; Chen, C.-M.

2014-02-01

We have combined molecular dynamics simulations and fold identification procedures to investigate the structure of 696 kinked and 120 unkinked transmembrane (TM) helices in the PDBTM database. Our main aim of this study is to understand the formation of helical kinks by simulating their quasi-equilibrium heating processes, which might be relevant to the prediction of their structural features. The simulated structural features of these TM helices, including the position and the angle of helical kinks, were analyzed and compared with statistical data from PDBTM. From quasi-equilibrium heating processes of TM helices with four very different relaxation time constants, we found that these processes gave comparable predictions of the structural features of TM helices. Overall, 95 % of our best kink position predictions have an error of no more than two residues and 75 % of our best angle predictions have an error of less than 15°. Various structure assessments have been carried out to assess our predicted models of TM helices in PDBTM. Our results show that, in 696 predicted kinked helices, 70 % have a RMSD less than 2 Å, 71 % have a TM-score greater than 0.5, 69 % have a MaxSub score greater than 0.8, 60 % have a GDT-TS score greater than 85, and 58 % have a GDT-HA score greater than 70. For unkinked helices, our predicted models are also highly consistent with their crystal structure. These results provide strong supports for our assumption that kink formation of TM helices in quasi-equilibrium heating processes is relevant to predicting the structure of TM helices.

Impacts of energy consumption and emissions on the trip cost without late arrival at the equilibrium state

NASA Astrophysics Data System (ADS)

Tang, Tie-Qiao; Wang, Tao; Chen, Liang; Shang, Hua-Yan

2017-08-01

In this paper, we apply a car-following model, fuel consumption model, emission model and electricity consumption model to explore the influences of energy consumption and emissions on each commuter's trip costs without late arrival at the equilibrium state. The numerical results show that the energy consumption and emissions have significant impacts on each commuter's trip cost without late arrival at the equilibrium state. The fuel cost and emission cost prominently enhance each commuter's trip cost and the trip cost increases with the number of vehicles, which shows that considering the fuel cost and emission cost in the trip cost will destroy the equilibrium state. However, the electricity cost slightly enhances each commuter's trip cost, but the trip cost is still approximately a constant, which indicates that considering the electricity cost in the trip cost does not destroy the equilibrium state.

Cuts, cancellations and the closed time path: The soft leptogenesis example

NASA Astrophysics Data System (ADS)

Garbrecht, Björn; Ramsey-Musolf, Michael J.

2014-05-01

By including all leading quantum-statistical effects at finite temperature, we show that no net asymmetry of leptons and sleptons is generated from soft leptogenesis, save the possible contribution from the resonant mixing of sneutrinos. This result contrasts with different conclusions appearing in the literature that are based on an incomplete inclusion of quantum statistics. We discuss vertex and wave-function diagrams as well as all different possible kinematic cuts that nominally lead to CP-violating asymmetries. The present example of soft leptogenesis may therefore serve as a paradigm in order to identify more generally applicable caveats relevant to alternative scenarios for baryogenesis and leptogenesis, and it may provide useful guidance in constructing viable models. For the vertex contributions, the intermediate on-shell particle is an out-of equilibrium singlet neutrino N (see Fig. 3). In this case, even when the subtraction of RIS is performed correctly, On the other hand, when the RIS that is to be subtracted corresponds to a particle that is in equilibrium, such as the scalar Higgs doublet H1 in Section 4 (see Fig. 7), no asymmetry is generated in first place. This type of subtraction of equilibrium RIS and the consequent vanishing of the CPV asymmetry has been missed in the context of a different model in Ref. [9]. Alternatively, there exists a way of deriving the leptogenesis kinetic equations following a set of rules that intrinsically respect the unitary evolution of the system while sidestepping the pitfalls of the RIS procedure: the Closed Time Path (CTP) formalism [10-15]. Rather than formulating the problem in terms of S-matrix elements and classical particle distribution functions, the evolution of Green functions of the quantum fields is calculated. In particular, the imaginary parts of self-energies correspond to the inclusive decay and production rates that are necessary in order to track the evolution of the asymmetry. This way, the somewhat heuristic procedure of RIS subtraction can be avoided [16-31].In the present work, we calculate the source terms for the asymmetry using the CTP formalism. As our main result, we demonstrate that the resulting asymmetry of the lepton number vanishes even when taking into account quantum statistical corrections. In particular, the corrections associated with the internal lines precisely cancel those associated with the final states that are included in Refs. [6-8]. Consequently, the sum of the lepton and slepton asymmetries is zero.

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

NASA Astrophysics Data System (ADS)

Guha, Atanu; Das, Prasanta Kumar

2018-05-01

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

Cell Division and Evolution of Biological Tissues

NASA Astrophysics Data System (ADS)

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

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

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

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

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

2010-08-01

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

Redistribution of flexibility in stabilizing antibody fragment mutants follows Le Châtelier's principle.

PubMed

Li, Tong; Tracka, Malgorzata B; Uddin, Shahid; Casas-Finet, Jose; Jacobs, Donald J; Livesay, Dennis R

2014-01-01

Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect.

Redistribution of Flexibility in Stabilizing Antibody Fragment Mutants Follows Le Châtelier’s Principle

PubMed Central

Li, Tong; Tracka, Malgorzata B.; Uddin, Shahid; Casas-Finet, Jose; Jacobs, Donald J.; Livesay, Dennis R.

2014-01-01

Le Châtelier’s principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier’s principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect. PMID:24671209

Numerical Experiments Based on the Catastrophe Model of Solar Eruptions

NASA Astrophysics Data System (ADS)

Xie, X. Y.; Ziegler, U.; Mei, Z. X.; Wu, N.; Lin, J.

2017-11-01

On the basis of the catastrophe model developed by Isenberg et al., we use the NIRVANA code to perform the magnetohydrodynamics (MHD) numerical experiments to look into various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope used to model the prominence levitating in the corona. These behaviors include the evolution in equilibrium heights of the flux rope versus the change in the background magnetic field, the corresponding internal equilibrium of the flux rope, dynamic properties of the flux rope after the system loses equilibrium, as well as the impact of the referential radius on the equilibrium heights of the flux rope. In our calculations, an empirical model of the coronal density distribution given by Sittler & Guhathakurta is used, and the physical diffusion is included. Our experiments show that the deviation of simulations in the equilibrium heights from the theoretical results exists, but is not apparent, and the evolutionary features of the two results are similar. If the flux rope is initially locate at the stable branch of the theoretical equilibrium curve, the flux rope will quickly reach the equilibrium position in the simulation after several rounds of oscillations as a result of the self-adjustment of the system; and the flux rope lose the equilibrium if the initial location of the flux rope is set at the critical point on the theoretical equilibrium curve. Correspondingly, the internal equilibrium of the flux rope can be reached as well, and the deviation from the theoretical results is somewhat apparent since the approximation of the small radius of the flux rope is lifted in our experiments, but such deviation does not affect the global equilibrium in the system. The impact of the referential radius on the equilibrium heights of the flux rope is consistent with the prediction of the theory. Our calculations indicate that the motion of the flux rope after the loss of equilibrium is consistent with which is predicted by the Lin-Forbes model and observations. Formation of the fast mode shock ahead of the flux rope is observed in our experiments. Outward motions of the flux rope are smooth, and magnetic energy is continuously converted into the other types of energy because both the diffusions are considered in calculations, and magnetic reconnection is allowed to occur successively in the current sheet behind the flux rope.

Capacity withholding in wholesale electricity markets: The experience in England and Wales

NASA Astrophysics Data System (ADS)

Quinn, James Arnold

This thesis examines the incentives wholesale electricity generators face to withhold generating capacity from centralized electricity spot markets. The first chapter includes a brief history of electricity industry regulation in England and Wales and in the United States, including a description of key institutional features of England and Wales' restructured electricity market. The first chapter also includes a review of the literature on both bid price manipulation and capacity bid manipulation in centralized electricity markets. The second chapter details a theoretical model of wholesale generator behavior in a single price electricity market. A duopoly model is specified under the assumption that demand is non-stochastic. This model assumes that duopoly generators offer to sell electricity at their marginal cost, but can withhold a continuous segment of their capacity from the market. The Nash equilibrium withholding strategy of this model involves each duopoly generator withholding so that it produces the Cournot equilibrium output. A monopoly model along the lines of the duopoly model is specified and simulated under the assumption that demand is stochastic. The optimal strategy depends on the degree of demand uncertainty. When there is a moderate degree of demand uncertainty, the optimal withholding strategy involves production inefficiencies. When there is a high degree of demand uncertainty, the optimal monopoly quantity is greater than the optimal output level when demand is non-stochastic. The third chapter contains an empirical examination of the behavior of generators in the wholesale electricity market in England and Wales in the early 1990's. The wholesale market in England and Wales is analyzed because the industry structure in the early 1990's created a natural experiment, which is described in this chapter, whereby one of the two dominant generators had no incentive to behave non-competitively. This chapter develops a classification methodology consistent with the equilibrium identified in the second chapter. The availability of generating units owned by the two dominant generators is analyzed based on this classification system. This analysis includes the use of sample statistics as well as estimates from a dynamic random effects probit model. The analysis suggests a minimal degree of capacity withholding.

Steepest entropy ascent model for far-nonequilibrium thermodynamics: Unified implementation of the maximum entropy production principle

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo

2014-10-01

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of nonequilibrium dynamics into a unified formulation valid in all these contexts, which extends to such frameworks the concept of steepest entropy ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. Actually, the present formulation constitutes a generalization also for the quantum thermodynamics framework. The analysis emphasizes that in the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near-thermodynamic-equilibrium limit, the metric tensor is directly related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far-nonequilibrium domain, most of the existing theories of nonequilibrium thermodynamics can be cast in such a way that the state exhibits the spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. The non-negativity of the entropy production is a general and readily proved feature of SEA dynamics. In several of the different approaches to nonequilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called maximum entropy production principle. Therefore, it is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far nonequilibrium states. The mathematical frameworks we consider are the following: (A) statistical or information-theoretic models of relaxation; (B) small-scale and rarefied gas dynamics (i.e., kinetic models for the Boltzmann equation); (C) rational extended thermodynamics, macroscopic nonequilibrium thermodynamics, and chemical kinetics; (D) mesoscopic nonequilibrium thermodynamics, continuum mechanics with fluctuations; and (E) quantum statistical mechanics, quantum thermodynamics, mesoscopic nonequilibrium quantum thermodynamics, and intrinsic quantum thermodynamics.

The potential energy landscape contribution to the dynamic heat capacity

NASA Astrophysics Data System (ADS)

Brown, Jonathan R.; McCoy, John D.

2011-05-01

The dynamic heat capacity of a simple polymeric, model glassformer was computed using molecular dynamics simulations by sinusoidally driving the temperature and recording the resultant energy. The underlying potential energy landscape of the system was probed by taking a time series of particle positions and quenching them. The resulting dynamic heat capacity demonstrates that the long time relaxation is the direct result of dynamics resulting from the potential energy landscape. Moreover, the equilibrium (low frequency) portion of the potential energy landscape contribution to the heat capacity is found to increase rapidly at low temperatures and at high packing fractions. This increase in the heat capacity is explained by a statistical mechanical model based on the distribution of minima in the potential energy landscape.

Cooperativity in Molecular Dynamics Structural Models and the Dielectric Spectra of 1,2-Ethanediol

NASA Astrophysics Data System (ADS)

Usacheva, T. M.

2018-05-01

Linear relationships are established between the experimental equilibrium correlation factor and the molecular dynamics (MD) mean value of the O-H···O bond angle and the longitudinal component of the unit vector of the mean statistical dipole moment of the cluster in liquid 1,2-ethanediol (12ED). The achievements of modern MD models in describing the experimental dispersion of the permittivity of 12ED by both continuous and discrete relaxation time spectra are analyzed. The advantage computer MD experiments have over dielectric spectroscopy for calculating relaxation time and determining the molecular diffusion mechanisms of the rearrangement of the network 12ED structure, which is more complex than water, is demonstrated.

Linear control of oscillator and amplifier flows*

NASA Astrophysics Data System (ADS)

Schmid, Peter J.; Sipp, Denis

2016-08-01

Linear control applied to fluid systems near an equilibrium point has important applications for many flows of industrial or fundamental interest. In this article we give an exposition of tools and approaches for the design of control strategies for globally stable or unstable flows. For unstable oscillator flows a feedback configuration and a model-based approach is proposed, while for stable noise-amplifier flows a feedforward setup and an approach based on system identification is advocated. Model reduction and robustness issues are addressed for the oscillator case; statistical learning techniques are emphasized for the amplifier case. Effective suppression of global and convective instabilities could be demonstrated for either case, even though the system-identification approach results in a superior robustness to off-design conditions.

A Dealer Model of Foreign Exchange Market with Finite Assets

NASA Astrophysics Data System (ADS)

Hamano, Tomoya; Kanazawa, Kiyoshi; Takayasu, Hideki; Takayasu, Misako

An agent-based model is introduced to study the finite-asset effect in foreign exchange markets. We find that the transacted price asymptotically approaches an equilibrium price, which is determined by the monetary balance between the pair of currencies. We phenomenologically derive a formula to estimate the equilibrium price, and we model its relaxation dynamics around the equilibrium price on the basis of a Langevin-like equation.

Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model

NASA Astrophysics Data System (ADS)

Cugliandolo, Leticia F.; Lozano, Gustavo S.; Nessi, Nicolás; Picco, Marco; Tartaglia, Alessandro

2018-06-01

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body random interactions. In the statistical physics framework, the potential energy is of the so-called p  =  2 kind, closely linked to the scalar field theory. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable model. We take initial conditions from the Boltzmann equilibrium measure at a temperature that can be above or below the static phase transition, typical of a disordered (paramagnetic) or of an ordered (disguised ferromagnetic) equilibrium phase. We subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian, obtained from an instantaneous global rescaling of the elements in the interaction random matrix. In the limit of infinitely many degrees of freedom, , we identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We next set the analysis of the system with finite number of degrees of freedom in terms of N non-linearly coupled modes. We argue that in the limit the modes decouple at long times. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the N  ‑  1 integrals of motion, notably, their scaling with N, and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs–Boltzmann behaviour of the global observables. We elaborate on the role played by these constants of motion after the quench and we briefly discuss the possible description of the asymptotic dynamics in terms of a generalised Gibbs ensemble.

Tidal Heating in Enceladus

NASA Astrophysics Data System (ADS)

Meyer, Jennifer; Wisdom, J.

2007-07-01

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

Mechanical approach to chemical transport

PubMed Central

Kocherginsky, Nikolai; Gruebele, Martin

2016-01-01

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components. PMID:27647899

Equilibrium pricing in an order book environment: Case study for a spin model

NASA Astrophysics Data System (ADS)

Meudt, Frederik; Schmitt, Thilo A.; Schäfer, Rudi; Guhr, Thomas

2016-07-01

When modeling stock market dynamics, the price formation is often based on an equilibrium mechanism. In real stock exchanges, however, the price formation is governed by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more generally, are compatible with the order book environment. We tackle this issue in the framework of a case study by embedding the Bornholdt-Kaizoji-Fujiwara spin model into the order book dynamics. To this end, we use a recently developed agent based model that realistically incorporates the order book. We find realistic stylized facts. We conclude for the studied case that equilibrium pricing is not needed and that the corresponding assumption of a ;fundamental; price may be abandoned.

Simplified Thermo-Chemical Modelling For Hypersonic Flow

NASA Astrophysics Data System (ADS)

Sancho, Jorge; Alvarez, Paula; Gonzalez, Ezequiel; Rodriguez, Manuel

2011-05-01

Hypersonic flows are connected with high temperatures, generally associated with strong shock waves that appear in such flows. At high temperatures vibrational degrees of freedom of the molecules may become excited, the molecules may dissociate into atoms, the molecules or free atoms may ionize, and molecular or ionic species, unimportant at lower temperatures, may be formed. In order to take into account these effects, a chemical model is needed, but this model should be simplified in order to be handled by a CFD code, but with a sufficient precision to take into account the physics more important. This work is related to a chemical non-equilibrium model validation, implemented into a commercial CFD code, in order to obtain the flow field around bodies in hypersonic flow. The selected non-equilibrium model is composed of seven species and six direct reactions together with their inverse. The commercial CFD code where the non- equilibrium model has been implemented is FLUENT. For the validation, the X38/Sphynx Mach 20 case is rebuilt on a reduced geometry, including the 1/3 Lref forebody. This case has been run in laminar regime, non catalytic wall and with radiative equilibrium wall temperature. The validated non-equilibrium model is applied to the EXPERT (European Experimental Re-entry Test-bed) vehicle at a specified trajectory point (Mach number 14). This case has been run also in laminar regime, non catalytic wall and with radiative equilibrium wall temperature.

Local thermodynamic equilibrium for globally disequilibrium open systems under stress

NASA Astrophysics Data System (ADS)

Podladchikov, Yury

2016-04-01

Predictive modeling of far and near equilibrium processes is essential for understanding of patterns formation and for quantifying of natural processes that are never in global equilibrium. Methods of both equilibrium and non-equilibrium thermodynamics are needed and have to be combined. For example, predicting temperature evolution due to heat conduction requires simultaneous use of equilibrium relationship between internal energy and temperature via heat capacity (the caloric equation of state) and disequilibrium relationship between heat flux and temperature gradient. Similarly, modeling of rocks deforming under stress, reactions in system open for the porous fluid flow, or kinetic overstepping of the equilibrium reaction boundary necessarily needs both equilibrium and disequilibrium material properties measured under fundamentally different laboratory conditions. Classical irreversible thermodynamics (CIT) is the well-developed discipline providing the working recipes for the combined application of mutually exclusive experimental data such as density and chemical potential at rest under constant pressure and temperature and viscosity of the flow under stress. Several examples will be presented.

On silicon group elements ejected by supernovae type IA

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

De, Soma; Timmes, F. X.; Brown, Edward F.

2014-06-01

There is evidence that the peak brightness of a Type Ia supernova is affected by the electron fraction Y {sub e} at the time of the explosion. The electron fraction is set by the aboriginal composition of the white dwarf and the reactions that occur during the pre-explosive convective burning. To date, determining the makeup of the white dwarf progenitor has relied on indirect proxies, such as the average metallicity of the host stellar population. In this paper, we present analytical calculations supporting the idea that the electron fraction of the progenitor systematically influences the nucleosynthesis of silicon group ejectamore » in Type Ia supernovae. In particular, we suggest the abundances generated in quasi-nuclear statistical equilibrium are preserved during the subsequent freeze-out. This allows potential recovery of Y {sub e} at explosion from the abundances recovered from an observed spectra. We show that measurement of {sup 28}Si, {sup 32}S, {sup 40}Ca, and {sup 54}Fe abundances can be used to construct Y {sub e} in the silicon-rich regions of the supernovae. If these four abundances are determined exactly, they are sufficient to recover Y {sub e} to 6%. This is because these isotopes dominate the composition of silicon-rich material and iron-rich material in quasi-nuclear statistical equilibrium. Analytical analysis shows the {sup 28}Si abundance is insensitive to Y {sub e}, the {sup 32}S abundance has a nearly linear trend with Y {sub e}, and the {sup 40}Ca abundance has a nearly quadratic trend with Y {sub e}. We verify these trends with post-processing of one-dimensional models and show that these trends are reflected in the model's synthetic spectra.« less

The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2015-06-01

In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By constructing suitable Lyapunov function, we show that the disease- free equilibrium is globally asymptotic stable whenever BRN is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable. Numerical result shows the dynamic of each compartment together with effect of multiple bio-agent intervention as a control to the dengue transmission.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method.

PubMed

Norris, Peter M; da Silva, Arlindo M

2016-07-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian Inference on a Statistical Model of Sub-Gridcolumn Moisture Variability Using High-Resolution Cloud Observations. Part 1: Method

NASA Technical Reports Server (NTRS)

Norris, Peter M.; Da Silva, Arlindo M.

2016-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC.

Monte Carlo Bayesian inference on a statistical model of sub-gridcolumn moisture variability using high-resolution cloud observations. Part 1: Method

PubMed Central

Norris, Peter M.; da Silva, Arlindo M.

2018-01-01

A method is presented to constrain a statistical model of sub-gridcolumn moisture variability using high-resolution satellite cloud data. The method can be used for large-scale model parameter estimation or cloud data assimilation. The gridcolumn model includes assumed probability density function (PDF) intra-layer horizontal variability and a copula-based inter-layer correlation model. The observables used in the current study are Moderate Resolution Imaging Spectroradiometer (MODIS) cloud-top pressure, brightness temperature and cloud optical thickness, but the method should be extensible to direct cloudy radiance assimilation for a small number of channels. The algorithm is a form of Bayesian inference with a Markov chain Monte Carlo (MCMC) approach to characterizing the posterior distribution. This approach is especially useful in cases where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach is not gradient-based and allows jumps into regions of non-zero cloud probability. The current study uses a skewed-triangle distribution for layer moisture. The article also includes a discussion of the Metropolis and multiple-try Metropolis versions of MCMC. PMID:29618847

A Unified Framework Integrating Parent-of-Origin Effects for Association Study

PubMed Central

Xiao, Feifei; Ma, Jianzhong; Amos, Christopher I.

2013-01-01

Genetic imprinting is the most well-known cause for parent-of-origin effect (POE) whereby a gene is differentially expressed depending on the parental origin of the same alleles. Genetic imprinting is related to several human disorders, including diabetes, breast cancer, alcoholism, and obesity. This phenomenon has been shown to be important for normal embryonic development in mammals. Traditional association approaches ignore this important genetic phenomenon. In this study, we generalize the natural and orthogonal interactions (NOIA) framework to allow for estimation of both main allelic effects and POEs. We develop a statistical (Stat-POE) model that has the orthogonal estimates of parameters including the POEs. We conducted simulation studies for both quantitative and qualitative traits to evaluate the performance of the statistical and functional models with different levels of POEs. Our results showed that the newly proposed Stat-POE model, which ensures orthogonality of variance components if Hardy-Weinberg Equilibrium (HWE) or equal minor and major allele frequencies is satisfied, had greater power for detecting the main allelic additive effect than a Func-POE model, which codes according to allelic substitutions, for both quantitative and qualitative traits. The power for detecting the POE was the same for the Stat-POE and Func-POE models under HWE for quantitative traits. PMID:23991061

Statistical investigation of simulated fed intestinal media composition on the equilibrium solubility of oral drugs.

PubMed

Zhou, Zhou; Dunn, Claire; Khadra, Ibrahim; Wilson, Clive G; Halbert, Gavin W

2017-03-01

Gastrointestinal fluid is a complex milieu and it is recognised that gut drug solubility is different to that observed in simple aqueous buffers. Simulated gastrointestinal media have been developed covering fasted and fed states to facilitate in vitro prediction of gut solubility and product dissolution. However, the combination of bile salts, phospholipids, fatty acids and proteins in an aqueous buffered system creates multiple phases and drug solubility is therefore a complex interaction between these components, which may create unique environments for each API. The impact on solubility can be assessed through a statistical design of experiment (DoE) approach, to determine the influence and relationships between factors. In this paper DoE has been applied to fed simulated gastrointestinal media consisting of eight components (pH, bile salt, lecithin, sodium oleate, monoglyceride, buffer, salt and pancreatin) using a two level D-optimal design with forty-four duplicate measurements and four centre points. The equilibrium solubility of a range of poorly soluble acidic (indomethacin, ibuprofen, phenytoin, valsartan, zafirlukast), basic (aprepitant, carvedilol, tadalafil, bromocriptine) and neutral (fenofibrate, felodipine, probucol, itraconazole) drugs was investigated. Results indicate that the DoE provides equilibrium solubility values that are comparable to literature results for other simulated fed gastrointestinal media systems or human intestinal fluid samples. For acidic drugs the influence of pH predominates but other significant factors related to oleate and bile salt or interactions between them are present. For basic drugs pH, oleate and bile salt have equal significance along with interactions between pH and oleate and lecithin and oleate. Neutral drugs show diverse effects of the media components particularly with regard to oleate, bile salt, pH and lecithin but the presence of monoglyceride, pancreatin and buffer have significant but smaller effects on solubility. There are fourteen significant interactions between factors mainly related to the surfactant components and pH, indicating that the solubility of neutral drugs in fed simulated media is complex. The results also indicate that the equilibrium solubility of each drug can exhibit individualistic behaviour associated with the drug's chemical structure, physicochemical properties and interaction with media components. The utility of DoE for fed simulated media has been demonstrated providing equilibrium solubility values comparable with similar in vitro systems whilst also providing greater information on the influence of media factors and their interactions. The determination of a drug's gastrointestinal solubility envelope provides useful limits that can potentially be applied to in silico modelling and in vivo experiments. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Ignition conditions relaxation for central hot-spot ignition with an ion-electron non-equilibrium model

NASA Astrophysics Data System (ADS)

Fan, Zhengfeng; Liu, Jie

2016-10-01

We present an ion-electron non-equilibrium model, in which the hot-spot ion temperature is higher than its electron temperature so that the hot-spot nuclear reactions are enhanced while energy leaks are considerably reduced. Theoretical analysis shows that the ignition region would be significantly enlarged in the hot-spot rhoR-T space as compared with the commonly used equilibrium model. Simulations show that shocks could be utilized to create and maintain non-equilibrium conditions within the hot spot, and the hot-spot rhoR requirement is remarkably reduced for achieving self-heating. In NIF high-foot implosions, it is observed that the x-ray enhancement factors are less than unity, which is not self-consistent and is caused by assuming Te =Ti. And from this non-consistency, we could infer that ion-electron non-equilibrium exists in the high-foot implosions and the ion temperature could be 9% larger than the equilibrium temperature.

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.

Radiation-induced equilibrium is a balance between tumor cell proliferation and T cell-mediated killing

PubMed Central

Liang, Hua; Deng, Liufu; Chmura, Steven; Burnette, Byron; Liadis, Nicole; Darga, Thomas; Beckett, Michael A.; Lingen, Mark W.; Witt, MaryEllyn; Weichselbaum, Ralph R.; Fu, Yang-Xin

2013-01-01

Local failures following radiation therapy are multifactorial and the contributions of the tumor and the host are complex. Current models of tumor equilibrium suggest that a balance exists between cell birth and cell death due to insufficient angiogenesis, immune effects, or intrinsic cellular factors. We investigated whether host immune responses contribute to radiation induced tumor equilibrium in animal models. We report an essential role for immune cells and their cytokines in suppressing tumor cell regrowth in two experimental animal model systems. Depletion of T cells or neutralization of interferon-gamma reversed radiation-induced equilibrium leading to tumor regrowth. We also demonstrate that PD-L1 blockade augments T cell responses leading to rejection of tumors in radiation induced equilibrium. We identify an active interplay between tumor cells and immune cells that occurs in radiation-induced tumor equilibrium and suggest a potential role for disruption of the PD-L1/PD-1 axis in increasing local tumor control. PMID:23630355

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 Model Analysis of (n,p) Cross Sections and Average Energy For Fission Neutron Spectrum

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

Odsuren, M.; Khuukhenkhuu, G.

2011-06-28

Investigation of charged particle emission reaction cross sections for fast neutrons is important to both nuclear reactor technology and the understanding of nuclear reaction mechanisms. In particular, the study of (n,p) cross sections is necessary to estimate radiation damage due to hydrogen production, nuclear heating and transmutations in the structural materials of fission and fusion reactors. On the other hand, it is often necessary in practice to evaluate the neutron cross sections of the nuclides for which no experimental data are available.Because of this, we carried out the systematical analysis of known experimental (n,p) and (n,a) cross sections for fastmore » neutrons and observed a systematical regularity in the wide energy interval of 6-20 MeV and for broad mass range of target nuclei. To explain this effect using the compound, pre-equilibrium and direct reaction mechanisms some formulae were deduced. In this paper, in the framework of the statistical model known experimental (n,p) cross sections averaged over the thermal fission neutron spectrum of U-235 are analyzed. It was shown that the experimental data are satisfactorily described by the statistical model. Also, in the case of (n,p) cross sections the effective average neutron energy for fission spectrum of U-235 was found to be around 3 MeV.« less

LONG-TERM STABLE EQUILIBRIA FOR SYNCHRONOUS BINARY ASTEROIDS

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

Jacobson, Seth A.; Scheeres, Daniel J.

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semimajor axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semimajor axis will contract to the equilibrium. If the observed population of small (0.1-10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observationalmore » tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical 'monolithic' geophysical model. The 'rubble pile' geophysical model proposed by Goldreich and Sari is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and Goldreich and Sari models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.« less

Equations of state for explosive detonation products: The PANDA model

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

Kerley, G.I.

1994-05-01

This paper discusses a thermochemical model for calculating equations of state (EOS) for the detonation products of explosives. This model, which was first presented at the Eighth Detonation Symposium, is available in the PANDA code and is referred to here as ``the Panda model``. The basic features of the PANDA model are as follows. (1) Statistical-mechanical theories are used to construct EOS tables for each of the chemical species that are to be allowed in the detonation products. (2) The ideal mixing model is used to compute the thermodynamic functions for a mixture of these species, and the composition ofmore » the system is determined from assumption of chemical equilibrium. (3) For hydrocode calculations, the detonation product EOS are used in tabular form, together with a reactive burn model that allows description of shock-induced initiation and growth or failure as well as ideal detonation wave propagation. This model has been implemented in the three-dimensional Eulerian code, CTH.« less

Dynamic response and transfer function of social systems: A neuro-inspired model of collective human activity patterns.

PubMed

Lymperopoulos, Ilias N

2017-10-01

The interaction of social networks with the external environment gives rise to non-stationary activity patterns reflecting the temporal structure and strength of exogenous influences that drive social dynamical processes far from an equilibrium state. Following a neuro-inspired approach, based on the dynamics of a passive neuronal membrane, and the firing rate dynamics of single neurons and neuronal populations, we build a state-of-the-art model of the collective social response to exogenous interventions. In this regard, we analyze online activity patterns with a view to determining the transfer function of social systems, that is, the dynamic relationship between external influences and the resulting activity. To this end, first we estimate the impulse response (Green's function) of collective activity, and then we show that the convolution of the impulse response with a time-varying external influence field accurately reproduces empirical activity patterns. To capture the dynamics of collective activity when the generating process is in a state of statistical equilibrium, we incorporate into the model a noisy input convolved with the impulse response function, thus precisely reproducing the fluctuations of stationary collective activity around a resting value. The outstanding goodness-of-fit of the model results to empirical observations, indicates that the model explains human activity patterns generated by time-dependent external influences in various socio-economic contexts. The proposed model can be used for inferring the temporal structure and strength of external influences, as well as the inertia of collective social activity. Furthermore, it can potentially predict social activity patterns. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Droz, Michel; Pekalski, Andrzej

2016-09-01

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

An entropic framework for modeling economies

NASA Astrophysics Data System (ADS)

Caticha, Ariel; Golan, Amos

2014-08-01

We develop an information-theoretic framework for economic modeling. This framework is based on principles of entropic inference that are designed for reasoning on the basis of incomplete information. We take the point of view of an external observer who has access to limited information about broad macroscopic economic features. We view this framework as complementary to more traditional methods. The economy is modeled as a collection of agents about whom we make no assumptions of rationality (in the sense of maximizing utility or profit). States of statistical equilibrium are introduced as those macrostates that maximize entropy subject to the relevant information codified into constraints. The basic assumption is that this information refers to supply and demand and is expressed in the form of the expected values of certain quantities (such as inputs, resources, goods, production functions, utility functions and budgets). The notion of economic entropy is introduced. It provides a measure of the uniformity of the distribution of goods and resources. It captures both the welfare state of the economy as well as the characteristics of the market (say, monopolistic, concentrated or competitive). Prices, which turn out to be the Lagrange multipliers, are endogenously generated by the economy. Further studies include the equilibrium between two economies and the conditions for stability. As an example, the case of the nonlinear economy that arises from linear production and utility functions is treated in some detail.

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.

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

Madland, D. G.; Kahler, A. C.

This paper presents a number of refinements to the original Los Alamos model of the prompt fission neutron spectrum and average prompt neutron multiplicity as derived in 1982. The four refinements are due to new measurements of the spectrum and related fission observables many of which were not available in 1982. Here, they are also due to a number of detailed studies and comparisons of the model with previous and present experimental results including not only the differential spectrum, but also integal cross sections measured in the field of the differential spectrum. The four refinements are (a) separate neutron contributionsmore » in binary fission, (b) departure from statistical equilibrium at scission, (c) fission-fragment nuclear level-density models, and (d) center-of-mass anisotropy. With these refinements, for the first time, good agreement has been obtained for both differential and integral measurements using the same Los Alamos model spectrum.« less

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

NASA Astrophysics Data System (ADS)

Chowdhury, Debashish

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

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model.

PubMed

Chen, Yunjie; Roux, Benoît

2015-08-11

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics—Monte Carlo Simulations Guided by a Coarse-Grained Model

PubMed Central

2015-01-01

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water. PMID:26574442

Phylogenies support out-of-equilibrium models of biodiversity.

PubMed

Manceau, Marc; Lambert, Amaury; Morlon, Hélène

2015-04-01

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium. © 2015 John Wiley & Sons Ltd/CNRS.

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

PubMed

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

2016-10-01

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

Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.

Precipitation in a boiling soup: is microphysics driving the statistical properties of intense turbulent convection?

NASA Astrophysics Data System (ADS)

Parodi, A.; von Hardenberg, J.; Provenzale, A.

2012-04-01

Intense precipitation events are often associated with strong convective phenomena in the atmosphere. A deeper understanding of how microphysics affects the spatial and temporal variability of convective processes is relevant for many hydro-meteorological applications, such as the estimation of rainfall using remote sensing techniques and the ability to predict severe precipitation processes. In this paper, high-resolution simulations (0.1-1 km) of an atmosphere in radiative-convective equilibrium are performed using the Weather Research and Forecasting (WRF) model by prescribing different microphysical parameterizations. The dependence of fine-scale spatio-temporal properties of convective structures on microphysical details are investigated and the simulation results are compared with the known properties of radar maps of precipitation fields. We analyze and discuss similarities and differences and, based also on previous results on the dependence of precipitation statistics on the raindrop terminal velocity, try to draw some general inferences.

Automated sampling assessment for molecular simulations using the effective sample size

PubMed Central

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

2010-01-01

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

Effects of sorption kinetics on the fate and transport of pharmaceuticals in estuaries.

PubMed

Liu, Dong; Lung, Wu-Seng; Colosi, Lisa M

2013-08-01

Many current fate and transport models based on the assumption of instantaneous sorption equilibrium of contaminants in the water column may not be valid for certain pharmaceuticals with long times to reach sorption equilibrium. In this study, a sorption kinetics model was developed and incorporated into a water quality model for the Patuxent River Estuary to evaluate the effect of sorption kinetics. Model results indicate that the assumption of instantaneous sorption equilibrium results in significant under-prediction of water column concentrations for some pharmaceuticals. The relative difference between predicted concentrations for the instantaneous versus kinetic approach is as large as 150% at upstream locations in the Patuxent Estuary. At downstream locations, where sorption processes have had sufficient time to reach equilibrium, the relative difference decreases to roughly 25%. This indicates that sorption kinetics affect a model's ability to capture accumulation of pharmaceuticals into riverbeds and the transport of pharmaceuticals in estuaries. These results offer strong evidence that chemicals are not removed from the water column as rapidly as has been assumed on the basis of equilibrium-based analyses. The findings are applicable not only for pharmaceutical compounds, but also for diverse contaminants that reach sorption equilibrium slowly. Copyright © 2013 Elsevier Ltd. All rights reserved.

Comparison of DNA decatenation by Escherichia coli topoisomerase IV and topoisomerase III: implications for non-equilibrium topology simplification

PubMed Central

Seol, Yeonee; Hardin, Ashley H.; Strub, Marie-Paule; Charvin, Gilles; Neuman, Keir C.

2013-01-01

Type II topoisomerases are essential enzymes that regulate DNA topology through a strand-passage mechanism. Some type II topoisomerases relax supercoils, unknot and decatenate DNA to below thermodynamic equilibrium. Several models of this non-equilibrium topology simplification phenomenon have been proposed. The kinetic proofreading (KPR) model postulates that strand passage requires a DNA-bound topoisomerase to collide twice in rapid succession with a second DNA segment, implying a quadratic relationship between DNA collision frequency and relaxation rate. To test this model, we used a single-molecule assay to measure the unlinking rate as a function of DNA collision frequency for Escherichia coli topoisomerase IV (topo IV) that displays efficient non-equilibrium topology simplification activity, and for E. coli topoisomerase III (topo III), a type IA topoisomerase that unlinks and unknots DNA to equilibrium levels. Contrary to the predictions of the KPR model, topo IV and topo III unlinking rates were linearly related to the DNA collision frequency. Furthermore, topo III exhibited decatenation activity comparable with that of topo IV, supporting proposed roles for topo III in DNA segregation. This study enables us to rule out the KPR model for non-equilibrium topology simplification. More generally, we establish an experimental approach to systematically control DNA collision frequency. PMID:23460205

Ergodicity in natural earthquake fault networks

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

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

2007-06-15

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

Delineating Spatial Patterns in the Yellowstone Hydrothermal System using Geothermometry

NASA Astrophysics Data System (ADS)

King, J.; Hurwitz, S.; Lowenstern, J. B.

2015-12-01

Yellowstone National Park is unmatched with regard to its quantity of active hydrothermal features. Origins of thermal waters in its geyser basins have been traced to mixing of a deep parent water with meteoric waters in shallow local reservoirs (Fournier, 1989). A mineral-solution equilibrium model was developed to calculate water-rock chemical re-equilibration temperatures in these shallow reservoirs. We use the GeoT program, which uses water composition data as input to calculate saturation indices of selected minerals; the "best-clustering" minerals are then statistically determined to infer reservoir temperatures (Spycher et al., 2013). We develop the method using water composition data from Heart Lake Geyser Basin (HLGB), for which both chemical and isotopic geothermometers predict a reservoir water temperature of 205°C ± 10°C (Lowenstern et al., 2012), and minerals found in drill cores in Yellowstone's geyser basins. We test the model for sensitivity to major element composition, pH, Total Inorganic Carbon (TIC) and selected minerals to optimize model parameters. Calculated temperatures are most accurate at pH values below 9.0, and closely match the equilibrium saturation indices of quartz, stilbite, microcline, and albite. The model is optimized with a TIC concentration that is consistent with the mass of diffuse CO2 flux in HLGB (Lowenstern et al., 2012). We then use water compositions from other thermal basins in Yellowstone in search of spatial variations in reservoir temperatures. We then compare the calculated temperatures with various SiO2 and cation geothermometers.

Learning of Chemical Equilibrium through Modelling-Based Teaching

ERIC Educational Resources Information Center

Maia, Poliana Flavia; Justi, Rosaria

2009-01-01

This paper presents and discusses students' learning process of chemical equilibrium from a modelling-based approach developed from the use of the "Model of Modelling" diagram. The investigation was conducted in a regular classroom (students 14-15 years old) and aimed at discussing how modelling-based teaching can contribute to students…

Role of delay and screening in controlling AIDS

NASA Astrophysics Data System (ADS)

Chauhan, Sudipa; Bhatia, Sumit Kaur; Gupta, Surbhi

2016-06-01

We propose a non-linear HIV/ AIDS model to analyse the spread and control of HIV/AIDS. The population is divided into three classes, susceptible, infective and AIDS patients. The model is developed under the assumptions of vertical transmission and time delay in infective class. Time delay is also included to show sexual maturity period of infected newborns. We study dynamics of the model and obtain the reproduction number. Now to control the epidemic, we study the model where aware infective class is also added, i.e., people are made aware of their medical status by way of screening. To make the model more realistic, we consider the situation where aware infective class also interacts with other people. The model is analysed qualitatively by stability theory of ODE. Stability analysis of both disease-free and endemic equilibrium is studied based on reproduction number. Also, it is proved that if (R0)1, R1 ≤ 1 then, disease free equilibrium point is locally asymptotically stable and if (R0)1, R1 > 1 then, disease free equilibrium is unstable. Also, the stability analysis of endemic equilibrium point has been done and it is shown that for (R0)1 > 1 endemic equilibrium point is stable. Global stability analysis of endemic equilibrium point has also been done. At last, it is shown numerically that the delay in sexual maturity of infected individuals result in less number of AIDS patients.

Condensate statistics in interacting and ideal dilute bose gases

PubMed

Kocharovsky; Kocharovsky; Scully

2000-03-13

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

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

NASA Astrophysics Data System (ADS)

van Lith, Janneke

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic. This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.

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.

Pb(II) adsorption by a novel activated carbon - alginate composite material. A kinetic and equilibrium study.

PubMed

Cataldo, Salvatore; Gianguzza, Antonio; Milea, Demetrio; Muratore, Nicola; Pettignano, Alberto

2016-11-01

The adsorption capacity of an activated carbon - calcium alginate composite material (ACAA-Ca) has been tested with the aim of developing a new and more efficient adsorbent material to remove Pb(II) ion from aqueous solution. The study was carried out at pH=5, in NaCl medium and in the ionic strength range 0.1-0.75molL -1 . Differential Pulse Anodic Stripping Voltammetry (DP-ASV) technique was used to check the amount of Pb(II) ion removed during kinetic and equilibrium experiments. Different kinetic (pseudo first order, pseudo second order and Vermuelen) and equilibrium (Langmuir and Freundlich) models were used to fit experimental data, and were statistically compared. Calcium alginate (AA-Ca) improves the adsorption capacity (q m ) of active carbon (AC) in the ACAA-Ca adsorbent material (e.g., q m =15.7 and 10.5mgg -1 at I=0.25molL -1 , for ACAA-Ca and AC, respectively). SEM-EDX and thermogravimetric (TGA) measurements were carried out in order to characterize the composite material. The results of the speciation study on the Pb(II) solution and of the characterization of the ACAA-Ca and of the pristine AA-Ca and AC were evaluated in order to explain the specific contribution of AC and AA-Ca to the adsorption of the metal ion. Copyright © 2016 Elsevier B.V. All rights reserved.

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

PubMed

Polak, Micha; Rubinovich, Leonid

2011-10-06

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

Regime-dependence of Impacts of Radar Rainfall Data Assimilation

NASA Astrophysics Data System (ADS)

Craig, G. C.; Keil, C.

2009-04-01

Experience from the first operational trials of assimilation of radar data in kilometre scale numerical weather prediction models (operating without cumulus parameterisation) shows that the positive impact of the radar data on convective precipitation forecasts typically decay within a few hours, although certain cases show much longer impacts. Here the impact time of radar data assimilation is related to characteristics of the meteorological environment. This QPF uncertainty is investigated using an ensemble of 10 forecasts at 2.8 km horizontal resolution based on different initial and boundary conditions from a global forecast ensemble. Control forecasts are compared with forecasts where radar reflectivity data is assimilated using latent heat nudging. Examination of different cases of convection in southern Germany suggests that the forecasts can be separated into two regimes using a convective timescale. Short impact times are associated with short convective timescales that are characteristic of equilibrium convection. In this regime the statistical properties of the convection are constrained by the large-scale forcing, and effects of the radar data are lost within a few hours as the convection rapidly returns to equilibrium. When the convective timescale is large (non-equilibrium conditions), the impact of the radar data is longer since convective systems are triggered by the latent heat nudging and are able to persist for many hours in the very unstable conditions present in these cases.

Improving high-altitude emp modeling capabilities by using a non-equilibrium electron swarm model to monitor conduction electron evolution

NASA Astrophysics Data System (ADS)

Pusateri, Elise Noel

An Electromagnetic Pulse (EMP) can severely disrupt the use of electronic devices in its path causing a significant amount of infrastructural damage. EMP can also cause breakdown of the surrounding atmosphere during lightning discharges. This makes modeling EMP phenomenon an important research effort in many military and atmospheric physics applications. EMP events include high-energy Compton electrons or photoelectrons that ionize air and produce low energy conduction electrons. A sufficient number of conduction electrons will damp or alter the EMP through conduction current. Therefore, it is important to understand how conduction electrons interact with air in order to accurately predict the EMP evolution and propagation in the air. It is common for EMP simulation codes to use an equilibrium ohmic model for computing the conduction current. Equilibrium ohmic models assume the conduction electrons are always in equilibrium with the local instantaneous electric field, i.e. for a specific EMP electric field, the conduction electrons instantaneously reach steady state without a transient process. An equilibrium model will work well if the electrons have time to reach their equilibrium distribution with respect to the rise time or duration of the EMP. If the time to reach equilibrium is comparable or longer than the rise time or duration of the EMP then the equilibrium model would not accurately predict the conduction current necessary for the EMP simulation. This is because transport coefficients used in the conduction current calculation will be found based on equilibrium reactions rates which may differ significantly from their non-equilibrium values. We see this deficiency in Los Alamos National Laboratory's EMP code, CHAP-LA (Compton High Altitude Pulse-Los Alamos), when modeling certain EMP scenarios at high altitudes, such as upward EMP, where the ionization rate by secondary electrons is over predicted by the equilibrium model, causing the EMP to short abruptly. The objective of the PhD research is to mitigate this effect by integrating a conduction electron model into CHAP-LA which can calculate the conduction current based on a non-equilibrium electron distribution. We propose to use an electron swarm model to monitor the time evolution of conduction electrons in the EMP environment which is characterized by electric field and pressure. Swarm theory uses various collision frequencies and reaction rates to study how the electron distribution and the resultant transport coefficients change with time, ultimately reaching an equilibrium distribution. Validation of the swarm model we develop is a necessary step for completion of the thesis work. After validation, the swarm model is integrated in the air chemistry model CHAP-LA employs for conduction electron simulations. We test high altitude EMP simulations with the swarm model option in the air chemistry model to show improvements in the computational capability of CHAP-LA. A swarm model has been developed that is based on a previous swarm model developed by Higgins, Longmire and O'Dell 1973, hereinafter HLO. The code used for the swarm model calculation solves a system of coupled differential equations for electric field, electron temperature, electron number density, and drift velocity. Important swarm parameters, including the momentum transfer collision frequency, energy transfer collision frequency, and ionization rate, are recalculated and compared to the previously reported empirical results given by HLO. These swarm parameters are found using BOLSIG+, a two term Boltzmann solver developed by Hagelaar and Pitchford 2005. BOLSIG+ utilizes updated electron scattering cross sections that are defined over an expanded energy range found in the atomic and molecular cross section database published by Phelps in the Phelps Database 2014 on the LXcat website created by Pancheshnyi et al. 2012. The swarm model is also updated from the original HLO model by including additional physical parameters such as the O2 electron attachment rate, recombination rate, and mutual neutralization rate. This necessitates tracking the positive and negative ion densities in the swarm model. Adding these parameters, especially electron attachment, is important at lower EMP altitudes where atmospheric density is high. We compare swarm model equilibrium temperatures and times using the HLO and BOLSIG+ coefficients for a uniform electric field of 1 StatV/cm for a range of atmospheric heights. This is done in order to test sensitivity to the swarm parameters used in the swarm model. It is shown that the equilibrium temperature and time are sensitive to the modifications in the collision frequency and ionization rate based on the updated electron interaction cross sections. We validate the swarm model by comparing ionization coefficients and equilibrium drift velocities to experimental results over a wide range of reduced electric field values. The final part of the PhD thesis work includes integrating the swarm model into CHAP-LA. We discuss the physics included in the CHAP-LA EMP model and demonstrate EMP damping behavior caused by the ohmic model at high altitudes. We report on numerical techniques for incorporation of the swarm model into CHAP-LA's Maxwell solver. This includes a discussion of integration techniques for Maxwell's equations in CHAP-LA using the swarm model calculated conduction current. We show improvements on EMP parameter calculations when modeling a high altitude, upward EMP scenario. This provides a novel computational capability that will have an important impact on the atmospheric and EMP research community.

Statistical Analysis of Hubble /WFC3 Transit Spectroscopy of Extrasolar Planets

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

Fu, Guangwei; Deming, Drake; Knutson, Heather

2017-10-01

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

Statistical Analysis of Hubble/WFC3 Transit Spectroscopy of Extrasolar Planets

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Statistical Analysis of Hubble/WFC3 Transit Spectroscopy of Extrasolar Planets

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A model on CME/Flare initiation: Loss of Equilibrium caused by mass loss of quiescent prominences

NASA Astrophysics Data System (ADS)

Miley, George; Chon Nam, Sok; Kim, Mun Song; Kim, Jik Su

2015-08-01

Coronal Mass Ejections (CMEs) model should give an answer to enough energy storage for giant bulk plasma into interplanetary space to escape against the sun’s gravitation and its explosive eruption. Advocates of ‘Mass Loading’ model (e.g. Low, B. 1996, SP, 167, 217) suggested a simple mechanism of CME initiation, the loss of mass from a prominence anchoring magnetic flux rope, but they did not associate the mass loss with the loss of equilibrium. The catastrophic loss of equilibrium model is considered as to be a prospective CME/Flare model to explain sudden eruption of magnetic flux systems. Isenberg, P. A., et al (1993, ApJ, 417, 368)developed ideal magnetohydrodynamic theory of the magnetic flux rope to show occurrence of catastrophic loss of equilibrium according to increasing magnetic flux transported into corona.We begin with extending their study including gravity on prominence’s material to obtain equilibrium curves in case of given mass parameters, which are the strengths of the gravitational force compared with the characteristic magnetic force. Furthermore, we study quasi-static evolution of the system including massive prominence flux rope and current sheet below it to obtain equilibrium curves of prominence’s height according to decreasing mass parameter in a properly fixed magnetic environment. The curves show equilibrium loss behaviors to imply that mass loss result in equilibrium loss. Released fractions of magnetic energy are greater than corresponding zero-mass case. This eruption mechanism is expected to be able to apply to the eruptions of quiescent prominences, which is located in relatively weak magnetic environment with 105 km of scale length and 10G of photospheric magnetic field.

Equivalences between refractive index and equilibrium water content of conventional and silicone hydrogel soft contact lenses from automated and manual refractometry.

PubMed

González-Méijome, José M; López-Alemany, Antonio; Lira, Madalena; Almeida, José B; Oliveira, M Elisabete C D Real; Parafita, Manuel A

2007-01-01

The purpose of the present study was to develop mathematical relationships that allow obtaining equilibrium water content and refractive index of conventional and silicone hydrogel soft contact lenses from refractive index measures obtained with automated refractometry or equilibrium water content measures derived from manual refractometry, respectively. Twelve HEMA-based hydrogels of different hydration and four siloxane-based polymers were assayed. A manual refractometer and a digital refractometer were used. Polynomial models obtained from the sucrose curves of equilibrium water content against refractive index and vice-versa were used either considering the whole range of sucrose concentrations (16-100% equilibrium water content) or a range confined to the equilibrium water content of current soft contact lenses (approximately 20-80% equilibrium water content). Values of equilibrium water content measured with the Atago N-2E and those derived from the refractive index measurement with CLR 12-70 by the applications of sucrose-based models displayed a strong linear correlation (r2 = 0.978). The same correlations were obtained when the models are applied to obtain refractive index values from the Atago N-2E and compared with those (values) given by the CLR 12-70 (r2 = 0.978). No significantly different results are obtained between models derived from the whole range of the sucrose solution or the model limited to the normal range of soft contact lens hydration. Present results will have implications for future experimental and clinical research regarding normal hydration and dehydration experiments with hydrogel polymers, and particularly in the field of contact lenses. 2006 Wiley Periodicals, Inc.

Sub-grid scale models for discontinuous Galerkin methods based on the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric; Duraisamy, Karthk

2017-11-01

The optimal prediction framework of Chorin et al., which is a reformulation of the Mori-Zwanzig (M-Z) formalism of non-equilibrium statistical mechanics, provides a framework for the development of mathematically-derived closure models. The M-Z formalism provides a methodology to reformulate a high-dimensional Markovian dynamical system as a lower-dimensional, non-Markovian (non-local) system. In this lower-dimensional system, the effects of the unresolved scales on the resolved scales are non-local and appear as a convolution integral. The non-Markovian system is an exact statement of the original dynamics and is used as a starting point for model development. In this work, we investigate the development of M-Z-based closures model within the context of the Variational Multiscale Method (VMS). The method relies on a decomposition of the solution space into two orthogonal subspaces. The impact of the unresolved subspace on the resolved subspace is shown to be non-local in time and is modeled through the M-Z-formalism. The models are applied to hierarchical discontinuous Galerkin discretizations. Commonalities between the M-Z closures and conventional flux schemes are explored. This work was supported in part by AFOSR under the project ''LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

Surface-dependent chemical equilibrium constants and capacitances for bare and 3-cyanopropyldimethylchlorosilane coated silica nanochannels.

PubMed

Andersen, Mathias Bækbo; Frey, Jared; Pennathur, Sumita; Bruus, Henrik

2011-01-01

We present a combined theoretical and experimental analysis of the solid-liquid interface of fused-silica nanofabricated channels with and without a hydrophilic 3-cyanopropyldimethylchlorosilane (cyanosilane) coating. We develop a model that relaxes the assumption that the surface parameters C(1), C(2), and pK(+) are constant and independent of surface composition. Our theoretical model consists of three parts: (i) a chemical equilibrium model of the bare or coated wall, (ii) a chemical equilibrium model of the buffered bulk electrolyte, and (iii) a self-consistent Gouy-Chapman-Stern triple-layer model of the electrochemical double layer coupling these two equilibrium models. To validate our model, we used both pH-sensitive dye-based capillary filling experiments as well as electro-osmotic current-monitoring measurements. Using our model we predict the dependence of ζ potential, surface charge density, and capillary filling length ratio on ionic strength for different surface compositions, which can be difficult to achieve otherwise. Copyright © 2010 Elsevier Inc. All rights reserved.

Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response

NASA Astrophysics Data System (ADS)

Guo, Ting; Liu, Haihong; Xu, Chenglin; Yan, Fang

2016-12-01

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium E0, the infectious equilibrium without immune response E1 and the infectious equilibrium with immune response E2. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point E2 are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that E0 is globally asymptotically stable when the basic reproductive numbers for viral infection R0 is less than unity. When the basic reproductive numbers for immune response R1 is less than unity and R0 is greater than unity, the equilibrium point E1 is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.

A Harris-Todaro Agent-Based Model to Rural-Urban Migration

NASA Astrophysics Data System (ADS)

Espíndola, Aquino L.; Silveira, Jaylson J.; Penna, T. J. P.

2006-09-01

The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.

Non-equilibrium Quasi-Chemical Nucleation Model

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy E.

2018-04-01

Quasi-chemical model, which is widely used for nucleation description, is revised on the basis of recent results in studying of non-equilibrium effects in reacting gas mixtures (Kolesnichenko and Gorbachev in Appl Math Model 34:3778-3790, 2010; Shock Waves 23:635-648, 2013; Shock Waves 27:333-374, 2017). Non-equilibrium effects in chemical reactions are caused by the chemical reactions themselves and therefore these contributions should be taken into account in the corresponding expressions for reaction rates. Corrections to quasi-equilibrium reaction rates are of two types: (a) spatially homogeneous (caused by physical-chemical processes) and (b) spatially inhomogeneous (caused by gas expansion/compression processes and proportional to the velocity divergency). Both of these processes play an important role during the nucleation and are included into the proposed model. The method developed for solving the generalized Boltzmann equation for chemically reactive gases is applied for solving the set of equations of the revised quasi-chemical model. It is shown that non-equilibrium processes lead to essential deviation of the quasi-stationary distribution and therefore the nucleation rate from its traditional form.

A rumor transmission model with incubation in social networks

NASA Astrophysics Data System (ADS)

Jia, Jianwen; Wu, Wenjiang

2018-02-01

In this paper, we propose a rumor transmission model with incubation period and constant recruitment in social networks. By carrying out an analysis of the model, we study the stability of rumor-free equilibrium and come to the local stable condition of the rumor equilibrium. We use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium. And when ℜ0 = 1, the new model occurs a transcritical bifurcation. Furthermore, numerical simulations are used to support the analysis. At last, some conclusions are presented.

Quantum description of light propagation in generalized media

NASA Astrophysics Data System (ADS)

Häyrynen, Teppo; Oksanen, Jani

2016-02-01

Linear quantum input-output relation based models are widely applied to describe the light propagation in a lossy medium. The details of the interaction and the associated added noise depend on whether the device is configured to operate as an amplifier or an attenuator. Using the traveling wave (TW) approach, we generalize the linear material model to simultaneously account for both the emission and absorption processes and to have point-wise defined noise field statistics and intensity dependent interaction strengths. Thus, our approach describes the quantum input-output relations of linear media with net attenuation, amplification or transparency without pre-selection of the operation point. The TW approach is then applied to investigate materials at thermal equilibrium, inverted materials, the transparency limit where losses are compensated, and the saturating amplifiers. We also apply the approach to investigate media in nonuniform states which can be e.g. consequences of a temperature gradient over the medium or a position dependent inversion of the amplifier. Furthermore, by using the generalized model we investigate devices with intensity dependent interactions and show how an initial thermal field transforms to a field having coherent statistics due to gain saturation.

Bayesian Atmospheric Radiative Transfer (BART) Code and Application to WASP-43b

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Cubillos, Patricio; Bowman, Oliver; Rojo, Patricio; Stemm, Madison; Lust, Nathaniel B.; Challener, Ryan; Foster, Austin James; Foster, Andrew S.; Blumenthal, Sarah D.; Bruce, Dylan

2016-01-01

We present a new open-source Bayesian radiative-transfer framework, Bayesian Atmospheric Radiative Transfer (BART, https://github.com/exosports/BART), and its application to WASP-43b. BART initializes a model for the atmospheric retrieval calculation, generates thousands of theoretical model spectra using parametrized pressure and temperature profiles and line-by-line radiative-transfer calculation, and employs a statistical package to compare the models with the observations. It consists of three self-sufficient modules available to the community under the reproducible-research license, the Thermochemical Equilibrium Abundances module (TEA, https://github.com/dzesmin/TEA, Blecic et al. 2015}, the radiative-transfer module (Transit, https://github.com/exosports/transit), and the Multi-core Markov-chain Monte Carlo statistical module (MCcubed, https://github.com/pcubillos/MCcubed, Cubillos et al. 2015). We applied BART on all available WASP-43b secondary eclipse data from the space- and ground-based observations constraining the temperature-pressure profile and molecular abundances of the dayside atmosphere of WASP-43b. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G. JB holds a NASA Earth and Space Science Fellowship.

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.

A general equilibrium model of a production economy with asset markets

NASA Astrophysics Data System (ADS)

Raberto, Marco; Teglio, Andrea; Cincotti, Silvano

2006-10-01

In this paper, a general equilibrium model of a monetary production economy is presented. The model is characterized by three classes of agents: a representative firm, heterogeneous households, and the government. Two markets (i.e., a labour market and a goods market, are considered) and two assets are traded in exchange of money, namely, government bonds and equities. Households provide the labour force and decide on consumption and savings, whereas the firm provides consumption goods and demands labour. The government receives taxes from households and pays interests on debt. The Walrasian equilibrium is derived analytically. The dynamics through quantity constrained equilibria out from the Walrasian equilibrium is also studied by means of computer simulations.

Modeling multicomponent ion exchange equilibrium utilizing hydrous crystalline silicotitanates by a multiple interactive ion exchange site model

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

Zheng, Z.; Anthony, R.G.; Miller, J.E.

1997-06-01

An equilibrium multicomponent ion exchange model is presented for the ion exchange of group I metals by TAM-5, a hydrous crystalline silicotitanate. On the basis of the data from ion exchange and structure studies, the solid phase is represented as Na{sub 3}X instead of the usual form of NaX. By using this solid phase representation, the solid can be considered as an ideal phase. A set of model ion exchange reactions is proposed for ion exchange between H{sup +}, Na{sup +}, K{sup +}, Rb{sup +}, and Cs{sup +}. The equilibrium constants for these reactions were estimated from experiments with simplemore » ion exchange systems. Bromley`s model for activity coefficients of electrolytic solutions was used to account for liquid phase nonideality. Bromley`s model parameters for CsOH at high ionic strength and for NO{sub 2}{sup {minus}} and Al(OH){sub 4}{sup {minus}} were estimated in order to apply the model for complex waste simulants. The equilibrium compositions and distribution coefficients of counterions were calculated for complex simulants typical of DOE wastes by solving the equilibrium equations for the model reactions and material balance equations. The predictions match the experimental results within 10% for all of these solutions.« less

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

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.

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

NASA Astrophysics Data System (ADS)

Vavylonis, Dimitrios

2009-03-01

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

Spent coffee grounds-based activated carbon preparation for sequestering of malachite green

NASA Astrophysics Data System (ADS)

Lim, Jun-Wei; Lam, Keat-Ying; Bashir, Mohammed J. K.; Yeong, Yin-Fong; Lam, Man-Kee; Ho, Yeek-Chia

2016-11-01

The key of reported work was to optimize the fabricating factors of spent coffee grounds-based activated carbon (SCG-bAC) used to sequester Malachite Green (MG) form aqueous solution via adsorption process. The fabricating factors of impregnation ratio with ortho-phosphoric acid, activation temperature and activation time were simultaneously optimized by central composite design (CCD) of response surface methodology (RSM) targeting on maximum removal of MG. At the optimum condition, 96.3% of MG was successfully removed by SCG-bAC at the impregnation ratio with ortho-phosphoric acid of 0.50, activation temperature of 554°C and activation time of 31.4 min. Statistical model that could predict the MG removal percentage was also derived and had been statistically confirmed to be significant. Subsequently, the MG adsorption equilibrium data was found well-fitted to Langmuir isotherm model, indicating the predominance of monolayer adsorption of MG on SCG-bAC surface. To conclude, the findings from the this study unveil the potential of spent coffee grounds as an alternative precursor in fabricating low-cost AC for the treatment of wastewater loaded with MG pollutant.

Dynamic scaling in natural swarms

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

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

NASA Technical Reports Server (NTRS)

Underhill, A. B.

1985-01-01

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

Incorporation of the equilibrium temperature approach in a Soil and Water Assessment Tool hydroclimatological stream temperature model

NASA Astrophysics Data System (ADS)

Du, Xinzhong; Shrestha, Narayan Kumar; Ficklin, Darren L.; Wang, Junye

2018-04-01

Stream temperature is an important indicator for biodiversity and sustainability in aquatic ecosystems. The stream temperature model currently in the Soil and Water Assessment Tool (SWAT) only considers the impact of air temperature on stream temperature, while the hydroclimatological stream temperature model developed within the SWAT model considers hydrology and the impact of air temperature in simulating the water-air heat transfer process. In this study, we modified the hydroclimatological model by including the equilibrium temperature approach to model heat transfer processes at the water-air interface, which reflects the influences of air temperature, solar radiation, wind speed and streamflow conditions on the heat transfer process. The thermal capacity of the streamflow is modeled by the variation of the stream water depth. An advantage of this equilibrium temperature model is the simple parameterization, with only two parameters added to model the heat transfer processes. The equilibrium temperature model proposed in this study is applied and tested in the Athabasca River basin (ARB) in Alberta, Canada. The model is calibrated and validated at five stations throughout different parts of the ARB, where close to monthly samplings of stream temperatures are available. The results indicate that the equilibrium temperature model proposed in this study provided better and more consistent performances for the different regions of the ARB with the values of the Nash-Sutcliffe Efficiency coefficient (NSE) greater than those of the original SWAT model and the hydroclimatological model. To test the model performance for different hydrological and environmental conditions, the equilibrium temperature model was also applied to the North Fork Tolt River Watershed in Washington, United States. The results indicate a reasonable simulation of stream temperature using the model proposed in this study, with minimum relative error values compared to the other two models. However, the NSE values were lower than those of the hydroclimatological model, indicating that more model verification needs to be done. The equilibrium temperature model uses existing SWAT meteorological data as input, can be calibrated using fewer parameters and less effort and has an overall better performance in stream temperature simulation. Thus, it can be used as an effective tool for predicting the changes in stream temperature regimes under varying hydrological and meteorological conditions. In addition, the impact of the stream temperature simulations on chemical reaction rates and concentrations was tested. The results indicate that the improved performance of the stream temperature simulation could significantly affect chemical reaction rates and the simulated concentrations, and the equilibrium temperature model could be a potential tool to model stream temperature in water quality simulations.

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

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

Rezai, Raheleh, E-mail: R_Rezai@sbu.ac.ir; Ebrahimi, Farshad, E-mail: Ebrahimi@sbu.ac.ir

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in themore » non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U{sup 2} IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior. -- Highlights: •We introduce for the first time the non-equilibrium method of STLS for Hubbard type models. •We determine the transport properties of SIAM using the non-equilibrium STLS method. •We compare our results with order-U2 IPT and NRG. •We show that non-equilibrium STLS, contrary to the GW and self-consistent RPA, produces the two Hubbard peaks in DOS. •We show that the method keeps the universal scaling behavior and correct exponential behavior of Kondo temperature.« less

The maximum entropy production principle: two basic questions.

PubMed

Martyushev, Leonid M

2010-05-12

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

The photon gas formulation of thermal radiation

NASA Technical Reports Server (NTRS)

Ried, R. C., Jr.

1975-01-01

A statistical consideration of the energy, the linear momentum, and the angular momentum of the photons that make up a thermal radiation field was presented. A general nonequilibrium statistical thermodynamics approach toward a macroscopic description of thermal radiation transport was developed and then applied to the restricted equilibrium statistical thermostatics derivation of the energy, linear momentum, and intrinsic angular momentum equations for an isotropic photon gas. A brief treatment of a nonisotropic photon gas, as an example of the results produced by the nonequilibrium statistical thermodynamics approach, was given. The relativistic variation of temperature and the invariance of entropy were illustrated.

Analysis of Hydrogen Generation through Thermochemical Gasification of Coconut Shell Using Thermodynamic Equilibrium Model Considering Char and Tar

PubMed Central

Rupesh, Shanmughom; Muraleedharan, Chandrasekharan; Arun, Palatel

2014-01-01

This work investigates the potential of coconut shell for air-steam gasification using thermodynamic equilibrium model. A thermodynamic equilibrium model considering tar and realistic char conversion was developed using MATLAB software to predict the product gas composition. After comparing it with experimental results the prediction capability of the model is enhanced by multiplying equilibrium constants with suitable coefficients. The modified model is used to study the effect of key process parameters like temperature, steam to biomass ratio, and equivalence ratio on product gas yield, composition, and heating value of syngas along with gasification efficiency. For a steam to biomass ratio of unity, the maximum mole fraction of hydrogen in the product gas is found to be 36.14% with a lower heating value of 7.49 MJ/Nm3 at a gasification temperature of 1500 K and equivalence ratio of 0.15. PMID:27433487

Analysis of Hydrogen Generation through Thermochemical Gasification of Coconut Shell Using Thermodynamic Equilibrium Model Considering Char and Tar.

PubMed

Rupesh, Shanmughom; Muraleedharan, Chandrasekharan; Arun, Palatel

2014-01-01

This work investigates the potential of coconut shell for air-steam gasification using thermodynamic equilibrium model. A thermodynamic equilibrium model considering tar and realistic char conversion was developed using MATLAB software to predict the product gas composition. After comparing it with experimental results the prediction capability of the model is enhanced by multiplying equilibrium constants with suitable coefficients. The modified model is used to study the effect of key process parameters like temperature, steam to biomass ratio, and equivalence ratio on product gas yield, composition, and heating value of syngas along with gasification efficiency. For a steam to biomass ratio of unity, the maximum mole fraction of hydrogen in the product gas is found to be 36.14% with a lower heating value of 7.49 MJ/Nm(3) at a gasification temperature of 1500 K and equivalence ratio of 0.15.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Technical Reports Server (NTRS)

Glass, Christopher E.

1990-01-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Astrophysics Data System (ADS)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Stability of the thermodynamic equilibrium - A test of the validity of dynamic models as applied to gyroviscous perpendicular magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Faghihi, Mustafa; Scheffel, Jan; Spies, Guenther O.

1988-05-01

Stability of the thermodynamic equilibrium is put forward as a simple test of the validity of dynamic equations, and is applied to perpendicular gyroviscous magnetohydrodynamics (i.e., perpendicular magnetohydrodynamics with gyroviscosity added). This model turns out to be invalid because it predicts exponentially growing Alfven waves in a spatially homogeneous static equilibrium with scalar pressure.

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

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

PubMed Central

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

2016-01-01

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

Stresses and elastic constants of crystalline sodium, from molecular dynamics

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

Schiferl, S.K.

1985-02-01

The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340K. The total adiabatic potential of a system of sodium atoms is represented by pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the resultsmore » to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. 45 refs., 10 figs., 4 tabs.« less

A survey of eight hot Jupiters in secondary eclipse using WIRCam at CFHT

NASA Astrophysics Data System (ADS)

Martioli, Eder; Colón, Knicole D.; Angerhausen, Daniel; Stassun, Keivan G.; Rodriguez, Joseph E.; Zhou, George; Gaudi, B. Scott; Pepper, Joshua; Beatty, Thomas G.; Tata, Ramarao; James, David J.; Eastman, Jason D.; Wilson, Paul Anthony; Bayliss, Daniel; Stevens, Daniel J.

2018-03-01

We present near-infrared high-precision photometry for eight transiting hot Jupiters observed during their predicted secondary eclipses. Our observations were carried out using the staring mode of the WIRCam instrument on the Canada-France-Hawaii Telescope (CFHT). We present the observing strategies and data reduction methods which delivered time series photometry with statistical photometric precision as low as 0.11 per cent. We performed a Bayesian analysis to model the eclipse parameters and systematics simultaneously. The measured planet-to-star flux ratios allowed us to constrain the thermal emission from the day side of these hot Jupiters, as we derived the planet brightness temperatures. Our results combined with previously observed eclipses reveal an excess in the brightness temperatures relative to the blackbody prediction for the equilibrium temperatures of the planets for a wide range of heat redistribution factors. We find a trend that this excess appears to be larger for planets with lower equilibrium temperatures. This may imply some additional sources of radiation, such as reflected light from the host star and/or thermal emission from residual internal heat from the formation of the planet.

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.

An analysis of numerical convergence in discrete velocity gas dynamics for internal flows

NASA Astrophysics Data System (ADS)

Sekaran, Aarthi; Varghese, Philip; Goldstein, David

2018-07-01

The Discrete Velocity Method (DVM) for solving the Boltzmann equation has significant advantages in the modeling of non-equilibrium and near equilibrium flows as compared to other methods in terms of reduced statistical noise, faster solutions and the ability to handle transient flows. Yet the DVM performance for rarefied flow in complex, small-scale geometries, in microelectromechanical (MEMS) devices for instance, is yet to be studied in detail. The present study focuses on the performance of the DVM for locally large Knudsen number flows of argon around sharp corners and other sources for discontinuities in the distribution function. Our analysis details the nature of the solution for some benchmark cases and introduces the concept of solution convergence for the transport terms in the discrete velocity Boltzmann equation. The limiting effects of the velocity space discretization are also investigated and the constraints on obtaining a robust, consistent solution are derived. We propose techniques to maintain solution convergence and demonstrate the implementation of a specific strategy and its effect on the fidelity of the solution for some benchmark cases.