Application of Tube Dynamics to Non-Statistical Reaction Processes

NASA Astrophysics Data System (ADS)

Gabern, F.; Koon, W. S.; Marsden, J. E.; Ross, S. D.; Yanao, T.

2006-06-01

A technique based on dynamical systems theory is introduced for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. In particular, we merge invariant manifold tube dynamics with Monte Carlo volume determination for accurate rate calculations. This methodology is applied to a three-degree-of-freedom model problem and some ideas on how it might be extended to higher-degree-of-freedom systems are presented.

Many Body Effects on Particle Diffusion in Polymer Nanocomposites

NASA Astrophysics Data System (ADS)

Dell, Zachary E.; Schweizer, Kenneth S.

2014-03-01

Recent statistical mechanical theories of nanoparticle motion in polymer melts and networks have focused on the dilute particle limit. By combining PRISM theory predictions for microscopic structural correlations, and a new formulation of self-consistent dynamical mode coupling theory, we extend dilute theories to finite filler loading. As a minimalist model, the polymer dynamics are first assumed to be unperturbed by the presence of the nanoparticles. The long time particle diffusivity in unentangled and entangled melts is determined as a function of polymer tube diameter and radius of gyration, nanoparticle diameter, and polymer-filler attraction strength under both constant volume and constant pressure situations. The influence of nanocomposite statistical structure (depletion, steric stabilization, bridging) on dynamics is also investigated. Using recent theoretical developments for predicting tube diameters in nanocomposites, the consequences of filler-induced tube dilation on nanoparticle motion is established. In entangled melts, increasing filler loading first modestly speeds up diffusion, and then dramatically when the inter-filler separation becomes smaller than the tube diameter. At very high loadings, a filler glass transition is generically predicted.

Dynamics of Markets

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2009-09-01

Preface; 1. Econophysics: why and what; 2. Neo-classical economic theory; 3. Probability and stochastic processes; 4. Introduction to financial economics; 5. Introduction to portfolio selection theory; 6. Scaling, pair correlations, and conditional densities; 7. Statistical ensembles: deducing dynamics from time series; 8. Martingale option pricing; 9. FX market globalization: evolution of the dollar to worldwide reserve currency; 10. Macroeconomics and econometrics: regression models vs. empirically based modeling; 11. Complexity; Index.

Nonperturbative study of dynamical SUSY breaking in N =(2 ,2 ) Yang-Mills theory

NASA Astrophysics Data System (ADS)

Catterall, Simon; Jha, Raghav G.; Joseph, Anosh

2018-03-01

We examine the possibility of dynamical supersymmetry breaking in two-dimensional N =(2 ,2 ) supersymmetric Yang-Mills theory. The theory is discretized on a Euclidean spacetime lattice using a supersymmetric lattice action. We compute the vacuum energy of the theory at finite temperature and take the zero-temperature limit. Supersymmetry will be spontaneously broken in this theory if the measured ground-state energy is nonzero. By performing simulations on a range of lattices up to 96 ×96 we are able to perform a careful extrapolation to the continuum limit for a wide range of temperatures. Subsequent extrapolations to the zero-temperature limit yield an upper bound on the ground-state energy density. We find the energy density to be statistically consistent with zero in agreement with the absence of dynamical supersymmetry breaking in this theory.

Maxwell's color statistics: from reduction of visible errors to reduction to invisible molecules.

PubMed

Cat, Jordi

2014-12-01

This paper presents a cross-disciplinary and multi-disciplinary account of Maxwell's introduction of statistical models of molecules for the composition of gases. The account focuses on Maxwell's deployment of statistical models of data in his contemporaneous color researches as established in Cambridge mathematical physics, especially by Maxwell's seniors and mentors. The paper also argues that the cross-disciplinary, or cross-domain, transfer of resources from the natural and social sciences took place in both directions and relied on the complex intra-disciplinary, or intra-domain, dynamics of Maxwell's researches in natural sciences, in color theory, physical astronomy, electromagnetism and dynamical theory of gases, as well as involving a variety of types of communicating and mediating media, from material objects to concepts, techniques and institutions.

Interactions Dominate the Dynamics of Visual Cognition

ERIC Educational Resources Information Center

Stephen, Damian G.; Mirman, Daniel

2010-01-01

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of…

Fluctuations and Noise in Stochastic Spread of Respiratory Infection Epidemics in Social Networks

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Emelyanova, Natalya; Demin, Sergey; Gafarov, Fail; Hänggi, Peter; Yulmetyeva, Dinara

2003-05-01

For the analysis of epidemic and disease dynamics complexity, it is necessary to understand the basic principles and notions of its spreading in long-time memory media. Here we considering the problem from a theoretical and practical viewpoint, presenting the quantitative evidence confirming the existence of stochastic long-range memory and robust chaos in a real time series of respiratory infections of human upper respiratory track. In this work we present a new statistical method of analyzing the spread of grippe and acute respiratory track infections epidemic process of human upper respiratory track by means of the theory of discrete non-Markov stochastic processes. We use the results of our recent theory (Phys. Rev. E 65, 046107 (2002)) for the study of statistical effects of memory in real data series, describing the epidemic dynamics of human acute respiratory track infections and grippe. The obtained results testify to an opportunity of the strict quantitative description of the regular and stochastic components in epidemic dynamics of social networks with a view to time discreteness and effects of statistical memory.

Effective control of complex turbulent dynamical systems through statistical functionals.

PubMed

Majda, Andrew J; Qi, Di

2017-05-30

Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among complex systems in science and engineering, including climate, material, and neural science. Control of these complex systems is a grand challenge, for example, in mitigating the effects of climate change or safe design of technology with fully developed shear turbulence. Control of flows in the transition to turbulence, where there is a small dimension of instabilities about a basic mean state, is an important and successful discipline. In complex turbulent dynamical systems, it is impossible to track and control the large dimension of instabilities, which strongly interact and exchange energy, and new control strategies are needed. The goal of this paper is to propose an effective statistical control strategy for complex turbulent dynamical systems based on a recent statistical energy principle and statistical linear response theory. We illustrate the potential practical efficiency and verify this effective statistical control strategy on the 40D Lorenz 1996 model in forcing regimes with various types of fully turbulent dynamics with nearly one-half of the phase space unstable.

Non-Born-Oppenheimer molecular dynamics of the spin-forbidden reaction O(3P) + CO(X 1Σ+) → CO2(tilde X{}^1Σ _g^ +)

NASA Astrophysics Data System (ADS)

Jasper, Ahren W.; Dawes, Richard

2013-10-01

The lowest-energy singlet (1 1A') and two lowest-energy triplet (1 3A' and 1 3A″) electronic states of CO2 are characterized using dynamically weighted multireference configuration interaction (dw-MRCI+Q) electronic structure theory calculations extrapolated to the complete basis set (CBS) limit. Global analytic representations of the dw-MRCI+Q/CBS singlet and triplet surfaces and of their CASSCF/aug-cc-pVQZ spin-orbit coupling surfaces are obtained via the interpolated moving least squares (IMLS) semiautomated surface fitting method. The spin-forbidden kinetics of the title reaction is calculated using the coupled IMLS surfaces and coherent switches with decay of mixing non-Born-Oppenheimer molecular dynamics. The calculated spin-forbidden association rate coefficient (corresponding to the high pressure limit of the rate coefficient) is 7-35 times larger at 1000-5000 K than the rate coefficient used in many detailed chemical models of combustion. A dynamical analysis of the multistate trajectories is presented. The trajectory calculations reveal direct (nonstatistical) and indirect (statistical) spin-forbidden reaction mechanisms and may be used to test the suitability of transition-state-theory-like statistical methods for spin-forbidden kinetics. Specifically, we consider the appropriateness of the "double passage" approximation, of assuming statistical distributions of seam crossings, and of applications of the unified statistical model for spin-forbidden reactions.

Neutral dynamics with environmental noise: Age-size statistics and species lifetimes

NASA Astrophysics Data System (ADS)

Kessler, David; Suweis, Samir; Formentin, Marco; Shnerb, Nadav M.

2015-08-01

Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for many empirical datasets in genetics and ecology. However, the restriction of the model to demographic [O (√{N }) ] noise yields relatively slow dynamics that appears to be in conflict with both short-term and long-term characteristics of the observed systems. Here we analyze two of these problems—age-size relationships and species extinction time—in the framework of a neutral theory with both demographic and environmental stochasticity. It turns out that environmentally induced variations of the demographic rates control the long-term dynamics and modify dramatically the predictions of the neutral theory with demographic noise only, yielding much better agreement with empirical data. We consider two prototypes of "zero mean" environmental noise, one which is balanced with regard to the arithmetic abundance, another balanced in the logarithmic (fitness) space, study their species lifetime statistics, and discuss their relevance to realistic models of community dynamics.

Molecular Dynamics of Dense Fluids: Simulation-Theory Symbiosis

NASA Astrophysics Data System (ADS)

Yip, Sidney

35 years ago Berni J. Alder showed the Boltzmann-Enskog kinetic theory failed to adequately account for the viscosity of fluids near solid density as determined by molecular dynamics simulation. This work, along with other notable simulation findings, provided great stimulus to the statistical mechanical studies of transport phenomena, particularly in dealing with collective effects in the time correlation functions of liquids. An extended theoretical challenge that remains partially resolved at best is the shear viscosity of supercooled liquids. How can one give a unified explanation of the so-called fragile and strong characteristic temperature behavior, with implications for the dynamics of glass transition? In this tribute on the occasion of his 90th birthday symposium, we recount a recent study where simulation, combined with heuristic (transition-state) and first principles (linear response) theories, identifies the molecular mechanisms governing glassy-state relaxation. Such an interplay between simulation and theory is progress from the early days; instead of simulation challenging theory, now simulation and theory complement each other.

Modern Quantum Field Theory II - Proceeeings of the International Colloquium

NASA Astrophysics Data System (ADS)

Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.

1995-08-01

The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory * Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)

Boltzmann, Darwin and Directionality theory

NASA Astrophysics Data System (ADS)

Demetrius, Lloyd A.

2013-09-01

Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and extinction. We also elucidate the relation between thermodynamic entropy, which pertains to the extent of energy spreading and sharing within inanimate matter, and evolutionary entropy, which refers to the rate of energy appropriation from the environment and allocation within living systems. We show that the entropic principle of thermodynamics is the limit as R→0, M→∞, (where R denote the resource production rate, and M denote population size) of the entropic principle of evolution. We exploit this relation between the thermodynamic and evolutionary tenets to propose a physico-chemical model of the transition from inanimate matter which is under thermodynamic selection, to living systems which are subject to evolutionary selection. Life history variation and the evolution of senescence The evolutionary dynamics of speciation and extinction Evolutionary trends in body size. The origin of sporadic forms of cancer and neurological diseases, and the evolution of cooperation are important recent applications of directionality theory. These applications, which draw from the medical sciences and sociobiology, appeal to methods which lie outside the formalism described in this report. A companion review, Demetrius and Gundlach (submitted for publication), gives an account of these applications.An important aspect of this report pertains to the connection between statistical mechanics and evolutionary theory and its implications towards understanding the processes which underlie the emergence of living systems from inanimate matter-a problem which has recently attracted considerable attention, Morowitz (1992), Eigen (1992), Dyson (2000), Pross (2012).The connection between the two disciplines can be addressed by appealing to certain extremal principles which are considered the mainstay of the respective theories.The extremal principle in statistical mechanics can be stated as follows:

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

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2006-03-01

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

Dynamical Systems Theory in Quantitative Psychology and Cognitive Science: A Fair Discrimination between Deterministic and Statistical Counterparts is Required.

PubMed

Gadomski, Adam; Ausloos, Marcel; Casey, Tahlia

2017-04-01

This article addresses a set of observations framed in both deterministic as well as statistical formal guidelines. It operates within the framework of nonlinear dynamical systems theory (NDS). It is argued that statistical approaches can manifest themselves ambiguously, creating practical discrepancies in psychological and cognitive data analyses both quantitatively and qualitatively. This is sometimes termed in literature as 'questionable research practices.' This communication points to the demand for a deeper awareness of the data 'initial conditions, allowing to focus on pertinent evolution constraints in such systems.' It also considers whether the exponential (Malthus-type) or the algebraic (Pareto-type) statistical distribution ought to be effectively considered in practical interpretations. The role of repetitive specific behaviors by patients seeking treatment is examined within the NDS frame. The significance of these behaviors, involving a certain memory effect seems crucial in determining a patient's progression or regression. With this perspective, it is discussed how a sensitively applied hazardous or triggering factor can be helpful for well-controlled psychological strategic treatments; those attributable to obsessive-compulsive disorders or self-injurious behaviors are recalled in particular. There are both inherent criticality- and complexity-exploiting (reduced-variance based) relations between a therapist and a patient that can be intrinsically included in NDS theory.

Quantum-like model of unconscious–conscious dynamics

PubMed Central

Khrennikov, Andrei

2015-01-01

We present a quantum-like model of sensation–perception dynamics (originated in Helmholtz theory of unconscious inference) based on the theory of quantum apparatuses and instruments. We illustrate our approach with the model of bistable perception of a particular ambiguous figure, the Schröder stair. This is a concrete model for unconscious and conscious processing of information and their interaction. The starting point of our quantum-like journey was the observation that perception dynamics is essentially contextual which implies impossibility of (straightforward) embedding of experimental statistical data in the classical (Kolmogorov, 1933) framework of probability theory. This motivates application of nonclassical probabilistic schemes. And the quantum formalism provides a variety of the well-approved and mathematically elegant probabilistic schemes to handle results of measurements. The theory of quantum apparatuses and instruments is the most general quantum scheme describing measurements and it is natural to explore it to model the sensation–perception dynamics. In particular, this theory provides the scheme of indirect quantum measurements which we apply to model unconscious inference leading to transition from sensations to perceptions. PMID:26283979

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Field-theoretic approach to fluctuation effects in neural networks

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

Buice, Michael A.; Cowan, Jack D.; Mathematics Department, University of Chicago, Chicago, Illinois 60637

A well-defined stochastic theory for neural activity, which permits the calculation of arbitrary statistical moments and equations governing them, is a potentially valuable tool for theoretical neuroscience. We produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes. Assuming that neural network activity is Markovian, we construct the effective spike model, which describes both neural fluctuations and response. This analysis leads to a systematic expansion of corrections to mean field theory, which for the effective spike model is a simple version of the Wilson-Cowan equation. We argue that neural activity governedmore » by this model exhibits a dynamical phase transition which is in the universality class of directed percolation. More general models (which may incorporate refractoriness) can exhibit other universality classes, such as dynamic isotropic percolation. Because of the extremely high connectivity in typical networks, it is expected that higher-order terms in the systematic expansion are small for experimentally accessible measurements, and thus, consistent with measurements in neocortical slice preparations, we expect mean field exponents for the transition. We provide a quantitative criterion for the relative magnitude of each term in the systematic expansion, analogous to the Ginsburg criterion. Experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience.« less

A mathematics for medicine: The Network Effect

PubMed Central

West, Bruce J.

2014-01-01

The theory of medicine and its complement systems biology are intended to explain the workings of the large number of mutually interdependent complex physiologic networks in the human body and to apply that understanding to maintaining the functions for which nature designed them. Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect. PMID:25538622

Future missions studies: Combining Schatten's solar activity prediction model with a chaotic prediction model

NASA Technical Reports Server (NTRS)

Ashrafi, S.

1991-01-01

K. Schatten (1991) recently developed a method for combining his prediction model with our chaotic model. The philosophy behind this combined model and his method of combination is explained. Because the Schatten solar prediction model (KS) uses a dynamo to mimic solar dynamics, accurate prediction is limited to long-term solar behavior (10 to 20 years). The Chaotic prediction model (SA) uses the recently developed techniques of nonlinear dynamics to predict solar activity. It can be used to predict activity only up to the horizon. In theory, the chaotic prediction should be several orders of magnitude better than statistical predictions up to that horizon; beyond the horizon, chaotic predictions would theoretically be just as good as statistical predictions. Therefore, chaos theory puts a fundamental limit on predictability.

Quantum Field Theory Approach to Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Marino, Eduardo C.

2017-09-01

Preface; Part I. Condensed Matter Physics: 1. Independent electrons and static crystals; 2. Vibrating crystals; 3. Interacting electrons; 4. Interactions in action; Part II. Quantum Field Theory: 5. Functional formulation of quantum field theory; 6. Quantum fields in action; 7. Symmetries: explicit or secret; 8. Classical topological excitations; 9. Quantum topological excitations; 10. Duality, bosonization and generalized statistics; 11. Statistical transmutation; 12. Pseudo quantum electrodynamics; Part III. Quantum Field Theory Approach to Condensed Matter Systems: 13. Quantum field theory methods in condensed matter; 14. Metals, Fermi liquids, Mott and Anderson insulators; 15. The dynamics of polarons; 16. Polyacetylene; 17. The Kondo effect; 18. Quantum magnets in 1D: Fermionization, bosonization, Coulomb gases and 'all that'; 19. Quantum magnets in 2D: nonlinear sigma model, CP1 and 'all that'; 20. The spin-fermion system: a quantum field theory approach; 21. The spin glass; 22. Quantum field theory approach to superfluidity; 23. Quantum field theory approach to superconductivity; 24. The cuprate high-temperature superconductors; 25. The pnictides: iron based superconductors; 26. The quantum Hall effect; 27. Graphene; 28. Silicene and transition metal dichalcogenides; 29. Topological insulators; 30. Non-abelian statistics and quantum computation; References; Index.

Identification of dynamic systems, theory and formulation

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1985-01-01

The problem of estimating parameters of dynamic systems is addressed in order to present the theoretical basis of system identification and parameter estimation in a manner that is complete and rigorous, yet understandable with minimal prerequisites. Maximum likelihood and related estimators are highlighted. The approach used requires familiarity with calculus, linear algebra, and probability, but does not require knowledge of stochastic processes or functional analysis. The treatment emphasizes unification of the various areas in estimation in dynamic systems is treated as a direct outgrowth of the static system theory. Topics covered include basic concepts and definitions; numerical optimization methods; probability; statistical estimators; estimation in static systems; stochastic processes; state estimation in dynamic systems; output error, filter error, and equation error methods of parameter estimation in dynamic systems, and the accuracy of the estimates.

On the statistical mechanics of species abundance distributions.

PubMed

Bowler, Michael G; Kelly, Colleen K

2012-09-01

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

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

Dynamical interpretation of conditional patterns

NASA Technical Reports Server (NTRS)

Adrian, R. J.; Moser, R. D.; Moin, P.

1988-01-01

While great progress is being made in characterizing the 3-D structure of organized turbulent motions using conditional averaging analysis, there is a lack of theoretical guidance regarding the interpretation and utilization of such information. Questions concerning the significance of the structures, their contributions to various transport properties, and their dynamics cannot be answered without recourse to appropriate dynamical governing equations. One approach which addresses some of these questions uses the conditional fields as initial conditions and calculates their evolution from the Navier-Stokes equations, yielding valuable information about stability, growth, and longevity of the mean structure. To interpret statistical aspects of the structures, a different type of theory which deals with the structures in the context of their contributions to the statistics of the flow is needed. As a first step toward this end, an effort was made to integrate the structural information from the study of organized structures with a suitable statistical theory. This is done by stochastically estimating the two-point conditional averages that appear in the equation for the one-point probability density function, and relating the structures to the conditional stresses. Salient features of the estimates are identified, and the structure of the one-point estimates in channel flow is defined.

Optimal Regulation of Structural Systems with Uncertain Parameters.

DTIC Science & Technology

1981-02-02

been addressed, in part, by Statistical Energy Analysis . Moti- vated by a concern with high frequency vibration and acoustical- structural...Parameter Systems," AFOSR-TR-79-0753 (May, 1979). 25. R. H. Lyon, Statistical Energy Analysis of Dynamical Systems: Theory and Applications, (M.I.T...Press, Cambridge, Mass., 1975). 26. E. E. Ungar, " Statistical Energy Analysis of Vibrating Systems," Trans. ASME, J. Eng. Ind. 89, 626 (1967). 139 27

Using Bayes' theorem for free energy calculations

NASA Astrophysics Data System (ADS)

Rogers, David M.

Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.

A High Precision Prediction Model Using Hybrid Grey Dynamic Model

ERIC Educational Resources Information Center

Li, Guo-Dong; Yamaguchi, Daisuke; Nagai, Masatake; Masuda, Shiro

2008-01-01

In this paper, we propose a new prediction analysis model which combines the first order one variable Grey differential equation Model (abbreviated as GM(1,1) model) from grey system theory and time series Autoregressive Integrated Moving Average (ARIMA) model from statistics theory. We abbreviate the combined GM(1,1) ARIMA model as ARGM(1,1)…

Thermal quantum time-correlation functions from classical-like dynamics

NASA Astrophysics Data System (ADS)

Hele, Timothy J. H.

2017-07-01

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here, we review recent progress in the field with the development of methods including centroid molecular dynamics , ring polymer molecular dynamics (RPMD) and thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from 'Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also apply the Matsubara formalism to reaction rate theory, rederiving t → 0+ quantum transition-state theory (QTST) and showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

Statistical inference for noisy nonlinear ecological dynamic systems.

PubMed

Wood, Simon N

2010-08-26

Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.

Theory and computation of non-RRKM lifetime distributions and rates in chemical systems with three or more degrees of freedom

NASA Astrophysics Data System (ADS)

Gabern, Frederic; Koon, Wang S.; Marsden, Jerrold E.; Ross, Shane D.

2005-11-01

The computation, starting from basic principles, of chemical reaction rates in realistic systems (with three or more degrees of freedom) has been a longstanding goal of the chemistry community. Our current work, which merges tube dynamics with Monte Carlo methods provides some key theoretical and computational tools for achieving this goal. We use basic tools of dynamical systems theory, merging the ideas of Koon et al. [W.S. Koon, M.W. Lo, J.E. Marsden, S.D. Ross, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics, Chaos 10 (2000) 427-469.] and De Leon et al. [N. De Leon, M.A. Mehta, R.Q. Topper, Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory, J. Chem. Phys. 94 (1991) 8310-8328.], particularly the use of invariant manifold tubes that mediate the reaction, into a tool for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. Previously, the main problem with the application of tube dynamics has been with the computation of volumes in phase spaces of high dimension. The present work provides a starting point for overcoming this hurdle with some new ideas and implements them numerically. Specifically, an algorithm that uses tube dynamics to provide the initial bounding box for a Monte Carlo volume determination is used. The combination of a fine scale method for determining the phase space structure (invariant manifold theory) with statistical methods for volume computations (Monte Carlo) is the main contribution of this paper. The methodology is applied here to a three degree of freedom model problem and may be useful for higher degree of freedom systems as well.

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.

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. 3: A stochastic rain fade control algorithm for satellite link power via non linear Markow filtering theory

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1991-01-01

The dynamic and composite nature of propagation impairments that are incurred on Earth-space communications links at frequencies in and above 30/20 GHz Ka band, i.e., rain attenuation, cloud and/or clear air scintillation, etc., combined with the need to counter such degradations after the small link margins have been exceeded, necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) Project by the implementation of optimal processing schemes derived through the use of the Rain Attenuation Prediction Model and nonlinear Markov filtering theory.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Dynamics of essential collective motions in proteins: Theory

NASA Astrophysics Data System (ADS)

Stepanova, Maria

2007-11-01

A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

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

2011-04-01

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

Analyzing complex networks evolution through Information Theory quantifiers

NASA Astrophysics Data System (ADS)

Carpi, Laura C.; Rosso, Osvaldo A.; Saco, Patricia M.; Ravetti, Martín Gómez

2011-01-01

A methodology to analyze dynamical changes in complex networks based on Information Theory quantifiers is proposed. The square root of the Jensen-Shannon divergence, a measure of dissimilarity between two probability distributions, and the MPR Statistical Complexity are used to quantify states in the network evolution process. Three cases are analyzed, the Watts-Strogatz model, a gene network during the progression of Alzheimer's disease and a climate network for the Tropical Pacific region to study the El Niño/Southern Oscillation (ENSO) dynamic. We find that the proposed quantifiers are able not only to capture changes in the dynamics of the processes but also to quantify and compare states in their evolution.

Interactions Dominate the Dynamics of Visual Cognition

PubMed Central

Stephen, Damian G.; Mirman, Daniel

2010-01-01

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of eye movements during classic visual cognitive tasks. The results reveal interaction-dominant dynamics in eye movements in each of the three tasks, and that fine-grained eye movements are modulated by task constraints. These findings reveal the interactive nature of cognitive processing and are consistent with theories that view cognition as an emergent property of processes that are broadly distributed over many scales of space and time rather than a componential assembly line. PMID:20070957

Pressure calculation in hybrid particle-field simulations

NASA Astrophysics Data System (ADS)

Milano, Giuseppe; Kawakatsu, Toshihiro

2010-12-01

In the framework of a recently developed scheme for a hybrid particle-field simulation techniques where self-consistent field (SCF) theory and particle models (molecular dynamics) are combined [J. Chem. Phys. 130, 214106 (2009)], we developed a general formulation for the calculation of instantaneous pressure and stress tensor. The expressions have been derived from statistical mechanical definition of the pressure starting from the expression for the free energy functional in the SCF theory. An implementation of the derived formulation suitable for hybrid particle-field molecular dynamics-self-consistent field simulations is described. A series of test simulations on model systems are reported comparing the calculated pressure with those obtained from standard molecular dynamics simulations based on pair potentials.

The Utilization of the Behavioral Sciences in Long Range Forecasting and Policy Planning Volume I. Appendices

DTIC Science & Technology

1976-08-01

foreign policy dynamics, the structure of a theory cannot in {.eneral be derived from statistical analysis of time series data ( Brunner (1071), Thorson...and where such scientific knowledge la applicable. Recent attention in theory and research on the bureaucratic, handling of foreign policy...process. Some of ^.z element» of thase concerns can be made explicit if we introduce modern systems theories which seek to treat organizations as

The birth of gravitational evolutionary dynamics of stellar systems (from Th. Wright to W. Herschel).

NASA Astrophysics Data System (ADS)

Eremeeva, A. J.

1995-05-01

Th. Wright, I. Kant and I. H. Lambert used well-known ideas about the structure and dynamics of the Solar system as a basis of their concepts of the stellar Universe. W. Herschel discovered the main features of the true, non-hierarchical large-scale structure of the Universe. He was also a pioneer of stellar dynamics with its new statistical laws and also of the theory of dynamical evolution in stellar systems at different scales.

Statistical effects in large N supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej Stanislaw

This thesis discusses statistical simplifications arising in supersymmetric gauge theories in the limit of large rank. Applications involve the physics of black holes and the problem of predicting the low energy effective theory from a landscape of string vacua. The first part of this work uses the AdS/CFT correspondence to explain properties of black holes. We establish that in the large charge sector of toric quiver gauge theories there exists a typical state whose structure is closely mimicked by almost all other states. Then, working in the settings of the half-BPS sector of N = 4 super-Yang-Mills theory, we show that in the dual gravity theory semiclassical observations cannot distinguish a pair of geometries corresponding to two generic heavy states. Finally, we argue on general grounds that these conclusions are exponentially enhanced in quantum cosmological settings. The results establish that one may consistently account for the entropy of a black hole with heavy states in the dual field theory and suggest that the usual properties of black holes arise as artifacts of imposing a semiclassical description on a quantum system. In the second half we develop new tools to determine the infrared behavior of quiver gauge theories in a certain class. We apply the dynamical results to a toy model of the landscape of effective field theories defined at some high energy scale, and derive firm statistical predictions for the low energy effective theory.

a Statistical Dynamic Approach to Structural Evolution of Complex Capital Market Systems

NASA Astrophysics Data System (ADS)

Shao, Xiao; Chai, Li H.

As an important part of modern financial systems, capital market has played a crucial role on diverse social resource allocations and economical exchanges. Beyond traditional models and/or theories based on neoclassical economics, considering capital markets as typical complex open systems, this paper attempts to develop a new approach to overcome some shortcomings of the available researches. By defining the generalized entropy of capital market systems, a theoretical model and nonlinear dynamic equation on the operations of capital market are proposed from statistical dynamic perspectives. The US security market from 1995 to 2001 is then simulated and analyzed as a typical case. Some instructive results are discussed and summarized.

On the gas phase fragmentation of protonated uracil: a statistical perspective.

PubMed

Rossich Molina, Estefanía; Salpin, Jean-Yves; Spezia, Riccardo; Martínez-Núñez, Emilio

2016-06-01

The potential energy surface of protonated uracil has been explored by an automated transition state search procedure, resulting in the finding of 1398 stationary points and 751 reactive channels, which can be categorized into isomerizations between pairs of isomers, unimolecular fragmentations and bimolecular reactions. The use of statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theory and Kinetic Monte Carlo (KMC) simulations allowed us to determine the relative abundances of each fragmentation channel as a function of the ion's internal energy. The KMC/RRKM product abundances are compared with novel mass spectrometry (MS) experiments in the collision energy range 1-6 eV. To facilitate the comparison between theory and experiments, further dynamics simulations are carried out to determine the fraction of collision energy converted into the ion's internal energy. The KMC simulations show that the major fragmentation channels are isocyanic acid and ammonia losses, in good agreement with experiments. The third predominant channel is water loss according to both theory and experiments, although the abundance obtained in the KMC simulations is very low, suggesting that non-statistical dynamics might play an important role in this channel. Isocyanic acid (HNCOH(+)) is also an important product in the KMC simulations, although its abundance is only significant at internal energies not accessible in the MS experiments.

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.

Waiting time distribution revealing the internal spin dynamics in a double quantum dot

NASA Astrophysics Data System (ADS)

Ptaszyński, Krzysztof

2017-07-01

Waiting time distribution and the zero-frequency full counting statistics of unidirectional electron transport through a double quantum dot molecule attached to spin-polarized leads are analyzed using the quantum master equation. The waiting time distribution exhibits a nontrivial dependence on the value of the exchange coupling between the dots and the gradient of the applied magnetic field, which reveals the oscillations between the spin states of the molecule. The zero-frequency full counting statistics, on the other hand, is independent of the aforementioned quantities, thus giving no insight into the internal dynamics. The fact that the waiting time distribution and the zero-frequency full counting statistics give a nonequivalent information is associated with two factors. Firstly, it can be explained by the sensitivity to different timescales of the dynamics of the system. Secondly, it is associated with the presence of the correlation between subsequent waiting times, which makes the renewal theory, relating the full counting statistics and the waiting time distribution, no longer applicable. The study highlights the particular usefulness of the waiting time distribution for the analysis of the internal dynamics of mesoscopic systems.

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

J.A. Krommes

Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed.more » An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.« less

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

PubMed

Attard, Phil

2005-04-15

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

Electrical Conductivity of Charged Particle Systems and Zubarev's Nonequilibrium Statistical Operator Method

NASA Astrophysics Data System (ADS)

Röpke, G.

2018-01-01

One of the fundamental problems in physics that are not yet rigorously solved is the statistical mechanics of nonequilibrium processes. An important contribution to describing irreversible behavior starting from reversible Hamiltonian dynamics was given by D. N. Zubarev, who invented the method of the nonequilibrium statistical operator. We discuss this approach, in particular, the extended von Neumann equation, and as an example consider the electrical conductivity of a system of charged particles. We consider the selection of the set of relevant observables. We show the relation between kinetic theory and linear response theory. Using thermodynamic Green's functions, we present a systematic treatment of correlation functions, but the convergence needs investigation. We compare different expressions for the conductivity and list open questions.

Analysis and Report on SD2000: A Workshop to Determine Structural Dynamics Research for the Millenium

DTIC Science & Technology

2000-04-10

interest. These include Statistical Energy Analysis (SEA), fuzzy structure theory, and approaches combining modal analysis and SEA. Non-determinism...34 arising with increasing frequency. This has led to Statistical Energy Analysis , in which a system is modelled as a collection of coupled subsystems...22. IUTAM Symposium on Statistical Energy Analysis . 1999 Ed. F.J. Fahy and W.G. Price. Kluwer Academic Publishing. • 23. R.S. Langley and P

Dynamic rain fade compensation techniques for the advanced communications technology satellite

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1992-01-01

The dynamic and composite nature of propagation impairments that are incurred on earth-space communications links at frequencies in and above the 30/20 GHz Ka band necessitate the use of dynamic statistical identification and prediction processing of the fading signal in order to optimally estimate and predict the levels of each of the deleterious attenuation components. Such requirements are being met in NASA's Advanced Communications Technology Satellite (ACTS) project by the implementation of optimal processing schemes derived through the use of the ACTS Rain Attenuation Prediction Model and nonlinear Markov filtering theory. The ACTS Rain Attenuation Prediction Model discerns climatological variations on the order of 0.5 deg in latitude and longitude in the continental U.S. The time-dependent portion of the model gives precise availability predictions for the 'spot beam' links of ACTS. However, the structure of the dynamic portion of the model, which yields performance parameters such as fade duration probabilities, is isomorphic to the state-variable approach of stochastic control theory and is amenable to the design of such statistical fade processing schemes which can be made specific to the particular climatological location at which they are employed.

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

Statistical Mechanical Theory of Coupled Slow Dynamics in Glassy Polymer-Molecule Mixtures

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth

The microscopic Elastically Collective Nonlinear Langevin Equation theory of activated relaxation in one-component supercooled liquids and glasses is generalized to polymer-molecule mixtures. The key idea is to account for dynamic coupling between molecule and polymer segment motion. For describing the molecule hopping event, a temporal casuality condition is formulated to self-consistently determine a dimensionless degree of matrix distortion relative to the molecule jump distance based on the concept of coupled dynamic free energies. Implementation for real materials employs an established Kuhn sphere model of the polymer liquid and a quantitative mapping to a hard particle reference system guided by the experimental equation-of-state. The theory makes predictions for the mixture dynamic shear modulus, activated relaxation time and diffusivity of both species, and mixture glass transition temperature as a function of molecule-Kuhn segment size ratio and attraction strength, composition and temperature. Model calculations illustrate the dynamical behavior in three distinct mixture regimes (fully miscible, bridging, clustering) controlled by the molecule-polymer interaction or chi-parameter. Applications to specific experimental systems will be discussed.

Statistical Inference in Graphical Models

DTIC Science & Technology

2008-06-17

fuse probability theory and graph theory in such a way as to permit efficient rep- resentation and computation with probability distributions. They...message passing. 59 viii 1. INTRODUCTION In approaching real-world problems, we often need to deal with uncertainty. Probability and statis- tics provide a...dynamic programming methods. However, for many sensors of interest, the signal-to-noise ratio does not allow such a treatment. Another source of

Analytical structure, dynamics, and coarse graining of a kinetic model of an active fluid

NASA Astrophysics Data System (ADS)

Gao, Tong; Betterton, Meredith D.; Jhang, An-Sheng; Shelley, Michael J.

2017-09-01

We analyze one of the simplest active suspensions with complex dynamics: a suspension of immotile "extensor" particles that exert active extensile dipolar stresses on the fluid in which they are immersed. This is relevant to several experimental systems, such as recently studied tripartite rods that create extensile flows by consuming a chemical fuel. We first describe the system through a Doi-Onsager kinetic theory based on microscopic modeling. This theory captures the active stresses produced by the particles that can drive hydrodynamic instabilities, as well as the steric interactions of rodlike particles that lead to nematic alignment. This active nematic system yields complex flows and disclination defect dynamics very similar to phenomenological Landau-deGennes Q -tensor theories for active nematic fluids, as well as by more complex Doi-Onsager theories for polar microtubule-motor-protein systems. We apply the quasiequilibrium Bingham closure, used to study suspensions of passive microscopic rods, to develop a nonstandard Q -tensor theory. We demonstrate through simulation that this B Q -tensor theory gives an excellent analytical and statistical accounting of the suspension's complex dynamics, at a far reduced computational cost. Finally, we apply the B Q -tensor model to study the dynamics of extensor suspensions in circular and biconcave domains. In circular domains, we reproduce previous results for systems with weak nematic alignment, but for strong alignment we find unusual dynamics with activity-controlled defect production and absorption at the boundaries of the domain. In biconcave domains, a Fredericks-like transition occurs as the width of the neck connecting the two disks is varied.

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.

On Mars too, expect macroweather

NASA Astrophysics Data System (ADS)

Boisvert, Jean-Philippe; Lovejoy, Shaun; Muller, Jan-Peter

2015-04-01

Terrestrial atmospheric and oceanic spectra show drastic transitions at τw ˜ 10 days and τow ˜ 1 year respectively; this has been theorized as the lifetime of planetary scale structures. For wind and temperature, the forms of the low and high frequency parts of the spectra (macroweather, weather) as well as the τw can be theoretically estimated, the latter depending notably on the solar induced turbulent energy flux. We extend the theory to other planets and test it using Viking lander and reanalysis data from Mars. When the Martian spectra are scaled by the theoretical amount, they agree very well with their terrestrial atmospheric counterparts. Although the usual interpretation of Martian atmospheric dynamics is highly mechanistic (e.g. wave and tidal explanations are invoked), trace moment analysis of the reanalysis fields shows that the statistics well respect the predictions of multiplicative cascade theories. This shows that statistical scaling can be compatible with conventional deterministic thinking. However, since we are usually interested in statistical knowledge, it is the former not the latter that is of primary interest. We discuss the implications for understanding planetary fluid dynamical systems.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Interactions dominate the dynamics of visual cognition.

PubMed

Stephen, Damian G; Mirman, Daniel

2010-04-01

Many cognitive theories have described behavior as the summation of independent contributions from separate components. Contrasting views have emphasized the importance of multiplicative interactions and emergent structure. We describe a statistical approach to distinguishing additive and multiplicative processes and apply it to the dynamics of eye movements during classic visual cognitive tasks. The results reveal interaction-dominant dynamics in eye movements in each of the three tasks, and that fine-grained eye movements are modulated by task constraints. These findings reveal the interactive nature of cognitive processing and are consistent with theories that view cognition as an emergent property of processes that are broadly distributed over many scales of space and time rather than a componential assembly line. Copyright 2009 Elsevier B.V. All rights reserved.

Quantum statistical effects in the mass transport of interstitial solutes in a crystalline solid

NASA Astrophysics Data System (ADS)

Woo, C. H.; Wen, Haohua

2017-09-01

The impact of quantum statistics on the many-body dynamics of a crystalline solid at finite temperatures containing an interstitial solute atom (ISA) is investigated. The Mori-Zwanzig theory allows the many-body dynamics of the crystal to be formulated and solved analytically within a pseudo-one-particle approach using the Langevin equation with a quantum fluctuation-dissipation relation (FDR) based on the Debye model. At the same time, the many-body dynamics is also directly solved numerically via the molecular dynamics approach with a Langevin heat bath based on the quantum FDR. Both the analytical and numerical results consistently show that below the Debye temperature of the host lattice, quantum statistics significantly impacts the ISA transport properties, resulting in major departures from both the Arrhenius law of diffusion and the Einstein-Smoluchowski relation between the mobility and diffusivity. Indeed, we found that below one-third of the Debye temperature, effects of vibrations on the quantum mobility and diffusivity are both orders-of-magnitude larger and practically temperature independent. We have shown that both effects have their physical origin in the athermal lattice vibrations derived from the phonon ground state. The foregoing theory is tested in quantum molecular dynamics calculation of mobility and diffusivity of interstitial helium in bcc W. In this case, the Arrhenius law is only valid in a narrow range between ˜300 and ˜700 K. The diffusivity becomes temperature independent on the low-temperature side while increasing linearly with temperature on the high-temperature side.

Statistical Physics of Population Genetics in the Low Population Size Limit

NASA Astrophysics Data System (ADS)

Atwal, Gurinder

The understanding of evolutionary processes lends itself naturally to theory and computation, and the entire field of population genetics has benefited greatly from the influx of methods from applied mathematics for decades. However, in spite of all this effort, there are a number of key dynamical models of evolution that have resisted analytical treatment. In addition, modern DNA sequencing technologies have magnified the amount of genetic data available, revealing an excess of rare genetic variants in human genomes, challenging the predictions of conventional theory. Here I will show that methods from statistical physics can be used to model the distribution of genetic variants, incorporating selection and spatial degrees of freedom. In particular, a functional path-integral formulation of the Wright-Fisher process maps exactly to the dynamics of a particle in an effective potential, beyond the mean field approximation. In the small population size limit, the dynamics are dominated by instanton-like solutions which determine the probability of fixation in short timescales. These results are directly relevant for understanding the unusual genetic variant distribution at moving frontiers of populations.

Unified force-level theory of multiscale transient localization and emergent elasticity in polymer solutions and melts

NASA Astrophysics Data System (ADS)

Dell, Zachary E.; Schweizer, Kenneth S.

A unified, microscopic, theoretical understanding of polymer dynamics in concentrated liquids from segmental to macromolecular scales remains an open problem. We have formulated a statistical mechanical theory for this problem that explicitly accounts for intra- and inter-molecular forces at the Kuhn segment level. The theory is self-consistently closed at the level of a matrix of dynamical second moments of a tagged chain. Two distinct regimes of isotropic transient localization are predicted. In semidilute solutions, weak localization is predicted on a mesoscopic length scale between segment and chain scales which is a power law function of the invariant packing length. This is consistent with the breakdown of Rouse dynamics and the emergence of entanglements. The chain structural correlations in the dynamically arrested state are also computed. In dense melts, strong localization is predicted on a scale much smaller than the segment size which is weakly dependent on chain connectivity and signals the onset of glassy dynamics. Predictions of the dynamic plateau shear modulus are consistent with the known features of emergent rubbery and glassy elasticity. Generalizations to treat the effects of chemical crosslinking and physical bond formation in polymer gels are possible.

Detecting temperature fluctuations at equilibrium.

PubMed

Dixit, Purushottam D

2015-05-21

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

Universality classes of fluctuation dynamics in hierarchical complex systems

NASA Astrophysics Data System (ADS)

Macêdo, A. M. S.; González, Iván R. Roa; Salazar, D. S. P.; Vasconcelos, G. L.

2017-03-01

A unified approach is proposed to describe the statistics of the short-time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

Statistical dependency in visual scanning

NASA Technical Reports Server (NTRS)

Ellis, Stephen R.; Stark, Lawrence

1986-01-01

A method to identify statistical dependencies in the positions of eye fixations is developed and applied to eye movement data from subjects who viewed dynamic displays of air traffic and judged future relative position of aircraft. Analysis of approximately 23,000 fixations on points of interest on the display identified statistical dependencies in scanning that were independent of the physical placement of the points of interest. Identification of these dependencies is inconsistent with random-sampling-based theories used to model visual search and information seeking.

Nonequilibrium thermodynamics and information theory: basic concepts and relaxing dynamics

NASA Astrophysics Data System (ADS)

Altaner, Bernhard

2017-11-01

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

Broken Symmetries and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.

Theory of hydromagnetic turbulence

NASA Technical Reports Server (NTRS)

Montgomery, D.

1983-01-01

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

A first-order statistical smoothing approximation for the coherent wave field in random porous random media

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-04-01

An important dissipation mechanism for waves in randomly inhomogeneous poroelastic media is the effect of wave-induced fluid flow. In the framework of Biot's theory of poroelasticity, this mechanism can be understood as scattering from fast into slow compressional waves. To describe this conversion scattering effect in poroelastic random media, the dynamic characteristics of the coherent wavefield using the theory of statistical wave propagation are analyzed. In particular, the method of statistical smoothing is applied to Biot's equations of poroelasticity. Within the accuracy of the first-order statistical smoothing an effective wave number of the coherent field, which accounts for the effect of wave-induced flow, is derived. This wave number is complex and involves an integral over the correlation function of the medium's fluctuations. It is shown that the known one-dimensional (1-D) result can be obtained as a special case of the present 3-D theory. The expression for the effective wave number allows to derive a model for elastic attenuation and dispersion due to wave-induced fluid flow. These wavefield attributes are analyzed in a companion paper. .

Nonlinear Synergistic Emergence and Predictability in Complex Systems: Theory and Hydro-Climatic Applications

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter

2017-04-01

Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is confirmed with robust nonlinear information diagnostics.

Effective field theory of dissipative fluids

DOE PAGES

Crossley, Michael; Glorioso, Paolo; Liu, Hong

2017-09-20

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less

Effective field theory of dissipative fluids

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

Crossley, Michael; Glorioso, Paolo; Liu, Hong

We develop an effctive fi eld theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a "fluid spacetime" and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z2 symmetry, to which we refer as the local KMSmore » condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.« less

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.

A state-of-the-art review of transportation systems evaluation techniques relevant to air transportation, volume 1. [urban planning and urban transportation using decision theory

NASA Technical Reports Server (NTRS)

Haefner, L. E.

1975-01-01

Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.

On the mode-coupling treatment of collective density fluctuations for quantum liquids: para-hydrogen and normal liquid helium.

PubMed

Kletenik-Edelman, Orly; Reichman, David R; Rabani, Eran

2011-01-28

A novel quantum mode coupling theory combined with a kinetic approach is developed for the description of collective density fluctuations in quantum liquids characterized by Boltzmann statistics. Three mode-coupling approximations are presented and applied to study the dynamic response of para-hydrogen near the triple point and normal liquid helium above the λ-transition. The theory is compared with experimental results and to the exact imaginary time data generated by path integral Monte Carlo simulations. While for liquid para-hydrogen the combination of kinetic and quantum mode-coupling theory provides semi-quantitative results for both short and long time dynamics, it fails for normal liquid helium. A discussion of this failure based on the ideal gas limit is presented.

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.

Nonadditive entropy Sq and nonextensive statistical mechanics: Applications in geophysics and elsewhere

NASA Astrophysics Data System (ADS)

Tsallis, Constantino

2012-06-01

The celebrated Boltzmann-Gibbs (BG) entropy, S BG = -kΣi p i ln p i, and associated statistical mechanics are essentially based on hypotheses such as ergodicity, i.e., when ensemble averages coincide with time averages. This dynamical simplification occurs in classical systems (and quantum counterparts) whose microscopic evolution is governed by a positive largest Lyapunov exponent (LLE). Under such circumstances, relevant microscopic variables behave, from the probabilistic viewpoint, as (nearly) independent. Many phenomena exist, however, in natural, artificial and social systems (geophysics, astrophysics, biophysics, economics, and others) that violate ergodicity. To cover a (possibly) wide class of such systems, a generalization (nonextensive statistical mechanics) of the BG theory was proposed in 1988. This theory is based on nonadditive entropies such as S_q = kfrac{{1 - sumnolimits_i {p_i^q } }} {{q - 1}}left( {S_1 = S_{BG} } right). Here we comment some central aspects of this theory, and briefly review typical predictions, verifications and applications in geophysics and elsewhere, as illustrated through theoretical, experimental, observational, and computational results.

Beyond Classical Information Theory: Advancing the Fundamentals for Improved Geophysical Prediction

NASA Astrophysics Data System (ADS)

Perdigão, R. A. P.; Pires, C. L.; Hall, J.; Bloeschl, G.

2016-12-01

Information Theory, in its original and quantum forms, has gradually made its way into various fields of science and engineering. From the very basic concepts of Information Entropy and Mutual Information to Transit Information, Interaction Information and respective partitioning into statistical synergy, redundancy and exclusivity, the overall theoretical foundations have matured as early as the mid XX century. In the Earth Sciences various interesting applications have been devised over the last few decades, such as the design of complex process networks of descriptive and/or inferential nature, wherein earth system processes are "nodes" and statistical relationships between them designed as information-theoretical "interactions". However, most applications still take the very early concepts along with their many caveats, especially in heavily non-Normal, non-linear and structurally changing scenarios. In order to overcome the traditional limitations of information theory and tackle elusive Earth System phenomena, we introduce a new suite of information dynamic methodologies towards a more physically consistent and information comprehensive framework. The methodological developments are then illustrated on a set of practical examples from geophysical fluid dynamics, where high-order nonlinear relationships elusive to the current non-linear information measures are aptly captured. In doing so, these advances increase the predictability of critical events such as the emergence of hyper-chaotic regimes in ocean-atmospheric dynamics and the occurrence of hydro-meteorological extremes.

Towards a Population Dynamics Theory for Evolutionary Computing: Learning from Biological Population Dynamics in Nature

NASA Astrophysics Data System (ADS)

Ma, Zhanshan (Sam)

In evolutionary computing (EC), population size is one of the critical parameters that a researcher has to deal with. Hence, it was no surprise that the pioneers of EC, such as De Jong (1975) and Holland (1975), had already studied the population sizing from the very beginning of EC. What is perhaps surprising is that more than three decades later, we still largely depend on the experience or ad-hoc trial-and-error approach to set the population size. For example, in a recent monograph, Eiben and Smith (2003) indicated: "In almost all EC applications, the population size is constant and does not change during the evolutionary search." Despite enormous research on this issue in recent years, we still lack a well accepted theory for population sizing. In this paper, I propose to develop a population dynamics theory forEC with the inspiration from the population dynamics theory of biological populations in nature. Essentially, the EC population is considered as a dynamic system over time (generations) and space (search space or fitness landscape), similar to the spatial and temporal dynamics of biological populations in nature. With this conceptual mapping, I propose to 'transplant' the biological population dynamics theory to EC via three steps: (i) experimentally test the feasibility—whether or not emulating natural population dynamics improves the EC performance; (ii) comparatively study the underlying mechanisms—why there are improvements, primarily via statistical modeling analysis; (iii) conduct theoretical analysis with theoretical models such as percolation theory and extended evolutionary game theory that are generally applicable to both EC and natural populations. This article is a summary of a series of studies we have performed to achieve the general goal [27][30]-[32]. In the following, I start with an extremely brief introduction on the theory and models of natural population dynamics (Sections 1 & 2). In Sections 4 to 6, I briefly discuss three categories of population dynamics models: deterministic modeling with Logistic chaos map as an example, stochastic modeling with spatial distribution patterns as an example, as well as survival analysis and extended evolutionary game theory (EEGT) modeling. Sample experiment results with Genetic algorithms (GA) are presented to demonstrate the applications of these models. The proposed EC population dynamics approach also makes survival selection largely unnecessary or much simplified since the individuals are naturally selected (controlled) by the mathematical models for EC population dynamics.

Scaling Behavior of Firm Growth

NASA Astrophysics Data System (ADS)

Stanley, Michael H. R.; Nunes Amaral, Luis A.; Buldyrev, Sergey V.; Havlin, Shlomo; Leschhorn, Heiko; Maass, Philipp; Salinger, Michael A.; Stanley, H. Eugene

1996-03-01

The theory of the firm is of considerable interest in economics. The standard microeconomic theory of the firm is largely a static model and has thus proved unsatisfactory for addressing inherently dynamic issues such as the growth of economies. In recent years, many have attempted to develop richer models that provide a more accurate representation of firm dynamics due to learning, innovative effort, and the development of organizational infrastructure. The validity of these new, inherently dynamic theories depends on their consistency with the statistical properties of firm growth, e.g. the relationship between growth rates and firm size. Using the Compustat database over the time period 1975-1991, we find: (i) the distribution of annual growth rates for firms with approximately the same sales displays an exponential form with the logarithm of growth rate, and (ii) the fluctuations in the growth rates --- measured by the width of this distribution --- scale as a power law with the firm sales. We place these findings of scaling behavior in the context of conventional economics by considering firm growth dynamics with temporal correlations and also, by considering a hierarchical organization of the departments of a firm.

Assessing information content and interactive relationships of subgenomic DNA sequences of the MHC using complexity theory approaches based on the non-extensive statistical mechanics

NASA Astrophysics Data System (ADS)

Karakatsanis, L. P.; Pavlos, G. P.; Iliopoulos, A. C.; Pavlos, E. G.; Clark, P. M.; Duke, J. L.; Monos, D. S.

2018-09-01

This study combines two independent domains of science, the high throughput DNA sequencing capabilities of Genomics and complexity theory from Physics, to assess the information encoded by the different genomic segments of exonic, intronic and intergenic regions of the Major Histocompatibility Complex (MHC) and identify possible interactive relationships. The dynamic and non-extensive statistical characteristics of two well characterized MHC sequences from the homozygous cell lines, PGF and COX, in addition to two other genomic regions of comparable size, used as controls, have been studied using the reconstructed phase space theorem and the non-extensive statistical theory of Tsallis. The results reveal similar non-linear dynamical behavior as far as complexity and self-organization features. In particular, the low-dimensional deterministic nonlinear chaotic and non-extensive statistical character of the DNA sequences was verified with strong multifractal characteristics and long-range correlations. The nonlinear indices repeatedly verified that MHC sequences, whether exonic, intronic or intergenic include varying levels of information and reveal an interaction of the genes with intergenic regions, whereby the lower the number of genes in a region, the less the complexity and information content of the intergenic region. Finally we showed the significance of the intergenic region in the production of the DNA dynamics. The findings reveal interesting content information in all three genomic elements and interactive relationships of the genes with the intergenic regions. The results most likely are relevant to the whole genome and not only to the MHC. These findings are consistent with the ENCODE project, which has now established that the non-coding regions of the genome remain to be of relevance, as they are functionally important and play a significant role in the regulation of expression of genes and coordination of the many biological processes of the cell.

Theory of Electronic, Atomic and Molecular Collisions.

DTIC Science & Technology

1983-09-01

coordinate in a reactive collision. Dynamical entropy Is defined as a statistical property of a dynamical scattering matrix, indexed by internal states of a...matrix U by enforcing certain internal symmetries that are a property of canonical transformation matrices (FCANON algorithm: Section IV...channels are present in Eq. (12). This low of accuracy is a property of the system of coupled differential equations, not of any particular method of

Ab initio studies on the photodissociation dynamics of the 1,1-difluoroethyl radical

NASA Astrophysics Data System (ADS)

Fritsche, Lukas; Bach, Andreas; Chen, Peter

2018-02-01

Born-Oppenheimer molecular dynamics trajectory calculations at the HCTH147/6-31G** level of theory simulate the dissociation dynamics of photolytically excited 1,1-difluoroethyl radicals. EOMCCSD/AUG-cc-pVDZ calculations show that an excitation energy of 94.82 kcal/mol is necessary to initiate photodissociation reactions. In contrast to photodissociation dynamics of ethyl radicals where a large discrepancy between actual dissociation rates and rates that are predicted by statistical rate theories, we find reaction rates of 5.1 × 1011 s-1 for the dissociation of an H atom, which is in perfect accord with what is predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) calculations and there is no indication of any nonstatistical effects. However, our trajectory calculations show a much larger fraction of C-C bond breakage reaction of 56% occurring than that expected by RRKM (only 16%).

Ab initio studies on the photodissociation dynamics of the 1,1-difluoroethyl radical.

PubMed

Fritsche, Lukas; Bach, Andreas; Chen, Peter

2018-02-28

Born-Oppenheimer molecular dynamics trajectory calculations at the HCTH147/6-31G** level of theory simulate the dissociation dynamics of photolytically excited 1,1-difluoroethyl radicals. EOMCCSD/AUG-cc-pVDZ calculations show that an excitation energy of 94.82 kcal/mol is necessary to initiate photodissociation reactions. In contrast to photodissociation dynamics of ethyl radicals where a large discrepancy between actual dissociation rates and rates that are predicted by statistical rate theories, we find reaction rates of 5.1 × 10 11 s -1 for the dissociation of an H atom, which is in perfect accord with what is predicted by Rice-Ramsperger-Kassel-Marcus (RRKM) calculations and there is no indication of any nonstatistical effects. However, our trajectory calculations show a much larger fraction of C-C bond breakage reaction of 56% occurring than that expected by RRKM (only 16%).

Network analysis applications in hydrology

NASA Astrophysics Data System (ADS)

Price, Katie

2017-04-01

Applied network theory has seen pronounced expansion in recent years, in fields such as epidemiology, computer science, and sociology. Concurrent development of analytical methods and frameworks has increased possibilities and tools available to researchers seeking to apply network theory to a variety of problems. While water and nutrient fluxes through stream systems clearly demonstrate a directional network structure, the hydrological applications of network theory remain under­explored. This presentation covers a review of network applications in hydrology, followed by an overview of promising network analytical tools that potentially offer new insights into conceptual modeling of hydrologic systems, identifying behavioral transition zones in stream networks and thresholds of dynamical system response. Network applications were tested along an urbanization gradient in Atlanta, Georgia, USA. Peachtree Creek and Proctor Creek. Peachtree Creek contains a nest of five long­term USGS streamflow and water quality gages, allowing network application of long­term flow statistics. The watershed spans a range of suburban and heavily urbanized conditions. Summary flow statistics and water quality metrics were analyzed using a suite of network analysis techniques, to test the conceptual modeling and predictive potential of the methodologies. Storm events and low flow dynamics during Summer 2016 were analyzed using multiple network approaches, with an emphasis on tomogravity methods. Results indicate that network theory approaches offer novel perspectives for understanding long­ term and event­based hydrological data. Key future directions for network applications include 1) optimizing data collection, 2) identifying "hotspots" of contaminant and overland flow influx to stream systems, 3) defining process domains, and 4) analyzing dynamic connectivity of various system components, including groundwater­surface water interactions.

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

NASA Astrophysics Data System (ADS)

Krot, A. M.

2007-08-01

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

Addressing the statistical mechanics of planet orbits in the solar system

NASA Astrophysics Data System (ADS)

Mogavero, Federico

2017-10-01

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

Synthesis of Systemic Functional Theory & Dynamical Systems Theory for Socio-Cultural Modeling

DTIC Science & Technology

2012-05-07

Kevin Judd Email: Kevin.Judd@uwa.edu.au Institution: University of Western Australia Mailing Address: School of Mathematics and Statistics...Performance: 6 May 2010 - 5 May 2012 Note: Kevin Judd was on extended medical leave in 2011. He did not contribute to the project during 2011-2012...the project. Marissa E Kwan Lin was the Research Associate for the project. Report Documentation Page Form ApprovedOMB No. 0704-0188 Public

Thermal Decomposition of 1,5-Dinitrobiuret (DNB): Direct Dynamics Trajectory Simulations and Statistical Modeling

DTIC Science & Technology

2011-05-03

18 . NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Dr. Tommy W. Hawkins a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE...branching using Rice-Ramsperger-Kassel-Marcus (RRKM) theory, 18 and finally to the analysis of inter-conversions of primary decomposition products...theory, 18 was employed to examine the properties of the reactant, intermediate complex and transition states as a function of the total internal energy

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Natural Selection as Coarsening

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2017-11-01

Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of evolutionary theory. Here I discuss a new conceptual link between evolution and statistical physics. I argue that natural selection can be viewed as a coarsening phenomenon, similar to the growth of domain size in quenched magnets or to Ostwald ripening in alloys and emulsions. In particular, I show that the most remarkable features of coarsening—scaling and self-similarity—have strict equivalents in evolutionary dynamics. This analogy has three main virtues: it brings a set of well-developed mathematical tools to bear on evolutionary dynamics; it suggests new problems in theoretical evolution; and it provides coarsening physics with a new exactly soluble model.

Natural Selection as Coarsening

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2018-07-01

Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of evolutionary theory. Here I discuss a new conceptual link between evolution and statistical physics. I argue that natural selection can be viewed as a coarsening phenomenon, similar to the growth of domain size in quenched magnets or to Ostwald ripening in alloys and emulsions. In particular, I show that the most remarkable features of coarsening—scaling and self-similarity—have strict equivalents in evolutionary dynamics. This analogy has three main virtues: it brings a set of well-developed mathematical tools to bear on evolutionary dynamics; it suggests new problems in theoretical evolution; and it provides coarsening physics with a new exactly soluble model.

Effect of Cell Aspect Ratio on Swarming Bacteria

NASA Astrophysics Data System (ADS)

Ilkanaiv, Bella; Kearns, Daniel B.; Ariel, Gil; Be'er, Avraham

2017-04-01

Swarming bacteria collectively migrate on surfaces using flagella, forming dynamic whirls and jets that consist of millions of individuals. Because some swarming bacteria elongate prior to actual motion, cell aspect ratio may play a significant role in the collective dynamics. Extensive research on self-propelled rodlike particles confirms that elongation promotes alignment, strongly affecting the dynamics. Here, we study experimentally the collective dynamics of variants of swarming Bacillus subtilis that differ in length. We show that the swarming statistics depends on the aspect ratio in a critical, fundamental fashion not predicted by theory. The fastest motion was obtained for the wild-type and variants that are similar in length. However, shorter and longer cells exhibit anomalous, non-Gaussian statistics and nonexponential decay of the autocorrelation function, indicating lower collective motility. These results suggest that the robust mechanisms to maintain aspect ratios may be important for efficient swarming motility. Wild-type cells are optimal in this sense.

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

Modeling Psychological Contract Violation using Dual Regime Models: An Event-based Approach.

PubMed

Hofmans, Joeri

2017-01-01

A good understanding of the dynamics of psychological contract violation requires theories, research methods and statistical models that explicitly recognize that violation feelings follow from an event that violates one's acceptance limits, after which interpretative processes are set into motion, determining the intensity of these violation feelings. Whereas theories-in the form of the dynamic model of the psychological contract-and research methods-in the form of daily diary research and experience sampling research-are available by now, the statistical tools to model such a two-stage process are still lacking. The aim of the present paper is to fill this gap in the literature by introducing two statistical models-the Zero-Inflated model and the Hurdle model-that closely mimic the theoretical process underlying the elicitation violation feelings via two model components: a binary distribution that models whether violation has occurred or not, and a count distribution that models how severe the negative impact is. Moreover, covariates can be included for both model components separately, which yields insight into their unique and shared antecedents. By doing this, the present paper offers a methodological-substantive synergy, showing how sophisticated methodology can be used to examine an important substantive issue.

OPEN PROBLEM: Orbits' statistics in chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Arnold, V.

2008-07-01

This paper shows how the measurement of the stochasticity degree of a finite sequence of real numbers, published by Kolmogorov in Italian in a journal of insurances' statistics, can be usefully applied to measure the objective stochasticity degree of sequences, originating from dynamical systems theory and from number theory. Namely, whenever the value of Kolmogorov's stochasticity parameter of a given sequence of numbers is too small (or too big), one may conclude that the conjecture describing this sequence as a sample of independent values of a random variables is highly improbable. Kolmogorov used this strategy fighting (in a paper in 'Doklady', 1940) against Lysenko, who had tried to disprove the classical genetics' law of Mendel experimentally. Calculating his stochasticity parameter value for the numbers from Lysenko's experiment reports, Kolmogorov deduced, that, while these numbers were different from the exact fulfilment of Mendel's 3 : 1 law, any smaller deviation would be a manifestation of the report's number falsification. The calculation of the values of the stochasticity parameter would be useful for many other generators of pseudorandom numbers and for many other chaotically looking statistics, including even the prime numbers distribution (discussed in this paper as an example).

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

NASA Astrophysics Data System (ADS)

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

2009-03-01

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

Theory of nonstationary Hawkes processes

NASA Astrophysics Data System (ADS)

Tannenbaum, Neta Ravid; Burak, Yoram

2017-12-01

We expand the theory of Hawkes processes to the nonstationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time-dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and the pattern and statistics of the external inputs. We illustrate the correlation structure using several examples in which neural network dynamics are modeled as a Hawkes process. In particular, we focus on the interplay between internally and externally generated oscillations and their signatures in the spike and rate correlation functions.

Further steps in the modeling of behavioural crowd dynamics, good news for safe handling. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Knopoff, Damián A.

2016-09-01

The recent review paper [4] constitutes a valuable contribution on the understanding, modeling and simulation of crowd dynamics in extreme situations. It provides a very comprehensive revision about the complexity features of the system under consideration, scaling and the consequent justification of the used methods. In particular, macro and microscopic models have so far been used to model crowd dynamics [9] and authors appropriately explain that working at the mesoscale is a good choice to deal with the heterogeneous behaviour of walkers as well as with the difficulty of their deterministic identification. In this way, methods based on the kinetic theory and statistical dynamics are employed, more precisely the so-called kinetic theory for active particles [7]. This approach has successfully been applied in the modeling of several complex dynamics, with recent applications to learning [2,8] that constitutes the key to understand communication and is of great importance in social dynamics and behavioral sciences.

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

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

PubMed

Minic, Djordje; Pleimling, Michel

2008-12-01

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

Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

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

2005-03-01

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

Applications of Ergodic Theory to Coverage Analysis

NASA Technical Reports Server (NTRS)

Lo, Martin W.

2003-01-01

The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce 'Coverage Analysis' or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem.

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.

The best motivator priorities parents choose via analytical hierarchy process

NASA Astrophysics Data System (ADS)

Farah, R. N.; Latha, P.

2015-05-01

Motivation is probably the most important factor that educators can target in order to improve learning. Numerous cross-disciplinary theories have been postulated to explain motivation. While each of these theories has some truth, no single theory seems to adequately explain all human motivation. The fact is that human beings in general and pupils in particular are complex creatures with complex needs and desires. In this paper, Analytic Hierarchy Process (AHP) has been proposed as an emerging solution to move towards too large, dynamic and complex real world multi-criteria decision making problems in selecting the most suitable motivator when choosing school for their children. Data were analyzed using SPSS 17.0 ("Statistical Package for Social Science") software. Statistic testing used are descriptive and inferential statistic. Descriptive statistic used to identify respondent pupils and parents demographic factors. The statistical testing used to determine the pupils and parents highest motivator priorities and parents' best priorities using AHP to determine the criteria chosen by parents such as school principals, teachers, pupils and parents. The moderating factors are selected schools based on "Standard Kualiti Pendidikan Malaysia" (SKPM) in Ampang. Inferential statistics such as One-way ANOVA used to get the significant and data used to calculate the weightage of AHP. School principals is found to be the best motivator for parents in choosing school for their pupils followed by teachers, parents and pupils.

Update on SU(2) gauge theory with NF = 2 fundamental flavours.

NASA Astrophysics Data System (ADS)

Drach, Vincent; Janowski, Tadeusz; Pica, Claudio

2018-03-01

We present a non perturbative study of SU(2) gauge theory with two fundamental Dirac flavours. This theory provides a minimal template which is ideal for a wide class of Standard Model extensions featuring novel strong dynamics, such as a minimal realization of composite Higgs models. We present an update on the status of the meson spectrum and decay constants based on increased statistics on our existing ensembles and the inclusion of new ensembles with lighter pion masses, resulting in a more reliable chiral extrapolation. Preprint: CP3-Origins-2017-048 DNRF90

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

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

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.

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

Spatial occupancy models for predicting metapopulation dynamics and viability following reintroduction

USGS Publications Warehouse

Chandler, Richard B.; Muths, Erin L.; Sigafus, Brent H.; Schwalbe, Cecil R.; Jarchow, Christopher J.; Hossack, Blake R.

2015-01-01

Synthesis and applications. This work demonstrates how spatio-temporal statistical models based on ecological theory can be applied to forecast the outcomes of conservation actions such as reintroduction. Our spatial occupancy model should be particularly useful when management agencies lack the funds to collect intensive individual-level data.

Influences of environment and disturbance on forest patterns in coastal Oregon watersheds.

Treesearch

Michael C. Wimberly; Thomas A. Spies

2001-01-01

Modern ecology often emphasizes the distinction between traditional theories of stable, environmentally structured communities and a new paradigm of disturbance driven, nonequilibrium dynamics. However, multiple hypotheses for observed vegetation patterns have seldom been explicitly tested. We used multivariate statistics and variation partitioning methods to assess...

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

PubMed

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

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

PubMed

Budiyono, Agung; Rohrlich, Daniel

2017-11-03

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

How Stuttering Develops: The Multifactorial Dynamic Pathways Theory

PubMed Central

Weber, Christine

2017-01-01

Purpose We advanced a multifactorial, dynamic account of the complex, nonlinear interactions of motor, linguistic, and emotional factors contributing to the development of stuttering. Our purpose here is to update our account as the multifactorial dynamic pathways theory. Method We review evidence related to how stuttering develops, including genetic/epigenetic factors; motor, linguistic, and emotional features; and advances in neuroimaging studies. We update evidence for our earlier claim: Although stuttering ultimately reflects impairment in speech sensorimotor processes, its course over the life span is strongly conditioned by linguistic and emotional factors. Results Our current account places primary emphasis on the dynamic developmental context in which stuttering emerges and follows its course during the preschool years. Rapid changes in many neurobehavioral systems are ongoing, and critical interactions among these systems likely play a major role in determining persistence of or recovery from stuttering. Conclusion Stuttering, or childhood onset fluency disorder (Diagnostic and Statistical Manual of Mental Disorders, 5th edition; American Psychiatric Association [APA], 2013), is a neurodevelopmental disorder that begins when neural networks supporting speech, language, and emotional functions are rapidly developing. The multifactorial dynamic pathways theory motivates experimental and clinical work to determine the specific factors that contribute to each child's pathway to the diagnosis of stuttering and those most likely to promote recovery. PMID:28837728

How Stuttering Develops: The Multifactorial Dynamic Pathways Theory.

PubMed

Smith, Anne; Weber, Christine

2017-09-18

We advanced a multifactorial, dynamic account of the complex, nonlinear interactions of motor, linguistic, and emotional factors contributing to the development of stuttering. Our purpose here is to update our account as the multifactorial dynamic pathways theory. We review evidence related to how stuttering develops, including genetic/epigenetic factors; motor, linguistic, and emotional features; and advances in neuroimaging studies. We update evidence for our earlier claim: Although stuttering ultimately reflects impairment in speech sensorimotor processes, its course over the life span is strongly conditioned by linguistic and emotional factors. Our current account places primary emphasis on the dynamic developmental context in which stuttering emerges and follows its course during the preschool years. Rapid changes in many neurobehavioral systems are ongoing, and critical interactions among these systems likely play a major role in determining persistence of or recovery from stuttering. Stuttering, or childhood onset fluency disorder (Diagnostic and Statistical Manual of Mental Disorders, 5th edition; American Psychiatric Association [APA], 2013), is a neurodevelopmental disorder that begins when neural networks supporting speech, language, and emotional functions are rapidly developing. The multifactorial dynamic pathways theory motivates experimental and clinical work to determine the specific factors that contribute to each child's pathway to the diagnosis of stuttering and those most likely to promote recovery.

Full of Sound and Fury, Signifying Nothing? A Reply to Dave Hill's "Race and Class in Britain: A Critique of the Statistical Basis for Critical Race Theory in Britain"

ERIC Educational Resources Information Center

Gillborn, David

2010-01-01

This paper is a reply to an earlier piece by Dave Hill, in this journal, that attacked critical race theory (CRT) in general and my own work in particular. I begin with a brief introduction to CRT which highlights the differences between the reality, of a broad and dynamic approach, as opposed to the simple and monolithic version constructed by…

The seasonal response of the Held-Suarez climate model to prescribed ocean temperature anomalies. II - Dynamical analysis

NASA Technical Reports Server (NTRS)

Phillips, T. J.

1984-01-01

The heating associated with equatorial, subtropical, and midlatitude ocean temperature anamolies in the Held-Suarez climate model is analyzed. The local and downstream response to the anomalies is analyzed, first by examining the seasonal variation in heating associated with each ocean temperature anomaly, and then by combining knowledge of the heating with linear dynamical theory in order to develop a more comprehensive explanation of the seasonal variation in local and downstream atmospheric response to each anomaly. The extent to which the linear theory of propagating waves can assist the interpretation of the remote cross-latitudinal response of the model to the ocean temperature anomalies is considered. Alternative hypotheses that attempt to avoid the contradictions inherent in a strict application of linear theory are investigated, and the impact of sampling errors on the assessment of statistical significance is also examined.

Deformation in Metallic Glass: Connecting Atoms to Continua

NASA Astrophysics Data System (ADS)

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

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

Flavor-singlet spectrum in multi-flavor QCD

NASA Astrophysics Data System (ADS)

Aoki, Yasumichi; Aoyama, Tatsumi; Bennett, Ed; Kurachi, Masafumi; Maskawa, Toshihide; Miura, Kohtaroh; Nagai, Kei-ichi; Ohki, Hiroshi; Rinaldi, Enrico; Shibata, Akihiro; Yamawaki, Koichi; Yamazaki, Takeshi

2018-03-01

Studying SU(3) gauge theories with increasing number of light fermions is relevant both for understanding the strong dynamics of QCD and for constructing strongly interacting extensions of the Standard Model (e.g. UV completions of composite Higgs models). In order to contrast these many-flavors strongly interacting theories with QCD, we study the flavor-singlet spectrum as an interesting probe. In fact, some composite Higgs models require the Higgs boson to be the lightest flavor-singlet scalar in the spectrum of a strongly interacting new sector with a well defined hierarchy with the rest of the states. Moreover, introducing many light flavors at fixed number of colors can influence the dynamics of the lightest flavor-singlet pseudoscalar. We present the on-going study of these flavor-singlet channels using multiple interpolating operators on high-statistics ensembles generated by the LatKMI collaboration and we compare results with available data obtained by the Lattice Strong Dynamics collaboration. For the theory with 8 flavors, the two collaborations have generated configurations that complement each others with the aim to tackle the massless limit using the largest possible volumes.

Flavor-singlet spectrum in multi-flavor QCD

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

Aoki, Yasamichi; Rinaldi, Enrico

2017-06-18

Studying SU(3) gauge theories with increasing number of light fermions is relevant both for understanding the strong dynamics of QCD and for constructing strongly interacting extensions of the Standard Model (e.g. UV completions of composite Higgs models). In order to contrast these many-flavors strongly interacting theories with QCD, we study the flavor-singlet spectrum as an interesting probe. In fact, some composite Higgs models require the Higgs boson to be the lightest flavor-singlet scalar in the spectrum of a strongly interacting new sector with a well defined hierarchy with the rest of the states. Moreover, introducing many light flavors at fixedmore » number of colors can influence the dynamics of the lightest flavor-singlet pseudoscalar. We present the on-going study of these flavor-singlet channels using multiple interpolating operators on high-statistics ensembles generated by the LatKMI collaboration and we compare results with available data obtained by the Lattice Strong Dynamics collaboration. For the theory with 8 flavors, the two collaborations have generated configurations that complement each others with the aim to tackle the massless limit using the largest possible volumes.« less

Making sense of metacommunities: dispelling the mythology of a metacommunity typology.

PubMed

Brown, Bryan L; Sokol, Eric R; Skelton, James; Tornwall, Brett

2017-03-01

Metacommunity ecology has rapidly become a dominant framework through which ecologists understand the natural world. Unfortunately, persistent misunderstandings regarding metacommunity theory and the methods for evaluating hypotheses based on the theory are common in the ecological literature. Since its beginnings, four major paradigms-species sorting, mass effects, neutrality, and patch dynamics-have been associated with metacommunity ecology. The Big 4 have been misconstrued to represent the complete set of metacommunity dynamics. As a result, many investigators attempt to evaluate community assembly processes as strictly belonging to one of the Big 4 types, rather than embracing the full scope of metacommunity theory. The Big 4 were never intended to represent the entire spectrum of metacommunity dynamics and were rather examples of historical paradigms that fit within the new framework. We argue that perpetuation of the Big 4 typology hurts community ecology and we encourage researchers to embrace the full inference space of metacommunity theory. A related, but distinct issue is that the technique of variation partitioning is often used to evaluate the dynamics of metacommunities. This methodology has produced its own set of misunderstandings, some of which are directly a product of the Big 4 typology and others which are simply the product of poor study design or statistical artefacts. However, variation partitioning is a potentially powerful technique when used appropriately and we identify several strategies for successful utilization of variation partitioning.

Nonlinear Dynamics of Complex Coevolutionary Systems in Historical Times

NASA Astrophysics Data System (ADS)

Perdigão, Rui A. P.

2016-04-01

A new theoretical paradigm for statistical-dynamical modeling of complex coevolutionary systems is introduced, with the aim to provide historical geoscientists with a practical tool to analyse historical data and its underlying phenomenology. Historical data is assumed to represent the history of dynamical processes of physical and socio-economic nature. If processes and their governing laws are well understood, they are often treated with traditional dynamical equations: deterministic approach. If the governing laws are unknown or impracticable, the process is often treated as if being random (even if it is not): statistical approach. Although single eventful details - such as the exact spatiotemporal structure of a particular hydro-meteorological incident - may often be elusive to a detailed analysis, the overall dynamics exhibit group properties summarized by a simple set of categories or dynamical regimes at multiple scales - from local short-lived convection patterns to large-scale hydro-climatic regimes. The overwhelming microscale complexity is thus conveniently wrapped into a manageable group entity, such as a statistical distribution. In a stationary setting whereby the distribution is assumed to be invariant, alternating regimes are approachable as dynamical intermittence. For instance, in the context of bimodal climatic oscillations such as NAO and ENSO, each mode corresponds to a dynamical regime or phase. However, given external forcings or longer-term internal variability and multiscale coevolution, the structural properties of the system may change. These changes in the dynamical structure bring about a new distribution and associated regimes. The modes of yesteryear may no longer exist as such in the new structural order of the system. In this context, aside from regime intermittence, the system exhibits structural regime change. New oscillations may emerge whilst others fade into the annals of history, e.g. particular climate fluctuations during the Little Ice Age. Traditional theories of stochastic processes and dynamical systems are grounded on the existence of so-called dynamical invariants; properties that remain unchanged as the dynamics unfold, assuming structural invariance and ergodicity of the underlying system. However, such theories are no longer optimal when trying to understand and model long-term historical records of coevolutionary systems. A new paradigm is thus needed. Therefore, we introduce a new class of dynamical systems that reinvent themselves as the dynamics unfold. Rather than only changing variables and parameters under a rigid framework, the governing laws are malleable themselves. The novel formulation captures and explains the coevolutionary dynamics of multiscale hydroclimatic systems, bringing along a physically sound understanding of their regimes, transitions and extremes over a long-term history.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Probabilistic Component Mode Synthesis of Nondeterministic Substructures

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Ferri, Aldo A.

1996-01-01

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. We present a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Life Cycle Theory and the Residential Mobility of Older Canadians

ERIC Educational Resources Information Center

Ostrovsky, Yuri

2004-01-01

This paper outlines a debate in the economics literature about the role of housing wealth in post-retirement consumption choices and provides a description of the patterns of the residential mobility, tenure, and dwelling-type transitions of older Canadians, using the newly available Statistics Canada Survey of Labour and Income Dynamics (SLID).…

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

Theory of dynamic barriers, activated hopping, and the glass transition in polymer melts

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth S.; Saltzman, Erica J.

2004-07-01

A statistical mechanical theory of collective dynamic barriers, slow segmental relaxation, and the glass transition of polymer melts is developed by combining, and in some aspects extending, methods of mode coupling, density functional, and activated hopping transport theories. A coarse-grained description of polymer chains is adopted and the melt is treated as a liquid of segments. The theory is built on the idea that collective density fluctuations on length scales considerably longer than the local cage scale are of primary importance in the deeply supercooled regime. The barrier hopping or segmental relaxation time is predicted to be a function primarily of a single parameter that is chemical structure, temperature, and pressure dependent. This parameter depends on the material-specific dimensionless amplitude of thermal density fluctuations (compressibility) and a reduced segmental density determined by the packing length and backbone characteristic ratio. Analytic results are derived for a crossover temperature Tc, collective barrier, and glass transition temperature Tg. The relation of these quantities to structural and thermodynamic properties of the polymer melt is established. A universal power-law scaling behavior of the relaxation time below Tc is predicted based on identification of a reduced temperature variable that quantifies the breadth of the supercooled regime. Connections between the ratio Tc/Tg, two measures of dynamic fragility, and the magnitude of the local relaxation time at Tg logically follow. Excellent agreement with experiment is found for these generic aspects, and the crucial importance of the experimentally observed near universality of the dynamic crossover time is established. Extensions of the theory to treat the full chain dynamics, heterogeneity, barrier fluctuations, and nonpolymeric thermal glass forming liquids are briefly discussed.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

DOE PAGES

Berges, J.; Schlichting, S.; Boguslavski, K.; ...

2015-11-05

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

Nonequilibrium fixed points in longitudinally expanding scalar theories: Infrared cascade, Bose condensation and a challenge for kinetic theory

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

Berges, J.; Schlichting, S.; Boguslavski, K.

In [Phys. Rev. Lett. 114, 061601 (2015)], we reported on a new universality class for longitudinally expanding systems, encompassing strongly correlated non-Abelian plasmas and N-component self-interacting scalar field theories. Using classical-statistical methods, we showed that these systems share the same self-similar scaling properties for a wide range of momenta in a limit where particles are weakly coupled but their occupancy is high. Here we significantly expand on our previous work and delineate two further self-similar regimes. One of these occurs in the deep infrared (IR) regime of very high occupancies, where the nonequilibrium dynamics leads to the formation of amore » Bose-Einstein condensate. The universal IR scaling exponents and the spectral index characterizing the isotropic IR distributions are described by an effective theory derived from a systematic large-N expansion at next-to-leading order. Remarkably, this effective theory can be cast as a vertex-resummed kinetic theory. The other novel self-similar regime occurs close to the hard physical scale of the theory, and sets in only at later times. In this study, we argue that the important role of the infrared dynamics ensures that key features of our results for scalar and gauge theories cannot be reproduced consistently in conventional kinetic theory frameworks.« less

Long-range memory and non-Markov statistical effects in human sensorimotor coordination

NASA Astrophysics Data System (ADS)

M. Yulmetyev, Renat; Emelyanova, Natalya; Hänggi, Peter; Gafarov, Fail; Prokhorov, Alexander

2002-12-01

In this paper, the non-Markov statistical processes and long-range memory effects in human sensorimotor coordination are investigated. The theoretical basis of this study is the statistical theory of non-stationary discrete non-Markov processes in complex systems (Phys. Rev. E 62, 6178 (2000)). The human sensorimotor coordination was experimentally studied by means of standard dynamical tapping test on the group of 32 young peoples with tap numbers up to 400. This test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere. The numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function, the memory functions of low orders and the first three points of the statistical spectrum of non-Markovity parameter. Our observations demonstrate, that with the regard to results of the standard dynamic tapping-test it is possible to divide all examinees into five different dynamic types. We have introduced the conflict coefficient to estimate quantitatively the order-disorder effects underlying life systems. The last one reflects the existence of disbalance between the nervous and the motor human coordination. The suggested classification of the neurophysiological activity represents the dynamic generalization of the well-known neuropsychological types and provides the new approach in a modern neuropsychology.

Simultaneous measurement of lipid and aqueous layers of tear film using optical coherence tomography and statistical decision theory

NASA Astrophysics Data System (ADS)

Huang, Jinxin; Clarkson, Eric; Kupinski, Matthew; Rolland, Jannick P.

2014-03-01

The prevalence of Dry Eye Disease (DED) in the USA is approximately 40 million in aging adults with about $3.8 billion economic burden. However, a comprehensive understanding of tear film dynamics, which is the prerequisite to advance the management of DED, is yet to be realized. To extend our understanding of tear film dynamics, we investigate the simultaneous estimation of the lipid and aqueous layers thicknesses with the combination of optical coherence tomography (OCT) and statistical decision theory. In specific, we develop a mathematical model for Fourier-domain OCT where we take into account the different statistical processes associated with the imaging chain. We formulate the first-order and second-order statistical quantities of the output of the OCT system, which can generate some simulated OCT spectra. A tear film model, which includes a lipid and aqueous layer on top of a rough corneal surface, is the object being imaged. Then we further implement a Maximum-likelihood (ML) estimator to interpret the simulated OCT data to estimate the thicknesses of both layers of the tear film. Results show that an axial resolution of 1 μm allows estimates down to nanometers scale. We use the root mean square error of the estimates as a metric to evaluate the system parameters, such as the tradeoff between the imaging speed and the precision of estimation. This framework further provides the theoretical basics to optimize the imaging setup for a specific thickness estimation task.

Entropy, a Unifying Concept: from Physics to Cognitive Psychology

NASA Astrophysics Data System (ADS)

Tsallis, Constantino; Tsallis, Alexandra C.

Together with classical, relativistic and quantum mechanics, as well as Maxwell electromagnetism, Boltzmann-Gibbs (BG) statistical mechanics constitutes one of the main theories of contemporary physics. This theory primarily concerns inanimate matter, and at its generic foundation we find nonlinear dynamical systems satisfying the ergodic hypothesis. This hypothesis is typically guaranteed for systems whose maximal Lyapunov exponent is positive. What happens when this crucial quantity is zero instead? We suggest here that, in what concerns thermostatistical properties, we typically enter what in some sense may be considered as a new world — the world of living systems — . The need emerges, at least for many systems, for generalizing the basis of BG statistical mechanics, namely the Boltzmann-Gibbs-von Neumann-Shannon en-tropic functional form, which connects the oscopic, thermodynamic quantity, with the occurrence probabilities of microscopic configurations. This unifying approach is briefly reviewed here, and its widespread applications — from physics to cognitive psychology — are overviewed. Special attention is dedicated to the learning/memorizing process in humans and computers. The present observations might be related to the gestalt theory of visual perceptions and the actor-network theory.

Kinetic theory for strongly coupled Coulomb systems

NASA Astrophysics Data System (ADS)

Dufty, James; Wrighton, Jeffrey

2018-01-01

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

PREFACE: Mathematical Aspects of Generalized Entropies and their Applications

NASA Astrophysics Data System (ADS)

Suyari, Hiroki; Ohara, Atsumi; Wada, Tatsuaki

2010-01-01

In the recent increasing interests in power-law behaviors beyond the usual exponential ones, there have been some concrete attempts in statistical physics to generalize the standard Boltzmann-Gibbs statistics. Among such generalizations, nonextensive statistical mechanics has been well studied for about the last two decades with many modifications and refinements. The generalization has provided not only a theoretical framework but also many applications such as chaos, multi-fractal, complex systems, nonequilibrium statistical mechanics, biophysics, econophysics, information theory and so on. At the same time as the developments in the generalization of statistical mechanics, the corresponding mathematical structures have also been required and uncovered. In particular, some deep connections to mathematical sciences such as q-analysis, information geometry, information theory and quantum probability theory have been revealed recently. These results obviously indicate an existence of the generalized mathematical structure including the mathematical framework for the exponential family as a special case, but the whole structure is still unclear. In order to make an opportunity to discuss the mathematical structure induced from generalized entropies by scientists in many fields, the international workshop 'Mathematical Aspects of Generalized Entropies and their Applications' was held on 7-9 July 2009 at Kyoto TERRSA, Kyoto, Japan. This volume is the proceedings of the workshop which consisted of 6 invited speakers, 14 oral presenters, 7 poster presenters and 63 other participants. The topics of the workshop cover the nonextensive statistical mechanics, chaos, cosmology, information geometry, divergence theory, econophysics, materials engineering, molecular dynamics and entropy theory, information theory and so on. The workshop was organized as the first attempt to discuss these mathematical aspects with leading experts in each area. We would like to express special thanks to all the invited speakers, the contributors and the participants at the workshop. We are also grateful to RIMS (Research Institute for Mathematical Science) in Kyoto University and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B), 18300003, 2009 for their support. Organizing Committee Editors of the Proceedings Hiroki Suyari (Chiba University, Japan) Atsumi Ohara (Osaka University, Japan) Tatsuaki Wada (Ibaraki University, Japan) Conference photograph

Shock Waves Propagation in Scope of the Nonlocal Theory of Dynamical Plasticity

NASA Astrophysics Data System (ADS)

Khantuleva, Tatyana A.

2004-07-01

From the point of view of the modern statistical mechanics the problems on shock compression of solids require a reformulation in terms of highly nonequilibrium effects arising inside the wave front. The self-organization during the multiscale and multistage momentum and energy exchange are originated by the correlation function. The theory of dynamic plasticity has been developed by the author on the base of the self-consistent nonlocal hydrodynamic approach had been applied to the shock wave propagation in solids. Nonlocal balance equations describe both the reversible wave type transport at the initial stage and the diffusive (dissipative) one in the end. The involved inverse influence of the mesoeffects on the wave propagation makes the formulation of problems self-consistent and involves a concept of the cybernetic control close-loop.

Wave theory of turbulence in compressible media

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease.

Checking the statistical theory of liquids by ultraacoustic measurements

NASA Technical Reports Server (NTRS)

Dima, V. N.

1974-01-01

The manner of theoretically obtaining radial distribution functions 9(r) for n-hexane as a function of temperature is described. With the aid of function g(r) the coefficient of dynamic viscosity and the coefficient of volumetric viscosity for temperatures ranging from 213 K to 273 K were calculated. With the aid of the two coefficients of viscosity the coefficient of absorption of ultrasounds in n-hexane referred to the square of the frequency was determined. The same values were measured experimentally. Comparison of theory with experiments resulted in satisfactory agreement.

Preliminary Characterization of Erythrocytes Deformability on the Entropy-Complexity Plane

PubMed Central

Korol, Ana M; D’Arrigo, Mabel; Foresto, Patricia; Pérez, Susana; Martín, Maria T; Rosso, Osualdo A

2010-01-01

We present an application of wavelet-based Information Theory quantifiers (Normalized Total Shannon Entropy, MPR-Statistical Complexity and Entropy-Complexity plane) on red blood cells membrane viscoelasticity characterization. These quantifiers exhibit important localization advantages provided by the Wavelet Theory. The present approach produces a clear characterization of this dynamical system, finding out an evident manifestation of a random process on the red cell samples of healthy individuals, and its sharp reduction of randomness on analyzing a human haematological disease, such as β-thalassaemia minor. PMID:21611139

From Theory to Air Force Practice: Applications and Non-Binary Extensions of Probabilistic Model-Building Genetic Algorithms

DTIC Science & Technology

2006-05-31

dynamics (MD) and kinetic Monte Carlo ( KMC ) procedures. In 2D surface modeling our calculations project speedups of 9 orders of magnitude at 300 degrees...programming is used to perform customized statistical mechanics by bridging the different time scales of MD and KMC quickly and well. Speedups in

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules.

PubMed

Mosheiff, Noga; Agmon, Haggai; Moriel, Avraham; Burak, Yoram

2017-06-01

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

PubMed Central

Mosheiff, Noga; Agmon, Haggai; Moriel, Avraham

2017-01-01

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal’s motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing. PMID:28628647

Direct dynamics simulation of dioxetane formation and decomposition via the singlet .O-O-CH2-CH2. biradical: Non-RRKM dynamics

NASA Astrophysics Data System (ADS)

Sun, Rui; Park, Kyoyeon; de Jong, Wibe A.; Lischka, Hans; Windus, Theresa L.; Hase, William L.

2012-07-01

Electronic structure calculations and direct chemical dynamics simulations are used to study the formation and decomposition of dioxetane on its ground state singlet potential energy surface. The stationary points for 1O2 + C2H4, the singlet .O-O-CH2-CH2. biradical, the transition state (TS) connecting this biradical with dioxetane, and the two transition states and gauche .O-CH2-CH2-O. biradical connecting dioxetane with the formaldehyde product molecules are investigated at different levels of electronic structure theory including UB3LYP, UMP2, MRMP2, and CASSCF and a range of basis sets. The UB3LYP/6-31G* method was found to give representative energies for the reactive system and was used as a model for the simulations. UB3LYP/6-31G* direct dynamics trajectories were initiated at the TS connecting the .O-O-CH2-CH2. biradical and dioxetane by sampling the TS's vibrational energy levels, and rotational and reaction coordinate energies, with Boltzmann distributions at 300, 1000, and 1500 K. This corresponds to the transition state theory model for trajectories that pass the TS. The trajectories were directed randomly towards both the biradical and dioxetane. A small fraction of the trajectories directed towards the biradical recrossed the TS and formed dioxetane. The remainder formed 1O2 + C2H4 and of these ˜ 40% went directly from the TS to 1O2 + C2H4 without getting trapped and forming an intermediate in the .O-O-CH2-CH2. biradical potential energy minimum, a non-statistical result. The dioxetane molecules which are formed dissociate to two formaldehyde molecules with a rate constant two orders of magnitude smaller than that predicted by Rice-Ramsperger-Kassel-Marcus theory. The reaction dynamics from dioxetane to the formaldehyde molecules do not follow the intrinsic reaction coordinate or involve trapping in the gauche .O-CH2-CH2-O. biradical potential energy minimum. Important non-statistical dynamics are exhibited for this reactive system.

Chern-Simons Term: Theory and Applications.

NASA Astrophysics Data System (ADS)

Gupta, Kumar Sankar

1992-01-01

We investigate the quantization and applications of Chern-Simons theories to several systems of interest. Elementary canonical methods are employed for the quantization of abelian and nonabelian Chern-Simons actions using ideas from gauge theories and quantum gravity. When the spatial slice is a disc, it yields quantum states at the edge of the disc carrying a representation of the Kac-Moody algebra. We next include sources in this model and their quantum states are shown to be those of a conformal family. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. The spin-statistics theorem is established for Chern-Simons dynamics using purely geometrical techniques. Chern-Simons action is associated with exotic spin and statistics in 2 + 1 dimensions. We study several systems in which the Chern-Simons action affects the spin and statistics. The first class of systems we study consist of G/H models. The solitons of these models are shown to obey anyonic statistics in the presence of a Chern-Simons term. The second system deals with the effect of the Chern -Simons term in a model for high temperature superconductivity. The coefficient of the Chern-Simons term is shown to be quantized, one of its possible values giving fermionic statistics to the solitons of this model. Finally, we study a system of spinning particles interacting with 2 + 1 gravity, the latter being described by an ISO(2,1) Chern-Simons term. An effective action for the particles is obtained by integrating out the gauge fields. Next we construct operators which exchange the particles. They are shown to satisfy the braid relations. There are ambiguities in the quantization of this system which can be exploited to give anyonic statistics to the particles. We also point out that at the level of the first quantized theory, the usual spin-statistics relation need not apply to these particles.

Communication: Dominance of extreme statistics in a prototype many-body Brownian ratchet.

PubMed

Hohlfeld, Evan; Geissler, Phillip L

2014-10-28

Many forms of cell motility rely on Brownian ratchet mechanisms that involve multiple stochastic processes. We present a computational and theoretical study of the nonequilibrium statistical dynamics of such a many-body ratchet, in the specific form of a growing polymer gel that pushes a diffusing obstacle. We find that oft-neglected correlations among constituent filaments impact steady-state kinetics and significantly deplete the gel's density within molecular distances of its leading edge. These behaviors are captured quantitatively by a self-consistent theory for extreme fluctuations in filaments' spatial distribution.

Hybrid perturbation methods based on statistical time series models

NASA Astrophysics Data System (ADS)

San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

2016-04-01

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

Noninvasive fetal QRS detection using an echo state network and dynamic programming.

PubMed

Lukoševičius, Mantas; Marozas, Vaidotas

2014-08-01

We address a classical fetal QRS detection problem from abdominal ECG recordings with a data-driven statistical machine learning approach. Our goal is to have a powerful, yet conceptually clean, solution. There are two novel key components at the heart of our approach: an echo state recurrent neural network that is trained to indicate fetal QRS complexes, and several increasingly sophisticated versions of statistics-based dynamic programming algorithms, which are derived from and rooted in probability theory. We also employ a standard technique for preprocessing and removing maternal ECG complexes from the signals, but do not take this as the main focus of this work. The proposed approach is quite generic and can be extended to other types of signals and annotations. Open-source code is provided.

Scaling in tournaments

NASA Astrophysics Data System (ADS)

Ben-Naim, E.; Redner, S.; Vazquez, F.

2007-02-01

We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q. The loser is eliminated. Extremal statistics of the initial distribution of player strengths governs the tournament outcome. For a uniform initial distribution of strengths, the rank of the winner, x*, decays algebraically with the number of players, N, as x*~N-β. Different decay exponents are found analytically for sequential dynamics, βseq=1-2q, and parallel dynamics, \\beta_par=1+\\frac{\\ln (1-q)}{\\ln 2} . The distribution of player strengths becomes self-similar in the long time limit with an algebraic tail. Our theory successfully describes statistics of the US college basketball national championship tournament.

The special theory of Brownian relativity: equivalence principle for dynamic and static random paths and uncertainty relation for diffusion.

PubMed

Mezzasalma, Stefano A

2007-03-15

The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.

Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing

NASA Technical Reports Server (NTRS)

Over, Thomas, M.; Gupta, Vijay K.

1994-01-01

Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.

Network dynamics: The World Wide Web

NASA Astrophysics Data System (ADS)

Adamic, Lada Ariana

Despite its rapidly growing and dynamic nature, the Web displays a number of strong regularities which can be understood by drawing on methods of statistical physics. This thesis finds power-law distributions in website sizes, traffic, and links, and more importantly, develops a stochastic theory which explains them. Power-law link distributions are shown to lead to network characteristics which are especially suitable for scalable localized search. It is also demonstrated that the Web is a "small world": to reach one site from any other takes an average of only 4 hops, while most related sites cluster together. Additional dynamical properties of the Web graph are extracted from diffusion processes.

Generalized Dynamic Equations Related to Condensation and Freezing Processes

NASA Astrophysics Data System (ADS)

Wang, Xingrong; Huang, Yong

2018-01-01

The generalized thermodynamic equation related to condensation and freezing processes was derived by introducing the condensation and freezing probability function into the dynamic framework based on the statistical thermodynamic fluctuation theory. As a result, the physical mechanism of some weather phenomena covered by using δ(0,1) can in turn be studied and uncovered. From the generalized dynamic equations, the tendency equation of the generalized potential vorticity (GPV) is derived. From the discussion of tendency equation of GPV, in some very thin transitional areas, GPV is found nonconserved because of the introduction of the condensation and freezing probability function, even in frictionless and moist adiabatic air motion.

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.

Revealing spatially heterogeneous relaxation in a model nanocomposite.

PubMed

Cheng, Shiwang; Mirigian, Stephen; Carrillo, Jan-Michael Y; Bocharova, Vera; Sumpter, Bobby G; Schweizer, Kenneth S; Sokolov, Alexei P

2015-11-21

The detailed nature of spatially heterogeneous dynamics of glycerol-silica nanocomposites is unraveled by combining dielectric spectroscopy with atomistic simulation and statistical mechanical theory. Analysis of the spatial mobility gradient shows no "glassy" layer, but the α-relaxation time near the nanoparticle grows with cooling faster than the α-relaxation time in the bulk and is ∼20 times longer at low temperatures. The interfacial layer thickness increases from ∼1.8 nm at higher temperatures to ∼3.5 nm upon cooling to near bulk Tg. A real space microscopic description of the mobility gradient is constructed by synergistically combining high temperature atomistic simulation with theory. Our analysis suggests that the interfacial slowing down arises mainly due to an increase of the local cage scale barrier for activated hopping induced by enhanced packing and densification near the nanoparticle surface. The theory is employed to predict how local surface densification can be manipulated to control layer dynamics and shear rigidity over a wide temperature range.

Revealing spatially heterogeneous relaxation in a model nanocomposite

DOE PAGES

Cheng, Shiwang; Mirigian, Stephen; Carrillo, Jan-Michael Y.; ...

2015-11-18

The detailed nature of spatially heterogeneous dynamics of glycerol-silica nanocomposites is unraveled by combining dielectric spectroscopy with atomistic simulation and statistical mechanical theory. Analysis of the spatial mobility gradient shows no glassy layer, but the -relaxation time near the nanoparticle grows with cooling faster than the -relaxation time in the bulk and is ~20 times longer at low temperatures. The interfacial layer thickness increases from ~1.8 nm at higher temperatures to ~3.5 nm upon cooling to near bulk T g. A real space microscopic description of the mobility gradient is constructed by synergistically combining high temperature atomistic simulation with theory.more » Our analysis suggests that the interfacial slowing down arises mainly due to an increase of the local cage scale barrier for activated hopping induced by enhanced packing and densification near the nanoparticle surface. As a result, the theory is employed to predict how local surface densification can be manipulated to control layer dynamics and shear rigidity over a wide temperature range.« less

Diffusion of innovations theory applied to global tobacco control treaty ratification.

PubMed

Valente, Thomas W; Dyal, Stephanie R; Chu, Kar-Hai; Wipfli, Heather; Fujimoto, Kayo

2015-11-01

This study applies diffusion of innovations theory to understand network influences on country ratification of an international health treaty, the Framework Convention for Tobacco Control (FCTC). From 2003 to 2014 approximately 90% of United Nations member countries ratified the FCTC. We hypothesized that communication between tobacco control advocates on GLOBALink, a 7000-member online communication forum in existence from 1992 to 2012, would be associated with the timing of treaty ratification. We further hypothesized dynamic network influences such that external influence decreased over time, internal influence increased over time, and the role of opinion leader countries varied over time. In addition we develop two concepts: Susceptibility and influence that uncover the micro-level dynamics of network influence. Statistical analyses lend support to the influence of co-subscriptions on GLOBALink providing a conduit for inter-country influences on treaty ratification and some support for the dynamic hypotheses. Analyses of susceptibility and infection indicated particularly influential countries. These results have implications for the study of policy diffusion as well as dynamic models of behavior change. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

Ranking Theory and Conditional Reasoning.

PubMed

Skovgaard-Olsen, Niels

2016-05-01

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohn's recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohn's (2013) ranking theoretic approach to conditionals. Copyright © 2015 Cognitive Science Society, Inc.

Unperturbed Schelling Segregation in Two or Three Dimensions

NASA Astrophysics Data System (ADS)

Barmpalias, George; Elwes, Richard; Lewis-Pye, Andrew

2016-09-01

Schelling's models of segregation, first described in 1969 (Am Econ Rev 59:488-493, 1969) are among the best known models of self-organising behaviour. Their original purpose was to identify mechanisms of urban racial segregation. But his models form part of a family which arises in statistical mechanics, neural networks, social science, and beyond, where populations of agents interact on networks. Despite extensive study, unperturbed Schelling models have largely resisted rigorous analysis, prior results generally focusing on variants in which noise is introduced into the dynamics, the resulting system being amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory (Young in Individual strategy and social structure: an evolutionary theory of institutions, Princeton University Press, Princeton, 1998). A series of recent papers (Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012); Barmpalias et al. in: 55th annual IEEE symposium on foundations of computer science, Philadelphia, 2014, J Stat Phys 158:806-852, 2015), has seen the first rigorous analyses of 1-dimensional unperturbed Schelling models, in an asymptotic framework largely unknown in statistical mechanics. Here we provide the first such analysis of 2- and 3-dimensional unperturbed models, establishing most of the phase diagram, and answering a challenge from Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012).

Models for inference in dynamic metacommunity systems

USGS Publications Warehouse

Dorazio, Robert M.; Kery, Marc; Royle, J. Andrew; Plattner, Matthias

2010-01-01

A variety of processes are thought to be involved in the formation and dynamics of species assemblages. For example, various metacommunity theories are based on differences in the relative contributions of dispersal of species among local communities and interactions of species within local communities. Interestingly, metacommunity theories continue to be advanced without much empirical validation. Part of the problem is that statistical models used to analyze typical survey data either fail to specify ecological processes with sufficient complexity or they fail to account for errors in detection of species during sampling. In this paper, we describe a statistical modeling framework for the analysis of metacommunity dynamics that is based on the idea of adopting a unified approach, multispecies occupancy modeling, for computing inferences about individual species, local communities of species, or the entire metacommunity of species. This approach accounts for errors in detection of species during sampling and also allows different metacommunity paradigms to be specified in terms of species- and location-specific probabilities of occurrence, extinction, and colonization: all of which are estimable. In addition, this approach can be used to address inference problems that arise in conservation ecology, such as predicting temporal and spatial changes in biodiversity for use in making conservation decisions. To illustrate, we estimate changes in species composition associated with the species-specific phenologies of flight patterns of butterflies in Switzerland for the purpose of estimating regional differences in biodiversity.

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

NASA Astrophysics Data System (ADS)

Krot, Alexander M.

2008-09-01

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

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Pilot-Wave Hydrodynamics

NASA Astrophysics Data System (ADS)

Bush, John W. M.

2015-01-01

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie's original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.

Relationship between microscopic dynamics in traffic flow and complexity in networks.

PubMed

Li, Xin-Gang; Gao, Zi-You; Li, Ke-Ping; Zhao, Xiao-Mei

2007-07-01

Complex networks are constructed in the evolution process of traffic flow, and the states of traffic flow are represented by nodes in the network. The traffic dynamics can then be studied by investigating the statistical properties of those networks. According to Kerner's three-phase theory, there are two different phases in congested traffic, synchronized flow and wide moving jam. In the framework of this theory, we study different properties of synchronized flow and moving jam in relation to complex network. Scale-free network is constructed in stop-and-go traffic, i.e., a sequence of moving jams [Chin. Phys. Lett. 10, 2711 (2005)]. In this work, the networks generated in synchronized flow are investigated in detail. Simulation results show that the degree distribution of the networks constructed in synchronized flow has two power law regions, so the distinction in topological structure can really reflect the different dynamics in traffic flow. Furthermore, the real traffic data are investigated by this method, and the results are consistent with the simulations.

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

NASA Astrophysics Data System (ADS)

Cui, Ping

The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.

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

PubMed

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

2018-05-04

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

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Statistical physics of balance theory

PubMed Central

Belaza, Andres M.; Hoefman, Kevin; Bramson, Aaron; van den Heuvel, Milan; Schoors, Koen

2017-01-01

Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads’ incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the “agents” involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data. PMID:28846726

Statistical physics of balance theory.

PubMed

Belaza, Andres M; Hoefman, Kevin; Ryckebusch, Jan; Bramson, Aaron; van den Heuvel, Milan; Schoors, Koen

2017-01-01

Triadic relationships are accepted to play a key role in the dynamics of social and political networks. Building on insights gleaned from balance theory in social network studies and from Boltzmann-Gibbs statistical physics, we propose a model to quantitatively capture the dynamics of the four types of triadic relationships in a network. Central to our model are the triads' incidence rates and the idea that those can be modeled by assigning a specific triadic energy to each type of triadic relation. We emphasize the role of the degeneracy of the different triads and how it impacts the degree of frustration in the political network. In order to account for a persistent form of disorder in the formation of the triadic relationships, we introduce the systemic variable temperature. In order to learn about the dynamics and motives, we propose a generic Hamiltonian with three terms to model the triadic energies. One term is connected with a three-body interaction that captures balance theory. The other terms take into account the impact of heterogeneity and of negative edges in the triads. The validity of our model is tested on four datasets including the time series of triadic relationships for the standings between two classes of alliances in a massively multiplayer online game (MMOG). We also analyze real-world data for the relationships between the "agents" involved in the Syrian civil war, and in the relations between countries during the Cold War era. We find emerging properties in the triadic relationships in a political network, for example reflecting itself in a persistent hierarchy between the four triadic energies, and in the consistency of the extracted parameters from comparing the model Hamiltonian to the data.

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

PubMed

Freed, Karl F

2014-10-14

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

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

NASA Astrophysics Data System (ADS)

Freed, Karl F.

2014-10-01

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

Time-dependence of graph theory metrics in functional connectivity analysis

PubMed Central

Chiang, Sharon; Cassese, Alberto; Guindani, Michele; Vannucci, Marina; Yeh, Hsiang J.; Haneef, Zulfi; Stern, John M.

2016-01-01

Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations. PMID:26518632

Time-dependence of graph theory metrics in functional connectivity analysis.

PubMed

Chiang, Sharon; Cassese, Alberto; Guindani, Michele; Vannucci, Marina; Yeh, Hsiang J; Haneef, Zulfi; Stern, John M

2016-01-15

Brain graphs provide a useful way to computationally model the network structure of the connectome, and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level. The majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity. However, recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan. In this study, we investigate the stationarity of brain network topology using a Bayesian hidden Markov model (HMM) approach that estimates the dynamic structure of graph theoretical measures of whole-brain functional connectivity. In addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures, we propose two estimators of temporal stationarity: the S-index and N-index. These indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures. We apply the method and proposed estimators to resting-state functional MRI data from healthy controls and patients with temporal lobe epilepsy. Our analysis shows that several graph theory measures, including small-world index, global integration measures, and betweenness centrality, may exhibit greater stationarity over time and therefore be more robust. Additionally, we demonstrate that accounting for subject-level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states. Our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity, and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations. Copyright © 2015 Elsevier Inc. All rights reserved.

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

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

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

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

Networks and the Epidemiology of Infectious Disease

PubMed Central

Danon, Leon; Ford, Ashley P.; House, Thomas; Jewell, Chris P.; Keeling, Matt J.; Roberts, Gareth O.; Ross, Joshua V.; Vernon, Matthew C.

2011-01-01

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues. PMID:21437001

Exploring the String Landscape: The Dynamics, Statistics, and Cosmology of Parallel Worlds

NASA Astrophysics Data System (ADS)

Ahlqvist, Stein Pontus

This dissertation explores various facets of the low-energy solutions in string theory known as the string landscape. Three separate questions are addressed - the tunneling dynamics between these vacua, the statistics of their location in moduli space, and the potential realization of slow-roll inflation in the flux potentials generated in string theory. We find that the tunneling transitions that occur between a certain class of supersymmetric vacua related to each other via monodromies around the conifold point are sensitive to the details of warping in the near-conifold regime. We also study the impact of warping on the distribution of vacua near the conifold and determine that while previous work has concluded that the conifold point acts as an accumulation point for vacua, warping highly dilutes the distribution in precisely this regime. Finally we investigate a novel form of inflation dubbed spiral inflation to see if it can be realized near the conifold point. We conclude that for our particular models, spiral inflation seems to rely on a de Sitter-like vacuum energy. As a result, whenever spiral inflation is realized, the inflation is actually driven by a vacuum energy.

Statistical inference to advance network models in epidemiology.

PubMed

Welch, David; Bansal, Shweta; Hunter, David R

2011-03-01

Contact networks are playing an increasingly important role in the study of epidemiology. Most of the existing work in this area has focused on considering the effect of underlying network structure on epidemic dynamics by using tools from probability theory and computer simulation. This work has provided much insight on the role that heterogeneity in host contact patterns plays on infectious disease dynamics. Despite the important understanding afforded by the probability and simulation paradigm, this approach does not directly address important questions about the structure of contact networks such as what is the best network model for a particular mode of disease transmission, how parameter values of a given model should be estimated, or how precisely the data allow us to estimate these parameter values. We argue that these questions are best answered within a statistical framework and discuss the role of statistical inference in estimating contact networks from epidemiological data. Copyright © 2011 Elsevier B.V. All rights reserved.

Moving From Static to Dynamic Models of the Onset of Mental Disorder: A Review.

PubMed

Nelson, Barnaby; McGorry, Patrick D; Wichers, Marieke; Wigman, Johanna T W; Hartmann, Jessica A

2017-05-01

In recent years, there has been increased focus on subthreshold stages of mental disorders, with attempts to model and predict which individuals will progress to full-threshold disorder. Given this research attention and the clinical significance of the issue, this article analyzes the assumptions of the theoretical models in the field. Psychiatric research into predicting the onset of mental disorder has shown an overreliance on one-off sampling of cross-sectional data (ie, a snapshot of clinical state and other risk markers) and may benefit from taking dynamic changes into account in predictive modeling. Cross-disciplinary approaches to complex system structures and changes, such as dynamical systems theory, network theory, instability mechanisms, chaos theory, and catastrophe theory, offer potent models that can be applied to the emergence (or decline) of psychopathology, including psychosis prediction, as well as to transdiagnostic emergence of symptoms. Psychiatric research may benefit from approaching psychopathology as a system rather than as a category, identifying dynamics of system change (eg, abrupt vs gradual psychosis onset), and determining the factors to which these systems are most sensitive (eg, interpersonal dynamics and neurochemical change) and the individual variability in system architecture and change. These goals can be advanced by testing hypotheses that emerge from cross-disciplinary models of complex systems. Future studies require repeated longitudinal assessment of relevant variables through either (or a combination of) micro-level (momentary and day-to-day) and macro-level (month and year) assessments. Ecological momentary assessment is a data collection technique appropriate for micro-level assessment. Relevant statistical approaches are joint modeling and time series analysis, including metric-based and model-based methods that draw on the mathematical principles of dynamical systems. This next generation of prediction studies may more accurately model the dynamic nature of psychopathology and system change as well as have treatment implications, such as introducing a means of identifying critical periods of risk for mental state deterioration.

Response formulae for n-point correlations in statistical mechanical systems and application to a problem of coarse graining

NASA Astrophysics Data System (ADS)

Lucarini, Valerio; Wouters, Jeroen

2017-09-01

Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories allow to construct operators describing the smooth change of the invariant measure of the system of interest as a function of the small parameter controlling the intensity of the perturbation. In particular, response theories can be developed both for stochastic and chaotic deterministic dynamical systems, where in the latter case stricter conditions imposing some degree of structural stability are required. In this paper we extend previous findings and derive general response formulae describing how n- point correlations are affected by perturbations to the vector flow. We also show how to compute the response of the spectral properties of the system to perturbations. We then apply our results to the seemingly unrelated problem of coarse graining in multiscale systems: we find explicit formulae describing the change in the terms describing the parameterisation of the neglected degrees of freedom resulting from applying perturbations to the full system. All the terms envisioned by the Mori-Zwanzig theory—the deterministic, stochastic, and non-Markovian terms—are affected at first order in the perturbation. The obtained results provide a more comprehensive understanding of the response of statistical mechanical systems to perturbations. They also contribute to the goal of constructing accurate and robust parameterisations and are of potential relevance for fields like molecular dynamics, condensed matter, and geophysical fluid dynamics. We envision possible applications of our general results to the study of the response of climate variability to anthropogenic and natural forcing and to the study of the equivalence of thermostatted statistical mechanical systems.

Universality of clone dynamics during tissue development

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Molecular dynamics study of the conformational properties of cyclohexadecane

NASA Astrophysics Data System (ADS)

Zhang, Renshi; Mattice, Wayne L.

1993-06-01

Molecular dynamics has been used for the first time for the study of the conformational properties of cyclohexadecane, c-C16H32. By analyzing a long molecular dynamics trajectory (14.5 ns) at 450 K, equilibrium statistics such as the relative populations of different isomeric conformers and the probability ratios, p(gt)/p(tt), p(gg)/p(tt), and p(gg)/p(gtg), of different conformational segments, have been studied. The dynamic properties including the transition modes of gauche migration and gauche-pair creation, which have been reported before in n-alkanes, and the auto- and cross-correlations of the bond dihedral angles, have also been obtained. It was possible to make direct comparisons on some of the statistics with theory and experiment. Most of the results extracted from the molecular dynamics trajectory lie in between previously reported experimental and theoretical values. Many previously predicted conformers have been confirmed by our simulations. The results of the population probability of the most populated conformer seems to suggest that an earlier discrepancy between the theoretical works and an experimental work originates from insufficient samplings in earlier theoretical works, rather than from their inaccurate force field.

Quantum signature of chaos and thermalization in the kicked Dicke model

NASA Astrophysics Data System (ADS)

Ray, S.; Ghosh, A.; Sinha, S.

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Quantum signature of chaos and thermalization in the kicked Dicke model.

PubMed

Ray, S; Ghosh, A; Sinha, S

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Influences of system uncertainties on the numerical transfer path analysis of engine systems

NASA Astrophysics Data System (ADS)

Acri, A.; Nijman, E.; Acri, A.; Offner, G.

2017-10-01

Practical mechanical systems operate with some degree of uncertainty. In numerical models uncertainties can result from poorly known or variable parameters, from geometrical approximation, from discretization or numerical errors, from uncertain inputs or from rapidly changing forcing that can be best described in a stochastic framework. Recently, random matrix theory was introduced to take parameter uncertainties into account in numerical modeling problems. In particular in this paper, Wishart random matrix theory is applied on a multi-body dynamic system to generate random variations of the properties of system components. Multi-body dynamics is a powerful numerical tool largely implemented during the design of new engines. In this paper the influence of model parameter variability on the results obtained from the multi-body simulation of engine dynamics is investigated. The aim is to define a methodology to properly assess and rank system sources when dealing with uncertainties. Particular attention is paid to the influence of these uncertainties on the analysis and the assessment of the different engine vibration sources. Examples of the effects of different levels of uncertainties are illustrated by means of examples using a representative numerical powertrain model. A numerical transfer path analysis, based on system dynamic substructuring, is used to derive and assess the internal engine vibration sources. The results obtained from this analysis are used to derive correlations between parameter uncertainties and statistical distribution of results. The derived statistical information can be used to advance the knowledge of the multi-body analysis and the assessment of system sources when uncertainties in model parameters are considered.

Development of a Probabilistic Component Mode Synthesis Method for the Analysis of Non-Deterministic Substructures

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Ferri, Aldo A.

1995-01-01

Standard methods of structural dynamic analysis assume that the structural characteristics are deterministic. Recognizing that these characteristics are actually statistical in nature, researchers have recently developed a variety of methods that use this information to determine probabilities of a desired response characteristic, such as natural frequency, without using expensive Monte Carlo simulations. One of the problems in these methods is correctly identifying the statistical properties of primitive variables such as geometry, stiffness, and mass. This paper presents a method where the measured dynamic properties of substructures are used instead as the random variables. The residual flexibility method of component mode synthesis is combined with the probabilistic methods to determine the cumulative distribution function of the system eigenvalues. A simple cantilever beam test problem is presented that illustrates the theory.

Statistical Mechanics of Turbulent Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

On the degree distribution of horizontal visibility graphs associated with Markov processes and dynamical systems: diagrammatic and variational approaches

NASA Astrophysics Data System (ADS)

Lacasa, Lucas

2014-09-01

Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical time series analysis and signal processing and (ii) characterizing classes of dynamical systems and stochastic processes using the tools of graph theory. Recent works show that the degree distribution of these graphs encapsulates much information on the signals' variability, and therefore constitutes a fundamental feature for statistical learning purposes. However, exact solutions for the degree distributions are only known in a few cases, such as for uncorrelated random processes. Here we analytically explore these distributions in a list of situations. We present a diagrammatic formalism which computes for all degrees their corresponding probability as a series expansion in a coupling constant which is the number of hidden variables. We offer a constructive solution for general Markovian stochastic processes and deterministic maps. As case tests we focus on Ornstein-Uhlenbeck processes, fully chaotic and quasiperiodic maps. Whereas only for certain degree probabilities can all diagrams be summed exactly, in the general case we show that the perturbation theory converges. In a second part, we make use of a variational technique to predict the complete degree distribution for special classes of Markovian dynamics with fast-decaying correlations. In every case we compare the theory with numerical experiments.

Brane Physics in M-theory

NASA Astrophysics Data System (ADS)

Argurio, Riccardo

1998-07-01

The thesis begins with an introduction to M-theory (at a graduate student's level), starting from perturbative string theory and proceeding to dualities, D-branes and finally Matrix theory. The following chapter treats, in a self-contained way, of general classical p-brane solutions. Black and extremal branes are reviewed, along with their semi-classical thermodynamics. We then focus on intersecting extremal branes, the intersection rules being derived both with and without the explicit use of supersymmetry. The last three chapters comprise more advanced aspects of brane physics, such as the dynamics of open branes, the little theories on the world-volume of branes and how the four dimensional Schwarzschild black hole can be mapped to an extremal configuration of branes, thus allowing for a statistical interpretation of its entropy. The original results were already reported in hep-th/9701042, hep-th/9704190, hep-th/9710027 and hep-th/9801053.

Extracting neuronal functional network dynamics via adaptive Granger causality analysis.

PubMed

Sheikhattar, Alireza; Miran, Sina; Liu, Ji; Fritz, Jonathan B; Shamma, Shihab A; Kanold, Patrick O; Babadi, Behtash

2018-04-24

Quantifying the functional relations between the nodes in a network based on local observations is a key challenge in studying complex systems. Most existing time series analysis techniques for this purpose provide static estimates of the network properties, pertain to stationary Gaussian data, or do not take into account the ubiquitous sparsity in the underlying functional networks. When applied to spike recordings from neuronal ensembles undergoing rapid task-dependent dynamics, they thus hinder a precise statistical characterization of the dynamic neuronal functional networks underlying adaptive behavior. We develop a dynamic estimation and inference paradigm for extracting functional neuronal network dynamics in the sense of Granger, by integrating techniques from adaptive filtering, compressed sensing, point process theory, and high-dimensional statistics. We demonstrate the utility of our proposed paradigm through theoretical analysis, algorithm development, and application to synthetic and real data. Application of our techniques to two-photon Ca 2+ imaging experiments from the mouse auditory cortex reveals unique features of the functional neuronal network structures underlying spontaneous activity at unprecedented spatiotemporal resolution. Our analysis of simultaneous recordings from the ferret auditory and prefrontal cortical areas suggests evidence for the role of rapid top-down and bottom-up functional dynamics across these areas involved in robust attentive behavior.

Theory of chaos regularization of tunneling in chaotic quantum dots.

PubMed

Lee, Ming-Jer; Antonsen, Thomas M; Ott, Edward; Pecora, Louis M

2012-11-01

Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.

Synchronization and Causality Across Time-scales: Complex Dynamics and Extremes in El Niño/Southern Oscillation

NASA Astrophysics Data System (ADS)

Jajcay, N.; Kravtsov, S.; Tsonis, A.; Palus, M.

2017-12-01

A better understanding of dynamics in complex systems, such as the Earth's climate is one of the key challenges for contemporary science and society. A large amount of experimental data requires new mathematical and computational approaches. Natural complex systems vary on many temporal and spatial scales, often exhibiting recurring patterns and quasi-oscillatory phenomena. The statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding of underlying mechanisms and a key for modeling and prediction of such systems. This study introduces and applies information theory diagnostics to phase and amplitude time series of different wavelet components of the observed data that characterizes El Niño. A suite of significant interactions between processes operating on different time scales was detected, and intermittent synchronization among different time scales has been associated with the extreme El Niño events. The mechanisms of these nonlinear interactions were further studied in conceptual low-order and state-of-the-art dynamical, as well as statistical climate models. Observed and simulated interactions exhibit substantial discrepancies, whose understanding may be the key to an improved prediction. Moreover, the statistical framework which we apply here is suitable for direct usage of inferring cross-scale interactions in nonlinear time series from complex systems such as the terrestrial magnetosphere, solar-terrestrial interactions, seismic activity or even human brain dynamics.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Visceral obesity and psychosocial stress: a generalised control theory model

NASA Astrophysics Data System (ADS)

Wallace, Rodrick

2016-07-01

The linking of control theory and information theory via the Data Rate Theorem and its generalisations allows for construction of necessary conditions statistical models of body mass regulation in the context of interaction with a complex dynamic environment. By focusing on the stress-related induction of central obesity via failure of HPA axis regulation, we explore implications for strategies of prevention and treatment. It rapidly becomes evident that individual-centred biomedical reductionism is an inadequate paradigm. Without mitigation of HPA axis or related dysfunctions arising from social pathologies of power imbalance, economic insecurity, and so on, it is unlikely that permanent changes in visceral obesity for individuals can be maintained without constant therapeutic effort, an expensive - and likely unsustainable - public policy.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

PubMed

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

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).

Nodal portraits of quantum billiards: Domains, lines, and statistics

NASA Astrophysics Data System (ADS)

Jain, Sudhir Ranjan; Samajdar, Rhine

2017-10-01

This is a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and chaotic classical dynamics but also between different geometric shapes of the billiard system itself. How a random superposition of plane waves can model chaotic eigenfunctions is discussed and the connections of the complex morphology of the nodal lines thereof to percolation theory and Schramm-Loewner evolution are highlighted. Various approaches to counting the nodal domains—using trace formulas, graph theory, and difference equations—are also illustrated with examples. The nodal patterns addressed pertain to waves on vibrating plates and membranes, acoustic and electromagnetic modes, wave functions of a "particle in a box" as well as to percolating clusters, and domains in ferromagnets, thus underlining the diversity and far-reaching implications of the problem.

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

PubMed

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-12-24

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.

Kinetic exchange models: From molecular physics to social science

NASA Astrophysics Data System (ADS)

Patriarca, Marco; Chakraborti, Anirban

2013-08-01

We discuss several multi-agent models that have their origin in the kinetic exchange theory of statistical mechanics and have been recently applied to a variety of problems in the social sciences. This class of models can be easily adapted for simulations in areas other than physics, such as the modeling of income and wealth distributions in economics and opinion dynamics in sociology.

Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State

NASA Astrophysics Data System (ADS)

Stoop, Ruedi; Gomez, Florian

2016-07-01

The cochlea provides a biological information-processing paradigm that we are only beginning to understand in its full complexity. Our work reveals an interacting network of strongly nonlinear dynamical nodes, on which even a simple sound input triggers subnetworks of activated elements that follow power-law size statistics ("avalanches"). From dynamical systems theory, power-law size distributions relate to a fundamental ground state of biological information processing. Learning destroys these power laws. These results strongly modify the models of mammalian sound processing and provide a novel methodological perspective for understanding how the brain processes information.

Application of Statistical Thermodynamics To Predict the Adsorption Properties of Polypeptides in Reversed-Phase HPLC.

PubMed

Tarasova, Irina A; Goloborodko, Anton A; Perlova, Tatyana Y; Pridatchenko, Marina L; Gorshkov, Alexander V; Evreinov, Victor V; Ivanov, Alexander R; Gorshkov, Mikhail V

2015-07-07

The theory of critical chromatography for biomacromolecules (BioLCCC) describes polypeptide retention in reversed-phase HPLC using the basic principles of statistical thermodynamics. However, whether this theory correctly depicts a variety of empirical observations and laws introduced for peptide chromatography over the last decades remains to be determined. In this study, by comparing theoretical results with experimental data, we demonstrate that the BioLCCC: (1) fits the empirical dependence of the polypeptide retention on the amino acid sequence length with R(2) > 0.99 and allows in silico determination of the linear regression coefficients of the log-length correction in the additive model for arbitrary sequences and lengths and (2) predicts the distribution coefficients of polypeptides with an accuracy from 0.98 to 0.99 R(2). The latter enables direct calculation of the retention factors for given solvent compositions and modeling of the migration dynamics of polypeptides separated under isocratic or gradient conditions. The obtained results demonstrate that the suggested theory correctly relates the main aspects of polypeptide separation in reversed-phase HPLC.

Collective stimulated Brillouin backscatter

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel; Rose, Harvey

2007-11-01

We develop the statistical theory of linear collective stimulated Brillouin backscatter (CBSBS) in spatially and temporally incoherent laser beam. Instability is collective because it does not depend on the dynamics of isolated hot spots (speckles) of laser intensity, but rather depends on averaged laser beam intensity, optic f/#, and laser coherence time, Tc. CBSBS has a much larger threshold than a classical coherent beam's in long-scale-length high temperature plasma. It is a novel regime in which Tc is too large for applicability of well-known statistical theories (RPA) but Tc must be small enough to suppress single speckle processes such as self-focusing. Even if laser Tc is too large for a priori applicability of our theory, collective forward SBS^1, perhaps enhanced by high Z dopant, and its resultant self-induced Tc reduction, may regain the CBSBS regime. We identified convective and absolute CBSBS regimes. The threshold of convective instability is inside the typical parameter region of NIF designs. Well above incoherent threshold, the coherent instability growth rate is recovered. ^1 P.M. Lushnikov and H.A. Rose, Plasma Physics and Controlled Fusion, 48, 1501 (2006).

Statistical physics of community ecology: a cavity solution to MacArthur’s consumer resource model

NASA Astrophysics Data System (ADS)

Advani, Madhu; Bunin, Guy; Mehta, Pankaj

2018-03-01

A central question in ecology is to understand the ecological processes that shape community structure. Niche-based theories have emphasized the important role played by competition for maintaining species diversity. Many of these insights have been derived using MacArthur’s consumer resource model (MCRM) or its generalizations. Most theoretical work on the MCRM has focused on small ecosystems with a few species and resources. However theoretical insights derived from small ecosystems many not scale up to large ecosystems with many resources and species because large systems with many interacting components often display new emergent behaviors that cannot be understood or deduced from analyzing smaller systems. To address these shortcomings, we develop a statistical physics inspired cavity method to analyze MCRM when both the number of species and the number of resources is large. Unlike previous work in this limit, our theory addresses resource dynamics and resource depletion and demonstrates that species generically and consistently perturb their environments and significantly modify available ecological niches. We show how our cavity approach naturally generalizes niche theory to large ecosystems by accounting for the effect of collective phenomena on species invasion and ecological stability. Our theory suggests that such phenomena are a generic feature of large, natural ecosystems and must be taken into account when analyzing and interpreting community structure. It also highlights the important role that statistical-physics inspired approaches can play in furthering our understanding of ecology.

Statistical ecology comes of age.

PubMed

Gimenez, Olivier; Buckland, Stephen T; Morgan, Byron J T; Bez, Nicolas; Bertrand, Sophie; Choquet, Rémi; Dray, Stéphane; Etienne, Marie-Pierre; Fewster, Rachel; Gosselin, Frédéric; Mérigot, Bastien; Monestiez, Pascal; Morales, Juan M; Mortier, Frédéric; Munoz, François; Ovaskainen, Otso; Pavoine, Sandrine; Pradel, Roger; Schurr, Frank M; Thomas, Len; Thuiller, Wilfried; Trenkel, Verena; de Valpine, Perry; Rexstad, Eric

2014-12-01

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1-4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data.

Statistical ecology comes of age

PubMed Central

Gimenez, Olivier; Buckland, Stephen T.; Morgan, Byron J. T.; Bez, Nicolas; Bertrand, Sophie; Choquet, Rémi; Dray, Stéphane; Etienne, Marie-Pierre; Fewster, Rachel; Gosselin, Frédéric; Mérigot, Bastien; Monestiez, Pascal; Morales, Juan M.; Mortier, Frédéric; Munoz, François; Ovaskainen, Otso; Pavoine, Sandrine; Pradel, Roger; Schurr, Frank M.; Thomas, Len; Thuiller, Wilfried; Trenkel, Verena; de Valpine, Perry; Rexstad, Eric

2014-01-01

The desire to predict the consequences of global environmental change has been the driver towards more realistic models embracing the variability and uncertainties inherent in ecology. Statistical ecology has gelled over the past decade as a discipline that moves away from describing patterns towards modelling the ecological processes that generate these patterns. Following the fourth International Statistical Ecology Conference (1–4 July 2014) in Montpellier, France, we analyse current trends in statistical ecology. Important advances in the analysis of individual movement, and in the modelling of population dynamics and species distributions, are made possible by the increasing use of hierarchical and hidden process models. Exciting research perspectives include the development of methods to interpret citizen science data and of efficient, flexible computational algorithms for model fitting. Statistical ecology has come of age: it now provides a general and mathematically rigorous framework linking ecological theory and empirical data. PMID:25540151

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

Nunes, Rafael C.; Abreu, Everton M.C.; Neto, Jorge Ananias

Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there through non-gaussian statistical theories proposed by Tsallis and Kaniadakis. The effect of these non-gaussian statistics in the cosmological context is to change the strength of the gravitational constant. In this paper, we consider the w CDM model modified by the non-gaussian statistics and investigate the compatibility of these non-gaussian modificationmore » with the cosmological observations. In order to analyze in which extend the cosmological data constrain these non-extensive statistics, we will use type Ia supernovae, baryon acoustic oscillations, Hubble expansion rate function and the linear growth of matter density perturbations data. We show that Tsallis' statistics is favored at 1σ confidence level.« less

How to Compute Electron Ionization Mass Spectra from First Principles.

PubMed

Bauer, Christoph Alexander; Grimme, Stefan

2016-06-02

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

Quantum Information Biology: From Theory of Open Quantum Systems to Adaptive Dynamics

NASA Astrophysics Data System (ADS)

Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB re ects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.

Theory of relativistic Brownian motion: the (1+3) -dimensional case.

PubMed

Dunkel, Jörn; Hänggi, Peter

2005-09-01

A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions.

Wave kinetics of random fibre lasers

PubMed Central

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

2015-01-01

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

Hopping and the Stokes–Einstein relation breakdown in simple glass formers

PubMed Central

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-01-01

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition—like that of other statistical systems—is exact when the spatial dimension d→∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, d=2,3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses. PMID:25288722

Hopping and the Stokes-Einstein relation breakdown in simple glass formers.

PubMed

Charbonneau, Patrick; Jin, Yuliang; Parisi, Giorgio; Zamponi, Francesco

2014-10-21

One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition--like that of other statistical systems--is exact when the spatial dimension d → ∞, the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions,d = 2, 3. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes-Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

Mean Field Analysis of Large-Scale Interacting Populations of Stochastic Conductance-Based Spiking Neurons Using the Klimontovich Method

NASA Astrophysics Data System (ADS)

Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.

2017-03-01

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.

Statistical Equilibria of Turbulence on Surfaces of Different Symmetry

NASA Astrophysics Data System (ADS)

Qi, Wanming; Marston, Brad

2012-02-01

We test the validity of statistical descriptions of freely decaying 2D turbulence by performing direct numerical simulations (DNS) of the Euler equation with hyperviscosity on a square torus and on a sphere. DNS shows, at long times, a dipolar coherent structure in the vorticity field on the torus but a quadrapole on the sphereootnotetextJ. Y-K. Cho and L. Polvani, Phys. Fluids 8, 1531 (1996).. A truncated Miller-Robert-Sommeria theoryootnotetextA. J. Majda and X. Wang, Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows (Cambridge University Press, 2006). can explain the difference. The theory conserves up to the second-order Casimir, while also respecting conservation laws that reflect the symmetry of the domain. We further show that it is equivalent to the phenomenological minimum-enstrophy principle by generalizing the work by Naso et al.ootnotetextA. Naso, P. H. Chavanis, and B. Dubrulle, Eur. Phys. J. B 77, 284 (2010). to the sphere. To explain finer structures of the coherent states seen in DNS, especially the phenomenon of confinement, we investigate the perturbative inclusion of the higher Casimir constraints.

Critical behavior in earthquake energy dissipation

NASA Astrophysics Data System (ADS)

Wanliss, James; Muñoz, Víctor; Pastén, Denisse; Toledo, Benjamín; Valdivia, Juan Alejandro

2017-09-01

We explore bursty multiscale energy dissipation from earthquakes flanked by latitudes 29° S and 35.5° S, and longitudes 69.501° W and 73.944° W (in the Chilean central zone). Our work compares the predictions of a theory of nonequilibrium phase transitions with nonstandard statistical signatures of earthquake complex scaling behaviors. For temporal scales less than 84 hours, time development of earthquake radiated energy activity follows an algebraic arrangement consistent with estimates from the theory of nonequilibrium phase transitions. There are no characteristic scales for probability distributions of sizes and lifetimes of the activity bursts in the scaling region. The power-law exponents describing the probability distributions suggest that the main energy dissipation takes place due to largest bursts of activity, such as major earthquakes, as opposed to smaller activations which contribute less significantly though they have greater relative occurrence. The results obtained provide statistical evidence that earthquake energy dissipation mechanisms are essentially "scale-free", displaying statistical and dynamical self-similarity. Our results provide some evidence that earthquake radiated energy and directed percolation belong to a similar universality class.

Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics

NASA Astrophysics Data System (ADS)

Parker, Jeffrey B.

2018-05-01

Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows using quasilinear (QL) theories and the statistical framework of a second-order cumulant expansion (CE2). A geometrical-optics (GO) reduction of CE2, derived under an assumption of separation of scales between the fluctuations and the zonal flow, is studied here numerically. The reduced model, CE2-GO, has a similar phase-space mathematical structure to the traditional wave-kinetic equation, but that wave-kinetic equation has been shown to fail to preserve enstrophy conservation and to exhibit an ultraviolet catastrophe. CE2-GO, in contrast, preserves nonlinear conservation of both energy and enstrophy. We show here how to retain these conservation properties in a pseudospectral simulation of CE2-GO. We then present nonlinear simulations of CE2-GO and compare with direct simulations of quasilinear (QL) dynamics. We find that CE2-GO retains some similarities to QL. The partitioning of energy that resides in the zonal flow is in good quantitative agreement between CE2-GO and QL. On the other hand, the length scale of the zonal flow does not follow the same qualitative trend in the two models. Overall, these simulations indicate that CE2-GO provides a simpler and more tractable statistical paradigm than CE2, but CE2-GO is missing important physics.

Models for inference in dynamic metacommunity systems

USGS Publications Warehouse

Dorazio, R.M.; Kery, M.; Royle, J. Andrew; Plattner, M.

2010-01-01

A variety of processes are thought to be involved in the formation and dynamics of species assemblages. For example, various metacommunity theories are based on differences in the relative contributions of dispersal of species among local communities and interactions of species within local communities. Interestingly, metacommunity theories continue to be advanced without much empirical validation. Part of the problem is that statistical models used to analyze typical survey data either fail to specify ecological processes with sufficient complexity or they fail to account for errors in detection of species during sampling. In this paper, we describe a statistical modeling framework for the analysis of metacommunity dynamics that is based on the idea of adopting a unified approach, multispecies occupancy modeling, for computing inferences about individual species, local communities of species, or the entire metacommunity of species. This approach accounts for errors in detection of species during sampling and also allows different metacommunity paradigms to be specified in terms of species-and location-specific probabilities of occurrence, extinction, and colonization: all of which are estimable. In addition, this approach can be used to address inference problems that arise in conservation ecology, such as predicting temporal and spatial changes in biodiversity for use in making conservation decisions. To illustrate, we estimate changes in species composition associated with the species-specific phenologies of flight patterns of butterflies in Switzerland for the purpose of estimating regional differences in biodiversity. ?? 2010 by the Ecological Society of America.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

NASA Astrophysics Data System (ADS)

Boué, Laurent; Dasgupta, Ratul; Laurie, Jason; L'Vov, Victor; Nazarenko, Sergey; Procaccia, Itamar

2011-08-01

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett.JTPLA20021-364010.1134/S002136401008014X 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Correlated Fluctuations in Strongly Coupled Binary Networks Beyond Equilibrium

NASA Astrophysics Data System (ADS)

Dahmen, David; Bos, Hannah; Helias, Moritz

2016-07-01

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

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

DOE PAGES

Benedict, Lorin X.; Surh, Michael P.; Stanton, Liam G.; ...

2017-04-10

Here, we use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n = 10 26cm –3, T i = 10 5K, and 10 7 K < Te < 10 9K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealingmore » to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.« 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).

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

PubMed

Mezzasalma, Stefano A

2007-12-04

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

Understanding quantum measurement from the solution of dynamical models

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Balian, Roger; Nieuwenhuizen, Theo M.

2013-04-01

The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N≫1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrix Dˆ(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final state Dˆ(t) that involves correlations between the system and the indications of the pointer, thus ensuring registration. Although Dˆ(t) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrix Dˆ(t) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on models are suggested, while the statistical interpretation is promoted for teaching.

Short-term climate variability and atmospheric teleconnections from satellite-observed outgoing longwave radiation. I Simultaneous relationships. II - Lagged correlations

NASA Technical Reports Server (NTRS)

Lau, K.-M.; Chan, P. H.

1983-01-01

Attention is given to the low-frequency variability of outgoing longwave radiation (OLR) fluctuations, their possible correlations over different parts of the globe, and their relationships with teleconnections obtained from other meteorological parameters, for example, geopotential and temperature fields. Simultaneous relationships with respect to the Southern Oscillation (Namais, 1978; Barnett, 1981) signal and the reference OLR fluctuation over the equatorial central Pacific are investigated. Emphasis is placed on the relative importance of the Southern Oscillation (SO) signal over preferred regions. Using lag cross-correlation statistics, possible lagged relationships between the tropics and midlatitudes and their relationships with the SO are then investigated. Only features that are consistent with present knowledge of the dynamics of the system are emphasized. Certain features which may not meet rigorous statistical significance tests but yet are either expected a priori from independent observations or are predicted from dynamical theories are also explored.

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

NASA Astrophysics Data System (ADS)

Zhang, Rui; Schweizer, Kenneth S.

2017-05-01

We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a "slaved" or "constraint release" fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values.

Correlated matrix-fluctuation-mediated activated transport of dilute penetrants in glass-forming liquids and suspensions

PubMed Central

Schweizer, Kenneth S.

2017-01-01

We formulate a microscopic, force-level statistical mechanical theory for the activated diffusion of dilute penetrants in dense liquids, colloidal suspensions, and glasses. The approach explicitly and self-consistently accounts for coupling between penetrant hopping and matrix dynamic displacements that actively facilitate the hopping event. The key new ideas involve two mechanistically (at a stochastic trajectory level) coupled dynamic free energy functions for the matrix and spherical penetrant particles. A single dynamic coupling parameter quantifies how much the matrix displaces relative to the penetrant when the latter reaches its transition state which is determined via the enforcement of a temporal causality or coincidence condition. The theory is implemented for dilute penetrants smaller than the matrix particles, with or without penetrant-matrix attractive forces. Model calculations reveal a rich dependence of the penetrant diffusion constant and degree of dynamic coupling on size ratio, volume fraction, and attraction strength. In the absence of attractions, a near exponential decrease of penetrant diffusivity with size ratio over an intermediate range is predicted, in contrast to the much steeper, non-exponential variation if one assumes local matrix dynamical fluctuations are not correlated with penetrant motion. For sticky penetrants, the relative and absolute influence of caging versus physical bond formation is studied. The conditions for a dynamic crossover from the case where a time scale separation between penetrant and matrix activated hopping exists to a “slaved” or “constraint release” fully coupled regime are determined. The particle mixture model is mapped to treat experimental thermal systems and applied to make predictions for the diffusivity of water, toluene, methanol, and oxygen in polyvinylacetate liquids and glasses. The theory agrees well with experiment with values of the penetrant-matrix size ratio close to their chemically intuitive values. PMID:28527449

Decoherence and thermalization of a pure quantum state in quantum field theory.

PubMed

Giraud, Alexandre; Serreau, Julien

2010-06-11

We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure, coherent quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N expansion of the two-particle-irreducible effective action at next-to-leading order, which includes scattering and memory effects. We demonstrate that, restricting one's attention (or ability to measure) to a subset of the infinite hierarchy of correlation functions, one observes an effective loss of purity or coherence and, on longer time scales, thermalization. We point out that the physics of decoherence is well described by classical statistical field theory.

Statistical properties of the stock and credit market: RMT and network topology

NASA Astrophysics Data System (ADS)

Lim, Kyuseong; Kim, Min Jae; Kim, Sehyun; Kim, Soo Yong

We analyzed the dependence structure of the credit and stock market using random matrix theory and network topology. The dynamics of both markets have been spotlighted throughout the subprime crisis. In this study, we compared these two markets in view of the market-wide effect from random matrix theory and eigenvalue analysis. We found that the largest eigenvalue of the credit market as a whole preceded that of the stock market in the beginning of the financial crisis and that of two markets tended to be synchronized after the crisis. The correlation between the companies of both markets became considerably stronger after the crisis as well.

Granular compaction by fluidization

NASA Astrophysics Data System (ADS)

Tariot, Alexis; Gauthier, Georges; Gondret, Philippe

2017-06-01

How to arrange a packing of spheres is a scientific question that aroused many fundamental works since a long time from Kepler's conjecture to Edward's theory (S. F. Edwards and R.B.S Oakeshott. Theory of powders. Physica A, 157: 1080-1090, 1989), where the role traditionally played by the energy in statistical problems is replaced by the volume for athermal grains. We present experimental results on the compaction of a granular pile immersed in a viscous fluid when submited to a continuous or bursting upward flow. An initial fluidized bed leads to a well reproduced initial loose packing by the settling of grains when the high enough continuous upward flow is turned off. When the upward flow is then turned on again, we record the dynamical evolution of the bed packing. For a low enough continuous upward flow, below the critical velocity of fluidization, a slow compaction dynamics is observed. Strikingly, a slow compaction can be also observed in the case of "fluidization taps" with bursts of fluid velocity higher than the critical fluidization velocity. The different compaction dynamics is discussed when varying the different control parameters of these "fluidization taps".

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.

Constitutive Modeling, Nonlinear Behavior, and the Stress-Optic Law

DTIC Science & Technology

2011-01-01

estimates of D̂ from dynamic mechanical measurements. Some results are shown in Figure 58 for a filled EPDM rubber [116]. There is rough agreement with...elastomers and filler-reinforced rubber . 5.1 Linearity and the superposition principle The problem of analyzing viscoelastic mechanical behavior is greatly...deformation such as shear. For crosslinked rubber the strain can be defined in terms of the strain function suggested by the statistical theories of

Statistical-Mechanical Study of Polyvinylidene Fluoride.

DTIC Science & Technology

1984-06-01

been thoroughly investigated. The time-dependence and microscopic origin of the poling . over... .DO 9 0nt7 OF I 1oNOV GS IS OSMLETE UNCLASSIFIED 84 07...8217% ._-.’.\\ ,’a ,> . m - _’ . - . -. . ...--- , .:-. - 3 The dynamics of the process, known as poling , by which piezoelectric activity is induced...was also studied theoretically. The very short poling times, of the order of microseconds, predicted by the theory have since been confirmed

Ionization-potential depression and dynamical structure factor in dense plasmas

NASA Astrophysics Data System (ADS)

Lin, Chengliang; Röpke, Gerd; Kraeft, Wolf-Dietrich; Reinholz, Heidi

2017-07-01

The properties of a bound electron system immersed in a plasma environment are strongly modified by the surrounding plasma. The modification of an essential quantity, the ionization energy, is described by the electronic and ionic self-energies, including dynamical screening within the framework of the quantum statistical theory. Introducing the ionic dynamical structure factor as the indicator for the ionic microfield, we demonstrate that ionic correlations and fluctuations play a critical role in determining the ionization potential depression. This is, in particular, true for mixtures of different ions with large mass and charge asymmetry. The ionization potential depression is calculated for dense aluminum plasmas as well as for a CH plasma and compared to the experimental data and more phenomenological approaches used so far.

Ab Initio and Monte Carlo Approaches For the MagnetocaloricEffect in Co- and In-Doped Ni-Mn-Ga Heusler Alloys

NASA Astrophysics Data System (ADS)

Sokolovskiy, Vladimir; Grünebohm, Anna; Buchelnikov, Vasiliy; Entel, Peter

2014-09-01

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

Characterizing water-metal interfaces and machine learning potential energy surfaces

NASA Astrophysics Data System (ADS)

Ryczko, Kevin

In this thesis, we first discuss the fundamentals of ab initio electronic structure theory and density functional theory (DFT). We also discuss statistics related to computing thermodynamic averages of molecular dynamics (MD). We then use this theory to analyze and compare the structural, dynamical, and electronic properties of liquid water next to prototypical metals including platinum, graphite, and graphene. Our results are built on Born-Oppenheimer molecular dynamics (BOMD) generated using density functional theory (DFT) which explicitly include van der Waals (vdW) interactions within a first principles approach. All calculations reported use large simulation cells, allowing for an accurate treatment of the water-electrode interfaces. We have included vdW interactions through the use of the optB86b-vdW exchange correlation functional. Comparisons with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional are also shown. We find an initial peak, due to chemisorption, in the density profile of the liquid water-Pt interface not seen in the liquid water-graphite interface, liquid watergraphene interface, nor interfaces studied previously. To further investigate this chemisorption peak, we also report differences in the electronic structure of single water molecules on both Pt and graphite surfaces. We find that a covalent bond forms between the single water molecule and the platinum surface, but not between the single water molecule and the graphite surface. We also discuss the effects that defects and dopants in the graphite and graphene surfaces have on the structure and dynamics of liquid water. Lastly, we introduce artificial neural networks (ANNs), and demonstrate how they can be used to machine learn electronic structure calculations. As a proof of principle, we show the success of an ANN potential energy surfaces for a dimer molecule with a Lennard-Jones potential.

Low-Dimensional Materials for Optoelectronic and Bioelectronic Applications

NASA Astrophysics Data System (ADS)

Hong, Tu

In this thesis, we first discuss the fundamentals of ab initio electronic structure theory and density functional theory (DFT). We also discuss statistics related to computing thermodynamic averages of molecular dynamics (MD). We then use this theory to analyze and compare the structural, dynamical, and electronic properties of liquid water next to prototypical metals including platinum, graphite, and graphene. Our results are built on Born-Oppenheimer molecular dynamics (BOMD) generated using density functional theory (DFT) which explicitly include van der Waals (vdW) interactions within a first principles approach. All calculations reported use large simulation cells, allowing for an accurate treatment of the water-electrode interfaces. We have included vdW interactions through the use of the optB86b-vdW exchange correlation functional. Comparisons with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional are also shown. We find an initial peak, due to chemisorption, in the density profile of the liquid water-Pt interface not seen in the liquid water-graphite interface, liquid watergraphene interface, nor interfaces studied previously. To further investigate this chemisorption peak, we also report differences in the electronic structure of single water molecules on both Pt and graphite surfaces. We find that a covalent bond forms between the single water molecule and the platinum surface, but not between the single water molecule and the graphite surface. We also discuss the effects that defects and dopants in the graphite and graphene surfaces have on the structure and dynamics of liquid water. Lastly, we introduce artificial neural networks (ANNs), and demonstrate how they can be used to machine learn electronic structure calculations. As a proof of principle, we show the success of an ANN potential energy surfaces for a dimer molecule with a Lennard-Jones potential.

Internet dynamics

NASA Astrophysics Data System (ADS)

Lukose, Rajan Mathew

The World Wide Web and the Internet are rapidly expanding spaces, of great economic and social significance, which offer an opportunity to study many phenomena, often previously inaccessible, on an unprecedented scale and resolution with relative ease. These phenomena are measurable on the scale of tens of millions of users and hundreds of millions of pages. By virtue of nearly complete electronic mediation, it is possible in principle to observe the time and ``spatial'' evolution of nearly all choices and interactions. This cyber-space therefore provides a view into a number of traditional research questions (from many academic disciplines) and creates its own new phenomena accessible for study. Despite its largely self-organized and dynamic nature, a number of robust quantitative regularities are found in the aggregate statistics of interesting and useful quantities. These regularities can be understood with the help of models that draw on ideas from statistical physics as well as other fields such as economics, psychology and decision theory. This thesis develops models that can account for regularities found in the statistics of Internet congestion and user surfing patterns and discusses some practical consequences. practical consequences.

Large scale structure constraints for a class of f(R) theories of gravity

NASA Astrophysics Data System (ADS)

Abebe, Amare; de la Cruz-Dombriz, Álvaro; Dunsby, Peter K. S.

2013-08-01

Over the past few years much attention has been given to the study of modified gravity theories in order to find a more natural explanation for the late time acceleration of the Universe. Nevertheless, a comparison of the matter power spectrum predictions made by these theories with available data has not yet been subjected to a detailed analysis. In the context of f(R) theories of gravity we study the predicted power spectra using both a dynamical systems approach for the background and solving for the matter perturbations without using the quasistatic approximation, comparing the theoretical results with several Sloan Digital Sky Survey data. The importance of studying the first order perturbed equations by assuming the correct background evolution and the relevance of the initial conditions are also stressed. We determine the statistical significance in relation to the observational data and demonstrate their conflict with existing observations.

Instantaneous and scale-versatile gourdron theory: pair momentum equation, quasi-stability concept, and statistical indeterminacy revealing masses of elementary, bio-molecular, and cosmic particles

NASA Astrophysics Data System (ADS)

Naitoh, Ken

2014-04-01

Flexible particles, including hadrons, atoms, hydrated biological molecules, cells, organs containing water, liquid fuel droplets in engines, and stars commonly break up after becoming a gourd shape rather than that of a string; this leads to cyto-fluid dynamics that can explain the proliferation, differentiation, and replication of biomolecules, onto-biology that clarifies the relationship between information, structure, and function, and the gourd theory that clarifies masses, including quark-leptons and Plank energy. The masses are related to the super-magic numbers, including the asymmetric silver ratio and symmetric yamato ratio, and reveal further mechanisms underlying symmetry breaking. This paper gives further theoretical basis and evidence, because the gourd theory reported previously is a little analogical and instinctive.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

DOE PAGES

Aluie, Hussein; Hecht, Matthew; Vallis, Geoffrey K.

2017-11-14

A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This study describes how the framework can be applied to ocean flows.

A statistical dynamics approach to the study of human health data: Resolving population scale diurnal variation in laboratory data

NASA Astrophysics Data System (ADS)

Albers, D. J.; Hripcsak, George

2010-02-01

Statistical physics and information theory is applied to the clinical chemistry measurements present in a patient database containing 2.5 million patients' data over a 20-year period. Despite the seemingly naive approach of aggregating all patients over all times (with respect to particular clinical chemistry measurements), both a diurnal signal in the decay of the time-delayed mutual information and the presence of two sub-populations with differing health are detected. This provides a proof in principle that the highly fragmented data in electronic health records has potential for being useful in defining disease and human phenotypes.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

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

Aluie, Hussein; Hecht, Matthew; Vallis, Geoffrey K.

A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This study describes how the framework can be applied to ocean flows.

Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement

NASA Astrophysics Data System (ADS)

Roldán, Édgar; Gupta, Shamik

2017-08-01

We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.

MHD Turbulence and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

Shebalin, John V

2014-01-01

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Evolving faceted surfaces: From continuum modeling, to geometric simulation, to mean-field theory

NASA Astrophysics Data System (ADS)

Norris, Scott A.

We first consider the directional solidification, in two dimensions, of a dilute binary alloy having a large anisotropy of surface energy, where the sample is pulled in a high-energy direction such that the planar state is thermodynamically prohibited. Analyses including reduction of dynamics, matched asymptotic analysis, and energy minimization are used to show that the interface assumes a faceted profile with small wavelength. Questions on stability and other dynamic behavior lead to the derivation of a facet-velocity law. This shows the that faceted steady solutions are stable in the absence of constitutional supercooling, while in its presence, coarsening replaces cell formation as the mechanism of instability. We next proceed to introduce a computational-geometry tool which, given a facet-velocity law, performs large-scale simulations of fully-faceted coarsening surfaces, first in the special case with only three allowed facet orientations (threefold symmetry), and then for arbitrary surfaces. Topological events including coarsening are comprehensively considered, and are treated explicitly by our method using both a priori knowledge of event outcomes and a novel graph-rewriting algorithm. While careful attention must be paid to both non-unique topological events and the imposition of a discrete time-stepping scheme, the resulting method allows rapid simulation of large surfaces and easy extraction of statistical data. Example statistics are provided for the threefold case based on simulations totaling one million facets. Finally, a mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the LSW theory of Ostwald ripening in two-phase systems, but the mechanism of coarsening in faceted surfaces requires the derivation of additional terms to model the coalescence of facets. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a generic framework for the investigation of faceted surfaces evolving under arbitrary dynamics.

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.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

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.

Symmetry breaking in clogging for oppositely driven particles

NASA Astrophysics Data System (ADS)

Glanz, Tobias; Wittkowski, Raphael; Löwen, Hartmut

2016-11-01

The clogging behavior of a symmetric binary mixture of colloidal particles that are driven in opposite directions through constrictions is explored by Brownian dynamics simulations and theory. A dynamical state with a spontaneously broken symmetry occurs where one species is flowing and the other is blocked for a long time, which can be tailored by the size of the constrictions. Moreover, we find self-organized oscillations in clogging and unclogging of the two species. Apart from statistical physics, our results are of relevance for fields like biology, chemistry, and crowd management, where ions, microparticles, pedestrians, or other particles are driven in opposite directions through constrictions.

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

NASA Technical Reports Server (NTRS)

Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback

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

Tiana-Alsina, J.; Torrent, M. C.; Masoller, C.

Low-frequency fluctuations (LFFs) represent a dynamical instability that occurs in semiconductor lasers when they are operated near the lasing threshold and subject to moderate optical feedback. LFFs consist of sudden power dropouts followed by gradual, stepwise recoveries. We analyze experimental time series of intensity dropouts and quantify the complexity of the underlying dynamics employing two tools from information theory, namely, Shannon's entropy and the Martin, Plastino, and Rosso statistical complexity measure. These measures are computed using a method based on ordinal patterns, by which the relative length and ordering of consecutive interdropout intervals (i.e., the time intervals between consecutive intensitymore » dropouts) are analyzed, disregarding the precise timing of the dropouts and the absolute durations of the interdropout intervals. We show that this methodology is suitable for quantifying subtle characteristics of the LFFs, and in particular the transition to fully developed chaos that takes place when the laser's pump current is increased. Our method shows that the statistical complexity of the laser does not increase continuously with the pump current, but levels off before reaching the coherence collapse regime. This behavior coincides with that of the first- and second-order correlations of the interdropout intervals, suggesting that these correlations, and not the chaotic behavior, are what determine the level of complexity of the laser's dynamics. These results hold for two different dynamical regimes, namely, sustained LFFs and coexistence between LFFs and steady-state emission.« less

Statistics of rocky coast erosion and percolation theory

NASA Astrophysics Data System (ADS)

Baldassarri, A.; Sapoval, B.

2012-04-01

The dynamics of rocky coasts is an erratic phenomenon featuring numerous small erosion events, but sometimes large dramatic collapses. In this sense, its study should not limit or rely on average erosion rates. Recent studies, based on historical as well as recent data, have indicated that the frequency of magnitude of erosion events display long tail distribution, similar to what observed in landslide. In other words the time evolution of a coast morphology does not enter the classical category of Gaussian process, but rather that of critical systems in physics. We recently proposed a minimal dynamical model of rocky coast erosion which is able to reproduce the diversity of rocky coast morphologies and their dynamics. This model is based on a single, simple ingredient, the retroaction of the coast morphology on the erosive power of the sea. It follows from the idea that erosion can spontaneously create irregular seashores, but, in turn, the geometrical irregularity of the coast participates to the damping of sea-waves, decreasing the average wave amplitude and erosive power. The resulting mutual self-stabilization dynamics of the sea erosion power and coastal irregular morphology leads spontaneously the system to a critical dynamics. Our results indicate then that rocky coast erosion and the statistical theory of percolation are closely related. In this framework, the sometimes fractal geometry of coastlines can be recovered and understood in terms of fractal dimension of the external perimeter of a percolation cluster. From a more practical point of view, the analogy with percolation interfaces means that the coast constitutes a strong, but possibly fragile, barrier to sea erosion, emerging from a self-organised selection process. Accordingly, the effect of a slow weathering degradation of the rocks mechanical properties, as well as other perturbations from natural or human cause, can trigger random and large erosion events difficult to predict and control. To the extent that these ideas apply, natural coasts should be "preserved" and managed with care.

Statistical characterization of speckle noise in coherent imaging systems

NASA Astrophysics Data System (ADS)

Yaroslavsky, Leonid; Shefler, A.

2003-05-01

Speckle noise imposes fundamental limitation on image quality in coherent radiation based imaging and optical metrology systems. Speckle noise phenomena are associated with properties of objects to diffusely scatter irradiation and with the fact that in recording the wave field, a number of signal distortions inevitably occur due to technical limitations inherent to hologram sensors. The statistical theory of speckle noise was developed with regard to only limited resolving power of coherent imaging devices. It is valid only asymptotically as much as the central limit theorem of the probability theory can be applied. In applications this assumption is not always applicable. Moreover, in treating speckle noise problem one should also consider other sources of the hologram deterioration. In the paper, statistical properties of speckle due to the limitation of hologram size, dynamic range and hologram signal quantization are studied by Monte-Carlo simulation for holograms recorded in near and far diffraction zones. The simulation experiments have shown that, for limited resolving power of the imaging system, widely accepted opinion that speckle contrast is equal to one holds only for rather severe level of the hologram size limitation. For moderate limitations, speckle contrast changes gradually from zero for no limitation to one for limitation to less than about 20% of hologram size. The results obtained for the limitation of the hologram sensor"s dynamic range and hologram signal quantization reveal that speckle noise due to these hologram signal distortions is not multiplicative and is directly associated with the severity of the limitation and quantization. On the base of the simulation results, analytical models are suggested.

Statistical analysis of 4 types of neck whiplash injuries based on classical meridian theory.

PubMed

Chen, Yemeng; Zhao, Yan; Xue, Xiaolin; Li, Hui; Wu, Xiuyan; Zhang, Qunce; Zheng, Xin; Wang, Tianfang

2015-01-01

As one component of the Chinese medicine meridian system, the meridian sinew (Jingjin, (see text), tendino-musculo) is specially described as being for acupuncture treatment of the musculoskeletal system because of its dynamic attributes and tender point correlations. In recent decades, the therapeutic importance of the sinew meridian has become revalued in clinical application. Based on this theory, the authors have established therapeutic strategies of acupuncture treatment in Whiplash-Associated Disorders (WAD) by categorizing four types of neck symptom presentations. The advantage of this new system is to make it much easier for the clinician to find effective acupuncture points. This study attempts to prove the significance of the proposed therapeutic strategies by analyzing data collected from a clinical survey of various WAD using non-supervised statistical methods, such as correlation analysis, factor analysis, and cluster analysis. The clinical survey data have successfully verified discrete characteristics of four neck syndromes, based upon the range of motion (ROM) and tender point location findings. A summary of the relationships among the symptoms of the four neck syndromes has shown the correlation coefficient as having a statistical significance (P < 0.01 or P < 0.05), especially with regard to ROM. Furthermore, factor and cluster analyses resulted in a total of 11 categories of general symptoms, which implies syndrome factors are more related to the Liver, as originally described in classical theory. The hypothesis of meridian sinew syndromes in WAD is clearly supported by the statistical analysis of the clinical trials. This new discovery should be beneficial in improving therapeutic outcomes.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Neutral Theory and Scale-Free Neural Dynamics

NASA Astrophysics Data System (ADS)

Martinello, Matteo; Hidalgo, Jorge; Maritan, Amos; di Santo, Serena; Plenz, Dietmar; Muñoz, Miguel A.

2017-10-01

Neural tissues have been consistently observed to be spontaneously active and to generate highly variable (scale-free distributed) outbursts of activity in vivo and in vitro. Understanding whether these heterogeneous patterns of activity stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as criticality has been argued to entail many possible important functional advantages in biological computing systems. Here, we employ a well-accepted model for neural dynamics to elucidate an alternative scenario in which diverse neuronal avalanches, obeying scaling, can coexist simultaneously, even if the network operates in a regime far from the edge of any phase transition. We show that perturbations to the system state unfold dynamically according to a "neutral drift" (i.e., guided only by stochasticity) with respect to the background of endogenous spontaneous activity, and that such a neutral dynamics—akin to neutral theories of population genetics and of biogeography—implies marginal propagation of perturbations and scale-free distributed causal avalanches. We argue that causal information, not easily accessible to experiments, is essential to elucidate the nature and statistics of neural avalanches, and that neutral dynamics is likely to play an important role in the cortex functioning. We discuss the implications of these findings to design new empirical approaches to shed further light on how the brain processes and stores information.

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits

PubMed Central

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-01-01

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits. DOI: http://dx.doi.org/10.7554/eLife.10056.001 PMID:26705334

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

PubMed

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

2016-11-01

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

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.

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

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

Khrennikov, Andrei

2010-08-15

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

Dynamic Capacity and Surface Fatigue Life for Spur and Helical Gears

NASA Technical Reports Server (NTRS)

Coy, J. J.; Townsend, D. P.; Zaretsky, E. V.

1975-01-01

A mathematical model for surface fatigue life of gear, pinion, or entire meshing gear train is given. The theory is based on a previous statistical approach for rolling-element bearings. Equations are presented which give the dynamic capacity of the gear set. The dynamic capacity is the transmitted tangential load which gives a 90 percent probability of survival of the gear set for one million pinion revolutions. The analytical results are compared with test data for a set of AISI 9310 spur gears operating at a maximum Hertz stress of 1.71 billion N/sq m and 10,000 rpm. The theoretical life predictions are shown to be good when material constants obtained from rolling-element bearing tests were used in the gear life model.

Universality in the dynamical properties of seismic vibrations

NASA Astrophysics Data System (ADS)

Chatterjee, Soumya; Barat, P.; Mukherjee, Indranil

2018-02-01

We have studied the statistical properties of the observed magnitudes of seismic vibration data in discrete time in an attempt to understand the underlying complex dynamical processes. The observed magnitude data are taken from six different geographical locations. All possible magnitudes are considered in the analysis including catastrophic vibrations, foreshocks, aftershocks and commonplace daily vibrations. The probability distribution functions of these data sets obey scaling law and display a certain universality characteristic. To investigate the universality features in the observed data generated by a complex process, we applied Random Matrix Theory (RMT) in the framework of Gaussian Orthogonal Ensemble (GOE). For all these six places the observed data show a close fit with the predictions of RMT. This reinforces the idea of universality in the dynamical processes generating seismic vibrations.

Counting statistics of chaotic resonances at optical frequencies: Theory and experiments

NASA Astrophysics Data System (ADS)

Lippolis, Domenico; Wang, Li; Xiao, Yun-Feng

2017-07-01

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016), 10.1103/PhysRevE.93.040201].

An Examination of Application of Artificial Neural Network in Cognitive Radios

NASA Astrophysics Data System (ADS)

Bello Salau, H.; Onwuka, E. N.; Aibinu, A. M.

2013-12-01

Recent advancement in software radio technology has led to the development of smart device known as cognitive radio. This type of radio fuses powerful techniques taken from artificial intelligence, game theory, wideband/multiple antenna techniques, information theory and statistical signal processing to create an outstanding dynamic behavior. This cognitive radio is utilized in achieving diverse set of applications such as spectrum sensing, radio parameter adaptation and signal classification. This paper contributes by reviewing different cognitive radio implementation that uses artificial intelligence such as the hidden markov models, metaheuristic algorithm and artificial neural networks (ANNs). Furthermore, different areas of application of ANNs and their performance metrics based approach are also examined.

Power spectra as a diagnostic tool in probing statistical/nonstatistical behavior in unimolecular reactions

NASA Astrophysics Data System (ADS)

Chang, Xiaoyen Y.; Sewell, Thomas D.; Raff, Lionel M.; Thompson, Donald L.

1992-11-01

The possibility of utilizing different types of power spectra obtained from classical trajectories as a diagnostic tool to identify the presence of nonstatistical dynamics is explored by using the unimolecular bond-fission reactions of 1,2-difluoroethane and the 2-chloroethyl radical as test cases. In previous studies, the reaction rates for these systems were calculated by using a variational transition-state theory and classical trajectory methods. A comparison of the results showed that 1,2-difluoroethane is a nonstatistical system, while the 2-chloroethyl radical behaves statistically. Power spectra for these two systems have been generated under various conditions. The characteristics of these spectra are as follows: (1) The spectra for the 2-chloroethyl radical are always broader and more coupled to other modes than is the case for 1,2-difluoroethane. This is true even at very low levels of excitation. (2) When an internal energy near or above the dissociation threshold is initially partitioned into a local C-H stretching mode, the power spectra for 1,2-difluoroethane broaden somewhat, but discrete and somewhat isolated bands are still clearly evident. In contrast, the analogous power spectra for the 2-chloroethyl radical exhibit a near complete absence of isolated bands. The general appearance of the spectrum suggests a very high level of mode-to-mode coupling, large intramolecular vibrational energy redistribution (IVR) rates, and global statistical behavior. (3) The appearance of the power spectrum for the 2-chloroethyl radical is unaltered regardless of whether the initial C-H excitation is in the CH2 or the CH2Cl group. This result also suggests statistical behavior. These results are interpreted to mean that power spectra may be used as a diagnostic tool to assess the statistical character of a system. The presence of a diffuse spectrum exhibiting a nearly complete loss of isolated structures indicates that the dissociation dynamics of the molecule will be well described by statistical theories. If, however, the power spectrum maintains its discrete, isolated character, as is the case for 1,2-difluoroethane, the opposite conclusion is suggested. Since power spectra are very easily computed, this diagnostic method may prove to be useful.

String Theory Methods for Condensed Matter Physics

NASA Astrophysics Data System (ADS)

Nastase, Horatiu

2017-09-01

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

Addressing group dynamics in a brief motivational intervention for college student drinkers.

PubMed

Faris, Alexander S; Brown, Janice M

2003-01-01

Previous research indicates that brief motivational interventions for college student drinkers may be less effective in group settings than individual settings. Social psychological theories about counterproductive group dynamics may partially explain this finding. The present study examined potential problems with group motivational interventions by comparing outcomes from a standard group motivational intervention (SGMI; n = 25), an enhanced group motivational intervention (EGMI; n = 27) designed to suppress counterproductive processes, and a no intervention control (n = 23). SGMI and EGMI participants reported disruptive group dynamics as evidenced by low elaboration likelihood, production blocking, and social loafing, though the level of disturbance was significantly lower for EGMI individuals (p = .001). Despite counteracting group dynamics in the EGMI condition, participants in the two interventions were statistically similar in post-intervention problem recognition and future drinking intentions. The results raise concerns over implementing individually-based interventions in group settings without making necessary adjustments.

Molecular dynamics simulation of melting of 2D glassy monatomic system

NASA Astrophysics Data System (ADS)

Nhu Tranh, Duong Thi; Van Hoang, Vo; Thu Hanh, Tran Thi

2018-01-01

The melting of two-dimensional (2D) glassy monatomic systems is studied using the molecular dynamics simulation with Lennard-Jones-Gauss interaction potential. The temperature dependence of various structural and dynamical properties of the systems during heating is analyzed and discussed via the radial distribution functions, the coordination number distributions, the ring statistics, the mobility of atoms and their clustering. Atomic mechanism of melting is also analyzed via tendency to increase mobility and breaking clusters of atoms upon heating. We found that melting of a 2D glass does not follow any theory of the melting of 2D crystals proposed in the past. The melting exhibits a homogeneous nature, i.e. liquid-like atoms occur homogeneously throughout the system and melting proceeds further leading to the formation of an entire liquid phase. In addition, we found a defined transition temperature region in which structural and dynamical properties of systems strongly change with increasing temperature.

Rethinking wave-kinetic theory applied to zonal flows

NASA Astrophysics Data System (ADS)

Parker, Jeffrey

2017-10-01

Over the past two decades, a number of studies have employed a wave-kinetic theory to describe fluctuations interacting with zonal flows. Recent work has uncovered a defect in this wave-kinetic formulation: the system is dominated by the growth of (arbitrarily) small-scale zonal structures. Theoretical calculations of linear growth rates suggest, and nonlinear simulations confirm, that this system leads to the concentration of zonal flow energy in the smallest resolved scales, irrespective of the numerical resolution. This behavior results from the assumption that zonal flows are extremely long wavelength, leading to the neglect of key terms responsible for conservation of enstrophy. A corrected theory, CE2-GO, is presented; it is free of these errors yet preserves the intuitive phase-space mathematical structure. CE2-GO properly conserves enstrophy as well as energy, and yields accurate growth rates of zonal flow. Numerical simulations are shown to be well-behaved and not dependent on box size. The steady-state limit simplifies into an exact wave-kinetic form which offers the promise of deeper insight into the behavior of wavepackets. The CE2-GO theory takes its place in a hierarchy of models as the geometrical-optics reduction of the more complete cumulant-expansion statistical theory CE2. The new theory represents the minimal statistical description, enabling an intuitive phase-space formulation and an accurate description of turbulence-zonal flow dynamics. This work was supported by an NSF Graduate Research Fellowship, a US DOE Fusion Energy Sciences Fellowship, and US DOE Contract Nos. DE-AC52-07NA27344 and DE-AC02-09CH11466.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

Strongly coupled gauge theories: What can lattice calculations teach us?

NASA Astrophysics Data System (ADS)

Hasenfratz, A.; Brower, R. C.; Rebbi, C.; Weinberg, E.; Witzel, O.

2017-12-01

The dynamical origin of electroweak symmetry breaking is an open question with many possible theoretical explanations. Strongly coupled systems predicting the Higgs boson as a bound state of a new gauge-fermion interaction form one class of candidate models. Due to increased statistics, LHC run II will further constrain the phenomenologically viable models in the near future. In the meanwhile it is important to understand the general properties and specific features of the different competing models. In this work we discuss many-flavor gauge-fermion systems that contain both massless (light) and massive fermions. The former provide Goldstone bosons and trigger electroweak symmetry breaking, while the latter indirectly influence the infrared dynamics. Numerical results reveal that such systems can exhibit a light 0++ isosinglet scalar, well separated from the rest of the spectrum. Further, when we set the scale via the vev of electroweak symmetry breaking, we predict a 2 TeV vector resonance which could be a generic feature of SU(3) gauge theories.

Attractive versus repulsive interactions in the Bose-Einstein condensation dynamics of relativistic field theories

NASA Astrophysics Data System (ADS)

Berges, J.; Boguslavski, K.; Chatrchyan, A.; Jaeckel, J.

2017-10-01

We study the impact of attractive self-interactions on the nonequilibrium dynamics of relativistic quantum fields with large occupancies at low momenta. Our primary focus is on Bose-Einstein condensation and nonthermal fixed points in such systems. For a model system, we consider O (N ) -symmetric scalar field theories. We use classical-statistical real-time simulations as well as a systematic 1 /N expansion of the quantum (two-particle-irreducible) effective action to next-to-leading order. When the mean self-interactions are repulsive, condensation occurs as a consequence of a universal inverse particle cascade to the zero-momentum mode with self-similar scaling behavior. For attractive mean self-interactions, the inverse cascade is absent, and the particle annihilation rate is enhanced compared to the repulsive case, which counteracts the formation of coherent field configurations. For N ≥2 , the presence of a nonvanishing conserved charge can suppress number-changing processes and lead to the formation of stable localized charge clumps, i.e., Q balls.

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons.

PubMed

Mensi, Skander; Hagens, Olivier; Gerstner, Wulfram; Pozzorini, Christian

2016-02-01

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter--describing somatic integration--and the spike-history filter--accounting for spike-frequency adaptation--dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na+-channel inactivation regulate the sensitivity to rapid input fluctuations.

BIG DATA AND STATISTICS

PubMed Central

Rossell, David

2016-01-01

Big Data brings unprecedented power to address scientific, economic and societal issues, but also amplifies the possibility of certain pitfalls. These include using purely data-driven approaches that disregard understanding the phenomenon under study, aiming at a dynamically moving target, ignoring critical data collection issues, summarizing or preprocessing the data inadequately and mistaking noise for signal. We review some success stories and illustrate how statistical principles can help obtain more reliable information from data. We also touch upon current challenges that require active methodological research, such as strategies for efficient computation, integration of heterogeneous data, extending the underlying theory to increasingly complex questions and, perhaps most importantly, training a new generation of scientists to develop and deploy these strategies. PMID:27722040

Poincaré resonances and the limits of trajectory dynamics.

PubMed Central

Petrosky, T; Prigogine, I

1993-01-01

In previous papers we have shown that the elimination of the resonance divergences in large Poincare systems leads to complex irreducible spectral representations for the Liouville-von Neumann operator. Complex means that time symmetry is broken and irreducibility means that this representation is implementable only by statistical ensembles and not by trajectories. We consider in this paper classical potential scattering. Our theory applies to persistent scattering. Numerical simulations show quantitative agreement with our predictions. PMID:11607428

Molecular dynamics studies of the thermal decomposition of 2,3-diazabicyclo(2.2.1)hept-2-ene

NASA Astrophysics Data System (ADS)

Sorescu, Dan C.; Thompson, Donald L.; Raff, Lionel M.

1995-05-01

The reaction dynamics of the thermal gas-phase decomposition of 2,3-diazabicyclo (2.2.1)hept-2-ene-exo, exo-5,6-d2 have been investigated using classical trajectory methods on a semiempirical potential-energy surface. The global potential is written as a superposition of different reaction channel potentials containing bond stretching, bending and torsional terms, connected by parametrized switching functions. Reaction channels for stepwise and concerted cleavage of the two C-N bonds of the reactant have both been considered in construction of the potential. The geometries of 2,3-diazabicyclo(2.2.1)hept-2-ene, the diazenyl biradical and of the transition state corresponding to breaking of the remaining C-N bond of diazenyl biradical have been determined at the second order Möller-Plesset perturbation theory (MP2/6-31G*) and at Hartree-Fock (HF/6-31G*) levels, respectively. The bond dissociation energies have been estimated using the available thermochemical data and previously reported results for bicyclo(2.1.0)pentane [J. Chem. Phys. 101, 3729 (1994)]. The equilibrium geometries predicted by the semiempirical potential for reactants and products, the barrier height for thermal nitrogen extrusion from 2,3-diazabicyclo(2.2.1)hept-2-ene and the fundamental vibrational frequencies are in good to excellent agreement with the measured or ab initio calculated values. Using a projection method of the instantaneous Cartesian velocities onto the normal mode vectors and classical trajectory calculations, the dissociation dynamics of 2,3-diazabicyclo(2.2.1)hept-2-ene-exo, exo-5,6-d2 are investigated at several excitation energies in the range 60-175 kcal/mol. The results show the following: (1) The thermal reaction takes place with a preference for inversion of configuration in the reaction products, the exo-labeled bicyclo(2.1.0) pentane being the major product. The exo/endo ratio of bicyclo(2.1.0) pentane isomers is found to vary between 1.8-2.2 for the energy range considered. (2) For random energization of the vibrational modes, the energy dependence of the rate coefficients can be described by a RRK expression. (3) The significant broadening and overlapping of the power spectral bands, together with the disappearance of characteristic features in the power spectra of the internal coordinates calculated at different energies, indicate high intramolecular vibrational redistribution rates and global statistical behavior. (4) The energy partitioning among products shows that the internal energy is preferentially distributed into the vibrational degrees of freedom in BCP, while N2 is formed with small amounts of rotational and vibrational energies. Overall, the distribution of energy among the product degrees of freedom follows statistical predictions in the internal energy range investigated. (5) Stepwise dissociation of the C-N bonds is the predominant mechanism which characterizes the N2 elimination from the parent molecule. (6) Although statistical theories of reaction rates, such as Rice-Ramsperger-Kassel-Marcus (RRKM) theory, are unable to predict the product exo/endo ratio, this is not a result of the breakdown of the statistical assumption inherent in these theories, but rather to the fact that statistical theory does not address mechanistic questions related to post transition-state events. Although the results show that there is a near microcanonical distribution of energy in the 1,3-cyclopentanediyl radical, the system does not have sufficient time to explore all of the energetically accessible configuration space prior to the closure of the 1-3 bridgehead bond. The result is a nonstatistical exo/endo product ratio that deviates from the statistically expected result of unity.

Meso-scale turbulence in living fluids

PubMed Central

Wensink, Henricus H.; Dunkel, Jörn; Heidenreich, Sebastian; Drescher, Knut; Goldstein, Raymond E.; Löwen, Hartmut; Yeomans, Julia M.

2012-01-01

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium 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. Here, 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. PMID:22908244

Meso-scale turbulence in living fluids.

PubMed

Wensink, Henricus H; Dunkel, Jörn; Heidenreich, Sebastian; Drescher, Knut; Goldstein, Raymond E; Löwen, Hartmut; Yeomans, Julia M

2012-09-04

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium 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. Here, 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.

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.

The knowledge instinct, cognitive algorithms, modeling of language and cultural evolution

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2008-04-01

The talk discusses mechanisms of the mind and their engineering applications. The past attempts at designing "intelligent systems" encountered mathematical difficulties related to algorithmic complexity. The culprit turned out to be logic, which in one way or another was used not only in logic rule systems, but also in statistical, neural, and fuzzy systems. Algorithmic complexity is related to Godel's theory, a most fundamental mathematical result. These difficulties were overcome by replacing logic with a dynamic process "from vague to crisp," dynamic logic. It leads to algorithms overcoming combinatorial complexity, and resulting in orders of magnitude improvement in classical problems of detection, tracking, fusion, and prediction in noise. I present engineering applications to pattern recognition, detection, tracking, fusion, financial predictions, and Internet search engines. Mathematical and engineering efficiency of dynamic logic can also be understood as cognitive algorithm, which describes fundamental property of the mind, the knowledge instinct responsible for all our higher cognitive functions: concepts, perception, cognition, instincts, imaginations, intuitions, emotions, including emotions of the beautiful. I present our latest results in modeling evolution of languages and cultures, their interactions in these processes, and role of music in cultural evolution. Experimental data is presented that support the theory. Future directions are outlined.

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

PubMed

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

2015-04-07

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

Effect of correction of aberration dynamics on chaos in human ocular accommodation.

PubMed

Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

2013-11-15

We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

Stalactite growth as a free-boundary problem: a geometric law and its platonic ideal.

PubMed

Short, Martin B; Baygents, James C; Beck, J Warren; Stone, David A; Toomey, Rickard S; Goldstein, Raymond E

2005-01-14

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.

Longitudinal flying qualities criteria for single-pilot instrument flight operations

NASA Technical Reports Server (NTRS)

Stengel, R. F.; Bar-Gill, A.

1983-01-01

Modern estimation and control theory, flight testing, and statistical analysis were used to deduce flying qualities criteria for General Aviation Single Pilot Instrument Flight Rule (SPIFR) operations. The principal concern is that unsatisfactory aircraft dynamic response combined with high navigation/communication workload can produce problems of safety and efficiency. To alleviate these problems. The relative importance of these factors must be determined. This objective was achieved by flying SPIFR tasks with different aircraft dynamic configurations and assessing the effects of such variations under these conditions. The experimental results yielded quantitative indicators of pilot's performance and workload, and for each of them, multivariate regression was applied to evaluate several candidate flying qualities criteria.

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.

Modeling Psychological Contract Violation using Dual Regime Models: An Event-based Approach

PubMed Central

Hofmans, Joeri

2017-01-01

A good understanding of the dynamics of psychological contract violation requires theories, research methods and statistical models that explicitly recognize that violation feelings follow from an event that violates one's acceptance limits, after which interpretative processes are set into motion, determining the intensity of these violation feelings. Whereas theories—in the form of the dynamic model of the psychological contract—and research methods—in the form of daily diary research and experience sampling research—are available by now, the statistical tools to model such a two-stage process are still lacking. The aim of the present paper is to fill this gap in the literature by introducing two statistical models—the Zero-Inflated model and the Hurdle model—that closely mimic the theoretical process underlying the elicitation violation feelings via two model components: a binary distribution that models whether violation has occurred or not, and a count distribution that models how severe the negative impact is. Moreover, covariates can be included for both model components separately, which yields insight into their unique and shared antecedents. By doing this, the present paper offers a methodological-substantive synergy, showing how sophisticated methodology can be used to examine an important substantive issue. PMID:29163316

The decay process of rotating unstable systems through the passage time distribution

NASA Astrophysics Data System (ADS)

Jiménez-Aquino, J. I.; Cortés, Emilio; Aquino, N.

2001-05-01

In this work we propose a general scheme to characterize, through the passage time distribution, the decay process of rotational unstable systems in the presence of external forces of large amplitude. The formalism starts with a matricial Langevin type equation formulated in the context of two dynamical representations given, respectively, by the vectors x and y, both related by a time dependent rotation matrix. The transformation preserves the norm of the vector and decouples the set of dynamical equations in the transformed space y. We study the dynamical characterization of the systems of two variables and show that the statistical properties of the passage time distribution are essentially equivalent in both dynamics. The theory is applied to the laser system studied in Dellunde et al. (Opt. Commun. 102 (1993) 277), where the effect of large injected signals on the transient dynamics of the laser has been studied in terms of complex electric field. The analytical results are compared with numerical simulation.

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

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

Thomas, Vaughan L.; Gayme, Dennice F.; Lieu, Binh K.

2014-10-15

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate thatmore » the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.« less

Edgeworth streaming model for redshift space distortions

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael; Haugg, Thomas

2015-09-01

We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N -body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc /h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc /h . To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N -body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.

On the Fluctuations that Order and Frustrate Liquid Water

NASA Astrophysics Data System (ADS)

Limmer, David Tyler

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

Transient response of nonlinear polymer networks: A kinetic theory

NASA Astrophysics Data System (ADS)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

NASA Technical Reports Server (NTRS)

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Maximum entropy models of ecosystem functioning

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

Bertram, Jason, E-mail: jason.bertram@anu.edu.au

2014-12-05

Using organism-level traits to deduce community-level relationships is a fundamental problem in theoretical ecology. This problem parallels the physical one of using particle properties to deduce macroscopic thermodynamic laws, which was successfully achieved with the development of statistical physics. Drawing on this parallel, theoretical ecologists from Lotka onwards have attempted to construct statistical mechanistic theories of ecosystem functioning. Jaynes’ broader interpretation of statistical mechanics, which hinges on the entropy maximisation algorithm (MaxEnt), is of central importance here because the classical foundations of statistical physics do not have clear ecological analogues (e.g. phase space, dynamical invariants). However, models based on themore » information theoretic interpretation of MaxEnt are difficult to interpret ecologically. Here I give a broad discussion of statistical mechanical models of ecosystem functioning and the application of MaxEnt in these models. Emphasising the sample frequency interpretation of MaxEnt, I show that MaxEnt can be used to construct models of ecosystem functioning which are statistical mechanical in the traditional sense using a savanna plant ecology model as an example.« less

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

NASA Technical Reports Server (NTRS)

Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Design of Neural Networks for Fast Convergence and Accuracy: Dynamics and Control

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Sparks, Dean W., Jr.

1997-01-01

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

Design of neural networks for fast convergence and accuracy: dynamics and control.

PubMed

Maghami, P G; Sparks, D R

2000-01-01

A procedure for the design and training of artificial neural networks, used for rapid and efficient controls and dynamics design and analysis for flexible space systems, has been developed. Artificial neural networks are employed, such that once properly trained, they provide a means of evaluating the impact of design changes rapidly. Specifically, two-layer feedforward neural networks are designed to approximate the functional relationship between the component/spacecraft design changes and measures of its performance or nonlinear dynamics of the system/components. A training algorithm, based on statistical sampling theory, is presented, which guarantees that the trained networks provide a designer-specified degree of accuracy in mapping the functional relationship. Within each iteration of this statistical-based algorithm, a sequential design algorithm is used for the design and training of the feedforward network to provide rapid convergence to the network goals. Here, at each sequence a new network is trained to minimize the error of previous network. The proposed method should work for applications wherein an arbitrary large source of training data can be generated. Two numerical examples are performed on a spacecraft application in order to demonstrate the feasibility of the proposed approach.

[Chaos theory: a fascinating concept for oncologists].

PubMed

Denis, F; Letellier, C

2012-05-01

The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

The development of ensemble theory. A new glimpse at the history of statistical mechanics

NASA Astrophysics Data System (ADS)

Inaba, Hajime

2015-12-01

This paper investigates the history of statistical mechanics from the viewpoint of the development of the ensemble theory from 1871 to 1902. In 1871, Ludwig Boltzmann introduced a prototype model of an ensemble that represents a polyatomic gas. In 1879, James Clerk Maxwell defined an ensemble as copies of systems of the same energy. Inspired by H.W. Watson, he called his approach "statistical". Boltzmann and Maxwell regarded the ensemble theory as a much more general approach than the kinetic theory. In the 1880s, influenced by Hermann von Helmholtz, Boltzmann made use of ensembles to establish thermodynamic relations. In Elementary Principles in Statistical Mechanics of 1902, Josiah Willard Gibbs tried to get his ensemble theory to mirror thermodynamics, including thermodynamic operations in its scope. Thermodynamics played the role of a "blind guide". His theory of ensembles can be characterized as more mathematically oriented than Einstein's theory proposed in the same year. Mechanical, empirical, and statistical approaches to foundations of statistical mechanics are presented. Although it was formulated in classical terms, the ensemble theory provided an infrastructure still valuable in quantum statistics because of its generality.

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.

Dynamic Scaling Theory of the Forced Translocation of a Semi-flexible Polymer Through a Nanopore

NASA Astrophysics Data System (ADS)

Lam, Pui-Man; Zhen, Yi

2015-10-01

We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P, its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size , where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by , where is an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.

Statistical significance approximation in local trend analysis of high-throughput time-series data using the theory of Markov chains.

PubMed

Xia, Li C; Ai, Dongmei; Cram, Jacob A; Liang, Xiaoyi; Fuhrman, Jed A; Sun, Fengzhu

2015-09-21

Local trend (i.e. shape) analysis of time series data reveals co-changing patterns in dynamics of biological systems. However, slow permutation procedures to evaluate the statistical significance of local trend scores have limited its applications to high-throughput time series data analysis, e.g., data from the next generation sequencing technology based studies. By extending the theories for the tail probability of the range of sum of Markovian random variables, we propose formulae for approximating the statistical significance of local trend scores. Using simulations and real data, we show that the approximate p-value is close to that obtained using a large number of permutations (starting at time points >20 with no delay and >30 with delay of at most three time steps) in that the non-zero decimals of the p-values obtained by the approximation and the permutations are mostly the same when the approximate p-value is less than 0.05. In addition, the approximate p-value is slightly larger than that based on permutations making hypothesis testing based on the approximate p-value conservative. The approximation enables efficient calculation of p-values for pairwise local trend analysis, making large scale all-versus-all comparisons possible. We also propose a hybrid approach by integrating the approximation and permutations to obtain accurate p-values for significantly associated pairs. We further demonstrate its use with the analysis of the Polymouth Marine Laboratory (PML) microbial community time series from high-throughput sequencing data and found interesting organism co-occurrence dynamic patterns. The software tool is integrated into the eLSA software package that now provides accelerated local trend and similarity analysis pipelines for time series data. The package is freely available from the eLSA website: http://bitbucket.org/charade/elsa.

A statistical mechanical theory of proton transport kinetics in hydrogen-bonded networks based on population correlation functions with applications to acids and bases.

PubMed

Tuckerman, Mark E; Chandra, Amalendu; Marx, Dominik

2010-09-28

Extraction of relaxation times, lifetimes, and rates associated with the transport of topological charge defects in hydrogen-bonded networks from molecular dynamics simulations is a challenge because proton transfer reactions continually change the identity of the defect core. In this paper, we present a statistical mechanical theory that allows these quantities to be computed in an unbiased manner. The theory employs a set of suitably defined indicator or population functions for locating a defect structure and their associated correlation functions. These functions are then used to develop a chemical master equation framework from which the rates and lifetimes can be determined. Furthermore, we develop an integral equation formalism for connecting various types of population correlation functions and derive an iterative solution to the equation, which is given a graphical interpretation. The chemical master equation framework is applied to the problems of both hydronium and hydroxide transport in bulk water. For each case it is shown that the theory establishes direct links between the defect's dominant solvation structures, the kinetics of charge transfer, and the mechanism of structural diffusion. A detailed analysis is presented for aqueous hydroxide, examining both reorientational time scales and relaxation of the rotational anisotropy, which is correlated with recent experimental results for these quantities. Finally, for OH(-)(aq) it is demonstrated that the "dynamical hypercoordination mechanism" is consistent with available experimental data while other mechanistic proposals are shown to fail. As a means of going beyond the linear rate theory valid from short up to intermediate time scales, a fractional kinetic model is introduced in the Appendix in order to describe the nonexponential long-time behavior of time-correlation functions. Within the mathematical framework of fractional calculus the power law decay ∼t(-σ), where σ is a parameter of the model and depends on the dimensionality of the system, is obtained from Mittag-Leffler functions due to their long-time asymptotics, whereas (stretched) exponential behavior is found for short times.

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers: a leading model to describe the onset of Johari-Goldstein processes and their relationship with fully cooperative processes.

PubMed

Crisanti, A; Leuzzi, L; Paoluzzi, M

2011-09-01

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. By varying the external thermodynamic parameters, a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.

Quantum-Like Model for Decision Making Process in Two Players Game. A Non-Kolmogorovian Model

NASA Astrophysics Data System (ADS)

Asano, Masanari; Ohya, Masanori; Khrennikov, Andrei

2011-03-01

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).

Characterization of Perovskite Oxide/Semiconductor Heterostructures

NASA Astrophysics Data System (ADS)

Walker, Phillip

The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions. For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained. This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.

Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics

NASA Astrophysics Data System (ADS)

Zhou, Da; Qian, Hong

2011-09-01

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

Impact resistance of fiber composites - Energy-absorbing mechanisms and environmental effects

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1985-01-01

Energy absorbing mechanisms were identified by several approaches. The energy absorbing mechanisms considered are those in unidirectional composite beams subjected to impact. The approaches used include: mechanic models, statistical models, transient finite element analysis, and simple beam theory. Predicted results are correlated with experimental data from Charpy impact tests. The environmental effects on impact resistance are evaluated. Working definitions for energy absorbing and energy releasing mechanisms are proposed and a dynamic fracture progression is outlined. Possible generalizations to angle-plied laminates are described.

Impact resistance of fiber composites: Energy absorbing mechanisms and environmental effects

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1983-01-01

Energy absorbing mechanisms were identified by several approaches. The energy absorbing mechanisms considered are those in unidirectional composite beams subjected to impact. The approaches used include: mechanic models, statistical models, transient finite element analysis, and simple beam theory. Predicted results are correlated with experimental data from Charpy impact tests. The environmental effects on impact resistance are evaluated. Working definitions for energy absorbing and energy releasing mechanisms are proposed and a dynamic fracture progression is outlined. Possible generalizations to angle-plied laminates are described.

Effects of cross-linking on partitioning of nanoparticles into a polymer brush: Coarse-grained simulations test simple approximate theories

NASA Astrophysics Data System (ADS)

Ozmaian, Masoumeh; Jasnow, David; Eskandari Nasrabad, Afshin; Zilman, Anton; Coalson, Rob D.

2018-01-01

The effect of cohesive contacts or, equivalently, dynamical cross-linking on the equilibrium morphology of a polymer brush infiltrated by nanoparticles that are attracted to the polymer strands is studied for plane-grafted brushes using coarse-grained molecular dynamics and approximate statistical mechanical models. In particular, the Alexander-de Gennes (AdG) and Strong Stretching Theory (SST) mean-field theory (MFT) models are considered. It is found that for values of the MFT cross-link strength interaction parameter beyond a certain threshold, both AdG and SST models predict that the polymer brush will be in a compact state of nearly uniform density packed next to the grafting surface over a wide range of solution phase nanoparticle concentrations. Coarse grained molecular dynamics simulations confirm this prediction, for both small nanoparticles (nanoparticle volume = monomer volume) and large nanoparticles (nanoparticle volume = 27 × monomer volume). Simulation results for these cross-linked systems are compared with analogous results for systems with no cross-linking. At the same solution phase nanoparticle concentration, strong cross-linking results in additional compression of the brush relative to the non-crosslinked analog and, at all but the lowest concentrations, to a lesser degree of infiltration by nanoparticles. For large nanoparticles, the monomer density profiles show clear oscillations moving outwards from the grafting surface, corresponding to a degree of layering of the absorbed nanoparticles in the brush as they pack against the grafting surface.

Influence of an amorphous wall on the distribution of localized excitations in a colloidal glass-forming liquid

NASA Astrophysics Data System (ADS)

Gokhale, Shreyas; Hima Nagamanasa, K.; Sood, A. K.; Ganapathy, Rajesh

2016-07-01

Elucidating the nature of the glass transition has been the holy grail of condensed matter physics and statistical mechanics for several decades. A phenomenological aspect that makes glass formation a conceptually formidable problem is that structural and dynamic correlations in glass-forming liquids are too subtle to be captured at the level of conventional two-point functions. As a consequence, a host of theoretical techniques, such as quenched amorphous configurations of particles, have been devised and employed in simulations and colloid experiments to gain insights into the mechanisms responsible for these elusive correlations. Very often, though, the analysis of spatio-temporal correlations is performed in the context of a single theoretical framework, and critical comparisons of microscopic predictions of competing theories are thereby lacking. Here, we address this issue by analysing the distribution of localized excitations, which are building blocks of relaxation as per the dynamical facilitation (DF) theory, in the presence of an amorphous wall, a construct motivated by the random first-order transition theory (RFOT). We observe that spatial profiles of the concentration of excitations exhibit complex features such as non-monotonicity and oscillations. Moreover, the smoothly varying part of the concentration profile yields a length scale {ξc} , which we compare with a previously computed length scale {ξ\\text{dyn}} . Our results suggest a method to assess the role of dynamical facilitation in governing structural relaxation in glass-forming liquids.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

The Elegance of Disordered Granular Packings: A Validation of Edwards' Hypothesis

NASA Technical Reports Server (NTRS)

Metzger, Philip T.; Donahue, Carly M.

2004-01-01

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement between theory and the empirics is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly due to the variable coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

NASA Astrophysics Data System (ADS)

Restrepo, Sebastian; Cerrillo, Javier; Strasberg, Philipp; Schaller, Gernot

2018-05-01

We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born–Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit.

Theories of quantum dissipation and nonlinear coupling bath descriptors

NASA Astrophysics Data System (ADS)

Xu, Rui-Xue; Liu, Yang; Zhang, Hou-Dao; Yan, YiJing

2018-03-01

The quest of an exact and nonperturbative treatment of quantum dissipation in nonlinear coupling environments remains in general an intractable task. In this work, we address the key issues toward the solutions to the lowest nonlinear environment, a harmonic bath coupled both linearly and quadratically with an arbitrary system. To determine the bath coupling descriptors, we propose a physical mapping scheme, together with the prescription reference invariance requirement. We then adopt a recently developed dissipaton equation of motion theory [R. X. Xu et al., Chin. J. Chem. Phys. 30, 395 (2017)], with the underlying statistical quasi-particle ("dissipaton") algebra being extended to the quadratic bath coupling. We report the numerical results on a two-level system dynamics and absorption and emission line shapes.

Animal Social Network Theory Can Help Wildlife Conservation.

PubMed

Snijders, Lysanne; Blumstein, Daniel T; Stanley, Christina R; Franks, Daniel W

2017-08-01

Many animals preferentially associate with certain other individuals. This social structuring can influence how populations respond to changes to their environment, thus making network analysis a promising technique for understanding, predicting, and potentially manipulating population dynamics. Various network statistics can correlate with individual fitness components and key population-level processes, yet the logical role and formal application of animal social network theory for conservation and management have not been well articulated. We outline how understanding of direct and indirect relationships between animals can be profitably applied by wildlife managers and conservationists. By doing so, we aim to stimulate the development and implementation of practical tools for wildlife conservation and management and to inspire novel behavioral research in this field. Copyright © 2017 Elsevier Ltd. All rights reserved.

Statistical mechanics of monatomic liquids

NASA Astrophysics Data System (ADS)

Wallace, Duane C.

1997-10-01

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

Multipactor threshold calculation of coaxial transmission lines in microwave applications with nonstationary statistical theory

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

Lin, S.; Li, Y.; Liu, C.

2015-08-15

This paper presents a statistical theory for the initial onset of multipactor breakdown in coaxial transmission lines, taking both the nonuniform electric field and random electron emission velocity into account. A general numerical method is first developed to construct the joint probability density function based on the approximate equation of the electron trajectory. The nonstationary dynamics of the multipactor process on both surfaces of coaxial lines are modelled based on the probability of various impacts and their corresponding secondary emission. The resonant assumption of the classical theory on the independent double-sided and single-sided impacts is replaced by the consideration ofmore » their interaction. As a result, the time evolutions of the electron population for exponential growth and absorption on both inner and outer conductor, in response to the applied voltage above and below the multipactor breakdown level, are obtained to investigate the exact mechanism of multipactor discharge in coaxial lines. Furthermore, the multipactor threshold predictions of the presented model are compared with experimental results using measured secondary emission yield of the tested samples which shows reasonable agreement. Finally, the detailed impact scenario reveals that single-surface multipactor is more likely to occur with a higher outer to inner conductor radius ratio.« less

Population dynamics of minimally cognitive individuals. Part I: Introducing knowledge into the dynamics

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

Schmieder, R.W.

The author presents a new approach for modeling the dynamics of collections of objects with internal structure. Based on the fact that the behavior of an individual in a population is modified by its knowledge of other individuals, a procedure for accounting for knowledge in a population of interacting objects is presented. It is assumed that each object has partial (or complete) knowledge of some (or all) other objects in the population. The dynamical equations for the objects are then modified to include the effects of this pairwise knowledge. This procedure has the effect of projecting out what the populationmore » will do from the much larger space of what it could do, i.e., filtering or smoothing the dynamics by replacing the complex detailed physical model with an effective model that produces the behavior of interest. The procedure therefore provides a minimalist approach for obtaining emergent collective behavior. The use of knowledge as a dynamical quantity, and its relationship to statistical mechanics, thermodynamics, information theory, and cognition microstructure are discussed.« less

Application of quantum master equation for long-term prognosis of asset-prices

NASA Astrophysics Data System (ADS)

Khrennikova, Polina

2016-05-01

This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a ;financial bath;. The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

The Statistical Segment Length of DNA: Opportunities for Biomechanical Modeling in Polymer Physics and Next-Generation Genomics.

PubMed

Dorfman, Kevin D

2018-02-01

The development of bright bisintercalating dyes for deoxyribonucleic acid (DNA) in the 1990s, most notably YOYO-1, revolutionized the field of polymer physics in the ensuing years. These dyes, in conjunction with modern molecular biology techniques, permit the facile observation of polymer dynamics via fluorescence microscopy and thus direct tests of different theories of polymer dynamics. At the same time, they have played a key role in advancing an emerging next-generation method known as genome mapping in nanochannels. The effect of intercalation on the bending energy of DNA as embodied by a change in its statistical segment length (or, alternatively, its persistence length) has been the subject of significant controversy. The precise value of the statistical segment length is critical for the proper interpretation of polymer physics experiments and controls the phenomena underlying the aforementioned genomics technology. In this perspective, we briefly review the model of DNA as a wormlike chain and a trio of methods (light scattering, optical or magnetic tweezers, and atomic force microscopy (AFM)) that have been used to determine the statistical segment length of DNA. We then outline the disagreement in the literature over the role of bisintercalation on the bending energy of DNA, and how a multiscale biomechanical approach could provide an important model for this scientifically and technologically relevant problem.

Statistical Analysis of Deflation in Covariance and Resultant Pc Values for AQUA, AURA and TERRA

NASA Technical Reports Server (NTRS)

Hasan, Syed O.

2016-01-01

This presentation will display statistical analysis performed for raw conjunction CDMs received for the EOS Aqua, Aura and Terra satellites within the period of February 2015 through July 2016. The analysis performed indicates a discernable deflation in covariance calculated at the JSpOC after the utilization of the dynamic drag consider parameter was implemented operationally in May 2015. As a result, the overall diminution in the conjunction plane intersection of the primary and secondary objects appears to be leading to reduced probability of collision (Pc) values for these conjunction events. This presentation also displays evidence for this theory with analysis of Pc trending plots using data calculated by the SpaceNav CRMS system.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Utah Virtual Lab: JAVA interactivity for teaching science and statistics on line.

PubMed

Malloy, T E; Jensen, G C

2001-05-01

The Utah on-line Virtual Lab is a JAVA program run dynamically off a database. It is embedded in StatCenter (www.psych.utah.edu/learn/statsampler.html), an on-line collection of tools and text for teaching and learning statistics. Instructors author a statistical virtual reality that simulates theories and data in a specific research focus area by defining independent, predictor, and dependent variables and the relations among them. Students work in an on-line virtual environment to discover the principles of this simulated reality: They go to a library, read theoretical overviews and scientific puzzles, and then go to a lab, design a study, collect and analyze data, and write a report. Each student's design and data analysis decisions are computer-graded and recorded in a database; the written research report can be read by the instructor or by other students in peer groups simulating scientific conventions.

The difference between a dynamic and mechanical approach to stroke treatment.

PubMed

Helgason, Cathy M

2007-06-01

The current classification of stroke is based on causation, also called pathogenesis, and relies on binary logic faithful to the Aristotelian tradition. Accordingly, a pathology is or is not the cause of the stroke, is considered independent of others, and is the target for treatment. It is the subject for large double-blind randomized clinical therapeutic trials. The scientific view behind clinical trials is the fundamental concept that information is statistical, and causation is determined by probabilities. Therefore, the cause and effect relation will be determined by probability-theory-based statistics. This is the basis of evidence-based medicine, which calls for the results of such trials to be the basis for physician decisions regarding diagnosis and treatment. However, there are problems with the methodology behind evidence-based medicine. Calculations using probability-theory-based statistics regarding cause and effect are performed within an automatic system where there are known inputs and outputs. This method of research provides a framework of certainty with no surprise elements or outcomes. However, it is not a system or method that will come up with previously unknown variables, concepts, or universal principles; it is not a method that will give a new outcome; and it is not a method that allows for creativity, expertise, or new insight for problem solving.

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

PubMed Central

Mensi, Skander; Hagens, Olivier; Gerstner, Wulfram; Pozzorini, Christian

2016-01-01

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na+-channel inactivation regulate the sensitivity to rapid input fluctuations. PMID:26907675

Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients

NASA Astrophysics Data System (ADS)

Yulmetyev, Renat; Demin, Sergey; Emelyanova, Natalya; Gafarov, Fail; Hänggi, Peter

2003-03-01

In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes (Phys. Rev. E 62 (5) (2000) 6178, Phys. Rev. E 64 (2001) 066132, Phys. Rev. E 65 (2002) 046107, Physica A 303 (2002) 427). The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year olds), young people (from 21 up to 29 year olds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differences between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.

Predictive Coding: A Fresh View of Inhibition in the Retina

NASA Astrophysics Data System (ADS)

Srinivasan, M. V.; Laughlin, S. B.; Dubs, A.

1982-11-01

Interneurons exhibiting centre--surround antagonism within their receptive fields are commonly found in peripheral visual pathways. We propose that this organization enables the visual system to encode spatial detail in a manner that minimizes the deleterious effects of intrinsic noise, by exploiting the spatial correlation that exists within natural scenes. The antagonistic surround takes a weighted mean of the signals in neighbouring receptors to generate a statistical prediction of the signal at the centre. The predicted value is subtracted from the actual centre signal, thus minimizing the range of outputs transmitted by the centre. In this way the entire dynamic range of the interneuron can be devoted to encoding a small range of intensities, thus rendering fine detail detectable against intrinsic noise injected at later stages in processing. This predictive encoding scheme also reduces spatial redundancy, thereby enabling the array of interneurons to transmit a larger number of distinguishable images, taking into account the expected structure of the visual world. The profile of the required inhibitory field is derived from statistical estimation theory. This profile depends strongly upon the signal: noise ratio and weakly upon the extent of lateral spatial correlation. The receptive fields that are quantitatively predicted by the theory resemble those of X-type retinal ganglion cells and show that the inhibitory surround should become weaker and more diffuse at low intensities. The latter property is unequivocally demonstrated in the first-order interneurons of the fly's compound eye. The theory is extended to the time domain to account for the phasic responses of fly interneurons. These comparisons suggest that, in the early stages of processing, the visual system is concerned primarily with coding the visual image to protect against subsequent intrinsic noise, rather than with reconstructing the scene or extracting specific features from it. The treatment emphasizes that a neuron's dynamic range should be matched to both its receptive field and the statistical properties of the visual pattern expected within this field. Finally, the analysis is synthetic because it is an extension of the background suppression hypothesis (Barlow & Levick 1976), satisfies the redundancy reduction hypothesis (Barlow 1961 a, b) and is equivalent to deblurring under certain conditions (Ratliff 1965).

A sub-ensemble theory of ideal quantum measurement processes

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Balian, Roger; Nieuwenhuizen, Theo M.

2017-01-01

In order to elucidate the properties currently attributed to ideal measurements, one must explain how the concept of an individual event with a well-defined outcome may emerge from quantum theory which deals with statistical ensembles, and how different runs issued from the same initial state may end up with different final states. This so-called "measurement problem" is tackled with two guidelines. On the one hand, the dynamics of the macroscopic apparatus A coupled to the tested system S is described mathematically within a standard quantum formalism, where " q-probabilities" remain devoid of interpretation. On the other hand, interpretative principles, aimed to be minimal, are introduced to account for the expected features of ideal measurements. Most of the five principles stated here, which relate the quantum formalism to physical reality, are straightforward and refer to macroscopic variables. The process can be identified with a relaxation of S + A to thermodynamic equilibrium, not only for a large ensemble E of runs but even for its sub-ensembles. The different mechanisms of quantum statistical dynamics that ensure these types of relaxation are exhibited, and the required properties of the Hamiltonian of S + A are indicated. The additional theoretical information provided by the study of sub-ensembles remove Schrödinger's quantum ambiguity of the final density operator for E which hinders its direct interpretation, and bring out a commutative behaviour of the pointer observable at the final time. The latter property supports the introduction of a last interpretative principle, needed to switch from the statistical ensembles and sub-ensembles described by quantum theory to individual experimental events. It amounts to identify some formal " q-probabilities" with ordinary frequencies, but only those which refer to the final indications of the pointer. The desired properties of ideal measurements, in particular the uniqueness of the result for each individual run of the ensemble and von Neumann's reduction, are thereby recovered with economic interpretations. The status of Born's rule involving both A and S is re-evaluated, and contextuality of quantum measurements is made obvious.

Dynamic loop gain increases upon adopting the supine body position during sleep in patients with obstructive sleep apnoea.

PubMed

Joosten, Simon A; Landry, Shane A; Sands, Scott A; Terrill, Philip I; Mann, Dwayne; Andara, Christopher; Skuza, Elizabeth; Turton, Anthony; Berger, Philip; Hamilton, Garun S; Edwards, Bradley A

2017-11-01

Obstructive sleep apnoea (OSA) is typically worse in the supine versus lateral sleeping position. One potential factor driving this observation is a decrease in lung volume in the supine position which is expected by theory to increase a key OSA pathogenic factor: dynamic ventilatory control instability (i.e. loop gain). We aimed to quantify dynamic loop gain in OSA patients in the lateral and supine positions, and to explore the relationship between change in dynamic loop gain and change in lung volume with position. Data from 20 patients enrolled in previous studies on the effect of body position on OSA pathogenesis were retrospectively analysed. Dynamic loop gain was calculated from routinely collected polysomnographic signals using a previously validated mathematical model. Lung volumes were measured in the awake state with a nitrogen washout technique. Dynamic loop gain was significantly higher in the supine than in the lateral position (0.77 ± 0.15 vs 0.68 ± 0.14, P = 0.012). Supine functional residual capacity (FRC) was significantly lower than lateral FRC (81.0 ± 15.4% vs 87.3 ± 18.4% of the seated FRC, P = 0.021). The reduced FRC we observed on moving to the supine position was predicted by theory to increase loop gain by 10.2 (0.6, 17.1)%, a value similar to the observed increase of 8.4 (-1.5, 31.0)%. Dynamic loop gain increased by a small but statistically significant amount when moving from the lateral to supine position and this may, in part, contribute to the worsening of OSA in the supine sleeping position. © 2017 Asian Pacific Society of Respirology.

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.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

NASA Astrophysics Data System (ADS)

Donges, Jonathan F.; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V.; Marwan, Norbert; Dijkstra, Henk A.; Kurths, Jürgen

2015-11-01

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients

NASA Technical Reports Server (NTRS)

Maine, R. E.; Iliff, K. W.

1981-01-01

Means of assessing the accuracy of maximum likelihood parameter estimates obtained from dynamic flight data are discussed. The most commonly used analytical predictors of accuracy are derived and compared from both statistical and simplified geometrics standpoints. The accuracy predictions are evaluated with real and simulated data, with an emphasis on practical considerations, such as modeling error. Improved computations of the Cramer-Rao bound to correct large discrepancies due to colored noise and modeling error are presented. The corrected Cramer-Rao bound is shown to be the best available analytical predictor of accuracy, and several practical examples of the use of the Cramer-Rao bound are given. Engineering judgement, aided by such analytical tools, is the final arbiter of accuracy estimation.

Ferroelectric hydration shells around proteins: electrostatics of the protein-water interface.

PubMed

LeBard, David N; Matyushov, Dmitry V

2010-07-22

Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric layer with large values of the average dipole moment magnitude and the dipole moment variance. The emergence of the new polarized mesophase dramatically alters the statistics of electrostatic fluctuations at the protein-water interface. The linear response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic fluctuations far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (approximately = 1 ns) component that freezes in at the temperature of the dynamical transition of proteins. The ferroelectric shell propagates 3-5 water diameters into the bulk.

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.

Why interdisciplinary research enriches the study of crime. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Donnay, Karsten

2015-03-01

The past several years have seen a rapidly growing interest in the use of advanced quantitative methodologies and formalisms adapted from the natural sciences to study a broad range of social phenomena. The research field of computational social science [1,2], for example, uses digital artifacts of human online activity to cast a new light on social dynamics. Similarly, the studies reviewed by D'Orsogna and Perc showcase a diverse set of advanced quantitative techniques to study the dynamics of crime. Methods used range from partial differential equations and self-exciting point processes to agent-based models, evolutionary game theory and network science [3].

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

NASA Astrophysics Data System (ADS)

Matsubara, Takahiko

2003-02-01

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

Deformed Materials: Towards a Theory of Materials Morphology Dynamics

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

Sethna, James P

This grant supported work on the response of crystals to external stress. Our primary work described how disordered structural materials break in two (statistical models of fracture in disordered materials), studied models of deformation bursts (avalanches) that mediate deformation on the microscale, and developed continuum dislocation dynamics models for plastic deformation (as when scooping ice cream bends a spoon, Fig. 9). Glass is brittle -- it breaks with almost atomically smooth fracture surfaces. Many metals are ductile -- when they break, the fracture surface is locally sheared and stretched, and it is this damage that makes them hard to break.more » Bone and seashells are made of brittle material, but they are strong because they are disordered -- lots of little cracks form as they are sheared and near the fracture surface, diluting the external force. We have studied materials like bone and seashells using simulations, mathematical tools, and statistical mechanics models from physics. In particular, we studied the extreme values of fracture strengths (how likely will a beam in a bridge break far below its design strength), and found that the traditional engineering tools could be improved greatly. We also studied fascinating crackling-noise precursors -- systems which formed microcracks of a broad range of sizes before they broke. Ductile metals under stress undergo irreversible plastic deformation -- the planes of atoms must slide across one another (through the motion of dislocations) to change the overall shape in response to the external force. Microscopically, the dislocations in crystals move in bursts of a broad range of sizes (termed 'avalanches' in the statistical mechanics community, whose motion is deemed 'crackling noise'). In this grant period, we resolved a longstanding mystery about the average shape of avalanches of fixed duration (using tools related to an emergent scale invariance), we developed the fundamental theory describing the shapes of avalanches and how they are affected by the edges of the microscope viewing window, we found that slow creep of dislocations can trigger an oscillating response explaining recent experiments, we explained avalanches under external voltage, and we have studied how avalanches in experiments on the microscale relate to deformation of large samples. Inside the crystals forming the metal, the dislocations arrange into mysterious cellular structures, usually ignored in theories of plasticity. Writing a natural continuum theory for dislocation dynamics, we found that it spontaneously formed walls -- much like models of traffic jams and sonic booms. These walls formed rather realistic cellular structures, which we examined in great detail -- our walls formed fractal structures with fascinating scaling properties, related to those found in turbulent fluids. We found, however, that the numerical and mathematical tools available to solve our equations were not flexible enough to incorporate materials-specific information, and our models did not show the dislocation avalanches seen experimentally. In the last year of this grant, we wrote an invited review article, explaining how plastic flow in metals shares features with other stressed materials, and how tools of statistical physics used in these other systems might be crucial for understanding plasticity.« less

Peptide dynamics by molecular dynamics simulation and diffusion theory method with improved basis sets

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

Hsu, Po Jen; Lai, S. K., E-mail: sklai@coll.phy.ncu.edu.tw; Rapallo, Arnaldo

Improved basis sets for the study of polymer dynamics by means of the diffusion theory, and tests on a melt of cis-1,4-polyisoprene decamers, and a toluene solution of a 71-mer syndiotactic trans-1,2-polypentadiene were presented recently [R. Gaspari and A. Rapallo, J. Chem. Phys. 128, 244109 (2008)]. The proposed hybrid basis approach (HBA) combined two techniques, the long time sorting procedure and the maximum correlation approximation. The HBA takes advantage of the strength of these two techniques, and its basis sets proved to be very effective and computationally convenient in describing both local and global dynamics in cases of flexible syntheticmore » polymers where the repeating unit is a unique type of monomer. The question then arises if the same efficacy continues when the HBA is applied to polymers of different monomers, variable local stiffness along the chain and with longer persistence length, which have different local and global dynamical properties against the above-mentioned systems. Important examples of this kind of molecular chains are the proteins, so that a fragment of the protein transthyretin is chosen as the system of the present study. This peptide corresponds to a sequence that is structured in β-sheets of the protein and is located on the surface of the channel with thyroxin. The protein transthyretin forms amyloid fibrils in vivo, whereas the peptide fragment has been shown [C. P. Jaroniec, C. E. MacPhee, N. S. Astrof, C. M. Dobson, and R. G. Griffin, Proc. Natl. Acad. Sci. U.S.A. 99, 16748 (2002)] to form amyloid fibrils in vitro in extended β-sheet conformations. For these reasons the latter is given considerable attention in the literature and studied also as an isolated fragment in water solution where both experimental and theoretical efforts have indicated the propensity of the system to form β turns or α helices, but is otherwise predominantly unstructured. Differing from previous computational studies that employed implicit solvent, we performed in this work the classical molecular dynamics simulation on a realistic model solution with the peptide embedded in an explicit water environment, and calculated its dynamic properties both as an outcome of the simulations, and by the diffusion theory in reduced statistical-mechanical approach within HBA on the premise that the mode-coupling approach to the diffusion theory can give both the long-range and local dynamics starting from equilibrium averages which were obtained from detailed atomistic simulations.« less

A solution to the online guidance problem for targeted reaches: proportional rate control using relative disparity tau.

PubMed

Anderson, Joe; Bingham, Geoffrey P

2010-09-01

We provide a solution to a major problem in visually guided reaching. Research has shown that binocular vision plays an important role in the online visual guidance of reaching, but the visual information and strategy used to guide a reach remains unknown. We propose a new theory of visual guidance of reaching including a new information variable, tau(alpha) (relative disparity tau), and a novel control strategy that allows actors to guide their reach trajectories visually by maintaining a constant proportion between tau(alpha) and its rate of change. The dynamical model couples the information to the reaching movement to generate trajectories characteristic of human reaching. We tested the theory in two experiments in which participants reached under conditions of darkness to guide a visible point either on a sliding apparatus or on their finger to a point-light target in depth. Slider apparatus controlled for a simple mapping from visual to proprioceptive space. When reaching with their finger, participants were forced, by perturbation of visual information used for feedforward control, to use online control with only binocular disparity-based information for guidance. Statistical analyses of trajectories strongly supported the theory. Simulations of the model were compared statistically to actual reaching trajectories. The results supported the theory, showing that tau(alpha) provides a source of information for the control of visually guided reaching and that participants use this information in a proportional rate control strategy.

Applying Sociocultural Theory to Teaching Statistics for Doctoral Social Work Students

ERIC Educational Resources Information Center

Mogro-Wilson, Cristina; Reeves, Michael G.; Charter, Mollie Lazar

2015-01-01

This article describes the development of two doctoral-level multivariate statistics courses utilizing sociocultural theory, an integrative pedagogical framework. In the first course, the implementation of sociocultural theory helps to support the students through a rigorous introduction to statistics. The second course involves students…

Chandrasekhar's dynamical friction and non-extensive statistics

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

Silva, J.M.; Lima, J.A.S.; De Souza, R.E.

2016-05-01

The motion of a point like object of mass M passing through the background potential of massive collisionless particles ( m || M ) suffers a steady deceleration named dynamical friction. In his classical work, Chandrasekhar assumed a Maxwellian velocity distribution in the halo and neglected the self gravity of the wake induced by the gravitational focusing of the mass M . In this paper, by relaxing the validity of the Maxwellian distribution due to the presence of long range forces, we derive an analytical formula for the dynamical friction in the context of the q -nonextensive kinetic theory. Inmore » the extensive limiting case ( q = 1), the classical Gaussian Chandrasekhar result is recovered. As an application, the dynamical friction timescale for Globular Clusters spiraling to the galactic center is explicitly obtained. Our results suggest that the problem concerning the large timescale as derived by numerical N -body simulations or semi-analytical models can be understood as a departure from the standard extensive Maxwellian regime as measured by the Tsallis nonextensive q -parameter.« less

Computational and experimental single cell biology techniques for the definition of cell type heterogeneity, interplay and intracellular dynamics.

PubMed

de Vargas Roditi, Laura; Claassen, Manfred

2015-08-01

Novel technological developments enable single cell population profiling with respect to their spatial and molecular setup. These include single cell sequencing, flow cytometry and multiparametric imaging approaches and open unprecedented possibilities to learn about the heterogeneity, dynamics and interplay of the different cell types which constitute tissues and multicellular organisms. Statistical and dynamic systems theory approaches have been applied to quantitatively describe a variety of cellular processes, such as transcription and cell signaling. Machine learning approaches have been developed to define cell types, their mutual relationships, and differentiation hierarchies shaping heterogeneous cell populations, yielding insights into topics such as, for example, immune cell differentiation and tumor cell type composition. This combination of experimental and computational advances has opened perspectives towards learning predictive multi-scale models of heterogeneous cell populations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Solution x-ray scattering and structure formation in protein dynamics

NASA Astrophysics Data System (ADS)

Nasedkin, Alexandr; Davidsson, Jan; Niemi, Antti J.; Peng, Xubiao

2017-12-01

We propose a computationally effective approach that builds on Landau mean-field theory in combination with modern nonequilibrium statistical mechanics to model and interpret protein dynamics and structure formation in small- to wide-angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analyzing experimental data in the case of Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data qualitatively with a good precision and over an extended temperature range. We explain experimental observations in terms of protein phase structure, and we make predictions for future experiments and for how to analyze data at different ambient temperature values. We conclude that the approach we propose has the potential to become a highly accurate, computationally effective, and predictive tool for analyzing S/WAXS data. For this, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.

Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis

NASA Astrophysics Data System (ADS)

Mantica, Giorgio; Perotti, Luca

2016-09-01

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.

A Review of Enhanced Sampling Approaches for Accelerated Molecular Dynamics

NASA Astrophysics Data System (ADS)

Tiwary, Pratyush; van de Walle, Axel

Molecular dynamics (MD) simulations have become a tool of immense use and popularity for simulating a variety of systems. With the advent of massively parallel computer resources, one now routinely sees applications of MD to systems as large as hundreds of thousands to even several million atoms, which is almost the size of most nanomaterials. However, it is not yet possible to reach laboratory timescales of milliseconds and beyond with MD simulations. Due to the essentially sequential nature of time, parallel computers have been of limited use in solving this so-called timescale problem. Instead, over the years a large range of statistical mechanics based enhanced sampling approaches have been proposed for accelerating molecular dynamics, and accessing timescales that are well beyond the reach of the fastest computers. In this review we provide an overview of these approaches, including the underlying theory, typical applications, and publicly available software resources to implement them.

Dissipation equation of motion approach to open quantum systems

NASA Astrophysics Data System (ADS)

Yan, YiJing; Jin, Jinshuang; Xu, Rui-Xue; Zheng, Xiao

2016-08-01

This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.

Non-commutative methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Millard, Andrew Clive

1997-09-01

Non-commutativity appears in physics almost hand in hand with quantum mechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantum mechanics transcends 'common sense', while the operators that generate a symmetry group are usually given in terms of their commutation relations. This thesis discusses a number of new developments which go beyond the usual stopping point of non-commuting quantities as matrices with complex elements. Chapter 2 shows how certain generalisations of quantum mechanics, from using complex numbers to using other (often non-commutative) algebras, can still be written as linear systems with symplectic phase flows. Chapter 3 deals with Adler's trace dynamics, a non-linear graded generalisation of Hamiltonian dynamics with supersymmetry applications, where the phase space coordinates are (generally non-commuting) operators, and reports on aspects of a demonstration that the statistical averages of the dynamical variables obey the rules of complex quantum field theory. The last two chapters discuss specific aspects of quaternionic quantum mechanics. Chapter 4 reports a generalised projective representation theory and presents a structure theorem that categorises quaternionic projective representations. Chapter 5 deals with a generalisation of the coherent states formalism and examines how it may be applied to two commonly used groups.

Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films

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

Mirigian, Stephen, E-mail: kschweiz@illinois.edu, E-mail: smirigian@gmail.com; Schweizer, Kenneth S., E-mail: kschweiz@illinois.edu, E-mail: smirigian@gmail.com

2015-12-28

We have constructed a quantitative, force level, statistical mechanical theory for how confinement in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a function of temperature, film thickness, and location in the film. The crucial idea is that relaxation speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the spatially longer range collective elasticity cost for large amplitude hopping. These two effects are fundamentally coupled. Quantitative predictions are made formore » how an apparent glass temperature depends on the film thickness and experimental probe technique, the emergence of a two-step decay and mobile layers in time domain measurements, signatures of confinement in frequency-domain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.« less

Detection theory for accurate and non-invasive skin cancer diagnosis using dynamic thermal imaging

PubMed Central

Godoy, Sebastián E.; Hayat, Majeed M.; Ramirez, David A.; Myers, Stephen A.; Padilla, R. Steven; Krishna, Sanjay

2017-01-01

Skin cancer is the most common cancer in the United States with over 3.5M annual cases. Presently, visual inspection by a dermatologist has good sensitivity (> 90%) but poor specificity (< 10%), especially for melanoma, which leads to a high number of unnecessary biopsies. Here we use dynamic thermal imaging (DTI) to demonstrate a rapid, accurate and non-invasive imaging system for detection of skin cancer. In DTI, the lesion is cooled down and the thermal recovery is recorded using infrared imaging. The thermal recovery curves of the suspected lesions are then utilized in the context of continuous-time detection theory in order to define an optimal statistical decision rule such that the sensitivity of the algorithm is guaranteed to be at a maximum for every prescribed false-alarm probability. The proposed methodology was tested in a pilot study including 140 human subjects demonstrating a sensitivity in excess of 99% for a prescribed specificity in excess of 99% for detection of skin cancer. To the best of our knowledge, this is the highest reported accuracy for any non-invasive skin cancer diagnosis method. PMID:28736673

Theory of activated glassy relaxation, mobility gradients, surface diffusion, and vitrification in free standing thin films.

PubMed

Mirigian, Stephen; Schweizer, Kenneth S

2015-12-28

We have constructed a quantitative, force level, statistical mechanical theory for how confinement in free standing thin films introduces a spatial mobility gradient of the alpha relaxation time as a function of temperature, film thickness, and location in the film. The crucial idea is that relaxation speeds up due to the reduction of both near-surface barriers associated with the loss of neighbors in the local cage and the spatial cutoff and dynamical softening near the vapor interface of the spatially longer range collective elasticity cost for large amplitude hopping. These two effects are fundamentally coupled. Quantitative predictions are made for how an apparent glass temperature depends on the film thickness and experimental probe technique, the emergence of a two-step decay and mobile layers in time domain measurements, signatures of confinement in frequency-domain dielectric loss experiments, the dependence of film-averaged relaxation times and dynamic fragility on temperature and film thickness, surface diffusion, and the relationship between kinetic experiments and pseudo-thermodynamic measurements such as ellipsometry.

Modeling Sensor Reliability in Fault Diagnosis Based on Evidence Theory

PubMed Central

Yuan, Kaijuan; Xiao, Fuyuan; Fei, Liguo; Kang, Bingyi; Deng, Yong

2016-01-01

Sensor data fusion plays an important role in fault diagnosis. Dempster–Shafer (D-R) evidence theory is widely used in fault diagnosis, since it is efficient to combine evidence from different sensors. However, under the situation where the evidence highly conflicts, it may obtain a counterintuitive result. To address the issue, a new method is proposed in this paper. Not only the statistic sensor reliability, but also the dynamic sensor reliability are taken into consideration. The evidence distance function and the belief entropy are combined to obtain the dynamic reliability of each sensor report. A weighted averaging method is adopted to modify the conflict evidence by assigning different weights to evidence according to sensor reliability. The proposed method has better performance in conflict management and fault diagnosis due to the fact that the information volume of each sensor report is taken into consideration. An application in fault diagnosis based on sensor fusion is illustrated to show the efficiency of the proposed method. The results show that the proposed method improves the accuracy of fault diagnosis from 81.19% to 89.48% compared to the existing methods. PMID:26797611

The rule of declining adaptability in microbial evolution experiments

PubMed Central

Couce, Alejandro; Tenaillon, Olivier A.

2015-01-01

One of the most recurrent observations after two decades of microbial evolution experiments regards the dynamics of fitness change. In a given environment, low-fitness genotypes are recurrently observed to adapt faster than their more fit counterparts. Since adaptation is the main macroscopic outcome of Darwinian evolution, studying its patterns of change could potentially provide insight into key issues of evolutionary theory, from fixation dynamics to the genetic architecture of organisms. Here, we re-analyze several published datasets from experimental evolution with microbes and show that, despite large differences in the origin of the data, a pattern of inverse dependence of adaptability with fitness clearly emerges. In quantitative terms, it is remarkable to observe little if any degree of idiosyncrasy across systems as diverse as virus, bacteria and yeast. The universality of this phenomenon suggests that its emergence might be understood from general principles, giving rise to the exciting prospect that evolution might be statistically predictable at the macroscopic level. We discuss these possibilities in the light of the various theories of adaptation that have been proposed and delineate future directions of research. PMID:25815007

A statistical mechanical model of economics

NASA Astrophysics Data System (ADS)

Lubbers, Nicholas Edward Williams

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

The Development of Bayesian Theory and Its Applications in Business and Bioinformatics

NASA Astrophysics Data System (ADS)

Zhang, Yifei

2018-03-01

Bayesian Theory originated from an Essay of a British mathematician named Thomas Bayes in 1763, and after its development in 20th century, Bayesian Statistics has been taking a significant part in statistical study of all fields. Due to the recent breakthrough of high-dimensional integral, Bayesian Statistics has been improved and perfected, and now it can be used to solve problems that Classical Statistics failed to solve. This paper summarizes Bayesian Statistics’ history, concepts and applications, which are illustrated in five parts: the history of Bayesian Statistics, the weakness of Classical Statistics, Bayesian Theory and its development and applications. The first two parts make a comparison between Bayesian Statistics and Classical Statistics in a macroscopic aspect. And the last three parts focus on Bayesian Theory in specific -- from introducing some particular Bayesian Statistics’ concepts to listing their development and finally their applications.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.

PubMed

Gilpin, William; Feldman, Marcus W

2017-07-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

DNA viewed as an out-of-equilibrium structure

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

DNA viewed as an out-of-equilibrium structure.

PubMed

Provata, A; Nicolis, C; Nicolis, G

2014-05-01

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

Quantum statistical mechanics of dense partially ionized hydrogen.

NASA Technical Reports Server (NTRS)

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

1972-01-01

The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

Quantifying economic fluctuations by adapting methods of statistical physics

NASA Astrophysics Data System (ADS)

Plerou, Vasiliki

2001-09-01

The first focus of this thesis is the investigation of cross-correlations between the price fluctuations of different stocks using the conceptual framework of random matrix theory (RMT), developed in physics to describe the statistical properties of energy-level spectra of complex nuclei. RMT makes predictions for the statistical properties of matrices that are universal, i.e., do not depend on the interactions between the elements comprising the system. In physical systems, deviations from the predictions of RMT provide clues regarding the mechanisms controlling the dynamics of a given system so this framework is of potential value if applied to economic systems. This thesis compares the statistics of cross-correlation matrix C-whose elements Cij are the correlation coefficients of price fluctuations of stock i and j-against the ``null hypothesis'' of a random matrix having the same symmetry properties. It is shown that comparison of the eigenvalue statistics of C with RMT results can be used to distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine cross-correlations between stocks. The interpretations and potential practical utility of these deviations are also investigated. The second focus is the characterization of the dynamics of stock price fluctuations. The statistical properties of the changes G Δt in price over a time interval Δ t are quantified and the statistical relation between G Δt and the trading activity-measured by the number of transactions NΔ t in the interval Δt is investigated. The statistical properties of the volatility, i.e., the time dependent standard deviation of price fluctuations, is related to two microscopic quantities: NΔt and the variance W2Dt of the price changes for all transactions in the interval Δ t. In addition, the statistical relationship between G Δt and the number of shares QΔt traded in Δ t is investigated.

Reported Theory Use by Digital Interventions for Hazardous and Harmful Alcohol Consumption, and Association With Effectiveness: Meta-Regression

PubMed Central

Crane, David; Brown, Jamie; Kaner, Eileen; Beyer, Fiona; Muirhead, Colin; Hickman, Matthew; Redmore, James; de Vocht, Frank; Beard, Emma; Michie, Susan

2018-01-01

Background Applying theory to the design and evaluation of interventions is likely to increase effectiveness and improve the evidence base from which future interventions are developed, though few interventions report this. Objective The aim of this paper was to assess how digital interventions to reduce hazardous and harmful alcohol consumption report the use of theory in their development and evaluation, and whether reporting of theory use is associated with intervention effectiveness. Methods Randomized controlled trials were extracted from a Cochrane review on digital interventions for reducing hazardous and harmful alcohol consumption. Reporting of theory use within these digital interventions was investigated using the theory coding scheme (TCS). Reported theory use was analyzed by frequency counts and descriptive statistics. Associations were analyzed with meta-regression models. Results Of 41 trials involving 42 comparisons, half did not mention theory (50% [21/42]), and only 38% (16/42) used theory to select or develop the intervention techniques. Significant heterogeneity existed between studies in the effect of interventions on alcohol reduction (I2=77.6%, P<.001). No significant associations were detected between reporting of theory use and intervention effectiveness in unadjusted models, though the meta-regression was underpowered to detect modest associations. Conclusions Digital interventions offer a unique opportunity to refine and develop new dynamic, temporally sensitive theories, yet none of the studies reported refining or developing theory. Clearer selection, application, and reporting of theory use is needed to accurately assess how useful theory is in this field and to advance the field of behavior change theories. PMID:29490895

Emerging geometry from maximally super-symmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

Vazquez, Samuel Enrique

In this thesis, we explore the emergence of space-time geometry, and string theory physics from N = 4 supersymmetric Yang-Mills (SYM) theory with gauge group U(N). This is done in the context of the anti-de-Sitter/conformal field theory correspondence (AdS/CFT). The main results of this thesis are the following. First, we study single trace perturbations around generic 1/2 BPS states of the theory. We do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show how these states can be mapped to dynamical lattices with boson statistics and periodic boundary conditions. By dynamical, we mean that the total boson occupation number is not conserved in general. Then, we show how to derive an effective sigma model for these systems which coincides with the Polyakov action of a probe string on a 1/2 BPS geometry (in the fast string limit). Secondly, we study non-supersymmetric perturbations of the vacuum which give rise to bosonic lattices with open boundary conditions. We also do this in the large N limit, and at one-loop in the 't-Hooft coupling. We show that these states are dual to open strings on D3-branes known as "Giant Gravitons". These lattice systems are also dynamical, but in some special cases, we show that we get an integrable spin chain with open boundary conditions. Next, we study single trace perturbations at strong coupling. We do this by taking a "dilute gas" approximation. We derive an all-loop result for the dispersion relation of the "magnons" which coincides with previous conjectures in the literature. What is more, we derive the geometrical picture of the so-called "giant magnon" string solution of Hofman and Maldacena, directly from the field theory. Finally, we explore the question of classical integrability of open strings on D-branes. In particular, we study the case of the giant gravitons, and compare the integrable structures on both sides of the AdS/CFT correspondence.

Special Features of Galactic Dynamics

NASA Astrophysics Data System (ADS)

Efthymiopoulos, Christos; Voglis, Nikos; Kalapotharakos, Constantinos

This is an introductory article to some basic notions and currently open problems of galactic dynamics. The focus is on topics mostly relevant to the so-called `new methods' of celestial mechanics or Hamiltonian dynamics, as applied to the ellipsoidal components of galaxies, i.e., to the elliptical galaxies and to the dark halos and bulges of disk galaxies. Traditional topics such as Jeans theorem, the role of a `third integral' of motion, Nekhoroshev theory, violent relaxation, and the statistical mechanics of collisionless stellar systems are first discussed. The emphasis is on modern extrapolations of these old topics. Recent results from orbital and global dynamical studies of galaxies are then shortly reviewed. The role of various families of orbits in supporting self-consistency, as well as the role of chaos in galaxies, are stressed. A description is then given of the main numerical techniques of integration of the N-body problem in the framework of stellar dynamics and of the results obtained via N-Body experiments. A final topic is the secular evolution and self-organization of galactic systems.

Contributions of Dynamic Systems Theory to Cognitive Development

ERIC Educational Resources Information Center

Spencer, John P.; Austin, Andrew; Schutte, Anne R.

2012-01-01

We examine the contributions of dynamic systems theory to the field of cognitive development, focusing on modeling using dynamic neural fields. After introducing central concepts of dynamic field theory (DFT), we probe empirical predictions and findings around two examples--the DFT of infant perseverative reaching that explains Piaget's A-not-B…

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

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

NASA Astrophysics Data System (ADS)

Kawakatsu, Toshihiro

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

General dynamical density functional theory for classical fluids.

PubMed

Goddard, Benjamin D; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A; Kalliadasis, Serafim

2012-09-21

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?

NASA Astrophysics Data System (ADS)

Riols, A.; Rincon, F.; Cossu, C.; Lesur, G.; Ogilvie, G. I.; Longaretti, P.-Y.

2017-02-01

In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo mechanisminvolving magnetorotational instability (MRI). This dynamo may notably contribute to explaining the time-variability of various accreting systems, as high-resolution simulations of MRI dynamo turbulence exhibit statistical self-organization into large-scale cyclic dynamics. However, understanding the physics underlying these statistical states and assessing their exact astrophysical relevance is theoretically challenging. The study of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has highlighted the role of turbulent magnetic diffusion in the seeming impossibility of a dynamo at low magnetic Prandtl number (Pm), a common regime in disks. Arguably though, these simple laminar structures may not be fully representative of the complex, statistically self-organized states expected in astrophysical regimes. Here, we aim at closing this seeming discrepancy by reporting the numerical discovery of exactly periodic, yet semi-statistical "chimeral MRI dynamo states" which are the organized outcome of a succession of MRI-unstable, non-axisymmetric dynamical stages of different forms and amplitudes. Interestingly, these states, while reminiscent of the statistical complexity of turbulent simulations, involve the same physical principles as simpler laminar cycles, and their analysis further confirms the theory that subcritical turbulent magnetic diffusion impedes the sustainment of an MRI dynamo at low Pm. Overall, chimera dynamo cycles therefore offer an unprecedented dual physical and statistical perspective on dynamos in rotating shear flows, which may prove useful in devising more accurate, yet intuitive mean-field models of time-dependent turbulent disk dynamos. Movies associated to Fig. 1 are available at http://www.aanda.org

Statistical mechanics of complex neural systems and high dimensional data

NASA Astrophysics Data System (ADS)

Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya

2013-03-01

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? Second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks.

Analysis of spontaneous MEG activity in mild cognitive impairment and Alzheimer's disease using spectral entropies and statistical complexity measures

NASA Astrophysics Data System (ADS)

Bruña, Ricardo; Poza, Jesús; Gómez, Carlos; García, María; Fernández, Alberto; Hornero, Roberto

2012-06-01

Alzheimer's disease (AD) is the most common cause of dementia. Over the last few years, a considerable effort has been devoted to exploring new biomarkers. Nevertheless, a better understanding of brain dynamics is still required to optimize therapeutic strategies. In this regard, the characterization of mild cognitive impairment (MCI) is crucial, due to the high conversion rate from MCI to AD. However, only a few studies have focused on the analysis of magnetoencephalographic (MEG) rhythms to characterize AD and MCI. In this study, we assess the ability of several parameters derived from information theory to describe spontaneous MEG activity from 36 AD patients, 18 MCI subjects and 26 controls. Three entropies (Shannon, Tsallis and Rényi entropies), one disequilibrium measure (based on Euclidean distance ED) and three statistical complexities (based on Lopez Ruiz-Mancini-Calbet complexity LMC) were used to estimate the irregularity and statistical complexity of MEG activity. Statistically significant differences between AD patients and controls were obtained with all parameters (p < 0.01). In addition, statistically significant differences between MCI subjects and controls were achieved by ED and LMC (p < 0.05). In order to assess the diagnostic ability of the parameters, a linear discriminant analysis with a leave-one-out cross-validation procedure was applied. The accuracies reached 83.9% and 65.9% to discriminate AD and MCI subjects from controls, respectively. Our findings suggest that MCI subjects exhibit an intermediate pattern of abnormalities between normal aging and AD. Furthermore, the proposed parameters provide a new description of brain dynamics in AD and MCI.

A comparative study of different ferrofluid constitutive equations.

NASA Astrophysics Data System (ADS)

Kaloni, Purna

2011-11-01

Ferrofluids are stable colloidal suspensions of fine ferromagnetic monodomain nanoparticles in a non-conducting carrier fluid. The particles are coated with a surfacant to avoid agglomeration and coagulation.Brownian motion keeps the nanoparticles from settling under gravity. In recent years these fluids have found several applications including in liquid seals in rotary shafts for vacuum system and in hard disk drives of personal computers, in cooling and damping of loud speakers, in shock absorbers and in biomedical applications. A continuum description of ferrofluids was initiated by Neuringer and Rosensweig but the theory had some limitations. In subsequent years,several authors have proposed generalization of the above theory.Some of these are based upon the internal particle rotation concept, some are phemonological, some are based upon a thermodynamic framework, some employ statistical approach and some have used the dynamic mean field approach. The results based upon these theories ane in early stages and inconclusive. Our purpose is, first, to critically examine the basic foundations of these equations and then study the pedictions obtained in all the theories related to an experimental as well as a theoretical study.

Dynamic cross-correlations between entangled biofilaments as they diffuse

PubMed Central

Tsang, Boyce; Dell, Zachary E.; Jiang, Lingxiang; Schweizer, Kenneth S.; Granick, Steve

2017-01-01

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales. PMID:28283664

Heat dissipation guides activation in signaling proteins.

PubMed

Weber, Jeffrey K; Shukla, Diwakar; Pande, Vijay S

2015-08-18

Life is fundamentally a nonequilibrium phenomenon. At the expense of dissipated energy, living things perform irreversible processes that allow them to propagate and reproduce. Within cells, evolution has designed nanoscale machines to do meaningful work with energy harnessed from a continuous flux of heat and particles. As dictated by the Second Law of Thermodynamics and its fluctuation theorem corollaries, irreversibility in nonequilibrium processes can be quantified in terms of how much entropy such dynamics produce. In this work, we seek to address a fundamental question linking biology and nonequilibrium physics: can the evolved dissipative pathways that facilitate biomolecular function be identified by their extent of entropy production in general relaxation processes? We here synthesize massive molecular dynamics simulations, Markov state models (MSMs), and nonequilibrium statistical mechanical theory to probe dissipation in two key classes of signaling proteins: kinases and G-protein-coupled receptors (GPCRs). Applying machinery from large deviation theory, we use MSMs constructed from protein simulations to generate dynamics conforming to positive levels of entropy production. We note the emergence of an array of peaks in the dynamical response (transient analogs of phase transitions) that draw the proteins between distinct levels of dissipation, and we see that the binding of ATP and agonist molecules modifies the observed dissipative landscapes. Overall, we find that dissipation is tightly coupled to activation in these signaling systems: dominant entropy-producing trajectories become localized near important barriers along known biological activation pathways. We go on to classify an array of equilibrium and nonequilibrium molecular switches that harmonize to promote functional dynamics.

Phenomenon of statistical instability of the third type systems—complexity

NASA Astrophysics Data System (ADS)

Eskov, V. V.; Gavrilenko, T. V.; Eskov, V. M.; Vokhmina, Yu. V.

2017-11-01

The problem of the existence and special properties of third type systems has been formulated within the new chaos-self-organization theory. In fact, a global problem of the possibility of the existence of steady-state regimes for homeostatic systems has been considered. These systems include not only medical and biological systems, but also the dynamics of meteorological parameters, as well as the ambient parameters of the environment in which humans are located. The new approach has been used to give a new definition for homeostatic systems (complexity).

Special issue of Computers and Fluids in honor of Cecil E. (Chuck) Leith

DOE PAGES

Zhou, Ye; Herring, Jackson

2017-05-12

Here, this special issue of Computers and Fluids is dedicated to Cecil E. (Chuck) Leith in honor of his research contributions, leadership in the areas of statistical fluid mechanics, computational fluid dynamics, and climate theory. Leith's contribution to these fields emerged from his interest in solving complex fluid flow problems--even those at high Mach numbers--in an era well before large scale supercomputing became the dominant mode of inquiry into these fields. Yet the issues raised and solved by his research effort are still of vital interest today.

Some loopholes to save quantum nonlocality

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2005-02-01

The EPR-chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality. The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non-Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to "reconstruct history" on the lines described by Orwell in "1984".

Special issue of Computers and Fluids in honor of Cecil E. (Chuck) Leith

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

Zhou, Ye; Herring, Jackson

Here, this special issue of Computers and Fluids is dedicated to Cecil E. (Chuck) Leith in honor of his research contributions, leadership in the areas of statistical fluid mechanics, computational fluid dynamics, and climate theory. Leith's contribution to these fields emerged from his interest in solving complex fluid flow problems--even those at high Mach numbers--in an era well before large scale supercomputing became the dominant mode of inquiry into these fields. Yet the issues raised and solved by his research effort are still of vital interest today.

Statistical behavior of time dynamics evolution of HIV infection

NASA Astrophysics Data System (ADS)

González, Ramón E. R.; Santos, Iury A. X.; Nunes, Marcos G. P.; de Oliveira, Viviane M.; Barbosa, Anderson L. R.

2017-09-01

We use the tools of the random matrix theory (RMT) to investigate the statistical behavior of the evolution of human immunodeficiency virus (HIV) infection. By means of the nearest-neighbor spacing distribution we have identified four distinct regimes of the evolution of HIV infection. We verified that at the beginning of the so-called clinical latency phase the concentration of infected cells grows slowly and evolves in a correlated way. This regime is followed by another one in which the correlation is lost and that in turn leads the system to a regime in which the increase of infected cells is faster and correlated. In the final phase, the one in which acquired immunodeficiency syndrome (AIDS) is stablished, the system presents maximum correlation as demonstrated by GOE distribution.

Crossed beam (E--VRT) energy transfer experiment

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

Hertel, I.V.; Hofmann, H.; Rost, K.A.

A molecular crossed beam apparatus which has been developed to perform electronic-to-vibrational, rotational, translational (E--V,R,T) energy transfer studies is described. Its capabilities are illustrated on the basis of a number of energy transfer spectra obtained for collision systems of the type Na*+Mol(..nu..,j) ..-->..Na+Mol (..nu..',j') where Na* represents a laser excited sodium atom and Mol a diatomic or polyatomic molecule. Because of the lack of reliable dynamic theories on quenching processes, statistical approaches such as the ''linearly forced harmonic oscillator'' and ''prior distributions'' have been used to model the experimental spectra. The agreement is found to be satisfactory, so even suchmore » simple statistics may be useful to describe (E--V,R,T) energy transfer processes in collision systems with small molecules.« less

Stationary statistical theory of two-surface multipactor regarding all impacts for efficient threshold analysis

NASA Astrophysics Data System (ADS)

Lin, Shu; Wang, Rui; Xia, Ning; Li, Yongdong; Liu, Chunliang

2018-01-01

Statistical multipactor theories are critical prediction approaches for multipactor breakdown determination. However, these approaches still require a negotiation between the calculation efficiency and accuracy. This paper presents an improved stationary statistical theory for efficient threshold analysis of two-surface multipactor. A general integral equation over the distribution function of the electron emission phase with both the single-sided and double-sided impacts considered is formulated. The modeling results indicate that the improved stationary statistical theory can not only obtain equally good accuracy of multipactor threshold calculation as the nonstationary statistical theory, but also achieve high calculation efficiency concurrently. By using this improved stationary statistical theory, the total time consumption in calculating full multipactor susceptibility zones of parallel plates can be decreased by as much as a factor of four relative to the nonstationary statistical theory. It also shows that the effect of single-sided impacts is indispensable for accurate multipactor prediction of coaxial lines and also more significant for the high order multipactor. Finally, the influence of secondary emission yield (SEY) properties on the multipactor threshold is further investigated. It is observed that the first cross energy and the energy range between the first cross and the SEY maximum both play a significant role in determining the multipactor threshold, which agrees with the numerical simulation results in the literature.

Optimal Recall from Bounded Metaplastic Synapses: Predicting Functional Adaptations in Hippocampal Area CA3

PubMed Central

Savin, Cristina; Dayan, Peter; Lengyel, Máté

2014-01-01

A venerable history of classical work on autoassociative memory has significantly shaped our understanding of several features of the hippocampus, and most prominently of its CA3 area, in relation to memory storage and retrieval. However, existing theories of hippocampal memory processing ignore a key biological constraint affecting memory storage in neural circuits: the bounded dynamical range of synapses. Recent treatments based on the notion of metaplasticity provide a powerful model for individual bounded synapses; however, their implications for the ability of the hippocampus to retrieve memories well and the dynamics of neurons associated with that retrieval are both unknown. Here, we develop a theoretical framework for memory storage and recall with bounded synapses. We formulate the recall of a previously stored pattern from a noisy recall cue and limited-capacity (and therefore lossy) synapses as a probabilistic inference problem, and derive neural dynamics that implement approximate inference algorithms to solve this problem efficiently. In particular, for binary synapses with metaplastic states, we demonstrate for the first time that memories can be efficiently read out with biologically plausible network dynamics that are completely constrained by the synaptic plasticity rule, and the statistics of the stored patterns and of the recall cue. Our theory organises into a coherent framework a wide range of existing data about the regulation of excitability, feedback inhibition, and network oscillations in area CA3, and makes novel and directly testable predictions that can guide future experiments. PMID:24586137

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Continuous Advances in QCD 2008

NASA Astrophysics Data System (ADS)

Peloso, Marco M.

2008-12-01

1. High-order calculations in QCD and in general gauge theories. NLO evolution of color dipoles / I. Balitsky. Recent perturbative results on heavy quark decays / J. H. Piclum, M. Dowling, A. Pak. Leading and non-leading singularities in gauge theory hard scattering / G. Sterman. The space-cone gauge, Lorentz invariance and on-shell recursion for one-loop Yang-Mills amplitudes / D. Vaman, Y.-P. Yao -- 2. Heavy flavor physics. Exotic cc¯ mesons / E. Braaten. Search for new physics in B[symbol]-mixing / A. J. Lenz. Implications of D[symbol]-D[symbol] mixing for new physics / A. A. Petrov. Precise determinations of the charm quark mass / M. Steinhauser -- 3. Quark-gluon dynamics at high density and/or high temperature. Crystalline condensate in the chiral Gross-Neveu model / G. V. Dunne, G. Basar. The strong coupling constant at low and high energies / J. H. Kühn. Quarkyonic matter and the phase diagram of QCD / L. McLerran. Statistical QCD with non-positive measure / J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot. From equilibrium to transport properties of strongly correlated fermi liquids / T. Schäfer. Lessons from random matrix theory for QCD at finite density / K. Splittorff, J. J. M. Verbaarschot -- 4. Methods and models of holographic correspondence. Soft-wall dynamics in AdS/QCD / B. Batell. Holographic QCD / N. Evans, E. Threlfall. QCD glueball sum rules and vacuum topology / H. Forkel. The pion form factor in AdS/QCD / H. J. Kwee, R. F. Lebed. The fast life of holographic mesons / R. C. Myers, A. Sinha. Properties of Baryons from D-branes and instantons / S. Sugimoto. The master space of N = 1 quiver gauge theories: counting BPS operators / A. Zaffaroni. Topological field congurations. Skyrmions in theories with massless adjoint quarks / R. Auzzi. Domain walls, localization and confinement: what binds strings inside walls / S. Bolognesi. Static interactions of non-abelian vortices / M. Eto. Vortices which do not abelianize dynamically: semi-classical origin of non-abelian monopoles / K. Konishi. A generalized construction for lumps and non-abelian vortices / W. Vinci -- 6. Dynamics in supersymmetric theories. Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory / B. Basso. SO(2M) and USp(2M) (hyper)Kähler quotients and lumps / S. B. Gudnason -- 7. Other developments. Gluinos condensing at the CCNI: 4096 CPUs weigh in / J. Giedt ... [et al.]. Baryon Regge trajectories and the 1/N[symbol] expansion / J. L. Goity, N. Matagne. Infrared behavior of the fermion propagator in unquenched QED[symbol] with finite threshold effects / Y. Hoshino. Gauge fields in accelerated frames / F. Lenz. QCD at complex coupling, large order in perturbation theory and the gluon condensate / Y. Meurice. 511 KeV line and other diffuse emissions as a trace of the dark matter / A. R. Zhitnitsky -- 8. Glimpses of the conference.

Homogeneous nucleation in supersaturated vapors of methane, ethane, and carbon dioxide predicted by brute force molecular dynamics.

PubMed

Horsch, Martin; Vrabec, Jadran; Bernreuther, Martin; Grottel, Sebastian; Reina, Guido; Wix, Andrea; Schaber, Karlheinz; Hasse, Hans

2008-04-28

Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a 10(6) particles were conducted with a massively parallel MD program. This leads to reliable statistics and makes nucleation rates down to the order of 10(30) m(-3) s(-1) accessible to the direct simulation approach. Simulation results are compared to the classical nucleation theory (CNT) as well as the modification of Laaksonen, Ford, and Kulmala (LFK) which introduces a size dependence of the specific surface energy. CNT describes the nucleation of ethane and carbon dioxide excellently over the entire studied temperature range, whereas LFK provides a better approach to methane at low temperatures.

The effect of the dynamic wet troposphere on radio interferometric measurements

NASA Technical Reports Server (NTRS)

Treuhaft, R. N.; Lanyi, G. E.

1987-01-01

A statistical model of water vapor fluctuations is used to describe the effect of the dynamic wet troposphere on radio interferometric measurements. It is assumed that the spatial structure of refractivity is approximated by Kolmogorov turbulence theory, and that the temporal fluctuations are caused by spatial patterns moved over a site by the wind, and these assumptions are examined for the VLBI delay and delay rate observables. The results suggest that the delay rate measurement error is usually dominated by water vapor fluctuations, and water vapor induced VLBI parameter errors and correlations are determined as a function of the delay observable errors. A method is proposed for including the water vapor fluctuations in the parameter estimation method to obtain improved parameter estimates and parameter covariances.

Mathematical and Computational Challenges in Population Biology and Ecosystems Science

NASA Technical Reports Server (NTRS)

Levin, Simon A.; Grenfell, Bryan; Hastings, Alan; Perelson, Alan S.

1997-01-01

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

A statistical state dynamics approach to wall turbulence.

PubMed

Farrell, B F; Gayme, D F; Ioannou, P J

2017-03-13

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

A statistical state dynamics approach to wall turbulence

PubMed Central

Gayme, D. F.; Ioannou, P. J.

2017-01-01

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation–perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or ‘band-limiting’ can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167577

Multiagent model and mean field theory of complex auction dynamics

NASA Astrophysics Data System (ADS)

Chen, Qinghua; Huang, Zi-Gang; Wang, Yougui; Lai, Ying-Cheng

2015-09-01

Recent years have witnessed a growing interest in analyzing a variety of socio-economic phenomena using methods from statistical and nonlinear physics. We study a class of complex systems arising from economics, the lowest unique bid auction (LUBA) systems, which is a recently emerged class of online auction game systems. Through analyzing large, empirical data sets of LUBA, we identify a general feature of the bid price distribution: an inverted J-shaped function with exponential decay in the large bid price region. To account for the distribution, we propose a multi-agent model in which each agent bids stochastically in the field of winner’s attractiveness, and develop a theoretical framework to obtain analytic solutions of the model based on mean field analysis. The theory produces bid-price distributions that are in excellent agreement with those from the real data. Our model and theory capture the essential features of human behaviors in the competitive environment as exemplified by LUBA, and may provide significant quantitative insights into complex socio-economic phenomena.

Assessing the accuracy of different simplified frictional rolling contact algorithms

NASA Astrophysics Data System (ADS)

Vollebregt, E. A. H.; Iwnicki, S. D.; Xie, G.; Shackleton, P.

2012-01-01

This paper presents an approach for assessing the accuracy of different frictional rolling contact theories. The main characteristic of the approach is that it takes a statistically oriented view. This yields a better insight into the behaviour of the methods in diverse circumstances (varying contact patch ellipticities, mixed longitudinal, lateral and spin creepages) than is obtained when only a small number of (basic) circumstances are used in the comparison. The range of contact parameters that occur for realistic vehicles and tracks are assessed using simulations with the Vampire vehicle system dynamics (VSD) package. This shows that larger values for the spin creepage occur rather frequently. Based on this, our approach is applied to typical cases for which railway VSD packages are used. The results show that particularly the USETAB approach but also FASTSIM give considerably better results than the linear theory, Vermeulen-Johnson, Shen-Hedrick-Elkins and Polach methods, when compared with the 'complete theory' of the CONTACT program.

Analysis of spontaneous EEG activity in Alzheimer's disease using cross-sample entropy and graph theory.

PubMed

Gomez, Carlos; Poza, Jesus; Gomez-Pilar, Javier; Bachiller, Alejandro; Juan-Cruz, Celia; Tola-Arribas, Miguel A; Carreres, Alicia; Cano, Monica; Hornero, Roberto

2016-08-01

The aim of this pilot study was to analyze spontaneous electroencephalography (EEG) activity in Alzheimer's disease (AD) by means of Cross-Sample Entropy (Cross-SampEn) and two local measures derived from graph theory: clustering coefficient (CC) and characteristic path length (PL). Five minutes of EEG activity were recorded from 37 patients with dementia due to AD and 29 elderly controls. Our results showed that Cross-SampEn values were lower in the AD group than in the control one for all the interactions among EEG channels. This finding indicates that EEG activity in AD is characterized by a lower statistical dissimilarity among channels. Significant differences were found mainly for fronto-central interactions (p <; 0.01, permutation test). Additionally, the application of graph theory measures revealed diverse neural network changes, i.e. lower CC and higher PL values in AD group, leading to a less efficient brain organization. This study suggests the usefulness of our approach to provide further insights into the underlying brain dynamics associated with AD.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited

NASA Astrophysics Data System (ADS)

Chaudhari, Mangesh I.; Rempe, Susan B.; Pratt, Lawrence R.

2017-10-01

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances.

PubMed

Chekroun, Mickaël David; Neelin, J David; Kondrashov, Dmitri; McWilliams, James C; Ghil, Michael

2014-02-04

Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them--as filtered through an observable of the system--is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap--defined as the distance between the subdominant RP resonance and the unit circle--plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño-Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally.

Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances

PubMed Central

Chekroun, Mickaël David; Neelin, J. David; Kondrashov, Dmitri; McWilliams, James C.; Ghil, Michael

2014-01-01

Despite the importance of uncertainties encountered in climate model simulations, the fundamental mechanisms at the origin of sensitive behavior of long-term model statistics remain unclear. Variability of turbulent flows in the atmosphere and oceans exhibits recurrent large-scale patterns. These patterns, while evolving irregularly in time, manifest characteristic frequencies across a large range of time scales, from intraseasonal through interdecadal. Based on modern spectral theory of chaotic and dissipative dynamical systems, the associated low-frequency variability may be formulated in terms of Ruelle-Pollicott (RP) resonances. RP resonances encode information on the nonlinear dynamics of the system, and an approach for estimating them—as filtered through an observable of the system—is proposed. This approach relies on an appropriate Markov representation of the dynamics associated with a given observable. It is shown that, within this representation, the spectral gap—defined as the distance between the subdominant RP resonance and the unit circle—plays a major role in the roughness of parameter dependences. The model statistics are the most sensitive for the smallest spectral gaps; such small gaps turn out to correspond to regimes where the low-frequency variability is more pronounced, whereas autocorrelations decay more slowly. The present approach is applied to analyze the rough parameter dependence encountered in key statistics of an El-Niño–Southern Oscillation model of intermediate complexity. Theoretical arguments, however, strongly suggest that such links between model sensitivity and the decay of correlation properties are not limited to this particular model and could hold much more generally. PMID:24443553

Predicting population dynamics from the properties of individuals: a cross-level test of dynamic energy budget theory.

PubMed

Martin, Benjamin T; Jager, Tjalling; Nisbet, Roger M; Preuss, Thomas G; Grimm, Volker

2013-04-01

Individual-based models (IBMs) are increasingly used to link the dynamics of individuals to higher levels of biological organization. Still, many IBMs are data hungry, species specific, and time-consuming to develop and analyze. Many of these issues would be resolved by using general theories of individual dynamics as the basis for IBMs. While such theories have frequently been examined at the individual level, few cross-level tests exist that also try to predict population dynamics. Here we performed a cross-level test of dynamic energy budget (DEB) theory by parameterizing an individual-based model using individual-level data of the water flea, Daphnia magna, and comparing the emerging population dynamics to independent data from population experiments. We found that DEB theory successfully predicted population growth rates and peak densities but failed to capture the decline phase. Further assumptions on food-dependent mortality of juveniles were needed to capture the population dynamics after the initial population peak. The resulting model then predicted, without further calibration, characteristic switches between small- and large-amplitude cycles, which have been observed for Daphnia. We conclude that cross-level tests help detect gaps in current individual-level theories and ultimately will lead to theory development and the establishment of a generic basis for individual-based models and ecology.

Understanding rapid evolution in predator‐prey interactions using the theory of fast‐slow dynamical systems.

PubMed

Cortez, Michael H; Ellner, Stephen P

2010-11-01

The accumulation of evidence that ecologically important traits often evolve at the same time and rate as ecological dynamics (e.g., changes in species' abundances or spatial distributions) has outpaced theory describing the interplay between ecological and evolutionary processes with comparable timescales. The disparity between experiment and theory is partially due to the high dimensionality of models that include both evolutionary and ecological dynamics. Here we show how the theory of fast-slow dynamical systems can be used to reduce model dimension, and we use that body of theory to study a general predator-prey system exhibiting fast evolution in either the predator or the prey. Our approach yields graphical methods with predictive power about when new and unique dynamics (e.g., completely out-of-phase oscillations and cryptic dynamics) can arise in ecological systems exhibiting fast evolution. In addition, we derive analytical expressions for determining when such behavior arises and how evolution affects qualitative properties of the ecological dynamics. Finally, while the theory requires a separation of timescales between the ecological and evolutionary processes, our approach yields insight into systems where the rates of those processes are comparable and thus is a step toward creating a general ecoevolutionary theory.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

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

NASA Astrophysics Data System (ADS)

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

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

Development of a dynamic computational model of social cognitive theory.

PubMed

Riley, William T; Martin, Cesar A; Rivera, Daniel E; Hekler, Eric B; Adams, Marc A; Buman, Matthew P; Pavel, Misha; King, Abby C

2016-12-01

Social cognitive theory (SCT) is among the most influential theories of behavior change and has been used as the conceptual basis of health behavior interventions for smoking cessation, weight management, and other health behaviors. SCT and other behavior theories were developed primarily to explain differences between individuals, but explanatory theories of within-person behavioral variability are increasingly needed as new technologies allow for intensive longitudinal measures and interventions adapted from these inputs. These within-person explanatory theoretical applications can be modeled as dynamical systems. SCT constructs, such as reciprocal determinism, are inherently dynamical in nature, but SCT has not been modeled as a dynamical system. This paper describes the development of a dynamical system model of SCT using fluid analogies and control systems principles drawn from engineering. Simulations of this model were performed to assess if the model performed as predicted based on theory and empirical studies of SCT. This initial model generates precise and testable quantitative predictions for future intensive longitudinal research. Dynamic modeling approaches provide a rigorous method for advancing health behavior theory development and refinement and for guiding the development of more potent and efficient interventions.

Non-Markovian quantum feedback networks II: Controlled flows

NASA Astrophysics Data System (ADS)

Gough, John E.

2017-06-01

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper, we build on the ideas presented by Bouten and van Handel [Quantum Stochastics and Information: Statistics, Filtering and Control (World Scientific, 2008)] and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes, Z, and the measured processes, Y, and to this end we make a distinction between what we call the input picture and the output picture. We should note that the input-output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent—we do this for the two main cases of quadrature measurement and photon-counting measurement. The theory is general enough to include a modulating filter which post-processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems. Finally, we give a brief argument as to why most of the rules for making instantaneous feedback connections [J. Gough and M. R. James, Commun. Math. Phys. 287, 1109 (2009)] ought to apply for controlled dynamical networks as well.

A review of dynamic inflow and its effect on experimental correlations

NASA Technical Reports Server (NTRS)

Gaonkar, G. H.; Peters, D. A.

1985-01-01

A review is given of the relationship between experimental data and the development of modern dynamic-inflow theory. Some of the most interesting data, first presented 10 years ago at the Dynamic Specialist's Meeting, is now reviewed in light of the newer theories. These pure blade-flapping data correlate very well with analyses that include the new dynamic inflow theory, thus verifying the theory. Experimental data are also presented for damping with coupled inplane and body motions. Although inclusion of dynamic inflow is often required to correlate this coupled data, the data cannot be used to verify any particular dynamic inflow theory due to the uncertainties in modeling the inplane degree of freedom. For verification, pure flapping is required. However, the coupled data do show that inflow is often important in such computations.

A theoretical study in extracting the essential features and dynamics of molecular motions: Intrinsic geometry methods for PF(5) pseudorotations and statistical methods for argon clusters

NASA Astrophysics Data System (ADS)

Panahi, Nima S.

We studied the problem of understanding and computing the essential features and dynamics of molecular motions through the development of two theories for two different systems. First, we studied the process of the Berry Pseudorotation of PF5 and the rotations it induces in the molecule through its natural and intrinsic geometric nature by setting it in the language of fiber bundles and graph theory. With these tools, we successfully extracted the essentials of the process' loops and induced rotations. The infinite number of pseudorotation loops were broken down into a small set of essential loops called "super loops", with their intrinsic properties and link to the physical movements of the molecule extensively studied. In addition, only the three "self-edge loops" generated any induced rotations, and then only a finite number of classes of them. Second, we studied applying the statistical methods of Principal Components Analysis (PCA) and Principal Coordinate Analysis (PCO) to capture only the most important changes in Argon clusters so as to reduce computational costs and graph the potential energy surface (PES) in three dimensions respectively. Both methods proved successful, but PCA was only partially successful since one will only see advantages for PES database systems much larger than those both currently being studied and those that can be computationally studied in the next few decades to come. In addition, PCA is only needed for the very rare case of a PES database that does not already include Hessian eigenvalues.

Symmetry, Statistics and Structure in MHD Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2007-01-01

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

"The Two Brothers": Reconciling Perceptual-Cognitive and Statistical Models of Musical Evolution.

PubMed

Jan, Steven

2018-01-01

While the "units, events and dynamics" of memetic evolution have been abstractly theorized (Lynch, 1998), they have not been applied systematically to real corpora in music. Some researchers, convinced of the validity of cultural evolution in more than the metaphorical sense adopted by much musicology, but perhaps skeptical of some or all of the claims of memetics, have attempted statistically based corpus-analysis techniques of music drawn from molecular biology, and these have offered strong evidence in favor of system-level change over time (Savage, 2017). This article argues that such statistical approaches, while illuminating, ignore the psychological realities of music-information grouping, the transmission of such groups with varying degrees of fidelity, their selection according to relative perceptual-cognitive salience, and the power of this Darwinian process to drive the systemic changes (such as the development over time of systems of tonal organization in music) that statistical methodologies measure. It asserts that a synthesis between such statistical approaches to the study of music-cultural change and the theory of memetics as applied to music (Jan, 2007), in particular the latter's perceptual-cognitive elements, would harness the strengths of each approach and deepen understanding of cultural evolution in music.

Statistical Model of Dynamic Markers of the Alzheimer's Pathological Cascade.

PubMed

Balsis, Steve; Geraci, Lisa; Benge, Jared; Lowe, Deborah A; Choudhury, Tabina K; Tirso, Robert; Doody, Rachelle S

2018-05-05

Alzheimer's disease (AD) is a progressive disease reflected in markers across assessment modalities, including neuroimaging, cognitive testing, and evaluation of adaptive function. Identifying a single continuum of decline across assessment modalities in a single sample is statistically challenging because of the multivariate nature of the data. To address this challenge, we implemented advanced statistical analyses designed specifically to model complex data across a single continuum. We analyzed data from the Alzheimer's Disease Neuroimaging Initiative (ADNI; N = 1,056), focusing on indicators from the assessments of magnetic resonance imaging (MRI) volume, fluorodeoxyglucose positron emission tomography (FDG-PET) metabolic activity, cognitive performance, and adaptive function. Item response theory was used to identify the continuum of decline. Then, through a process of statistical scaling, indicators across all modalities were linked to that continuum and analyzed. Findings revealed that measures of MRI volume, FDG-PET metabolic activity, and adaptive function added measurement precision beyond that provided by cognitive measures, particularly in the relatively mild range of disease severity. More specifically, MRI volume, and FDG-PET metabolic activity become compromised in the very mild range of severity, followed by cognitive performance and finally adaptive function. Our statistically derived models of the AD pathological cascade are consistent with existing theoretical models.

Reported Theory Use by Digital Interventions for Hazardous and Harmful Alcohol Consumption, and Association With Effectiveness: Meta-Regression.

PubMed

Garnett, Claire; Crane, David; Brown, Jamie; Kaner, Eileen; Beyer, Fiona; Muirhead, Colin; Hickman, Matthew; Redmore, James; de Vocht, Frank; Beard, Emma; Michie, Susan

2018-02-28

Applying theory to the design and evaluation of interventions is likely to increase effectiveness and improve the evidence base from which future interventions are developed, though few interventions report this. The aim of this paper was to assess how digital interventions to reduce hazardous and harmful alcohol consumption report the use of theory in their development and evaluation, and whether reporting of theory use is associated with intervention effectiveness. Randomized controlled trials were extracted from a Cochrane review on digital interventions for reducing hazardous and harmful alcohol consumption. Reporting of theory use within these digital interventions was investigated using the theory coding scheme (TCS). Reported theory use was analyzed by frequency counts and descriptive statistics. Associations were analyzed with meta-regression models. Of 41 trials involving 42 comparisons, half did not mention theory (50% [21/42]), and only 38% (16/42) used theory to select or develop the intervention techniques. Significant heterogeneity existed between studies in the effect of interventions on alcohol reduction (I 2 =77.6%, P<.001). No significant associations were detected between reporting of theory use and intervention effectiveness in unadjusted models, though the meta-regression was underpowered to detect modest associations. Digital interventions offer a unique opportunity to refine and develop new dynamic, temporally sensitive theories, yet none of the studies reported refining or developing theory. Clearer selection, application, and reporting of theory use is needed to accurately assess how useful theory is in this field and to advance the field of behavior change theories. ©Claire Garnett, David Crane, Jamie Brown, Eileen Kaner, Fiona Beyer, Colin Muirhead, Matthew Hickman, James Redmore, Frank de Vocht, Emma Beard, Susan Michie. Originally published in the Journal of Medical Internet Research (http://www.jmir.org), 28.02.2018.

Group entropies, correlation laws, and zeta functions.

PubMed

Tempesta, Piergiulio

2011-08-01

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

Mechanical Metamaterials with Negative Compressibility Transitions

NASA Astrophysics Data System (ADS)

Motter, Adilson

2015-03-01

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

Reactive trajectories of the Ru2+/3+ self-exchange reaction and the connection to Marcus' theory.

PubMed

Tiwari, Ambuj; Ensing, Bernd

2016-12-22

Outer sphere electron transfer between two ions in aqueous solution is a rare event on the time scale of first principles molecular dynamics simulations. We have used transition path sampling to generate an ensemble of reactive trajectories of the self-exchange reaction between a pair of Ru 2+ and Ru 3+ ions in water. To distinguish between the reactant and product states, we use as an order parameter the position of the maximally localised Wannier center associated with the transferring electron. This allows us to align the trajectories with respect to the moment of barrier crossing and compute statistical averages over the path ensemble. We compare our order parameter with two typical reaction coordinates used in applications of Marcus theory of electron transfer: the vertical gap energy and the solvent electrostatic potential at the ions.

Evidence against the continuum structure underlying motivation measures derived from self-determination theory.

PubMed

Chemolli, Emanuela; Gagné, Marylène

2014-06-01

Self-determination theory (SDT) proposes a multidimensional conceptualization of motivation in which the different regulations are said to fall along a continuum of self-determination. The continuum has been used as a basis for using a relative autonomy index as a means to create motivational scores. Rasch analysis was used to verify the continuum structure of the Multidimensional Work Motivation Scale and of the Academic Motivation Scale. We discuss the concept of continuum against SDT's conceptualization of motivation and argue against the use of the relative autonomy index on the grounds that evidence for a continuum structure underlying the regulations is weak and because the index is statistically problematic. We suggest exploiting the full richness of SDT's multidimensional conceptualization of motivation through the use of alternative scoring methods when investigating motivational dynamics across life domains.

Fuzzy logic of Aristotelian forms

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

Perlovsky, L.I.

1996-12-31

Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties.more » In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority and adaptivity, implements Aristotelian theory of Forms (theory of mind). Thus, 2300 years after Aristotle, a logic is developed suitable for his theory of mind.« less

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs.

PubMed

Giugliano, Michele; La Camera, Giancarlo; Fusi, Stefano; Senn, Walter

2008-11-01

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

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

PubMed Central

Aquilanti, Vincenzo; Coutinho, Nayara Dantas

2017-01-01

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

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

PubMed

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

2017-04-28

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d  < 0, to those where d  > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d  = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d  > 0 or for a negative binomial distribution if d  < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super -Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub -Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti -Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'. © 2017 The Author(s).

Statistics of resonances for a class of billiards on the Poincaré half-plane

NASA Astrophysics Data System (ADS)

Howard, P. J.; Mota-Furtado, F.; O'Mahony, P. F.; Uski, V.

2005-12-01

The lower boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of billiards with classical dynamics varying from fully integrable to completely chaotic. The quantum scattering problem in these open billiards is described and the statistics of both real and imaginary parts of the resonant momenta are investigated. The evolution of the resonance positions is followed as the boundary is varied which leads to large changes in their distribution. The transition to arithmetic chaos in Artin's billiard, which is responsible for the Poissonian level-spacing statistics of the bound states in the continuum (cusp forms) at the same time as the formation of a set of resonances all with width \\frac{1}{4} and real parts determined by the zeros of Riemann's zeta function, is closely examined. Regimes are found which obey the universal predictions of random matrix theory (RMT) as well as exhibiting non-universal long-range correlations. The Brody parameter is used to describe the transitions between different regimes.

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT).

PubMed

Biswas, M E; Chatzis, I; Ioannidis, M A; Chen, P

2005-06-01

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)

Nurse executive transformational leadership and organizational commitment.

PubMed

Leach, Linda Searle

2005-05-01

To investigate the relationship between nurse executive leadership and organizational commitment among nurses in acute care hospitals. A key challenge for organizations is to maximize the contributions of all workers by cultivating their commitment. Nurse leaders are in a position to influence organizational commitment among nurses. The theoretical constructs underlying this study are the transformational leadership theory and the Etzioni's organizational theory. A cross-sectional, field survey of nurse executives, nurse managers, and staff nurses was conducted to assess nurse executive transformational and transactional leadership and their relationship to organizational commitment. Hypotheses were tested using correlational analysis, and univariate statistics were used to describe the sample. An inverse relationship between nurse executive transformational and transactional leadership and alienative (highly negative) organizational commitment was statistically significant. A positive association was demonstrated between nurse executive leadership and nurse manager leadership. This study supports the effect of nurse executive leadership on nurse manager leadership and on organizational commitment among nurses despite role distance. To the extent that transformational leadership is present, alienative organizational commitment is reduced. This relationship shows the importance of nurse executive leadership in organizational involvement among nurses in the dynamic context of contemporary hospital settings.

Statistical Hierarchy of Varying Speed of Light Cosmologies

NASA Astrophysics Data System (ADS)

Salzano, Vincenzo; Da¸browski, Mariusz P.

2017-12-01

Many varying speed of light (VSL) theories have been developed recently. Here we address the issue of their observational verification in a fully comprehensive way. By using the most updated cosmological probes, we test three different candidates for a VSL theory (Barrow & Magueijo, Avelino & Martins, and Moffat). We consider many different Ansätze for both the functional form of c(z) and the dark energy dynamics. We compare these results using a reliable statistical tool such as the Bayesian evidence. We find that the present cosmological data are perfectly compatible with any of these VSL scenarios, but for the Moffat model there is a higher Bayesian evidence ratio in favor of VSL rather than the c = constant ΛCDM scenario. Moreover, in such a scenario, the VSL signal can help to strengthen constraints on the spatial curvature (with indication toward an open universe), to clarify some properties of dark energy (exclusion of a cosmological constant at 2σ level), and is also falsifiable in the near future owing to peculiar issues that differentiate this model from the standard one. Finally, we apply an information prior and entropy prior in order to put physical constraints on the models, though still in favor Moffat’s proposal.

Statistics of chemical gradients in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Le Borgne, T.; Huck, P. D.; Dentz, M.; Villermaux, E.

2017-12-01

As they create chemical disequilibrium and drive mixing fluxes, spatial gradients in solute concentrations exert a strong control on mixing and biogeochemical reactions in the subsurface. Large concentration gradients may develop in particular at interfaces between surface water and groundwater bodies, such as hyporheic zones, sea water - surface water interfaces or recharge areas. They also develop around contaminant plumes and fluids injected in subsurface operations. While macrodispersion theories predict smooth gradients, decaying in time due to dispersive dissipation, we show that concentration gradients are sustained by flow heterogeneity and have broadly distributed values. We present a general theory predicting the statistics of concentration gradients from the flow heterogeneity (Le Borgne et al., 2017). Analytical predictions are validated from high resolution simulations of transport in heterogeneous Darcy fields ranging from low to high permeability variances and low to high Peclet numbers. This modelling framework hence opens new perspectives for quantifying the dynamics of chemical gradients and the kinetics of associated biogeochemical reactions in heterogeneous subsurface environments.Reference:Le Borgne T., P.D. Huck, M. Dentz and E. Villermaux (2017) Scalar gradients in stirred mixtures and the deconstruction of random fields, J. of Fluid Mech. vol. 812, pp. 578-610 doi:10.1017/jfm.2016.799

Zone of Proximal Development (ZPD) as an Emergent System: A Dynamic Systems Theory Perspective.

PubMed

Karimi-Aghdam, Saeed

2017-03-01

This paper sets out to present a novel construal of one of the notions of Vygotskian cultural-historical theory viz., zone of proximal development (ZPD) drawing upon dynamic systems theory. The principal thesis maintains that ZDP is an emergent and dynamic system which is engendered by a dialectical concatenation of psychogenesic and sociogenesic facets of human development over time. It is reasoned that Vygotskian cultural-historical theory of human development, by invoking dialectical logic, has transcended Cartesian substance dualism and in turn has proffered a monistic and process-anchored ontology for emerging becoming of human consciousness. Likewise, it is contended that dynamic systems theory, having assumed fluent flux of reality with a capital R as its ontological axiom, entails a consilience of cognitive and contextual conceptual schemes to describe, explain, and optimize human development. The paper concludes by drawing some interpretive conclusions in regard to ZPD from dynamic systems theory perspective.

Toward an affective neuroscience account of financial risk taking.

PubMed

Wu, Charlene C; Sacchet, Matthew D; Knutson, Brian

2012-01-01

To explain human financial risk taking, economic, and finance theories typically refer to the mathematical properties of financial options, whereas psychological theories have emphasized the influence of emotion and cognition on choice. From a neuroscience perspective, choice emanates from a dynamic multicomponential process. Recent technological advances in neuroimaging have made it possible for researchers to separately visualize perceptual input, intermediate processing, and motor output. An affective neuroscience account of financial risk taking thus might illuminate affective mediators that bridge the gap between statistical input and choice output. To test this hypothesis, we conducted a quantitative meta-analysis (via activation likelihood estimate or ALE) of functional magnetic resonance imaging experiments that focused on neural responses to financial options with varying statistical moments (i.e., mean, variance, skewness). Results suggested that different statistical moments elicit both common and distinct patterns of neural activity. Across studies, high versus low mean had the highest probability of increasing ventral striatal activity, but high versus low variance had the highest probability of increasing anterior insula activity. Further, high versus low skewness had the highest probability of increasing ventral striatal activity. Since ventral striatal activity has been associated with positive aroused affect (e.g., excitement), whereas anterior insular activity has been associated with negative aroused affect (e.g., anxiety) or general arousal, these findings are consistent with the notion that statistical input influences choice output by eliciting anticipatory affect. The findings also imply that neural activity can be used to predict financial risk taking - both when it conforms to and violates traditional models of choice.

Toward an Affective Neuroscience Account of Financial Risk Taking

PubMed Central

Wu, Charlene C.; Sacchet, Matthew D.; Knutson, Brian

2012-01-01

To explain human financial risk taking, economic, and finance theories typically refer to the mathematical properties of financial options, whereas psychological theories have emphasized the influence of emotion and cognition on choice. From a neuroscience perspective, choice emanates from a dynamic multicomponential process. Recent technological advances in neuroimaging have made it possible for researchers to separately visualize perceptual input, intermediate processing, and motor output. An affective neuroscience account of financial risk taking thus might illuminate affective mediators that bridge the gap between statistical input and choice output. To test this hypothesis, we conducted a quantitative meta-analysis (via activation likelihood estimate or ALE) of functional magnetic resonance imaging experiments that focused on neural responses to financial options with varying statistical moments (i.e., mean, variance, skewness). Results suggested that different statistical moments elicit both common and distinct patterns of neural activity. Across studies, high versus low mean had the highest probability of increasing ventral striatal activity, but high versus low variance had the highest probability of increasing anterior insula activity. Further, high versus low skewness had the highest probability of increasing ventral striatal activity. Since ventral striatal activity has been associated with positive aroused affect (e.g., excitement), whereas anterior insular activity has been associated with negative aroused affect (e.g., anxiety) or general arousal, these findings are consistent with the notion that statistical input influences choice output by eliciting anticipatory affect. The findings also imply that neural activity can be used to predict financial risk taking – both when it conforms to and violates traditional models of choice. PMID:23129993

Technology transfer from the science of medicine to the real world: the potential role played by artificial adaptive systems.

PubMed

Grossi, Enzo

2007-01-01

The author describes a refiguration of medical thought that originates from nonlinear dynamics and chaos theory. The coupling of computer science and these new theoretical bases coming from complex systems mathematics allows the creation of "intelligent" agents capable of adapting themselves dynamically to problems of high complexity: the artificial neural networks (ANNs). ANNs are able to reproduce the dynamic interaction of multiple factors simultaneously, allowing the study of complexity; they can also draw conclusions on an individual basis and not as average trends. These tools can allow a more efficient technology transfer from the science of medicine to the real world, overcoming many obstacles responsible for the present translational failure. They also contribute to a new holistic vision of the human subject person, contrasting the statistical reductionism that tends to squeeze or even delete the single subject, sacrificing him to his group of belongingness. A remarkable contribution to this individual approach comes from fuzzy logic, according to which there are no sharp limits between opposite things, such as wealth and disease. This approach allows one to partially escape from the probability theory trap in situations where it is fundamental to express a judgement based on a single case and favor a novel humanism directed to the management of the patient as an individual subject person.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

The physics of flocking: Correlation as a compass from experiments to theory

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Giardina, Irene; Grigera, Tomás S.

2018-01-01

Collective behavior in biological systems is a complex topic, to say the least. It runs wildly across scales in both space and time, involving taxonomically vastly different organisms, from bacteria and cell clusters, to insect swarms and up to vertebrate groups. It entails concepts as diverse as coordination, emergence, interaction, information, cooperation, decision-making, and synchronization. Amid this jumble, however, we cannot help noting many similarities between collective behavior in biological systems and collective behavior in statistical physics, even though none of these organisms remotely looks like an Ising spin. Such similarities, though somewhat qualitative, are startling, and regard mostly the emergence of global dynamical patterns qualitatively different from individual behavior, and the development of system-level order from local interactions. It is therefore tempting to describe collective behavior in biology within the conceptual framework of statistical physics, in the hope to extend to this new fascinating field at least part of the great predictive power of theoretical physics. In this review we propose that the conceptual cornerstone of this ambitious program be that of correlation. To illustrate this idea we address the case of collective behavior in bird flocks. Two key threads emerge, as two sides of one single story: the presence of scale-free correlations and the dynamical mechanism of information transfer. We discuss first static correlations in starling flocks, in particular the experimental finding of their scale-free nature, the formulation of models that account for this fact using maximum entropy, and the relation of scale-free correlations to information transfer. This is followed by a dynamic treatment of information propagation (propagation of turns across a flock), starting with a discussion of experimental results and following with possible theoretical explanations of those, which require the addition of behavioral inertia to existing theories of flocking. We finish with the definition and analysis of space-time correlations and their relevance to the detection of inertial behavior in the absence of external perturbations.

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.

Role of the Pair Correlation Function in the Dynamical Transition Predicted by Mode Coupling Theory

NASA Astrophysics Data System (ADS)

Nandi, Manoj Kumar; Banerjee, Atreyee; Dasgupta, Chandan; Bhattacharyya, Sarika Maitra

2017-12-01

In a recent study, we have found that for a large number of systems the configurational entropy at the pair level Sc 2, which is primarily determined by the pair correlation function, vanishes at the dynamical transition temperature Tc. Thus, it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this, we describe the dynamics of the system at the mean field level and, using the concepts of the dynamical density functional theory, show that the dynamical transition temperature depends only on the pair correlation function. Thus, this theory is similar in spirit to the microscopic mode coupling theory (MCT). However, unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature that is similar to Tc. This implies that the information of the dynamical transition temperature is embedded in the pair correlation function.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

PubMed Central

2017-01-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies. PMID:28678792

Beyond δ: Tailoring marked statistics to reveal modified gravity

NASA Astrophysics Data System (ADS)

Valogiannis, Georgios; Bean, Rachel

2018-01-01

Models which attempt to explain the accelerated expansion of the universe through large-scale modifications to General Relativity (GR), must satisfy the stringent experimental constraints of GR in the solar system. Viable candidates invoke a “screening” mechanism, that dynamically suppresses deviations in high density environments, making their overall detection challenging even for ambitious future large-scale structure surveys. We present methods to efficiently simulate the non-linear properties of such theories, and consider how a series of statistics that reweight the density field to accentuate deviations from GR can be applied to enhance the overall signal-to-noise ratio in differentiating the models from GR. Our results demonstrate that the cosmic density field can yield additional, invaluable cosmological information, beyond the simple density power spectrum, that will enable surveys to more confidently discriminate between modified gravity models and ΛCDM.

The mortality of companies

PubMed Central

Daepp, Madeleine I. G.; Hamilton, Marcus J.; West, Geoffrey B.; Bettencourt, Luís M. A.

2015-01-01

The firm is a fundamental economic unit of contemporary human societies. Studies on the general quantitative and statistical character of firms have produced mixed results regarding their lifespans and mortality. We examine a comprehensive database of more than 25 000 publicly traded North American companies, from 1950 to 2009, to derive the statistics of firm lifespans. Based on detailed survival analysis, we show that the mortality of publicly traded companies manifests an approximately constant hazard rate over long periods of observation. This regularity indicates that mortality rates are independent of a company's age. We show that the typical half-life of a publicly traded company is about a decade, regardless of business sector. Our results shed new light on the dynamics of births and deaths of publicly traded companies and identify some of the necessary ingredients of a general theory of firms. PMID:25833247

The mortality of companies.

PubMed

Daepp, Madeleine I G; Hamilton, Marcus J; West, Geoffrey B; Bettencourt, Luís M A

2015-05-06

The firm is a fundamental economic unit of contemporary human societies. Studies on the general quantitative and statistical character of firms have produced mixed results regarding their lifespans and mortality. We examine a comprehensive database of more than 25 000 publicly traded North American companies, from 1950 to 2009, to derive the statistics of firm lifespans. Based on detailed survival analysis, we show that the mortality of publicly traded companies manifests an approximately constant hazard rate over long periods of observation. This regularity indicates that mortality rates are independent of a company's age. We show that the typical half-life of a publicly traded company is about a decade, regardless of business sector. Our results shed new light on the dynamics of births and deaths of publicly traded companies and identify some of the necessary ingredients of a general theory of firms.

State Estimation Using Dependent Evidence Fusion: Application to Acoustic Resonance-Based Liquid Level Measurement.

PubMed

Xu, Xiaobin; Li, Zhenghui; Li, Guo; Zhou, Zhe

2017-04-21

Estimating the state of a dynamic system via noisy sensor measurement is a common problem in sensor methods and applications. Most state estimation methods assume that measurement noise and state perturbations can be modeled as random variables with known statistical properties. However in some practical applications, engineers can only get the range of noises, instead of the precise statistical distributions. Hence, in the framework of Dempster-Shafer (DS) evidence theory, a novel state estimatation method by fusing dependent evidence generated from state equation, observation equation and the actual observations of the system states considering bounded noises is presented. It can be iteratively implemented to provide state estimation values calculated from fusion results at every time step. Finally, the proposed method is applied to a low-frequency acoustic resonance level gauge to obtain high-accuracy measurement results.

A statistic-thermodynamic model for the DOM degradation in the estuary

NASA Astrophysics Data System (ADS)

Zheng, Quanan; Chen, Qin; Zhao, Haihong; Shi, Jiuxin; Cao, Yong; Wang, Dan

2008-03-01

This study aims to clarify the role of dissolved salts playing in the degradation process of terrestrial dissolved organic matter (DOM) at a scale of molecular movement. The molecular thermal movement is perpetual motion. In a multi-molecular system, this random motion also causes collision between the molecules. Seawater is a multi-molecular system consisting from water, salt, and terrestrial DOM molecules. This study attributes the DOM degradation in the estuary to the inelastic collision of DOM molecule with charged salt ions. From statistic-thermodynamic theories of molecular collision, the DOM degradation model and the DOM distribution model are derived. The models are validated by the field observations and satellite data. Thus, we conclude that the inelastic collision between the terrestrial DOM molecules and dissolved salt ions in seawater is a decisive dynamic mechanism for rapid loss of terrestrial DOM.

Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence

NASA Technical Reports Server (NTRS)

Morin, Lee; Shebalin, John; Fu, Terry; Nguyen, Phu; Shum, Victor

2010-01-01

We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Advanced functional network analysis in the geosciences: The pyunicorn package

NASA Astrophysics Data System (ADS)

Donges, Jonathan F.; Heitzig, Jobst; Runge, Jakob; Schultz, Hanna C. H.; Wiedermann, Marc; Zech, Alraune; Feldhoff, Jan; Rheinwalt, Aljoscha; Kutza, Hannes; Radebach, Alexander; Marwan, Norbert; Kurths, Jürgen

2013-04-01

Functional networks are a powerful tool for analyzing large geoscientific datasets such as global fields of climate time series originating from observations or model simulations. pyunicorn (pythonic unified complex network and recurrence analysis toolbox) is an open-source, fully object-oriented and easily parallelizable package written in the language Python. It allows for constructing functional networks (aka climate networks) representing the structure of statistical interrelationships in large datasets and, subsequently, investigating this structure using advanced methods of complex network theory such as measures for networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn allows to study the complex dynamics of geoscientific systems as recorded by time series by means of recurrence networks and visibility graphs. The range of possible applications of the package is outlined drawing on several examples from climatology.

Chemodetection in fluctuating environments: receptor coupling, buffering, and antagonism.

PubMed

Lalanne, Jean-Benoît; François, Paul

2015-02-10

Variability in the chemical composition of the extracellular environment can significantly degrade the ability of cells to detect rare cognate ligands. Using concepts from statistical detection theory, we formalize the generic problem of detection of small concentrations of ligands in a fluctuating background of biochemically similar ligands binding to the same receptors. We discover that in contrast with expectations arising from considerations of signal amplification, inhibitory interactions between receptors can improve detection performance in the presence of substantial environmental variability, providing an adaptive interpretation to the phenomenon of ligand antagonism. Our results suggest that the structure of signaling pathways responsible for chemodetection in fluctuating and heterogeneous environments might be optimized with respect to the statistics and dynamics of environmental composition. The developed formalism stresses the importance of characterizing nonspecific interactions to understand function in signaling pathways.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

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

Normalized value coding explains dynamic adaptation in the human valuation process.

PubMed

Khaw, Mel W; Glimcher, Paul W; Louie, Kenway

2017-11-28

The notion of subjective value is central to choice theories in ecology, economics, and psychology, serving as an integrated decision variable by which options are compared. Subjective value is often assumed to be an absolute quantity, determined in a static manner by the properties of an individual option. Recent neurobiological studies, however, have shown that neural value coding dynamically adapts to the statistics of the recent reward environment, introducing an intrinsic temporal context dependence into the neural representation of value. Whether valuation exhibits this kind of dynamic adaptation at the behavioral level is unknown. Here, we show that the valuation process in human subjects adapts to the history of previous values, with current valuations varying inversely with the average value of recently observed items. The dynamics of this adaptive valuation are captured by divisive normalization, linking these temporal context effects to spatial context effects in decision making as well as spatial and temporal context effects in perception. These findings suggest that adaptation is a universal feature of neural information processing and offer a unifying explanation for contextual phenomena in fields ranging from visual psychophysics to economic choice.

Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

NASA Astrophysics Data System (ADS)

Melgarejo, Miguel; Obregon, Nelson

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Computational Models for Nanoscale Fluid Dynamics and Transport Inspired by Nonequilibrium Thermodynamics1

PubMed Central

Radhakrishnan, Ravi; Yu, Hsiu-Yu; Eckmann, David M.; Ayyaswamy, Portonovo S.

2017-01-01

Traditionally, the numerical computation of particle motion in a fluid is resolved through computational fluid dynamics (CFD). However, resolving the motion of nanoparticles poses additional challenges due to the coupling between the Brownian and hydrodynamic forces. Here, we focus on the Brownian motion of a nanoparticle coupled to adhesive interactions and confining-wall-mediated hydrodynamic interactions. We discuss several techniques that are founded on the basis of combining CFD methods with the theory of nonequilibrium statistical mechanics in order to simultaneously conserve thermal equipartition and to show correct hydrodynamic correlations. These include the fluctuating hydrodynamics (FHD) method, the generalized Langevin method, the hybrid method, and the deterministic method. Through the examples discussed, we also show a top-down multiscale progression of temporal dynamics from the colloidal scales to the molecular scales, and the associated fluctuations, hydrodynamic correlations. While the motivation and the examples discussed here pertain to nanoscale fluid dynamics and mass transport, the methodologies presented are rather general and can be easily adopted to applications in convective heat transfer. PMID:28035168

Coupling functions: Universal insights into dynamical interaction mechanisms

NASA Astrophysics Data System (ADS)

Stankovski, Tomislav; Pereira, Tiago; McClintock, Peter V. E.; Stefanovska, Aneta

2017-10-01

The dynamical systems found in nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. A coherent and comprehensive review is presented encompassing the rapid progress made recently in the analysis, understanding, and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics, and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

Localization and elasticity in entangled polymer liquids as a mesoscopic glass transition

NASA Astrophysics Data System (ADS)

Schweizer, Kenneth

2010-03-01

The reptation-tube model is widely viewed as the correct zeroth order model for entangled linear polymer dynamics under quiescent conditions. Its key ansatz is the existence of a mesoscopic dynamical length scale that prohibits transverse chain motion beyond a tube diameter of order 3-10 nm. However, the theory is phenomenological and lacks a microscopic foundation, and many fundamental questions remain unanswered. These include: (i) where does the confining tube field come from and can it be derived from statistical mechanics? (ii) what is the microscopic origin of the magnitude, and power law scaling with concentration and packing length, of the plateau shear modulus? (iii) is the tube diameter time-dependent? (iv) does the confinement field contribute to elasticity ? (v) do entanglement constraints have a finite strength? Building on our new force-level theories for the dynamical crossover and activated barrier hopping in glassy colloidal suspensions and polymer melts, a first principles self-consistent theory has been developed for entangled polymers. Its basic physical elements, and initial results that address the questions posed above, will be presented. The key idea is that beyond a critical degree of polymerization, the chain connectivity and excluded volume induced intermolecular correlation hole drives temporary localization on an intermediate length scale resulting in a mesoscopic ``ideal kinetic glass transition.'' Large scale isotropic motion is effectively quenched due to the emergence of chain length dependent entropic barriers. However, the barrier height is not infinite, resulting in softening of harmonic localization at large displacements, temporal increase of the confining length scale, and a finite strength of entanglement constraints which can be destroyed by applied stress.

Cycle expansions: From maps to turbulence

NASA Astrophysics Data System (ADS)

Lan, Y.

2010-03-01

We present a derivation, a physical explanation and applications of cycle expansions in different dynamical systems, ranging from simple one-dimensional maps to turbulence in fluids. Cycle expansion is a newly devised powerful tool for computing averages of physical observables in nonlinear chaotic systems which combines many innovative ideas developed in dynamical systems, such as hyperbolicity, invariant manifolds, symbolic dynamics, measure theory and thermodynamic formalism. The concept of cycle expansion has a deep root in theoretical physics, bearing a close analogy to cumulant expansion in statistical physics and effective action functional in quantum field theory, the essence of which is to represent a physical system in a hierarchical way by utilizing certain multiplicative structures such that the dominant parts of physical observables are captured by compact, maneuverable objects while minor detailed variations are described by objects with a larger space and time scale. The technique has been successfully applied to many low-dimensional dynamical systems and much effort has recently been made to extend its use to spatially extended systems. For one-dimensional systems such as the Kuramoto-Sivashinsky equation, the method turns out to be very effective while for more complex real-world systems including the Navier-Stokes equation, the method is only starting to yield its first fruits and much more work is needed to enable practical computations. However, the experience and knowledge accumulated so far is already very useful to a large set of research problems. Several such applications are briefly described in what follows. As more research effort is devoted to the study of complex dynamics of nonlinear systems, cycle expansion will undergo a fast development and find wide applications.

Interactions of social, terrestrial, and marine sub-systems in the Galapagos Islands, Ecuador.

PubMed

Walsh, Stephen J; Mena, Carlos F

2016-12-20

Galapagos is often cited as an example of the conflicts that are emerging between resource conservation and economic development in island ecosystems, as the pressures associated with tourism threaten nature, including the iconic and emblematic species, unique terrestrial landscapes, and special marine environments. In this paper, two projects are described that rely upon dynamic systems models and agent-based models to examine human-environment interactions. We use a theoretical context rooted in complexity theory to guide the development of our models that are linked to social-ecological dynamics. The goal of this paper is to describe key elements, relationships, and processes to inform and enhance our understanding of human-environment interactions in the Galapagos Islands of Ecuador. By formalizing our knowledge of how systems operate and the manner in which key elements are linked in coupled human-natural systems, we specify rules, relationships, and rates of exchange between social and ecological features derived through statistical functions and/or functions specified in theory or practice. The processes described in our models also have practical applications in that they emphasize how political policies generate different human responses and model outcomes, many detrimental to the social-ecological sustainability of the Galapagos Islands.

Tachyon dynamics — for neutrinos?

NASA Astrophysics Data System (ADS)

Schwartz, Charles

2018-04-01

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles), we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process, we come to recognize that the labels given to “in” and “out” states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

Evolution of FX Markets via Globalization of Capital

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

This paper is about money, and why today's foreign exchange (FX) markets are unstable. According to the literature [1], FX markets were fundamentally different before and after WW I. Any attempt to discuss this topic within standard economic theory necessarily fails because money/liquidity/uncertainty is completely excluded from that theory [2]. Fortunately, our market dynamics models adequately serve our purpose. Eichengreen [1] has presented a stimulating history of the evolution of FX markets from the gold standard of the late nineteenth century through the Bretton Woods Agreement (post WWII-1971) and later the floating currencies of our present market deregulation era (1971-present). He asserts a change from stability to instability over the time interval of WWI. Making his argument precise, we describe how speculators could have made money systematically from a market in statistical equilibrium. The present era normal liquid FX markets are in contrast very hard, to a first approximation impossible, to beat, and consequently are described as `martingales'. The ideas of martingales and options/hedging were irrelevant in the pre-WWI era. I end my historical discussion with the empirical evidence for the stochastic model that describes FX market dynamics quantitatively accurately during the last 7-17 years [3].

A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics.

PubMed

Zarai, Yoram; Margaliot, Michael; Tuller, Tamir

2017-01-01

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Photo-induced reactions from efficient molecular dynamics with electronic transitions using the FIREBALL local-orbital density functional theory formalism.

PubMed

Zobač, Vladimír; Lewis, James P; Abad, Enrique; Mendieta-Moreno, Jesús I; Hapala, Prokop; Jelínek, Pavel; Ortega, José

2015-05-08

The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.

Interactions of social, terrestrial, and marine sub-systems in the Galapagos Islands, Ecuador

PubMed Central

Walsh, Stephen J.; Mena, Carlos F.

2016-01-01

Galapagos is often cited as an example of the conflicts that are emerging between resource conservation and economic development in island ecosystems, as the pressures associated with tourism threaten nature, including the iconic and emblematic species, unique terrestrial landscapes, and special marine environments. In this paper, two projects are described that rely upon dynamic systems models and agent-based models to examine human–environment interactions. We use a theoretical context rooted in complexity theory to guide the development of our models that are linked to social–ecological dynamics. The goal of this paper is to describe key elements, relationships, and processes to inform and enhance our understanding of human–environment interactions in the Galapagos Islands of Ecuador. By formalizing our knowledge of how systems operate and the manner in which key elements are linked in coupled human–natural systems, we specify rules, relationships, and rates of exchange between social and ecological features derived through statistical functions and/or functions specified in theory or practice. The processes described in our models also have practical applications in that they emphasize how political policies generate different human responses and model outcomes, many detrimental to the social–ecological sustainability of the Galapagos Islands. PMID:27791072

Dynamical density functional theory for microswimmers

NASA Astrophysics Data System (ADS)

Menzel, Andreas M.; Saha, Arnab; Hoell, Christian; Löwen, Hartmut

2016-01-01

Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.

Multi-Agent Market Modeling of Foreign Exchange Rates

NASA Astrophysics Data System (ADS)

Zimmermann, Georg; Neuneier, Ralph; Grothmann, Ralph

A market mechanism is basically driven by a superposition of decisions of many agents optimizing their profit. The oeconomic price dynamic is a consequence of the cumulated excess demand/supply created on this micro level. The behavior analysis of a small number of agents is well understood through the game theory. In case of a large number of agents one may use the limiting case that an individual agent does not have an influence on the market, which allows the aggregation of agents by statistic methods. In contrast to this restriction, we can omit the assumption of an atomic market structure, if we model the market through a multi-agent approach. The contribution of the mathematical theory of neural networks to the market price formation is mostly seen on the econometric side: neural networks allow the fitting of high dimensional nonlinear dynamic models. Furthermore, in our opinion, there is a close relationship between economics and the modeling ability of neural networks because a neuron can be interpreted as a simple model of decision making. With this in mind, a neural network models the interaction of many decisions and, hence, can be interpreted as the price formation mechanism of a market.

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.

Statistical field theory of futures commodity prices

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Yu, Miao

2018-02-01

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

Information properties of morphologically complex words modulate brain activity during word reading

PubMed Central

Hultén, Annika; Lehtonen, Minna; Lagus, Krista; Salmelin, Riitta

2018-01-01

Abstract Neuroimaging studies of the reading process point to functionally distinct stages in word recognition. Yet, current understanding of the operations linked to those various stages is mainly descriptive in nature. Approaches developed in the field of computational linguistics may offer a more quantitative approach for understanding brain dynamics. Our aim was to evaluate whether a statistical model of morphology, with well‐defined computational principles, can capture the neural dynamics of reading, using the concept of surprisal from information theory as the common measure. The Morfessor model, created for unsupervised discovery of morphemes, is based on the minimum description length principle and attempts to find optimal units of representation for complex words. In a word recognition task, we correlated brain responses to word surprisal values derived from Morfessor and from other psycholinguistic variables that have been linked with various levels of linguistic abstraction. The magnetoencephalography data analysis focused on spatially, temporally and functionally distinct components of cortical activation observed in reading tasks. The early occipital and occipito‐temporal responses were correlated with parameters relating to visual complexity and orthographic properties, whereas the later bilateral superior temporal activation was correlated with whole‐word based and morphological models. The results show that the word processing costs estimated by the statistical Morfessor model are relevant for brain dynamics of reading during late processing stages. PMID:29524274

Data mining of molecular dynamics data reveals Li diffusion characteristics in garnet Li7La3Zr2O12

PubMed Central

Chen, Chi; Lu, Ziheng; Ciucci, Francesco

2017-01-01

Understanding Li diffusion in solid conductors is essential for the next generation Li batteries. Here we show that density-based clustering of the trajectories computed using molecular dynamics simulations helps elucidate the Li diffusion mechanism within the Li7La3Zr2O12 (LLZO) crystal lattice. This unsupervised learning method recognizes lattice sites, is able to give the site type, and can identify Li hopping events. Results show that, while the cubic LLZO has a much higher hopping rate compared to its tetragonal counterpart, most of the Li hops in the cubic LLZO do not contribute to the diffusivity due to the dominance of back-and-forth type jumps. The hopping analysis and local Li configuration statistics give evidence that Li diffusivity in cubic LLZO is limited by the low vacancy concentration. The hopping statistics also shows uncorrelated Poisson-like diffusion for Li in the cubic LLZO, and correlated diffusion for Li in the tetragonal LLZO in the temporal scale. Further analysis of the spatio-temporal correlation using site-to-site mutual information confirms the weak site dependence of Li diffusion in the cubic LLZO as the origin for the uncorrelated diffusion. This work puts forward a perspective on combining machine learning and information theory to interpret results of molecular dynamics simulations. PMID:28094317

Information properties of morphologically complex words modulate brain activity during word reading.

PubMed

Hakala, Tero; Hultén, Annika; Lehtonen, Minna; Lagus, Krista; Salmelin, Riitta

2018-06-01

Neuroimaging studies of the reading process point to functionally distinct stages in word recognition. Yet, current understanding of the operations linked to those various stages is mainly descriptive in nature. Approaches developed in the field of computational linguistics may offer a more quantitative approach for understanding brain dynamics. Our aim was to evaluate whether a statistical model of morphology, with well-defined computational principles, can capture the neural dynamics of reading, using the concept of surprisal from information theory as the common measure. The Morfessor model, created for unsupervised discovery of morphemes, is based on the minimum description length principle and attempts to find optimal units of representation for complex words. In a word recognition task, we correlated brain responses to word surprisal values derived from Morfessor and from other psycholinguistic variables that have been linked with various levels of linguistic abstraction. The magnetoencephalography data analysis focused on spatially, temporally and functionally distinct components of cortical activation observed in reading tasks. The early occipital and occipito-temporal responses were correlated with parameters relating to visual complexity and orthographic properties, whereas the later bilateral superior temporal activation was correlated with whole-word based and morphological models. The results show that the word processing costs estimated by the statistical Morfessor model are relevant for brain dynamics of reading during late processing stages. © 2018 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

The Statistical Mechanics of Ideal Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2002-01-01

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Data mining of molecular dynamics data reveals Li diffusion characteristics in garnet Li7La3Zr2O12

NASA Astrophysics Data System (ADS)

Chen, Chi; Lu, Ziheng; Ciucci, Francesco

2017-01-01

Understanding Li diffusion in solid conductors is essential for the next generation Li batteries. Here we show that density-based clustering of the trajectories computed using molecular dynamics simulations helps elucidate the Li diffusion mechanism within the Li7La3Zr2O12 (LLZO) crystal lattice. This unsupervised learning method recognizes lattice sites, is able to give the site type, and can identify Li hopping events. Results show that, while the cubic LLZO has a much higher hopping rate compared to its tetragonal counterpart, most of the Li hops in the cubic LLZO do not contribute to the diffusivity due to the dominance of back-and-forth type jumps. The hopping analysis and local Li configuration statistics give evidence that Li diffusivity in cubic LLZO is limited by the low vacancy concentration. The hopping statistics also shows uncorrelated Poisson-like diffusion for Li in the cubic LLZO, and correlated diffusion for Li in the tetragonal LLZO in the temporal scale. Further analysis of the spatio-temporal correlation using site-to-site mutual information confirms the weak site dependence of Li diffusion in the cubic LLZO as the origin for the uncorrelated diffusion. This work puts forward a perspective on combining machine learning and information theory to interpret results of molecular dynamics simulations.

Information Dynamics and Aspects of Musical Perception

NASA Astrophysics Data System (ADS)

Dubnov, Shlomo

Musical experience has been often suggested to be related to forming of expectations, their fulfillment or denial. In terms of information theory, expectancies and predictions serve to reduce uncertainty about the future and might be used to efficiently represent and "compress" data. In this chapter we present an information theoretic model of musical listening based on the idea that expectations that arise from past musical material are framing our appraisal of what comes next, and that this process eventually results in creation of emotions or feelings. Using a notion of "information rate" we can measure the amount of information between past and present in the musical signal on different time scales using statistics of sound spectral features. Several musical pieces are analyzed in terms of short and long term information rate dynamics and are compared to analysis of musical form and its structural functions. The findings suggest that a relation exists between information dynamics and musical structure that eventually leads to creation of human listening experience and feelings such as "wow" and "aha".

Dynamic structural disorder in supported nanoscale catalysts

NASA Astrophysics Data System (ADS)

Rehr, J. J.; Vila, F. D.

2014-04-01

We investigate the origin and physical effects of "dynamic structural disorder" (DSD) in supported nano-scale catalysts. DSD refers to the intrinsic fluctuating, inhomogeneous structure of such nano-scale systems. In contrast to bulk materials, nano-scale systems exhibit substantial fluctuations in structure, charge, temperature, and other quantities, as well as large surface effects. The DSD is driven largely by the stochastic librational motion of the center of mass and fluxional bonding at the nanoparticle surface due to thermal coupling with the substrate. Our approach for calculating and understanding DSD is based on a combination of real-time density functional theory/molecular dynamics simulations, transient coupled-oscillator models, and statistical mechanics. This approach treats thermal and dynamic effects over multiple time-scales, and includes bond-stretching and -bending vibrations, and transient tethering to the substrate at longer ps time-scales. Potential effects on the catalytic properties of these clusters are briefly explored. Model calculations of molecule-cluster interactions and molecular dissociation reaction paths are presented in which the reactant molecules are adsorbed on the surface of dynamically sampled clusters. This model suggests that DSD can affect both the prefactors and distribution of energy barriers in reaction rates, and thus can significantly affect catalytic activity at the nano-scale.

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.

Nonthermal steady states after an interaction quench in the Falicov-Kimball model.

PubMed

Eckstein, Martin; Kollar, Marcus

2008-03-28

We present the exact solution of the Falicov-Kimball model after a sudden change of its interaction parameter using nonequilibrium dynamical mean-field theory. For different interaction quenches between the homogeneous metallic and insulating phases the system relaxes to a nonthermal steady state on time scales on the order of variant Planck's over 2pi/bandwidth, showing collapse and revival with an approximate period of h/interaction if the interaction is large. We discuss the reasons for this behavior and provide a statistical description of the final steady state by means of generalized Gibbs ensembles.

Changes of instability thresholds of rotor due to bearing misalignments

NASA Technical Reports Server (NTRS)

Springer, H.; Ecker, H.; Gunter, E. J.

1985-01-01

The influence of bearing misalignment upon the dynamic characteristics of statistically indeterminant rotor bearing systems is investigated. Both bearing loads and stability speed limits of a rotor may be changed significantly by magnitude and direction of bearing misalignment. The useful theory of short journal bearings is introduced and simple analytical expressions, governing the misalignment problem, are carried out. Polar plots for the bearing load capacities and stability maps, describing the speed limit in terms of misalignment, are presented. These plots can be used by the designer to estimate deviations between calculation and experimental data due to misalignment effects.

A general solution for the registration of optical multispectral scanners

NASA Technical Reports Server (NTRS)

Rader, M. L.

1974-01-01

The paper documents a general theory for registration (mapping) of data sets gathered by optical scanners such as the ERTS satellite MSS and the Skylab S-192 MSS. This solution is generally applicable to scanners which have rotating optics. Navigation data and ground control points are used in a statistically weighted adjustment based on a mathematical model of the dynamics of the spacecraft and the scanner system. This adjustment is very similar to the well known photogrammetric adjustments used in aerial mapping. Actual tests have been completed on NASA aircraft 24 channel MSS data, and the results are very encouraging.

Thermodynamics of inequalities: From precariousness to economic stratification

NASA Astrophysics Data System (ADS)

Smerlak, Matteo

2016-01-01

Growing economic inequalities are observed in several countries throughout the world. Following Pareto, the power-law structure of these inequalities has been the subject of much theoretical and empirical work. But their nonequilibrium dynamics, e.g. after a policy change, remains incompletely understood. Here we introduce a thermodynamical theory of inequalities based on the analogy between economic stratification and statistical entropy. Within this framework we identify the combination of upward mobility with precariousness as a fundamental driver of inequality. We formalize this statement by a "second-law" inequality displaying upward mobility and precariousness as thermodynamic conjugate variables. We estimate the time scale for the "relaxation" of the wealth distribution after a sudden change of the after-tax return on capital. Our method can be generalized to gain insight into the dynamics of inequalities in any Markovian model of socioeconomic interactions.

Entropy and econophysics

NASA Astrophysics Data System (ADS)

Rosser, J. Barkley

2016-12-01

Entropy is a central concept of statistical mechanics, which is the main branch of physics that underlies econophysics, the application of physics concepts to understand economic phenomena. It enters into econophysics both in an ontological way through the Second Law of Thermodynamics as this drives the world economy from its ecological foundations as solar energy passes through food chains in dissipative process of entropy rising and production fundamentally involving the replacement of lower entropy energy states with higher entropy ones. In contrast the mathematics of entropy as appearing in information theory becomes the basis for modeling financial market dynamics as well as income and wealth distribution dynamics. It also provides the basis for an alternative view of stochastic price equilibria in economics, as well providing a crucial link between econophysics and sociophysics, keeping in mind the essential unity of the various concepts of entropy.

Lessons from Inferentialism for Statistics Education

ERIC Educational Resources Information Center

Bakker, Arthur; Derry, Jan

2011-01-01

This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when…

Relativistic Fluid Dynamics Far From Local Equilibrium

NASA Astrophysics Data System (ADS)

Romatschke, Paul

2018-01-01

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

Theory and experimental evidence of phonon domains and their roles in pre-martensitic phenomena

NASA Astrophysics Data System (ADS)

Jin, Yongmei M.; Wang, Yu U.; Ren, Yang

2015-12-01

Pre-martensitic phenomena, also called martensite precursor effects, have been known for decades while yet remain outstanding issues. This paper addresses pre-martensitic phenomena from new theoretical and experimental perspectives. A statistical mechanics-based Grüneisen-type phonon theory is developed. On the basis of deformation-dependent incompletely softened low-energy phonons, the theory predicts a lattice instability and pre-martensitic transition into elastic-phonon domains via 'phonon spinodal decomposition.' The phase transition lifts phonon degeneracy in cubic crystal and has a nature of phonon pseudo-Jahn-Teller lattice instability. The theory and notion of phonon domains consistently explain the ubiquitous pre-martensitic anomalies as natural consequences of incomplete phonon softening. The phonon domains are characterised by broken dynamic symmetry of lattice vibrations and deform through internal phonon relaxation in response to stress (a particular case of Le Chatelier's principle), leading to previously unexplored new domain phenomenon. Experimental evidence of phonon domains is obtained by in situ three-dimensional phonon diffuse scattering and Bragg reflection using high-energy synchrotron X-ray single-crystal diffraction, which observes exotic domain phenomenon fundamentally different from usual ferroelastic domain switching phenomenon. In light of the theory and experimental evidence of phonon domains and their roles in pre-martensitic phenomena, currently existing alternative opinions on martensitic precursor phenomena are revisited.

Control Theory and Statistical Generalizations.

ERIC Educational Resources Information Center

Powers, William T.

1990-01-01

Contrasts modeling methods in control theory to the methods of statistical generalizations in empirical studies of human or animal behavior. Presents a computer simulation that predicts behavior based on variables (effort and rewards) determined by the invariable (desired reward). Argues that control theory methods better reflect relationships to…

A model for two-dimensional bursty turbulence in magnetized plasmas

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

Servidio, Sergio; Primavera, Leonardo; Carbone, Vincenzo

2008-01-15

The nonlinear dynamics of two-dimensional electrostatic interchange modes in a magnetized plasma is investigated through a simple model that replaces the instability mechanism due to magnetic field curvature by an external source of vorticity and mass. Simulations in a cylindrical domain, with a spatially localized and randomized source at the center of the domain, reveal the eruption of mushroom-shaped bursts that propagate radially and are absorbed by the boundaries. Burst sizes and the interburst waiting times exhibit power-law statistics, which indicates long-range interburst correlations, similar to what has been found in sandpile models for avalanching systems. It is shown frommore » the simulations that the dynamics can be characterized by a Yaglom relation for the third-order mixed moment involving the particle number density as a passive scalar and the ExB drift velocity, and hence that the burst phenomenology can be described within the framework of turbulence theory. Statistical features are qualitatively in agreement with experiments of intermittent transport at the edge of plasma devices, and suggest that essential features such as transport can be described by this simple model of bursty turbulence.« less

Alignment-free genetic sequence comparisons: a review of recent approaches by word analysis

PubMed Central

Steele, Joe; Bastola, Dhundy

2014-01-01

Modern sequencing and genome assembly technologies have provided a wealth of data, which will soon require an analysis by comparison for discovery. Sequence alignment, a fundamental task in bioinformatics research, may be used but with some caveats. Seminal techniques and methods from dynamic programming are proving ineffective for this work owing to their inherent computational expense when processing large amounts of sequence data. These methods are prone to giving misleading information because of genetic recombination, genetic shuffling and other inherent biological events. New approaches from information theory, frequency analysis and data compression are available and provide powerful alternatives to dynamic programming. These new methods are often preferred, as their algorithms are simpler and are not affected by synteny-related problems. In this review, we provide a detailed discussion of computational tools, which stem from alignment-free methods based on statistical analysis from word frequencies. We provide several clear examples to demonstrate applications and the interpretations over several different areas of alignment-free analysis such as base–base correlations, feature frequency profiles, compositional vectors, an improved string composition and the D2 statistic metric. Additionally, we provide detailed discussion and an example of analysis by Lempel–Ziv techniques from data compression. PMID:23904502

A probabilistic drought forecasting framework: A combined dynamical and statistical approach

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

Yan, Hongxiang; Moradkhani, Hamid; Zarekarizi, Mahkameh

In order to improve drought forecasting skill, this study develops a probabilistic drought forecasting framework comprised of dynamical and statistical modeling components. The novelty of this study is to seek the use of data assimilation to quantify initial condition uncertainty with the Monte Carlo ensemble members, rather than relying entirely on the hydrologic model or land surface model to generate a single deterministic initial condition, as currently implemented in the operational drought forecasting systems. Next, the initial condition uncertainty is quantified through data assimilation and coupled with a newly developed probabilistic drought forecasting model using a copula function. The initialmore » condition at each forecast start date are sampled from the data assimilation ensembles for forecast initialization. Finally, seasonal drought forecasting products are generated with the updated initial conditions. This study introduces the theory behind the proposed drought forecasting system, with an application in Columbia River Basin, Pacific Northwest, United States. Results from both synthetic and real case studies suggest that the proposed drought forecasting system significantly improves the seasonal drought forecasting skills and can facilitate the state drought preparation and declaration, at least three months before the official state drought declaration.« less