Nonlinear generalized Langevin equations
Robert Zwanzig
1973-01-01
Exact generalized Langevin equations are derived for arbitrarily nonlinear systems interacting with specially chosen heat baths. An example is displayed in which the Langevin equation is nonlinear but approximately Markovian.
H. Keith McDowell; A. M. Clogston
1998-01-01
Molecular time scale generalized Langevin equation (MTGLE) theory is discussed as an approach to condensed phase dynamics. A polynomial maximum entropy (MaxEnt) process for imaging required MTGLE spectral densities based on knowledge of the moments of the spectral density is introduced. The process is based on the use of interpolation polynomials which serve both to image the spectral density as
Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations
Zahlten, Claus [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: C.Zahlten@gmx.de; Hernandez, Andres [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: A.Hernandez@thphys.uni-heidelberg.de; Schmidt, Michael G. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: M.G.Schmidt@thphys.uni-heidelberg.de
2009-10-15
The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (
Langevin equation in effective theory of interacting QCD pomerons in the limit of large $N_c$
S. Bondarenko
2007-05-08
Effective field theory of interacting BFKL pomerons is investigated and Langevin equations for the theory, which arise after the introduction of additional auxiliary field, are obtained. The Langevin equations are considered for the case of interacting BFKL pomerons with both splitting and merging vertexes and for the interaction which includes additional "toy" four pomeron interaction vertex. In the latest case an analogy with the Regge field theory in zero dimensions (RFT-0) was used in order to obtain this "toy" four pomeron interaction vertex. The comparison between the Langevin equations obtained in the frameworks of dipole and RFT approaches is performed, the interpretation of results is given and possible implementation of obtained equations is discussed.
Kunimasa Miyazaki; David R. Reichman
2005-01-01
In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field-theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove that the derived equations are consistent with the fluctuation-dissipation theorem. We also discuss the generalization of the result given here to real fluids, and the possible description
On the quantum langevin equation
G. W. Ford; M. Kac
1987-01-01
The quantum Langevin equation is the Heisenberg equation of motion for the (operator) coordinate of a Brownian particle coupled to a heat bath. We give an elementary derivation of this equation for a simple coupled-oscillator model of the heat bath.
The chemical Langevin equation Daniel T. Gillespiea)
Mangel, Marc
The chemical Langevin equation Daniel T. Gillespiea) Research Department, Code 4T4100D, Naval Air master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other
Complex Langevin Equations and Schwinger-Dyson Equations
Gerald Guralnik; Cengiz Pehlevan
2008-08-19
Stationary distributions of complex Langevin equations are shown to be the complexified path integral solutions of the Schwinger-Dyson equations of the associated quantum field theory. Specific examples in zero dimensions and on a lattice are given. Relevance to the study of quantum field theory phase space is discussed.
Edinburgh Research Explorer The complex chemical Langevin equation
Millar, Andrew J.
Edinburgh Research Explorer The complex chemical Langevin equation Citation for published version: Schnoerr, D, Sanguinetti, G & Grima, R 2014, 'The complex chemical Langevin equation' Journal of Chemical
The complex chemical Langevin equation
Schnoerr, David [School of Biological Sciences, University of Edinburgh (United Kingdom); School of Informatics, University of Edinburgh (United Kingdom); Sanguinetti, Guido [School of Informatics, University of Edinburgh (United Kingdom); Grima, Ramon [School of Biological Sciences, University of Edinburgh (United Kingdom)
2014-07-14
The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.
Langevin equation approach to reactor noise analysis: stochastic transport equation
A. Z. Akcasu; A. M. Stolle
1993-01-01
The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source
Quantum Langevin equations for optomechanical systems
Alberto Barchielli; Bassano Vacchini
2015-06-24
We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry requirements and equipartition at equilibrium, while the environment is described by quantum Bose fields in a suitable non-Fock representation which allows for the introduction of temperature. A generic spectral density of the environment can be described by introducing its state trough a suitable P-representation. Including interaction of the mechanical oscillator with a cavity mode via radiation pressure we obtain a description of a simple optomechanical system in which, besides the Langevin equations for the system, one has the exact input-output relations for the quantum noises. The whole theory is valid at arbitrarily low temperature. This allows the exact calculation of the stationary value of the mean energy of the mechanical oscillator, as well as both homodyne and heterodyne spectra. The present analysis allows in particular to study possible cooling scenarios and to obtain the exact connection between observed spectra and fluctuation spectra of the position of the mechanical oscillator.
Global optimization via the Langevin equation
Basilis Gidas
1985-01-01
We provide a simple proof of the convergence of the cooling algorithms, i.e., the annealing algorithm and the Langevin equation. The convergence is established for temperature schedules which are very near to optimal ones. Our methods are based on Differential Equations techniques.
Boltzmann-Langevin equation, dynamical instability and multifragmentation
NASA Astrophysics Data System (ADS)
Zhang, Feng-Shou; Suraud, Eric
1993-12-01
By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40Ca+ 40Ca system, we can compute with confidence physical observables related to recent multifragmentation data.
Boltzmann-Langevin equation, dynamical instability and multifragmentation
Feng-Shou Zhang; Eric Suraud
1993-01-01
By using simulations of the Boltzmann-Langevin equation which incorporates dynamical fluctuations beyond usual transport theories and by coupling it with a coalescence model, we obtain information on multifragmentation in heavy-ion collisions. From a calculation of the 40Ca+40Ca system, we can compute with confidence physical observables related to recent multifragmentation data.
Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre 'Kurchatov Institute,' (Russian Federation)
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Langevin and diffusion equation of turbulent fluid flow
NASA Astrophysics Data System (ADS)
Brouwers, J. J. H.
2010-08-01
A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C0, which arises from Lagrangian similarity theory. The value of C0 in high Reynolds number turbulence is 5-6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C0-1 including terms next to leading order in C0-1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O(C0-2) in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O(C0-1). The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.
The generalized Schrödinger–Langevin equation
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co [Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, Distrito Capital (Colombia); Miret-Artés, Salvador, E-mail: s.miret@iff.csic.es [Instituto de Física Fundamental, CSIC, Serrano 123, 28006, Madrid (Spain)
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.
Langevin equation as a stochastic differential equation in nuclear physics
Asano, T.; Wada, T.; Ohta, M. [Department of Physics, Konan University, 8-9-1 Okamoto, Kobe 658-8501 (Japan); Takigawa, N. [Department of Physics, Tohoku University, Sendai, 980-8578 (Japan)
2007-02-26
Two kinds of stochastic integrals, Ito integral and Stratonovich integral, are applied for solving Langevin equation. In the case of the simplified Langevin equation for over-damped motion, the fission rate obtained with Stratonovich integral is significantly larger than that with Ito integral. On the other hand, in the case where the random force acts on the momentum variables, the two integrals give essentially the same results. The condition for the difference with two integrals to appear is discussed. The proper treatment of the double stochastic integral is necessary to obtain a high numerical accuracy.
S. Chaturvedi; A. K. Kapoor; V. Srinivasan
1984-01-01
A class of Langevin equations is formulated as a field theory in superspace. The Ward Takahashi identities associated with the hidden supersymmetry are derived which in turn are shown to lead to the fluctuation dissipation theorems.
Another derivation of generalized Langevin equations
Dengler, R
2015-01-01
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others can well be called a pearl of theoretical physics. The derivation relies on classical mechanics, and encompasses everything an omnipotent engineer can construct from point particles and potentials: solids, liquids, liquid crystals, conductors, polymers, systems with spin-like degrees of freedom ... Einstein relations and Onsager reciprocity theorem come for free. It apparently not has widely found its way into textbooks, but has been reproduced dozens of times on the fly with many references to the literature and without adding much substantially new. Here we follow the tradition, but strive to produce a self-contained text. Furthermore, we address questions that naturally arise in the derivation. Among other things the meaning of the divergence of the Poisson brackets is explained, and the role of nonlinear damping coefficients is clarified.
Numerical Integration of the Langevin Equation: Monte Carlo Simulation
Donald L. Ermak; Helen Buckholz
1980-01-01
Monte Carlo simulation techniques are derived for solving the ordinary Langevin equation of motion for a Brownian particle in the presence of an external force. These methods allow considerable freedom in selecting the size of the time step, which is restricted only by the rate of change in the external force. This approach is extended to the generalized Langevin equation
Self-consistent generalized Langevin equation for colloidal mixtures
NASA Astrophysics Data System (ADS)
Chávez-Rojo, Marco Antonio; Medina-Noyola, Magdaleno
2005-09-01
A self-consistent theory of collective and tracer diffusion in colloidal mixtures is presented. This theory is based on exact results for the partial intermediate scattering functions derived within the framework of the generalized Langevin equation formalism, plus a number of conceptually simple and sensible approximations. The first of these consists of a Vineyard-like approximation between collective and tracer diffusion, which writes the collective dynamics in terms of the memory function related to tracer diffusion. The second consists of interpolating this only unknown memory function between its two exact limits at small and large wave vectors; for this, a phenomenologically determined, but not arbitrary, interpolating function is introduced: a Lorentzian with its inflection point located at the first minimum of the partial static structure factor. The small wave-vector exact limit involves a time-dependent friction function, for which we take a general approximate result, previously derived within the generalized Langevin equation formalism. This general result expresses the time-dependent friction function in terms of the partial intermediate scattering functions, thus closing the system of equations into a fully self-consistent scheme. This extends to mixtures a recently proposed self-consistent theory developed for monodisperse suspensions [Yeomans-Reyna and Medina-Noyola, Phys. Rev. E 64, 066114 (2001)]. As an illustration of its quantitative accuracy, its application to a simple model of a binary dispersion in the absence of hydrodynamic interactions is reported.
Philip R. Johnson; B. L. Hu
2001-06-01
We apply the open systems concept and the influence functional formalism introduced in Paper I to establish a stochastic theory of relativistic moving spinless particles in a quantum scalar field. The stochastic regime resting between the quantum and semi-classical captures the statistical mechanical attributes of the full theory. Applying the particle-centric world-line quantization formulation to the quantum field theory of scalar QED we derive a time-dependent (scalar) Abraham-Lorentz-Dirac (ALD) equation and show that it is the correct semiclassical limit for nonlinear particle-field systems without the need of making the dipole or non-relativistic approximations. Progressing to the stochastic regime, we derive multiparticle ALD-Langevin equations for nonlinearly coupled particle-field systems. With these equations we show how to address time-dependent dissipation/noise/renormalization in the semiclassical and stochastic limits of QED. We clarify the the relation of radiation reaction, quantum dissipation and vacuum fluctuations and the role that initial conditions may play in producing non-Lorentz invariant noise. We emphasize the fundamental role of decoherence in reaching the semiclassical limit, which also suggests the correct way to think about the issues of runaway solutions and preacceleration from the presence of third derivative terms in the ALD equation. We show that the semiclassical self-consistent solutions obtained in this way are ``paradox'' and pathology free both technically and conceptually. This self-consistent treatment serves as a new platform for investigations into problems related to relativistic moving charges.
Computing generalized Langevin equations and generalized Fokker–Planck equations
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-01-01
The Mori–Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker–Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori–Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems. PMID:19549838
Probability Density Function Method for Langevin Equations with Colored Noise
Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.
2013-04-05
We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.
Harting, Jens
Coupled Langevin Equations for the North Atlantic Oscillation Pedro Lind, Alejandro Mora, Jason Gallas, Maria Haase · Introduction: (i) The North Atlantic Oscillation (NAO). (ii) The Langevin equation. (iii) Langevin equations and time-series. · A Langevin equation for the NAO index. · Analyzing the NAO
From Langevin to Fokker-Planck equation (Dated: May 5, 2014)
Rácz, Zoltán
From Langevin to Fokker-Planck equation (Dated: May 5, 2014) Stochastic differential equations, and provide an interpretation of the stochastic differential equations (Langevin description) which in the overdamped limit The Langevin description of Brownian motion was given earlier in terms of Langevin
The generalized Langevin equation, autocorrelations, and plasma resistivity
K. Zuchowski
1975-01-01
Langevin's equation is generalized and treated as a phenomenologically stochastic equation to describe Brownian movements. The differences between the usual and the generalized equations and the motivation for using the latter to describe phenomena in plasma are reviewed. The correctness of fluctuational-dissipational theorems obtained for plasma is investigated utilizing known values of autocorrelation of the electric field and determining therefrom
Simplified simulation of Boltzmann-Langevin equation
Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Randrup, J. [Lawrence Berkeley Lab., CA (United States)
1994-06-01
We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density.
A path integral approach to the Langevin equation
Ashok K. Das; Sudhakar Panda; J. R. L. Santos
2015-01-07
We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.
Hopping parameter expansion to all orders using the complex Langevin equation
Aarts, G; Sexty, D; Stamatescu, I -O
2015-01-01
We propose two novel formulations of the hopping parameter expansion for finite density QCD using Wilson fermions, while keeping the gauge action intact. We use the complex Langevin equation to circumvent the sign problem in the theory. We perform simulations at very high order of the expansion, such that convergence is directly observable. We compare results to the full QCD results, and see agreement at sufficiently high orders. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.
Hopping parameter expansion to all orders using the complex Langevin equation
G. Aarts; E. Seiler; D. Sexty; I. -O. Stamatescu
2015-03-30
We propose two novel formulations of the hopping parameter expansion for finite density QCD using Wilson fermions, while keeping the gauge action intact. We use the complex Langevin equation to circumvent the sign problem in the theory. We perform simulations at very high order of the expansion, such that convergence is directly observable. We compare results to the full QCD results, and see agreement at sufficiently high orders. These results provide support for the use of complex Langevin dynamics to study QCD at nonzero density, both in the full and the expanded theory, and for the convergence of the latter.
Stochastic Langevin equations: Markovian and non-Markovian dynamics
R. L. S. Farias; Rudnei O. Ramos; L. A. da Silva
2009-10-10
Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is analyzed in details. The conditions for when the equation in a local form can be considered a good approximation are then explicitly specified. We study both the cases of additive and multiplicative noises, including system dependent dissipation terms, according to the Fluctuation-Dissipation theorem.
The treatment of heavy-ion collisions by Langevin equations
P. Fröbrich; S. Y. Xu
1988-01-01
Fusion and deep-inelastic heavy-ion collisions are treated by Langevin equations within the framework of the surface friction model. Cross sections are calculated by Monte Carlo sampling of trajectories. An important result is that in contrast to what is usually assumed statistical fluctuations play a significant role in analysing heavy ion fusion data. It is demonstrated that in the analysis of
Non-Markovian Langevin Equation Applied to Heavy Ion Collisions
Hisao Matsuzaki; Tatsuo Tsukamoto
1981-01-01
The time evolution of the energy dissipation in heavy ion collisions is expressed by a non-Markovian Langevin equation which has two relaxation times. It is suggested that the kinetic energy above the Coulomb barrier dissipates rapidly with the same relaxation time as the fase process of the mass transport.
Langevin equations for quasi-linear wave-particle interaction. F. Castejn and S. Eguilior
Langevin equations for quasi-linear wave-particle interaction. F. Castejón and S. Eguilior the trajectories of single particles using Langevin equations. Moreover, there is a correspondence between F-P equation and Langevin ones and the latter can be obtained from the former using Ito or Stratonovich
Analysis of a few numerical integration methods for the Langevin equation
Skeel, Robert
Analysis of a few numerical integration methods for the Langevin equation WEI WANG* and ROBERT D for the Langevin equation and use the modified equation approach to analyse their accuracy. We show that for the harmonic oscillator, the BBK integrator converges weakly with order 1 while the vGB82 and Langevin impulse
Non-Markovian diffusion over a saddle with a Generalized Langevin equation
Paris-Sud XI, Université de
Non-Markovian diffusion over a saddle with a Generalized Langevin equation David Boilley and Yoann barrier is exactly solved with a non-Markovian Generalized Langevin Equation. For a short relaxation time.50.EY, 05.40.-a, 25.70.Jj 1 Introduction The phenomenological Langevin equation [1], or its Klein
Generalized Langevin Equation for Tracer Diffusion in Atomic Liquids
Patricia Mendoza-Méndez; Leticia López-Flores; Luis E. Sánchez-Díaz; Magdaleno Medina-Noyola
2012-05-25
We derive the time-evolution equation that describes the Brownian motion of labeled individual tracer particles in a simple model atomic liquid (i.e., a system of $N$ particles whose motion is governed by Newton's second law, and interacting through spherically symmetric pairwise potentials). We base our derivation on the generalized Langevin equation formalism, and find that the resulting time evolution equation is formally identical to the generalized Langevin equation that describes the Brownian motion of individual tracer particles in a colloidal suspension in the absence of hydrodynamic interactions. This formal dynamic equivalence implies the long-time indistinguishability of some dynamic properties of both systems, such as their mean squared displacement, upon a well-defined time scaling. This prediction is tested here by comparing the results of molecular and Brownian dynamics simulations performed on the hard sphere system.
Solution of quantum Langevin equation: approximations, theoretical and numerical aspects.
Banerjee, Dhruba; Bag, Bidhan Chandra; Banik, Suman Kumar; Ray, Deb Shankar
2004-05-15
Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot. PMID:15267831
Boltzmann-Langevin theory of Coulomb drag
NASA Astrophysics Data System (ADS)
Chen, W.; Andreev, A. V.; Levchenko, A.
2015-06-01
We develop a Boltzmann-Langevin description of the Coulomb drag effect in clean double-layer systems with large interlayer separation d as compared to the average interelectron distance ?F. Coulomb drag arises from density fluctuations with spatial scales of order d . At low temperatures, their characteristic frequencies exceed the intralayer equilibration rate of the electron liquid, and Coulomb drag may be treated in the collisionless approximation. As temperature is raised, the electron mean free path becomes short due to electron-electron scattering. This leads to local equilibration of electron liquid, and consequently drag is determined by hydrodynamic density modes. Our theory applies to both the collisionless and the hydrodynamic regimes, and it enables us to describe the crossover between them. We find that drag resistivity exhibits a nonmonotonic temperature dependence with multiple crossovers at distinct energy scales. At the lowest temperatures, Coulomb drag is dominated by the particle-hole continuum, whereas at higher temperatures of the collision-dominated regime it is governed by the plasmon modes. We observe that fast intralayer equilibration mediated by electron-electron collisions ultimately renders a stronger drag effect.
A Langevin equation description of dynamic nuclear deformation
Roeth, N.L.
1992-01-01
A model of dynamic nuclear deformation is developed in which the collective degrees of freedom of a nucleus are coupled to subcollective degrees of freedom by means of friction and fluctuation forces in the equations of motion for the collective degrees of freedom. The Langevin equation is a stochastic differential equation that includes friction and fluctuation terms, so it is used as the equation of motion in this model. The necessary inertia and friction parameters are obtained using the Werner-Wheeler approximation, and the fluctuation parameter is obtained by applying the fluctuation-dissipation theorem. It is shown that a second order Runge-Kutta method for numerical solution of the Langevin equation is much better than the commonly employed Euler method. Poor random number generators are shown to have serious negative effects in a Langevin simulation. Several case studies are described, including a model employing the (c, h, [alpha]) shape parameterization with h set equal to zero to reduce it to two dimensions. This parameterization allows scission into fragments of varying relative sizes, providing a suitable model for study for mass distributions, transient times, and the importance of dynamics on distributions and scission rates.
Second-Order Langevin Equation in Quantized Hamilton Dynamics Eric M. HEATWOLE and Oleg V. PREZHDO
Second-Order Langevin Equation in Quantized Hamilton Dynamics Eric M. HEATWOLE and Oleg V. PREZHDO December 29, 2007; accepted January 23, 2008; published March 25, 2008) We derive a semi-classical Langevin: semiclassical dynamics, closure, Langevin equation, canonical ensemble, fluctuationdissipation theorem
An adaptive stepsize method for the chemical Langevin equation
NASA Astrophysics Data System (ADS)
Ilie, Silvana; Teslya, Alexandra
2012-05-01
Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.
The Boltzmann-Langevin equation and its application to intermediate mass fragment production
E. Suraud; S. Ayik; J. Stryjewski; M. Belkacem
1990-01-01
We present the first simulations of the Boltzmann-Langevin equation recently introduced for taking into account high order correlations not contained in extended mean field theories. This framework is very promising for phenomena involving large fluctuations such as presumably the formation of Intermediate Mass Fragments in heavy ion collisions at some tens of MeV\\/A. We apply the simulation to this energy
The theory of concentrated Langevin distributions
Geoffrey S. Watson
1984-01-01
The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp ?[mu]'x, where x and the modal vector [mu] are unit vectors in q. ? (>=0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are
Lattice Perturbation Theory by Langevin Dynamics
Francesco Di Renzo; Giuseppe Marchesini; Paolo Marenzoni; Enrico Onofri
1993-08-07
We present an application of the standard Langevin dynamics to the problem of weak coupling perturbative expansions for Lattice QCD. This method can be applied to the computation of the most general observables. In this preliminary work we will concentrate in particular on the computation of the perturbative terms of the $1\\times 1$ Wilson loop, up to fourth order. It is shown that a stochastic gauge fixing is a possible solution to the problem of divergent fluctuations which affect higher order coefficients.
The Langevin Equation for a Quantum Heat Bath
S. Attal; A. Joye
2006-12-17
We compute the quantum Langevin equation (or quantum stochastic differential equation) representing the action of a quantum heat bath at thermal equilibrium on a simple quantum system. These equations are obtained by taking the continuous limit of the Hamiltonian description for repeated quantum interactions with a sequence of photons at a given density matrix state. In particular we specialise these equations to the case of thermal equilibrium states. In the process, new quantum noises are appearing: thermal quantum noises. We discuss the mathematical properties of these thermal quantum noises. We compute the Lindblad generator associated with the action of the heat bath on the small system. We exhibit the typical Lindblad generator that provides thermalization of a given quantum system.
Two Langevin equations in the Doi-Peliti formalism
Kazunori Itakura; Jun Ohkubo; Shin-ichi Sasa
2009-12-09
A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \\rightleftarrows X+X$ is investigated as an illustrative example.
Solving the generalized Langevin equation with the algebraically correlated noise
NASA Astrophysics Data System (ADS)
Srokowski, T.; P?oszajczak, M.
1998-04-01
We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.
Fluctuation-dissipation relation for nonlinear Langevin equations.
Kumaran, V
2011-04-01
It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion. PMID:21599134
Balanced model reduction of partially observed Langevin equations: an averaging principle
Carsten Hartmann
2011-01-01
We study balanced model reduction of partially observed stochastic differential equations of Langevin type. Upon balancing, the Langevin equation turns into a singularly perturbed system of equations with slow and fast degrees of freedom. We prove that in the limit of vanishing small Hankel singular values (i.e. for infinite scale separation between fast and slow variables), its solution converges to
Langevin approach to the statistical theory of a bounded plasma
Zagorodnii, A.G.; Usenko, A.S.; Yakimenko, I.P.
1993-02-01
A Langevin approach is developed which allows a correlation theory of a semi-infinite nonequilibrium plasma to be derived which includes the intrinsic thermal fields of the external medium. The results obtained using the fluctuation-dissipation theorem and those found by the Langevin approach including a distribution of random sources throughout the entire space are shown to be equivalent. The spectrum of the thermal radiation emitted from a half-space of nonisothermal plasma into an external medium having a nonzero temperature is calculated. 29 refs.
Correlations in a generalized elastic model: fractional Langevin equation approach.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-12-01
The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach. PMID:21230641
Schofield, Jeremy
Langevin equation for the extended Rayleigh model with an asymmetric bath Alexander V. Plyukhin piston is consid- ered. The nonlinear Langevin equation for the motion of the piston is derived from appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions
Schofield, Jeremy
Langevin equation for the Rayleigh model with finite-range interactions Alexander V. Plyukhin October 2003 Both linear and nonlinear Langevin equations are derived directly from the Liouville equation of the Langevin equation, as well as statistical properties of random force, may depend not only on the mass ratio
Langevin dynamics of the deconfinement transition for pure gauge theory
Ana Júlia Mizher; Eduardo S. Fraga; Gastão Krein
2006-04-17
We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).
Fractional Langevin equation: Overdamped, underdamped, and critical behaviors
NASA Astrophysics Data System (ADS)
Burov, S.; Barkai, E.
2008-09-01
The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) ?c=0.402±0.002 marks a transition to a nonmonotonic underdamped phase, (ii) ?R=0.441… marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) ??1=0.527… and (iv) ??2=0.707… mark transitions to a double-peak phase of the “loss” when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal.
Description of quantum noise by a Langevin equation
NASA Technical Reports Server (NTRS)
Metiu, H.; Schon, G.
1984-01-01
General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.
Complex Langevin equations and their applications to quantum statistical and lattice field models
NASA Astrophysics Data System (ADS)
Gausterer, H.; Klauder, J. R.
1986-06-01
We discuss the calculation of statistical averages of variables lying on S1 or S2 using (complex) Langevin equations. Assuming that the drift term is proportional to the gradient of a possibly complex function S(\\{xi\\}), xi?S1 or S2 we give the general form of such Langevin equations. These variables cause unphysical singularities and computational problems; thus we transform them to those of the embedding Euclidean space. We show in several examples that these modified (complex) Langevin equations have good convergence properties using an improved two-stage Runge-Kutta algorithm.
Shimizu, Akira
Quantum Langevin equations for semiconductor light-emitting devices and the photon statistics the microscopic quantum Langevin equations QLEs we derive the effective semiconductor QLEs and the associated into a squeezed state of light 16 . The former mechanism, on the other hand, is often described by the Langevin
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
NASA Astrophysics Data System (ADS)
Schmidt, Julian; Meistrenko, Alex; van Hees, Hendrik; Xu, Zhe; Greiner, Carsten
2015-03-01
We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function, and then we study numerically the impact of time-correlated noise on the time evolution of a (1 +1 )-dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.
A comparison of the velocity spectra obtained with the Boltzmann and Boltzmann-Langevin equations
Stryjewski, J.; Ayik, S.; Belkacem, M.; Suraud, E. (Grand Accelerateur National d'Ions Lourds (GANIL), 14 - Caen (France))
1990-01-01
The velocity spectra of Intermediate Mass Fragments produced in the reaction {sup 12}C {plus} {sup 12}C at 30, 40, 50, and 60 MeV/A are studied using both the Boltzmann and the Boltzmann-Langevin approaches. We find that the velocity distribution obtained with the stochastic Boltzmann-Langevin equation is significantly different from that obtained with the standard (non-stochastic) Boltzmann equation. 7 refs., 1 fig.
Philip R. Johnson; B. L. Hu
2002-01-01
We apply the open systems concept and the influence functional formalism\\u000aintroduced in Paper I to establish a stochastic theory of relativistic moving\\u000aspinless particles in a quantum scalar field. The stochastic regime resting\\u000abetween the quantum and semi-classical captures the statistical mechanical\\u000aattributes of the full theory. Applying the particle-centric world-line\\u000aquantization formulation to the quantum field theory of
Chiral Langevin theory for non-Abelian plasmas
Yukinao Akamatsu; Naoki Yamamoto
2015-01-13
Charged plasmas with chirality imbalance are unstable and tend to reduce the imbalance. This chiral plasma instability is, however, not captured in (anomalous) hydrodynamics for high-temperature non-Abelian plasmas. We derive a Langevin-type classical effective theory with anomalous parity-violating effects for non-Abelian plasmas that describes the chiral plasma instability at the magnetic scale. We show that the time scale of the instability is of order $[g^4 T \\ln(1/g)]^{-1}$ at weak coupling.
Paris-Sud XI, Université de
Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases
A Bohmian approach to the non-Markovian non-linear Schrödinger-Langevin equation
NASA Astrophysics Data System (ADS)
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro
2015-05-01
In this work, a non-Markovian non-linear Schrödinger-Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.
A reference trajectory approach to Langevin equations in gas phase collision dynamics
George C. Schatz; Mark D. Moser
1980-01-01
In this paper, a new approach to the development of Langevin-like equations for studying gas phase collisional energy tranfer and other dynamical problems is introduced based on the use of reference trajectories to describe memory effects and nonlinear interactions. In this development, the exact equations of motion are first expressed in terms of the deviations of the coordinates and momenta
Complex Langevin method applied to the 2D $SU(2)$ Yang--Mills theory
Hiroki Makino; Hiroshi Suzuki; Daisuke Takeda
2015-03-10
The complex Langevin method in conjunction with the gauge cooling is applied to the 2D lattice $SU(2)$ Yang--Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.
Complex Langevin method applied to the 2D $SU(2)$ Yang--Mills theory
Makino, Hiroki; Takeda, Daisuke
2015-01-01
The complex Langevin method in conjunction with the gauge cooling is applied to the 2D lattice $SU(2)$ Yang--Mills theory that is analytically solvable. We obtained strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.
Critical comparison of Kramers' fission width with the stationary width from the Langevin equation
Sadhukhan, Jhilam; Pal, Santanu [Physics Group, Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700 064 (India)
2009-06-15
It is shown that Kramers' fission width, originally derived for a system with constant inertia, can be extended to systems with a deformation-dependent collective inertia, which is the case for nuclear fission. The predictions of Kramers' width for systems with variable inertia are found to be in very good agreement with the stationary fission widths obtained by solving the corresponding Langevin equations.
Langevin equation with stochastic damping - Possible application to critical binary fluid
NASA Technical Reports Server (NTRS)
Jasnow, D.; Gerjuoy, E.
1975-01-01
We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.
S. Ayik; Y. B. Ivanov; V. N. Russkikh; W. Noerenberg
1993-01-01
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
T. Srokowski
2001-01-01
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some
Scaled Langevin equation for complex systems: New linear scaling relation for weight factor
S. Fujita; S. S. Lee; J. Koyama
1997-01-01
A set of scaled Langevin equations is proposed to study a long time tail of correlation functions for two model systems (Type I and Type II). Each system is composed of elements which are grouped into clusters according to dynamical activations for external forces. The clusters in Type I are characterized by linear scaling rules in repetitive operations, whereas the
J. S. Hasstrom; D. L. Ermak
1997-01-01
Vertical dispersion of material in the convective boundary layer, CBL, is dramatically different than in natural or stable boundary layers, as has been shown by field and laboratory experiments. Lagrangian stochastic modeling based on the Langevin equation has been shown to be useful for simulating vertical dispersion in the CBL. This modeling approach can account for the effects of the
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel; Peter Hänggi
2006-01-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
A. Mollgaard; K. Splittorff
2014-12-08
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at non-zero chemical potential. The successful match with the analytic prediction for the chiral condensate is established through a shift of matrix integration variables and choosing a polar representation for the new matrix elements before complexification. Furthermore, we test the proposal to work with a Langevin-time dependent quark mass and find that it allows us to control the fluctuations of the phase of the fermion determinant throughout the Langevin trajectory.
NASA Astrophysics Data System (ADS)
Levasseur, Laurence Perreault
2013-10-01
We present a new, recursive approach to stochastic inflation which is self-consistent and solves multiple problems that plagued a certain number of previous studies, in particular, in realistic contexts where the background spacetime is taken to be dynamical, where there is more than one field present (especially with a mass hierarchy), or where the role played by backreaction is suspected to be important. We first review the formalism of stochastic inflation as it is usually heuristically presented, that is, deriving the Langevin equations from the field equations of motion, and summarize previous results on the subject. We demonstrate where inconsistent approximations to the Langevin equations are commonly made and show how these can be avoided. This setup shares many similarities with quantum Brownian motion and out-of-equilibrium statistical quantum dynamics. We hence review how path integral techniques can be applied to the stochastic inflationary context. We show that this formalism is consistent with the standard approach. We then develop a natural perturbative expansion and use it to calculate the one-loop corrected Langevin equations.
Fractional Brownian motion and generalized Langevin equation motion in confined geometries
Jae-Hyung Jeon; Ralf Metzler
2010-01-06
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time averaged mean squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume, and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single particle trajectory data.
Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution
NASA Astrophysics Data System (ADS)
Kanazawa, Kiyoshi; Sano, Tomohiko G.; Sagawa, Takahiro; Hayakawa, Hisao
2015-06-01
We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601-090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.
NASA Astrophysics Data System (ADS)
Haga, Taiki
2015-05-01
We investigate a novel type of Langevin model that describes the nonequilibrium dynamics of a classical particle interacting with a spatially extended environment. In this model, a particle, which interacts with the environment through the nonlinear interaction Hamiltonian, is driven by a constant external force, and subsequently, it reaches a nontrivial nonequilibrium steady state. We derive an effective Langevin equation for the particle in the nonequilibrium steady states. Using this equation, we calculate the effective temperature defined as the ratio of the correlation function of the velocity fluctuation to the linear response function with respect to a small perturbation. As a result, it is shown that the effective temperature associated with the time scale of the particle is identical to the kinetic temperature if the time scale of the environment and that of the particle are well separated. Furthermore, a noteworthy expression, which relates the kinetic temperature with the curvature of the driving force-mean velocity curve, is derived.
QUANTUM LANGEVIN MOLECULAR DYNAMIC DETERMINATION OF THE SOLAR-INTERIOR EQUATION OF STATE
Dai Jiayu; Hou Yong; Yuan Jianmin, E-mail: jmyuan@nudt.edu.c [Department of Physics, College of Science, National University of Defense Technology, Changsha 410073 (China)
2010-10-01
The equation of state (EOS) of the solar interior is accurately and smoothly determined from ab initio simulations named quantum Langevin molecular dynamics in the pressure range of 58 Mbar {<=}P {<=} 4.6 x 10{sup 5} Mbar at the temperature range of 1 eV {<=}T {<=} 1500 eV. The central pressure is calculated and compared with other models. The effect of heavy elements such as carbon and oxygen on the EOS is also discussed.
Fluctuation limits of a locally regulated population and generalized Langevin equations
NASA Astrophysics Data System (ADS)
Savov, Mladen; Wang, Shi-Dong
2015-06-01
We consider a locally regulated spatial population model introduced by Bolker and Pacala. Based on the deterministic approximation studied by Fournier and Méléard, we prove that the fluctuation theorem holds under some mild moment conditions. The limiting process is shown to be an infinite-dimensional Gaussian process solving a generalized Langevin equation. In particular, we further consider its properties in one dimension case, which is characterized as a time-inhomogeneous Ornstein-Uhlenbeck process.
Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem
Ludvig Lizana; Tobias Ambjornsson; Alessandro Taloni; Eli Barkai; Michael A. Lomholt
2010-04-28
In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a new harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models.
A Langevin equation approach to electron transfer reactions in the diabatic basis
Song Xiaogeng; Van Voorhis, Troy [Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States); Wang Haobin [Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003 (United States)
2008-10-14
A linear Langevin equation that governs the population dynamics of electron transfer reactions is derived. The noise in the Langevin equation is eliminated by treating the diabatic population fluctuations as the relevant variables, leaving only the memory kernel responsible for the population relaxation. Within the memory kernel, the diabatic coupling is treated perturbatively and a second order expansion is found to give a simple closed form expression for the kernel. The accuracy of the second order truncation is maximized by performing a fixed rotation of the diabatic electronic states that minimizes the first order free energy of the system and thus minimizes the effect of the perturbation on the thermodynamics. The resulting two-hop Langevin equation (THLE) is then validated by applying it to a simple spin-boson model, where exact results exist. Excellent agreement is found in a wide parameter range, even where the perturbation is moderately strong. Results obtained in the rotated electronic basis are found to be consistently more accurate than those from the unrotated basis. These benchmark calculations also allow us to demonstrate the advantage of treating the population fluctuations instead of the populations as the relevant variables, as only the former lead to reliable results at long time. Thus, the THLE appears to provide a viable alternative to established methods - such as Ehrenfest dynamics or surface hopping--for the treatment of nonadiabatic effects in electron transfer simulations.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
P?oszajczak, M.; Srokowski, T.
1997-05-01
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
Langevin description of Markov master equations II: Noise correlations
NASA Astrophysics Data System (ADS)
Hanggi, P.
1981-09-01
In this paper we examine the cumulant properties of generally multiplicative noise of stochastically equivalent stochastic differential equations (SDE) for a given (integro) master equation. For an Ito-SDE we obtain as a necessary consequence that the noise f I (t) possesses a ?-correlated 2-nd order conditioned cumulant < f I( t 1) f I( t 2)|x( t *)=x> if t *?max{ t 2, t1}. For time points { t 1?t2...?tn-1=tn} the conditioned cumulants of f I (t) of order n>2 generally contain memory contributions, but vanish if t n-1
Kwok, Sau Fa, E-mail: kwok@dfi.uem.br
2012-08-15
A Langevin equation with multiplicative white noise and its corresponding Fokker-Planck equation are considered in this work. From the Fokker-Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: Black-Right-Pointing-Pointer Fokker-Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. Black-Right-Pointing-Pointer Transformation of diffusion processes into the Wiener process in different prescriptions is provided. Black-Right-Pointing-Pointer The prescription parameter is associated with the growth rate for a Gompertz-type model.
The Schr\\"odinger-Langevin equation with and without thermal fluctuations
Katz, Roland
2015-01-01
The Schr\\"odinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications. We focus on two open issues relative to its solutions. We first show that the Madelung/polar transformation of the wavefunction leads to a nonzero friction for the excited states of the quantum subsystem. We then study analytically and numerically the SL equation ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states, quantum noises and their production are discussed and a detailed analysis is carried with two kinds of noise and potential.
NASA Astrophysics Data System (ADS)
Srokowski, T.
2001-09-01
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.
Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations
2013-01-01
In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328
Laws of large numbers and langevin approximations for stochastic neural field equations.
Riedler, Martin G; Buckwar, Evelyn
2013-01-01
In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model.Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328
Dissipative condensation of ion channels described by a Langevin-Kelvin equation
NASA Astrophysics Data System (ADS)
Fromherz, Peter; Zeiler, Andreas
1994-07-01
The lateral motion of protein molecules in a fluid lipid membrane is treated by Langevin equations. Long-range attractive forces are taken into account which arise from the interaction of electrophoretic charges with voltage gradients caused by ion flow through open channels and leaks. Clusters of molecules are formed above a threshold of the concentration gradient of ions across the membrane. Within the clusters we observe coexistence of crystalline order in their center and liquid-like order in a wide interfacial region. The parameters are chosen to match the physical conditions of a synapse between neurons, such a cluster formation represents a model for memory formation.
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
NASA Astrophysics Data System (ADS)
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still ? correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel; Peter Hänggi
2006-01-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian\\u000amotion is derived from a microscopic collision model. The model assumes that a\\u000aheavy point-like Brownian particle interacts with the lighter heat bath\\u000aparticles via elastic hard-core collisions. First, the commonly known,\\u000anon-relativistic LE is deduced from this model, by taking into account the\\u000anon-relativistic conservation laws for momentum and kinetic
Sandev, Trifce, E-mail: trifce.sandev@drs.gov.mk [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of)] [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Metzler, Ralf, E-mail: rmetzler@uni-potsdam.de [Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm (Germany) [Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm (Germany); Department of Physics, Tampere University of Technology, FI-33101 Tampere (Finland); Tomovski, Živorad, E-mail: tomovski@pmf.ukim.mk [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)] [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)
2014-02-15
We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
NASA Astrophysics Data System (ADS)
Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad
2014-02-01
We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
Internal noise driven generalized Langevin equation from a nonlocal continuum model
Saikat Sarkar; Shubhankar Roy Chowdhury; Debasish Roy; Ram Mohan Vasu
2015-03-10
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree-of-freedom (DOF), is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum. A constraint equation, similar to a fluctuation dissipation theorem (FDT), is shown to statistically relate the internal noise to the other parameters in the GLE.
Non-Gaussian statistics, classical field theory, and realizable Langevin models
Krommes, J.A.
1995-11-01
The direct-interaction approximation (DIA) to the fourth-order statistic Z {approximately}{l_angle}{lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (``spurious vertices``) is described. It is shown how to derive an improved representation, that realizes cumulants through O({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z{sub DIA}{sup M} to Z{sub DIA} is derived. Both Z{sub DIA} and Z{sub DIA}{sup M} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example.
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
NASA Astrophysics Data System (ADS)
Grima, Ramon; Thomas, Philipp; Straube, Arthur V.
2011-08-01
The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?-3/2 for reaction systems which do not obey detailed balance and at least accurate to order ?-2 for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?-1/2 and variance estimates accurate to order ?-3/2. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.
NASA Technical Reports Server (NTRS)
Aronowitz. Sheldon
1980-01-01
The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Huckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (approximately 3 - 10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce--the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH > CH > CO > NO, when these entities were sufficiently distant. The nature of the silica grain and that of the "cold" desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.
NASA Technical Reports Server (NTRS)
Aronowitz, S.; Chang, S.
1980-01-01
The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Hueckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (about 3-10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce - the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH greater than CH greater than CO greater than NO, when these entities were sufficiently distant. The nature of the silica grain and that of the 'cold' desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Jörn Dunkel; Peter Hänggi
2006-09-25
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still $\\gd$-correlated (white noise) but does \\emph{no} longer correspond to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
NASA Astrophysics Data System (ADS)
Yu, Hsiu-Yu; Eckmann, David M.; Ayyaswamy, Portonovo S.; Radhakrishnan, Ravi
2015-05-01
We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.
Kim, Min-Geun; Jang, Hong-Lae [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Cho, Seonho, E-mail: secho@snu.ac.kr [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)
2013-05-01
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations
NASA Astrophysics Data System (ADS)
Hasegawa, Yoshihiko
2015-04-01
We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.
Dong Keun Song; Hyuksang Chang; Sang Soo Kim; Kikuo Okuyama
2005-01-01
The effect of Brownian diffusive particle trajectory of nanoparticles on the transfer function of the low pressure Differential Mobility Analyzer (LPDMA) was evaluated by a numerical simulation of the Langevin dynamic equation. The results of the simulation were compared with previously reported experimental results (Seto et al. 1997; Seol et al. 2000) and Stolzenburg's transfer function (1988). As the operational
Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.
Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Igli?, Veronika; Igli?, Aleš
2011-06-01
Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles. PMID:21613667
Generalized Langevin equation for solids. I. Rigorous derivation and main properties
NASA Astrophysics Data System (ADS)
Kantorovich, L.
2008-09-01
We demonstrate explicitly that the derivation by Adelman and Doll (AD) [J. Chem. Phys. 64, 2375 (1976)] of the generalized Langevin equation (GLE) to describe dynamics of an extended solid system by considering its finite subsystem is inconsistent because it relies on performing statistical averages over the entire system when establishing properties of the random force. This results in the random force representing a nonstationary process opposite to one of the main assumptions made in AD that the random force corresponds to a stationary stochastic process. This invalidates the derivation of the Brownian (or Langevin) form of the GLE in AD. Here we present a different and more general approach in deriving the GLE. Our method generalizes that of AD in two main aspects: (i) the structure of the finite region can be arbitrary (e.g., anharmonic), and (ii) ways are indicated in which the method can be implemented exactly if the phonon Green’s function of the harmonic environment region surrounding the anharmonic region is known, which is, e.g., the case when the environment region represents a part of a periodic solid (the bulk or a surface). We also show that in general after the local perturbation has ceased, the system returns to thermodynamic equilibrium with the distribution function for region 1 being canonical with respect to an effective interaction between atoms, which includes instantaneous response of the surrounding region. Note that our method does not rely on the assumption made in AD that the stochastic force correlation function depends on the times difference only (i.e., the random force corresponds to a stationary random process). In fact, we demonstrate explicitly that generally this is not the case. Still, the correct GLE can be obtained, which satisfies exactly the fluctuation-dissipation theorem.
AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation
Koehl, Patrice; Delarue, Marc
2010-01-01
The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727
Complex Langevin dynamics for SU(3) gauge theory in the presence of a theta term
Lorenzo Bongiovanni; Gert Aarts; Erhard Seiler; Denes Sexty
2014-11-04
One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta term. On the lattice such a term is complex: hence it introduces a sign problem which, in general, limits the applicability of standard Monte Carlo methods. Here we will discuss the approach of complex Langevin dynamics and show results for both real and imaginary values of theta. We also report on our experience with the gradient flow for real and imaginary theta.
Ooi, C. H. Raymond; Scully, Marlan O.; Sun, Qingqing; Zubairy, M. Suhail
2007-01-01
Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory C. H. Raymond Ooi,1,2,3,4 Qingqing Sun,2 M. Suhail Zubairy,2 and Marlan O. Scully1,2,3 1Max-Planck-Institut f?r Quantenoptik, D-85748... University, New Jersey 08544, USA 4Department of Physics, KAIST, Guseong-dong, Yuseong-gu, Daejeon, 305-701 Korea #1;Received 26 November 2006; revised manuscript received 27 December 2006; published 31 January 2007; publisher error corrected 5 February...
Ooi, C. H. Raymond; Scully, Marlan O.; Sun, Qingqing; Zubairy, M. Suhail
2007-01-01
Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory C. H. Raymond Ooi,1,2,3,4 Qingqing Sun,2 M. Suhail Zubairy,2 and Marlan O. Scully1,2,3 1Max-Planck-Institut f?r Quantenoptik, D-85748... University, New Jersey 08544, USA 4Department of Physics, KAIST, Guseong-dong, Yuseong-gu, Daejeon, 305-701 Korea #1;Received 26 November 2006; revised manuscript received 27 December 2006; published 31 January 2007; publisher error corrected 5 February...
Wu, C.-H.; Lee, D.-S. [Department of Physics, National Dong-Hwa University, Hualien, Taiwan (China)
2005-06-15
We employ the Schwinger-Keldysh formalism to study the nonequilibrium dynamics of the mirror with perfect reflection moving in a quantum field. In the case where the mirror undergoes the small displacement, the coarse-grained effective action is obtained by integrating out the quantum field with the method of influence functional. The semiclassical Langevin equation is derived, and is found to involve two levels of backreaction effects on the dynamics of mirrors: radiation reaction induced by the motion of the mirror and backreaction dissipation arising from fluctuations in quantum field via a fluctuation-dissipation relation. Although the corresponding theorem of fluctuation and dissipation for the case with the small mirror's displacement is of model independence, the study from the first principles derivation shows that the theorem is also independent of the regulators introduced to deal with short-distance divergences from the quantum field. Thus, when the method of regularization is introduced to compute the dissipation and fluctuation effects, this theorem must be fulfilled as the results are obtained by taking the short-distance limit in the end of calculations. The backreaction effects from vacuum fluctuations on moving mirrors are found to be hardly detected while those effects from thermal fluctuations may be detectable.
NASA Astrophysics Data System (ADS)
Haas, Kevin R.; Yang, Haw; Chu, Jhih-Wei
2013-09-01
The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology.
Higher-order time integration of Coulomb collisions in a plasma using Langevin equations
Dimits, A.M., E-mail: dimits1@llnl.gov [Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, CA 94511-0808 (United States); Cohen, B.I. [Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, CA 94511-0808 (United States)] [Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, CA 94511-0808 (United States); Caflisch, R.E.; Rosin, M.S.; Ricketson, L.F. [Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90036 (United States)] [Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90036 (United States)
2013-06-01
The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler–Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(?t) vs. O(?t{sup 1/2})] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler–Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.
Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches
Jakob Schluttig; Denitsa Alamanova; Volkhard Helms; Ulrich S. Schwarz
2008-09-17
We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20-9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5-95 percent. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modelling of the dynamics of large protein complexes.
NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-02-01
We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.
Classical Noise IV: Langevin Methods
Melvin Lax
1966-01-01
A Langevin theory for linear and nonlinear, stationary and nonstationary, processes is developed and compared with Markoff methods. For short correlation times tauc, we find the Markoff process that is a good approximation to the Langevin process for Deltat>tauc. Conversely, given the diffusion coefficients Dn of a Markoff process, we find the moments (to all orders) of the Langevin forces
Copperman, J; Guenza, M G
2014-11-20
We utilize a multiscale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin equation for protein dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal-mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free-energy landscape of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with nuclear magnetic resonance relaxation experiments. Fundamental to this approach is the inclusion of internal dissipation, which is absent in any rigid-body hydrodynamical modeling scheme. PMID:25356856
Dhruba Banerjee; Bidhan Chandra Bag; Suman Kumar Banik; Deb Shankar Ray
2003-03-04
Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\\bf 65}, 021109 (2002); {\\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot.
Ooi, C. H. Raymond; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.
2007-01-01
Publisher?s Note: Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory [Phys. Rev. A 75, 013820 (2007)] C. H. Raymond Ooi, Qingqing Sun, M. Suhail Zubairy, and Marlan O. Scully #1;Received 1...
Langevin evolution of disoriented chiral condensate
NASA Astrophysics Data System (ADS)
Bettencourt, Luís. M. A.; Rajagopal, Krishna; Steele, James V.
2001-10-01
As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilibrium behavior of the quantum field theory of pions and ? fields over a wide range of temperatures. Finally, we estimate the viscosity ?(T), which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting ?(T) is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics.
Chaichian, M; Tureanu, A; Zahabi, A
2010-06-01
We propose to take advantage of using the Wiener path integrals as the formal solution for the joint probability densities of coupled Langevin equations describing particles suspended in a fluid under the effect of viscous and random forces. Our obtained formal solution, giving the expression for the Lyapunov exponent, (i) will provide the description of all the features and the behavior of such a system, e.g., the aggregation phenomenon recently studied in the literature using appropriate approximations, (ii) can be used to determine the occurrence and the nature of the aggregation-nonaggregation phase transition which we have shown for the one-dimensional case, and (iii) allows the use of a variety of approximative methods appropriate for the physical conditions of the problem such as instanton solutions in the WKB approximation in the aggregation phase for the one-dimensional case as presented in this paper. The use of instanton approximation gives the same result for the Lyapunov exponent in the aggregation phase, previously obtained by other authors using a different approximative method. The case of nonaggregation is also considered in a certain approximation using the general path integral expression for the one-dimensional case. PMID:20866524
Yu Chen; Feng-Shou Zhang; Jun Su
2009-01-01
A new attempt of calculation for the total reaction cross sections (sigmaR) has been carried out within the isospindependent Boltzmann-Langevin equation in the intermediate energy heavy-ion collision of isotopes of C. The sigmaR of both stable and exotic nuclei are reproduced rather well. The incident energy and isospin dependencies of sigmaR have been investigated. It is found that the isospin
V. Delgado; J. Breton; A. Hardisson; C. Girardet
1987-01-01
A numerical integration of the Langevin equations connected to the motions of a diatomic molecule trapped in a rare gas matrix is performed using a Runge–Kutta procedure and a Monte Carlo–Metropolis sampling for the initial configurations of the so-called primary system (cf. paper I). The rotational energy transfer from the molecule to the crystal is shown to strongly depend on
NASA Astrophysics Data System (ADS)
Pankavich, S.; Shreif, Z.; Miao, Y.; Ortoleva, P.
2009-05-01
The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.
Generalized Langevin models of molecular dynamics simulations with applications to ion channels
Krishnamurthy, Vikram
Generalized Langevin models of molecular dynamics simulations with applications to ion channels Dan dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical
Langevin dynamics of the pure SU(2) deconfining transition
E. S. Fraga; G. Krein; A. J. Mizher
2007-08-30
We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU(2) gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise.
NASA Astrophysics Data System (ADS)
Chen, Yu; Zhang, Feng-Shou; Su, Jun
2009-11-01
A new attempt of calculation for the total reaction cross sections (?R) has been carried out within the isospindependent Boltzmann-Langevin equation in the intermediate energy heavy-ion collision of isotopes of C. The ?R of both stable and exotic nuclei are reproduced rather well. The incident energy and isospin dependencies of ?R have been investigated. It is found that the isospin effect is comparatively remarkable at intermediate energy. It is also found that 15-18C are neutron skin nuclei but for 19C and 20C we cannot draw a conclusion whether they have halo structures.
Langevin Stabilization of Molecular Dynamics Jes'us A. Izaguirre
Izaguirre, Jesús A.
Langevin Stabilization of Molecular Dynamics Jes'us A. Izaguirre Department of Computer Science multiple time stepping integrators, Langevin Molly (LM) and Br¨ungerBrooksKarplusMolly (BBK a discretization of the Langevin equation that is exact for constant force, and BBKM uses the popular Br
Langevin stabilization of molecular dynamics Jesus A. Izaguirrea)
Skeel, Robert
Langevin stabilization of molecular dynamics Jesu´s A. Izaguirrea) Department of Computer Science, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly LM and Bru uses a discretization of the Langevin equation that is exact for the constant force, and BBKM uses
Turchenkov, D A; Boronovski?, S E; Nartsissov, Ia R
2013-01-01
Changes in the state of the central nervous system, leading to the development of pathological processes, are directly associated with a state of neurons, particularly with their conductivity in synaptic cleft region. The synaptic flexibility plays a key role in environmental adaptation, which manifests in dynamic changes of synaptic properties. However more attention was paid rather to their functional, than physical-chemical properties. We present the results of simulation of potential determining ions in synaptic contact area using Langevin dynamics. Diffusion and self-diffusion coefficients were calculated. It is shown that the range of variability of the diffusion coefficient of ions in perimembrane space, caused by variable viscosity and dielectric conductivity of electrolyte can reach 20%. These physical-chemical synaptic parameters can be considered as relevant for synaptic flexibility. PMID:25486759
2013-01-01
Changes in the state of the central nervous system, leading to the development of pathological processes, are directly associated with a state of neurons, particularly with their conductivity in synaptic cleft region. The synaptic flexibility plays a key role in environmental adaptation, which manifests in dynamic changes of synaptic properties. However more attention was paid rather to their functional, than physical-chemical properties. We present the results of simulation of potential determining ions in synaptic contact area using Langevin dynamics. Diffusion and self-diffusion coefficients were calculated. It is shown that the range of variability of the diffusion coefficient of ions in perimembrane space, caused by variable viscosity and dielectric conductivity of electrolyte can reach 20%. These physical-chemical synaptic parameters can be considered as relevant for synaptic flexibility. PMID:25508890
Langevin description of nonequilibrium quantum fields
NASA Astrophysics Data System (ADS)
Gautier, F.; Serreau, J.
2012-12-01
We consider the nonequilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly nonlocal, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.
Langevin Evolution of Disoriented Chiral Condensate
Bettencourt, L M A; Steele, J V; Bettencourt, Luis M.A.; Rajagopal, Krishna; Steele, James V.
2001-01-01
As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a t...
Prolongation theory. A new nonlinear Schroedinger equation
Roy, S.; Chowdhury, A.R.
1987-07-01
The authors discuss a new kind of nonlinear Schroedinger equation from the viewpoint of prolongation theory. It is shown that the equation possess a Lax pair with a 3 x 3 matrix structure. It is further demonstrated that by a multiple scale perturbation of Zakharov et al. it can be reduced to the usual KdV equation.
Number Theory I: Tools and Diophantine Equations
Cohen, Henri
i Number Theory I: Tools and Diophantine Equations II: Analytic and Modern Methods by Henri COHEN "explicit number theory," not including the essential algorithmic aspects, which are for the most part of the reader that he or she is familiar with the standard basic theory of number fields, up to and including
Entropy theory for derivation of infiltration equations
NASA Astrophysics Data System (ADS)
Singh, Vijay P.
2010-03-01
An entropy theory is formulated for modeling the potential rate of infiltration in unsaturated soils. The theory is composed of six parts: (1) Shannon entropy, (2) principle of maximum entropy (POME), (3) specification of information on infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, (5) derivation of the probability distribution of infiltration, and (6) derivation of infiltration equations. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two-term, Green-Ampt, Overton, and Holtan equations, and the determination of the least biased probability distributions of these infiltration equations and their entropies. The theory leads to the expression of parameters of the derived infiltration equations in terms of measurable quantities (or information), called constraints, and in this sense these equations are rendered nonparametric. Furthermore, parameters of these infiltration equations can be expressed in terms of three measurable quantities: initial infiltration, steady infiltration, and soil moisture retention capacity. Using parameters so obtained, infiltration rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the rates computed using parameters of these equations obtained by calibration. It is found that infiltration parameter values yielded by the entropy theory are good approximations.
Relativistic Boltzmann-Langevin model for high energy heavy-ion collisions
Sakir Ayik
1991-01-01
The Boltzmann-Langevin model proposed earlier for intermediate energy heavy-ion collisions is developed further on the basis of Walecka-type field theory for describing fluctuation dynamics at high energies. Incorporating correlations into the equation of motion and treating them statistically, in analogy with brownian motion, gives rise to a stochastic transport equation for the single-particle density matrix. In the semi-classical limit, this
Dhruba Banerjee; Bidhan Chandra Bag; Suman Kumar Banik; Deb Shankar Ray
2003-01-01
Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\\\\bf 65}, 021109 (2002); {\\\\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\\\\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical
Relativistic Langevin Dynamics in Expanding Media
Min He; Hendrik van Hees; Pol B. Gossiaux; Rainer J. Fries; Ralf Rapp
2013-05-27
We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann/Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the pre-point (Ito) and post-point (H\\"anggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions.
Relativistic Langevin dynamics in expanding media.
He, Min; van Hees, Hendrik; Gossiaux, Pol B; Fries, Rainer J; Rapp, Ralf
2013-09-01
We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann-Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the prepoint (Ito) and postpoint (Hänggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions. PMID:24125244
Relativistic Langevin dynamics in expanding media
NASA Astrophysics Data System (ADS)
He, Min; van Hees, Hendrik; Gossiaux, Pol B.; Fries, Rainer J.; Rapp, Ralf
2013-09-01
We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann-Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the prepoint (Ito) and postpoint (Hänggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an “elliptic flow” transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions.
Dhruba Banerjee; Bidhan Chandra Bag; Suman Kumar Banik; Deb Shankar Ray
2003-01-01
Based on a coherent state representation of noise operator and an ensemble\\u000aaveraging procedure we have recently developed [Phys. Rev. E {\\\\bf 65}, 021109\\u000a(2002); {\\\\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to\\u000aderive the equations for time evolution of {\\\\it true} probability distribution\\u000afunctions in $c$-number phase space. We extend the treatment to develop a\\u000anumerical
Symmetry of Differential Equations and Quantum Theory
NASA Astrophysics Data System (ADS)
Yerchuck, Dmitri; Dovlatova, Alla; Alexandrov, Andrey
2014-03-01
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.
The Boltzmann Equation in Scalar Field Theory
NASA Astrophysics Data System (ADS)
Brandt, F. T.; Frenkel, J.; Guerra, A.
We derive the classical transport equation, in scalar field theory with a g2V(?) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action ? which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for ? in the static case.
F. Weysser; A. M. Puertas; M. Fuchs; Th. Voigtmann
2010-10-15
We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor, and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantiative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behaviour are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.
Nonlinear quantum equations: Classical field theory
NASA Astrophysics Data System (ADS)
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-01
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q ? 1. The main characteristic of this field theory consists on the fact that besides the usual ? (x,t), a new field ? (x,t) needs to be introduced in the Lagrangian, as well. The field ? (x,t), which is defined by means of an additional equation, becomes ? ^{*}(x,t) only when q ? 1. The solutions for the fields ? (x,t) and ? (x,t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E2 = p2c2 + m2c4, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Localised distributions and criteria for correctness in complex Langevin dynamics
Gert Aarts; Pietro Giudice; Erhard Seiler
2013-06-13
Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker-Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected.
Langevin representation of Coulomb collisions for bi-Maxwellian plasmas
Hellinger, Petr, E-mail: Petr.Hellinger@ig.cas.c [Astronomical Institute, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Atmospheric Physics, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Travnicek, Pavel M. [Astronomical Institute, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Atmospheric Physics, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Geophysics and Planetary Physics, UCLA, Los Angeles 90095-1567 (United States)
2010-07-20
Langevin model corresponding to the Fokker-Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.
Boltzmann-Langevin transport model for heavy-ion collisions
Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States)]|[Joint Institute for Heavy-Ion Research, Oak Ridge, TN (United States)
1994-06-01
Heavy-ion collisions at intermediate energies exhibit catastrophic phenomena which requires descriptions based on stochastic transport models. First, the Boltzmann-Langevin model, which provides an example of such stochastic approaches, is briefly described. Then, a projection method for obtaining numerical solutions of the Boltzmann-Langevin equation is discussed. Finally, some applications of the model to heavy-ion collisions are presented.
Boltzmann-Langevin Transport Model for Heavy-Ion Collisions
Sakir Ayik
1994-01-01
Heavy-ion collisions at intermediate energies exhibit catastrophic phenomena which requires descriptions based on stochastic transport models. First, the Boltzmann-Langevin model, which provides an example of such stochastic approaches, is briefly described. Then, a projection method for obtaining numerical solutions of the Boltzmann-Langevin equation is discussed. Finally, some applications of the model to heavy-ion collisions are presented.
Langevin's `Twin Paradox' paper revisited
J. H. Field
2008-11-21
An in-depth and mathematically-detailed analysis of Langevin's popular 1911 article on the special theory of relativity is presented. For the reader's convenience, English translations of large parts of the original French text are given. The self-contradictory nature of many of Langevin's assertions is pointed out. Of special interest is the analysis of the exchange of light signals between the travelling and stay-at-home twins in Langevin's thought experiment, in which antinomies are found in the conventional relativistic treatment. Their resolution shows that the physical basis of the differential aging effect in the experiment is not `length contraction', as in the conventional interpretation, but instead the application of the correct relative velocity transformation formula. The spurious nature of the correlated `length contraction' and `relativity of simultaneity' effects of conventional special relativity is also demonstrated. In consequence, an argument given, claiming to demonstrate that an upper limit of $c$ on the speed of any physical signal is required by causality, is invalid. Its conclusion is also in contradiction with astronomical observations and the results of a recent experiment.
Theory and applications of the Vlasov equation
Pegoraro, F; Manfredi, G; Morrison, P J
2015-01-01
Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and applications of the Vlasov equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of scientific results involving the Vlasov equation. In this editorial, after some introductory notes, a brief account is given of the main points addressed in these papers and of the perspectives they open.
Brownian motion from Boltzmann's equation.
NASA Technical Reports Server (NTRS)
Montgomery, D.
1971-01-01
Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.
Controlling complex Langevin dynamics at finite density
Gert Aarts; Lorenzo Bongiovanni; Erhard Seiler; Denes Sexty; Ion-Olimpiu Stamatescu
2013-05-06
At nonzero chemical potential the numerical sign problem in lattice field theory limits the use of standard algorithms based on importance sampling. Complex Langevin dynamics provides a possible solution, but it has to be applied with care. In this review, we first summarise our current understanding of the approach, combining analytical and numerical insight. In the second part we study SL(N,C) gauge cooling, which was introduced recently as a tool to control complex Langevin dynamics in nonabelian gauge theories. We present new results in Polyakov chain models and in QCD with heavy quarks and compare various adaptive cooling implementations.
Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid
Yukinao Akamatsu; Tetsuo Hatsuda; Tetsufumi Hirano
2009-01-01
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Itô discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space\\/conformal field theory (AdS\\/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is
Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid
Yukinao Akamatsu; Tetsuo Hatsuda; Tetsufumi Hirano
2009-01-01
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Ito discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space\\/conformal field theory (AdS\\/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
New Langevin and gradient thermostats for rigid body dynamics.
Davidchack, R L; Ouldridge, T E; Tretyakov, M V
2015-04-14
We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator. PMID:25877569
Stochastic Langevin Model for Flow and Transport in Porous Media
Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.; Meakin, Paul
2008-07-25
A new stochastic Lagrangian model for fluid flow and transport in porous media is described. The fluid is represented by particles whose flow and dispersion in a continuous porous medium is governed by a Langevin equation. Changes in the properties of the fluid particles (e.g. the solute concentration) due to molecular diffusion is governed by the advection-diffusion equation. The separate treatment of advective and diffusive mixing in the stochastic model has an advantage over the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing leading to over-prediction of mixing induced effective reaction rates. The stochastic model predicts much lower reaction product concentrations in mixing induced reactions. In addition the dispersion theory predicts more stable fronts (with a higher effective fractal dimension) than the stochastic model during the growth of Rayleigh-Taylor instabilities.
Is Schroedinger equation consistent with information theory?
R. P. Venkataraman
2000-07-03
It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann integrable density function that has real or imaginary zeros or singularities at end points of $[a,b] \\epsilon R$, a new variational formulation for quantum mechanics is proposed that yields a system of Euler-Lagrange equations that are non-linear. It is proved that the solutions of this system are unique, orthonormal and complete. One dimensional harmonic oscillator has been solved.
Complex Langevin dynamics: criteria for correctness
Gert Aarts; Frank A. James; Erhard Seiler; Ion-Olimpiu Stamatescu
2011-10-26
The complex Langevin method is a leading candidate for solving the sign problem occurring in various physical situations, notably QCD at finite chemical potential. Its most vexing problem is `convergence to the wrong limit', where the simulation gives a well defined, but incorrect, result. Here, we first outline a formal justification of the method and identify points at which it might fail. From these we derive a condition that must be satisfied in order for correct results to be obtained. We then apply these ideas to the three-imensional SU(3) spin model at finite chemical potential and show strong indications that complex Langevin dynamics yields correct results in this theory.
OFFICE OF CONGRESSMAN JIM LANGEVIN
Rhode Island, University of
of effort to build skilled economy in Rhode Island WARWICK, RI Continuing his Rhode Island Skilled Economy (RISE) Tour, Congressman Jim Langevin (D part in its success," said Langevin. "Focusing our attention on high
Dynamical systems theory for the Gardner equation
NASA Astrophysics Data System (ADS)
Saha, Aparna; Talukdar, B.; Chatterjee, Supriya
2014-02-01
The Gardner equation ut+auux+bu2ux+?uxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=?(?), ? =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ? with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and ?. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].
A unified theory of zero power and power reactor noise via backward master equations
I. Pázsit; Z. F. Kuang; A. K. Prinja
2002-01-01
Traditionally, zero power noise, i.e. inherent neutronic fluctuations in a steady medium, and power reactor noise are treated as two separate phenomena. They dominate at different power levels and are described via different mathematical tools (master equations and the Langevin equation, respectively). Because of these differences, there has been known no joint or unified description, based on first principles rather
Towards Collinear Evolution Equations in Electroweak Theory
M. Ciafaloni; P. Ciafaloni; D. Comelli
2001-11-09
We consider electroweak radiative corrections to hard inclusive processes at the TeV scale, and we investigate how collinear logarithms factorize in a spontaneously broken gauge theory, similarly to the DGLAP analysis in QCD. Due to the uncancelled double logs noticed previously, we find a factorization pattern which is qualitatively different from the analogous one in QCD. New types of splitting functions emerge which are needed to describe the initial beam charges and are infrared-sensitive, that is dependent on an infrared cutoff provided, ultimately, by the symmetry breaking scale. We derive such splitting functions at one-loop level in the example of SU(2) gauge theory, and we also discuss the structure functions' evolution equations, under the assumption that isospin breaking terms present in the Ward identities of the theory are sufficiently subleading at higher orders.
Electronic Journal of Qualitative Theory of Differential Equations
NSDL National Science Digital Library
Burton, T. A. (Theodore Allen), 1935-
Created by the Bolyai Institute at the University of Szeged, the "Electronic Journal of Qualitative Theory of Differential Equations" publishes peer-reviewed articles related to "the qualitative theory (stability, periodicity, soundness, etc.) of differential equations (ODE's, PDE's, integral equations, functional differential equations, etc.) and their applications." Proceedings of conferences are also available in the journal.
Langevin Model for Reactive Transport in Porous Media
Tartakovsky, Alexandre M.
2010-08-05
A meso-scale stochastic Lagrangian particle model is presented and used to simulate conservative and reactive transport in porous media. In the stochastic model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. Molecular diffusion and sub-pore-scale Taylor-type dispersion is modeled by effective stochastic advection-diffusion equation.In the meso-scale stochastic model the molecular and sub-pore-scale Taylor type dispersion is modeled by stochastic advection-diffusion equation. The advective velocity (the solution of langevin flow equation) causes the mechanical dispersion of a solute. A smoothed particle hydrodynamics method was used to solve the meso-scale transport equations. The comparison of the meso-scale model with pore-scale and Darcy-scale models shows that: 1) for a wide range of Peclet numbers the meso-scale model predicts the mass of reaction product more accurately than the macro-scale model; 2) for small Peclet numbers predictions of both the meso-scale and the macro-scale models agree well with a prediction of the pore-scale model; 3)the accuracy of the meso-scale model deteriorates with the increasing Peclet number but more slowly than the accuracy of the macro-scale model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing.
Comparison of Kernel Equating and Item Response Theory Equating Methods
ERIC Educational Resources Information Center
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi
2009-05-01
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Itô discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor RAA and the elliptic flow v2 for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The RAA for electrons with large transverse momentum (pT>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.
Langevin Dynamics of Heavy Quarks in 5D Holographic QCD models
Nitti, Francesco [Laboratoire APC, Universite Paris 7, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13 (France)
2011-05-23
I discuss the holographic approach to the Langevin equation describing the motion of a heavy quark propagating through the deconfined Quark-Gluon Plasma (QGP). The Langevin diffusion coefficients are directly related to the jet quenching parameter, which enters in the reconstruction of RHIC events involving heavy probes. After a brief review of the Langevin equation, I discuss the calculation of the Langevin coefficients in 5-dimensional holographic duals. Finally, I discuss the results for the jet quenching parameter in a phenomenological holographic QCD model.
A Generally Covariant Wave Equation for Grand Unified Field Theory
Myron W. Evans
2003-01-01
A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is
Notes 01. The fundamental assumptions and equations of lubrication theory
San Andres, Luis
2009-01-01
The fundamental assumption in Lubrication Theory. Derivation of thin film flow equations from Navier-Stokes equations. Importance of fluid inertia effects in thin film flows. Some fluid physical properties...
On extremals of the entropy production by ‘Langevin-Kramers’ dynamics
NASA Astrophysics Data System (ADS)
Muratore-Ginanneschi, Paolo
2014-05-01
We refer as ‘Langevin-Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin-Kramers models differs from the now well-understood case of Langevin-Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge-Ampère-Kantorovich optimal mass-transport equations.
Fission process of low excited nuclei with Langevin approach
Y. Aritomo; S. Chiba
2013-10-11
Fragment mass distributions from the fission of U and Pu isotopes at low excitation energies are studied using a dynamical model based on the fluctuation-dissipation theorem formulated as Langevin equations. The present calculations reproduced the overall trend of the asymmetric mass distribution without parameter adjustment for the first time using the Langevin approach. The Langevin trajectories show a complicated time evolution on the potential surface, which causes the time delay of fission, showing that dynamical treatment is vital. It was found that the shell effect of the potential energy landscape has a dominant role in determining the mass distribution, although it is rather insensitive to the strength of dissipation. Nevertheless, it is essential to include the effect of dissipation, since it has a crucial role in giving "fluctuation" to Langevin trajectories as well as for explaining the multiplicities of pre-scission neutrons as the excitation energy increases. Therefore, the present approach can serve as a basis for more refined analysis.
Thermodynamic restrictions on the constitutive equations of electromagnetic theory
NASA Technical Reports Server (NTRS)
Coleman, B. D.; Dill, E. H.
1971-01-01
Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences
On Theories Explaining the Success of the Gravity Equation
Simon J. Evenett; Wolfgang Keller
2001-01-01
We examine whether two important theories of trade, the Heckscher-Ohlin theory and the Increasing Returns theory, can account for the empirical success of the so-called gravity equation. Since versions of both theories can predict this equation, we tackle the model identification problem by conditioning bilateral trade relations on factor endowment differences and on the share of intra-industry trade. Only for
Collective Langevin Dynamics of Flexible Cytoskeletal Fibers
Francois Nedelec; Dietrich Foethke
2009-03-30
We develop a numerical method to simulate mechanical objects in a viscous medium at a scale where inertia is negligible. Fibers, spheres and other voluminous objects are represented with points. Different types of connections are used to link the points together and in this way create composite mechanical structures. The motion of such structures in a Brownian environment is described by a first-order multivariate Langevin equation. We propose a computationally efficient method to integrate the equation, and illustrate the applicability of the method to cytoskeletal modeling with several examples.
Theory of relativistic Brownian motion: the (1+1)-dimensional case.
Dunkel, Jörn; Hänggi, Peter
2005-01-01
We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (prepoint discretization rule) versus the Stratonovich (midpoint discretization rule) dilemma: It is found that the relativistic Langevin equation in the Hänggi-Klimontovich interpretation (with the postpoint discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented. PMID:15697675
Test Equating: Mean, Linear, Equipercentile, and Item Response Theory.
ERIC Educational Resources Information Center
Felan, George D.
This paper discusses the four major types of test equating: (1) mean; (2) linear; (3) equipercentile; and (4) item response theory. The single-group, equivalent-group, and anchor-test data collection designs are presented as methods used for test equating. Issues related to assumptions and equating error are also addressed. The advantages and…
Langevin dynamics and decoherence of heavy quarks at high temperatures
Yukinao Akamatsu
2015-05-25
Langevin equation of heavy quarks in high-temperature quark-gluon plasma is derived. The dynamics of heavy quark color is coupled with the phase space dynamics and causes a macroscopic superposition state of heavy quark momentum. Decoherence of the superposition state allows us classical description. The time scale of decoherence gives an appropriate discretization time scale $\\Delta t \\sim \\sqrt{M/\\gamma}$ for the classical Langevin equation, where $M$ is heavy quark mass and $\\gamma$ is heavy quark momentum diffusion constant.
Langevin dynamics and decoherence of heavy quarks at high temperatures
Akamatsu, Yukinao
2015-01-01
Langevin equation of heavy quarks in high-temperature quark-gluon plasma is derived. The dynamics of heavy quark color is coupled with the phase space dynamics and causes a macroscopic superposition state of heavy quark momentum. Decoherence of the superposition state allows us classical description. The time scale of decoherence gives an appropriate discretization time scale $\\Delta t \\sim \\sqrt{M/\\gamma}$ for the classical Langevin equation, where $M$ is heavy quark mass and $\\gamma$ is heavy quark momentum diffusion constant.
Gert Aarts
2009-05-05
Stochastic quantization can potentially be used to simulate theories with a complex action due to a nonzero chemical potential. We study complex Langevin dynamics in the relativistic Bose gas analytically, using a mean field approximation. We concentrate on the region with a Silver Blaze problem and discuss convergence, stability, fixed points, and the severeness of the sign problem. The real distribution satisfying the extended Fokker-Planck equation is constructed and its nonlocal form is explained. Finally, we compare the mean field results in finite volume with the numerical data presented in Ref. [1].
Langevin molecular dynamics derived from Ehrenfest dynamics
Anders Szepessy
2011-03-30
Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio, $M$, of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy $o(M^{-1/2})$ on bounded time intervals and by $o(1)$ on unbounded time intervals, which makes the small $\\mathcal{O}(M^{-1/2})$ friction and $o(M^{-1/2})$ diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperture, derived by a stability and consistency argument: starting with any equilibrium measure of the Ehrenfest Hamiltonian system, the initial electron distribution is sampled from the equilibrium measure conditioned on the nuclei positions, which after long time leads to the nuclei positions in a Gibbs distribution (i.e. asymptotic stability); by consistency the original equilibrium measure is then a Gibbs measure.The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuation-dissipation relation.
P. N. Nadtochy; A. V. Karpov; G. D. Adeev; D. V. Vanin
2002-01-01
A stochastic approach to fission dynamics based on three-dimensional Langevin equations was applied to calculate a fission fragment mass-energy distribution from a number of excited compound nuclei formed in reactions induced by heavy ions. The evaporation of prescission light particles along Langevin fission trajectories from the ground state of the compound nucleus to its scission have been taken into account
A. V. Karpov; P. N. Nadtochy; D. V. Vanin; G. D. Adeev
2001-01-01
A stochastic approach to fission dynamics based on three-dimensional Langevin equations was applied to calculate fission fragment mass-energy distribution from a number of excited compound nuclei formed in reactions induced by heavy ions. Evaporation of prescission light particles along Langevin fission trajectories from the ground state of the compound nucleus to its scission has been taken into account using a
Langevin Stabilization of Multiscale Mollified Molecular Dynamics
Izaguirre, Jesús A.
Langevin Stabilization of Multiscale Mollified Molecular Dynamics Jes'us A. Izaguirre Department. Langevin Molly (LM) is introduced in this paper. It uses the mollified impulse method for the Newtonian term and the Langevin impulse method for the Langevin term. A parallel version of LM is available
Applications of the theory of evolution equations to general relativity
Alan D. Rendall
2001-09-07
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are presented. After this recent applications of Fuchsian equations are described, with particular attention to work on the structure of singularities of solutions of the Einstein equations coupled to a massless scalar field. Next the relations between analytical and numerical studies of the Einstein equations are discussed. Finally an attempt is made to identify fruitful directions for future research within the analytic approach to the study of the Einstein equations.
The Langevin Approach: a simple stochastic method for complex phenomena
Reinke, Nico; Medjroubi, Wided; Lind, Pedro G; Wächter, Matthias; Peinke, Joachim
2015-01-01
We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin equation. Moreover, it can be applied not only to processes in time, but also to processes in scale, given that the data available shows ergodicity. This chapter introduces the mathematical foundations of the Langevin approach and describes how to implement it numerically. A specific application of the method is presented, namely to a turbulent velocity field measured in the laboratory, retrieving the corresponding energy cascade and comparing with the results from a computational simulation of that experiment. In addition, we describe a physical interpretation bridging between processes in time and in scale. Finally, we describe extensions of the method for time series reconstruction and applications to other fields such as finance, medicine, geophysics and renewable ener...
Generating transition paths by Langevin bridges
NASA Astrophysics Data System (ADS)
Orland, Henri
2011-05-01
We propose a novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time tf. These paths are weighted with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a non-local stochastic differential equation. In the limit of short times, we show that this complicated non-solvable equation can be simplified into an approximate local stochastic differential equation. For longer times, the paths generated by this approximate equation do not satisfy the correct statistics, but this can be corrected by an adequate reweighting of the trajectories. In all cases, the paths are statistically independent and provide a representative sample of transition paths. The method is illustrated on the one-dimensional quartic oscillator.
Generalized Bent Functions Philippe Langevin
Faccanoni, Gloria
Generalized Bent Functions Philippe Langevin #12; #12; 3. GENERALIZED BENT FUNCTIONS 3 Abstract. In this paper, we compare the the binary bent functions and the generalized bent functions on the metric and degree points of view
Langevin description of fusion, deep-inelastic collisions and heavy-ion-induced fission
P. Frobrich; I. I. Gontchar
1998-01-01
The description of fusion of heavy ions, deep-inelastic heavy-ion collisions and heavy-ion-induced fission in the framework of Langevin equations is reviewed. The Langevin equations are derived within an idealized schematic model. These equations are applied with the aim to reproduce the experimental data. In order to be able to do so the potential and the transport coefficients are not taken
Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
N. C. Cassol-Seewald; R. L. S. Farias; E. S. Fraga; G. Krein; Rudnei O. Ramos
2012-05-15
We consider the Langevin lattice dynamics for a spontaneously broken lambda phi^4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
Stability in functional differential equations established using fixed point theory
Chuhua Jin; Jiaowan Luo
2008-01-01
In this paper we consider a nonlinear scalar delay differential equation with variable delays and give some new conditions for the boundedness and stability by means of Krasnoselskii’s fixed point theory. A stability theorem with a necessary and sufficient condition is proved. The results in [T.A. Burton, Stability by fixed point theory or Liapunov’s theory: A comparison, Fixed Point Theory
THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES
The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...
Behavioral Momentum Theory: Equations and Applications
ERIC Educational Resources Information Center
Nevin, John A.; Shahan, Timothy A.
2011-01-01
Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…
Item Response Theory Equating Using Bayesian Informative Priors.
ERIC Educational Resources Information Center
de la Torre, Jimmy; Patz, Richard J.
This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…
The Equations of Motion in Einstein's New Unified Field Theory
Joseph Callaway
1953-01-01
It is shown that the field equations of Einstein's latest unified field theory do not lead to the Lorentz equations of motion for charged particles in an electromagnetic field, if these particles are considered to be singularities of the field. To a fourth-order approximation, the motion of such particles is not influenced by the electromagnetic field, no matter how much
Langevin dynamics with space-time periodic nonequilibrium forcing
R. Joubaud; G. Pavliotis; G. Stoltz
2014-09-08
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez. In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level -- a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.
Unions of Equational Monadic Theories Piotr Ho man
Hoffman, Piotr
Unions of Equational Monadic Theories Piotr Ho#11;man Institute of Informatics, Warsaw University, Poland piotrek@mimuw.edu.pl Abstract. We investigate the decidability of unions of decidable equa- tional. This allows us to make use of the equiv- alence between monoid amalgams and unions of monadic theories. We
Multipolar test body equations of motion in generalized gravity theories
Yuri N. Obukhov; Dirk Puetzfeld
2015-05-07
We give an overview of the derivation of multipolar equations of motion of extended test bodies for a wide set of gravitational theories beyond the standard general relativistic framework. The classes of theories covered range from simple generalizations of General Relativity, e.g. encompassing additional scalar fields, to theories with additional geometrical structures which are needed for the description of microstructured matter. Our unified framework even allows to handle theories with nonminimal coupling to matter, and thereby for a systematic test of a very broad range of gravitational theories.
Some remarks on Lefschetz thimbles and complex Langevin dynamics
Gert Aarts; Lorenzo Bongiovanni; Erhard Seiler; Denes Sexty
2014-10-24
Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some findings for the quartic model, and for U(1) and SU(2) models in the presence of a determinant, which have some features not discussed before, due to a singular drift. We find evidence for a relation between classical runaways and stable thimbles, and give an example of a degenerate fixed point. We typically find that the distributions sampled in complex Langevin dynamics are related to the thimble(s), but with some important caveats, for instance due to the presence of unstable fixed points in the Langevin dynamics.
Einleitung Hydrodynamik Langevin Lattice-Boltzmann Langevin-Hydrodynamik und die
Kierfeld, Jan
Einleitung Hydrodynamik Langevin Lattice-Boltzmann Langevin-Hydrodynamik und die Lattice 12.6.2014 #12;Einleitung Hydrodynamik Langevin Lattice-Boltzmann Übersicht 1 Einleitung 2 Grundlagen der Hydrodynamik 3 Die Langevin-Gleichung und Brownsche Dynamik 4 Die Lattice-Boltzmann-Methode #12
A Langevin approach to stock market fluctuations and crashes
Jean-Philippe Bouchaud; Rama Cont
1998-01-01
: We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on\\u000a an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize\\u000a the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an “up-down”\\u000a symmetry breaking term
Proposal for a running coupling JIMWLK equation
Lappi, T
2014-01-01
In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.
Proposal for a running coupling JIMWLK equation
T. Lappi; H. Mäntysaari
2014-03-28
In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.
Integral equation theory for correcting truncation errors in molecular simulations
NASA Astrophysics Data System (ADS)
Kast, Stefan M.; Friedemann Schmidt, K.; Schilling, Bernd
2003-01-01
Various strategies for correcting structural and energetic artefacts of molecular simulations with truncated potentials based on integral equation theory are described and applied to liquid water. The performance of the methods is examined for a range of cutoff distances and different shifted-force potentials. With the recently enhanced damped Coulomb potential (D. Zahn, B. Schilling, S.M. Kast, J. Phys. Chem. B, 106 (2002) 10725), parameterised and corrected by integral equation theory, radial distribution functions and excess internal energy very close to the Ewald simulation limit are obtained from a simulation with a cutoff distance of only 6 Å.
Wang, Chi-Jen [Ames Laboratory; Ackerman, David M. [Ames Laboratory; Slowing, Igor I. [Ames Laboratory; Evans, James W. [Ames Laboratory
2014-07-14
Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P?(R?Rc)?, where passing is sterically blocked for R?Rc, with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.
NASA Astrophysics Data System (ADS)
Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.; Evans, James W.
2014-07-01
Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ˜(R-Rc)?, where passing is sterically blocked for R ?Rc, with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.
EQUATIONS OF MOTION THEORY FOR ELECTRON AFFINITIES Jack SIMONS
Simons, Jack
EQUATIONS OF MOTION THEORY FOR ELECTRON AFFINITIES Jack SIMONS Chemistry Department and Henry-mail: simons@chemistry.utah.edu Received August 18, 2004 Accepted October 11, 2004 One of this author of Small Molecules" (Simons J., Smith W. D.: J. Chem. Phys. 1973, 58, 4899). For this reason, the author
Basic equations of the theory of reinforced media
V. V. Bolotin
1965-01-01
The author derives the basic equations of the theory of composite elastic media obtained by reinforcing some elastic medium with a large number of linear or planar elastic elements with high strength and deformation resistance. The argument is based on macrostructural considerations. The stress-strain state of each of the reinforcing elements is considered with allowance for interaction with the matrix
Deciding knowledge in security protocols under (many more) equational theories
Abadi, MartÃn
Deciding knowledge in security protocols under (many more) equational theories MartÂ´in Abadi & CNRS, Nancy, France Abstract In the analysis of security protocols, the knowledge of at- tackers-commutative functions. 1 Introduction The design and analysis of security protocols typically relies on reasoning about
Deciding Knowledge in Security Protocols under (Many More) Equational Theories
Martín Abadi; Véronique Cortier
2005-01-01
In the analysis of security protocols, the knowledge of at- tackers is often described in terms of message deducibility and indistinguishability relations. In this paper, we pursue the study of these two relations. We establish general de- cidability theorems for both. These theorems require only loose, abstract conditions on the equational theory for mes- sages. They subsume previous results for
Deciding knowledge in security protocols under (many more) equational theories
Cortier, VÃ©ronique
Deciding knowledge in security protocols under (many more) equational theories Martâ??ï¿½n Abadi & CNRS, Nancy, France Abstract In the analysis of security protocols, the knowledge of atÂ tackersÂcommutative functions. 1 Introduction The design and analysis of security protocols typically relies on reasoning about
O. I. Mokhov; L. D. Landau
2007-01-01
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions\\u000a of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of\\u000a flat torsionless potential submanifolds. We show that all flat torsionless potential submanifolds in pseudo-Euclidean spaces bear natural structures\\u000a of Frobenius algebras on their tangent spaces.
Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory
Yi-Fang Chang
2010-08-17
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.
Vaclav Zatloukal
2015-04-30
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory. Throughout, we use the mathematical formalism of geometric algebra and geometric calculus, which allows to perform completely coordinate-free manipulations.
Boltzmann-Langevin One-Body dynamics for fermionic systems
P. Napolitani; M. Colonna
2013-02-01
A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional approaches, as a projection on suitable subspaces. The advantage of this model is to be specifically adapted to describe processes characterised by instabilities, like the formation of fragments from a hot nuclear system, and by dissipation, like the transparency in nucleus-nucleus collisions.
Basic equations, theory and principle of computational stock market (III)—basic theories
Yun Tian-quan
2000-01-01
By basic equations, two basic theories are presented: 1. Theory of stock' s value ?* (t) = ?*(0) exp(ar*2 t); 2. Theory of conservation of stock' s energy. Let stock' s energy ? be defined as a quadratic function of stock' s price\\u000a ? and its derivative\\u000a $$\\\\dot v,\\\\phi = {\\\\rm A}v^2 + Bv\\\\dot v + C\\\\dot v^2 + Dv$$
Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid
Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)
2009-05-15
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Ito discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R{sub AA} and the elliptic flow v{sub 2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The R{sub AA} for electrons with large transverse momentum (p{sub T}>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.
Fluid moment hierarchy equations derived from quantum kinetic theory
F. Haas; M. Marklund; G. Brodin; J. Zamanian
2009-10-27
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.
Field equations and conservation laws in the nonsymmetric gravitational theory
J. Légaré; J. W. Moffat
1995-01-01
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an “Einstein plus fields”
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436
On a relativistic Fokker-Planck equation in kinetic theory
José Antonio Alcántara Félix; Simone Calogero
2011-05-13
A relativistic kinetic Fokker-Planck equation that has been recently proposed in the physical literature is studied. It is shown that, in contrast to other existing relativistic models, the one considered in this paper is invariant under Lorentz transformations in the absence of friction. A similar property (invariance by Galilean transformations in the absence of friction) is verified in the non-relativistic case. In the first part of the paper some fundamental mathematical properties of the relativistic Fokker-Planck equation are established. In particular, it is proved that the model is compatible with the finite propagation speed of particles in relativity. In the second part of the paper, two non-linear relativistic mean-field models are introduced. One is obtained by coupling the relativistic Fokker-Planck equation to the Maxwell equations of electrodynamics, and is therefore of interest in plasma physics. The other mean-field model couples the Fokker-Planck dynamics to a relativistic scalar theory of gravity (the Nordstr\\"om theory) and is therefore of interest in gravitational physics. In both cases the existence of steady states for all possible prescribed values of the mass is established. In the gravitational case this result is better than for the corresponding non-relativistic model, the Vlasov-Poisson-Fokker-Planck system, for which existence of steady states is known only for small mass.
Langevin diffusion of heavy quarks in non-conformal holographic backgrounds
U. Gursoy; E. Kiritsis; L. Mazzanti; F. Nitti
2010-12-27
The Langevin diffusion process of a relativistic heavy quark in a non-conformal holographic setup is discussed. The bulk geometry is a general, five-dimensional asymptotically AdS black hole. The heavy quark is described by a trailing string attached to a flavor brane, moving at constant velocity. From the equations describing linearized fluctuations of the string world-sheet, the correlation functions defining a generalized Langevin process are constructed via the AdS/CFT prescription. In the local limit, analytic expressions for the Langevin diffusion and friction coefficients are obtained in terms of the bulk string metric. Modified Einstein relations between these quantities are also derived. The spectral densities associated to the Langevin correlators are analyzed, and simple analytic expressions are obtained in the small and large frequency limits. Finally, a numerical analysis of the jet-quenching parameter, and a comparison to RHIC phenomenology are performed in the case of Improved Holographic QCD.
On Some Nonlinear Integral Equation in the (Super)String Theory
D. V. Prokhorenko
2006-11-25
In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Temporal breakdown and Borel resummation in the complex Langevin method
A. Duncan; M. Niedermaier
2012-09-25
We reexamine the Parisi-Klauder conjecture for complex e^{i\\theta/2} \\phi^4 measures with a Wick rotation angle 0 Langevin equation have the same t -> 0 asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t, including their t -> infinity equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the `correct' result for t larger than a finite t_c. The breakdown time t_c increases powerlike for decreasing strength of the noise's imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.
Chemical Master versus Chemical Langevin for First-Order Reaction Networks
Desmond J. Higham; Raya Khanin
Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such mod- els have been particularly successful in computational cell biology, and in this case, the interactions are typically rst-order. The Chemical Langevin Equation is a stochastic dieren tial equation that can be regarded as an approximation to the underlying jump process.
Chemical Master versus Chemical Langevin for First-Order Reaction Networks
Desmond J. Higham; Raya Khaniny
2008-01-01
Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such mod- els have been particularly successful in computational cell biology, and in this case, the interactions are typically rst-order. The Chemical Langevin Equation is a stochastic dieren tial equation that can be regarded as an approximation to the underlying jump process.
Langevin description of fusion, deep-inelastic collisions and heavy-ion-induced fission
NASA Astrophysics Data System (ADS)
Fröbrich, P.; Gontchar, I. I.
1998-01-01
The description of fusion of heavy ions, deep-inelastic heavy-ion collisions and heavy-ion-induced fission in the framework of Langevin equations is reviewed. The Langevin equations are derived within an idealized schematic model. These equations are applied with the aim to reproduce the experimental data. In order to be able to do so the potential and the transport coefficients are not taken from the schematic model but from the phenomenological surface friction model in the case of fusion and deep-inelastic collisions. In the case of heavy-ion-induced fission we deal mainly with a model which is a combination of a dynamical Langevin and a statistical model description. Here again the input is chosen phenomenologically in such a way that a universal reproduction of the data for a large multitude of observables is possible. Comparison with related work of other authors is performed.
Integrals and integral equations in linearized wing theory
NASA Technical Reports Server (NTRS)
Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B
1951-01-01
The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed.
Homogenization theory for periodic potentials in the Schrödinger equation
NASA Astrophysics Data System (ADS)
Náraigh, Lennon Ó.; O'Kiely, Doireann
2013-01-01
We use homogenization theory to derive asymptotic solutions of the Schrödinger equation for periodic potentials. This approach provides a rigorous framework in which the key concepts in solid-state physics naturally arise (Bloch waves, band gaps, effective mass, and group velocity). We solve the resulting spectral cell problem using numerical spectral methods, and validate our solution in an analytically-solvable case. Finally, we briefly discuss the convergence of our asymptotic approach and we prove that the ground-state k = 0 effective mass is never less than the ordinary inertial mass.
Non-perturbative evolution equations for the tricritical theory
Flavio S. Nogueira
1996-12-23
The N component scalar tricritical theory is considered in a non-perturbative setting. We derive non-perturbative beta functions for the relevant couplings in $d\\leq 3$. The beta functions are obtained through the use of an exact evolution equation for the so called effective average action. In d=3 it is established the existence of an ultraviolet stable fixed point for N>4. This confirms earlier results obtained using the 1/N expansion where such a fixed point is believed to exist at least for $N\\gtrsim 1000$.
Lattice-Boltzmann-Langevin simulations of binary mixtures.
Thampi, Sumesh P; Pagonabarraga, Ignacio; Adhikari, R
2011-10-01
We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations. PMID:22181309
Alexander Gorbatsievich; Ernst Schmutzer
2012-05-17
The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.
Continuum Regularized Yang-Mills Theory
Lorenzo Adlai Sadun
1987-01-01
Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d -dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all
Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing
NASA Astrophysics Data System (ADS)
Joubaud, R.; Pavliotis, G. A.; Stoltz, G.
2015-01-01
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez in (J Math Biol, 56(6):765-792 2008). In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level—a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.
Classical irregular block, = 2 pure gauge theory and Mathieu equation
NASA Astrophysics Data System (ADS)
Pi?tek, Marcin; Pietrykowski, Artur R.
2014-12-01
Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.
Langevin Stabilization of Multiscale Molli ed Molecular Dynamics
Izaguirre, Jesús A.
Langevin Stabilization of Multiscale Molli ed Molecular Dynamics Jesus A. Izaguirre Department function. Langevin Molly (LM) is introduced in this paper. It uses the molli ed impulse method for the Newtonian term and the Langevin impulse method for the Langevin term. A parallel version of LM is available
Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids
E. Zaccarelli; G. Foffi; F. Sciortino; P. Tartaglia; K. A. Dawson
2001-01-15
The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are gaussian distributed, are equivalent to the random-phase-approximation for the static structure factor and to the well known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests that MCT is the canonical mean-field theory of the fluid dynamics.
A Utility-Theory-Consistent System-of-Demand-Equations Approach to Household Travel Choice
Kockelman, Kara M.
Microeconomic Foundations 18 Roy's Identity in a Two-Budget Framework 22 Theory-Implied Constraints 27 NonA Utility-Theory-Consistent System-of-Demand-Equations Approach to Household Travel Choice by Kara Fall 1998 #12;A Utility-Theory-Consistent System-of-Demand-Equations Approach to Household Travel
Computational fixed point theory for differential delay equations with multiple time lags
Lessard, Jean-Philippe
Computational fixed point theory for differential delay equations with multiple time lags Jean nontrivial periodic solutions for a delay equation with three time lags. 1 Introduction Fixed point theory, that we describe here as computational fixed point theory, to the context of proving, in a direct
Covariant Field Equations of the M Theory Five-Brane
P. S. Howe; E. Sezgin; P. C. West
1997-02-14
The component form of the equations of motion for the 5-brane in eleven-dimensions is derived from the superspace equations. These equations are fully covariant in six-dimensions. It is shown that double-dimensional reduction of the bosonic equations gives the equations of motion for a 4-brane in ten dimensions governed by the Born-Infeld action.
Langevin Dynamics of Heavy Flavors in Relativistic Heavy-Ion Collisions
W. M. Alberico; A. Beraudo; A. de Pace; A. Molinari; M. Monteno; M. Nardi; F. Prino
2011-01-01
We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution
On the Reliability of the Langevin Pertubative Solution in Stochastic Inflation
Jerome Martin; Marcello Musso
2005-11-29
A method to estimate the reliability of a perturbative expansion of the stochastic inflationary Langevin equation is presented and discussed. The method is applied to various inflationary scenarios, as large field, small field and running mass models. It is demonstrated that the perturbative approach is more reliable than could be naively suspected and, in general, only breaks down at the very end of inflation.
Diffusion in the special theory of relativity.
Herrmann, Joachim
2009-11-01
The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion. PMID:20364950
Heavy quark master equations in the Lindblad form at high temperatures
Yukinao Akamatsu
2015-04-13
We derive the quantum master equations for heavy quark systems in a high-temperature quark- gluon plasma in the Lindblad form. The master equations are derived in the influence functional formalism for open quantum systems in perturbation theory. These master equations have a wide range of applications, such as decoherence of a heavy quarkonium and Langevin dynamics of a heavy quark in the quark-gluon plasma. We also show the equivalence between the quarkonium master equations in the recoilless limit and the Schroedinger equations with stochastic potential.
QUASI-EQUATIONAL THEORIES OF 1-UNARY JOEL ADLER AND J. B. NATION
Nation, James B.
QUASI-EQUATIONAL THEORIES OF 1-UNARY ALGEBRAS JOEL ADLER AND J. B. NATION Abstract. Let Mr,r+1. quasivariety, quasi-equational theory, 1-unary algebra. 1 #12;2 JOEL ADLER AND J. B. NATION Then T fails
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
V. A. Pletyukhov; V. I. Strazhev
2010-02-03
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
On the invariance of constitutive equations according to the kinetic theory of gases
Charles G. Speziale
1984-01-01
Iterative techniques for solving the Boltzmann equation in the kinetic theory of gases yield expressions for the stress tensor and heat flux vector that are analogous to constitutive equations in continuum mechanics. However, these expressions are not generally invariant under the Euclidean group of transformations, whereas constitutive equations in continuum mechanics are usually required to be by the principle of
Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy
Wang, Shouhong
Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy Tian Ma II. Principle of Interaction Dynamics III. Unified Field Equations Coupling Four Forces IV. Duality V, June, 2012, http://arxiv.org/abs/1206.5078 2. Tian Ma & Shouhong Wang, Unified Field Equations Coupling
Basic equations, theory and principle of computational stock market (I) —Basic equations
Yun Tianquan
1999-01-01
This paper studies computational stock market by using network model and similar methodology used in solid mechanics. Four\\u000a simultaneous basic equations, i.e., equation of interest rate and amount of circulating fund, equations of purchasing and\\u000a selling of share, equation of changing rate of share price, and equation of interest rate, share price and its changing rate,\\u000a have been established. Discussions
Complex Langevin simulation of quantum vortex nucleation in the Bose-Einstein condensate
Tomoya Hayata; Arata Yamamoto
2014-11-19
The ab-initio simulation of quantum vortex nucleation in the Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the two-component boson field theory at a finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.
Klimontovich Langevin approach to the fluctuation-dissipation theorem for a nonlocal plasma
V. V. Belyi
2005-01-01
Using the Klimontovich-Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is derived. It is shown that not only the dissipation but also the time and space derivatives of the dispersion determine the amplitude and the width
Kinetic-theory approach to Gluon Self-energy beyond Hard Thermal Loops
Zheng Xiaoping; Li Jiarong
2002-02-16
We compare the effective dynamics of soft fields, based on temperature field theory, with the mean field dynamics from non-Abelian kinetic theory. We derive the polarization tensor with the leading logarithmic factor $\\log({gT\\over\\mu})$ from the effective Boltzmann-Langevin equation given by Litim and Manuel. The tensor is identical with effective one-loop contributions within the hard thermal loop effective theory.
Generalized gradient flow equation and its application to super Yang-Mills theory
NASA Astrophysics Data System (ADS)
Kikuchi, Kengo; Onogi, Tetsuya
2014-11-01
We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that the super gauge symmetry is preserved in the gradient flow. Furthermore, choosing an appropriate modification term to damp the gauge degrees of freedom, we obtain a gradient flow equation which is closed within the Wess-Zumino gauge.
Temporal breakdown and Borel resummation in the complex Langevin method
Duncan, A., E-mail: tony@dectony.phyast.pitt.edu; Niedermaier, M., E-mail: mnie@pitt.edu
2013-02-15
We reexamine the Parisi-Klauder conjecture for complex e{sup i{theta}/2}{phi}{sup 4} measures with a Wick rotation angle 0{<=}{theta}/2{<=}{pi}/2 interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t{yields}0 asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t, including their t{yields}{infinity} equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the 'correct' result for t larger than a finite t{sub c}. The breakdown time t{sub c} increases powerlike for decreasing strength of the noise's imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure. - Highlights: Black-Right-Pointing-Pointer The Parisi-Klauder conjecture is reexamined for complex e{sup i{theta}/2}{phi}{sup 4} measures. Black-Right-Pointing-Pointer The time dependent moments are evaluated by temporal Borel resummation. Black-Right-Pointing-Pointer The results disagree with the Langevin simulations beyond a critical time t{sub c}. Black-Right-Pointing-Pointer t{sub c} increases with decreasing strength of the noise's imaginary part. Black-Right-Pointing-Pointer The technical reason for the breakdown is identified.
The Boltzmann-Langevin model for nuclear collisions
NASA Astrophysics Data System (ADS)
Ayik, S.; Suraud, E.; Belkacem, M.; Boilley, D.
1992-08-01
An extension of the one-body transport models is developed by incorporating correlations into the equation of motion in a stochastic approximation. In the semiclassical limit, this yields the Boltzmann-Langevin Equation for the fluctuating single-particle density in the phase-space. In order to investigate the gross-properties of density fluctuations in heavy-ion collisions, a number of calculations have been carried out. These calculations reveal that large dynamical fluctuations are introduced into the momentum space during the early stages of the collision, which cause the nuclear system to decay into a great variety of final channels. The effects of the fluctuations on the kaon production in heavy-ion collisions at sub-threshold energies are also investigated.
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
M. R. James
2005-03-29
In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom.
S. Fabi; G. S. Karatheodoris
2011-04-20
In this note we demonstrate the equation of motion for test particles in an ambient gravitational field for the teleparallel theory of gravity, considered as a generalized gauge theory, using a computational scheme due to Feynman. It can be thought of as the Wong equation for a generalized gauge theory. The Wong and Lorentz equations become identical when the generators of a generalized non-abelian gauge theory are taken to be the local translation generators.
Langevin process reflected at a partially elastic boundary I
Paris-Sud XI, Université de
Langevin process reflected at a partially elastic boundary I Emmanuel Jacob Universit´e Paris VI Paris cedex 05 e-mail: emmanuel.jacob@normalesup.org Abstract: Consider a Langevin process: Primary 60J50; secondary 60H15, 60K05, 60G10. Keywords and phrases: Langevin process, second order
Modelling the variability of complex systems by means of Langevin
Peinke, Joachim
Modelling the variability of complex systems by means of Langevin processes On the application . . . . . . . . . . . . . . . . 1 1.2 Reconstructing the dynamics of Langevin processes . . . . . . . . . . 3 1.3 Stochastic modelling of experimental data . . . . . . . . . . . . . . . 5 1.4 Extension to Langevin-like processes
LU TP 9313 On Langevin Updating in Multilayer Perceptrons
Lunds Universitet,
LU TP 9313 On Langevin Updating in Multilayer Perceptrons Thorsteinn R¨ognvaldsson 1 Department Computation Abstract: The Langevin updating rule, in which noise is added to the weights during learning such per formance improvements achieved with a very simple method, the socalled Langevin updating (LV
Complex Langevin method: When can it be trusted? Gert Aarts*
Aarts, Gert
Complex Langevin method: When can it be trusted? Gert Aarts* Department of Physics, Swansea extent the complex Langevin method, which is in principle capable of solving the so-called sign problems. INTRODUCTION The complex Langevin method solves in principle the sign problems arising in simulations
C. Foias; D. D. Holm; E. S. Titi
2001-03-23
We show here the global, in time, regularity of the three dimensional viscous Camassa-Holm (Lagrangian Averaged Navier-Stokes-alpha) equations. We also provide estimates, in terms of the physical parameters of the equations, for the Hausdorff and fractal dimensions of their global attractor. In analogy with the Kolmogorov theory of turbulence, we define a small spatial scale, \\ell_{\\epsilon}, as the scale at which the balance occurs in the mean rates of nonlinear transport of energy and viscous dissipation of energy. Furthermore, we show that the number of degrees of freedom in the long-time behavior of the solutions to these equations is bounded from above by (L/\\ell_{epsilon})^3, where L is a typical large spatial scale (e.g., the size of the domain). This estimate suggests that the Landau-Lifshitz classical theory of turbulence is suitable for interpreting the solutions of the NS-alpha equations. Hence, one may consider these equations as a closure model for the Reynolds averaged Navier-Stokes equations (NSE). We study this approach, further, in other related papers. Finally, we discuss the relation of the NS-alpha model to the NSE by proving a convergence theorem, that as the length scale alpha tends to zero a subsequence of solutions of the NS-alpha equations converges to a weak solution of the three dimensional NSE.
Morse-type index theory for flows and periodic solutions for Hamiltonian equations
Charles Conley; Eduard Zehnder
1984-01-01
An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic solutions of a time-dependent (periodic in time) and asymptotically linear Hamiltonian equation.
On Langevin Updating in Multilayer Perceptrons
Thorsteinn Rögnvaldsson
1994-01-01
The Langevin updating rule, in which noise is added to the weights during learning, is presented and shown to improve learning on problems with initially ill-conditioned Hessians. This is particularly important for multilayer perceptrons with many hidden layers, that often have ill-conditioned Hessians. In addition, Manhattan updating is shown to have a similar effect.
A Stochastic Modification of the Schrodinger-Newton Equation
Bera, Sayantani; Singh, Tejinder P
2015-01-01
The Schrodinger-Newton [SN] equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation by itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrodinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diosi - Penrose criterion for the decoherence time. We also write down the master equation corresponding to this stochastic SN equation. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.
A Stochastic Modification of the Schrodinger-Newton Equation
Sayantani Bera; Ravi Mohan; Tejinder P. Singh
2015-04-22
The Schrodinger-Newton [SN] equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation by itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrodinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diosi - Penrose criterion for the decoherence time. We also write down the master equation corresponding to this stochastic SN equation. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.
Classical Field Theory and Analogy Between Newton's and Maxwell's Equations
Z. Oziewicz
1993-12-02
A bivertical classical field theory include the Newtonian mechanics and Maxwell's electromagnetic field theory as the special cases. This unification allows to recognize the formal analogies among the notions of Newtonian mechanics and Maxwell's electrodynamics.
Explicit Solutions for a Riccati Equation from Transport Theory
Xu, Hongguo
on the eigenvalues of an associated matrix. We use the formulas to explore some new properties of the minimal demonstrate the properties of the new methods. Keywords. non-symmetric Riccati equation, secular equation of the special form XA + DX - XBX - C = 0, (1) with A = - peT , D = - epT , B = ppT , C = eeT Institut f
Proofs by Induction in Equational Theories with Constructors
Gérard P. Huet; Jean-marie Hullot
1980-01-01
We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to proofs of algebraic summation
Scaling theory for homogenization of the Maxwell equations
NASA Astrophysics Data System (ADS)
Vinogradov, Alexei P.
1997-11-01
The wide application of composite materials is a distinctive feature of modern technologies. This encourages scientists dealing with radio physics and optics, to search for new type of artificial materials. Recently such investigations have shifted in the field of materials with weak spatial dispersion: chiral, omega materials, artificial magnets, etc. By weak spatial dispersion we mean that the constitutive relations are still local but constitutive parameters depend upon a wavenumber k. It is the dependence that is responsible for non-encountered-in-nature properties of the materials such as chirality [a first order in (ka) effect] or artificial magnetism [a second order in (ka effect)]. Here a is a typical size of an inclusion. Certainly, all these effects are small enough unless there is a resonance interaction of electromagnetic wave with an inclusion. Near the resonance frequency the effects are significant and perturbation theory in (ka) fails. Nevertheless it is convenient to describe the effects in terms of orders in (ka), understanding this as a matter of classification. In spite of physical clarity of the classification the constitutive relations are treated in terms of multipole expansion. The multipoles naturally appear at field expansion in (d/R) where d is the source size and R is the distance between the source and recorder. Such an expansion is useful in 'molecular optics' approximation where d very much less than r, with r to be a mean distance between the 'molecules.' Though the 'molecular optics' ceases to be a good approximation if we deal with composites where d approximately equals r, the mean current in the right hand side of the Maxwell equations is still expressed through multipoles (see Fig. 1). Below we consider the reasons justifying this sight on things even if we are working beyond the 'molecular optics' approximation. To repel an accusation in abstract contemplation let us consider examples of the 'multipole' media. Permeable composites made of non-permeable ingredients are well known. The simplest example is a composite loaded with highly conducting spherical inclusions. Due to eddy currents there appears a magnetic moment of the inclusion and the composite exhibits properties of diamagnetic. The inclusions of more complicated structure can exhibit resonant excitation resulting in induced magnetic moment. Examples of such inclusions are open rings, dielectric spheres, helix and bi-helix. In this case depending upon the relation between the working and resonant frequencies we can observe both diamagnetism or paramagnetism. Q-medium is more smart system. As the system of identical dielectric spheres is a permeable material, the system of different in size spheres may be non-permeable. The concentrations and radii may be chosen so that one part of spheres is excited in diamagnetic mode and the other in paramagnetic. Such a system is described by its quadrupole moment (see Fig. 1). Putting quantum mechanics apart we shall consider a classical composite material. The adjective 'classical' means that the scale of inhomogeneity is large enough to describe the reply of material on electromagnetic disturbance in terms of local constitutive equations Di equals (epsilon) ((omega) ,r)Ej ji equals (sigma) ((omega) ,r)Ej where (epsilon) ((omega) ,r), (sigma) ((omega) ,r) are local permittivity and conductivity.
Stellar convection theory. I - The anelastic modal equations
NASA Technical Reports Server (NTRS)
Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J.-P.
1976-01-01
Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.
Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
Hsu, David; Hsu, Murielle
2009-01-01
We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj PMID:19594920
Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation
C. Duval; H. P. Künzle
1984-01-01
The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schrödinger equation. Matter current and stress-energy tensor follow correctly from the
Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation
C. Duval; H. P. Kuenzle
1984-01-01
The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the
Theory of collisional invariants for the Master kinetic equation
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2015-06-01
The paper investigates the integral conservation properties of the Master kinetic equation, which provides an exact kinetic statistical description for the Boltzmann-Sinai classical dynamical system. It is proved that, besides the customary Boltzmann collisional invariants, this equation admits also a class of generalized collisional invariants (GCI). The result applies only when the number N and the diameter ? of hard-spheres are finite. This includes the case of dilute gases for which suitable asymptotic ordering conditions hold. However, when the Boltzmann-Grad limit is performed on the Master kinetic equation, it is shown that the existence of GCI is not permitted anymore.
On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations
Michael K. -H. Kiessling; Carlo Lancellotti
2004-09-27
We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.
Denicol, G. S. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Koide, T. [Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany); Rischke, D. H. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany)
2010-10-15
We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.
MA6000A: Theory of Partial Differential Equations Lecture Notes
Burton, Geoffrey R.
are given functions. We always assume the symmetry condition aij = aji, i, j = 1, . . . , n. If we have an equation that does not satisfy the last condition, then we can replace aij by ~aij = 1 2(aij +aji) in order
Quantum theory of rotational isomerism and Hill equation
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R. [I. Javakhishvili Tbilisi State University, 3, I. Chavchavadze Avenue, 0179 Tbilisi (Georgia); Chotorlishvili, L. [Institut fuer Physik, Martin-Luther Universitat Halle-Wittenberg, Heinrich-Damerow-Str. 4, 06120 Halle (Germany)
2012-06-15
The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.
Dynamic field theory and equations of motion in cosmology
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-01
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast ?? / ? ? 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits ?? / ? ? 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
Alex Kaivarainen
2000-03-25
1. The state equation for real gas 2. New state equation for condensed matter 3.Vapor pressure 4. Surface tension 5. Mesoscopic theory of thermal conductivity 6. Mesoscopic theory of viscosity for liquids and solids 7. Brownian diffusion 8. Self-diffusion in liquids and solids 9. Mesoscopic approach to proton conductivity in water, ice and other systems, containing hydrogen bonds 10. Regulation of pH and shining of water by electromagnetic and acoustic fields
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Ivanov, Sergei D; Kühn, Oliver
2015-01-01
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation (GLE), which can be rigorously derived by means of a linear projection (LP) technique. Within this framework a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here we discuss that this task is most naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importa...
Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites
NASA Astrophysics Data System (ADS)
Zaburdaev, Vasily; Uppaluri, Sravanti; Pfohl, Thomas; Engstler, Markus; Friedrich, Rudolf; Stark, Holger
2011-05-01
The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite’s survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.
The general theory of linear difference equations over the invertible max-plus algebra
Sydney, University of
The general theory of linear difference equations over the invertible max-plus algebra Nalini Joshi of linear differ- ence equations over the invertible max-plus algebra. The result provides an analogue the invertible max-plus algebra. The classical results of Birkhoff were extended for systems of q- difference
The general theory of linear difference equations over the invertible max-plus algebra
Sydney, University of
The general theory of linear difference equations over the invertible max-plus algebra underlying systems of linear diffe* *r- ence equations over the invertible max-plus algebra. The result the invertible max-plus algebra. The classical results of Birkhoff were extended for systems of q- difference
Gabrielle Jost
1986-01-01
The application of the method of the modified fundamental solution of integral equations to exterior boundary value problems from the theory of electromagnetic waves was investigated. The modification of the fundamental solution for the scalar Helmholtz equation is presented. It is shown that this solution can be considered as a dyadic. The existence proofs for three electromagnetic boundary value problems
1. Theory for Liquid Heat Capacity I ) Polynomial equation (HC_CPLEQN)
Hong, Deog Ki
1. Theory for Liquid Heat Capacity I ) Polynomial equation (HC_CPLEQN) Polynomial equation is used for Heat capacity of ideal gas. = = 3 0 )( i i i L p TATC (1) where, T is Kelvin and )(TC L p is kJ/kg-mol.K. II ) Corresponding States Method for Liquid Heat Capacity (HC_CPLCSP) The expression based
1. Theory for Heat Capacity of Ideal Gas I ) KDB correlation equation (HC_CPGEQN)
Hong, Deog Ki
1. Theory for Heat Capacity of Ideal Gas I ) KDB correlation equation (HC_CPGEQN) Polynomial equation is used for Heat capacity of ideal gas. = = 4 0 0 )( i i ip TATC (1) where, T is Kelvin and )( 0 TCp is kJ/kg-mol.K. 2. KDB Routines for Calculation of Ideal Gas Heat Capacity KDB Ideal gas heat
A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF
A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF REINFORCED RANDOM WALKS Howard A and elucidating remarks. 1 #12;2 REACTION DIFFUSION EQUATIONS I. Introduction. In order to understand the production and release of diusible sub- stances or short range interactions due to local modi#12;cations
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
ERIC Educational Resources Information Center
Brossman, Bradley G.; Lee, Won-Chan
2013-01-01
The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the multidimensional item response theory (MIRT) framework. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure was…
Stochastic regulator theory for a class of abstract wave equations
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
General Relativistic Elastic Perturbation Theory and PN JV Equation
Chongming Xu; Xuejun Wu; Michael Soffel
2002-01-01
After pioneering works by Brumberg and Kopejkin1, Damour, Soffel and Xu2,3,4 (called DSX in the following) laid the foundation for a modern theory of general relativistic celestial mechanics at the first post-Newtonian approximation of Einstein's theory of gravity. This general relativistic DSX-formalism is not complete unless the time evolution of the (mass- and current-) multipole moments of the various astronomical
Spherically symmetric solutions of modified field equations in f(R) theories of gravity
Tuomas Multamaki; Iiro Vilja
2006-10-25
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In particular, we show that for a large class models, including e.g. the f(R)=R-\\mu^4/R model, the Schwarzschild-de Sitter metric is an exact solution of the field equations. The significance of these solutions is discussed in light of solar system constraints on $f(R)$ theories of gravity.
Gas adsorption isotherm equation based on vacancy solution theory
Solot Suwanayuen; Ronald P. Danner
1980-01-01
Pennsylvania State University's new isotherm equation for pure gas adsorption treats the adsorption equilbrium as an osmotic equilibrium between two ''vacancy'' solutions having different compositions. One solution represents the gas phase and the other the adsorbed phase. The vacancy solution is composed of adsorbates and vacancies (imaginary entities defined as the vacuum space that acts as the solvent for the
Integral equations arising in the kinetic theory of gases
Shouchuan Hu; Mohammad Khavanin; WAN Zhuang
1989-01-01
A criterion of k-set contractions for a class of nonlinear operators is established and then used to prove the existence of a solution in L for the nonlinear integral equation. Results of this paper are generalizations 3,4.
Langevin dynamics of heavy flavors in relativistic heavy-ion collisions
W. M. Alberico; A. Beraudo; A. De Pace; A. Molinari; M. Monteno; M. Nardi; F. Prino
2010-01-01
We study the stochastic dynamics of c and b quarks, produced in hard initial\\u000aprocesses, in the hot medium created after the collision of two relativistic\\u000aheavy ions. This is done through the numerical solution of the relativistic\\u000aLangevin equation. The latter requires the knowledge of the friction and\\u000adiffusion coefficients, whose microscopic evaluation is performed treating\\u000aseparately the contribution
Heavy-quark Langevin dynamics and single-electron spectra in nucleus-nucleus collisions
A. Beraudo; W. M. Alberico; A. De Pace; A. Molinari; M. Monteno; M. Nardi; F. Prino
2011-01-01
The stochastic dynamics of heavy quarks in the fireball produced in heavy-ion collisions is followed through numerical simulations based on the Langevin equation. The modification of the final pT spectra (RAA) of c and b quarks, hadrons and single-electrons with respect to pp collisions is studied. The transport coefficients are evaluated treating separately the contribution of soft and hard collisions.
Symmetries of generating functionals of Langevin processes with colored multiplicative noise
Camille Aron; Giulio Biroli; Leticia F. Cugliandolo
2010-11-22
We present a comprehensive study of the symmetries of the generating functionals of generic Langevin processes with multiplicative colored noise. We treat both Martin-Siggia-Rose-Janssen-deDominicis and supersymmetric formalisms. We summarize the relations between observables that they imply including fluctuation relations, fluctuation-dissipation theorems, and Schwinger-Dyson equations. Newtonian dynamics and their invariances follow in the vanishing friction limit.
Newton-Schrödinger Equations are not derivable from General Relativity + Quantum Field Theory
C. Anastopoulos; B. L. Hu
2014-02-16
In this note we show that Newton-Schr\\"odinger Equations (NSEs) [arXiv:1210.0457 and references therein] do not follow from general relativity (GR) and quantum field theory (QFT) by way of two considerations: 1) Taking the nonrelativistic limit of the semiclassical Einstein equation, the central equation of relativistic semiclassical gravity, a fully covariant theory based on GR+QFT with self-consistent backreaction of quantum matter on the spacetime dynamics; 2) Working out a model [see C. Anastopoulos and B. L. Hu, Class. Quant. Grav. 30, 165007 (2013), arXiv:1305.5231] with a matter scalar field interacting with weak gravity, in procedures analogous to the derivation of the nonrelativistic limit of quantum electrodynamics. We conclude that the coupling of classical gravity with quantum matter can only be via mean fields, there are no $N$-particle NSEs and theories based on Newton-Schr\\"odinger equations assume unknown physics.
Investigation on Kane dynamic equations based on screw theory for open-chain manipulators
Liu Wu-fa; Gong Zhen-bang; Wang Qin-que
2005-01-01
First, screw theory, product of exponential formulas and Jacobian matrix are introduced. Then definitions are given about\\u000a active force wrench, inertial force wrench, partial velocity twist, generalized active force, and generalized inertial force\\u000a according to screw theory. After that Kane dynamic equations based on screw theory for open-chain manipulators have been derived.\\u000a Later on how to compute the partial velocity
Unified Theory of Wave-Particle Duality, the Schrödinger Equations, and Quantum Diffraction
Greyson Gilson
2014-09-03
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Based on the unified theory of wave-particle duality, a straightforward derivation of the Schr\\"odinger equations is presented where previously no such derivation was considered to be possible. A new theory of quantum diffraction is subsequently developed.
Pure gauge configurations and solutions to fermionic superstring field theory equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, I. Ya; Gorbachev, R. V.; Medvedev, P. B.
2009-07-01
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of nonpolynomial and cubic string field theory are discussed. To have the possibility of dealing with both GSO(+) and GSO(-) sectors in the uniform way, a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open-string field theories truncated pure gauge configurations parametrized by wedge states play an essential role. The matrix form of this parametrization for NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equations of motion on the subspace of the wedge states. The perturbation expansion is corrected by adding extra terms that are just those necessary for the equation of motion contracted with the solution itself to be satisfied.
Application of integral equation theory to polyolefin liquids and blends
Curro, J.G.; Weinhold, J.D.
1997-11-01
The ability to model the packing of polymers in melts and blends is important in many polymer applications. One significant application is the development of new polymer blends. It would be exceedingly helpful to the materials chemist if molecular modeling could be employed to predict the thermodynamics and phase behavior of hypothetical polymer alloys before embarking on a time consuming and expensive synthesis program. The well known Flory-Huggins theory has been remarkably successful in describing many aspects of polymer mixing from a qualitative point of view. This theory is known, however, to suffer from several deficiencies which can be traceable to the fact that: (1) it is a lattice model requiring both monomer components to have the same volume; and (2) a mean field or random mixing approximation is made which effectively ignores chain connectivity. Because of these limitations the Flory-Huggins theory does not include packing effects and cannot be used to make quantitative molecular engineering calculations. Recently Curro and Schweizer developed a new approach for treating polymer liquids and mixtures which the authors call PRISM theory. This is an extension to polymers of the Reference Interaction Site Model (RISM Theory) developed by Chandler and Andersen to describe the statistical mechanics of small molecule liquids. The PRISM theory is a continuous space description of a polymer liquid, which includes chain connectivity and nonrandom mixing effects in a computationally tractable manner. The primary output from PRISM calculations is the average structure or packing of the amorphous liquid given by the radial distribution function denoted as g(r). This radial distribution function is employed to deduce thermodynamic or structural properties of interest. Here, the authors describe the theoretical approach and demonstrate its application to polyethylene, isotactic polypropylene, syndiotactic polypropylene, and polyisobutylene liquids and blends.
Equation-of-motion coupled cluster perturbation theory revisited
Eriksen, Janus J., E-mail: janusje@chem.au.dk; Jørgensen, Poul; Olsen, Jeppe [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark)] [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark); Gauss, Jürgen [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)] [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Linear Newtonian perturbation theory from the Schrödinger-Poisson equations
Nilanjan Banik; Adam J. Christopherson; Pierre Sikivie; Elisa Maria Todarello
2015-04-22
We obtain solutions to the coupled Schr\\"odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships between descriptions of cold dark matter in terms of a pressureless fluid, in terms of a wavefunction, of a classical scalar field, and a quantum scalar field. We identify the regimes where the various descriptions coincide and where they differ.
Linear Newtonian perturbation theory from the Schrödinger-Poisson equations
NASA Astrophysics Data System (ADS)
Banik, Nilanjan; Christopherson, Adam J.; Sikivie, Pierre; Todarello, Elisa Maria
2015-06-01
We obtain solutions to the coupled Schrödinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships between descriptions of cold dark matter in terms of a pressureless fluid, in terms of a wave function, of a classical scalar field, and a quantum scalar field. We identify the regimes where the various descriptions coincide and where they differ.
Stochastic quantization in field theory with a fundamental mass
Petriashvili, G.G.
1986-08-01
Stochastic quantization of fermions is developed in the framework of quantum field theory with non-Euclidean momentum space. Analogs of the Langevin and Fokker-Planck equations taking into account the new geometrical properties of the momentum space are obtained by using Grassmann variables to describe the non-Euclidean Fermi fields. It is shown that the stochastic method and the second-quantization method are equivalent in path-integral terms.
Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
Santosh K. Das; Francesco Scardina; Salvatore Plumari; Vincenzo Greco
2014-09-19
The propagation of heavy quarks in the quark-gluon plasma (QGP) has been often treated within the framework of the Langevin equation (LV), i.e. assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_{HQ}/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra and consequently on nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but with a modified diffusion coefficient by about $\\sim 15-50\\%$ depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures $T\\gtrsim \\, 250\\,\\rm MeV$ the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultra-relativistic heavy-ion collisions. Finally, we have shown the possible impact of this study on $R_{AA}(p_T)$ and $v_2(p_T)$ for a realistic simulation of relativistic HIC. For larger $m_D$ the elliptic flow can be about $50\\%$ larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of $R_{AA}(p_T)$ and $v_2(p_T)$.
Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Dorn, Harald; Torrielli, Alessandro
2004-01-01
The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this treatment to the case of U(N) Yang-Mills defined on the noncommutative plane. We deal with all the subtleties which arise in their two-dimensional geometric procedure, using where needed results from the perturbative computations of the noncommutative Wilson loop available in the literature. The open Wilson line contribution present in the non-commutative version of the loop equation drops out in the resulting usual differential equations. These equations for all N have the same form as in the commutative case for Nrightarrowinfty. However, the additional supplementary input from factorization properties allowing to solve the equations in the commutative case is no longer valid.
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
NASA Astrophysics Data System (ADS)
Nakamura, K.
2009-06-01
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.
Topological field theories in n-dimensional spacetimes and Cartan's equations
Cuesta, Vladimir; Vergara, Jose David [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, 70-543, Ciudad de Mexico (Mexico); Montesinos, Merced; Velazquez, Mercedes [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Instituto Politecnico Nacional 2508, San Pedro Zacatenco, 07360, Gustavo A. Madero, Ciudad de Mexico (Mexico)
2008-09-15
Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing additional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.
Nakamura, Y. [Department of Electronic and Photonic Systems, Waseda University, Tokyo 169-8555 (Japan)], E-mail: nakamura@aoni.waseda.jp; Sunaga, T. [Department of Physics, Waseda University, Tokyo 169-8555 (Japan)], E-mail: tomoka@fuji.waseda.jp; Mine, M. [Waseda University Honjo Senior High School, 1136 Nishitomida, Honjo, Saitama 367-0035 (Japan)], E-mail: mine@waseda.jp; Okumura, M. [CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015 (Japan); CREST (JST), 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012 (Japan)], E-mail: okumura.masahiko@jaea.go.jp; Yamanaka, Y. [Department of Electronic and Photonic Systems, Waseda University, Tokyo 169-8555 (Japan)], E-mail: yamanaka@waseda.jp
2010-02-15
The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Vladislav Kravchenko; Dominic Rochon; Sebastien Tremblay
2007-12-21
Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We show that real parts of the solutions of one of these Vekua-type operators are solutions of the considered Klein-Gordon equation. Using hyperbolic pseudoanalytic function theory, we then obtain explicit construction of infinite systems of solutions of the Klein-Gordon equation with potential. Finally, we give some examples of application of the proposed procedure.
2015-01-01
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts. PMID:24555448
David A. Sivak; John D. Chodera; Gavin E. Crooks
2014-04-09
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently-developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.
Telleparallel Lagrange Geometry and a Unified Field Theory: Linearization of the Field Equations
M. I. Wanas; Nabil L. Youssef; A. M. Sid-Ahmed
2011-07-03
The present paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav., 27 (2010), 045005 (29pp)" \\cite{WNA}. In this paper, we apply a linearization scheme on the field equations obtained in \\cite{WNA}. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space loose their dependence on the positional argument $x$. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first order of approximation. Finally, an approximate solution of the vertical field equations is obtained.
Coarse-grained forms for equations describing the microscopic motion of particles in a fluid
NASA Astrophysics Data System (ADS)
Das, Shankar P.; Yoshimori, Akira
2013-10-01
Exact equations of motion for the microscopically defined collective density ??(x,t) and the momentum density ?(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.
Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
Yukinao Akamatsu; Tetsuo Hatsuda; Tetsufumi Hirano
2008-09-24
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in It\\^{o} discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the AdS/CFT correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R_{AA} and the elliptic flow v_{2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy ion collisions. The R_{AA} for electrons with large transverse momentum (p_{T} > 3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.
Heavy Quark Diffusion with Relativistic Langevin Dynamics in the Quark-Gluon Fluid
Akamatsu, Yukinao; Hirano, Tetsufumi
2008-01-01
The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in It\\^{o} discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the AdS/CFT correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R_{AA} and the elliptic flow v_{2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy ion collisions. The R_{AA} for electrons with large transverse momentum (p_{T} > 3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.
DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
A. V. Kotikov; L. N. Lipatov
2001-12-28
We discuss DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the leading and next-to-leading approximations. Eigenvalues of the BFKL kernel in this model turn out to be analytic functions of the conformal spin. It allows us to find the residues of the anomalous dimensions of the twist-2 operators in the points j=1,0,-1, ... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. The holomorphic separability of the BFKL kernel and the integrability of the DGLAP dynamics in this model are also discussed.
A Padé approximant to the inverse Langevin function
A. Cohen
1991-01-01
Application of the methodology of Pade approximants to a Taylor expansion of the inverse Langevin function led to an accurate analytical expression. The approximation, retaining a finite extendibility of the Langevin spring, enables a convenient analysis of experimental data and analytical manipulations of material models.
Long time step molecular dynamics using targeted Langevin stabilization
Izaguirre, JesÃºs A.
Long time step molecular dynamics using targeted Langevin stabilization Qun Ma JesÂ´us A. Izaguirre, IN 46556-0309, USA #12;Long time step molecular dynamics using targeted Langevin stabilization Abstract We introduce the B-spline Mollified Impulse (MOLLY) and the Targeted MOLLY (TM) for molecular dynamics (MD). TM
Inverse-scattering theory at a fixed energy for the Klein-Gordon equation
NASA Astrophysics Data System (ADS)
Shehadeh, Z. F.; Alam, M. M.; Malik, F. B.
1999-02-01
The inverse-scattering theory at a fixed energy for the scattering of a particle by a potential in the Schrödinger equation formulated by Alam and Malik, which is based on the earlier work of Hooshyar and Razavy, is extended, in this paper, to the scattering of spinless particles at relativistic energies governed by the Klein-Gordon equation. The differential equation is replaced by a set of difference equations. This reduces the inverse-scattering problem to solving a continued fraction equation. The solution provides the values of the potential at a number of points which are equal to (one plus the number of partial waves). The theory is tested for three widely different complex potentials, one of which is relevant to pion-nucleus scattering. The points of the potentials determined from the inverse-scattering formalism are in accord with the actual ones in all three cases. Since the Klein-Gordon equation is effectively a Schrödinger equation with an energy-dependent potential, the method may, in the appropriate cases, be suitable for the latter case.
Irreversible Langevin samplers and variance reduction: a large deviations approach
NASA Astrophysics Data System (ADS)
Rey-Bellet, Luc; Spiliopoulos, Konstantinos
2015-07-01
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists of constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e. they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose variance is not reduced reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.
Irreversible Langevin samplers and variance reduction: a large deviation approach
Luc Rey-Bellet; Kostantinos Spiliopoulos
2015-04-22
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e., they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose variance is not reduced reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.
Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory
Watson, P.; Reinhardt, H. [Institut fuer Theoretische Physik, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)
2007-02-27
Coulomb gauge Yang-Mills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The Ward-Takahashi identity arising from this non-standard transform is shown to be automatically satisfied by the equations of motion.
Theory of Partial Differential Equations (155010) Exercises WC #8 (Week 03) 2012.01.20
Al Hanbali, Ahmad
the mean value property for harmonic functions in a bounded domain D R2, u(x) = 1 2R B(x,R) u(y) ds in that domain. (b) Use, instead, the representation theorem for (twice continuously differentiable) functionsTheory of Partial Differential Equations (155010) Exercises WC #8 (Week 03) 2012.01.20 01
Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures
Franz Baader; Klaus U. Schulz
1992-01-01
Most of the work on the combination of unification algorithms for the union of disjoint equational theories has been restricted to algorithms which compute finite complete sets of unifiers. Thus the developed combination methods usually cannot be used to combine decision procedures, i.e., algorithms which just decide solvability of unification problems without computing unifiers. In this paper we describe a
The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
Orfeu Bertolami; Claudio Gomes
2014-06-23
We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.
Arun Yethiraj; Kenneth S. Schweizer
1993-01-01
The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and Curro [J. Chem. Phys. 91, 5059 (1989); Chem. Phys. 149, 105 (1990)] (in which the critical temperature is proportional
Asymptotic Standard Errors for Item Response Theory True Score Equating of Polytomous Items
ERIC Educational Resources Information Center
Cher Wong, Cheow
2015-01-01
Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Kinetic Theory of Evaporation and Condensation Hydrodynamic Equation and Slip Boundary Condition
Yoshio Sone; Yoshimoto Onishi
1978-01-01
The steady behavior of a gas in contact with its condensed phase of arbitrary shape is investigated on the basis of kinetic theory. The Knudsen number of the system (the mean free path of the gas molecules divided by the characteristic length of the system) being assumed to be fairly small, the hydrodynamic equations for the macroscopic quantities, the velocity,
DGLAP and BFKL equations in the N=4 supersymmetric gauge theory
A. V. Kotikov; L. N. Lipatov
2003-01-01
We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions ? of
Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory
ERIC Educational Resources Information Center
Muthen, Bengt; Asparouhov, Tihomir
2012-01-01
This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…
A unified theory of zero power and power reactor noise via backward master equations
Pázsit, Imre
A unified theory of zero power and power reactor noise via backward master equations I. Pa´ zsit a, *, Z.F. Kuang a,b , A.K. Prinja c a Department of Reactor Physics, Chalmers University of Technology neutronic fluctuations in a steady medium, and power reactor noise are treated as two separate phenomena
Using the gravity equation to differentiate among alternative theories of trade
Robert C. Feenstra; James R. Markusen; Andrew K. Rose
2001-01-01
The simple gravity equation explains a great deal about the data on bilateral trade flows and is consistent with several theoretical models of trade. We argue that alternative theories nevertheless predict subtle differences in key parameter values, depending on whether goods are homogeneous or differentiated and whether or not there are barriers to entry. Our empirical work for differentiated goods
EVOLUTION EQUATIONS AND doi:10.3934/eect.2013.2.379 CONTROL THEORY
Rosier, Lionel - Institut de Mathématiques Élie Cartan, Université Henri Poincaré
derived from an industrial setting for which tanks filled with liquid are to be moved to different steadyEVOLUTION EQUATIONS AND doi:10.3934/eect.2013.2.379 CONTROL THEORY Volume 2, Number 2, June 2013 pp. 379402 CONTROLLABILITY OF A 1-D TANK CONTAINING A FLUID MODELED BY A BOUSSINESQ SYSTEM Dugan Nina
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
ERIC Educational Resources Information Center
Brossman, Bradley Grant
2010-01-01
The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted.…
Testing a theory of aircraft noise annoyance: A structural equation analysis
Maarten Kroesen; Eric J. E. Molin; Bert van Wee
2008-01-01
Previous research has stressed the relevance of nonacoustical factors in the perception of aircraft noise. However, it is largely empirically driven and lacks a sound theoretical basis. In this paper, a theoretical model which explains noise annoyance based on the psychological stress theory is empirically tested. The model is estimated by applying structural equation modeling based on data from residents
New field equations in the 5-dimensional projective unified field theory
E. Schmutzer
1995-01-01
New field equations of the Projective Unified Field Theory are presented which avoid potential difficulties of former versions with respect to the equivalence principle. The physical interpretation of this new version remains unchanged: constancy of the gravitational constant, electromagnetic polarization of the vacuum, definiteness of the energy of the stationary scalaric field, etc. Furthermore, the Klein-Gordon field and the Dirac
Chongming Xuand; Xuejun Wu; Michael Soffel; Sergei Klioner
2003-01-01
In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as a uniformly rotating, stationary
Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
Gert Aarts; Frank A. James
2012-01-25
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and assess in particular the justification of this approach, using analyticity at small mu^2 and the criteria for correctness developed recently. Finite-stepsize effects are discussed in some detail and a higher-order algorithm is employed to eliminate leading stepsize corrections. Our results strongly indicate that complex Langevin dynamics is reliable in this theory in both phases, including the critical region. This is in sharp contrast to the case of the XY model, where correct results were obtained in only part of the phase diagram.
Coherent state path integral and Langevin equation of interacting fermions
B. Mieck
2002-01-01
Interacting fermions, electrons and holes in a semiconductor, are coupled to a thermal reservoir of bosons which yield the fluctuating noise. We use a coherent state path integral formulation on the time contour for non-equilibrium systems in terms of anticommuting variables which replace the fermionic creation- and annihilation operators in the time development operator. An auxiliary commuting field ?x(tp), defined
The Langevin equation from Markovian Quantum Central Limits
John Gough
2006-11-18
This paper has been withdrawn by the author. The central result is now included in quant-ph/0309056 (as in the journal publication!). An erratum on the Heisenberg perturbation series estimate is also included therein.
Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties
NASA Astrophysics Data System (ADS)
Fodor, Étienne; Grebenkov, Denis S.; Visco, Paolo; van Wijland, Frédéric
2015-03-01
We review equilibrium properties for the dynamics of a single particle evolving in a visco-elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time-reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed.
Analysis of Numerical Errors in Solving Particle Langevin Equations
to lead to signi cant bias. The following section describes the model problem. The models are then solved usually has the form 6] 7], dx = ;(x ;hxi) T dt + bdW (1) where hxi is the mean or expectation of x
NASA Astrophysics Data System (ADS)
Nakamura, K.
2007-01-01
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
On the invariance of constitutive equations according to the kinetic theory of gases
NASA Astrophysics Data System (ADS)
Speziale, Charles G.
1984-05-01
Iterative techniques for solving the Boltzmann equation in the kinetic theory of gases yield expressions for the stress tensor and heat flux vector that are analogous to constitutive equations in continuum mechanics. However, these expressions are not generally invariant under the Euclidean group of transformations, whereas constitutive equations in continuum mechanics are usually required to be by the principle of material frame indifference. This disparity in invariance properties has led some previous investigators to argue that Euclidean invariance should be discarded as a contraint on constitutive equations. It is proven mathematically in this paper that the results of the Chapman-Enskog iterative procedure have no direct bearing on this issue. In order to settle this question, it is necessary to examine mathematically the effect of superimposed rigid body rotations on solutions of the Boltzmann equation. A preliminary investigation along these lines is presented which suggests that the kinetic theory is consistent with material frame indifference in at least a strong approximate sense provided that the disparity in the time scales of the microscopic and macroscopic motions is extremely large—a condition which is usually a prerequisite for the existence of constitutive equations.
Stolle
1991-01-01
The expressions for the power spectral density of the noise equivalent sources have been calculated explicitly for the (a) stochastic transport equation, (b) the one-speed transport equaton, (c) the one-speed Pâ equations, (d) the one-speed diffusion equation and (e) the point kinetic equation. The stochastic nature of Fick's law in (d) has been emphasized. The Langevin technique has been applied
Myron W. Evans
2004-01-01
The first and second Maurer-Cartan structure relations are combined with the Evans field equation [1] for differential forms to build a grand unified field theory based on differential geometry. The tetrad or vielbein plays a central role in this theory, and all four fields currently thought to exist in nature can be described by the same equations, the tangent space
Stochastic thermodynamics for delayed Langevin systems.
Jiang, Huijun; Xiao, Tiejun; Hou, Zhonghuai
2011-06-01
We discuss stochastic thermodynamics (ST) for delayed Langevin systems in this paper. By using the general principles of ST, the first-law-like energy balance and trajectory-dependent entropy s(t) can be well defined in a way that is similar to that in a system without delay. Because the presence of time delay brings an additional entropy flux into the system, the conventional second law (?s(tot))?0 no longer holds true, where ?s(tot) denotes the total entropy change along a stochastic path and (·) stands for the average over the path ensemble. With the help of a Fokker-Planck description, we introduce a delay-averaged trajectory-dependent dissipation functional ?[?(t)] which involves the work done by a delay-averaged force F(x,t) along the path ?(t) and equals the medium entropy change ?s(m)[x(t)] in the absence of delay. We show that the total dissipation functional R=?s+?, where ?s denotes the system entropy change along a path, obeys (R)?0, which could be viewed as the second law in the delayed system. In addition, the integral fluctuation theorem (e(-R))=1 also holds true. We apply these concepts to a linear Langevin system with time delay and periodic external force. Numerical results demonstrate that the total entropy change (?s(tot)) could indeed be negative when the delay feedback is positive. By using an inversing-mapping approach, we are able to obtain the delay-averaged force F(x,t) from the stationary distribution and then calculate the functional R as well as its distribution. The second law (R)?0 and the fluctuation theorem are successfully validated. PMID:21797339
V. N. Pokrovskii
1970-01-01
The system of equations of motion for a liquid and a solid with internal parameters — scalars and second-order tensors — is written out in the linear approximation. From the system of equations for the class of motions with velocity gradients independent of the coordinates there follows the known equation of the linear theory of viscoelasticity. It is shown that
Boyer, Edmond
Jean Stratonovitch - Langevin's twin paradox and the forwards and backwards movement of a rotating in accordance with predictions of special relativity. Langevin's twin paradox and the forwards and backwards movement of a rotating cylinder experiment Jean Stratonovitch 1 LANGEVIN'S TWIN PARADOX Langevin slightly
Sako, Akifumi; Suzuki, Toshiya [Department of Mathematics, Faculty of Science and Technology, Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522 (Japan); Department of Physics, Faculty of Engineering, Musashi Institute of Technology 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan and Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610 (Japan)
2006-11-15
We investigate the Seiberg-Witten monopole equations on noncommutative (N.C.) R{sup 4} at the large N.C. parameter limit, in terms of the equivariant cohomology. In other words, N=2 supersymmetric U(1) gauge theories with a hypermultiplet on N.C.R{sup 4} are studied. It is known that after topological twisting partition functions of N>1 supersymmetric theories on N.C. R{sup 2D} are invariant under the N.C. parameter shift; then the partition functions can be calculated by its dimensional reduction. At the large N.C. parameter limit, the Seiberg-Witten monopole equations are reduced to ADHM equations with the Dirac equation reduced to the 0 dimension. The equations are equivalent to the dimensional reduction of non-Abelian U(N) Seiberg-Witten monopole equations in N{yields}{infinity}. The solutions of the equations are also interpreted as a configuration of a brane antibrane system. The theory has global symmetries under torus actions originated in space rotations and gauge symmetries. We investigate the Seiberg-Witten monopole equations reduced to the 0 dimension and the fixed point equations of the torus actions. We show that the Dirac equation reduced to the 0 dimension is automatically satisfied when the fixed point equations and the ADHM equations are satisfied. Then, we find that the Seiberg-Witten equations reduced to the 0 dimension and fixed point equations of the torus action are equivalent to just the ADHM equations with the fixed point equations. For finite N, it is known that the fixed points of the ADHM data are isolated and are classified by the Young diagrams. We also give a new proof of this statement by solving the ADHM equations and the fixed point equations concretely and by giving graphical interpretations of the field components and these equations.
Stochastic treatment of disoriented chiral condensates within a Langevin description
NASA Astrophysics Data System (ADS)
Xu, Zhe; Greiner, Carsten
2000-08-01
Applying a microscopically motivated semiclassical Langevin description of the linear sigma model we investigate for various different scenarios the stochastic evolution of a disoriented chiral condensate (DCC) in a rapidly expanding system. Some particular emphasis is put on the numerical realization of colored noise in order to treat the underlying dissipative and non-Markovian stochastic equations of motion. A comparison with an approximate Markovian (i.e., instantaneous) treatment of dissipation and noise will be made in order to identify the possible influence of memory effects in the evolution of the chiral order parameter. Assuming a standard Rayleigh cooling term to simulate a D-dimensional scaling expansion we present the probability distribution in the low momentum pion number stemming from the relaxing zero mode component of the chiral field. The best DCC signal is expected for initial conditions centered around ~0 as would be the case of effective light ``pions'' close to the phase transition. By choosing appropriate idealized global parameters for the expansion our findings show that an experimentally feasible DCC, if it does exist in nature, has to be a rare event with some finite probability following a nontrivial and non-Poissonian distribution on an event by event basis. DCCs might then be identified experimentally by inspecting higher order factorial cumulants ?m (m>=3) in the sampled distribution.
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations.
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D; Kühn, Oliver
2015-06-28
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom. PMID:26133413
Langevin simulation of rf collisional multipactor breakdown of gases.
Conde, L; Pérez, F; de Lara, J; Alfonseca, M; Raboso, D
2009-06-01
The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed. PMID:19658608
Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions
Anischenko, Yu. A., E-mail: yuri.anischenko@gmail.com; Adeev, G. D. [Omsk State University (Russian Federation)
2012-08-15
A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {l_brace}c, h, {alpha}{r_brace} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k{sub s} 0.25 and k{sub s} = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k{sub s} in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z{sup 2}/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k{sub s} with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, Left-Pointing-Angle-Bracket n{sub pre}(M) Right-Pointing-Angle-Bracket , and between, this multiplicity and the kinetic energy of fission fragments, Left-Pointing-Angle-Bracket n{sub pre}(E{sub k}) Right-Pointing-Angle-Bracket , are also presented.
Modular anomaly equation, heat kernel and S-duality in N=2 theories
M. Billó; M. Frau; L. Gallot; A. Lerda; I. Pesando
2013-09-09
We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such that it reduces to a Legendre transform.
Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory
F. Haas; J. Zamanian; M. Marklund; G. Brodin
2009-12-23
The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.
First order string theory and the Kodaira-Spencer equations. II
NASA Astrophysics Data System (ADS)
Gamayun, O.; Marshakov, A.
2009-09-01
The first-order bosonic string theory, perturbed by primary operator, corresponding to the deformation of target-space complex structure is considered. We compute the correlation functions in this theory and study their divergencies. It is found, that consistency of these correlation functions with the world-sheet conformal invariance requires the Kodaira-Spencer equations to be satisfied by target-space Beltrami differentials. This statement is checked explicitly for the three-point and four-point correlators, containing one probe operator. We discuss the origin of these divergences and their relation with beta-functions or effective action and polyvertex structures in BRST approach.
Equations of Motion of Glashow-Salam-Weinberg Theory after Spontaneous Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ebner, Dieter W.
While for quantum field theoretical calculations it is sufficient to know the Lagrangian, we give here the field equations of the unified gauge-theory of weak and electromagnetic interactions after spontaneous symmetry breaking. With this approach, inhomogeneous Lorentz conditions for the massive vector bosons Z, W[stack +/- ] are obtained.Translated AbstractBewegungsgleichungen der Glashow-Salam-Weinberg-Theorie nach spontaner SymmetriebrechungWährend es für quantenfeldtheoretische Rechnungen ausreichend ist, die Lagrangefunktion zu kennen, geben wir hier die Feldgleichungen der einheitlichen Eichtheorie der schwachen und elektromagnetischen Wechselwirkung nach spontaner Symmetriebrechung an. Auf diese Weise werden inhomogene Lorentzbedingungen für die massiven Vektorbosonen Z?, W[stack ?+/- ] erhalten.
Gegechkori, A. E., E-mail: gecktor@gmail.com; Adeev, G. D. [Omsk State University (Russian Federation)
2011-01-15
Angular distributions of fission fragments were calculated within a multidimensional approach to the fission dynamics of excited nuclei, and the results of these calculations are presented. The evolution of the shape parameters of a fissile nucleus was described by the set of three-dimensional Langevin equations for collective coordinates introduced on the basis of the (c, h, a) parametrization. The evolution of the orientation degree of freedom (K mode, K being the projection of the total angular momentum on the symmetry axis of the nucleus under study) was described with the aid of the Langevin equation in an overdampedmode. The coupled Langevin equations for the shape and K-mode collective coordinates were integrated simultaneously. The friction parameter for the K mode was set to 0.077 (MeV Multiplication-Sign 10{sup -21} s){sup -1/2}, which is the estimate obtained previously for this quantity in calculating angular distributions of excited compound nuclei with allowance for the effects of the orientation degree of freedom. The developed model was used to analyze the anisotropy of angular distribution of fission fragments in {sup 16}O+{sup 208}Pb, {sup 16}O+{sup 232}Th, and {sup 16}O + {sup 238}U reactions over a broad interval of projectile-ion energies. The results of the calculations show that the developedmodel, usedwith the above value of the friction parameter for theK mode, leads to a rather good description of experimental data on the anisotropy of angular distributions of fission fragments. The effect of the dimensionality of the dynamicalmodel used to describe the evolution of the shape of a fissile nucleus on the results obtained by calculating the anisotropy of angular distributions is discussed.
RG equation for additively separable NN potentials in effective field theory
NASA Astrophysics Data System (ADS)
Park, Tae-Sun
2014-12-01
We study an additively separable form of an NN potential of the form V( p, k) = ½ v( p) + ½ v( k) and construct the renormalization group equation that preserves the on-shell scattering data. By applying the separable form to 1 S 0 NN system, its relation to effective field theory that consists of NN contact interactions is discussed, with explicit evaluation up to next-to-leading order.
NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories
A. V. Kotikov; L. N. Lipatov
2000-01-01
We study next-to-leading corrections to the integral kernel of the BFKL equation for high-energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension ? of the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY,
Closed String Field Theory: Quantum Action and the BV Master Equation
Barton Zwiebach
1992-01-01
The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra $L_\\\\infty$, and the higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation.
Equation of motion for a spherically-symmetric shell in the relativistic theory of gravity
O. V. Monovskii
1996-01-01
In the framework of the relativistic theory of gravity, the equation of motion for a spherically-symmetric singular shell is derived and integrated in the first approximation of the Newton potential U = m\\/r. We use the covariant energy-momentum conservation law for matter in the effective Riemannian space and, independently, the energy-momentum conservation law for the matter + gravity system in
Boris Gurevich
2007-01-01
Predictions of Biot's theory (BT) of poroelasticity [J. Acoust. Soc. Am. 28, 168 (1956)] and de Boer's theory of porous media (TPM) [Theory of Porous Media (Springer, Berlin, 2000)] for the low-frequency bulk modulus of a fluid-saturated porous medium are compared with the Gassmann equation [Vierteljahrsschr. Naturforsch. Ges. Zur. 96, 1 (1951)]. It is shown that BT is consistent with
Symmetry energy and pion production in the Boltzmann-Langevin approach
NASA Astrophysics Data System (ADS)
Xie, Wen-Jie; Su, Jun; Zhu, Long; Zhang, Feng-Shou
2013-01-01
Based on the improved isospin-dependent Boltzmann-Langevin model which incorporates the dynamical fluctuations, we study the ? production in central heavy ion collisions at different incident energies from 250 to 1200A MeV. It is found that the ? multiplicity is sensitive to the nuclear equation of state. At ? subthreshold energy, the fluctuations have a larger effect on the ? multiplicity. The ?-/?+ ratios as a probe of nuclear symmetry energy are calculated with different stiffness of symmetry energy. The results favor a supersoft symmetry energy of the potential term in comparison with the FOPI data, which supports the one obtained by the usual Boltzmann-Uehling-Uhlenbeck model.
A Revisiting of the L^2 -Stability Theory of the Boltzmann Equation Near Global Maxwellians
NASA Astrophysics Data System (ADS)
Ha, Seung-Yeal; Xiao, Qinghua
2015-04-01
We study the L^2 -stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the L^2 -distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in L^2 -topology. Our local-in-time L^2 -stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657-688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the L^2 -stability theory for the Boltzmann equation near a global Maxwellian. For this L^2 -stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform L^2 -stability of the Boltzmann equation.
N=1 Super Yang-Mills Theory in Ito Calculus
Naohito Nakazawa
2006-08-23
The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM_4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an '' almost Wess-Zumino gauge ''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM_10, the IIB matirx model is studied in this context.
Stochastic Gravity: Theory and Applications
B. L. Hu; E. Verdaguer
2008-02-05
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole
Three new branched chain equations of state based on Wertheim's perturbation theory
NASA Astrophysics Data System (ADS)
Marshall, Bennett D.; Chapman, Walter G.
2013-05-01
In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.
The solids-flux theory--confirmation and extension by using partial differential equations.
Diehl, Stefan
2008-12-01
The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts. PMID:18926553
Aminova, Asya V [Kazan State University, Kazan (Russian Federation); Aminov, Nail' A-M [Kazan State Technological University, Kazan (Russian Federation)
2010-06-29
In the framework of the projective geometric theory of systems of differential equations, which is being developed by the authors, conditions which ensure that a family of graphs of solutions of a system of m second-order ordinary differential equations y-vector-ddot=f-vector(t,y-vector,y-vector-dot) with m unknown functions y{sup 1}(t),...,y{sup m}(t) can be straightened (that is, transformed into a family of straight lines) by means of a local diffeomorphism of the variables of the system which takes it to the form z-vector''=0 (straightens the system) are investigated. It is shown that the system to be straightened must be cubic with respect to the derivatives of the unknown functions. Necessary and sufficient conditions for straightening the system are found, which have the form of differential equations for the coefficients of the system or are stated in terms of symmetries of the system. For m=1 the system consists of a single equation y-ddot=f-vector(t,y,y-dot), and the tests obtained reduce to the conditions for straightening this equations which were derived by Lie in 1883. Bibliography: 34 titles.
Unification of classical nucleation theories via unified It\\^{o}-Stratonovich stochastic equation
Durán-Olivencia, Miguel A
2015-01-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\\"{o}ring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that form a recent update of CNT [J.F. Lutsko and M.A. Dur\\'{a}n-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diff...
Unification of classical nucleation theories via unified Itô-Stratonovich stochastic equation
Miguel A. Durán-Olivencia; James F. Lutsko
2015-05-14
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\\"{o}ring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that form a recent update of CNT [J.F. Lutsko and M.A. Dur\\'{a}n-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer.
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
Modular anomaly equations in N=2* theories and their large-N limit
Billo, M; Fucito, F; Lerda, A; Morales, J F; Poghossian, R; Pacifici, D Ricci
2014-01-01
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.
An anisotropic constitutive equation for the stress tensor of blood based on mixture theory
Massoudi, Mehrdad; Antaki, J.F.
2008-09-12
Based on ideas proposed by Massoudi and Rajagopal (M-R), we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells (RBCs) suspended in plasma, where the plasma behaves as a linearly viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
Modular anomaly equations in N=2* theories and their large-N limit
M. Billo; M. Frau; F. Fucito; A. Lerda; J. F. Morales; R. Poghossian; D. Ricci Pacifici
2014-06-27
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on S^4 at large N localises around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.
NASA Astrophysics Data System (ADS)
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-05-01
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.
Exceptional thermodynamics: The equation of state of G(2) gauge theory
Mattia Bruno; Michele Caselle; Marco Panero; Roberto Pellegrini
2015-03-12
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G(2) gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
Exceptional thermodynamics: the equation of state of G2 gauge theory
NASA Astrophysics Data System (ADS)
Bruno, Mattia; Caselle, Michele; Panero, Marco; Pellegrini, Roberto
2015-03-01
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G2 gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU( N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU( N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-05-21
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules. PMID:26001441
Gravitational Field Equations and Theory of Dark Matter and Dark Energy
Tian Ma; Shouhong Wang
2012-07-11
The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential $\\varphi$ are derived using the Einstein-Hilbert functional, and the scalar potential $\\varphi$ is a natural outcome of the divergence-free constraint of the variational elements. Gravitation is now described by the Riemannian metric $g_{ij}$, the scalar potential $\\varphi$ and their interactions, unified by the new gravitational field equations. Associated with the scalar potential $\\varphi$ is the scalar potential energy density $\\frac{c^4}{8\\pi G} \\Phi=\\frac{c^4}{8\\pi G} g^{ij}D_iD_j \\varphi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe. The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: $\\int_M \\Phi dM=0$. The sum of this new potential energy density $\\frac{c^4}{8\\pi G} \\Phi$ and the coupling energy between the energy-momentum tensor $T_{ij}$ and the scalar potential field $\\varphi$ gives rise to a new unified theory for dark matter and dark energy: The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies. In addition, the scalar curvature of space-time obeys $R=\\frac{8\\pi G}{c^4} T + \\Phi$. Furthermore, the new field equations resolve a few difficulties encountered by the classical Einstein field equations.
Continuum regularization of gauge theory with fermions
Chan, H.S.
1987-03-01
The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)
Algebraic Principles of Quantum Field Theory II: Quantum Coordinates and WDVV Equation
Jae-Suk Park
2011-02-08
This paper is about algebro-geometrical structures on a moduli space $\\CM$ of anomaly-free BV QFTs with finite number of inequivalent observables or in a finite superselection sector. We show that $\\CM$ has the structure of F-manifold -- a linear pencil of torsion-free flat connection with unity on the tangent space, in quantum coordinates. We study the notion of quantum coordinates for the family of QFTs, which determines the connection 1-form as well as every quantum correlation function of the family in terms of the 1-point functions of the initial theory. We then define free energy for an unital BV QFT and show that it is another avatar of morphism of QFT algebra. These results are consequences of the solvability of refined quantum master equation of the theory. We also introduce the notion of a QFT integral and study some properties of BV QFT equipped with a QFT integral. We show that BV QFT with a non-degenerate QFT integral leads to the WDVV equation---the formal Frobenius manifold structure on $\\CM$---if it admits a semi-classical solution of quantum master equation.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
NASA Astrophysics Data System (ADS)
Qin, Hong; Burby, Joshua W.; Davidson, Ronald C.
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby-Walsh theory
NASA Astrophysics Data System (ADS)
Feng, Quanxiong; Jiang, Lian; Liu, Mingquan; Wan, Huan; Chen, Li; Xiao, Wei
2014-07-01
Fluid substitution in carbonate rocks is more difficult than it is in clastic rocks for two reasons. Firstly, the rock physics modeling uncertainties in carbonate rocks, this is due to the difficulty of accurately acquiring the moduli of carbonate rocks' solid matrix because the experimental data on carbonate rocks have not been as thoroughly studied as silici-clastic sedimentary rocks. Secondly, due to the complex pore systems of carbonate rocks, it is very difficult to model pore geometry of carbonates, and hence hard to assess how the elastic properties change as fluid saturation changes based on the traditional Biot and Gassmann theories. In order to solve these problems, we present a new fluid substitution equation of carbonate rocks using the Gassmann equation and Eshelby-Walsh theory (GEW) in this paper. Then, the specific procedures of how to calculate the moduli of carbonate rocks' solid matrix and how to measure the effect of pore geometry in fluid substitution based on the new fluid substation equation were illustrated by experimental testing about 12 carbonate rock samples in different fluid saturation scenarios and logging data. Finally, we further compared the new fluid substitution method with the conventional Gassmann fluid substitution based on the experimental data. The results verified that the new method is more accurate and reliable in the fluid substitution of complex carbonate rocks.
Field theory and weak Euler-Lagrange equation for classical particle-field systems.
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry. PMID:25375609
Energy and equations of motion in a tentative theory of gravity with a privileged reference frame
Mayeul Arminjon
2007-09-04
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as in special relativity was expressed in terms of these distorted local standards, and was found to imply geodesic motion. Here, the formulation of motion is reexamined in the most general situation. A consistent Newton law can still be defined, which accounts for the time variation of the space metric, but it is not compatible with geodesic motion for a time-dependent field. The energy of a test particle is defined: it is constant in the static case. Starting from 'dust', a balance equation is then derived for the energy of matter. If the Newton law is assumed, the field equation of the theory allows to rewrite this as a true conservation equation, including the gravitational energy. The latter contains a Newtonian term, plus the square of the relative rate of the local velocity of gravitation waves (or that of light), the velocity being expressed in terms of absolute standards.
Energy and equations of motion in a tentative theory of gravity with a privileged reference frame
Arminjon, Mayeul
1996-01-01
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as in special relativity was expressed in terms of these distorted local standards, and was found to imply geodesic motion. Here, the formulation of motion is reexamined in the most general situation. A consistent Newton law can still be defined, which accounts for the time variation of the space metric, but it is not compatible with geodesic motion for a time-dependent field. The energy of a test particle is defined: it is constant in the static case. Starting from 'dust', a balance equation is then derived for the energy of matter. If the Newton law is assumed, the field equation of the theory allows to rewrite this as a true conservation equation, including the gravitational energy. The latter contains a Newtonian term, plus the square of the relative rate of the local ve...
B. M. Zupnik
1995-12-06
We consider the $SYM^1_6$ harmonic-superspace system of equations that contains superfield constraints and equations of motion for the simplest six-dimensional supersymmetric gauge theory. A special $A$-frame of the analytic basis is introduced where a kinematic equation for the harmonic connection $A^{\\s--}$ can be solved . A dynamical equation in this frame is equivalent to the zero-curvature equation corresponding to the covariant conservation of analyticity. Using a simple harmonic gauge condition for the gauge group $SU(2)$ we derive the superfield equations that produce the general $SYM^1_6$ solution . An analogous approach for the analysis of integrability conditions for the $SYM^2_4$-theory and $SYM$-supergravity-matter systems in harmonic superspace is discussed briefly.
Cosmology in generalized Horndeski theories with second-order equations of motion
Ryotaro Kase; Shinji Tsujikawa
2014-08-29
We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\\phi_I$ ($I=1,2\\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\\partial_{\\mu}\\phi_I\\partial^{\\mu}\\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\\phi_I$ are generally suppressed relative to that for the dark energy field $\\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.
Michael K. Salemi
1995-01-01
How close is observed Federal Reserve policy to policy that would be optimal in the control-theory sense? The question is addressed by using an inverse-control methodology. Federal Reserve policy is characterized by a feedback equation for either changes in the interest rate or money stock. Optimal policy is characterized by solution of the Ricatti equation. Parameters are estimated that characterize
Pure gauge configurations and tachyon solutions to string field theories equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.
2009-05-01
In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.
Elasticity theory equations and fracture condition for materials of varying moduli
Oleinikov, A.I.
1986-11-01
Many massive rocks and composite materials belong to the class of materials of varying moduli with definite distinct deformation and strength properties under tension and compression. The results of experiments indicate that the difference between the properties of materials of different moduli is not limited to tension and compression cases but can also appear clearly for any change in the form of the state of stress. Elasticity theory equations are constructed here to describe the strain of materials of varying moduli as well as the dependence of the strength properties on the form of the state of strain. Tests were done on coal, limestone, diabase and cement and results are shown. Using the dependencies obtained, Poisson's ratio and the elastic modulus can be calculated for these rocks. The equations and conditions of fracture proposed, are written in a simple invariant form.
Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
R. Giachetti; V. Grecchi
2009-05-13
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.
Langevin modelling of high-frequency Hang-Seng index data
NASA Astrophysics Data System (ADS)
Tang, Lei-Han
2003-06-01
Accurate statistical characterization of financial time series, such as compound stock indices, foreign currency exchange rates, etc., is fundamental to investment risk management, pricing of derivative products and financial decision making. Traditionally, such data were analyzed and modeled from a purely statistics point of view, with little concern on the specifics of financial markets. Increasingly, however, attention has been paid to the underlying economic forces and the collective behavior of investors. Here we summarize a novel approach to the statistical modeling of a major stock index (the Hang Seng index). Based on mathematical results previously derived in the fluid turbulence literature, we show that a Langevin equation with a variable noise amplitude correctly reproduces the ubiquitous fat tails in the probability distribution of intra-day price moves. The form of the Langevin equation suggests that, despite the extremely complex nature of financial concerns and investment strategies at the individual's level, there exist simple universal rules governing the high-frequency price move in a stock market.
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Chekhov, Leonid [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom)] [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom); Eynard, Bertrand [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France)] [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Ribault, Sylvain [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France) [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5 (France)
2013-02-15
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
Renormalization-group theory for the phase-field crystal equation
NASA Astrophysics Data System (ADS)
Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.
2006-07-01
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.
EYM equations in the presence of q-stars is scalar-tensor gravitational theories
Athanasios Prikas
2005-03-10
We study Einstein-Yang-Mills equations in the presence of a gravitating non-topological soliton field configuration consisted of a Higgs doublet, in Brans-Dicke and general scalar-tensor gravitational theories. The results of General Relativity are reproduced in the $\\omega_{\\textrm{BD}},\\omega_0\\to\\infty$ limit. The numerical solutions correspond to a soliton star with a non-abelian gauge field. We study the effects of the coupling constant, the frequency of the Higgs field and the Brans-Dicke field on the soliton parameters
Didactic derivation of the special theory of relativity from the Klein-Gordon equation
NASA Astrophysics Data System (ADS)
Arod?, H.
2014-09-01
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are ‘discovered’ as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound |{\\bf v}| is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition (‘addition’) of velocities.
Current noise spectra and mechanisms with dissipaton equation of motion theory.
Jin, Jinshuang; Wang, Shikuan; Zheng, Xiao; Yan, YiJing
2015-06-21
Based on the Yan's dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels. PMID:26093551
Renormalization-group theory for the phase-field crystal equation.
Athreya, Badrinarayan P; Goldenfeld, Nigel; Dantzig, Jonathan A
2006-07-01
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time. PMID:16907101
Equation of state of hot and dense QCD: resummed perturbation theory confronts lattice data
NASA Astrophysics Data System (ADS)
Mogliacci, Sylvain; Andersen, Jens O.; Strickland, Michael; Su, Nan; Vuorinen, Aleksi
2013-12-01
We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak coupling expression for the pressure, motivated by dimensional reduction. Finally, we compare the exact one-loop HTLpt and resummed dimensional reduction results with state-of-the-art lattice calculations and a recent mass-expanded three-loop HTLpt calculation.
Robert J. Buenker
2004-11-10
The erroneous prediction of the speed of light in dispersive media has been looked upon historically as unequivocal proof that Newton's corpuscular theory is incorrect. Examination of his arguments shows that they were only directly applicable to the momentum of photons, however, leaving open the possibility that the cause of his mistake was the unavailability of a suitable mechanical theory to enable a correct light speed prediction, rather than his use of a particle model. It is shown that Hamilton's canonical equations of motion remove Newton's error quantitatively, and also lead to the most basic formulas of quantum mechanics without reference to any of the pioneering experiments of the late nineteenth century. An alternative formulation of the wave-particle duality principle is then suggested which allows the phenomena of interference and diffraction to be understood in terms of statistical distributions of large populations of photons or other particles.
Lathiotakis, Nektarios N; Rubio, Angel; Gidopoulos, Nikitas I
2014-01-01
We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this...
Ning Wu; Dahua Zhang
2005-01-01
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of
Fission rate in multi-dimensional Langevin calculations
Nadtochy, P. N.; Kelic, A.; Schmidt, K.-H. [GSI, Plankstr. 1, D-64291 Darmstadt (Germany)
2007-06-15
Experimental data on nuclear dissipation have often been interpreted using one-dimensional model calculations of the Langevin or Fokker-Planck type. In the present work, the influence of the dimensionality of the deformation space on the time dependence of the fission process has been investigated in a systematic and quantitative way. In particular, the dependence of the transient time and the stationary value of the fission rate on the number of collective coordinates involved in Langevin calculations is investigated for the one-body and two-body dissipation mechanisms. We show that the results of Langevin-type calculations change appreciably if the deformation space is extended up to three dimensions.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
DOI: 10.1002/jcc.21883 Comparison Between Self-Guided Langevin Dynamics
DOI: 10.1002/jcc.21883 Comparison Between Self-Guided Langevin Dynamics and Molecular Dynamics-resolution predictions. The methods are self-guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nose
Langevin simulations of a model for ultrathin magnetic films Lucas Nicolao* and Daniel A. Stariolo
Stariolo, Daniel Adrián
Langevin simulations of a model for ultrathin magnetic films Lucas Nicolao* and Daniel A. Stariolo show results from simulations of the Langevin dynamics of a two-dimensional scalar model with competing
FokkerPlanck and Langevin analyses of noise accompanying the amplification of optical
Eisenstein, Gadi
FokkerÂPlanck and Langevin analyses of noise accompanying the amplification of optical pulses Langevin equa- tion. Multicanonical Monte Carlo simulations ensure efficient calculations of the pdfs whose
Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.
2011-01-01
A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed. PMID:21950847
NASA Astrophysics Data System (ADS)
Gurevich, Boris
2007-08-01
Predictions of Biot's theory (BT) of poroelasticity [J. Acoust. Soc. Am. 28, 168 (1956)] and de Boer's theory of porous media (TPM) [Theory of Porous Media (Springer, Berlin, 2000)] for the low-frequency bulk modulus of a fluid-saturated porous medium are compared with the Gassmann equation [Vierteljahrsschr. Naturforsch. Ges. Zur. 96, 1 (1951)]. It is shown that BT is consistent with the Gassmann equation, whereas TPM is not. It is further shown that the bulk modulus of a suspension of solid particles in a fluid as predicted by TPM is only correct if the particles are incompressible.
The Dirac spectrum in Complex Langevin Simulations of QCD
K. Splittorff
2014-12-01
We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields: At low temperatures the small eigenvalues of the Dirac operator must be inside the quark mass for chemical potentials as large as a third of the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of complex Langevin simulations must accumulate at the origin.
The Layzer-Irvine Equation for Scalar-Tensor Theories: A Test of Modified Gravity N-body Simulations
Hans A. Winther
2013-08-21
The Layzer-Irvine equation describes energy conservation for a pressure less fluid interacting though quasi-Newtonian gravity in an expanding Universe. We here derive a Layzer-Irvine equation for scalar field theories where the scalar field is coupled to the matter fields, and show applications of this equation by applying it to N-body simulations of modified gravity theories. There it can be used as both a dynamical test of the accuracy of the solution and the numerical implementation when solving the equation of motion. We also present an equation that can be used as a new static test for an arbitrary matter distribution. This allows us to test the N- body scalar field solver using a matter distribution which resembles what we actually encounter in numerical simulations.
Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim
2012-03-28
We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying. PMID:22462841
NASA Astrophysics Data System (ADS)
Vinš, Václav; Hrubý, Jan; Planková, Barbora
2012-04-01
The study presents some preliminary results of the density gradient theory (GT) combined with two different equations of state (EoS): the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT), namely its perturbed-chain (PC) modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation) or bubbles (boiling, cavitation). However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.
Stochastic theory of an optical vortex in nonlinear media.
Kuratsuji, Hiroshi
2013-07-01
A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes. PMID:23944571
On confined McKean Langevin processes satisfying the mean no-permeability boundary condition
Paris-Sud XI, Université de
On confined McKean Langevin processes satisfying the mean no-permeability boundary condition Mireille Bossy Jean-Fran¸cois Jabir August 22, 2011 Abstract We construct a confined Langevin type process aimed to satisfy a mean no-permeability condition at the boundary. This Langevin process lies
Paris-Sud XI, Université de
LANGEVIN AND HESSIAN WITH FISHER APPROXIMATION STOCHASTIC SAMPLING FOR PARAMETER ESTIMATION´eration 33405 Talence, France ABSTRACT We have studied two efficient sampling methods, Langevin and Hes- sian in a single iteration, and of the Langevin MH, as it requires only first order derivative computations. Index
Stariolo, Daniel Adrián
Langevin dynamics of fluctuation-induced first-order phase transitions: Self-consistent Hartree July 2006; revised manuscript received 18 September 2006; published 21 February 2007 The Langevin of the self-consistent Hartree approximation with direct simulations of the Langevin dynamics, confirming
MOLECULAR PHYSICS, 2002, VOL. 100, NO. 24, 38853891 An impulse integrator for Langevin dynamics
Skeel, Robert
MOLECULAR PHYSICS, 2002, VOL. 100, NO. 24, 3885±3891 An impulse integrator for Langevin dynamics the leapfrog StoÈ rmer±Verlet method. The appropriate generalization to simple Langevin dynamics is unclear considerations suggest that the impulse method is the best basic method for simple Langevin dynamics
ccsd-00018001,version1-26Jan2006 Reflecting a Langevin Process
Paris-Sud XI, Université de
ccsd-00018001,version1-26Jan2006 Reflecting a Langevin Process at an Absorbing Boundary Jean), et C.N.R.S. UMR 7599 175, rue du Chevaleret F-75013 Paris, France Summary. We consider a Langevin reflected, and study some properties of this reflecting solution. Key words. Langevin process, absorbing
Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics
Schlick, Tamar
Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics Daniel A. Beard October 1999; accepted 8 February 2000 Two algorithms are presented for integrating the Langevin dynamics. Our new approaches refine the common Brownian dynamics BD scheme, which approximates the Langevin
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification
Hou, Thomas Yizhao
Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification P for dynamic data integration using the Langevin algorithms. Based on a coarse-scale model of the problem, we compute the proposals of the Langevin algorithms using the coarse-scale gradient of the target
On The Weights of Binary Irreducible Cyclic Yves Aubry and Philippe Langevin
Paris-Sud XI, Université de
On The Weights of Binary Irreducible Cyclic Codes Yves Aubry and Philippe Langevin Universit´e du Sud Toulon-Var, Laboratoire GRIM F-83270 La Garde, France, {langevin,yaubry}@univ-tln.fr, WWW home page: http://{langevin,yaubry}.univ-tln.fr Abstract. This paper is devoted to the study of the weights
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics
Boyer, Edmond
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics Assyr Abdulle1 , Gilles Langevin dynamics up to an arbitrary order is discussed. Our characterization relies on backward error of the invariant measure of the Langevin dynamics. Numerical experiments confirm our theoretical findings. Key
On the derivation of the equations of motion in theories of gravity
Shmuel Kanieland; Yakov Itin
2001-01-01
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant a novel algorithm for the derivation of the equations of motion from the field equations. It is: 1. Compute a static, spherically
High-frequency Waves in Gravitational Theories with Fourth-order Derivative Equations
NASA Astrophysics Data System (ADS)
Borzeszkowski, H.-H. V.
For Einstein's gravitational equations with fourth-order corrections being proportional to the square of an elementary length l, we discuss the behaviour of high-frequency waves. It is shown that (1) only waves with lengths can generate a macroscopic avarage background (for < l, only the terms l2 are decisive such that one has the same situation as in a pure fourth-order theory without Einstein term which cannot be interpreted as gravitational theory), (2) for l the background metric is purely determined via the second-order derivative Einstein tensor (formally one obtains the same equations for the background as in the non-modified Einsteinian theory), and (3) only waves corresponding to the massless and the massive spin-two gravitons contribute to background curvature; in the geometrical-optics approximation, these both particle sorts are moving independent of each other and satisfy a conservation law for the total number of m = 0 and massive spin-two gravitons, respectively.The results obtained in this paper corroborate partly the conclusions drawn in the weak-field approximation [11, 15, 18].
Optimal scaling of discrete approximations to Langevin diffusions
Gareth O. Roberts; S. Rosenthal
1998-01-01
We consider the optimal scaling problem for proposal distributions in Hastings-Metropolis algorithms derived from Langevin diusions. We prove an asymp- totic diusion limit theorem and show that the relative eciency of the algorithm can be characterised by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that as a function of
The Complex Langevin method: When can it be trusted?
Gert Aarts; Erhard Seiler; Ion-Olimpiu Stamatescu
2010-03-17
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.
Complex Langevin method: When can it be trusted?
Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu [Department of Physics, Swansea University, Swansea (United Kingdom); Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Institut fuer Theoretische Physik, Universitaet Heidelberg and FEST, Heidelberg (Germany)
2010-03-01
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.
Exponential Convergence of Langevin Diffusions and Their Discrete Approximations
G. O. Roberts; R. L. Tweedie; Colorado State
1997-01-01
In this paper we consider a continous time method of approximating a givendistribution ? using the Langevin diffusion dL t = dW t +12 r log ?(L t )dt:We find conditions under which this diffusion converges exponentially quicklyto ? or does not: in one dimension, these are essentially that for distributionswith exponential tails of the form ?(x) \\/ exp(\\\\Gammafljxjfi), 0
Exponential convergence of Langevin distributions and their discrete approximations
Gareth O. Roberts; Richard L. Tweedie
1996-01-01
In this paper we consider a continuous-time method of approximating a given distribution [math] using the Langevin diffusion [math] . We find conditions under which this diffusion converges exponentially quickly to [math] or does not: in one dimension, these are essentially that for distributions with exponential tails of the form [math] , [math] , exponential convergence occurs if and only
Exploring the phase diagram of QCD with complex Langevin simulations
Aarts, Gert
diagram. phenomena: the evolution of the early universe, neutron stars and heavy-ion collision experimentsExploring the phase diagram of QCD with complex Langevin simulations Gert Aarts1, Felipe Attanasio1,2, Benjamin Jäger1, Erhard Seiler3, Dénes Sexty4,5, Ion-Olimpiu Stamatescu4. 1Department of Physics, College
Routage IP au niveau h^ote Philippe Langevin
Faccanoni, Gloria
Routage IP au niveau h^ote Philippe Langevin Oct 2007, Nov 2008, Nov 2011. #12;Protocole IP Interface rÂ´eseau Routeur Livraison physique Routage IP Adresse multicast Filtrage et translation d'adresse Algorithme de routage Travaux-Pratiques #12;Mod`ele TCP/IP Le protocole IP (Internet Protocole) constitue la
Stochastic Processes in Vision: From Langevin to Beltrami
Sochen, Nir
Stochastic Processes in Vision: From Langevin to Beltrami Nir A. Sochen Department of Applied are widely used in low level vision are presented as a result of an underlying stochastic process. The short rediscover the Beltrami flow which was advocated recently [5, 7, 2, 8]. It is further generalized
VARIANCE REDUCTION FOR IRREVERSIBLE LANGEVIN SAMPLERS AND DIFFUSION ON GRAPHS
Rey-Bellet, Luc
VARIANCE REDUCTION FOR IRREVERSIBLE LANGEVIN SAMPLERS AND DIFFUSION ON GRAPHS LUC REY and slow motion in the orthogonal direction. This result helps understanding the variance reduction, which large deviations rate function for the empirical measure of the process, a smaller variance for the long
Tu, Fei-Quan; Chen, Yi-Xin, E-mail: fqtuzju@foxmail.com, E-mail: yxchen@zimp.zju.edu.cn [Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027 (China)
2013-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Ho?ava-Lifshitz(HL) theory.
Titov, Anatoly
INSTITUT MAX VON LAUE - PAUL LANGEVIN07.04.11 V.V.Nesvizhevsky #12;INSTITUT MAX VON LAUE - PAUL LANGEVIN07.04.1107.04.11 V.V.Nesvizhevsky High-flux ILL reactor EMBL ILL ESRF #12;INSTITUT MAX VON LAUE - PAUL LANGEVIN07.04.1107.04.11 V.V.Nesvizhevsky Institut Laue-Langevin (ILL), Grenoble, France World
N. Nakazawa
1995-08-22
We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in a field theory of loops. The corresponding Fokker-Planck hamiltonian defines a non-critical string field theory. We study both orientable and non-orientable interactions of loops in terms of matrix models and take the continuum limit for one-matrix case. As a consequence, we show the equivalence of stochastic quantization of matrix models in loop space to the transfer-matrix formalism in dynamical triangulation of random surfaces. We also clarifies the origin of Virasoro algebra in this context.
Bogdan G. Dimitrov
2009-11-05
In a previous paper, the general approach for treatment of algebraic equations of different order in gravity theory was exposed, based on the important distinction between covariant and contravariant metric tensor components. In the present second part of the paper it has been shown that a multivariable cubic algebraic equation can also be parametrized by means of complicated, irrational and non-elliptic functions, depending on the elliptic Weierstrass function and its derivative. As a model example, the proposed before cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian has been investigated. This is quite different from the standard algebraic geometry approach, where only the parametrization of two-dimensional cubic algebraic equations has been considered. Also, the possible applications in modern cosmological theories has been commented.
Wide range equation of state for fluid hydrogen from density functional theory
Wang, Cong; Zhang, Ping [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China) [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Center for Applied Physics and Technology, Peking University, Beijing 100871 (China)
2013-09-15
Wide range equation of state (EOS) for liquid hydrogen is ultimately obtained by combining two kinds of density functional theory (DFT) molecular dynamics simulations, namely, first-principles molecular dynamics simulations and orbital-free molecular dynamics simulations. Specially, the present introduction of short cutoff radius pseudopotentials enables the EOS to be available in the range from 9.82 × 10{sup ?4} to 1.347 × 10{sup 3} g/cm{sup 3} and up to 5 × 10{sup 7} K. By comprehensively comparing with various attainable experimental and theoretical data, we derive the conclusion that our DFT-EOS can be readily and reliably applied to hydrodynamic simulations of the inertial confinement fusion.
Solution of the one-dimensional consolidation theory equation with a pseudospectral method
Sepulveda, N.
1991-01-01
The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.
Subrata Bhattacharjee; Matthew D. King; Chris Paolini
Temperature and velocity fields in a downward flame spread over flat solid fuels in a gravitational field are numerically simulated and compared with available experimental measurements and a simplified theory. The two-dimensional steady numerical model solves the mass, energy, species-mass, and momentum equations in the gas phase and the energy equation in the solid phase and includes gas-phase and pyrolysis
NASA Astrophysics Data System (ADS)
Godtliebsen, Ian H.; Hansen, Mads Bøttger; Christiansen, Ove
2015-01-01
We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10-2. With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format.
Single-particle Langevin model of particle temperature in dusty plasmas R. A. Quinn and J. Goree*
Goree, John
Single-particle Langevin model of particle temperature in dusty plasmas R. A. Quinn and J. Goree to predict the particle kinetic temperature. A Langevin approach is developed, generalizing a familiar temperature T based on a single-particle Langevin analysis. The Langevin approach has previously been used
NASA Technical Reports Server (NTRS)
Majda, G.
1985-01-01
A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.
Multinomial diffusion equation
Balter, Ariel I.; Tartakovsky, Alexandre M.
2011-06-24
We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N {yields} {infinity}, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
Marcel Ovidiu Vlad; John Ross
2002-01-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are
NASA Astrophysics Data System (ADS)
Planková, Barbora; Hrubý, Jan; Vinš, Václav
2013-05-01
We combined the density gradient theory (DGT) with the PC-SAFT and Peng-Robinson equations of state to model the homogeneous droplet nucleation and compared it to the classical nucleation theory (CNT) and experimental data. We also consider the effect of capillary waves on the surface tension. DGT predicts nucleation rates smaller than the CNT and slightly improves the temperature-dependent deviation of the predicted and experimental nucleation rates.
A kinetic-theory approach to turbulent chemically reacting flows
NASA Technical Reports Server (NTRS)
Chung, P. M.
1976-01-01
The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.
Heavy-quark Langevin dynamics and single-electron spectra in nucleus-nucleus collision
W. M. Alberico; A. Beraudo; A. De Pace; A. Molinari; M. Monteno; M. Nardi; F. Prino
2010-07-23
The stochastic dynamics of heavy quarks in the fireball produced in heavy-ion collisions is followed through numerical simulations based on the Langevin equation. The modification of the final p_T spectra (R_AA) of c and b quarks, hadrons and single-electrons with respect to pp collisions is studied. The transport coefficients are evaluated treating separately the contribution of soft and hard collisions. The initial heavy-quark spectra are generated according to NLO-pQCD, accounting for nuclear effects through recent nPDFs. The evolution of the medium is obtained from the output of two hydro-codes (ideal and viscous). The heavy-quark fragmentation into hadrons and their final semileptonic decays are implemented according to up to date experimental data. A comparison with RHIC data for non-photonic electron spectra is given.
Theoretical understanding of the problem with a singular drift term in the complex Langevin method
Nishimura, Jun
2015-01-01
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur in general when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
Theoretical understanding of the problem with a singular drift term in the complex Langevin method
Jun Nishimura; Shinji Shimasaki
2015-04-30
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur in general when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
Langevin dynamics of heavy flavors in relativistic heavy-ion collisions
W. M. Alberico; A. Beraudo; A. De Pace; A. Molinari; M. Monteno; M. Nardi; F. Prino
2010-09-13
We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution of soft and hard collisions. The evolution of the background medium is described by ideal/viscous hydrodynamics. Below the critical temperature the heavy quarks are converted into hadrons, whose semileptonic decays provide single-electron spectra to be compared with the current experimental data measured at RHIC. We focus on the nuclear modification factor R_AA and on the elliptic-flow coefficient v_2, getting, for sufficiently large p_T, a reasonable agreement.
Transport properties and Langevin dynamics of heavy quarks and quarkonia in the Quark Gluon Plasma
NASA Astrophysics Data System (ADS)
Beraudo, A.; De Pace, A.; Alberico, W. M.; Molinari, A.
2009-12-01
Quark Gluon Plasma transport coefficients for heavy quarks and QQ¯ pairs are computed through an extension of the results obtained for a hot QED plasma by describing the heavy-quark propagation in the eikonal approximation and by weighting the gauge-field configurations with the Hard Thermal Loop effective action. It is shown that such a model allows to correctly reproduce, at leading logarithmic accuracy, the results obtained by other independent approaches. The results are then inserted into a relativistic Langevin equation allowing to follow the evolution of the heavy-quark momentum spectra. Our numerical findings are also compared with the ones obtained in a strongly-coupled scenario, namely with the transport coefficients predicted (though with some limitations and ambiguities) by the AdS/CFT correspondence.
Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach
NASA Astrophysics Data System (ADS)
Beraudo, A.; De Pace, A.; Monteno, M.; Prino, F.; Alberico, W. M.; Molinari, A.; Nardi, M.
2014-03-01
A snapshot of the results for heavy-flavour observables in heavy-ion (AA) collisions at RHIC and LHC obtained with our transport calculations is displayed. The initial charm and beauty production is simulated through pQCD tools (POWHEG+PYTHIA) and is validated through the comparison with data from pp collisions. The propagation of c and b quarks in the medium formed in heavy-ion collisions is studied through a transport setup based on the relativistic Langevin equation. With respect to past works we perform a more systematic study, providing results with different choices of transport coefficients, either from weak-coupling calculations or from lattice-QCD simulations. Our findings are compared to a rich set of experimental data (D-mesons, non-photonic electrons, non-prompt J/?'s) which have meanwhile become accessible.
Signals for the QCD phase transition and critical point in a Langevin dynamical model
NASA Astrophysics Data System (ADS)
Herold, Christoph; Yan, Yu-Peng; Bleicher, Marcus
2013-03-01
The search for the critical point is one of the central issues that will be investigated in the upcoming FAIR project. For a profound theoretical understanding of the expected signals we go beyond thermodynamic studies and present a fully dynamical model for the chiral and deconfinement phase transition in heavy ion collisions. The corresponding order parameters are propagated by Langevin equations of motions on a thermal background provided by a fluid dynamically expanding plasma of quarks. By that we are able to describe nonequilibrium effects occurring during the rapid expansion of a hot fireball. For an evolution through the phase transition the formation of a supercooled phase and its subsequent decay crucially influence the trajectories in the phase diagram and lead to a significant reheating of the quark medium at highest baryon densities. Furthermore, we find inhomogeneous structures with high density domains along the first order transition line within single events.
Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach
A. Beraudo; A. De Pace; M. Monteno; F. Prino; W. M. Alberico; A. Molinari; M. Nardi
2013-07-29
A snapshot of the results for heavy-flavour observables in heavy-ion (AA) collisions at RHIC and LHC obtained with our transport calculations is displayed. The initial charm and beauty production is simulated through pQCD tools (POWHEG+PYTHIA) and is validated through the comparison with data from pp collisions. The propagation of c and b quarks in the medium formed in heavy-ion collisions is studied through a transport setup based on the relativistic Langevin equation. With respect to past works we perform a more systematic study, providing results with different choices of transport coefficients, either from weak-coupling calculations or from lattice-QCD simulations. Our findings are compared to a rich set of experimental data (D-mesons, non-photonic electrons, non-prompt J/\\psi's) which have meanwhile become accessible.
Heavy-quark Langevin dynamics and single-electron spectra in nucleus-nucleus collision
Alberico, W M; De Pace, A; Molinari, A; Monteno, M; Nardi, M; Prino, F
2011-01-01
The stochastic dynamics of heavy quarks in the fireball produced in heavy-ion collisions is followed through numerical simulations based on the Langevin equation. The modification of the final p_T spectra (R_AA) of c and b quarks, hadrons and single-electrons with respect to pp collisions is studied. The transport coefficients are evaluated treating separately the contribution of soft and hard collisions. The initial heavy-quark spectra are generated according to NLO-pQCD, accounting for nuclear effects through recent nPDFs. The evolution of the medium is obtained from the output of two hydro-codes (ideal and viscous). The heavy-quark fragmentation into hadrons and their final semileptonic decays are implemented according to up to date experimental data. A comparison with RHIC data for non-photonic electron spectra is given.
Heavy-quark Langevin dynamics and single-electron spectra in nucleus-nucleus collisions
NASA Astrophysics Data System (ADS)
Beraudo, A.; Alberico, W. M.; De Pace, A.; Molinari, A.; Monteno, M.; Nardi, M.; Prino, F.
2011-01-01
The stochastic dynamics of heavy quarks in the fireball produced in heavy-ion collisions is followed through numerical simulations based on the Langevin equation. The modification of the final pT spectra (RAA) of c and b quarks, hadrons and single-electrons with respect to pp collisions is studied. The transport coefficients are evaluated treating separately the contribution of soft and hard collisions. The initial heavy-quark spectra are generated according to NLO-pQCD, accounting for nuclear effects through recent nPDFs. The evolution of the medium is obtained from the output of two hydro-codes (ideal and viscous). The heavy-quark fragmentation into hadrons and their final semileptonic decays are implemented according to up-to-date experimental data. A comparison with RHIC data for non-photonic electron spectra is given.
Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach
Beraudo, A; Monteno, M; Prino, F; Alberico, W M; Molinari, A; Nardi, M
2014-01-01
A snapshot of the results for heavy-flavour observables in heavy-ion (AA) collisions at RHIC and LHC obtained with our transport calculations is displayed. The initial charm and beauty production is simulated through pQCD tools (POWHEG+PYTHIA) and is validated through the comparison with data from pp collisions. The propagation of c and b quarks in the medium formed in heavy-ion collisions is studied through a transport setup based on the relativistic Langevin equation. With respect to past works we perform a more systematic study, providing results with different choices of transport coefficients, either from weak-coupling calculations or from lattice-QCD simulations. Our findings are compared to a rich set of experimental data (D-mesons, non-photonic electrons, non-prompt J/\\psi's) which have meanwhile become accessible.
Langevin dynamics of heavy flavors in relativistic heavy-ion collisions
Alberico, W M; De Pace, A; Molinari, A; Monteno, M; Nardi, M; Prino, F
2011-01-01
We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution of soft and hard collisions. The evolution of the background medium is described by ideal/viscous hydrodynamics. Below the critical temperature the heavy quarks are converted into hadrons, whose semileptonic decays provide single-electron spectra to be compared with the current experimental data measured at RHIC. We focus on the nuclear modification factor R_AA and on the elliptic-flow coefficient v_2, getting, for sufficiently large p_T, a reasonable agreement.
Langevin Dynamics of Heavy Flavors in Relativistic Heavy-Ion Collisions
NASA Astrophysics Data System (ADS)
Alberico, W. M.; Beraudo, A.; de Pace, A.; Molinari, A.; Monteno, M.; Nardi, M.; Prino, F.
We study the stochastic dynamics of c and b quarks, produced in hard initial processes, in the hot medium created after the collision of two relativistic heavy ions. This is done through the numerical solution of the relativistic Langevin equation. The latter requires the knowledge of the friction and diffusion coefficients, whose microscopic evaluation is performed treating separately the contribution of soft and hard collisions. The evolution of the background medium is described by ideal/viscous hydrodynamics. Below the critical temperature the heavy quarks are converted into hadrons, whose semileptonic decays provide single-electron spectra to be compared with the current experimental data measured at RHIC. We focus on the nuclear modification factor RAA and on the elliptic-flow coefficient v2, getting, for sufficiently large pT, a reasonable agreement.
SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS
J. QIANG; R. RYNE; S. HABIB
2000-05-01
In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the friction and diffusion coefficients are computed from first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators.
Transport properties and Langevin dynamics of heavy quarks and quarkonia in the Quark Gluon Plasma
A. Beraudo; A. De Pace; W. M. Alberico; A. Molinari
2009-09-22
Quark Gluon Plasma transport coefficients for heavy quarks and quark-antiquark pairs are computed through an extension of the results obtained for a hot QED plasma by describing the heavy-quark propagation in the eikonal approximation and by weighting the gauge field configurations with the Hard Thermal Loop effective action. It is shown that such a model allows to correctly reproduce, at leading logarithmic accuracy, the results obtained by other independent approaches. The results are then inserted into a relativistic Langevin equation allowing to follow the evolution of the heavy-quark momentum spectra. Our numerical findings are also compared with the ones obtained in a strongly-coupled scenario, namely with the transport coefficients predicted (though with some limitations and ambiguities) by the AdS/CFT correspondence.
Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems
NASA Astrophysics Data System (ADS)
Walter, J.; Hartmann, C.; Maddocks, J. H.
2011-11-01
The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of ( n - d) curvilinear coordinatesparametrizingthe manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these ( n - d) configuration coordinates. Starting from this Lagrangian an unconstrained Hamiltonian H( q, p) on 2( n- d) dimensional phase space can then typically be defined in the standard way via a Legendre transform. Furthermore, if the system is in contact with a heat bath, the associated Langevin and Fokker-Planck equations can be introduced. Provided that an appropriate fluctuation-dissipation condition is satisfied, there will be a canonical equilibrium distribution of the Gibbs form exp(-? H) with respect to the flat measure dqdp in these 2( n - d) dimensional curvilinear phase space coordinates. The existence of ( n - d) coordinates satisfying the constraints is often guaranteed locally by an implicit function theorem. Nevertheless in many examples these coordinates cannot be constructed in any tractable form, even locally, so that other approaches are of interest. In ambient space formulations the dynamics are defined in the full original n-dimensional configuration space, and associated 2 n-dimensional phase space, with some version of Lagrange multipliers introduced so that the 2( n - d) dimensional sub-manifold of phase space implied by the holonomic constraints and their time derivative, is invariant under the dynamics. In this article we review ambient space formulations, and explain that for constrained dynamics there is in fact considerable freedom in how a Hamiltonian form of the dynamics can be constructed. We then discuss and contrast the Langevin and Fokker-Planck equations and their equilibrium distributions for the different forms of ambient space dynamics.
A new approach to the equation of state of silicate melts: An application of the theory of hard melts based on the hard sphere mixture model of a liquid. We assign a hard sphere for each cation. The effective size of a hard sphere for each component in silicate melts is determined. The temperature
Yonghua Huang; Qizheng Liao; Shimin Wei; Lei Guo
2010-01-01
Aiming at the dynamics of a front-wheel drive bicycle, a precise and effective mathematical model was constructed by use of Kane dynamics equations in form of screw theory in this paper. Firstly, partial velocity matrixes were achieved by recursion derivation of velocities and angular velocities of links. Then, dynamical model was developed according to the derived partial velocity matrixes. And
Ning Wu; Dahua Zhang
2005-08-01
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of gravity, the equation of motion of a classical mass point in gravitational gauge field is given by Newton's second law of motion. A relativistic form of the gravitational force on a mass point is deduced in this paper. Based on the spherical symmetric solution of the field equation and Newton's second law of motion, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity. From the study in this paper, an important qualitative conclusion on the nature of gravity is that gravity can be treated as a kind of physical interactions in flat Minkowski space-time, and the equation of motion of mass point in gravitational field can be given by Newton's second law of motion.
NASA Astrophysics Data System (ADS)
Wu, Rengmao; Zhang, Yaqin; Benítez, Pablo; Miñano, Juan C.
2014-12-01
The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L2 Monge-Kantorovich (LMK) theory, and introduce an efficient approach for finding the optimal mapping of the LMK problem. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.
Protein displacements under external forces: An atomistic Langevin dynamics approach.
Gnandt, David; Utz, Nadine; Blumen, Alexander; Koslowski, Thorsten
2009-02-28
We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples. In an environment akin to dilute solutions, even small proteins show relaxation times up to 50 ns. Atomically resolved Langevin dynamics computations have been performed for the stretched gramicidin A ion channel. PMID:19256629
NASA Astrophysics Data System (ADS)
Srokowski, Tomasz
2013-05-01
The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution similar to a Gaussian but tails have a power-law form. Dependence of the mean first passage time on model parameters is discussed. Properties of the stochastic resonance, emerging as a peak in the plot of the spectral amplification against the temperature, are discussed for various sets of the model parameters. The amplification rises with the memory and is largest for the cases corresponding to the large passage time.
NASA Astrophysics Data System (ADS)
Brödel, Johannes; He, Song
2010-06-01
Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in mathcal{N} = 4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed employing the recently proposed Grassmannian integral in mathcal{N} = 4 super Yang-Mills theory. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.
A Kinetic Theory Approach to Quantum Gravity
B. L. Hu
2002-04-22
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).
Kinoshita, Masahiro
2008-01-14
The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties. PMID:18205459
Testing a theory of aircraft noise annoyance: a structural equation analysis.
Kroesen, Maarten; Molin, Eric J E; van Wee, Bert
2008-06-01
Previous research has stressed the relevance of nonacoustical factors in the perception of aircraft noise. However, it is largely empirically driven and lacks a sound theoretical basis. In this paper, a theoretical model which explains noise annoyance based on the psychological stress theory is empirically tested. The model is estimated by applying structural equation modeling based on data from residents living in the vicinity of Amsterdam Airport Schiphol in The Netherlands. The model provides a good model fit and indicates that concern about the negative health effects of noise and pollution, perceived disturbance, and perceived control and coping capacity are the most important variables that explain noise annoyance. Furthermore, the model provides evidence for the existence of two reciprocal relationships between (1) perceived disturbance and noise annoyance and (2) perceived control and coping capacity and noise annoyance. Lastly, the model yielded two unexpected results. Firstly, the variables noise sensitivity and fear related to the noise source were unable to explain additional variance in the endogenous variables of the model and were therefore excluded from the model. And secondly, the size of the total effect of noise exposure on noise annoyance was relatively small. The paper concludes with some recommended directions for further research. PMID:18537376
ERIC Educational Resources Information Center
Ryan, Joseph; Brockmann, Frank
2009-01-01
Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…
NASA Astrophysics Data System (ADS)
Barth, Eric; Schlick, Tamar
1998-08-01
We present an efficient new method termed LN for propagating biomolecular dynamics according to the Langevin equation that arose fortuitously upon analysis of the range of harmonic validity of our normal-mode scheme LIN. LN combines force linearization with force splitting techniques and disposes of LIN's computationally intensive minimization (anharmonic correction) component. Unlike the competitive multiple-timestepping (MTS) schemes today—formulated to be symplectic and time-reversible—LN merges the slow and fast forces via extrapolation rather than "impulses;" the Langevin heat bath prevents systematic energy drifts. This combination succeeds in achieving more significant speedups than these MTS methods which are limited by resonance artifacts to an outer timestep less than some integer multiple of half the period of the fastest motion (around 4-5 fs for biomolecules). We show that LN achieves very good agreement with small-timestep solutions of the Langevin equation in terms of thermodynamics (energy means and variances), geometry, and dynamics (spectral densities) for two proteins in vacuum and a large water system. Significantly, the frequency of updating the slow forces extends to 48 fs or more, resulting in speedup factors exceeding 10. The implementation of LN in any program that employs force-splitting computations is straightforward, with only partial second-derivative information required, as well as sparse Hessian/vector multiplication routines. The linearization part of LN could even be replaced by direct evaluation of the fast components. The application of LN to biomolecular dynamics is well suited for configurational sampling, thermodynamic, and structural questions.
NASA Astrophysics Data System (ADS)
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E.
2015-03-01
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Híjar, Humberto
2015-02-01
We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490
Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory
Bylaska, Eric J.; Holst, Michael; Weare, John H.
2009-04-14
Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn-Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy e (in atomic units) was esitmated to be v (e;Z) = 122:37 * Z2:2346 /1:1173 , and the number of floating point operations per minimization step for a system of NA atoms was found to be 0(N3A*v(e,Z0) (e.g. Z=26, e=0.0015 au, and NA=100, the memory requirement and computational cost would be ~0.2 terabytes and ~25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric based refinement strategy to fix the error near the singularities.
Galvao, C.A. [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil)] [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil); Nutku, Y. [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)] [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)
1996-12-01
mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}
Jean-Michel Caillol; Jean-Luc Raimbault
2001-01-01
We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous Coulomb fluids with additional short-range interactions. This formalism is applied to derive the equation of state of the restricted primitive model of electrolytes in the low fugacity regime