Quasirelativistic Langevin equation.
Plyukhin, A V
2013-11-01
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A noncovariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically while their interaction is treated classically, i.e., by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (nonrelativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than, relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation and thus is qualitatively important.
Manufactured Turbulence with Langevin equations
Mishra, Aashwin
2016-01-01
By definition, Manufactured turbulence(MT) is purported to mimic physical turbulence rather than model it. The MT equations are constrained to be simple to solve and provide an inexpensive surrogate to Navier-Stokes based Direct Numerical Simulations (DNS) for use in engineering applications or theoretical analyses. In this article, we investigate one approach in which the linear inviscid aspects of MT are derived from a linear approximation of the Navier-Stokes equations while the non-linear and viscous physics are approximated via stochastic modeling. The ensuing Langevin MT equations are used to compute planar, quadratic turbulent flows. While much work needs to be done, the preliminary results appear promising.
Numerical simulation of the fractional Langevin equation
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Guo Peng
2012-01-01
Full Text Available In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional Langevin equation.
The complex chemical Langevin equation
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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.
The complex chemical Langevin equation.
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
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.
Relativistic Langevin equation for runaway electrons
Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.
2016-10-01
The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.
Self-guided Langevin dynamics via generalized Langevin equation.
Wu, Xiongwu; Brooks, Bernard R; Vanden-Eijnden, Eric
2016-03-05
Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.
Nonergodic solutions of the generalized Langevin equation.
Plyukhin, A V
2011-06-01
It is known that in the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory function), the generalized Langevin equation may have nonergodic solutions that do not relax to equilibrium values. It is shown that the equation may have nonergodic (nonstationary) solutions even if the integral of the memory function is finite and diffusion is normal.
Langevin equation path integral ground state.
Constable, Steve; Schmidt, Matthew; Ing, Christopher; Zeng, Tao; Roy, Pierre-Nicholas
2013-08-15
We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties.
Langevin equation with two fractional orders
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Lim, S.C. [Faculty of Engineering, Multimedia University, Jalan Multimedia, Cyberjaya 63100, Selangor Darul Ehsan (Malaysia)], E-mail: sclim@mmu.edu.my; Li Ming [School of Information Science and Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241 (China)], E-mail: mli@ee.ecnu.edu.cn; Teo, L.P. [Faculty of Information Technology, Multimedia University, Jalan Multimedia, Cyberjaya 63100, Selangor Darul Ehsan (Malaysia)], E-mail: lpteo@mmu.edu.my
2008-10-13
A new type of fractional Langevin equation of two different orders is introduced. The solutions for this equation, known as the fractional Ornstein-Uhlenbeck processes, based on Weyl and Riemann-Liouville fractional derivatives are obtained. The basic properties of these processes are studied. An example of the spectral density of ocean wind speed which has similar spectral density as that of Weyl fractional Ornstein-Uhlenbeck process is given.
Langevin Equations for Reaction-Diffusion Processes
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Generalized Langevin equation with tempered memory kernel
Liemert, André; Sandev, Trifce; Kantz, Holger
2017-01-01
We study a generalized Langevin equation for a free particle in presence of a truncated power-law and Mittag-Leffler memory kernel. It is shown that in presence of truncation, the particle from subdiffusive behavior in the short time limit, turns to normal diffusion in the long time limit. The case of harmonic oscillator is considered as well, and the relaxation functions and the normalized displacement correlation function are represented in an exact form. By considering external time-dependent periodic force we obtain resonant behavior even in case of a free particle due to the influence of the environment on the particle movement. Additionally, the double-peak phenomenon in the imaginary part of the complex susceptibility is observed. It is obtained that the truncation parameter has a huge influence on the behavior of these quantities, and it is shown how the truncation parameter changes the critical frequencies. The normalized displacement correlation function for a fractional generalized Langevin equation is investigated as well. All the results are exact and given in terms of the three parameter Mittag-Leffler function and the Prabhakar generalized integral operator, which in the kernel contains a three parameter Mittag-Leffler function. Such kind of truncated Langevin equation motion can be of high relevance for the description of lateral diffusion of lipids and proteins in cell membranes.
The Fractional Langevin Equation: Brownian Motion Revisited
Mainardi, Francesco
2008-01-01
We have revisited the Brownian motion on the basis of the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo on 1966. The importance of our approach is to model the Brownian motion more realistically than the usual one based on the classical Langevin equation, in that it takes into account also the retarding effects due to hydrodynamic backflow, i.e. the added mass and the Basset memory drag. On the basis of the two fluctuation-dissipation theorems and of the techniques of the Fractional Calculus we have provided the analytical expressions of the correlation functions (both for the random force and the particle velocity) and of the mean squared particle displacement. The random force has been shown to be represented by a superposition of the usual white noise with a "fractional" noise. The velocity correlation function is no longer expressed by a simple exponential but exhibits a slower decay, proportional to $t^{-3/2}$ as $t \\to \\infty...
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.
Critical exponent of the fractional Langevin equation.
Burov, S; Barkai, E
2008-02-22
We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal.
Deriving Langevin equations in curved spacetime
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Ramos, Rudnei O.; Tavares, Romulo F. [Universidade do Estado do Rio de Janeiro (UERJ), Rio de Janeiro, RJ (Brazil)
2013-07-01
Full text: Warm inflation is an inflationary scenario where the interactions between the inflaton and other degrees of freedom are considered. The effective equation of motion for the inflaton is in general of the form of a Langevin equation, that includes both quantum and thermal effects and where these effects manifest in the form of dissipation and stochastic noise terms, which are related by a generalized fluctuation-dissipation relation. The dissipation term is related to the interactions of the inflaton with other degrees of freedom of the thermal bath that can be obtained from the appropriate Feynman propagators. As the inflaton evolves into an expanding metric, these effects have to be taken into account when calculating the Green functions and consequently the Feynman propagators. In this work we present the considerations that must be made to calculate the Green functions in curved space (expanding metric) and in the presence of radiation in order to proper derive the effective evolution of the inflaton in the warm-inflation scenario. (author)
A Langevin equation approach to electron transfer reactions in the diabatic basis.
Song, XiaoGeng; Wang, Haobin; Van Voorhis, Troy
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.
Conditions for the validity of the quantum Langevin equation.
Frenkel, J; Taylor, J C
2012-01-01
From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.
Fractional Langevin equation and Riemann-Liouville fractional derivative.
Sau Fa, Kwok
2007-10-01
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.
Scaling of ballistic deposition from a Langevin equation.
Haselwandter, Christoph A; Vvedensky, Dimitri D
2006-04-01
An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions.
Langevin equation for systems with a preferred spatial direction
Belousov, Roman; Cohen, E. G. D.; Rondoni, Lamberto
2016-09-01
In this paper, we generalize the theory of Brownian motion and the Onsager-Machlup theory of fluctuations for spatially symmetric systems to equilibrium and nonequilibrium steady-state systems with a preferred spatial direction, due to an external force. To do this, we extend the Langevin equation to include a bias, which is introduced by an external force and alters the Gaussian structure of the system's fluctuations. In addition, by solving this extended equation, we provide a physical interpretation for the statistical properties of the fluctuations in these systems. Connections of the extended Langevin equation with the theory of active Brownian motion are discussed as well.
Numerical simulation of generalized Langevin equation with arbitrary correlated noise.
Lü, Kun; Bao, Jing-Dong
2005-12-01
A generalized Langevin equation with arbitrary correlated noise and associated frequency-dependent friction is simulated, which can lead to anomalous diffusion. The algorithm is realized by using the Fourier transform technique to generate noise and the stochastic Runge-Kutta method to solve the whole equation. Application to an acoustic phonon model, initial preparation-dependent ballistic diffusion, is shown.
Langevin equation model of dispersion in the convective boundary layer
Energy Technology Data Exchange (ETDEWEB)
Nasstrom, J S
1998-08-01
This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well
Langevin equation approach to diffusion magnetic resonance imaging.
Cooke, Jennie M; Kalmykov, Yuri P; Coffey, William T; Kerskens, Christian M
2009-12-01
The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a fractional generalization of the Langevin equation proposed by Lutz [E. Lutz, Phys. Rev. E 64, 051106 (2001)] pertaining to the fractional Brownian motion of a free particle coupled to a fractal heat bath. The results compare favorably with diffusion-weighted experiments acquired in human neuronal tissue using a 3 T MRI scanner.
Nuclear fission problem and Langevin equation
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M Sakhaee
2011-12-01
Full Text Available A combined dynamical and statistical model for fission was employed in our calculation. There is no doubt that a Langevin description plus a Monte Carlo treatment of the evaporation processes provide the most adequate dynamical description. In this paper, we would consider a strongly shaped dependent friction force and we use the numerical method rather than the analytical one. The objective of this article is to calculate the time dependent fission widths of the 224Th nucleus. The fission widths were calculated with both chaos-weighted wall friction (CWWF and wall friction (WF dissipations. The calculations are repeated for 100000 trajectories. The result was compared to the others' work. We use nuclear elongation coordinate with time and it is necessary to repeat the small steps many times to improve the accuracy.
Supersymmetric Langevin equation to explore free-energy landscapes.
Mossa, Alessandro; Clementi, Cecilia
2007-04-01
The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.
Temperature dependent fission fragment distribution in the Langevin equation
Institute of Scientific and Technical Information of China (English)
WANG Kun; MA Yu-Gang; ZHENG Qing-Shan; CAI Xiang-Zhou; FANG De-Qing; FU Yao; LU Guang-Cheng; TIAN Wen-Dong; WANG Hong-Wei
2009-01-01
The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.
Generalized Langevin equation formulation for anomalous polymer dynamics
Panja, D.
2010-01-01
For reproducing the anomalous—i.e., sub-diffusive or super-diffusive—behavior in some stochastic dynamical systems, the generalized Langevin equation (GLE) has gained considerable popularity in recent years. Motivated by the question of whether or not a system with anomalous dynamics can have the GL
Data-driven parameterization of the generalized Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Lei, Huan; Baker, Nathan A.; Li, Xiantao
2016-11-29
We present a data-driven approach to determine the memory kernel and random noise of the generalized Langevin equation. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. Further, we show that such an approximation can be constructed to arbitrarily high order. Within these approximations, the generalized Langevin dynamics can be embedded in an extended stochastic model without memory. We demonstrate how to introduce the stochastic noise so that the fluctuation-dissipation theorem is exactly satisfied.
Phase-space geometry of the generalized Langevin equation.
Bartsch, Thomas
2009-09-28
The generalized Langevin equation is widely used to model the influence of a heat bath upon a reactive system. This equation will here be studied from a geometric point of view. A dynamical phase space that represents all possible states of the system will be constructed, the generalized Langevin equation will be formally rewritten as a pair of coupled ordinary differential equations, and the fundamental geometric structures in phase space will be described. It will be shown that the phase space itself and its geometric structure depend critically on the preparation of the system: A system that is assumed to have been in existence forever has a larger phase space with a simpler structure than a system that is prepared at a finite time. These differences persist even in the long-time limit, where one might expect the details of preparation to become irrelevant.
Langevin and diffusion equation of turbulent fluid flow
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 C 0 , which arises from Lagrangian similarity theory. The value of C 0 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.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2010-01-01
Full Text Available We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments. However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation. This gives rise to the fractional Langevin equation with a single index. Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
Isoscaling of the Fission Fragments with Langevin Equation
Institute of Scientific and Technical Information of China (English)
WANG Kun; TIAN Wen-Dong; ZHONG Chen; ZHOU Xing-Fei; MA Yu-Gang; WEI Yi-Bin; CAI Xiang-Zhou; CHEN Jin-Gen; FANG De-Qing; GUO Wei; MA Guo-Liang; SHEN Wen-Qing
2005-01-01
@@ The Langevin equation is used to simulate the fission process of 112Sn + 112Sn and 116Sn + 116Sn. The mass distribution of the fission fragments are given by assuming the process of symmetric fission or asymmetric fission with the Gaussian probability sampling. The isoscaling behaviour has been observed from the analysis of fission fragments of both the reactions, and the isoscaling parameter α seems to be sensitive to the width of fission probability and the beam energy.
An adaptive stepsize method for the chemical Langevin equation.
Ilie, Silvana; Teslya, Alexandra
2012-05-14
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.
Transient aging in fractional Brownian and Langevin-equation motion.
Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf
2013-12-01
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t=0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on t(a) is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.
An Analysis of Vehicular Traffic Flow Using Langevin Equation
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Çağlar Koşun
2015-08-01
Full Text Available Traffic flow data are stochastic in nature, and an abundance of literature exists thereof. One way to express stochastic data is the Langevin equation. Langevin equation consists of two parts. The first part is known as the deterministic drift term, the other as the stochastic diffusion term. Langevin equation does not only help derive the deterministic and random terms of the selected portion of the city of Istanbul traffic empirically, but also sheds light on the underlying dynamics of the flow. Drift diagrams have shown that slow lane tends to get congested faster when vehicle speeds attain a value of 25 km/h, and it is 20 km/h for the fast lane. Three or four distinct regimes may be discriminated again from the drift diagrams; congested, intermediate, and free-flow regimes. At places, even the intermediate regime may be divided in two, often with readiness to congestion. This has revealed the fact that for the selected portion of the highway, there are two main states of flow, namely, congestion and free-flow, with an intermediate state where the noise-driven traffic flow forces the flow into either of the distinct regimes.
Data-driven parameterization of the generalized Langevin equation.
Lei, Huan; Baker, Nathan A; Li, Xiantao
2016-12-13
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
Data-driven parameterization of the generalized Langevin equation
Lei, Huan; Li, Xiantao
2016-01-01
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
Reconstruction of the modified discrete Langevin equation from persistent time series.
Czechowski, Zbigniew
2016-05-01
The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.
Self-consistent generalized Langevin equation for colloidal mixtures.
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.
On the environmental modes for the generalized Langevin equation.
Kawai, Shinnosuke
2015-09-07
The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
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.
Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
2004-01-01
The standard Langevin equation is a first order stochastic differential equation where the driving noise term is a Brownian motion. The marginal probability density is a solution to a linear partial differential equation called the Fokker-Planck equation. If the Brownian motion is replaced by so...... to a corresponding Langevin difference equation. Similar doubt can be traced in Grigoriu's work [Stochastic Calculus(2002)].......-called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...
On fractional Langevin equation involving two fractional orders
Baghani, Omid
2017-01-01
In numerical analysis, it is frequently needed to examine how far a numerical solution is from the exact one. To investigate this issue quantitatively, we need a tool to measure the difference between them and obviously this task is accomplished by the aid of an appropriate norm on a certain space of functions. For example, Sobolev spaces are indispensable part of theoretical analysis of partial differential equations and boundary integral equations, as well as are necessary for the analysis of some numerical methods for the solving of such equations. But most of articles that appear in this field usually use ‖.‖∞ in the space of C[a, b] which is very restrictive. In this paper, we introduce a new norm that is convenient for the fractional and singular differential equations. Using this norm, the existence and uniqueness of initial value problems for nonlinear Langevin equation with two different fractional orders are studied. In fact, the obtained results could be used for the classical cases. Finally, by two examples we show that we cannot always speak about the existence and uniqueness of solutions just by using the previous methods.
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Fractional Langevin equation: overdamped, underdamped, and critical behaviors.
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) alpha_{c}=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alpha_{R}=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_{chi_{1}}=0.527... and (iv) alpha_{chi_{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.
Recovering hidden dynamical modes from the generalized Langevin equation
Kawai, Shinnosuke; Miyazaki, Yusuke
2016-09-01
In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.
Bifurcation dynamics of the tempered fractional Langevin equation.
Zeng, Caibin; Yang, Qigui; Chen, YangQuan
2016-08-01
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Bifurcation dynamics of the tempered fractional Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Derivation of the generalized Langevin equation in nonstationary environments.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2011-03-21
The generalized Langevin equation (GLE) is extended to the case of nonstationary bath. The derivation starts with the Hamiltonian equation of motion of the total system including the bath, without any assumption on the form of Hamiltonian or the distribution of the initial condition. Then the projection operator formulation is utilized to obtain a low-dimensional description of the system dynamics surrounded by the nonstationary bath modes. In contrast to the ordinary GLE, the mean force becomes a time-dependent function of the position and the velocity of the system. The friction kernel is found to depend on both the past and the current times, in contrast to the stationary case where it only depends on their difference. The fluctuation-dissipation theorem, which relates the statistical property of the random force to the friction kernel, is also derived for general nonstationary cases. The resulting equation of motion is as simple as the ordinary GLE, and is expected to give a powerful framework to analyze the dynamics of the system surrounded by a nonstationary bath.
c -number quantum generalized Langevin equation for an open system
Kantorovich, L.; Ness, H.; Stella, L.; Lorenz, C. D.
2016-11-01
We derive a c -number generalized Langevin equation (GLE) describing the evolution of the expectation values xixit of the atomic position operators xi of an open system. The latter is coupled linearly to a harmonic bath kept at a fixed temperature. The equations of motion contain a non-Markovian friction term with the classical kernel [L. Kantorovich, Phys. Rev. B 78, 094304 (2008), 10.1103/PhysRevB.78.094304] and a zero mean non-Gaussian random force with correlation functions that depend on the initial preparation of the open system. We used a density operator formalism without assuming that initially the combined system was decoupled. The only approximation made in deriving quantum GLE consists of assuming that the Hamiltonian of the open system at time t can be expanded up to the second order with respect to operators of atomic displacements ui=xi-t (the "harmonization" approximation). The noise is introduced to ensure that sampling many quantum GLE trajectories yields exactly the average one. An explicit expression for the pair correlation function of the noise, consistent with the classical limit, is also proposed. Unlike the usually considered quantum operator GLE, the proposed c -number quantum GLE can be used in direct molecular dynamic simulations of open systems under general equilibrium or nonequilibrium conditions.
Description of quantum noise by a Langevin equation
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.
Directory of Open Access Journals (Sweden)
Smarandache F.
2010-04-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schroedinger equation.
Directory of Open Access Journals (Sweden)
Chen Yi
2011-01-01
Full Text Available We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
Figueiredo Camargo, R.; Capelas de Oliveira, E.; Vaz, J.
2009-12-01
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect.
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.
Langevin equation with fluctuating diffusivity: A two-state model.
Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji
2016-07-01
Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.
Energy Technology Data Exchange (ETDEWEB)
Viana, A., E-mail: Antoine.Viana@g2elab.grenoble-inp.f [Grenoble Electrical Engineering Lab (CNRS UMR5269), Universite de Grenoble, ENSE3, BP 46, 38402 Saint Martin d' Heres (France); Coulomb, J.-L.; Rouve, L.-L.; Cauffet, G. [Grenoble Electrical Engineering Lab (CNRS UMR5269), Universite de Grenoble, ENSE3, BP 46, 38402 Saint Martin d' Heres (France)
2010-01-15
The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.
Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Hu, Bei Lok
2016-01-01
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally-related spacetime is known. For example, from the Minkowski solution of Martin and Verdaguer, those of the Einstein-Langevin equations in conformally-flat spacetimes, especially for spatially-flat Friedmann-Robertson-Walker models, can be readily obtained.
Conformally related Einstein-Langevin equations for metric fluctuations in stochastic gravity
Satin, Seema; Cho, H. T.; Hu, Bei Lok
2016-09-01
For a conformally coupled scalar field we obtain the conformally related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally related spacetimes. In particular, we analyze the transformations of the influence action, the stress energy tensor, the noise kernel and the dissipation kernel. In due course the fluctuation-dissipation relation is also discussed. The analysis in this paper thereby facilitates a general solution to the Einstein-Langevin equation once the solution of the equation in a simpler, conformally related spacetime is known. For example, from the Minkowski solution of Martín and Verdaguer, those of the Einstein-Langevin equations in conformally flat spacetimes, especially for spatially flat Friedmann-Robertson-Walker models, can be readily obtained.
Grothaus, Martin
2012-01-01
In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivate...
Indian Academy of Sciences (India)
C. S. Leung; J. Y. Wei; T. Harko; Z. Kovacs
2011-03-01
In this paper, we introduce a simplified model for explaining the observations of optical intra-day variability (IDV) of the BL Lac Objects. We assume that the source of the IDV are the stochastic oscillations of an accretion disk around a supermassive black hole. The stochastic fluctuations on the vertical direction of the accretion disk are described by using a Langevin type equation with a damping term and a random, white noise type force. Furthermore, preliminary numerical simulation results are presented, which are based on the numerical analysis of the Langevin stochastic differential equation.
Kirchner, Jens; Meyer, Wolfgang; Elsholz, Markus; Hensel, Bernhard
2007-08-01
Using the Langevin equation we develop the model of a stochastic process subject to a given time-dependent regulatory mechanism. The effects of this nonstationarity on the statistical properties of the time series, i.e., on global and conditional probability densities and on the moments of the distribution, are derived. Application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the Langevin equation for time series of heart rate.
Fokker-Planck description for a linear delayed Langevin equation with additive Gaussian noise
Giuggioli, Luca; McKetterick, Thomas John; Kenkre, V. M.; Chase, Matthew
2016-09-01
We construct an equivalent probability description of linear multi-delay Langevin equations subject to additive Gaussian white noise. By exploiting the time-convolutionless transform and a time variable transformation we are able to write a Fokker-Planck equation (FPE) for the 1-time and for the 2-time probability distributions valid irrespective of the regime of stability of the Langevin equations. We solve exactly the derived FPEs and analyze the aging dynamics by studying analytically the conditional probability distribution. We discuss explicitly why the initially conditioned distribution is not sufficient to describe fully out a non-Markov process as both preparation and observation times have bearing on its dynamics. As our analytic procedure can also be applied to linear Langevin equations with memory kernels, we compare the non-Markov dynamics of a one-delay system with that of a generalized Langevin equation with an exponential as well as a power law memory. Application to a generalization of the Green-Kubo formula is also presented.
Datta, Sambhu N
2005-12-22
A quantum mechanical form of the Langevin equation is derived from an explicit consideration of the molecule-medium interaction, as advocated by Simons in 1978, and by using two identities in the interaction picture. This can be easily reduced to the classical regime, and further simplified to the macroscopic Langevin equation by considering the stochastic Langevin force autocorrelation function. One of the so-called Einstein relations appears as a byproduct. By following the methodology proposed by Simons, an exact expression for the momentum autocorrelation function is obtained. The latter can be used to calculate the zero-frequency macroscopic diffusion coefficient that is observed to satisfy the second Einstein relation. The formalism described above gives rise to the possibility of explicitly computing the transport characteristics such as friction constant and diffusion coefficient from the corresponding quantum statistical mechanical expressions. A discussion on the Langevin equation becomes complete only when the corresponding Fokker-Planck equation is obtained. Therefore, the probability of the evolution of states with a particular absolute magnitude of linear momentum from those of another momentum eigenvalue is quantum mechanically defined. This probability appears as a special average value of a projection operator and as a special projection operator correlation function. A classical identity is introduced that is shown to be valid also for the quantum mechanically defined probability function. By using this identity, the so-called Fokker-Planck equation for the evolution probability is easily established.
Langevin equation for the extended Rayleigh model with an asymmetric bath.
Plyukhin, Alexander V; Schofield, Jeremy
2004-02-01
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the nonlinear Langevin equation are derived. The transient solution of the nonlinear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.
Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2015-11-15
The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.
Perturbative and non-perturbative aspects non-Abelian Boltzmann-Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Boedeker, Dietrich. E-mail: bodeker@physik.uni-bielefeld.de
2002-12-30
We study the Boltzmann-Langevin equation which describes the dynamics of hot Yang-Mills fields with typical momenta of order of the magnetic screening scale g{sup 2}T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/g){sup -1}. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g{sup 2}T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann-Langevin equation.
A Langevin-Type Stochastic Differential Equation on a Space of Generalized Functionals
1988-08-01
Acknowledgements. The authors wish to thank Professors D. Dawson and L. Gorostiza for valuable discussions of the problems studied in this paper. The second...Convergence of Probability Measures, Wiley. New York-London-Sydney-Toronto, 1968. [2] T. Bojdecki and L.G. Gorostiza : Langevin equation for V’-valued Caussian
A simple model for Brownian motion leading to the Langevin equation
Grooth, de Bart G.
1999-01-01
A simple one-dimensional model is presented for the motion of a Brownian particle. It is shown how the collisions between a Brownian particle and its surrounding molecules lead to the Langevin equation, the power spectrum of the stochastic force, and the equipartition of kinetic energy.
Langevin equation with stochastic damping - Possible application to critical binary fluid
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.
Energy Technology Data Exchange (ETDEWEB)
Menezes, G.; Svaiter, N.F. E-mail: gsm@cbpf.br; nfuxsvai@cbpf.br
2006-04-15
We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient. (author)
Savović, Svetislav; Djordjevich, Alexandar
2002-05-20
The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based on the computer-simulated Langevin force. The solution matches the solution of the power-flow equation reported previously. Conceptually important steps of this work include (i) the expression of the power-flow equation in a form of the diffusion equation that is known to represent the solution of the stochastic differential equation describing processes with random perturbations and (ii) the recognition that mode coupling in multimode optical fibers is caused by random perturbations.
Baczewski, Andrew D
2013-01-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation (GLE) with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the ...
Brett, Tobias; Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Institute of Scientific and Technical Information of China (English)
MU Wei-Hua; OU-YANG Zhong-Can; Li Xiao-Qing
2011-01-01
The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reflect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems.By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2010-12-21
A framework recently developed for the extraction of a dynamic reaction coordinate to mediate reactions buried in a multidimensional Langevin equation is extended to the generalized Langevin equations without a priori assumption of the forms of the potential (in general, nonlinearly coupled systems) and the friction kernel. The equation of motion with memory effect can be transformed into an equation without memory at the cost of an increase in the dimensionality of the system, and hence the theoretical framework developed for the (nonlinear) Langevin formulation can be generalized to the non-Markovian process with colored noise. It is found that the increased dimension can be physically interpreted as effective modes of the fluctuating environment. As an illustrative example, we apply this theory to a multidimensional generalized Langevin equation for motion on the Müller-Brown potential surface with an exponential friction kernel. Numerical simulations find a boundary between the highly reactive region and the less reactive region in the space of initial conditions. The location of the boundary is found to depend significantly on both the memory kernel and the nonlinear couplings. The theory extracts a reaction coordinate whose sign determines the fate of the reaction taking into account thermally fluctuating environments, memory effect, and nonlinearities. It is found that the location of the boundary of reactivity is satisfactorily reproduced as the zero of the statistical average of the new reaction coordinate, which is an analytical functional of both the original position coordinates and velocities of the system, and of the properties of the environment.
Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation.
Ilie, Silvana
2012-12-21
Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.
Jeon, Jae-Hyung; Metzler, Ralf
2010-02-01
Motivated by subdiffusive motion of biomolecules 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.
General Laser Intensity Langevin Equation in a Single-Mode Laser Model
Institute of Scientific and Technical Information of China (English)
KE Sheng-Zhi; CAO Li; WU Da-Jin; YAO Kai-Lun
2001-01-01
A two-dimensional single-mode laser model is investigated, with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing λq, we can unify the two opposite intensity Langevin equations which correspond to the two special cases for ｜λq｜ → 0 and ｜λq｜ → 1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when λq varies.
Harko, Tiberiu; Mocanu, Gabriela
2014-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra...
Viñales, A. D.; Despósito, M. A.
2006-01-01
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
Entropy production in non-equilibrium systems described by the generalized Langevin equation
Sevilla, Francisco J.; Piña-Perez, Omar
2014-03-01
The generalized Langevin equation for a charged particle under the influence of time-dependent external fields, is employed to study the effects of non-Markovian dissipative terms in the entropy production of non-equilibrium states exhibiting non-zero mass flux. We present results for the case in which the fluctuation-dissipation relation holds. FJS and OPP acknowledge financial support from PAPIIT-IN113114 and PAEP-UNAM respectively.
Directory of Open Access Journals (Sweden)
Jessada Tariboon
2014-01-01
Full Text Available We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.
Chou, Chia-Chun
2017-02-01
The Schrödinger-Langevin equation is approximately solved by propagating individual quantum trajectories for barrier transmission problems. Equations of motion are derived through use of the derivative propagation method, which leads to a hierarchy of coupled differential equations for the amplitude of the wave function and the spatial derivatives of the complex action along each trajectory. Computational results are presented for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator. Frictional effects on the trajectory, the transmitted wave packet, and the transmission probability are analyzed.
Foundation of fractional Langevin equation: harmonization of a many-body problem.
Lizana, Ludvig; Ambjörnsson, Tobias; Taloni, Alessandro; Barkai, Eli; Lomholt, Michael A
2010-05-01
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 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 and a relation derived by Kollmann.
A path-integral Langevin equation treatment of low-temperature doped helium clusters.
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-14
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.
Study of dissipative dynamics in fission of hot nuclei using Langevin equation
Chaudhuri, G
2004-01-01
The fission of highly excited compound nuclei formed in heavy ion induced fusion reactions has emerged as a topic of considerable interest in the recent years. Dissipative dynamical models based on the Langevin equation were developed and were applied successfully for fission dynamics of highly excited heavy nuclei. However, Wall Friction(WF), the standard version of nuclear friction when incorporated in the Langevin dynamical model was not able to reproduce simultaneously experimental data for both prescission neutron multiplicity and fission probability. Consequently, an empirical reduction in the strength of the wall friction was found necessary to reproduce the experimental numbers by many workers. Interestingly, a modification of the wall friction was proposed recently where the reduction was achieved microscopically. This modified version is known as the chaos weighted wall friction(CWWF) which takes into account non-integrability of single particle motion. The work in my thesis aims at using this stron...
Fast Ice Detection for Wind Turbine Blades via the Langevin Equation
Fang, Haijun; Wang, Linpeng
2016-09-01
In this paper, a software-based algorithm for fast detection of ice on wind turbine blades is developed. The Langevin equation is used to create an entire or partial power curve with the high frequency data of wind speed and electrical power. Such a power curve is called the Langevin Power Curve (LPC). The LPC is obtained periodically. The period can be adjusted to be from 1 minute to 1 hour. For our application, the period is set to 5 minutes to allow enough data to generate an entire or partial LPC and then ice may be detected within a short period of time. The obtained LPC is compared to a reference power curve and then an ice index is calculated given that the condition for ice accretion is met. If the ice index is much higher or lower than 1, it may be concluded that there is ice on the anemometer or the blades of a wind turbine.
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.
Anomalous diffusion in nonhomogeneous media: time-subordinated Langevin equation approach.
Srokowski, Tomasz
2014-03-01
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Lévy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process subordinated to a random time: it separately takes into account effects related to the medium structure and the memory. Density distributions and moments are derived from the solutions of the corresponding Langevin equation and compared with the numerical calculations for the exact problem. Both subdiffusion and enhanced diffusion are predicted. Distribution of the process satisfies the fractional Fokker-Planck equation.
Implicit numerical schemes for the stochastic Liouville equation in Langevin form.
Håkansson, Pär; Nair, Prasanth B
2011-05-28
We present and numerically test implicit as well as explicit numerical schemes for solving the Stochastic Liouville Equation in Langevin form. It is found that implicit schemes provide significant gain in robustness, for example, when nonsecular Hamiltonian terms cannot be ignored in electron and nuclear spin resonance. Implicit schemes open up several spectroscopic relaxation problems for direct interpretation using the Stochastic Liouville Equation. To illustrate the proposed numerical schemes, studies are presented for an electron paramagnetic resonance problem involving a coordinated copper complex and a fluorescence problem.
Langevin equation with colored noise for constant-temperature molecular dynamics simulations.
Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele
2009-01-16
We discuss the use of a Langevin equation with a colored (correlated) noise to perform constant-temperature molecular dynamics. Since the equations of motion are linear in nature, it is easy to predict the response of a Hamiltonian system to such a thermostat and to tune at will the relaxation time of modes of different frequency. This allows one to optimize the time needed for equilibration and to generate independent configurations. We show how this frequency-dependent response can be exploited to control the temperature of Car-Parrinello-like dynamics without affecting the adiabatic separation of the electronic degrees of freedom from the vibrations of the ions.
Brett, Tobias; Galla, Tobias
2013-06-21
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
Energy Technology Data Exchange (ETDEWEB)
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.
Laws of large numbers and langevin approximations for stochastic neural field equations.
Riedler, Martin G; Buckwar, Evelyn
2013-01-23
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.
Baczewski, Andrew D; Bond, Stephen D
2013-07-28
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks
Indian Academy of Sciences (India)
Chun Sing Leung; Gabriela Mocanu; Tiberiu Harko
2014-09-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation–dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
Indian Academy of Sciences (India)
Wang Zhi-Yun; Chen Pei-Jie
2016-06-01
A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent $H$. The results show that as $H$ increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.
Yang, Bo; Zhang, Xiao; Zhang, Lu; Luo, Mao-Kang
2016-08-01
The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.
Naqvi, K R
2005-01-01
Ornstein and his coauthors, who constructed a dynamical theory of Brownian motion, taking the equation $mdv/dt =-\\zeta v+X$ as their starting point, usually named the equation after Einstein alone or after both Einstein and Langevin; furthermore, Ornstein, who was the first to extract from this equation the correct expression for $\\bar{\\Delta^2}$, the mean-squared distance covered by a Brownian particle, credited de Haas-Lorentz, rather than Langevin, for finding the stationary limit of $\\bar{\\Delta^2}$. A glance at Einstein's 1907 paper, titled ``Theoretical remarks on Brownian motion'', should suffice to convince one that it is not unfair to attribute the {\\it conception} of the above equation, now universally known as the Langevin equation, to Einstein. Langevin's avowed aim in his 1908 article was to recover, through a route that was `infinitely more simple', Einstein's 1905 expression for the diffusion coefficient, but a careful reading of Langevin's paper shows that--depending on how one interprets his ...
On the Generalized Langevin Equation for a Rouse Bead in a Nonequilibrium Bath
Vandebroek, Hans; Vanderzande, Carlo
2017-04-01
We present the reduced dynamics of a bead in a Rouse chain which is submerged in a bath containing a driving agent that renders it out-of-equilibrium. We first review the generalized Langevin equation of the middle bead in an equilibrated bath. Thereafter, we introduce two driving forces. Firstly, we add a constant force that is applied to the first bead of the chain. We investigate how the generalized Langevin equation changes due to this perturbation for which the system evolves towards a steady state after some time. Secondly, we consider the case of stochastic active forces which will drive the system to a nonequilibrium state. Including these active forces results in an extra contribution to the second fluctuation-dissipation relation. The form of this active contribution is analysed for the specific case of Gaussian, exponentially correlated active forces. We also discuss the resulting rich dynamics of the middle bead in which various regimes of normal diffusion, subdiffusion and superdiffusion can be present.
A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation
Energy Technology Data Exchange (ETDEWEB)
Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co
2015-05-15
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.
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
Grima, Ramon; Thomas, Philipp; Straube, Arthur V
2011-08-28
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 Ω(-3∕2) for reaction systems which do not obey detailed balance and at least accurate to order Ω(-2) for systems obeying detailed balance, where Ω 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 Ω(-1∕2) and variance estimates accurate to order Ω(-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.
Usang, M. D.; Ivanyuk, F. A.; Ishizuka, C.; Chiba, S.
2016-10-01
Nuclear fission is treated by using the Langevin dynamical description with macroscopic and microscopic transport coefficients (mass and friction tensors), and it is elucidated how the microscopic (shell and pairing) effects in the transport coefficients, especially their dependence on temperature, affects various fission observables. We found that the microscopic transport coefficients, calculated by linear response theory, change drastically as a function of temperature: in general, the friction increases with growing temperature while the mass tensor decreases. This temperature dependence brings a noticeable change in the mass distribution and kinetic energies of fission fragments from nuclei around 236U at an excitation energy of 20 MeV. The prescission kinetic energy decreases from 25 MeV at low temperature to about 2.5 MeV at high temperature. In contrast, the Coulomb kinetic energy increases as the temperature increases. Interpolating the microscopic transport coefficients among the various temperatures enabled our Langevin equation to use the microscopic transport coefficients at a deformation-dependent local temperature of the dynamical evolution. This allowed us to compare directly the fission observables of both macroscopic and microscopic calculations, and we found almost identical results under the conditions considered in this work.
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C
2010-04-28
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m(1) pairs of reversible reactions and m(2) irreversible reactions there is another, simple formulation of the CLE with only m(1) + m(2) Wiener processes, whereas the standard approach uses 2(m(1) + m(2)). We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch.
Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O
2014-11-01
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-09-01
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied.
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.
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 delta 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.
Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Institute of Scientific and Technical Information of China (English)
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
Accelerating the convergence of path integral dynamics with a generalized Langevin equation.
Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele
2011-02-28
The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.
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.
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.
Grebenkov, Denis S; Vahabi, Mahsa
2014-01-01
We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan
2015-08-01
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, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present 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 phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.
Institute of Scientific and Technical Information of China (English)
XING Yong-Zhong
2009-01-01
The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.
Jafari, G Reza; Sahimi, Muhammad; Rasaei, M Reza; Tabar, M Reza Rahimi
2011-02-01
Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs ϕ(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=ϕ(h+δh)-ϕ(h) is a stationary and Markov process, characterized by a Markov length scale h(M). The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y(0),h(0)) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured.
Mélykúti, Bence
2010-01-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.
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
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
Koehl, Patrice; Delarue, Marc
2010-02-14
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
Mankin, R; Laas, K; Sauga, A
2011-06-01
The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.
The Schrödinger–Langevin equation with and without thermal fluctuations
Energy Technology Data Exchange (ETDEWEB)
Katz, R., E-mail: roland.katz@subatech.in2p3.fr; Gossiaux, P.B., E-mail: Pol-Bernard.Gossiaux@subatech.in2p3.fr
2016-05-15
The Schrödinger–Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.
Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei
2013-09-28
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.
Lázaro-Lázaro, Edilio; Mendoza-Méndez, Patricia; Elizondo-Aguilera, Luis Fernando; Perera-Burgos, Jorge Adrián; Ramírez-González, Pedro Ezequiel; Pérez-Ángel, Gabriel; Castañeda-Priego, Ramón; Medina-Noyola, Magdaleno
2017-05-01
A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from a ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.
Institute of Scientific and Technical Information of China (English)
Liu Jian; Wang Hai-Yan; Bao Jing-Dong
2013-01-01
A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed,which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling.This model allows ballistic diffusion and classical localization simultaneously,in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken.The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium,however,when the system starts from nonthermal conditions,it does not approach the equilibration even though a nonlinear potential is used to bound the particle,this can be confirmed by the zeroth law of thermodynamics.In the dynamics of Brownian localization,due to the memory damping function inducing a constant term,our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum.The coupled oscillator chain with a fixed end boundary acts as a heat bath,which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration,we investigate this problem from the viewpoint of nonergodicity.
Cugliandolo, Leticia F.; Lecomte, Vivien
2017-08-01
The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known Ito prescription (dB2 = dt ) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.
Sanghi, T; Aluru, N R
2013-03-28
In this work, we combine our earlier proposed empirical potential based quasi-continuum theory, (EQT) [A. V. Raghunathan, J. H. Park, and N. R. Aluru, J. Chem. Phys. 127, 174701 (2007)], which is a coarse-grained multiscale framework to predict the static structure of confined fluids, with a phenomenological Langevin equation to simulate the dynamics of confined fluids in thermal equilibrium. An attractive feature of this approach is that all the input parameters to the Langevin equation (mean force profile of the confined fluid and the static friction coefficient) can be determined using the outputs of the EQT and the self-diffusivity data of the corresponding bulk fluid. The potential of mean force profile, which is a direct output from EQT is used to compute the mean force profile of the confined fluid. The density profile, which is also a direct output from EQT, along with the self-diffusivity data of the bulk fluid is used to determine the static friction coefficient of the confined fluid. We use this approach to compute the mean square displacement and survival probabilities of some important fluids such as carbon-dioxide, water, and Lennard-Jones argon confined inside slit pores. The predictions from the model are compared with those obtained using molecular dynamics simulations. This approach of combining EQT with a phenomenological Langevin equation provides a mathematically simple and computationally efficient means to study the impact of structural inhomogeneity on the self-diffusion dynamics of confined fluids.
Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics.
Yeomans-Reyna, L; Chávez-Rojo, M A; Ramírez-González, P E; Juárez-Maldonado, R; Chávez-Páez, M; Medina-Noyola, M
2007-10-01
This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.
Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George
2016-05-01
The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.
Directory of Open Access Journals (Sweden)
Christianto V.
2010-07-01
Full Text Available In this article, we find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schrödinger equation.
Energy Technology Data Exchange (ETDEWEB)
Nadler, Boaz [Department of Mathematics, Yale University, New-Haven, CT 06520 (United States); Schuss, Zeev [Department of Applied Mathematics, Tel-Aviv University, Ramat-Aviv 69978, Tel-Aviv (Israel); Singer, Amit [Department of Applied Mathematics, Tel-Aviv University, Ramat-Aviv 69978, Tel-Aviv (Israel); Eisenberg, R S [Department of Molecular Biophysics and Physiology, Rush Medical Center, 1750 Harrison Street, Chicago, IL 60612 (United States)
2004-06-09
Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels.
Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches.
Schluttig, Jakob; Alamanova, Denitsa; Helms, Volkhard; Schwarz, Ulrich S
2008-10-21
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 to 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%. 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 modeling of the dynamics of large protein complexes.
A Discussion on Whether 15-20C Are All Skin Nuclei via Isospin-dependent Boltzmann-Langevin Equation
Institute of Scientific and Technical Information of China (English)
CHEN Yu; ZHANG Feng-Shou; SU Jun
2009-01-01
A new attempt of calculation for the total reaction cross sections (σR) has been carried out within the isospin-dependent Boltzmann-Langevin equation in the intermediate energy heavy-ion collision of isotopes of G. The σR of both stable and exotic nuclei are reproduced rather well. The incident energy and isospin dependencies of σR have been investigated. It is found that the isospin effect is comparatively remarkable at intermediate energy. It is also found that ~(15-18)C are neutron skin nuclei but for ~(19)C and ~(20)C we cannot draw a conclusion whether they have halo structures.
Despósito, M A; Viñales, A D
2008-03-01
We investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized Langevin equation. Using Laplace analysis together with Tauberian theorems we derive asymptotic expressions for the mean values, variances, and velocity autocorrelation function in terms of the long-time behavior of the memory kernel and the correlation function of the random force. The internal and external noise cases are analyzed. A simple criterion to determine if the diffusion process is normal or anomalous is established.
Colmenares, Pedro J; López, Floralba; Olivares-Rivas, Wilmer
2009-12-01
We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.
Copperman, J; Guenza, M G
2015-07-23
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.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas, E-mail: pnroy@uwaterloo.ca [Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Gajda, Janusz; Magdziarz, Marcin
2010-07-01
In this paper we introduce a Langevin-type model of subdiffusion with tempered α-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales. We derive general properties of tempered anomalous diffusion from the theory of tempered α-stable processes, in particular we find the form of the fractional Fokker-Planck equation corresponding to the tempered subdiffusion. We also construct an algorithm of simulation of sample paths of the introduced process. We apply the algorithm to approximate solutions of the fractional Fokker-Planck equation and to study statistical properties of the tempered subdiffusion via Monte Carlo methods.
Inelastic X-ray scattering on liquid benzene analyzed using a generalized Langevin equation
Yoshida, Koji; Fukuyama, Nami; Yamaguchi, Toshio; Hosokawa, Shinya; Uchiyama, Hiroshi; Tsutsui, Satoshi; Baron, Alfred Q. R.
2017-07-01
The dynamic structure factor, S(Q,ω), of liquid benzene was measured by meV-resolved inelastic X-ray scattering (IXS) and analyzed using a generalized Langevin model with a memory function including fast, μ-relaxation and slow, structural, α-relaxation. The model well reproduced the experimental S(Q,ω) of liquid benzene. The dispersion relation of the collective excitation energy yields the high-frequency sound velocity for liquid benzene as related to the α-relaxation. The ratio of the high-frequency to the adiabatic sound velocity is approximately 1.5, larger to that of carbon tetrachloride and smaller than those of methanol and water, reflecting the nature of intermolecular interactions.
Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.
Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Iglič, Veronika; Iglič, 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.
Attanasio, Felipe
2013-01-01
Nesta Dissertação apresentamos um estudo numéerico em uma dimensão espacial da equação de Ginzburg-Landau-Langevin (GLL), com ênfase na aplicabilidade de um método de perturbação estocástico e na mecânica estatística de defeitos topológicos em modelos de campos escalares reais. Revisamos brevemente conceitos de mecânica estatística de sistemas em equilíbrio e próximos a ele e apresentamos como a equação de GLL pode ser usada em sistemas que exibem transições de fase, na quantização estocástic...
Barocchi, Fabrizio; Bafile, Ubaldo; Sampoli, Marco
2012-02-01
We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected.
Abe, Yuya; Fukushima, Kenji
2016-11-01
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian ansatz. We find that the Gaussian ansatz captures the essential and even quantitative features of the CLE results quite well when they converge to the exact answer, as well as the border of the unstable region where the CLE converges to a wrong answer. The Gaussian ansatz is therefore useful for looking into this convergence problem and we find that the exact answer in the unstable region is nicely reproduced by another solution that is naively excluded from the stability condition. We consider the Gaussian probability distributions corresponding to multiple solutions along the Lefschetz thimble to discuss the stability and the locality. Our results suggest a prescription to improve the convergence of the CLE simulation to the exact answer.
Akimoto, Takuma; Yamamoto, Eiji
2016-06-01
We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.
Abe, Yuya
2016-01-01
We investigate a simple model using the numerical simulation in the complex Langevin equation (CLE) and the analytical approximation with the Gaussian Ansatz. We find that the Gaussian Ansatz captures the essential and even quantitative features of the CLE results quite well including unwanted behavior in the unstable region where the CLE converges to a wrong answer. The Gaussian Ansatz is therefore useful for looking into this convergence problem and we find that the exact answer in the unstable region is nicely reproduced by another solution that is naively excluded from the stability condition. We consider the Gaussian probability distributions corresponding to multiple solutions along the Lefschetz thimble to discuss the stability and the locality. Our results suggest a prescription to improve the convergence of the CLE simulation to the exact answer.
Berthoumieux, Hélène
2016-01-01
Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a non-equilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a Chemical Langevin Equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, estimate the deviation of the fluctuation-dissipation theorem and the range of...
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.
Energy Technology Data Exchange (ETDEWEB)
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.
Basharov, A. M.
2012-09-01
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.
Sotiropoulos, Vassilios; Kaznessis, Yiannis N
2008-01-07
Models involving stochastic differential equations (SDEs) play a prominent role in a wide range of applications where systems are not at the thermodynamic limit, for example, biological population dynamics. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to systems of stiff SDEs with multiple multiplicative noise. The algorithm is validated using a subclass of SDEs called chemical Langevin equations that appear in the description of dilute chemical kinetics models, with important applications mainly in biology. Three representative examples are used to test and report on the behavior of the proposed scheme. We demonstrate the advantages and disadvantages over fixed time step integration schemes of the proposed method, showing that the adaptive time step method is considerably more stable than fixed step methods with no excessive additional computational overhead.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-14
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.
Pankavich, Stephen; Miao, Yinglong; Ortoleva, Peter
2010-01-01
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 ...
Berthoumieux, H.
2016-07-01
Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined.
Berthoumieux, H
2016-07-01
Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined.
Gupta, Shamik; Bandyopadhyay, Malay
2011-10-01
We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
Popov, Alexander V; Hernandez, Rigoberto
2013-09-01
Kawai and Komatsuzaki [J. Chem. Phys. 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys. 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys. 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.
Pankavich, S; Shreif, Z; Miao, Y; Ortoleva, P
2009-05-21
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.
Olivares-Rivas, Wilmer; Colmenares, Pedro J.
2016-09-01
The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.
Uneyama, Takashi; Miyaguchi, Tomoshige; Akimoto, Takuma
2015-09-01
The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.
Overdamped fractional Langevin equation and its stochastic resonance%过阻尼分数阶Langevin方程及其随机共振术
Institute of Scientific and Technical Information of China (English)
高仕龙; 钟苏川; 韦鹍; 马洪
2012-01-01
By choosing an appropriate damping kernel function of generalized Langevin equation, fractional Langevin equation （FLE） is derived in the case of overdamped condition. With the theory of anomalous diffusion and the memory of fractional derivatives, the physical meaning of FLE is discussed. Moreover, the internal mechanism of stochastic resonance about FLE is obtained. Finally, the numerical simulation shows that in a certain range of the order, stochastic resonance appears in FLE, and it is evident that the SNR gain in fractional Langevin equation is better than that of the integer-order situation.%通过对广义Langevin方程阻尼核函数的适当选取，在过阻尼的情形下，推导出分数阶Langevin方程．给合反常扩散理论和分数阶导数的记忆性，讨论了分数阶Langevin方程的物理意义，进而得出分数阶Langevin方程产生随机共振的内在机理．数值模拟表明，在一定的阶数范围内，分数阶Langevin方程可以产生随机共振，并且分数阶下的信噪比增益好于整数阶情形．
Ververis, Antonios; Schmuck, Markus
2017-09-01
We consider upscaled/homogenized Cahn-Hilliard/Ginzburg-Landau phase field equations as mesoscopic formulations for interfacial dynamics in strongly heterogeneous domains such as porous media. A recently derived effective macroscopic formulation, which takes systematically the pore geometry into account, is computationally validated. To this end, we compare numerical solutions obtained by fully resolving the microscopic pore-scale with solutions of the upscaled/homogenized porous media formulation. The theoretically derived convergence rate O (ɛ 1 / 4) is confirmed for circular pore-walls. An even better convergence of O (ɛ1) holds for square shaped pore-walls. We also compute the homogenization error over time for different pore geometries. We find that the quality of the time evolution shows a complex interplay between pore geometry and heterogeneity. Finally, we study the coarsening of interfaces in porous media with computations of the homogenized equation and the microscopic formulation fully resolving the pore space. We recover the experimentally validated and theoretically rigorously derived coarsening rate of O (t 1 / 3) in the periodic porous media setting. In the case of critical quenching and after adding thermal noise to the microscopic porous media formulation, we observe that the influence of thermal fluctuations on the coarsening rate shows after a short, expected phase of universal coarsening, a sharp transition towards a different regime.
Bouzat, Sebastián
2016-01-01
One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.
Optimal Transmission Policies for Energy Harvesting Two-hop Networks
Orhan, Oner
2012-01-01
In this paper, a two-hop communication system with energy harvesting nodes is considered. Unlike battery powered wireless nodes, both the source and the relay are able to harvest energy from environment during communication, therefore, both data and energy causality over the two hops need to be considered. Assuming both nodes know the harvested energies in advance, properties of optimal transmission policies to maximize the delivered data by a given deadline are identified. Using these properties, optimal power allocation and transmission schedule for the case in which both nodes harvest two energy packets is developed.
Beyond complex Langevin equations
Wosiek, Jacek
2016-01-01
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex slope. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time. Such construction is then explicitly carried through in the second part of this presentation. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The approach is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field -- a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an amusing interpretation of ...
Colmenero, J
2015-07-28
We show that the universal behavior of the Rouse-mode relaxation in polymer systems - which has been recently reported from experimental data [S. Arrese-Igor, et al., Phys. Rev. Lett., 2014, 113, 078302] - can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation formalism and (ii) a memory function which takes into account the coupling between intra-chain dynamics and collective dynamics. This approach opens the way for generalizing the magnitudes probing chain dynamics in polymer systems.
On the Effective Capacity of Two-Hop Communication Systems
Qiao, Deli; Velipasalar, Senem
2010-01-01
In this paper, two-hop communication between a source and a destination with the aid of an intermediate relay node is considered. Both the source and intermediate relay node are assumed to operate under statistical quality of service (QoS) constraints imposed as limitations on the buffer overflow probabilities. It is further assumed that the nodes send the information at fixed power levels and have perfect channel side information. In this scenario, the maximum constant arrival rates that can be supported by this two-hop link are characterized by finding the effective capacity. Through this analysis, the impact upon the throughput of having buffer constraints at the source and intermediate-hop nodes is identified.
Minier, J P; Chibbaro, S
2010-01-01
The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Physics Reports, Vol. 352/1-3, 2001 ]. Consequently, the present work is mainly focused on complementary aspects, that are often overlooked and that require particular attention. In particular, the following points are analysed : the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of twoway coupling, the theoretical and numerical evaluations of particle averages and the fulfilment of the particle mass-continuity constraint. The theoretical model is developed within the PDF formalism. The important-physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation (SDE) written in continuous time (Langevin equations) for the veloci...
Duplex Schemes in Multiple Antenna Two-Hop Relaying
Directory of Open Access Journals (Sweden)
Anja Klein
2008-04-01
Full Text Available A novel scheme for two-hop relaying defined as space division duplex (SDD relaying is proposed. In SDD relaying, multiple antenna beamforming techniques are applied at the intermediate relay station (RS in order to separate downlink and uplink signals of a bi-directional two-hop communication between two nodes, namely, S1 and S2. For conventional amplify-and-forward two-hop relaying, there appears a loss in spectral efficiency due to the fact that the RS cannot receive and transmit simultaneously on the same channel resource. In SDD relaying, this loss in spectral efficiency is circumvented by giving up the strict separation of downlink and uplink signals by either time division duplex or frequency division duplex. Two novel concepts for the derivation of the linear beamforming filters at the RS are proposed; they can be designed either by a three-step or a one-step concept. In SDD relaying, receive signals at S1 are interfered by transmit signals of S1, and receive signals at S2 are interfered by transmit signals of S2. An efficient method in order to combat this kind of interference is proposed in this paper. Furthermore, it is shown how the overall spectral efficiency of SDD relaying can be improved if the channels from S1 and S2 to the RS have different qualities.
Effective Capacity of Two-Hop Wireless Communication Systems
Qiao, Deli; Velipasalar, Senem
2011-01-01
A two-hop wireless communication link in which a source sends data to a destination with the aid of an intermediate relay node is studied. It is assumed that there is no direct link between the source and the destination, and the relay forwards the information to the destination by employing the decode-and-forward scheme. Both the source and intermediate relay nodes are assumed to operate under statistical quality of service (QoS) constraints imposed as limitations on the buffer overflow probabilities. The maximum constant arrival rates that can be supported by this two-hop link in the presence of QoS constraints are characterized by determining the effective capacity of such links as a function of the QoS parameters and signal-to-noise ratios at the source and relay, and the fading distributions of the links. The analysis is performed for both full-duplex and half-duplex relaying. Through this study, the impact upon the throughput of having buffer constraints at the source and intermediate relay nodes is ide...
Lucarini, Valerio; Willeit, Matteo
2011-01-01
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies and show, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation...
Turchenkov, D A; Boronovskiĭ, 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.
Bettencourt, L M A
2001-01-01
I consider several Langevin and Fokker-Planck classes of dynamics for scalar field theories in contact with a thermal bath at temperature T. These models have been applied recently in the numerical description of the dynamics of second order phase transitions and associated topological defect formation as well as in other studies of these critical phenomena. Closed form solutions of the Fokker-Planck equation are given for the harmonic potential and a dynamical mean-field approximation is developed. These methods allow for an analytical discussion of the behavior of the theories in several circumstances of interest such as critical slowing down at a second order transition and the development of spinodal instabilities. These insights allow for a more detailed understanding of several numerical studies in the literature.
The Langevin Limit of the Nosé-Hoover-Langevin Thermostat
Frank, J.E.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nos\\'{e}-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of
The Langevin limit of the Nosé-Hoover-Langevin thermostat
Frank, J.; Gottwald, G.A.
2011-01-01
In this note we study the asymptotic limit of large variance in a stochastically perturbed thermostat model, the Nosé-Hoover-Langevin device. We show that in this limit, the model reduces to a Langevin equation with one-dimensional Wiener process, and that the perturbation is in the direction of the
Queue-Aware Distributive Resource Control for Delay-Sensitive Two-Hop MIMO Cooperative Systems
Wang, Rui; Cui, Ying
2010-01-01
In this paper, we consider a queue-aware distributive resource control algorithm for two-hop MIMO cooperative systems. We shall illustrate that relay buffering is an effective way to reduce the intrinsic half-duplex penalty in cooperative systems. The complex interactions of the queues at the source node and the relays are modeled as an average-cost infinite horizon Markov Decision Process (MDP). The traditional approach solving this MDP problem involves centralized control with huge complexity. To obtain a distributive and low complexity solution, we introduce a linear structure which approximates the value function of the associated Bellman equation by the sum of per-node value functions. We derive a distributive two-stage two-winner auction-based control policy which is a function of the local CSI and local QSI only. Furthermore, to estimate the best fit approximation parameter, we propose a distributive online stochastic learning algorithm using stochastic approximation theory. Finally, we establish techn...
Some properties of the Langevin model for dispersion
De Baas, A.F.
1988-01-01
The Langevin Equation is used to describe dispersion of pollutants in the atmosphere. The theoretical background for the equation is discussed in length and a review on previous treatments and applications is given. It is shown that the Langevin equation can describe dispersion in complex circumstan
Two-hop Secure Communication Using an Untrusted Relay
He, Xiang
2009-01-01
We consider a source-destination pair that can only communicate through an untrusted intermediate relay node. The intermediate node is willing to employ a designated relaying scheme to facilitate reliable communication between the source and the destination. Yet, the information it relays needs to be kept secret from it. In this two-hop communication scenario, where the use of the untrusted relay node is essential, we find that a positive secrecy rate is achievable. The center piece of the achievability scheme is the help provided by either the destination node with transmission capability, or an external "good samaritan" node. In either case, the helper performs cooperative jamming that confuses the eavesdropping relay and disables it from being able to decipher what it is relaying. We next derive an upper bound on the secrecy rate for this system. We observe that the gap between the upper bound and the achievable rate vanishes as the power of the relay node goes to infinity. Overall, the paper presents a ca...
Ness, H; Stella, L; Lorenz, C D; Kantorovich, L
2017-04-28
We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference ΔT between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (T≳500 K) and temperature differences (ΔT≳500 K), the chains, with N>18 atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (T≲500 K) and temperature differences (ΔT≲400 K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (N≤15). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.
Event Driven Langevin simulations of Hard Spheres
Scala, Antonio
2011-01-01
The blossoming of interest in colloids and nano-particles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two new algorithms for the simulation of the Langevin dynamics of hard-spheres.
Banerjee, Dhruba; Bag, Bidhan Chandra; Banik, Suman Kumar; Ray, Deb Shankar
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 method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, alon...
An attempt toward the generalized Langevin dynamics simulation
Directory of Open Access Journals (Sweden)
B.Kim
2008-03-01
Full Text Available An attempt to generalize the Langevin dynamics simulation method is presented based on the generalized Langevin theory of liquids, in which the dynamics of both solute and solvent is treated by the generalized Langevin equations, but the integration of the equation of motion of solute is made in the manner similar to the ordinary molecular dynamics simulation with discretized time steps along a trajectory. A preliminary result is derived based on an assumption of the uniform solvent density. The result is regarded to be a microscopic generalization of the phenomenological Langevin theory for the harmonic oscillator immersed in a continuum solvent developed by Wang and Uhlenbeck.
Collinearly improved JIMWLK evolution in Langevin form
Hatta, Yoshitaka
2016-01-01
The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and beyond. We propose a method for resumming such logarithmic corrections to all orders, at the level of the Langevin formulation of the JIMWLK equation. The ensuing, collinearly-improved Langevin equation features generalized Wilson line operators, which depend not only upon rapidity (the logarithm of the longitudinal momentum), but also upon the transverse size of the color neutral projectile to which the Wilson lines belong. This additional scale dependence is built up during the evolution, via the condition that the successive emissions of soft gluons be ordered in time. The presence of this transverse scale in the Langevin equation furthermore allows for the resummation of the one-loop running coupling corrections.
From shape to randomness: A classification of Langevin stochasticity
Eliazar, Iddo; Cohen, Morrel H.
2013-01-01
The Langevin equation-perhaps the most elemental stochastic differential equation in the physical sciences-describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output-based on the shape of the Langevin equation’s potential field.
Bottlenecks in Two-Hop Ad Hoc Networks - Dividing Radio Capacity in a Smart Way
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.; Mandjes, M.; van der Mei, R.; Nunez Queija, R.
In two-hop ad hoc networks the available radio capacity tends to be equally shard among the contending stations, which may lead to bottleneck situations in case of unbalanced traffic routing. We propose a generic model for evaluating adaptive capacity sharing strategies. We use infinite-state
Performance of Ad Hoc Networks with Two-Hop Relay Routing and Limited Packet Lifetime
Al Hanbali, Ahmad; Nain, Philippe; Altman, Eitan
2006-01-01
Considered is a mobile ad hoc network consisting of three types of nodes (source, destination and relay nodes) and using the two-hop relay routing protocol. Packets at relay nodes are assumed to have a limited lifetime in the network. All nodes are moving inside a bounded region according to some ra
Langevin model for reactive transport in porous media
Tartakovsky, Alexandre M.
2010-08-01
Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)10.1103/PhysRevLett.101.044502]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy 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
Analysis of multifrequency langevin composite ultrasonic transducers.
Lin, Shuyu
2009-09-01
The multimode coupled vibration of Langevin composite ultrasonic transducers with conical metal mass of large cross-section is analyzed. The coupled resonance and anti-resonance frequency equations are derived and the effective electromechanical coupling coefficient is analyzed. The effect of the geometrical dimensions on the resonance frequency, the anti-resonance frequency, and the effective electromechanical coupling coefficient is studied. It is illustrated that when the radial dimension is large compared with the longitudinal dimension, the vibration of the Langevin transducer becomes a multifrequency multimode coupled vibration. Numerical methods are used to simulate the coupled vibration; the simulated results are in good agreement with those from the analytical results. Some Langevin transducers of large cross-section are designed and manufactured and their resonance frequencies are measured. It can be seen that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with the measured results. It is expected that by properly choosing the dimensions, multifrequency Langevin transducers can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry, and other applications.
The resonant behavior of an over-damped linear fractional Langevin equation%线性过阻尼分数阶Langevin方程的共振行为
Institute of Scientific and Technical Information of China (English)
钟苏川; 高仕龙; 韦鹍; 马洪
2012-01-01
通过将广义Langevin方程中的系统内噪声建模为分数阶高斯噪声，推导出分数阶Langevin方程，其分数阶导数项阶数由系统内噪声的Hurst指数所确定．讨论了处于强噪声环境下的线性过阻尼分数阶Langevin方程在周期信号激励下的共振行为，利用Shapiro—Loginov公式和Laplace变换，推导了系统响应的一、二阶稳态矩和稳态响应振幅、方差的解析表达式．分析表明，适当参数下，系统稳态响应振幅和方差随噪声的某些特征参数、周期激励信号的频率及系统部分参数的变化出现了广义的随机共振现象．%By choosing the internal noise as a fractional Gaussian noise, we obtain the fractional Langevin equation. We explore the phenomenon of stochastic resonance in an over-damped linear fractional Langevin equation subjected to an external sinusoidal forcing. The influence of fluctuations of environmental parameters on the dynamics of the system is modeled by a dichotomous noise.Using the Shapiro-Loginov formula and the Laplace transformation technique, we obtain the exact expressions of the first and second moment of the output signal, the mean particle displacement and the variance of the output signal in the long-time limit t→∞.Finally, the numerical simulation shows that the over-damped linear fractional Langevin equation reveals a lot of dynamic behaviors and the stochastic resonance （SR） in a wide sense can be found with internal noise and external noise.
Institute of Scientific and Technical Information of China (English)
蒋泽南; 房超; 孙立风
2011-01-01
研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路.%Some ideas concerning the properties of Langevin equation and its applications to the protein folding process are introduced in this paper. Continuous mapping of Langevin equation is constructed in the phase space and a clear inhomogeneous distribution at position of the Brownian particles is discovered, which is consistent with the hypothesis of the nonergodicity of space structure of protein molecule in the folding process. Besides, a random coil with the same compactness index as proteins in the denatured state is obtained by simulation under the self-avoiding walk condition. Taking the hydrophobic effects as well as the renormalization model into consideration, we present the method to simulate the process of protein shrinking from a random coil to a molten globule.
Markovian Process and Novel Secure Algorithm for Big Data in Two-Hop Wireless Networks
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K. Thiagarajan
2015-06-01
Full Text Available This paper checks the correctness of our novel algorithm for secure, reliable and flexible transmission of big data in two-hop wireless networks using cooperative jamming scheme of attacker location unknown through Markovian process. Big data has to transmit in two-hop from source-to-relay and relay-to-destination node by deploying security in physical layer. Based on our novel algorithm, the nodes of the network can be identifiable, the probability value of the data absorbing nodes namely capture node C, non-capture node NC, eavesdropper node E, in each level depends upon the present level to the next level, the probability of transition between two nodes is same at all times in a given time slot to ensure more secure transmission of big data. In this paper, maximum probability for capture nodes is considered to justify the efficient transmission of big data through Markovian process.
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
Energy Technology Data Exchange (ETDEWEB)
Rodean, H.C.
1994-01-26
Three models for scalar diffusion in turbulent flow (eddy diffusivity, random displacement, and on the Langevin equation) are briefly described. These models random velocity increment based Fokker-Planck equation is introduced as are then examined in more detail in the reverse order. The Fokker-Planck equation is the Eulerian equivalent of the Lagrangian Langevin equation, and the derivation of e outlined. The procedure for obtaining the deterministic and stochastic components of the Langevin equation from Kolmogorov`s 1941 inertial range theory and the Fokker-Planck equation is described. it is noted that a unique form of the Langevin equation can be determined for diffusion in one dimension but not in two or three. The Langevin equation for vertical diffusion in the non-Gaussian convective boundary layer is presented and successively simplified for Gaussian inhomogeneous turbulence and Gaussian homogeneous turbulence in turn. The Langevin equation for Gaussian inhomogeneous turbulence is mathematically transformed into the random displacement model. It is shown how the Fokker-Planck equation for the random displacement model is identical in form to the partial differential equation for the eddy diffusivity model. It is noted that the Langevin model is applicable in two cases in which the other two are not valid: (1) very close in time and distance to the point of scalar release and (2) the non-Gaussian convective boundary layer. The two- and three-dimensional cases are considered in Part III.
Snook, Ian
2007-01-01
The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book.* Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes
Upsilon suppression in the Schrödinger-Langevin approach
Gossiaux, P. B.; Katz, R.
2016-12-01
We treat the question of bottomonia suppression in ultrarelativistic heavy ion collisions (URHIC) as a dynamical open quantum problem, tackled for the first time using the Schrödinger-Langevin equation. Coupling this equation to the EPOS2 event generator, predictions are made for the nuclear modification factor of ϒ (1 S) and ϒ (2 S).
Upsilon suppression in the Schr\\"odinger-Langevin approach
Gossiaux, Pol Bernard
2016-01-01
We treat the question of bottomonia suppression in ultrarelativistic heavy ion collisions (URHIC) as a dynamical open quantum problem, tackled for the first time using the Schr\\"odinger-Langevin equation. Coupling this equation to the EPOS2 event generator, predictions are made for the nuclear modification factor of $\\Upsilon (1S)$ and $\\Upsilon (2S)$.
Two critical issues in Langevin simulation of gas flows
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jun [James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom and State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences (China); Fan, Jing [State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
2014-12-09
A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.
From the Underdamped Generalized Elastic Model to the Single Particle Langevin Description
Directory of Open Access Journals (Sweden)
Alessandro Taloni
2017-01-01
Full Text Available The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit.
Performance Evaluation of Two-Hop Wireless Link under Nakagami-m Fading
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Afsana Nadia
2013-08-01
Full Text Available Now-a-days, intense research is going on two-hop wireless link under different fading conditions with its remedial measures. In this paper work, a two-hop link under three different conditions is considered: (i MIMO on both hops, (ii MISO in first hop and SIMO in second hop and finally (iii SIMO in first hop and MISO in second hop. The three models used here give the flexibility of using STBC (Space Time Block Coding and combining scheme on any of the source to relay (S-R and relay to destination (R-D link. Even incorporation of Transmitting Antenna Selection (TAS is possible on any link. Here, the variation of SER (Symbol Error Rate is determined against mean SNR (Signal-to-Noise Ratio of R-D link for three different modulation schemes: BPSK, 8-PSK and 16-PSK, taking the number of antennas and SNR of S-R link as parameters under Nakagami -m fading condition.
Applications of Langevin and Molecular Dynamics methods
Lomdahl, P. S.
Computer simulation of complex nonlinear and disordered phenomena from materials science is rapidly becoming an active and new area serving as a guide for experiments and for testing of theoretical concepts. This is especially true when novel massively parallel computer systems and techniques are used on these problems. In particular the Langevin dynamics simulation technique has proven useful in situations where the time evolution of a system in contact with a heat bath is to be studied. The traditional way to study systems in contact with a heat bath has been via the Monte Carlo method. While this method has indeed been used successfully in many applications, it has difficulty addressing true dynamical questions. Large systems of coupled stochastic ODE's (or Langevin equations) are commonly the end result of a theoretical description of higher dimensional nonlinear systems in contact with a heat bath. The coupling is often local in nature, because it reflects local interactions formulated on a lattice, the lattice for example represents the underlying discreteness of a substrate of atoms or discrete k-values in Fourier space. The fundamental unit of parallelism thus has a direct analog in the physical system the authors are interested in. In these lecture notes the authors illustrate the use of Langevin stochastic simulation techniques on a number of nonlinear problems from materials science and condensed matter physics that have attracted attention in recent years. First, the authors review the idea behind the fluctuation-dissipation theorem which forms that basis for the numerical Langevin stochastic simulation scheme. The authors then show applications of the technique to various problems from condensed matter and materials science.
Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation
Nagaev, K. E.
2016-08-01
We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.
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...
Energy-efficient two-hop LTE resource allocation in high speed trains with moving relays
Alsharoa, Ahmad M.
2014-05-01
High-speed railway system equipped with moving relay stations placed on the middle of the ceiling of each train wagon is investigated. The users inside the train are served in two hops via the 3GPP Long Term Evolution (LTE) technology. The objective of this work is to maximize the number of served users by respecting a specific quality-of-service constraint while minimizing the total power consumption of the eNodeB and the moving relays. We propose an efficient algorithm based on the Hungarian method to find the optimal resource allocation over the LTE resource blocks in order to serve the maximum number of users with the minimum power consumption. Moreover, we derive a closed-form expression for the power allocation problem. Our simulation results illustrate the performance of the proposed scheme and compare it with various previously developed algorithms as well as with the direct transmission scenario. © 2014 IFIP.
Decentralized Fair Scheduling in Two-Hop Relay-Assisted Cognitive OFDMA Systems
Wang, Rui; Cui, Ying
2010-01-01
In this paper, we consider a two-hop relay-assisted cognitive downlink OFDMA system (named as secondary system) dynamically accessing a spectrum licensed to a primary network, thereby improving the efficiency of spectrum usage. A cluster-based relay-assisted architecture is proposed for the secondary system, where relay stations are employed for minimizing the interference to the users in the primary network and achieving fairness for cell-edge users. Based on this architecture, an asymptotically optimal solution is derived for jointly controlling data rates, transmission power, and subchannel allocation to optimize the average weighted sum goodput where the proportional fair scheduling (PFS) is included as a special case. This solution supports decentralized implementation, requires small communication overhead, and is robust against imperfect channel state information at the transmitter (CSIT) and sensing measurement. The proposed solution achieves significant throughput gains and better user-fairness compa...
THROUGHPUT ANALYSIS OF TWO-HOP WIRELESS NETWORKS WITH NETWORK CODING
Institute of Scientific and Technical Information of China (English)
Wu Yongchao; Chi Kaikai; Zhu Yihua
2013-01-01
A Two-hop Wireless Network (TWN) is the basic topology structure that provides network coding opportunity for improving throughput.Network coding on a homogeneous TWN,in which all the data flows have the same packet size and all the links have the same transmission rate,has been extensively investigated.In this paper,network coding on more practical heterogeneous TWNs,featured by various packet sizes and transmission rates,is studied.Based on the Markov model,the throughput of the proposed network coding scheme,together with the throughput gain,is derived,which matches the simulation results very well.Numerical analyses indicate that,encoding the packets with close size and close transmission rate and enlarging buffer size at the relay node help in improving the throughput gain.
Detect-and-forward in two-hop relay channels: a metrics-based analysis
Benjillali, Mustapha
2010-06-01
In this paper, we analyze the coded performance of a cooperative system with multiple parallel relays using "Detect-and-Forward" (DetF) strategy where each relay demodulates the overheard signal and forwards the detected binary words. The proposed method is based on the probabilistic characterization of the reliability metrics given under the form of L-values. First, we derive analytical expressions of the probability density functions (PDFs) of the L-values in the elementary two-hop DetF relay channel with different source-relay channel state information assumptions. Then, we apply the obtained expressions to calculate the theoretically achievable rates and compare them with the practical throughput of a simulated turbo-coded transmission. Next, we derive tight approximations for the end-to-end coded bit error rate (BER) of a general cooperative scheme with multiple parallel relays. Simulation results demonstrate the accuracy of our derivations for different cooperation configurations and conditions. © 2010 IEEE.
Global Langevin model of multidimensional biomolecular dynamics
Schaudinnus, Norbert; Lickert, Benjamin; Biswas, Mithun; Stock, Gerhard
2016-11-01
Molecular dynamics simulations of biomolecular processes are often discussed in terms of diffusive motion on a low-dimensional free energy landscape F ( 𝒙 ) . To provide a theoretical basis for this interpretation, one may invoke the system-bath ansatz á la Zwanzig. That is, by assuming a time scale separation between the slow motion along the system coordinate x and the fast fluctuations of the bath, a memory-free Langevin equation can be derived that describes the system's motion on the free energy landscape F ( 𝒙 ) , which is damped by a friction field and driven by a stochastic force that is related to the friction via the fluctuation-dissipation theorem. While the theoretical formulation of Zwanzig typically assumes a highly idealized form of the bath Hamiltonian and the system-bath coupling, one would like to extend the approach to realistic data-based biomolecular systems. Here a practical method is proposed to construct an analytically defined global model of structural dynamics. Given a molecular dynamics simulation and adequate collective coordinates, the approach employs an "empirical valence bond"-type model which is suitable to represent multidimensional free energy landscapes as well as an approximate description of the friction field. Adopting alanine dipeptide and a three-dimensional model of heptaalanine as simple examples, the resulting Langevin model is shown to reproduce the results of the underlying all-atom simulations. Because the Langevin equation can also be shown to satisfy the underlying assumptions of the theory (such as a delta-correlated Gaussian-distributed noise), the global model provides a correct, albeit empirical, realization of Zwanzig's formulation. As an application, the model can be used to investigate the dependence of the system on parameter changes and to predict the effect of site-selective mutations on the dynamics.
Langevin dynamics of the pure SU(2) deconfining transition
Fraga, E S; Mizher, A J
2007-01-01
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.
Description of dynamics of stock prices by a Langevin approach
Institute of Scientific and Technical Information of China (English)
Huang Zi-Gang; Chen Yong; Zhang Yong; Wang Ying-Hai
2007-01-01
We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S&P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.
Analysis of the call blocking rate of two-hop-relay cellular system in the dead spots
Institute of Scientific and Technical Information of China (English)
LU Wei-feng; WU Meng
2007-01-01
In a traditional cellular system, the call requests initiated by mobile stations (MSs) must be carried through a base station (BS) via the cellular interface, but when MSs are located in the dead spots, their call requests will be blocked because the MSs cannot communicate with the BS. It is considered to relay these blocked calls requested using Ad-hoc network, which will improve the performance of the system as a whole. This article first introduces a novel architecture of the two-hop-relay cellular system in the dead spots, and then analyzes and compares the call blocking rate of the traditional cellular and the two-hop-relay cellular system respectively under three different conditions. The first and second conditions are the traditional cellular system without and with taking account of the effect of the dead spots. The third condition is the two-hop-relay cellular system with taking account of the effect of the dead spots. Numerical analytical result shows that the two-hop-relay cellular system can obtain lower call blocking rate than the traditional cellular system when considering the effect of dead spots. Consequently, this novel architecture can resolve the problem of coverage limitation of a traditional cellular system effectively.
Probabilistic Routing Based on Two-Hop Information in Delay/Disruption Tolerant Networks
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Xu Wang
2015-01-01
Full Text Available We investigate an opportunistic routing protocol in delay/disruption tolerant networks (DTNs where the end-to-end path between source and destination nodes may not exist for most of the time. Probabilistic routing protocol using history of encounters and transitivity (PRoPHET is an efficient history-based routing protocol specifically proposed for DTNs, which only utilizes the delivery predictability of one-hop neighbors to make a decision for message forwarding. In order to further improve the message delivery rate and to reduce the average overhead of PRoPHET, in this paper we propose an improved probabilistic routing algorithm (IPRA, where the history information of contacts for the immediate encounter and two-hop neighbors has been jointly used to make an informed decision for message forwarding. Based on the Opportunistic Networking Environment (ONE simulator, the performance of IPRA has been evaluated via extensive simulations. The results show that IPRA can significantly improve the average delivery rate while achieving a better or comparable performance with respect to average overhead, average delay, and total energy consumption compared with the existing algorithms.
Energy/bandwidth-Saving Cooperative Spectrum Sensing for Two-hopWRAN
Directory of Open Access Journals (Sweden)
Ming-Tuo Zhou
2014-07-01
Full Text Available A two-hop wireless regional area network (WRAN providing monitoring services operating in Television White Space (TVWS, i.e., IEEE P802.22b, may employ a great number of subscriber customer-premises equipments (S-CPEs possibly without mains power supply, leading to requirement of cost-effective and power-saving design. This paper proposes a framework of cooperative spectrum sensing (CSS and an energy/bandwidth saving CSS scheme to P802.22b. In each round of sensing, S-CPEs with SNRs lower than a predefined threshold are excluded from reporting sensing results. Numerical results show that the fused missed-detection probability and false alarmprobability could remainmeeting sensing requirements, and the overall fused error probability changes very little. With 10 S-CPEs, it is possible to save more than 40% of the energy/bandwidth on a Rayleigh channel. The principle proposed can apply to other advanced sensing technologies capable of detecting primary signals with low average SNR.
Energy-efficient power allocation of two-hop cooperative systems with imperfect channel estimation
Amin, Osama
2015-06-08
Recently, much attention has been paid to the green design of wireless communication systems using energy efficiency (EE) metrics that should capture all energy consumption sources to deliver the required data. In this paper, we formulate an accurate EE metric for cooperative two-hop systems that use the amplify-and-forward relaying scheme. Different from the existing research that assumes the availability of perfect channel state information (CSI) at the communication cooperative nodes, we assume a practical scenario, where training pilots are used to estimate the channels. The estimated CSI can be used to adapt the available resources of the proposed system in order to maximize the EE. Two estimation strategies are assumed namely disintegrated channel estimation, which assumes the availability of channel estimator at the relay, and cascaded channel estimation, where the relay is not equipped with channel estimator and only forwards the received pilot(s) in order to let the destination estimate the cooperative link. The channel estimation cost is reflected on the EE metric by including the estimation error in the signal-to-noise term and considering the energy consumption during the estimation phase. Based on the formulated EE metric, we propose an energy-aware power allocation algorithm to maximize the EE of the cooperative system with channel estimation. Furthermore, we study the impact of the estimation parameters on the optimized EE performance via simulation examples.
IEATH: Improved Energy Aware and Two Hop Multipath Routing Protocol in Wireless Sensor Networks
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S. Saqaeeyan
2012-06-01
Full Text Available Wireless sensor networks in terms of energy sources are limited. Furthermore due to this type of network infrastructure wireless communications and channel errors not possible to reach the correct packet to the destination exists; hence the proposing algorithms to improve the quality of service in these networks and sending packets are very important. In this paper we proposed a reliable and energy aware packet delivery mechanism to ensure quality of service in wireless sensor networks. In our proposed algorithm to ensure that a packet of information sent to the destination, the multi-path Forwarding method is used; So that several copies of an information packet via separate routes are sent to the destination, also routing decisions in this way occurs by considering the remaining energy in the neighborhood of nodes that are located in two hop of sender node. Simulation results show that the rate of release of data packets reduced in this way and thus the reliability of packet is increased, also the energy efficiency of sensor nodes effectively improved. Therefore this algorithm increase overall lifetime in wireless sensor networks.
Exploring Relay Cooperation for Secure and Reliable Transmission in Two-HopWireless Networks
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Yulong Shen
2014-03-01
Full Text Available This work considers the problem of secure and reliable information transmission via relay cooperation in two-hop relay wireless networks without the information of both eavesdropper channels and locations. While previous work on this problem mainly studied infinite networks and their asymptotic behavior and scaling law results, this papers focuses on a more practical network with finite number of system nodes and explores the corresponding exact result on the number of eavesdroppers one network can tolerate to ensure desired secrecy and reliability. We first study the scenario where path-loss is equal between all pairs of nodes and consider two transmission protocols there, one adopts an optimal but complex relay selection process with less load balance capacity while the other adopts a random but simple relay selection process with good load balance capacity. Theoretical analysis and numerical results are then provided to determine the maximum number of eavesdroppers one network can tolerate to ensure a desired performance in terms of the secrecy outage probability and transmission outage probability. We further extend our study to the more general scenario where path-loss between each pair of nodes also depends on the distance between them, for which a new transmission protocol with both preferable relay selection and good load balance as well as the corresponding theoretical analysis and numerical results are presented.
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2013-12-01
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
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Huang, Yandong [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China); Rüdiger, Sten [Institute of Physics, Humboldt-Universität zu Berlin (Germany); Shuai, Jianwei, E-mail: jianweishuai@xmu.edu.cn [Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005 (China)
2013-12-13
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K{sup +} channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Langevin Diffusion in Holographic Backgrounds with Hyperscaling Violation
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J. Sadeghi
2014-01-01
Full Text Available We consider a relativistic heavy quark which moves in the quark-gluon plasmas. By using the holographic methods, we analyze the Langevin diffusion process of this relativistic heavy quark. This heavy quark is described by a trailing string attached to a flavor brane and moving at constant velocity. The fluctuations of this string are related to the thermal correlators and the correlation functions are precisely the kinds of objects that we compute in the gravity dual picture. We obtain the action of the trailing string in hyperscaling violation backgrounds and we then find the equations of motion. These equations lead us to constructing the Langevin correlator which helps us to obtain the Langevin constants. Using the Langevin correlators we derive the spectral densities and simple analytic expressions in the small- and large-frequency limits. We examine our works for planar and R-charged black holes with hyperscaling violation and find new constraints on θ in the presence of velocity v.
Complex saddle points and the sign problem in complex Langevin simulation
Hayata, Tomoya; Tanizaki, Yuya
2015-01-01
We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
Institute of Scientific and Technical Information of China (English)
LI Ping; RONG Meng-tian; HUANG Lei; YU Dan
2006-01-01
This paper presented a scheme of two-hop cellular network with fixed relay nodes (FRN). Based on this scheme, co-channel interference and signal interference ratio(SIR) received by base station(BS) and FRN were analyzed. Both the theoretical analysis and simulation results show that the SIR can be improved significantly when relays are employed in the network. The higher spectral efficiency can be obtained due to the improved two-hop link quality through the use of adaptive modulation and coding (AMC). The antenna height of FRN and the cell radius of BS and that of FRN influence SIR received by BS and FRN and the system spectral efficiency greatly. The proper antenna height of FRN and cell radius of BS and that of FRN were also given to get the highest spectral efficiency.
Einstein's Clocks and Langevin's Twins
Weinstein, Galina
2012-01-01
In 1905 Einstein presented the Clock Paradox and in 1911 Paul Langevin expanded Einstein's result to human observers, the "Twin Paradox." I will explain the crucial difference between Einstein and Langevin. Einstein did not present the so-called "Twin Paradox." Later Einstein continued to speak about the clock paradox. Einstein might not have been interested in the question: what happens to the observers themselves. The reason for this could be the following; Einstein dealt with measurement procedures, clocks and measuring rods. Einstein's observers were measuring time with these clocks and measuring rods. Einstein might not have been interested in so-called biology of the observers, whether these observers were getting older, younger, or whether they have gone any other changes; these changes appeared to be out of the scope of his "Principle of relativity" or kinematics. The processes and changes occurring within observers seemed to be good for philosophical discussions. Later writers criticized Einstein's c...
Localised distributions and criteria for correctness in complex Langevin dynamics
Energy Technology Data Exchange (ETDEWEB)
Aarts, Gert, E-mail: g.aarts@swan.ac.uk [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Giudice, Pietro, E-mail: p.giudice@uni-muenster.de [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Seiler, Erhard, E-mail: ehs@mppmu.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)
2013-10-15
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. -- Highlights: •Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. •Connection between criteria for correctness and breakdown. •Solution of the Fokker–Planck equation in the case of real noise. •Analytical determination of support in complexified space.
Rapid sampling of reactive Langevin trajectories via noise-space Monte Carlo.
Dickson, B M
2007-08-14
A noise-space Monte Carlo approach to sampling reactive Langevin trajectories is introduced and compared to a configuration based approach. The noise sampling is shown to overcome the slow relaxation of the configuration based method. Furthermore, the noise sampling is shown to sample multiple pathways with the correct probabilities without any additional work being required formally or algorithmically. The path sampling proceeds without any introduction of fictitious interactions and includes only the parameters appearing in Langevin's equation.
Boltzmann-Langevin one-body dynamics for fermionic systems
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Napolitani P.
2012-07-01
Full Text Available 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.
The modified Langevin description for probes in a nonlinear medium
Krüger, Matthias; Maes, Christian
2017-02-01
When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe’s effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is no longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.
Does the complex Langevin method give unbiased results?
Salcedo, L L
2016-01-01
We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action $S(x)$ is convergent, it produces an equivalent complex probability distribution $P(x)$ which ideally would coincide with $e^{-S(x)}$. We show that the projected Fokker-Planck equation fulfilled by $P(x)$ may contain an anomalous term whose form is made explicit. Such term spoils the relation $P(x)=e^{-S(x)}$, introducing a bias in the expectation values. Through the analysis of several periodic and non-periodic one-dimensional problems, using either exact or numerical solutions of the Fokker-Planck equation on the complex plane, it is shown that the anomaly is present quite generally. In fact, an anomaly is expected whenever the Langevin walker needs only a finite time to go to infinity and come back, and this is the case for typical actions. We conjecture that the anomaly is the rule rather than the excepti...
Does the complex Langevin method give unbiased results?
Salcedo, L. L.
2016-12-01
We investigate whether the stationary solution of the Fokker-Planck equation of the complex Langevin algorithm reproduces the correct expectation values. When the complex Langevin algorithm for an action S (x ) is convergent, it produces an equivalent complex probability distribution P (x ) which ideally would coincide with e-S (x ). We show that the projected Fokker-Planck equation fulfilled by P (x ) may contain an anomalous term whose form is made explicit. Such a term spoils the relation P (x )=e-S (x ), introducing a bias in the expectation values. Through the analysis of several periodic and nonperiodic one-dimensional problems, using either exact or numerical solutions of the Fokker-Planck equation on the complex plane, it is shown that the anomaly is present quite generally. In fact, an anomaly is expected whenever the Langevin walker needs only a finite time to go to infinity and come back, and this is the case for typical actions. We conjecture that the anomaly is the rule rather than the exception in the one-dimensional case; however, this could change as the number of variables involved increases.
Langevin- Science and vigilance; Langevin - Science et vigilance
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Bensaude-Vincent, B.
1987-12-31
Paul Langevin personifies the figure of popular scientist, buried in the Pantheon, because he was in all great fights: to diffuse knowledge, for improvement and democratization of teaching, for justice and peace. Great theoretician of physics, comparable to Einstein whom he rejoined the approach, he was a fertile discoverer, author, in particular, of a proceeding to detect submarines. He fought politically, regardless of his career, in the ranges of pacifists and opponents of fascism. This book reveals, in his warm diversity, a badly known personality, in spite of the legend in his lifetime. (N.C.).
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.
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Qian Cao
2014-01-01
Full Text Available This paper investigates the consensus problem for multiagent systems with nonlinear dynamics and time delays. A distributed adaptive consensus protocol is proposed in which the time delays are explicitly included in the adaptive algorithm. It is shown that the resultant closed loop system involves doubly larger time delays, making the stability analysis nontrivial. Stability condition on maximum tolerable time delay is established and controlled by the proposed two-hop adaptive algorithm. The explicit expression of the delay margin is derived and analyzed in the frequency domain. Both the agent state errors and the estimation parameter errors converge to zero. A simulation example is illustrated to verify the theory results.
On Complex Langevin Dynamics and the Evaluation of Observables
Durakovic, Amel; Tranberg, Anders
2014-01-01
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously established, extends this idea to cases where the action is complex-valued by complexifying the basic degrees of freedom, all observables and allowing the stochastic process to probe the complexified configuration space. We review the method for a previously studied one-dimensional toy model, the U(1) one link model. We confirm that complex Langevin dynamics only works for a certain range of parameters, misestimating observables otherwise. A curious effect is observed where all moments of the basic stochastic variable are misestimated, although these misestimated moments may be used to construct, by a Taylor series, other observables that are reproduced correctly. This suggests a subtle but not completely resolved relationship between the original complex integration measur...
Langevin description of fission fragment charge distribution from excited nuclei
Karpov, A V
2002-01-01
A stochastic approach to fission dynamics based on a set of three-dimensional Langevin equations was applied to calculate fission-fragment charge distribution of compound nucleus sup 2 sup 3 sup 6 U. The following collective coordinates have been chosen - elongation coordinate, neck-thickness coordinate, and charge-asymmetry coordinate. The friction coefficient of charge mode has been calculated in the framework of one-body and two-body dissipation mechanisms. Analysis of the results has shown that Langevin approach is appropriate for investigation of isobaric distribution. Moreover, the dependences of the variance of the charge distribution on excitation energy and on the two-body viscosity coefficient has been studied
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Sana Ezzine
2017-01-01
Full Text Available Powerline network is recognized as a favorable infrastructure for Smart Grid to transmit information in the network thanks to its broad coverage and low cost deployment. The existing works are trying to improve and adapt transmission techniques to reduce Powerline Communication (PLC channel attenuation and exploit the limited bandwidth to support high data rate over long distances. Two-hop relaying BroadBand PLC (BB-PLC system, in which Orthogonal Frequency Division Multiplexing (OFDM is used, is considered in this paper. We derive and compare the PLC channel capacity and the end-to-end Average BER (ABER for OFDM-based direct link (DL BB-PLC system and for OFDM-based two-hop relaying BB-PLC system for Amplify and Forward (AF and Decode and Forward (DF protocols. We analyze the improvements when we consider the direct link in a cooperative communication when the relay node only transmits the correctly decoded signal. Maximum ratio combining is employed at the destination node to detect the transmitted signal. In addition, in this paper, we highlight the impact of the relay location on the channel capacity and ABER for AF and DF transmission protocols. Moreover, an efficient use of the direct link was also investigated in this paper.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Fractional Langevin model of memory in financial markets.
Picozzi, Sergio; West, Bruce J
2002-10-01
The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series.
Uncertainty quantification for generalized Langevin dynamics
Hall, Eric J.; Katsoulakis, Markos A.; Rey-Bellet, Luc
2016-12-01
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of the GLE where other well known sensitivity analysis techniques such as the likelihood ratio method are not applicable to key parameters of interest. These easily implemented estimators are formed by coupling the nominal and perturbed dynamics appearing in the finite difference through a common driving noise or common random path. After developing a general framework for variance reduction via coupling, we demonstrate the optimality of the common random path coupling in the sense that it produces a minimal variance surrogate for the difference estimator relative to sampling dynamics driven by independent paths. In order to build intuition for the common random path coupling, we evaluate the efficiency of the proposed estimators for a comprehensive set of examples of interest in particle dynamics. These reduced variance difference estimators are also a useful tool for performing global sensitivity analysis and for investigating non-local perturbations of parameters, such as increasing the number of Prony modes active in an extended variable GLE.
Fractional Langevin model of gait variability
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Latka Miroslaw
2005-08-01
Full Text Available Abstract The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.
Scaling of Langevin and molecular dynamics persistence times of nonhomogeneous fluids.
Olivares-Rivas, Wilmer; Colmenares, Pedro J
2012-01-01
The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics.
The derivation and approximation of coarse-grained dynamics from Langevin dynamics
Ma, Lina; Li, Xiantao; Liu, Chun
2016-11-01
We present a derivation of a coarse-grained description, in the form of a generalized Langevin equation, from the Langevin dynamics model that describes the dynamics of bio-molecules. The focus is placed on the form of the memory kernel function, the colored noise, and the second fluctuation-dissipation theorem that connects them. Also presented is a hierarchy of approximations for the memory and random noise terms, using rational approximations in the Laplace domain. These approximations offer increasing accuracy. More importantly, they eliminate the need to evaluate the integral associated with the memory term at each time step. Direct sampling of the colored noise can also be avoided within this framework. Therefore, the numerical implementation of the generalized Langevin equation is much more efficient.
Justification of the complex Langevin method with the gauge cooling procedure
Nagata, Keitaro; Shimasaki, Shinji
2015-01-01
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus...
Testing dynamic stabilisation in complex Langevin simulations
Attanasio, Felipe
2016-01-01
Complex Langevin methods have been successfully applied in theories that suffer from a sign problem such as QCD with a chemical potential. We present and illustrate a novel method (dynamic stabilisation) that ensures that Complex Langevin simulations stay close to the SU(3) manifold, which lead to correct and improved results in the framework of pure Yang-Mills simulations and QCD in the limit of heavy quarks.
Fluctuation theorems for total entropy production in generalized Langevin systems
Ghosh, Bappa; Chaudhury, Srabanti
2017-01-01
The validity of the fluctuation theorems for total entropy production of a colloidal particle embedded in a non-Markovian heat bath driven by a time-dependent force in a harmonic potential is probed here. The dynamics of the system is modeled by the generalized Langevin equation with colored noise. The distribution function of the total entropy production is calculated and the detailed fluctuation theorem contains a renormalized temperature term which arises due to the non-Markovian characteristics of the thermal bath.
Jansen, Thomas la Cour; Knoester, Jasper
2007-01-01
We combine numerical Langevin simulations with numerical integration of the Schrodinger equation to calculate two-dimensional infrared spectra of ultrafast chemical exchange. This provides a tool to model and interpret such spectra of molecules undergoing chemical processes, such as isomerization an
A Second-Order Stochastic Leap-Frog Algorithm for Langevin Simulation
Qiang, J; Qiang, Ji; Habib, Salman
2000-01-01
Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
Complex saddle points and the sign problem in complex Langevin simulation
Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya
2016-10-01
We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
Complex saddle points and the sign problem in complex Langevin simulation
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Tomoya Hayata
2016-10-01
Full Text Available We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.
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Hee-Nam Cho
2010-01-01
Full Text Available This paper considers coordinated transmission for interference mitigation and power allocation in a correlated two-user two-hop multi-input multioutput (MIMO relay system. The proposed transmission scheme utilizes statistical channel state information (CSI (e.g., transmit correlation to minimize the cochannel interference (CCI caused by the relay. To this end, it is shown that the CCI can be represented in terms of the eigenvalues and the angle difference between the eigenvectors of the transmit correlation matrix of the intended and CCI channel, and that the condition minimizing the CCI can be characterized by the correlation amplitude and the phase difference between the transmit correlation coefficients of these channels. Then, a coordinated user-scheduling strategy is designed with the use of eigen-beamforming to minimize the CCI in an average sense. The transmit power of the base station and relay is optimized under separate power constraint. Analytic and numerical results show that the proposed scheme can maximize the achievable sum rate when the principal eigenvectors of the transmit correlation matrix of the intended and the CCI channel are orthogonal to each other, yielding a sum rate performance comparable to that of the minimum mean-square error-based coordinated beamforming which uses instantaneous CSI.
Controlling complex Langevin dynamics at finite density
Energy Technology Data Exchange (ETDEWEB)
Aarts, Gert; Bongiovanni, Lorenzo [Swansea University, Department of Physics, College of Science, Swansea (United Kingdom); Seiler, Erhard [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Sexty, Denes [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); Stamatescu, Ion-Olimpiu [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); FEST, Heidelberg (Germany)
2013-07-15
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. (orig.)
Isothermal Langevin dynamics in systems with power-law spatially dependent friction.
Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded
2016-07-01
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c1, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.
Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
Cassol-Seewald, N C; Fraga, E S; Krein, G; Ramos, R O
2007-01-01
We consider the nonequilibrium dynamics of the formation of a condensate in a spontaneously broken lambda phi4 scalar field theory, incorporating additive and multiplicative noise terms to study the role of fluctuation and dissipation. The corresponding stochastic Ginzburg-Landau-Langevin (GLL) equation is derived from the effective action, and solved on a (3+1)-dimensional lattice. Particular attention is devoted to the renormalization of the stochastic GLL equation in order to obtain lattice-independent equilibrium results.
Institute of Scientific and Technical Information of China (English)
闫勇; 姜泽军; 梅冬成; 周凌云
2002-01-01
本文对具有加性和乘性白噪声关联的单模激光模型的统计性质进行了研究.从一个具有交叉关联噪声与单模激光与立方模随机等价郎之万方程,计算了稳态激光光强度的平均值、协方差和偏斜率.并与早期结果比较,阐明了考虑郎之万方程修正项对描述激光系统统计性质的重要性.%The stationary properties of a singlemode laser with correlations between additive and multiplicative whitenoise terms are investigated.The mean,variance,and skewness of the steadystate laser intensity are calculated through a Langevin equation(LE) derived by Long which is always stochastically equivalent to the single mode cubic laser model when additive and multiplicative noises are correlated.Compared with the result obtained by Zhu,the consideration of modification item in LE when addivtive and multiplicative noises are correlated is important for describing statistical properties of the laser system.
Langevin Monte Carlo filtering for target tracking
Iglesias Garcia, Fernando; Bocquel, Melanie; Driessen, Hans
2015-01-01
This paper introduces the Langevin Monte Carlo Filter (LMCF), a particle filter with a Markov chain Monte Carlo algorithm which draws proposals by simulating Hamiltonian dynamics. This approach is well suited to non-linear filtering problems in high dimensional state spaces where the bootstrap filte
Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
Das, Santosh K; Greco, Vincenzo
2013-01-01
The propagation of heavy quarks through the quark-gluon plasma (QGP) has been often treated within the framework of Langevin equation (LV), i.e. assuming the heavy flavor momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a thorough study of the approximations involved in Langevin dynamics by mean of a direct comparison with the solution of 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_q/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra with time and consequently on the so-called 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 the estimate of the underlying diffusion coefficient can differ by about $\\sim 15-50\\%$ depending on t...
Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion
Chen, Yao; Wang, Xudong; Deng, Weihua
2017-10-01
This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.
Langevin process reflected on a partially elastic boundary II
Jacob, Emmanuel
2011-01-01
A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the critical value 0.1630, the bounces of the reflected process accumulate in a finite time. We show that nonetheless the particle is not necessarily absorbed after this time. We define a "resurrected" reflected process as a recurrent extension of the absorbed process, and study some of its properties. We also prove that this resurrected reflected process is the unique solution to the stochastic partial differential equation describing the model. Our approach consists in defining the process conditioned on never being absorbed, via an h-transform, and then giving the Ito excursion measure of the recurrent extension thanks to a formula fairly similar to Imhof's relation.
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...
Exactly solvable nonequilibrium Langevin relaxation of a trapped nanoparticle
Salazar, Domingos S. P.; Lira, Sérgio A.
2016-11-01
In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system’s energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.
Langevin Simulation of Non-Uniform Granular Gases
Institute of Scientific and Technical Information of China (English)
张端明; 雷雅洁; 潘贵军; 郁伯铭
2003-01-01
We present and study a fractal model of a non-uniform granular system for the first time, based on which we numerically solve the dynamics actions in the system successfully in one-dimensional case. The multi-mixture is composed of N different particles, whose granularity distribution has the fractal characteristic. The particles are subject to inelastic mutual collisions and obey to Langevin equation between collisions. Far from the equilibrium,i.e. the given typical relaxation time T of the driving Brownian process is much larger than the mean collision time Tc, the results of simulation indicate that the degree of inhomogeneity in the granularity distribution signed by the fractal dimension D of size distribution has great influence on the dynamics actions of the system. The velocity distribution deviates obviously from the Gaussian distribution and the particles cluster more pronouncedly with the larger value of D in the system. The velocity distribution and spatial clusterization change with D are presented.
Error Analysis of Modified Langevin Dynamics
Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia
2016-08-01
We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.
Institute of Scientific and Technical Information of China (English)
Sasanka ARE; Markos A.KATSOULAKIS; Anders SZEPESSY
2009-01-01
Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting particles on a surface, at a detailed atomistic level. However such algorithms are typically computationally expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarse-grained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarse-grained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarse-grained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.
Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons
DEFF Research Database (Denmark)
Olsen, Thomas; Schiøtz, Jakob
2010-01-01
quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum......We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain...... mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution...
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Complex Langevin dynamics for chiral random matrix theory
Mollgaard, A.; Splittorff, K.
2013-12-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Complex Langevin Dynamics for chiral Random Matrix Theory
Mollgaard, A
2013-01-01
We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.
Fodor, Z; Sexty, D; Török, C
2015-01-01
We study lattice QCD at non-vanishing chemical potential using the complex Langevin equation. We compare the results with multi-parameter reweighting both from $\\mu=0$ and phase quenched ensembles. We find a good agreement for lattice spacings below $\\approx$0.15 fm. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4, 6$ and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
Efficient Algorithms for Langevin and DPD Dynamics.
Goga, N; Rzepiela, A J; de Vries, A H; Marrink, S J; Berendsen, H J C
2012-10-09
In this article, we present several algorithms for stochastic dynamics, including Langevin dynamics and different variants of Dissipative Particle Dynamics (DPD), applicable to systems with or without constraints. The algorithms are based on the impulsive application of friction and noise, thus avoiding the computational complexity of algorithms that apply continuous friction and noise. Simulation results on thermostat strength and diffusion properties for ideal gas, coarse-grained (MARTINI) water, and constrained atomic (SPC/E) water systems are discussed. We show that the measured thermal relaxation rates agree well with theoretical predictions. The influence of various parameters on the diffusion coefficient is discussed.
Beyond complex Langevin equations I: two simple examples
Wosiek, Jacek
2015-01-01
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases discussed here. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex inverse dispersion parameter. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time.
Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems.
Ratynskaia, S; Regnoli, G; Rypdal, K; Klumov, B; Morfill, G
2009-10-01
Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. The grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements xi(tau) on time scales tau tau(Delta). The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales. These intermittency features are quantitatively modeled by a single-particle Itô-Langevin stochastic equation with a nonlinear drift term.
Sun, Tianjia; Xie, Xiang; Li, Guolin; Gu, Yingke; Deng, Yangdong; Wang, Zhihua
2012-11-01
This paper presents a wireless power transfer system for a motion-free capsule endoscopy inspection. Conventionally, a wireless power transmitter in a specifically designed jacket has to be connected to a strong power source with a long cable. To avoid the power cable and allow patients to walk freely in a room, this paper proposes a two-hop wireless power transfer system. First, power is transferred from a floor to a power relay in the patient's jacket via strong coupling. Next, power is delivered from the power relay to the capsule via loose coupling. Besides making patients much more conformable, the proposed techniques eliminate the sources of reliability issues arisen from the moving cable and connectors. In the capsule, it is critical to enhance the power conversion efficiency. This paper develops a switch-mode rectifier (rectifying efficiency of 93.6%) and a power combination circuit (enhances combining efficiency by 18%). Thanks to the two-hop transfer mechanism and the novel circuit techniques, this system is able to transfer an average power of 24 mW and a peak power of 90 mW from the floor to a 13 mm × 27 mm capsule over a distance of 1 m with the maximum dc-to-dc power efficiency of 3.04%.
Exact series model of Langevin transducers with internal losses.
Nishamol, P A; Ebenezer, D D
2014-03-01
An exact series method is presented to analyze classical Langevin transducers with arbitrary boundary conditions. The transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders. All three cylinders are of the same diameter. The length to diameter ratio is arbitrary. Complex piezoelectric and elastic coefficients are used to model internal losses. Solutions to the exact linearized governing equations for each cylinder include four series. Each term in each series is an exact solution to the governing equations. Bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions, respectively, are used in the series. Asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti-symmetric sets of functions. All interface and boundary conditions are satisfied in a weighted-average sense. The computed input electrical admittance, displacement, and stress in transducers are presented in tables and figures, and are in very good agreement with those obtained using atila-a finite element package for the analysis of sonar transducers. For all the transducers considered in the analysis, the maximum difference between the first three resonance frequencies calculated using the present method and atila is less than 0.03%.
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 (Δs(tot))≥0 no longer holds true, where Δs(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 η[χ(t)] which involves the work done by a delay-averaged force F(x,t) along the path χ(t) and equals the medium entropy change Δs(m)[x(t)] in the absence of delay. We show that the total dissipation functional R=Δs+η, where Δs 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 (Δs(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.
Mücke, Tanja A; Milan, Patrick; Peinke, Joachim
2015-01-01
Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power...
A Langevin model for low density pedestrian dynamics
Corbetta, Alessandro; Lee, Chung-Min; Benzi, Roberto; Muntean, Adrian; Toschi, Federico
The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D.; Kühn, Oliver
2015-06-01
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 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.
Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D., E-mail: sergei.ivanov@uni-rostock.de; Kühn, Oliver [Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock (Germany)
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.
Bifurcations in Boltzmann–Langevin one body dynamics for fermionic systems
Energy Technology Data Exchange (ETDEWEB)
Napolitani, P., E-mail: napolita@ipno.in2p3.fr [IPN, CNRS/IN2P3, Université Paris-Sud 11, 91406 Orsay cedex (France); Colonna, M. [INFN-LNS, Laboratori Nazionali del Sud, 95123 Catania (Italy)
2013-10-07
We investigate the occurrence of bifurcations in the dynamical trajectories depicting central nuclear collisions at Fermi energies. The quantitative description of the reaction dynamics is obtained within a new transport model, based on the solution of the Boltzmann–Langevin equation in three dimensions, with a broad applicability for dissipative fermionic dynamics. Dilute systems formed in central collisions are shown to fluctuate between two energetically favourable mechanisms: reverting to a compact shape or rather disintegrating into several fragments. The latter result can be connected to the recent observation of bimodal distributions for quantities characterising fragmentation processes and may suggest new investigations.
A Langevin Approach to a Classical Brownian Oscillator in an Electromagnetic Field
Espinoza Ortiz, J. S.; Bauke, F. C.; Lagos, R. E.
2016-08-01
We consider a charged Brownian particle bounded by an harmonic potential, embedded in a Markovian heat bath and driven from equilibrium by external electric and magnetic fields. We develop a quaternionic-like (or Pauli spinor-like) representation, hitherto exploited in classical Lorentz related dynamics. Within this formalism, in a very straight forward and elegant fashion, we compute the exact solution for the resulting generalized Langevin equation, for the case of a constant magnetic field. For the case the source electromagnetic fields satisfy Maxwell's equations, yielding spinor-like Mathieu equations, we compute the solutions within the JWKB approximation. With the solutions at hand we further compute spatial, velocities and crossed time correlations. In particular we study the (kinetically defined) nonequilbrium temperature. Therefore, we can display the system's time evolution towards equilibrium or towards non equilibrium (steady or not) states.
Some remarks on Lefschetz thimbles and complex Langevin dynamics
Aarts, Gert; Seiler, Erhard; Sexty, Denes
2014-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Paty, M. [Paris-7 Univ., 75 (France)
1999-05-01
This article is a short biography of the French physicist Paul Langevin. P.Langevin epitomizes the whole physics of the first half of the last century. His formation made him both an experimenter and a theorist of a great value. His fields of interest were: ionized gas, electron physics, radiation physics and the electrodynamics of moving bodies. P.Langevin was one of the first to fully understand the implications of the relativity theory set up by A.Einstein and he became a fervent supporter of new ideas in physics, he discussed and analysed the interpretations of quantum physics since the very beginning of this new branch of physics. (A.C.)
Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events
Fürstenau, Norbert; Mittendorf, Monika
2016-12-01
We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations "Xaver" and "Christian", 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.
Majka, M.; Góra, P. F.
2016-10-01
While the origins of temporal correlations in Langevin dynamics have been thoroughly researched, the understanding of spatially correlated noise (SCN) is rather incomplete. In particular, very little is known about the relation between friction and SCN. In this article, starting from the microscopic, deterministic model, we derive the analytical formula for the spatial correlation function in the particle-bath interactions. This expression shows that SCN is the inherent component of binary mixtures, originating from the effective (entropic) interactions. Further, employing this spatial correlation function, we postulate the thermodynamically consistent Langevin equation driven by the Gaussian SCN and calculate the adequate fluctuation-dissipation relation. The thermodynamical consistency is achieved by introducing the spatially variant friction coefficient, which can be also derived analytically. This coefficient exhibits a number of intriguing properties, e.g., the singular behavior for certain types of interactions. Eventually, we apply this new theory to the system of two charged particles in the presence of counter-ions. Such particles interact via the screened-charge Yukawa potential and the inclusion of SCN leads to the emergence of the anomalous frictionless regime. In this regime the particles can experience active propulsion leading to the transient attraction effect. This effect suggests a nonequilibrium mechanism facilitating the molecular binding of the like-charged particles.
SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS
Energy Technology Data Exchange (ETDEWEB)
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.
On complex Langevin dynamics and zeroes of the measure II: Fermionic determinant
Aarts, G; Sexty, D; Stamatescu, I -O
2016-01-01
Lattice QCD at non-vanishing chemical potential is studied using the complex Langevin equation (CLE). One of the conditions for the correctness of the results of the CLE is that the zeroes of the measure coming from the fermionic determinant are outside of the distribution of the configurations, or at least in a region where support for the distribution is very much suppressed. We investigate this issue for Heavy Dense QCD (HDQCD) and full QCD at high temperatures. In HDQCD it is found that the configurations move closest to the zeroes of the measure around the critical chemical potential of the onset transition, where the sign problem is diminished, but results remain largely unaffected. In full QCD at high temperatures the investigation of the spectrum of the Dirac operator yields a similar observation: the results are unaffected by the issue of the poles.
Hasegawa, Hideo
2007-02-01
We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker-Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.
Infrared Divergence Separated for Stochastic Force - Langevin Evolution in the Inflationary Era
Morikawa, Masahiro
2016-01-01
Inflation in the early Universe is a grand phase transition which have produced the seeds of all the structures we now observe. We focus on the non-equilibrium aspect of this phase transition especially the inevitable infrared (IR) divergence associated to the the quantum and classical fields during the inflation. There is a long history of research for removing this IR divergence for healthy perturbation calculations. On the other hand, the same IR divergence is quite relevant and have developed the primordial density fluctuations in the early Universe. We develop a unified formalism in which the IR divergence is clearly separated from the microscopic quantum field theory but only appear in the statistical classical structure. We derive the classical Langevin equation for the order parameter within the quantum field theory through the instability of the de Sitter vacuum during the inflation. This separation process is relevant in general to develop macroscopic structures and to derive the basic properties of...
Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach
Directory of Open Access Journals (Sweden)
Beraudo A.
2014-03-01
Full Text Available 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/ψ’s which have meanwhile become accessible.
Understanding the problem with logarithmic singularities in the complex Langevin method
Nishimura, Jun
2015-01-01
In recent years, there has been remarkable progress in theoretical justification of the complex Langevin method, which is a promising method for evading the sign problem in the path integral with a complex weight. There still remains, however, an issue concerning occasional failure of this method in the case where the action involves logarithmic singularities such as the one appearing from the fermion determinant in finite density QCD. In this talk, we point out that this failure is due to the breakdown of the relation between the complex weight which satisfies the Fokker-Planck equation and the probability distribution generated by the stochastic process. In fact, this kind of failure can occur in general when the stochastic process involves a singular drift term. We show, however, in simple examples, that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
Energy Technology Data Exchange (ETDEWEB)
Reeves, Daniel B., E-mail: dbr@Dartmouth.edu [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States); Weaver, John B. [Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755 (United States); Department of Radiology, Geisel School of Medicine, Hanover, New Hampshire 03755 (United States)
2015-11-30
Magnetic nanoparticles have been studied intensely because of their possible uses in biomedical applications. Biosensing using the rotational freedom of particles has been used to detect biomarkers for cancer, hyperthermia therapy has been used to treat tumors, and magnetic particle imaging is a promising new imaging modality that can spatially resolve the concentration of nanoparticles. There are two mechanisms by which the magnetization of a nanoparticle can rotate, a fact that poses a challenge for applications that rely on precisely one mechanism. The challenge is exacerbated by the high sensitivity of the dominant mechanism to applied fields. Here, we demonstrate stochastic Langevin equation simulations for the combined rotation in magnetic nanoparticles exposed to oscillating applied fields typical to these applications to both highlight the existing relevant theory and quantify which mechanism should occur in various parameter ranges.
On the condition for correct convergence in the complex Langevin method
Shimasaki, Shinji; Nishimura, Jun
2016-01-01
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, while it works, for instance, in finite density QCD in the deconfinement phase or in the heavy dense limit. Here we revisit the argument for justification of the CLM and point out a subtlety in using the time-evolved observables, which play a crucial role in the argument. This subtlety requires that the probability distribution of the drift term should fall off exponentially or faster at large magnitude. We demonstrate our claim in some examples such as chiral Random Matrix Theory and show that our criterion is indeed useful in judging whether the results obtained by the CLM are trustable or not.
Mass-energy distribution of fragments in Langevin dynamics of fission induced by heavy ions
Directory of Open Access Journals (Sweden)
Vanin D. V.
2012-12-01
Full Text Available Four-dimensional Langevin equation was employed to calculate mass-energy distributions of fission fragments of highly excited compound nuclei. The research took into account not only three shape collective coordinates introduced on the basis of {c,h,α}-parametrization but also orientation degree of freedom (K-state— spin about the symmetry axis. Overdamped Langevin equation was used to describe the evolution of the K-state. Friction tensor was calculated using the “wall+window” model of the modified one-body dissipation mechanism with a reduction coeffcient from the “wall” formula ks. The calculations have been performed with ks = 0:25 and ks = 1:0. To learn more about the role of the dissipation effects the calculations have also been done with use of the chaoticity measure of nucleon movements in the nuclear shape configuration as ks parameter. Calculations were performed for the large number of compound nuclei with Z2/A parameter in the range 21 ≤ Z2/A ≤ 44. The goal was to study the mass-energy distributions not only for heavy nuclei but also for light nuclei close to the Businaro-Gallone point. Mass-energy distributions and variances of the mass fragments are well reproduced in the applied calculations for all considered compound nuclei. It was shown that inclusion of the K-state in the dynamical model produces considerable increase of the mass and energy variances. Inclusion of the chaoticity measure to the friction tensor provides a better agreement with the experiment results on mass variances.
Langevin dynamics of the deconfinement transition for pure gauge theory
Fraga, E S; Krein, G; Fraga, Eduardo S.; Mizher, Ana J\\'ulia; Krein, Gast\\~ao
2007-01-01
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).
Langevin dynamics of the deconfinement transition for pure gauge theory
Mizher, Ana Júlia; Fraga, Eduardo S.; Krein, Gastão Inácio [UNESP
2006-01-01
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).
Langevin dynamics of the deconfinement transition for pure gauge theory
Energy Technology Data Exchange (ETDEWEB)
Mizher, Ana Julia; Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Inst. de Fisica; Krein, Gastao [Universidade Estadual Paulista (UNESP), Sao Paulo, SP (Brazil). Inst. de Fisica Teorica
2007-06-15
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). (author)
Langevin study of neutron emission in the reactions 16O+181Ta and 19F+178Hf
Institute of Scientific and Technical Information of China (English)
YE Wei; WU Feng; YANG Hong-Wei
2008-01-01
The pre-scission neutrons measured in the reactions 16O+181Ta and 19F+178Hf are studied via a Langevin equation coupled with a statistical decay model.We find that because of the mass asymmetry of different entrance channels,the spin distributions of compound nuclei would be different,consequently,the measured neutrons in these two reactions would also different.This means that the entrance channel will affect the particle emission in the fission process of hot nuclei.
Langevin Formalism as the Basis for the Unification of Population Dynamics
de Vladar, Harold P.
2005-03-01
We are presenting a simple reformulation to population dynamics that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. The model shows that even when a population is density-dependent the dynamics of its growth rate does not depend explicitly neither on population size nor on the carrying capacity. Actually, the growth rate is uncoupled from the population size equation. The model has only two parameters: a Malthusian parameter ρ and an interaction coefficient θ. Distinct values of these parameters reproduce the family of θ-logistics, the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. Stochastic perturbations to the Malthusian parameter leads to a Langevin form of stochastic differential equation consisting of a family of cubic potentials perturbed with multiplicative noise. Using these equtions, we derive the stationary Fokker Plank distribution which which shows that in the stationary dynamics, density dependent populations fluctuate around a mean size that is shifted from the carrying capacity proportionally to the noise intensity. We also study which kinds of populations are susceptible to noise induced transitions.
Langevin dynamics of financial systems: A second-order analysis
Canessa, E.
2001-07-01
We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat Cq, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that Cq can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point.
Causal influence in linear Langevin networks without feedback
Auconi, Andrea; Giansanti, Andrea; Klipp, Edda
2017-04-01
The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However, a widely accepted formal definition of causal influence between observables is still missing. In the framework of linear Langevin networks without feedback (linear response models) we propose a measure of causal influence based on a new decomposition of information flows over time. We discuss its main properties and we compare it with other information measures like the transfer entropy. We are currently unable to extend the definition of causal influence to systems with a general feedback structure and nonlinearities.
Langevin model for a Brownian system with directed motion
Ambía, Francisco; Híjar, Humberto
2016-08-01
We propose a model for an active Brownian system that exhibits one-dimensional directed motion. This system consists of two Brownian spherical particles that interact through an elastic potential and have time-dependent radii. We suggest an algorithm by which the sizes of the particles can be varied, such that the center of mass of the system is able to move at an average constant speed in one direction. The dynamics of the system is studied theoretically using a Langevin model, as well as from Brownian Dynamics simulations.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A
2016-01-01
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...
Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei
2013-12-12
The dynamics of a protein along a well-defined coordinate can be formally projected onto the form of an overdamped Lagevin equation. Here, we present a comprehensive statistical-learning framework for simultaneously quantifying the deterministic force (the potential of mean force, PMF) and the stochastic force (characterized by the diffusion coefficient, D) from single-molecule Förster-type resonance energy transfer (smFRET) experiments. The likelihood functional of the Langevin parameters, PMF and D, is expressed by a path integral of the latent smFRET distance that follows Langevin dynamics and realized by the donor and the acceptor photon emissions. The solution is made possible by an eigen decomposition of the time-symmetrized form of the corresponding Fokker-Planck equation coupled with photon statistics. To extract the Langevin parameters from photon arrival time data, we advance the expectation-maximization algorithm in statistical learning, originally developed for and mostly used in discrete-state systems, to a general form in the continuous space that allows for a variational calculus on the continuous PMF function. We also introduce the regularization of the solution space in this Bayesian inference based on a maximum trajectory-entropy principle. We use a highly nontrivial example with realistically simulated smFRET data to illustrate the application of this new method.
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 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.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-05
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
On basic equation of statistical physics
Institute of Scientific and Technical Information of China (English)
邢修三
1996-01-01
Considering that thermodynamic irreversibility, the principle of entropy increase and hydrodynamic equations cannot be derived rigorously and in a unified way from the Liouville equations, the anomalous Langevin equation in Liouville space or its equivalent generalized Liouville equation is proposed as a basic equation of statistical physics. This equation reflects the fact that the law of motion of statistical thermodynamics is stochastic, but not deterministic. From that the nonequilibrium entropy, the principle of entropy increase, the theorem of minimum entropy production and the BBGKY diffusion equation hierarchy have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation, etc. have been derived from the BBGKY diffusion equation hierarchy. This equation has the same equilibrium solution as that of the Liouville equation. All these are unified and rigorous without adding any extra assumption. But it is difficult to prove that th
Institute of Scientific and Technical Information of China (English)
He Zhuo-Ran; Wu Tai-Lin; Ouyang Qi; Tu Yu-Hai
2012-01-01
Recent extensive studies of Escherichia coli (E.coli) chemotaxis have achieved a deep understanding of its microscopic control dynamics.As a result,various quantitatively predictive models have been developed to describe the chemotactic behavior of E.coli motion.However,a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient.Apart from the traditional Keller-Segel (K-S) equation,many existing population-level models developed from the microscopic dynamics are integro-PDEs.The difficulty comes mainly from cell tumbles which yield a velocity jumping process.Here,we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision.The resulting model not only quantitatively reproduces the results of pathway-based single-cell simulators,but also provides new inside information on the mechanism of E.coli chemotaxis.Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.
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.
QUANTUM LANGEVIN THEORY OF WHISPERING-GALLERY-MODE MICROSPHERE LASER
Institute of Scientific and Technical Information of China (English)
CHAI JIN-HUA; LU YI-QUN; LEUNG PUI-TANG
2000-01-01
A quantum Langevin theory of whispering-gallery-mode microsphere laser theory is developed. The linear and nonlinear analysis are made for laser operation below and above the threshold. In these analysis, corresponding to the specific property of microsphere, the effect of inversion fluctuation is treated. The coherence functions of laser field are calculated, and the intensity, the amplitude fluctuation and the linewidth of the field are obtained, which are connected with the enhancement factor of whispering-gallery-mode microsphere. It is shown that the strong couple and strong pumping are useful for the amplification of intensity and the decrease of linewidth below the threshold. It is also shown that, for the laser action above threshold, the variances of photon number and the linewidth of internal field are related to the enhancement factor and the square of the enhancement factor, respectively.
Complex Langevin: Etiology and Diagnostics of its Main Problem
Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu
2011-01-01
The complex Langevin method is a leading candidate for solving the so-called sign problem occurring in various physical situations. Its most vexing problem is that in some cases it produces `convergence to the wrong limit'. In the first part of the paper we go through the formal justification of the method, identify points at which it may fail and identify a necessary and sufficient criterion for correctness. This criterion would, however, require checking infinitely many identities, and therefore is somewhat academic. We propose instead a truncation to the check of a few identities; this still gives a necessary criterion, but a priori it is not clear whether it remains sufficient. In the second part we carry out a detailed study of two toy models: first we identify the reasons why in some cases the method fails, second we test the efficiency of the truncated criterion and find that it works perfectly at least in the toy models studied.
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
Zygalakis, K. C.
2011-01-01
In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
Mollgaard, A
2014-01-01
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.
Full simulation of chiral random matrix theory at nonzero chemical potential by complex Langevin
Mollgaard, A.; Splittorff, K.
2015-02-01
It is demonstrated that the complex Langevin method can simulate chiral random matrix theory at nonzero 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.
Langevin-Poisson-EQT: A dipolar solvent based quasi-continuum approach for electric double layers
Mashayak, S. Y.; Aluru, N. R.
2017-01-01
Water is a highly polar solvent. As a result, electrostatic interactions of interfacial water molecules play a dominant role in determining the distribution of ions in electric double layers (EDLs). Near a surface, an inhomogeneous and anisotropic arrangement of water molecules gives rise to pronounced variations in the electrostatic and hydration energies of ions. Therefore, a detailed description of the structural and dielectric properties of water is important to study EDLs. However, most theoretical models ignore the molecular effects of water and treat water as a background continuum with a uniform dielectric permittivity. Explicit consideration of water polarization and hydration of ions is both theoretically and numerically challenging. In this work, we present an empirical potential-based quasi-continuum theory (EQT) for EDL, which incorporates the polarization and hydration effects of water explicitly. In EQT, water molecules are modeled as Langevin point dipoles and a point dipole based coarse-grained model for water is developed systematically. The space dependence of the dielectric permittivity of water is included in the Poisson equation to compute the electrostatic potential. In addition, to reproduce hydration of ions, ion-water coarse-grained potentials are developed. We demonstrate the EQT framework for EDL by simulating NaCl aqueous electrolyte confined inside slit-like capacitor channels at various ion concentrations and surface charge densities. We show that the ion and water density predictions from EQT agree well with the reference molecular dynamics simulations.
A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics.
Smith, E R; Müller, E A; Craster, R V; Matar, O K
2016-12-06
Molecular dynamics simulations are employed to develop a theoretical model to predict the fluid-solid contact angle as a function of wall-sliding speed incorporating thermal fluctuations. A liquid bridge between counter-sliding walls is studied, with liquid-vapour interface-tracking, to explore the impact of wall-sliding speed on contact angle. The behaviour of the macroscopic contact angle varies linearly over a range of capillary numbers beyond which the liquid bridge pinches off, a behaviour supported by experimental results. Nonetheless, the liquid bridge provides an ideal test case to study molecular scale thermal fluctuations, which are shown to be well described by Gaussian distributions. A Langevin model for contact angle is parametrised to incorporate the mean, fluctuation and auto-correlations over a range of sliding speeds and temperatures. The resulting equations can be used as a proxy for the fully-detailed molecular dynamics simulation allowing them to be integrated within a continuum-scale solver.
Directory of Open Access Journals (Sweden)
Mazurek K.
2013-12-01
Full Text Available The fission dynamics described by solving differential equations of the Langevin type in three dimensional space of the deformation parameters is very sensitive on the choice of the macroscopic components such as potential energy models. The mass or charge distribution or total kinetic energy has been already shown to be different when one uses the Finite Range Liquid Drop Model or Lublin - Strasbourg Drop model. Also the shape-dependent congruence or shape-dependent Wigner energy and A0 terms are important especially for the fission of medium mass nuclei. We would like to make step forward and answer the question about the varying of the post-scission multiplicity by including different PES. Up to now there are only few experimental data for the medium mass nuclei where the pre- and post- scission emission has been estimated and isotopic distributions have been shown. The isotopic distributions of the fission products for light compound nucleus such as 111 In with two beam energies (Ebeam = 10.6 AMeV and 5.9 AMeV and two heavy systems: 229Np with Ebeam = 7.4 AMeV and 260 No (Ebeam = 6 AMeV and 7.5 AMeV have been studied theoretically. The agreement with the experimental data is discussed.
Rosinberg, M L; Munakata, T; Tarjus, G
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
Complex Langevin for Lattice QCD at $T=0$ and $\\mu \\ge 0$
Sinclair, D K
2016-01-01
QCD at finite quark-/baryon-number density, which describes nuclear matter, has a sign problem which prevents direct application of standard simulation methods based on importance sampling. When such finite density is implemented by the introduction of a quark-number chemical potential $\\mu$, this manifests itself as a complex fermion determinant. We apply simulations using the Complex Langevin Equation (CLE) which can be applied in such cases. However, this is not guaranteed to give correct results, so that extensive tests are required. In addition, gauge cooling is required to prevent runaway behaviour. We test these methods on 2-flavour lattice QCD at zero temperature on a small ($12^4$) lattice at an intermediate coupling $\\beta=6/g^2=5.6$ and relatively small quark mass $m=0.025$, over a range of $\\mu$ values from $0$ to saturation. While this appears to show the correct phase structure with a phase transition at $\\mu \\approx m_N/3$ and a saturation density of $3$ at large $\\mu$, the observables show dep...
Examination of isospin effects in multi-dimensional Langevin fission dynamics
Energy Technology Data Exchange (ETDEWEB)
Nadtochy, P.N., E-mail: nadtochy@na.infn.i [Istituto Nazionale di Fisica Nucleare, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Vardaci, E.; Di Nitto, A.; Brondi, A.; La Rana, G.; Moro, R. [Istituto Nazionale di Fisica Nucleare, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Via Cinthia, 80126 Napoli (Italy); Cinausero, M.; Prete, G. [Laboratori Nazionali di Legnaro dell' Istituto Nazionale di Fisica Nucleare, Legnaro (Padova) (Italy); Gelli, N.; Lucarelli, F. [Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica, Firenze (Italy)
2010-03-08
One-dimensional and three-dimensional dynamical fission calculations based on Langevin equations are performed for the compound nuclei {sup 194}Pb, {sup 200}Pb, {sup 206}Pb, {sup 182}Hg, and {sup 204}Hg to investigate the influence of the compound nucleus isospin on the prescission particle multiplicities and on the fission fragment mass-energy distribution. It is found that the prescission neutron, proton, and alpha particle multiplicities have approximately the same sensitivity to the dissipation strength for a given nucleus. This is at variance with conclusions of recent papers. The sensitivity of the calculated prescission particle multiplicities to the dissipation strength becomes higher with decreasing isospin of fissioning compound nucleus, and the increase of prescission particle multiplicities could reach 200%, when the reduction coefficient of one-body viscosity k{sub s} increases from 0.1 to 1, for the most neutron deficient nuclei considered. The variances of fission fragment mass and kinetic energy distributions are less sensitive to the change of dissipation strength than the prescission light particle multiplicities. A comparison to experimental data concerning {sup 200}Pb nucleus is also presented.
Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin-Huxley neurons
Huang, Yan-Dong; Xiang, Li; Shuai, Jian-Wei
2015-12-01
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin-Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude. Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 11125419), the National Natural Science Foundation of China (Grant No. 10925525), and the Funds for the Leading Talents of Fujian Province, China.
Heat dissipation and information flow for delayed bistable Langevin systems near coherence resonance
Xiao, Tiejun
2016-11-01
In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.
Blending Brownian motion and heat equation
Cristiani, Emiliano
2015-01-01
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
Sääskilahti, K; Oksanen, J; Tulkki, J
2013-07-01
Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.
Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics
Energy Technology Data Exchange (ETDEWEB)
Marian, J; Venturini, G; Hansen, B; Knap, J; Ortiz, M; Campbell, G
2009-05-08
The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the Quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's ({beta} = 0; {gamma} = 1/2) method, leading to a robust numerical behavior and energy conservation. In its current form, the method only allows for wave propagations supported by the less compliant of the two meshes across a heterogeneous boundary, which requires the use of overdamped dynamics to avoid spurious heating due to reflected vibrations. We have applied the method to two independent crystallographic systems characterized by different interatomic potentials (Al and Ta) and have measured thermal expansion in order to quantify the vibrational entropy loss due to homogenization. We rationalize the results in terms of system size, mesh coarseness, and nodal cluster diameter within the framework of the quasiharmonic approximation. For Al, we find that the entropy loss introduced by mesh coarsening varies linearly with the element size, and that volumetric effects are not critical in driving the anharmonic behavior of the simulated systems. In Ta, the anomalies of the interatomic potential employed result in negative and zero thermal expansion at low and high temperatures, respectively.
Exploring Complex-Langevin Methods for Finite-Density QCD
Sinclair, D K
2015-01-01
QCD at non-zero chemical potential ($\\mu$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm with Gauge Cooling in addition to adaptive methods, to prevent runaway behaviour. Simulations are performed at zero temperature on a $12^4$ lattice with 2 quarks which are light enough that $m_N/3$ is significantly larger than $m_\\pi/2$. Preliminary results are qualitatively as expected. The quark-number density is close to zero for $\\mu < m_N/3$, beyond which it increases, eventually reaching its saturation value of $3$ for $\\mu$ sufficiently large. The chiral condensate decreases as $\\mu$ is increased approaching zero at saturation, while the plaquette increases towards its quenched value. We have yet to observe the transition to nuclear matter at $\\mu \\approx m_N/3$, presumably because the runs for $\\mu$ between $m_N/3$ and saturation have yet to equilibrate.
Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations.
Ou, Zhaoyang; Muthukumar, M
2006-04-21
We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.
Langevin dynamics for the chiral transition and DCC formation
Energy Technology Data Exchange (ETDEWEB)
Kroff, Daniel; Fraga, Eduardo S. [Universidade Federal do Rio de Janeiro (IF/UFRJ), RJ (Brazil). Inst. de Fisica
2011-07-01
Full text: The theory of the strong interactions allows for the formation of metastable exotic configurations of the vacuum. Such metastable states can, in principle, be produced in high-energy heavy ion collisions taking place in accelerators like the LHC and in cosmic rays in the atmosphere. In this work, we consider disoriented chiral condensates (DCC), treating them through an effective field theory - the linear-sigma model couple to quarks - and consider possible consequences for ultra-energetic cosmic ray observations performed by the Pierre Auger observatory. After a high-energy collision, the state of the system can be chirally rotated from its true vacuum orientation. Later, this disoriented state (DCC) will relax into the ordinary vacuum configuration, emitting pions. This leads to an asymmetry between charged and neutral pions. This is especially interesting in the context of cosmic rays, where the primary collision in the atmosphere presents favorable conditions for the formation of DCCs. Such exotics might be related to the Centauro and Anti-Centauro events observed by Lattes and collaborators in high-energy cosmic rays experiments. We consider the possibility of DCC formation during a first-order chiral transition, studying the order parameter evolution in a Langevin description. We analyse the DCC influence on the typical time scales of transition and also calculate the pion production rate. (author)
Self-diffusion in a system of interacting Langevin particles.
Dean, D S; Lefèvre, A
2004-06-01
The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.
Hadamard-type fractional differential equations, inclusions and inequalities
Ahmad, Bashir; Ntouyas, Sotiris K; Tariboon, Jessada
2017-01-01
This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.
Using the complex Langevin equation to solve the sign problem of QCD
Energy Technology Data Exchange (ETDEWEB)
Sexty, Denes [Bergische Univ. Wuppertal (Germany)
2016-11-01
Using the resources of SuperMUC we have been able to calculate the reweighting results and compare them to the CLE for lattice sizes up to Nt=8. This did not allow the exploration of the phase transition line. It's an open question whether increasing the lattice size will allow us to go to smaller temperatures. The cost of larger lattices is of course increasing, especially the reweighting becomes much more expensive at larger volumes, as it's cost is proportional to the spatial volume cubed. An other important open question is the question of the poles: the fermionic drift term has singularities on the complex manifold, which in some cases can lead to the breakdown of the method, but it is unknown what its effect is on QCD, especially at low temperatures.
Panja, D.
2010-01-01
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagge
量子噪音与量子Langevin方程%Quantum Noise and Quantum Langevin Equation
Institute of Scientific and Technical Information of China (English)
文万信; 靳根明
2002-01-01
介绍了量子噪音和量子Langevin方程, 并与经典噪音和经典Langevin方程进行了比较. 量子噪音来源于两种途径, 第一种与经典噪音相似, 第二种则起源于Heisengberg测不准原理. 同时, 也简略给出了量子Langevin方程的推导.
An exactly solvable model for Brownian motion : I. Derivation of the Langevin equation
Ullersma, P.
1966-01-01
The motion of an elastically bound particle, linearly coupled with a bath of N harmonic oscillators is calculated exactly. The interaction is assumed to be rather weak and to vary slowly as function of the frequencies of the oscillators. The bath is chosen at the initial time in thermal equilibrium.
Stochastic processes and applications diffusion processes, the Fokker-Planck and Langevin equations
Pavliotis, Grigorios A
2014-01-01
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to eq...
Directory of Open Access Journals (Sweden)
Jing Zhao
2013-01-01
Full Text Available We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the G2 algorithm.
Nadtochy, P. N.; Ryabov, E. G.; Cheredov, A. V.; Adeev, G. D.
2016-10-01
A stochastic approach based on four-dimensional Langevin fission dynamics is applied to the calculation of a wide set of experimental observables of excited compound nuclei from 199Pb to 248Cf formed in reactions induced by heavy ions. In the model under investigation, the tilting degree of freedom ( K coordinate) 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 {c,h,α} parametrization. The evolution of the K coordinate is described by means of the Langevin equation in the overdamped regime. The friction tensor for the shape collective coordinates is calculated under the assumption of the modified version of the one-body dissipation mechanism, where the reduction coefficient ks of the contribution from the "wall" formula is introduced. The calculations are performed both for the constant values of the coefficient ks and for the coordinate-dependent reduction coefficient ks(q) which is found on the basis of the "chaos-weighted wall formula". Different possibilities of the deformation-dependent dissipation coefficient (γK) for the K coordinate are investigated. The presented results demonstrate that an impact of the ks and γK parameters on the calculated observable fission characteristics can be selectively probed. It was found that it is possible to describe the experimental data consistently with the deformation-dependent γK(q) coefficient for shapes featuring a neck, which predicts quite small values of γK=0.0077 (MeV zs)-1/2 and constant γK=0.1-0.4 (MeV zs)-1/2 for compact shapes featuring no neck.
Stochastic nonlinear differential equation generating 1/f noise.
Kaulakys, B; Ruseckas, J
2004-08-01
Starting from the simple point process model of 1/f noise, we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise, in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived. The solution of the equation exhibits the power-law distribution. The process with 1/f noise is demonstrated by the numerical solution of the derived equation with the appropriate restriction of the diffusion of the signal in some finite interval.
Gauge cooling in complex Langevin for lattice QCD with heavy quarks
Energy Technology Data Exchange (ETDEWEB)
Seiler, Erhard, E-mail: ehs@mppmu.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany); Sexty, Dénes, E-mail: d.sexty@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg (Germany); Stamatescu, Ion-Olimpiu, E-mail: I.O.Stamatescu@thphys.uni-heidelberg.de [Institut für Theoretische Physik, Universität Heidelberg (Germany)
2013-06-10
We employ a new method, “gauge cooling”, to stabilize complex Langevin simulations of QCD with heavy quarks. The results are checked against results obtained with reweighting; we find agreement within the estimated errors, except for strong gauge coupling in the confinement region. The method allows us to go to previously unaccessible high densities.
Electron-hole recombination in disordered organic semiconductors: Validity of the Langevin formula
van der Holst, J. J. M.; van Oost, F. W. A.; Coehoorn, R.; Bobbert, P. A.
2009-12-01
Accurate modeling of electron-hole recombination in organic light-emitting diodes (OLEDs) is essential for developing a complete description of their functioning. Traditionally, the recombination rate is described by the Langevin formula, with a proportionality factor equal to the sum of the electron and hole mobilities. In the disordered organic semiconductors used in OLEDs these mobilities have been shown to depend strongly on the carrier densities and on the electric field. Moreover, the energetic disorder leads to percolating pathways for the electron and hole currents, which may or may not be correlated. To answer the question whether the Langevin formula is still valid under such circumstances we perform Monte Carlo simulations of the recombination rate for Gaussian energetic disorder. We vary the disorder energy, the temperature, the densities, and mobility ratio of electrons and holes, the electric field, and the type of correlation between the electron and hole energies. We find that at zero electric field the Langevin formula is surprisingly well obeyed, provided that a change in the charge-carrier mobilities due to the presence of charge carriers of the opposite type is taken into account. Deviations from the Langevin formula at finite electric field are small at the field scale relevant for OLED modeling.
Institute of Scientific and Technical Information of China (English)
李平; 戎蒙恬; 薛义生; 喻丹; 刘涛
2007-01-01
研究了两跳固定中继蜂窝网的频率规划问题.与其他固定中继蜂窝网的研究不同,假设了固定中继节点与其所属基站链路上没有任何性能增强技术,并在此假设条件下,根据复用分割原则,提出了两种新的中继频率规划方案.同时将提出的频率规划方案与基于信道借用的频率规划方案及传统无中继的频率规划方案进行了比较.理论分析和仿真结果表明, 所提出的频率规划方案不但能提高小区边缘用户的服务质量,且与基于信道借用的频率规划方案相比,能够获得更大的系统性能提高.研究结果还表明,为了充分发挥固定中继网络的潜力,有必要在固定中继节点与其所属基站链路上引入性能增强技术.%The frequency planning for a cellular system enhanced with two-hop fixed relay nodes (FRNs) is investigated. It is assumed that there is no performance-enhancing technique on the base station (BS)-FRN links. Under the assumed condition, two frequency planning schemes are proposed by the principle of reuse partitioning (RP). The frequency planning schemes are compared with the channel-borrowing-based frequency planning scheme and the conventional frequency planning scheme without relaying. Theoretical analysis and simulation results show that the proposed schemes can improve the service quality for mobile terminals close to cell boundaries and provide better performance over the channel-borrowing-based frequency planning. Finally, to fully exploit the potentials of FRN enhanced cellular system, some performance enhancing techniques on BS-FRN links are indispensable.
基于复用分割技术的两跳蜂窝网的频谱分配方案%Reuse partitioning based frequency planning for two-hop cellular network
Institute of Scientific and Technical Information of China (English)
李平; 戎蒙恬; 薛义生
2007-01-01
根据复用分割原则,提出2种新的两跳固定中继蜂窝网的频谱分配方案,即:侧重于覆盖面积的频谱分配方案和侧重于频谱效率的频谱分配方案.相对于侧重频谱效率的频谱分配方案,侧重于覆盖面积的频谱分配方案有较大的频谱复用距离,从而能够提供更好的链路质量,其重点在于解决覆盖问题.同时,相对于侧重覆盖面积的频谱分配方案,侧重于频谱效率的频谱分配方案的频谱复用距离较小,从而有更高的频谱利用率,其重点在于解决频谱效率问题.与基于信道借用的频谱分配方案及传统无中继频谱分配方案比较,理论分析和仿真结果表明,提出的侧重于覆盖面积的频谱分配方案能提供最好的覆盖,同时侧重于频谱效率的频谱分配方案能得到最大的面积频谱效率.%Following the principle of reuse partitioning, two new frequency planning schemes are proposed, the coverage-oriented scheme and the efficiency-oriented scheme, for the cellular system with two-hop fixed relay nodes (FRNs). Compared with the efficiency-oriented scheme, the coverage-oriented scheme has higher reuse distances and is developed with emphasis on the coverage, while compared with the coverage-oriented scheme,the efficiency-oriented scheme has smaller reuse distances and is developed with emphasis on the spectral efficiency. Taking uplink as an example, both simplified analysis and intensive computer simulations are presented to offer comparisons among FRN enhanced systems with the proposed schemes, with a known channel-borrowing based frequency planning scheme and the conventional cellular system without relaying.Studies show that the FRN enhanced system with the coverage-oriented scheme provides the best coverage,while that with the efficiency-oriented scheme offers the highest area spectral efficiency.
Mesoscopic virial equation for nonequilibrium statistical mechanics
Falasco, G.; Baldovin, F.; Kroy, K.; Baiesi, M.
2016-09-01
We derive a class of mesoscopic virial equations governing energy partition between conjugate position and momentum variables of individual degrees of freedom. They are shown to apply to a wide range of nonequilibrium steady states with stochastic (Langevin) and deterministic (Nosé-Hoover) dynamics, and to extend to collective modes for models of heat-conducting lattices. A macroscopic virial theorem ensues upon summation over all degrees of freedom. It allows for the derivation of generalised (nonequilibrium) equations of state that involve average dissipative heat flows besides genuine state variables, as exemplified for inertial Brownian motion with solid friction and overdamped active Brownian particles subject to inhomogeneous pressure.
Modeling near-barrier collisions of heavy ions based on a Langevin-type approach
Karpov, A. V.; Saiko, V. V.
2017-08-01
Background: Multinucleon transfer in low-energy nucleus-nucleus collisions is proposed as a method of production of yet-unknown neutron-rich nuclei hardly reachable by other methods. Purpose: Modeling of dynamics of nuclear reactions induced by heavy ions in their full complexity of competing reaction channels remains to be a challenging task. The work is aimed at development of such a model and its application to the analysis of multinucleon transfer in deep inelastic collisions of heavy ions leading, in particular, to formation of neutron-rich isotopes in the vicinity of the N =126 shell closure. Method: Multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations has been proposed. It is combined with a statistical model for simulation of de-excitation of primary reaction fragments. The model provides a continuous description of the system evolution starting from the well-separated target and projectile in the entrance channel of the reaction up to the formation of final reaction products. Results: A rather complete set of experimental data available for reactions 136Xe+198Pt,208Pb,209Bi was analyzed within the developed model. The model parameters have been determined. The calculated energy, mass, charge, and angular distributions of reaction products, their various correlations as well as cross sections for production of specific isotopes agree well with the data. On this basis, optimal experimental conditions for synthesizing the neutron-rich nuclei in the vicinity of the N =126 shell were formulated and the corresponding cross sections were predicted. Conclusions: The production yields of neutron-rich nuclei with N =126 weakly depend on the incident energy. At the same time, the corresponding angular distributions are strongly energy dependent. They are peaked at grazing angles for larger energies and extend up to the forward angles at low near-barrier collision energies. The corresponding cross sections exceed 100 nb for
The Langevin Approach: An R Package for Modeling Markov Processes
Directory of Open Access Journals (Sweden)
Philip Rinn
2016-08-01
Full Text Available We describe an 'R' package developed by the research group 'Turbulence, Wind energy' 'and Stochastics' (TWiSt at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
The Langevin Approach: An R Package for Modeling Markov Processes
Rinn, Philip; Wächter, Matthias; Peinke, Joachim
2016-01-01
We describe an R package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg, which extracts the (stochastic) evolution equation underlying a set of data or measurements. The method can be directly applied to data sets with one or two stochastic variables. Examples for the one-dimensional and two-dimensional cases are provided. This framework is valid under a small set of conditions which are explicitly presented and which imply simple preliminary test procedures to the data. For Markovian processes involving Gaussian white noise, a stochastic differential equation is derived straightforwardly from the time series and captures the full dynamical properties of the underlying process. Still, even in the case such conditions are not fulfilled, there are alternative versions of this method which we discuss briefly and provide the user with the necessary bibliography.
Li, Daming
2016-01-01
We consider the massive Thirring model at finite density in 0+1 dimension. The fermion bag approach, Langevin dynamics and complex Langevin dynamics are adopted to attack the sign problem for this model. Compared with the complex Langevin dynamics, both fermion bag approach and Langvin dynamics avoid the sign problem. The fermion density and chiral condensate, which are obtained by these numerical methods, are compared with the exact results. The advantages of the fermion bag approach over the other numerical methods are also discussed.
Variational estimation of the drift for stochastic differential equations from the empirical density
Batz, Philipp; Ruttor, Andreas; Opper, Manfred
2016-08-01
We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation. The minimization of an empirical estimate of the variational functional using kernel based regularization can be performed in closed form. We demonstrate the performance of the method on second order, Langevin-type equations and show how the method can be generalized to other noise models.
Variational estimation of the drift for stochastic differential equations from the empirical density
Batz, Philipp; Opper, Manfred
2016-01-01
We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation. The minimization of an empirical estimate of the variational functional using kernel based regularization can be performed in closed form. We demonstrate the performance of the method on second order, Langevin-type equations and show how the method can be generalized to other noise models.
Horowitz, Jordan M.
2015-01-01
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations are large, the discrete Chemical Master Equation can be approximated with a continuous diffusion process, like the Chemical Langevin Equation or Low Noise Approximation. In this paper, we investigate to what extent these diffusion approximations inherit the s...
Constant pressure and temperature discrete-time Langevin molecular dynamics.
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Complex Langevin in Lattice QCD: dynamic stabilisation and the phase diagram
Aarts, Gert; Jäger, Benjamin; Sexty, Dénes
2016-01-01
Complex Langevin simulations provide an alternative to sample path integrals with complex weights and therefore are suited to determine the phase diagram of QCD from first principles. We use our proposed method of Dynamic Stabilisation (DS) to ensure improved convergence to the right limit and present new systematic tests of this technique. We also show results on QCD in the limit of heavy quarks and an analysis of DS compared to known results from reweighting.
Langevin model of the temperature and hydration dependence of protein vibrational dynamics.
Moritsugu, Kei; Smith, Jeremy C
2005-06-23
The modification of internal vibrational modes in a protein due to intraprotein anharmonicity and solvation effects is determined by performing molecular dynamics (MD) simulations of myoglobin, analyzing them using a Langevin model of the vibrational dynamics and comparing the Langevin results to a harmonic, normal mode model of the protein in vacuum. The diagonal and off-diagonal Langevin friction matrix elements, which model the roughness of the vibrational potential energy surfaces, are determined together with the vibrational potentials of mean force from the MD trajectories at 120 K and 300 K in vacuum and in solution. The frictional properties are found to be describable using simple phenomenological functions of the mode frequency, the accessible surface area, and the intraprotein interaction (the displacement vector overlap of any given mode with the other modes in the protein). The frictional damping of a vibrational mode in vacuum is found to be directly proportional to the intraprotein interaction of the mode, whereas in solution, the friction is proportional to the accessible surface area of the mode. In vacuum, the MD frequencies are lower than those of the normal modes, indicating intramolecular anharmonic broadening of the associated potential energy surfaces. Solvation has the opposite effect, increasing the large-amplitude vibrational frequencies relative to in vacuum and thus vibrationally confining the protein atoms. Frictional damping of the low-frequency modes is highly frequency dependent. In contrast to the damping effect of the solvent, the vibrational frequency increase due to solvation is relatively temperature independent, indicating that it is primarily a structural effect. The MD-derived vibrational dynamic structure factor and density of states are well reproduced by a model in which the Langevin friction and potential of mean force parameters are applied to the harmonic normal modes.
Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method
Fukushima, Kenji
2015-01-01
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave-functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave-functions on a grid using a toy model and confirm their well-localized behavior.
First results of the EXILL and FATIMA campaign at the Institut Laue Langevin
Energy Technology Data Exchange (ETDEWEB)
Jolie, Jan; Regis, Jean-Marc; Saed-Samii, Nima; Warr, Nigel [IKP, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Wilmsen, Dennis [IKP, Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); GANIL, BP 55027 (France); France, Gilles de; Clement, Emmanuel [GANIL, BP 55027 (France); Blanc, Aurelien; Jentschel, Michael; Koester, Uli; Mutti, Paolo; Soldner, Thorsten [ILL, 71 Av. des Martyrs, 38042 Grenoble (France); Simpson, Gary [University of Western Scotland, Paisley, PA1 2BE (United Kingdom); UIrban, Waldek [Faculty of Physics, University of Warsaw, 02-093 Warsaw (Poland); Bruce, Alison; Lalskovski, Stefan [SCEM, University of Brighton, Brighton BN2 4GJ (United Kingdom); Fraile, Luis [Grupo de Fisica Nuclear, Universidad Complutese, 28040 Madrid (Spain); Kroell, Thorsten [Institut fuer Kernphysik, TU Darmstadt, Darmstadt (Germany); Podolyak, Zsolt; Regan, Patrick [Dept. of Physics, University of Surrey, Guildford GU2 7XH (United Kingdom); Korten, Wolfram [CEA, Centre de Saclay, IRFU, 91191 Gif-sur-Yvette (France); Ur, Calin; Marginean, Nicu [Horia Hulubei NIPNE, 77125 Bucharest (Romania)
2015-07-01
At the PF1B cold neutron beam line at the Institut Laue Langevin the EXILL and FATIMA array consisting of 8 EXOGAM clover Ge detectors and 16 LaBr3(Ce) scintillators was used for the measurement of lifetimes using the generalised centroid difference method. The studied nuclei were formed by the (n,γ) and (n,fission) reactions. We report on the set-up and present first results on {sup 90}Zr and {sup 196}Pt.
Complex Langevin Dynamics in 1+1d QCD at Non-Zero Densities
Schmalzbauer, Sebastian
2016-01-01
We present our results obtained from gauge cooled complex Langevin simulations in 1+1d QCD at non-zero densities in the strong coupling regime with unrooted staggered fermions. For small quark masses there are regions of the chemical potential where this method fails to reproduce correct results. In these parameter ranges we studied the effect of different gauge cooling schemes on the distributions of the fermion determinant as well as of observables.
On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models
Aarts, Gert; Sexty, Denes; Stamatescu, Ion-Olimpiu
2016-01-01
In the complex Langevin approach to lattice simulations at nonzero density, zeroes of the fermion determinant lead to a meromorphic drift and hence a need to revisit the theoretical derivation. We discuss how poles in the drift affect the formal justification of the approach and then explore the various potential issues in simple models, in a manner that is applicable to heavy dense and full QCD.
Towards the heavy dense QCD phase diagram using Complex Langevin simulations
Aarts, Gert; Jäger, Benjamin; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu
2015-01-01
Monte Carlo methods cannot probe far into the QCD phase diagram with a real chemical potential, due to the famous sign problem. Complex Langevin simulations, using adaptive step-size scaling and gauge cooling, are suited for sampling path integrals with complex weights. We report here on tests of the deconfinement transition in pure Yang-Mills SU(3) simulations and present an update on the QCD phase diagram in the limit of heavy and dense quarks.
Results on the heavy-dense QCD phase diagram using complex Langevin
Aarts, Gert; Jäger, Benjamin; Sexty, Dénes
2016-01-01
Complex Langevin simulations have been able to successfully reproduce results from Monte Carlo methods in the region where the sign problem is mild and make predictions when it is exponentially hard. We present here our study of the QCD phase diagram and the boundary between the confined and deconfined phases in the limit of heavy and dense quarks (HDQCD) for 3 different lattice volumes. We also briefly discuss instabilities encountered in our simulations.
PSPICE controlled-source models of analogous circuit for Langevin type piezoelectric transducer
Institute of Scientific and Technical Information of China (English)
2007-01-01
The design and construction of wide-band and high efficiency acoustical projector has long been considered an art beyond the capabilities of many smaller groups. Langevin type piezoelectric transducers have been the most candidate of sonar array system applied in underwater communication. The transducers are fabricated, by bolting head mass and tail mass on both ends of stacked piezoelectric ceramic, to satisfy the multiple, conflicting design for high power transmitting capability. The aim of this research is to study the characteristics of Langevin type piezoelectric transducer that depend on different metal loading. First, the Mason equivalent circuit is used to model the segmented piezoelectric ceramic, then, the impedance network of tail and head masses is deduced by the Newton’s theory. To obtain the optimal solution to a specific design formulation, PSPICE controlled-source programming techniques can be applied. A valid example of the application of PSPICE models for Langevin type transducer analysis is presented and the simulation results are in good agreement with the experimental measurements.
PSPICE controlled-source models of analogous circuit for Langevin type piezoelectric transducer
Institute of Scientific and Technical Information of China (English)
CHEN YeongChin; WU MenqJiun; LIU WeiKuo
2007-01-01
The design and construction of wide-band and high efficiency acoustical projector has long been considered an art beyond the capabilities of many smaller groups.Langevin type piezoelectric transducers have been the most candidate of sonar array system applied in underwater communication.The transducers are fabricated,by bolting head mass and tail mass on both ends of stacked piezoelectric ceramic,to satisfy the multiple,conflicting design for high power transmitting capability.The aim of this research is to study the characteristics of Langevin type piezoelectric transducer that depend on different metal loading.First,the Mason equivalent circuit is used to model the segmented piezoelectric ceramic,then,the impedance network of tail and head masses is deduced by the Newton's theory.To obtain the optimal solution to a specific design formulation,PSPICE controlled-source programming techniques can be applied.A valid example of the application of PSPICE models for Langevin type transducer analysis is presented and the simulation results are in good agreement with the experimental measurements.
Nagata, Keitaro; Shimasaki, Shinji
2016-01-01
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper we revisit the argument for justification of the method. Starting with a finite Langevin step-size $\\epsilon$, we find that the $\\epsilon\\rightarrow 0$ limit is actually subtle, although the previous argument used a continuous Langevin time from the outset. We also point out a subtlety in the use of time-evolved observables, which play a crucial role in the argument. This subtlety appears when the probability of the drift term is not suppressed exponentially at large magnitude. We claim that the failures of the method previously considered to occur for different reasons should be understood in this way. Using...
Institute of Scientific and Technical Information of China (English)
郭秀清; 王旭焕
2013-01-01
讨论了分数阶Langevin方程的非局部狄利克雷边值问题,利用Leray-Schauder's和压缩映像原理,分别得到了方程的解的存在及唯一性.%In this paper,a new type of Langevin equation with fractional orders with Nonlocal Dirichlet Boundary Value Problems is considered.By using Leray-Schauder's fixed point theorem and Banach's contraction mapping principle,we obtain the existence and uniqueness results of the solution.
Zhou, Yanjun; Yin, Cangtao
2016-12-01
The Fokker-Planck equation (FPE) of the unimolecular reaction with Tsallis distribution is established by means of approximation to the master equation. The memory effect, taken into transition probability, is relevant and important for lots of anomalous phenomena. The Taylor expansion for large volume is applied to derive the power-law FPE. The steady-state solution of FPE and microscopic dynamics Ito-Langevin equation of concentration variables are therefore obtained and discussed. Two unimolecular reactions are taken as examples and the concentration distributions with different power-law parameters are analyzed, which may imply strong memory effect of hopping process.
Non-linear Langevin model for the early-stage dynamics of electrospinning jets
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
New source for ultracold neutrons at the Institut Laue-Langevin
Piegsa, F. M.; Fertl, M.; Ivanov, S. N.; Kreuz, M.; Leung, K. K. H.; Schmidt-Wellenburg, P.; Soldner, T.; Zimmer, O.
2014-07-01
A new intense superthermal source for ultracold neutrons (UCN) was installed at a dedicated beam line at the Institut Laue-Langevin. Incident neutrons with a wavelength of 0.89 nm are converted to UCN in a 5-liter volume filled with superfluid He4 at a temperature of about 0.7 K. The UCN can be extracted to room temperature experiments. We present the cryogenic setup of the source, a characterization of the cold neutron beam, and UCN production measurements, where a UCN density in the production volume of at least 55 per cm3 was determined.
New source for ultracold neutrons at the Institut Laue-Langevin
Piegsa, F M; Ivanov, S N; Kreuz, M; Leung, K K H; Schmidt-Wellenburg, P; Soldner, T; Zimmer, O
2014-01-01
A new intense superthermal source for ultracold neutrons (UCN) has been installed at a dedicated beam line at the Institut Laue-Langevin. Incident neutrons with a wavelength of 0.89 nm are converted to UCN in a five liter volume filled with superfluid $^4$He at a temperature of about 0.7 K. The UCN can be extracted to room temperature experiments. We present the cryogenic setup of the source, a characterization of the cold neutron beam, and UCN production measurements, where a UCN density in the production volume of at least 55 per cm$^3$ was determined.
Energy Technology Data Exchange (ETDEWEB)
Lisin, E. A.; Lisina, I. I.; Vaulina, O. S.; Petrov, O. F. [Joint Institute for High Temperatures of the Russian Academy of Sciences, 13 bd.2 Izhorskaya St., Moscow 125412, Russia and Moscow Institute of Physics and Technology, 9 Institutskiy Per., Dolgoprudny, Moscow Region 141700 (Russian Federation)
2015-03-15
Solution of the inverse Langevin problem is presented for open dissipative systems with anisotropic interparticle interaction. Possibility of applying this solution for experimental determining the anisotropic interaction forces between dust particles in complex plasmas with ion flow is considered. For this purpose, we have tested the method on the results of numerical simulation of chain structures of particles with quasidipole-dipole interaction, similar to the one occurring due to effects of ion focusing in gas discharges. Influence of charge spatial inhomogeneity and fluctuations on the results of recovery is also discussed.
Pastorino, C; Kreer, T; Müller, M; Binder, K
2007-08-01
In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-01-01
We study full QCD at finite density and low temperature with light quark mass using the complex Langevin method. Since the singular drift problem turns out to be mild on a $4^3 \\times 8$ lattice we use, the gauge cooling is performed only to control the unitarity norm in this exploratory study. We report on our preliminary data obtained from the complex Langevin simulation up to certain Langevin time. While the data are still noisy due to lack of statistics, the onset of the baryon number density seems to occur at larger $\\mu$ than half the pion mass, which is the value for the phase quenched QCD. The validity of our simulation is tested by the recently proposed criterion based on the probability distribution of the drift term.
Aarts, Gert
2010-01-01
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at larger chemical potential by comparison with the world line method. While complex Langevin works for larger beta, we find that it fails for smaller beta, in the region of the phase diagram corresponding to the disordered phase. Diagnostic tests are developed to identify symptoms correlated with incorrect convergence. We argue that the erroneous behaviour at smaller beta is not due to the sign problem, but rather resembles dynamics observed in complex Langevin simulations of simple models with complex noise.
Distributed-order diffusion equations and multifractality: Models and solutions
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Fractional L\\'{e}vy-driven Ornstein--Uhlenbeck processes and stochastic differential equations
Fink, Holger; 10.3150/10-BEJ281
2011-01-01
Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\\'{e}vy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper integrals, the long-time behavior of FLPs is derived. This is sufficient to define the fractional L\\'{e}vy-Ornstein-Uhlenbeck process (FLOUP) pathwise as an improper Riemann-Stieltjes integral. We show further that the FLOUP is the unique stationary solution of the corresponding Langevin equation. Furthermore, we calculate the autocovariance function and prove that its increments exhibit long-range dependence. Exploiting the Langevin equation, we consider SDEs driven by FLPs of bounded $p$-variation for $p<2$ and construct solutions using the corresponding FLOUP. Finally, we consider examples of such SDEs, includin...
Wosiek, Jacek
2015-01-01
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by doubling the number of real variables. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The construction is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field -- a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an intriguing interpretation of new variables is alluded to.
Inhabitant Distribution Model Based on Langevin Equation%基于Langevin方程的居民分布模型
Institute of Scientific and Technical Information of China (English)
高峰; 姚荣涵; 王殿海
2005-01-01
分析了影响居民分布的因素,描述了居民分布曲线;根据居民分布曲线与Langevin方程曲线的相似性,建立了基于Langevin方程的居民分布模型;通过模型求解过程,说明了模型参数在居民分布中的实际意义.居民分布的Langevin模型可以定量描述城市居民分布规律,揭示城市居民分布的宏观现象,为城市新建居民小区及改造交通系统提供科学的理论依据.
Pahlavani, M. R.; Mirfathi, S. M.
2017-07-01
Neutron multiplicity prior to scission and evaluation of mass distribution of fission fragments with the fission time scale for neutron induced fission of plutonium isotopes are investigated using a dynamical Langevin approach. Also, mass yield of fragments and prompt neutron multiplicity in different time scales of the fission process are compared with experimental data. Reasonable agreement is achieved between calculated and available experimental data.
Excitability in a stochastic differential equation model for calcium puffs.
Rüdiger, S
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review
Directory of Open Access Journals (Sweden)
Eric Paquet
2015-01-01
Full Text Available Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods.
A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II
Energy Technology Data Exchange (ETDEWEB)
Uchida, Waka; Kimura, Yoshiro; Wakabayashi, Masamitsu [Department of Biomolecular Engineering, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama 226-8503 (Japan); Hatakeyama, Makoto; Ogata, Koji; Nakamura, Shinichiro [RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Yokojima, Satoshi [Tokyo University of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan and RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2013-12-10
We have performed three QM/Langevin-MD simulations for oxygen-evolving complex (OEC) and surrounding residues, which are different configurations of the oxidation numbers on Mn atoms in the Mn{sub 4}O{sub 5}Ca cluster. By analyzing these trajectories, we have observed sensitivity of the change to the configuration of Mn oxidation state on O atoms of carboxyl on three amino acids, Glu354, Ala344, and Glu333. The distances from Mn to O atoms in residues contacting with the Mn{sub 4}O{sub 5}Ca cluster were analyzed for the three trajectories. We found the good correlation of the distances among the simulations. However, the distances with Glu354, Ala344, and Glu333 have not shown the correlation. These residues can be sensitive index of the changes of Mn oxidation numbers.
A Langevin Canonical Approach to the Study of Quantum Stochastic Resonance in Chiral Molecules
Directory of Open Access Journals (Sweden)
Germán Rojas-Lorenzo
2016-09-01
Full Text Available A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
Yang, Xihua; Shang, Jie; Xue, Bolin; Zhou, Yuanyuan; Xiao, Min
2014-05-19
We conduct theoretical studies on the effects of various parameters on generation of multipartite continuous-variable entanglement via atomic spin wave induced by the strong coupling and probe fields in the Λ-type electromagnetically induced transparency configuration in a realistic atomic ensemble by using the Heisenberg-Langevin formalism. It is shown that the increase of the atomic density and/or Rabi frequencies of the scattering fields, as well as the decrease of the coherence decay rate of the lower doublet would strengthen the degree of multipartite entanglement. This provides a clear evidence that the creation of multicolor multipartite entangled narrow-band fields to any desired number with a long correlation time can be achieved conveniently by using atomic spin wave in an atomic ensemble with large optical depth, which may find interesting applications in quantum information processing and quantum networks.
Test for a universal behavior of Dirac eigenvalues in the complex Langevin method
Ichihara, Terukazu; Kashiwa, Kouji
2016-01-01
We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for correct convergence case, while it follows the Ginibre ensemble for wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for correct convergence case.
A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics.
Mabey, P; Richardson, S; White, T G; Fletcher, L B; Glenzer, S H; Hartley, N J; Vorberger, J; Gericke, D O; Gregori, G
2017-01-30
The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas.
Improving the transient response of a bolt-clamped Langevin transducer using a parallel resistor.
Chang, Kuo Tsi
2003-08-01
This paper suggests a parallel resistor to reduce DC time constant and DC response time of the transient response, induced immediately after an AC voltage connected to a bolt-clamped Langevin transducer (BLT) is switched off. An equivalent circuit is first expressed. Then, an open-circuit transient response at the terminals induced by initial states is derived and measured, and thus parameters for losses of the BLT device are estimated by DC and AC time constants of the transient response. Moreover, a driving and measuring system is designed to determine transient response and steady-state responses of the BLT device, and a parallel resistor is connected to the BLT device to reduce the DC time constant. Experimental results indicate that the DC time constant greatly exceeds the AC time constant without the parallel resistor, and greatly decreases from 42 to 1 ms by a 100-kOmega parallel resistor.
The new powder diffractometer D1B of the Institut Laue Langevin
Puente Orench, I.; Clergeau, J. F.; Martínez, S.; Olmos, M.; Fabelo, O.; Campo, J.
2014-11-01
D1B is a medium resolution high flux powder diffractometer located at the Institut Laue Langevin, ILL. D1B a suitable instrument for studying a large variety of polycrystalline materials. D1B runs since 1998 as a CRG (collaborating research group) instrument, being exploited by the CNRS (Centre National de la Recherche Scientifique, France) and CSIC (Consejo Superior de Investigaciones Cientificas, Spain). In 2008 the Spanish CRG started an updating program which included a new detector and a radial oscillating collimator (ROC). The detector, which has a sensitive height of 100mm, covers an angular range of 128°. Its 1280 gold wires provide a neutron detection point every 0.1°. The ROC is made of 198 gadolinium- based absorbing collimation blades, regular placed every 0.67°. Here the present characteristics of D1B are reviewed and the different experimental performances will be presented.
Nagata, Keitaro; Shimasaki, Shinji
2015-01-01
The complex Langevin method has been attracting much attention as a solution to the sign problem since the method was shown to work in finite density QCD in the deconfined phase by using the so-called gauge cooling procedure. Whether it works also in the confined phase with light quarks is still an open question, though. In order to shed light on this question, we apply the method to the chiral Random Matrix Theory, which describes the epsilon regime of finite density QCD. Earlier works reported that a naive implementation of the method fails to reproduce the known exact results and that the problem can be solved by choosing a suitable coordinate. In this work we stick to the naive implementation, and show that a generalized gauge cooling procedure can be used to avoid the problem.
Test for a universal behavior of Dirac eigenvalues in the complex Langevin method
Ichihara, Terukazu; Nagata, Keitaro; Kashiwa, Kouji
2016-05-01
We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at nonzero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an unfolding procedure for the Dirac eigenvalues obtained in the CL method. For large quark mass, we find that the NNS distribution obeys the Ginibre ensemble as expected. For small quark mass, the NNS distribution follows the Wigner surmise for the correct convergence case, while it follows the Ginibre ensemble for the wrong convergence case. The Wigner surmise is physically reasonable from the chemical potential independence of the ChRMT. The Ginibre ensemble is known to be favored in a phase-quenched QCD at finite chemical potential. Our result suggests a possibility that the originally universal behavior of the NNS distribution is preserved even in the CL method for the correct convergence case.
Han, Jie
2014-01-01
We investigate time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of reflection boundary of potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of passing probability over the saddle point of inverse harmonic potential.
A simulation method of combinding boundary element method with generalized Langevin dynamics
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new simulation approach to incorporate hydration force into generalized Langevin dynamics (GLD) is developed in this note. The hydration force determined by the boundary element method (BEM) is taken into account as the mean force terms of solvent including Coulombic interactions with the induced surface charge and the surface pressure of solvent. The exponential model is taken for the friction kernel. A simulation study has been performed on the cyclic undecapeptide cyclosporin A (CPA). The results obtained from the new method (GLDBEM) have been analyzed and compared with that obtained from the molecular dynamics (MD) simulation and the conventional stochastic dynamics (SD) simulation. We have found that the results obtained from GLDBEM show the obvious improvement over the SD simulation technique in the study of molecular structure and dynamic properties.
Developing Itô stochastic differential equation models for neuronal signal transduction pathways.
Manninen, Tiina; Linne, Marja-Leena; Ruohonen, Keijo
2006-08-01
Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical
Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics
Banerjee, Dhruba; Banik, S K; Ray, D S; Banerjee, Dhruba; Bag, Bidhan Chandra; Banik, Suman Kumar; Ray, Deb Shankar
2002-01-01
We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\\it true probability distribution functions} and is independent of path integral technique...
The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
DEFF Research Database (Denmark)
Riotto, Antonio; Sloth, Martin Snoager
2011-01-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature...... the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators...
Institute of Scientific and Technical Information of China (English)
唐宏伟; 徐明; 孙彩霞
2014-01-01
Energy consumption and latency are two major problems that are primarily considered in the design of medium access control (MAC)protocols in wireless sensor networks (WSNs).A new low-latency,energy-efficient and receiver-initiated asynchronous MAC protocol in WSNs is proposed.By precisely predicting the receiver’s wakeup time,THO-MAC protocol can schedule the sender to listen to the channel,such that it can reduce the sender’s energy waste of idle listening.On the other hand,in order to reduce packet delivery latency,THO-MAC protocol chooses the forwarders in the sender’s two-hop forwarders set to minimize the two-hop forwarding latency.The performance of THO-MAC protocol in terms of detailed NS2 simulation is evaluated.The simulation results show that the THO-MAC protocol reduces 35 .5%and 1 8%packet delivery latency,while saving 23.5% and 15.5% sensor energy consumption,compared with RI-MAC and Any-MAC,the two state-of-the-art MAC protocols.%功耗与延迟是无线传感器网络介质访问控制协议设计首要考虑的两个问题。提出了一种新的传感器网络低延迟、低功耗、接收节点初始化异步介质访问控制协议---THO-MAC协议。通过准确预测接收节点的唤醒时间，THO-MAC 协议调度发送节点侦听信道，从而减少发送节点空闲侦听能量浪费。THO-MAC协议在发送节点两跳转发节点集中选择使报文两跳转发延迟最小的转发节点，从而降低报文传输延迟。使用NS2模拟器对THO-MAC协议进行了详细模拟。模拟结果显示，与RI-MAC和Any-MAC协议相比，THO-MAC协议可以减少35．5％和18％的报文传输延迟，同时节省23．5％和15．5％的节点功耗。
Rosinberg, M. L.; Tarjus, G.; Munakata, T.
2017-02-01
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015), 10.1103/PhysRevE.91.042114] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.
Magnus, Wilhelm
2004-01-01
The hundreds of applications of Hill's equation in engineering and physics range from mechanics and astronomy to electric circuits, electric conductivity of metals, and the theory of the cyclotron. New applications are continually being discovered and theoretical advances made since Liapounoff established the equation's fundamental importance for stability problems in 1907. Brief but thorough, this volume offers engineers and mathematicians a complete orientation to the subject.""Hill's equation"" connotes the class of homogeneous, linear, second order differential equations with real, period
Quantum particle interacting with a metallic particle: Spectra from quantum Langevin theory
Loh, W. M. Edmund; Ooi, C. H. Raymond
2017-01-01
The effect of a nearby metallic particle on the quantum optical properties of a quantum particle in the four-level double Raman configuration is studied using the quantum Langevin approach. We obtain analytical expressions for the correlated quantum fields of Stokes and anti-Stokes photons emitted from the system and perform analysis on how the interparticle distance, the direction of observation or detection, the strengths of controllable laser fields, the presence of surface plasmon resonance, and the number density of the quantum particle affect the quantum spectra of the Stokes and anti-Stokes fields. We explore the physics behind the quantum-particle-metallic-nanoparticle interaction within the dipole approximation, that is, when the interparticle distance is much larger than the sizes of the particles. Our results show the dependence of the spectra on the interparticle distance in the form of oscillatory behavior with damping as the interparticle distance increases. At weaker laser fields the enhancement of quantum fields which manifests itself in the form of a Fano dip in the central peak of the spectra becomes significant. Also, the quantum-particle-metallic-nanoparticle coupling, which is affected by the size of the metallic nanoparticle and the number density of the quantum particle, changes the angular dependence of the spectra by breaking the angular rotational symmetry. In the presence of surface plasmon resonance the oscillatory dependence of the spectra on the interparticle distance and angles of observation becomes even stronger due to the plasmonic enhancement effect.
Ito, Yuta
2016-01-01
In many interesting physical systems, the determinant which appears from integrating out fermions becomes complex, and its phase plays a crucial role in the determination of the vacuum. An example of this is QCD at low temperature and high density, where various exotic fermion condensates are conjectured to form. Another example is the Euclidean version of the type IIB matrix model for 10d superstring theory, where spontaneous breaking of the SO(10) rotational symmetry down to SO(4) is expected to occur. When one applies the complex Langevin method to these systems, one encounters the singular-drift problem associated with the appearance of nearly zero eigenvalues of the Dirac operator. Here we propose to avoid this problem by deforming the action with a fermion bilinear term. The results for the original system are obtained by extrapolations with respect to the deformation parameter. We demonstrate the power of this approach by applying it to a simple matrix model, in which spontaneous symmetry breaking from...
Argument for justification of the complex Langevin method and the condition for correct convergence
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-12-01
The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper we revisit the argument for justification of the method. In particular, we point out a subtlety in the use of time-evolved observables, which play a crucial role in the previous argument. This requires that the probability of the drift term should fall off exponentially or faster at large magnitude. We argue that this is actually a necessary and sufficient condition for the method to be justified. Using two simple examples, we show that our condition tells us clearly whether the results obtained by the method are trustable or not. We also discuss a new possibility for the gauge cooling, which can reduce the magnitude of the drift term directly.
Sule, N; Rice, S A; Gray, S K; Scherer, N F
2015-11-16
Understanding the formation of electrodynamically interacting assemblies of metal nanoparticles requires accurate computational methods for determining the forces and propagating trajectories. However, since computation of electromagnetic forces occurs on attosecond to femtosecond timescales, simulating the motion of colloidal nanoparticles on milliseconds to seconds timescales is a challenging multi-scale computational problem. Here, we present a computational technique for performing accurate simulations of laser-illuminated metal nanoparticles. In the simulation, we self-consistently combine the finite-difference time-domain method for electrodynamics (ED) with Langevin dynamics (LD) for the particle motions. We demonstrate the ED-LD method by calculating the 3D trajectories of a single 100-nm-diameter Ag nanoparticle and optical trapping and optical binding of two and three 150-nm-diameter Ag nanoparticles in simulated optical tweezers. We show that surface charge on the colloidal metal nanoparticles plays an important role in their optically driven self-organization. In fact, these simulations provide a more complete understanding of the assembly of different structures of two and three Ag nanoparticles that have been observed experimentally, demonstrating that the ED-LD method will be a very useful tool for understanding the self-organization of optical matter.
Pusch, Andreas; Wuestner, Sebastian; Hamm, Joachim M; Tsakmakidis, Kosmas L; Hess, Ortwin
2012-03-27
Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin
2014-03-05
In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum-classical correspondence in terms of mean displacement, mean-squared displacement, and the corresponding variance in the first-order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth-order energy of quantum mechanics EQM (0). This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to EQM (0), while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function-based vibrational second-order perturbation theory, for the whole frequency range from ∼4400 cm(-1) (H2 ) to ∼160 cm(-1) (Na2 ). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero-point energy effects are significant.
A Langevin model for the Dynamic Contact Angle Parameterised Using Molecular Dynamics
Smith, Edward; Muller, Erich; Craster, Richard; Matar, Omar
2016-11-01
An understanding of droplet spreading is essential in a diverse range of applications, including coating processes, dip feed reactors, crop spraying and biomedical treatments such as surfactant replacement theory. The default modelling tools for engineering fluid dynamics assume that the continuum hypothesis is valid. The contact line motion is very difficult to capture in this paradigm and requires some form of closure model, often tuned a priori to experiments. Molecular dynamics (MD), by assuming only an inter-molecular potential, reproduces the full detail of the three-phase contact line with no additional modelling assumptions. This provides an ideal test-bed to understand contact line motion. In this talk, MD results for a sheared liquid bridge are presented. The evolution and fluctuations of the dynamic contact angle are paramterised over a range of wall sliding speeds and temperatures. A Langevin model is proposed to reproduce the fluctuations and evolution of the contact angle. Results from this model are compared to molecular simulation data showing excellent agreement. The potential applications of this model, as well as limitation and possible extensions, are discussed. EPSRC UK platform Grant MACIPh (EP/L020564/1).
Ultrasonic linear motor using the L-B mode Langevin transducer with an exponential horn
Institute of Scientific and Technical Information of China (English)
2008-01-01
An ultrasonic linear motor is proposed and fabricated by using the longitudinal and bending vibration double mode bolt-clamped Langevin type transducer to meet high power and speed requirements in the aerospace and semiconductor industries.The elliptical trajectory of the driving tip is formed by exciting the longitudinal and bending vibration with phase difference,which generates thrust force and normal force,respectively.An exponential shape horn is adopted to achieve a high linear speed.The classical theory of the transducer horn is used to determine the transducer's longitudinal resonance frequency and configuration dimensions.FEM analysis is used to degenerate the longitudinal and bending vibration resonant frequencies.The different locations of the driving tip on the horn cause different elliptical-shaped vibration trajectories,and how the trajectory's shape variation influences motor mechanical output is studied by using the FEM method.Simulation analysis and experiment results show that the motor has better performance when the driving tip is located at the antinode of the bending wave.Typical output of the prototype is no-load velocity of 480 mm/s and maximum driving force of 25 N.
A Langevin dynamics simulation study of the tribology of polymer loop brushes.
Yin, Fang; Bedrov, Dmitry; Smith, Grant D; Kilbey, S Michael
2007-08-28
The tribology of surfaces modified with doubly bound polymer chains (loops) has been investigated in good solvent conditions using Langevin dynamics simulations. The density profiles, brush interpenetration, chain inclination, normal forces, and shear forces for two flat substrates modified by doubly bound bead-necklace polymers and equivalent singly bound polymers (twice as many polymer chains of 12 the molecular weight of the loop chains) were determined and compared as a function of surface separation, grafting density, and shear velocity. The doubly bound polymer layers showed less interpenetration with decreasing separation than the equivalent singly bound layers. Surprisingly, this difference in interpenetration between doubly bound polymer and singly bound polymer did not result in decreased friction at high shear velocity possibly due to the decreased ability of the doubly bound chains to deform in response to the applied shear. However, at lower shear velocity, where deformation of the chains in the flow direction is less pronounced and the difference in interpenetration is greater between the doubly bound and singly bound chains, some reduction in friction was observed.
Studying on Opinion Evolution by Hamilton-Jacobi Equation
Feng, Chen-Jie; Huo, Jie; Hao, Rui; Wang, Xu-Ming
2016-01-01
A physical description of an opinion evolution is conducted based on the Hamilton-Jacobi equation derived from a generalized potential and the corresponding Langevin equation. The investigation mainly focuses on the heterogeneities such as age, connection circle and overall quality of the participants involved in the opinion exchange process. The evolutionary patterns of opinion can be described by solution of the Hamilton-Jacobi equation, information entropy. The results show that the overall qualities of the participants play critical roles in forming an opinion. The higher the overall quality is, the easier the consensus can reach. The solution also demonstrates that the age and the connection circle of the agents play equally important roles in forming an opinion. The essence of the age, overall quality, and connection circle corresponds to the maturity of thought (opinion inertia), reason and intelligence, influence strength of the environment, respectively. So the information entropy distributes in the ...
The probability equation for the cosmological comoving curvature perturbation
Energy Technology Data Exchange (ETDEWEB)
Riotto, Antonio; Sloth, Martin S., E-mail: antonio.riotto@pd.infn.it, E-mail: sloth@cern.ch [CERN, PH-TH Division, CH-1211, Genève 23 (Switzerland)
2011-10-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.
Second-order variational equations for N-body simulations
Rein, Hanno
2016-01-01
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such impro...
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Directory of Open Access Journals (Sweden)
Lloyd K. Williams
1987-01-01
Full Text Available In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of the linear second-order ordinary differential equations which are solved herewith.
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Dynamic Equations and Nonlinear Dynamics of Cascade Two-Photon Laser
Institute of Scientific and Technical Information of China (English)
XIE Xia; HUANG Hong-Bin; QIAN Feng; ZHANG Ya-Jun; YANG Peng; QI Guan-Xiao
2006-01-01
We derive equations and study nonlinear dynamics of cascade two-photon laser, in which the electromagnetic field in the cavity is driven by coherently prepared three-level atoms and classical field injected into the cavity. The dynamic equations of such a system are derived by using the technique of quantum Langevin operators, and then are studied numerically under different driving conditions. The results show thgt under certain conditions the cascade twophoton laser can generate chaotic, period doubling, periodic, stable and bistable states. Chaos can be inhibited by atomic populations, atomic coherences, and injected classical field. In addition, no chaos occurs in optical bistability.
Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe; Saitta, Antonino Marco; Casula, Michele
2017-06-13
We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo solution of the electronic part with the path integral formalism for the quantum nuclear dynamics. On the one hand, the path integral molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational quantum Monte Carlo can provide Born-Oppenheimer potential energy surfaces with a precision comparable to the most-advanced post-Hartree-Fock approaches, and with a favorable scaling with the system size. In order to cope with the intrinsic noise due to the stochastic nature of quantum Monte Carlo methods, we generalize the path integral molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of quantum Monte Carlo nuclear forces. The variational parameters of the quantum Monte Carlo wave function are evolved during the nuclear dynamics, such that the Born-Oppenheimer potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well-controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated, even in the presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be also very efficient in the case of noiseless (deterministic) ionic forces. The new implementation is validated on the Zundel ion (H5O2(+)) by direct comparison with standard path integral Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Multi-diffusive nonlinear Fokker-Planck equation
Ribeiro, Mauricio S.; Casas, Gabriela A.; Nobre, Fernando D.
2017-02-01
Nonlinear Fokker-Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker-Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker-Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker-Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Energy Technology Data Exchange (ETDEWEB)
Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu [Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125 (United States)
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Horowitz, Jordan M
2015-07-28
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.
Small delay approximation of stochastic delay differential equations
Guillouzic, Steve; L'heureux, Ivan; Longtin, André
1999-04-01
Delay differential equations evolve in an infinite-dimensional phase space. In this paper, we consider the effect of external fluctuations (noise) on delay differential equations involving one variable, thus leading to univariate stochastic delay differential equations (SDDE's). For small delays, a univariate nondelayed stochastic differential equation approximating such a SDDE is presented. Another approximation, complementary to the first, is also obtained using an average of the SDDE's drift term over the delayed dynamical variable, which defines a conditional average drift. This second approximation is characterized by the fact that the diffusion term is identical to that of the original SDDE. For small delays, our approach yields a steady-state probability density and a conditional average drift which are in close agreement with numerical simulations of the original SDDE. We illustrate this scheme with the delayed linear Langevin equation and a stochastic version of the delayed logistic equation. The technique can be used with any type of noise, and is easily generalized to multiple delays.
Kong, Wei; Yang, Fang; Liu, Songfen; Shi, Feng
2016-10-01
A Langevin dynamics simulation method is used to study the two-dimensional (2D) equilibrium structure of complex plasmas while considering an external magnetic field. The traditional Yukawa potential and a modified Yukawa potential according to Shukla et al. [Phys. Lett. A 291, 413 (2001); Shukla and Mendonca, Phys. Scr. T113 82 (2004)] and Salimullah et al. [Phys. Plasmas 10, 3047 (2003)] respectively, are employed to account for the interaction of the charged dust particles. It is found that the collisions between neutral gas and charged dust particles have minor effects on the 2D equilibrium structure of the system. Based on the modified Yukawa potential, studies on the 2D equilibrium structure show that the traditional Yukawa potential is still suitable for describing the magnetized complex plasmas, even if the shielding distance of charged dust particles is affected by the strong external magnetic field.
Energy Technology Data Exchange (ETDEWEB)
Lee, Dong-Jin; Lee, Sun-Kyu, E-mail: skyee@gist.ac.kr [School of Mechatronics, Gwangju Institute of Science and Technology, 123 Cheomdangwagi-ro, Buk-gu, Gwangju 500-712 (Korea, Republic of)
2015-01-15
This paper presents a design and control system for an XY stage driven by an ultrasonic linear motor. In this study, a hybrid bolt-clamped Langevin-type ultrasonic linear motor was manufactured and then operated at the resonance frequency of the third longitudinal and the sixth lateral modes. These two modes were matched through the preload adjustment and precisely tuned by the frequency matching method based on the impedance matching method with consideration of the different moving weights. The XY stage was evaluated in terms of position and circular motion. To achieve both fine and stable motion, the controller consisted of a nominal characteristics trajectory following (NCTF) control for continuous motion, dead zone compensation, and a switching controller based on the different NCTFs for the macro- and micro-dynamics regimes. The experimental results showed that the developed stage enables positioning and continuous motion with nanometer-level accuracy.
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Energy Technology Data Exchange (ETDEWEB)
Mekkaoui, A. [Institute for Energy and Climate Research-Plasma Physics, Research Center Juelich GmbH, Association FZJ-Euratom, D-52425 Juelich (Germany)
2013-01-15
A stochastic differential equation for intermittent plasma density dynamics in magnetic fusion edge plasma is derived, which is consistent with the experimentally measured gamma distribution and the theoretically expected quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the nonlinear Langevin representation of the beta process, which leads to a root-square nonlinearity.
Second-order variational equations for N-body simulations
Rein, Hanno; Tamayo, Daniel
2016-07-01
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.
Institute of Scientific and Technical Information of China (English)
樊华; 李理; 袁坚; 山秀明
2009-01-01
为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战,本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了.此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题.%One of the big challenges in the field of Intemet research is to elucidate the relationship between micro-algorithms of the flow control protocols and macro-properties of the Intemet with a proper model. In this paper, we build up a Langevin equation under the transmission control protocol using deductive method. Then we analyze the effectiveness of the active queue management based on the Langevin model. We have proved that there is a phase transition sequence from smooth state to congestion state then to paralysis state in all such kind of algorithms. We also provide explicit formulas of the critical points in terms of the system parameters. Although the model used in this paper focuses on a specific algorithm, we believe this method has a great potential in analyzing and understanding various network congestion control algorithms.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or
Vortex polarity in 2-D magnetic dots by Langevin dynamics simulations
Energy Technology Data Exchange (ETDEWEB)
Depondt, Ph., E-mail: depondt@insp.jussieu.f [Institut des NanoSciences de Paris, Universite Pierre et Marie Curie, UMR 7588 CNRS, 75252 Paris Cedex 05 (France); Levy, J.-C.S., E-mail: jean-claude.levy@univ-paris-diderot.f [Materiaux et Phenomenes Quantiques, Universite Denis Diderot, UMR 7162 CNRS, 75013 Paris (France); Mertens, F.G., E-mail: franz.mertens@uni-bayreuth.d [Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany)
2011-01-17
Two-dimensional magnetic plots of finite size were simulated by integrating the Landau-Lifshitz equation for the isotropic Heisenberg model with a systematic exploration of the effect of dipole-dipole interactions of various strengths d, at a low temperature. Structures with or without vortices are observed, and in the cases in which vortices are present, out-of-plane contributions show only for relatively weak dipolar strengths: the integrated intensity of the out-of-plane component decreases roughly as 1/d with increasing dipolar strength while the vortex core width decreases as d{sup -1/2}. The coexistence of several vortices with an out-of-plane component seems limited to a narrow d-range, at least for the sample sizes studied. The size limit below which the vortices disappear decreases roughly as 1/d.
Banik, S K; Ray, D S; Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar
2002-01-01
Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\\it exact} quantum analogues of their classical counterparts. The present work is {\\it independent} of path integral techniques. The theory as developed here is a natural ext...
The Kramers-Moyal Equation of the Cosmological Comoving Curvature Perturbation
Riotto, Antonio
2011-01-01
Fluctuations of the comoving curvature perturbation with wavelengths larger than the horizon length are governed by a Langevin equation whose stochastic noise arise from the quantum fluctuations that are assumed to become classical at horizon crossing. The infrared part of the curvature perturbation performs a random walk under the action of the stochastic noise and, at the same time, it suffers a classical force caused by its self-interaction. By a path-interal approach and, alternatively, by the standard procedure in random walk analysis of adiabatic elimination of fast variables, we derive the corresponding Kramers-Moyal equation which describes how the probability distribution of the comoving curvature perturbation at a given spatial point evolves in time and is a generalization of the Fokker-Planck equation. This approach offers an alternative way to study the late time behaviour of the correlators of the curvature perturbation from infrared effects.
Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017-09-01
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach.
Monte Carlo simulations of spatial noise and Langevin equation%空间噪声和Langevin方程的Monte Carlo模拟
Institute of Scientific and Technical Information of China (English)
周妍; 包景东
2007-01-01
为了能够模拟Langevin方程中具有任意关联的色噪声,克服由于不知道产生色噪声的微分方程而无法模拟的缺点,该文给出了一个模拟色噪声的方法.在离散的Fourier空间中产生一个噪声序列,再经过离散Fourier逆变换得到所需要的色噪声序列.该方法也适用于模拟空间噪声.以一维时间色噪声以及二维空间短程关联的噪声为例,讨论了用离散Fourier变换来产生色噪声的具体方法.用该方法得到的噪声实际关联,能够与理论值较好地吻合.
Elliptic flow and nuclear modification factors of D-mesons at FAIR in a Hybrid-Langevin approach
Lang, Thomas; Steinheimer, Jan; Bleicher, Marcus
2013-01-01
The Compressed Baryonic Matter (CBM) experiment at the Facility for Anti-proton and Ion Research (FAIR) will provide new possibilities for charm-quark ($D$-meson) observables in heavy-ion collisions at low collision energies and high baryon densities. To predict the collective flow and nuclear modification factors of charm quarks in this environment, we apply a Langevin approach for the transport of charm quarks in the UrQMD (hydrodynamics + Boltzmann) hybrid model. Due to the inclusion of event-by-event fluctuations and a full (3+1) dimensional hydrodynamical evolution, the UrQMD hybrid approach provides a realistic evolution of the matter produced in heavy-ion collisions. As drag and diffusion coefficients we use a resonance approach for elastic heavy-quark scattering and assume a decoupling temperature of the charm quarks from the hot medium of $130\\, \\MeV$. Hadronization of the charm quarks to $D$-mesons by coalescence is included. Since the initial charm-quark distribution at FAIR is unknown, we utilize ...
Sharma, A. S.; Setty, V. A.
2015-12-01
Multiscale fluctuations in large and complex data are usually characterized by a power law with a scaling exponent but many systems require more than one exponent and thus exhibit crossover behavior. The scaling exponents, such as Hurst exponents, represent the nature of correlation in the system and the crossover shows the presence of more than one type of correlation. An accurate characterization of the crossover behavior is thus needed for a better understanding of the inherent correlations in the system, and is an important method of Big Data analysis. A multi-step process is developed for accurate computation of the crossover behavior. First the detrended fluctuation analysis is used to remove the trends in the data and the scaling exponents are computed. The crossover point is then computed by a Hyperbolic regression technique, with no prior assumptions. The time series data of the magnetic field variations during substorms in the Earth's magnetosphere is analyzed with these techniques and yields a crossover behavior with a time scale of ~4 hrs. A Langevin model derived from the data provides an excellent fit to the crossover in the scaling exponents and a good model of magnetospheric dynamics. The combination of fluctuation analysis and mathematical modeling thus yields a comprehensive approach in the analysis of Big Data.
Inferring hidden states in Langevin dynamics on large networks: Average case performance
Bravi, B.; Opper, M.; Sollich, P.
2017-01-01
We present average performance results for dynamical inference problems in large networks, where a set of nodes is hidden while the time trajectories of the others are observed. Examples of this scenario can occur in signal transduction and gene regulation networks. We focus on the linear stochastic dynamics of continuous variables interacting via random Gaussian couplings of generic symmetry. We analyze the inference error, given by the variance of the posterior distribution over hidden paths, in the thermodynamic limit and as a function of the system parameters and the ratio α between the number of hidden and observed nodes. By applying Kalman filter recursions we find that the posterior dynamics is governed by an "effective" drift that incorporates the effect of the observations. We present two approaches for characterizing the posterior variance that allow us to tackle, respectively, equilibrium and nonequilibrium dynamics. The first appeals to Random Matrix Theory and reveals average spectral properties of the inference error and typical posterior relaxation times; the second is based on dynamical functionals and yields the inference error as the solution of an algebraic equation.
Stochastic differential equations and turbulent dispersion
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.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Roy, Dibyendu
2008-06-01
Through an exact analysis using quantum Langevin dynamics, we demonstrate the crossover from ballistic to diffusive thermal transport in a harmonic chain with each site connected to Ohmic heat reservoirs. The temperatures of the two heat baths at the boundaries are specified from the beginning, whereas the temperatures of the interior heat reservoirs are determined self-consistently by demanding that in the steady state, on average, there is no heat current between any such (self-consistent) reservoir and the harmonic chain. The essence of our study is that the effective mean free path separating the ballistic regime of transport from the diffusive one emerges naturally.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Nagata, Keitaro; Shimasaki, Shinji
2016-01-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a gene...
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-07-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
Indian Academy of Sciences (India)
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Energy Technology Data Exchange (ETDEWEB)
Mekkaoui, Abdessamad [IEK-4 Forschungszentrum Juelich 52428 (Germany)
2013-07-01
A method to derive stochastic differential equations for intermittent plasma density dynamics in magnetic fusion edge plasma is presented. It uses a measured first four moments (mean, variance, Skewness and Kurtosis) and the correlation time of turbulence to write a Pearson equation for the probability distribution function of fluctuations. The Fokker-Planck equation is then used to derive a Langevin equation for the plasma density fluctuations. A theoretical expectations are used as a constraints to fix the nonlinearity structure of the stochastic differential equation. In particular when the quadratically nonlinear dynamics is assumed, then it is shown that the plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. Strong criteria for statistical discrimination of experimental time series are proposed as an alternative to the Kurtosis-Skewness scaling. This scaling is broadly used in contemporary literature to characterize edge turbulence, but it is inappropriate because a large family of distributions could share this scaling. Strong criteria allow us to focus on the relevant candidate distribution and approach a nonlinear structure of edge turbulence model.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving fractional differential equations.
On polynomial solutions to Fokker-Planck and sinked density evolution equations
Zuparic, Mathew
2015-04-01
We analytically solve for the time dependent solutions of various density evolution models. With specific forms of the diffusion, drift and sink coefficients, the eigenfunctions can be expressed in terms of hypergeometric functions. We obtain the relevant discrete and continuous spectra for the eigenfunctions. With non-zero sink terms the discrete spectra eigenfunctions are generalizations of well known orthogonal polynomials: the so-called associated-Laguerre, Bessel, Fisher-Snedecor and Romanovski functions. We use MacRobert’s proof to obtain closed form expressions for the continuous normalization of the Romanovski density function. Finally, we apply our results to obtain the analytical solutions associated with the Bertalanffy-Richards-Langevin equation.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Fractional Chemotaxis Diffusion Equations
Langlands, T A M
2010-01-01
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Developmental Partial Differential Equations
Duteil, Nastassia Pouradier; Rossi, Francesco; Boscain, Ugo; Piccoli, Benedetto
2015-01-01
In this paper, we introduce the concept of Developmental Partial Differential Equation (DPDE), which consists of a Partial Differential Equation (PDE) on a time-varying manifold with complete coupling between the PDE and the manifold's evolution. In other words, the manifold's evolution depends on the solution to the PDE, and vice versa the differential operator of the PDE depends on the manifold's geometry. DPDE is used to study a diffusion equation with source on a growing surface whose gro...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com
2015-08-15
We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.
Hazewinkel, M.
1995-01-01
Dedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an original space-
Shabat, A. B.
2016-12-01
We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.
Dissipative Boussinesq equations
Dutykh, D; Dias, Fr\\'{e}d\\'{e}ric; Dutykh, Denys
2007-01-01
The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
than the classical method in the solution of the aforementioned differential equation. Keywords: ... present a successful approximation of shell ... displacement function. .... only applicable to cylindrical shell subject to ..... (cos. 4. 4. 4. 3 β. + β. + β. -. = β. - β x x e ex. AL. xA w. Substituting equations (29); (30) and (31) into.
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Kuksin, Sergei; Maiocchi, Alberto
In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Introduction to functional equations
Sahoo, Prasanna K
2011-01-01
Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections hig
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Reuse Partitioning-Based Frequency Assignment in Fixed Two-Hop Relay Cellular Network
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In relay cellular network, relay links will consume extra frequency resources, which makes radio resource allocation become more complex and important. A new frequency allocation scheme is proposed to increase cell capacity and improve signal-to-interference ratio (SIR) of users located at cell edges. By dividing cell into different parts and configuring each of these parts with a unique reuse factor, this scheme improves spectral utilization efficiency and avoids inter-cell interference effectively. Optimal combinations of reuse factors and locations of relay nodes are also addressed and investigated. Computer simulation results show that, by employing the proposed scheme, maximum cell capacity gains of about 50%, 35% and 30% can be achieved in comparison with conventional cellular network scheme, traditional reuse partitioning scheme and reuse-adjacent-cell-frequencies scheme, respectively. Moreover, since in the proposed scheme resources are dynamically allocated among relay nodes, more benefits can be obtained in comparison with fixed resource allocation schemes under non-uniform traffic distribution.
Feedback Reduction in Broadcast and two Hop Multiuser Networks: A Compressed Sensing Approach
Shibli, Hussain J.
2013-05-21
In multiuser wireless networks, the base stations (BSs) rely on the channel state information (CSI) of the users to in order to perform user scheduling and downlink transmission. While the downlink channels can be easily estimated at all user terminals via a single broadcast, several key challenges are faced during uplink (feedback) transmission. Firstly, the noisy and fading feedback channels are usually unknown at the base station, and therefore, channel training is usually required from all users. Secondly, the amount of air-time required for feedback transmission grows linearly with the number of users. This domination of the network resources by feedback information leads to increased scheduling delay and outdated CSI at the BS. In this thesis, we tackle the above challenges and propose feedback reduction algorithms based on the theory of compressive sensing (CS). The proposed algorithms encompass both single and dual hop wireless networks, and; i) permit the BS to obtain CSI with acceptable recovery guarantees under substantially reduced feedback overhead, ii) are agnostic to the statistics of the feedback channels, and iii) utilize the apriori statistics of the additive noise to identify strong users. Numerical results show that the proposed algorithms are able to reduce the feedback overhead, improve detection at the BS, and achieve a sum-rate close to that obtained by noiseless dedicated feedback algorithms.
A performance study of two hop transmission in mixed underlay RF and FSO fading channels
Ansari, Imran Shafique
2014-04-01
In this work, we present the performance analysis of a dual-hop transmission system composed of asymmetric radio frequency (RF) and free-space optical (FSO) links in underlay cognitive networks. For the RF link, we consider an underlay cognitive network where the secondary users share the spectrum with licensed primary users, where indoor femtocells act as a practical example for such networks. More specifically, we assume that the RF link is subject to an interference constraint. The FSO link accounts for pointing errors and both types of detection techniques (i.e. intensity modulation/direct detection (IM/DD) as well as heterodyne detection). On the other hand, RF link is modeled by the Rayleigh fading distribution that applies power control to maintain the interference at the primary network below a specific threshold whereas the FSO link is modeled by a unified Gamma-Gamma fading distribution. With this model, we derive new exact closed-form expressions for the cumulative distribution function, the probability density function, the moment generating function, and the moments of the end-to-end signal-to-interference plus noise ratio of these systems in terms of the Meijer\\'s G functions. We then capitalize on these results to offer new exact closed-form expressions for the outage probability, the higher-order amount of fading, and the average error rate for binary and Mary modulation schemes, all in terms of Meijer\\'s G functions. All our new analytical results are verified via computer-based Monte-Carlo simulations and are illustrated by some selected numerical results.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Institute of Scientific and Technical Information of China (English)
A.I.Arbab
2013-01-01
A unified complex model of Maxwell's equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell's equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell's equations to include longitudinal waves.A formal analogy between this formulation and Dirac's equation is also discussed.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Singular Renormalization Group Equations
Minoru, HIRAYAMA; Department of Physics, Toyama University
1984-01-01
The possible behaviour of the effective charge is discussed in Oehme and Zimmermann's scheme of the renormalization group equation. The effective charge in an example considered oscillates so violently in the ultraviolet limit that the bare charge becomes indefinable.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Functional Equations and Fourier Analysis
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.