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1

Langevin theory of fluctuations in the discrete Boltzmann equation

NASA Astrophysics Data System (ADS)

The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, a fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.

Gross, M.; Cates, M. E.; Varnik, F.; Adhikari, R.

2011-03-01

2

Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (

Zahlten, Claus [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: C.Zahlten@gmx.de; Hernandez, Andres [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: A.Hernandez@thphys.uni-heidelberg.de; Schmidt, Michael G. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)], E-mail: M.G.Schmidt@thphys.uni-heidelberg.de

2009-10-15

3

Langevin Equation on Fractal Curves

We analyse a random motion of a particle on a fractal curve, using Langevin approach. This involves defining a new velocity in terms of mass of the fractal curve, as defined in recent work. The geometry of the fractal curve, hence plays an important role in this analysis. A Langevin equation with a particular noise model is thus proposed and solved using techniques of the newly developed $F^\\alpha$-Calculus .

Seema Satin; A. D. Gangal

2014-04-28

4

Langevin equations for fluctuating surfaces.

Exact Langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam. We consider two types of model: deposition models, where growth proceeds by the deposition and instantaneous local relaxation of particles, with no subsequent movement, and models with concurrent random deposition and surface diffusion. Starting from a Chapman-Kolmogorov equation the deposition, relaxation, and hopping rules of these models are first expressed as transition rates within a master equation for the joint height probability density function. The Kramers-Moyal-van Kampen expansion of the master equation in terms of an appropriate "largeness" parameter yields, according to a limit theorem due to Kurtz [Stoch. Proc. Appl. 6, 223 (1978)], a Fokker-Planck equation that embodies the statistical properties of the original lattice model. The statistical equivalence of this Fokker-Planck equation, solved in terms of the associated Langevin equation, and solutions of the Chapman-Kolmogorov equation, as determined by kinetic Monte Carlo (KMC) simulations of the lattice transition rules, is demonstrated by comparing the surface roughness and the lateral height correlations obtained from the two formulations for the Edwards-Wilkinson [Proc. R. Soc. London Ser. A 381, 17 (1982)] and Wolf-Villain [Europhys. Lett. 13, 389 (1990)] deposition models, and for a model with random deposition and surface diffusion. In each case, as the largeness parameter is increased, the Langevin equation converges to the surface roughness and lateral height correlations produced by KMC simulations for all times, including the crossover between different scaling regimes. We conclude by examining some of the wider implications of these results, including applications to heteroepitaxial systems and the passage to the continuum limit. PMID:16383589

Chua, Alvin L-S; Haselwandter, Christoph A; Baggio, Chiara; Vvedensky, Dimitri D

2005-11-01

5

The complex chemical Langevin equation

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 com...

Schnoerr, David; Grima, Ramon

2014-01-01

6

The complex chemical Langevin equation

NASA Astrophysics Data System (ADS)

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.

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2014-07-01

7

Nuclear fission with a Langevin equation

A microscopically derived Langevin equation is applied to thermally induced nuclear fission. An important memory effect is pointed out and discussed. A strong friction coefficient, estimated from microscopic quantities, tends to decrease the stationary limit of the fission rate and to increase the transient time. The calculations are performed with a collective mass depending on the collective variable and with

David Boilley; Eric Suraud; Abe Yasuhisa; Sakir Ayik

1993-01-01

8

Fractional dynamics from the ordinary Langevin equation.

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing. The probability to find the resulting process at the real time is defined by the integral relationship between the probability densities of the parent and directing processes. The corresponding master equation becomes the fractional Fokker-Planck equation. We show that the resulting process has non-Markovian properties, all its moments are finite, the fluctuation-dissipation relation and the H-theorem hold. PMID:12636657

Stanislavsky, A A

2003-02-01

9

Chapter 4. The Green Kubo Relations 4.1 The Langevin Equation

Chapter 4. The Green Kubo Relations 4.1 The Langevin Equation 4.2 Mori-Zwanzig Theory 4.3 Shear Viscosity 4.4 Green-Kubo Relations for Navier-Stokes Transport Coefficients #12;4.1 The Langevin Equation

Evans, Denis

10

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., E-mail: basharov@gmail.com [National Research Centre 'Kurchatov Institute,' (Russian Federation)

2012-09-15

11

A numerical solution of a nonlinear Langevin Equation

NASA Astrophysics Data System (ADS)

A one-dimensional Langevin Equation in which the friction term and the stochastic force term depend nonlinearly on the velocity is presented. Assuming that the Maxwell distribution is the stationary solution of the Fokker Planck Equation (which is equivalent to the nonlinear Langevin Equation) we derive a generalization of the Fluctuation Dissipation theorem. A numerical algorithm is developed which allows us to integrate the nonlinear Langevin Equation. From this numerical solution correlation functions are obtained.

Gerling, Rainer W.

1984-09-01

12

Langevin equation, Fokker-Planck equation and cell migration.

Cell migration can be characterized by two independent variables: the speed, v, and the migration angle, phi. Each variable can be described by a stochastic differential equation--a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory. PMID:8364419

Schienbein, M; Gruler, H

1993-05-01

13

NonGaussian statistics, classical field theory, and realizable Langevin models John A. Krommes

NonÂGaussian statistics, classical field theory, and realizable Langevin models John A. Krommes to classical statistical dynamics. It does not follow from the original genÂ eralized Langevin equation (GLE theories with nonÂGaussian corrections (``spurious vertices'') is described. It is shown how to derive

14

Langevin Equation for Particle in Thermal Photon Bath

The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed.

Z. Haba; H. Kleinert

2001-06-16

15

Self-consistent generalized Langevin equation for colloidal mixtures

NASA Astrophysics Data System (ADS)

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.

Chávez-Rojo, Marco Antonio; Medina-Noyola, Magdaleno

2005-09-01

16

Langevin theory of anomalous Brownian motion made simple

NASA Astrophysics Data System (ADS)

During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.

Tóthová, Jana; Vasziová, Gabriela; Glod, Lukáš; Lisý, Vladimír

2011-05-01

17

Simplified simulation of Boltzmann-Langevin equation

We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density.

Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Randrup, J. [Lawrence Berkeley Lab., CA (United States)

1994-06-01

18

Non-Gaussian equilibrium distributions arising from the Langevin equation.

We study the Langevin equation of a point particle driven by random noise, modeled as a two-state Markov process. The corresponding master equation differs from the Fokker-Planck equation. In equilibrium, the velocity of the particle is distributed according to a binomial power law. We discuss transient (i.e., nonequilibrium) behavior, and the consequences of non-Markovian noise statistics. PMID:11863509

Annunziato, Mario

2002-02-01

19

Ergodic Properties of the Non-Markovian Langevin Equation

We discuss the dissipative dynamics of a classical particle coupled to an infinitely extended heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation is driven by colored noise. Our method works in arbitrary space dimension,

VOJKAN JAKIŠ?; CLAUDE-ALAIN PILLET

1997-01-01

20

Quantum annealing and the Schrödinger-Langevin-Kostin equation

NASA Astrophysics Data System (ADS)

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.

de Falco, Diego; Tamascelli, Dario

2009-01-01

21

Generalized Langevin equation for tracer diffusion in atomic liquids

NASA Astrophysics Data System (ADS)

We derive the time-evolution equation that describes the Brownian motion of labeled individual tracer particles in a simple model atomic liquid (i.e., a system of N particles whose motion is governed by Newton’s second law, and interacting through spherically symmetric pairwise potentials). We base our derivation on the generalized Langevin equation formalism, and find that the resulting time evolution equation is formally identical to the generalized Langevin equation that describes the Brownian motion of individual tracer particles in a colloidal suspension in the absence of hydrodynamic interactions. This formal dynamic equivalence implies the long-time indistinguishability of some dynamic properties of both systems, such as their mean squared displacement, upon a well-defined time scaling. This prediction is tested here by comparing the results of molecular and Brownian dynamics simulations performed on the hard sphere system.

Mendoza-Méndez, Patricia; López-Flores, Leticia; Vizcarra-Rendón, Alejandro; Sánchez-Díaz, Luis E.; Medina-Noyola, Magdaleno

2014-01-01

22

A path integral approach to the Langevin equation

We study the Langevin equation both with a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevian equation.

Ashok K. Das; Sudhakar Panda; J. R. L. Santos

2014-11-02

23

A path integral approach to the Langevin equation

We study the Langevin equation both with a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevian equation.

Das, Ashok K; Santos, J R L

2014-01-01

24

Transient aging in fractional Brownian and Langevin-equation motion.

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. PMID:24483403

Kursawe, Jochen; Schulz, Johannes; Metzler, Ralf

2013-12-01

25

A new algorithm for numerical simulation of Langevin equations

Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\\Delta t$, are obtained so as to reproduce within that order a corresponding transition density of the Fokker-Planck equations, in the weak Taylor approximation scheme. A great advantage of our method is its straightforwardness such that direct perturbative calculations produce the algorithm as an end result, so that the procedure is tractable by computer. Examples in general form for curved space cases as well as flat space cases are given in some order of approximations. Simulations are performed for specific examples of U(1) system and SU(2) systems, respectively.

H. Nakajima; S. Furui

1996-10-15

26

Langevin theory of anomalous Brownian motion made simple

During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely

Jana Tóthová; Gabriela Vasziová; Lukás Glod; Vladimír Lisý

2011-01-01

27

Elimination of inertia from a Generalized Langevin Equation: Applications to microbead rheology of inertia from a Generalized Langevin Equation: Applications to microbead rheology modeling and data micron-sized particle in a method called passive microbead rheology. Data analysis of passive microbead

Schieber, Jay D.

28

Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then 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.

Julian Schmidt; Alex Meistrenko; Hendrik van Hees; Carsten Greiner

2014-07-24

29

Coupled Langevin Equations for the North Atlantic Oscillation Pedro Lind, Alejandro Mora, Jason Gallas, Maria Haase Â· Introduction: (i) The North Atlantic Oscillation (NAO). (ii) The Langevin equation://www.ldeo.columbia.edu/NAO The North Atlantic Oscillation (NAO) #12;The impact of NAO reach from the upper atmosphere to the bottom

Harting, Jens

30

Derivation of the generalized Langevin equation in nonstationary environments

NASA Astrophysics Data System (ADS)

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.

Kawai, Shinnosuke; Komatsuzaki, Tamiki

2011-03-01

31

NASA Astrophysics Data System (ADS)

Near-field and resonance effects have a strong influence on nanoscale electromagnetic energy transfer, and detailed understanding of these effects is required for the design of new, optimized nano-optical devices. We provide a comprehensive microscopic view of electromagnetic energy transfer phenomena by introducing quantum Langevin heat baths as local noise sources in the equations of motion for the thermally fluctuating electric dipoles forming dielectric bodies. The theory is, in a sense, the microscopic generalization of the well-known fluctuational electrodynamics theory and thereby provides an alternative and conceptually simple way to calculate the local emission and absorption rates from the local Langevin bath currents. We apply the model to study energy transfer between silicon carbide nanoparticles located in a microcavity formed of two mirrors and next to a surface supporting propagating surface modes. The results show that the heat current between dipoles placed in a cavity oscillates as a function of their position and separation and can be enhanced by several orders of magnitude as compared to the free-space heat current with a similar interparticle distance. The predicted enhancement can be viewed as a many-body generalization of the well-known cavity Purcell effect. Similar effects are also observed in the interparticle heat transfer between dipoles located next to a surface of a polar material supporting surface phonon polaritons.

Sääskilahti, K.; Oksanen, J.; Tulkki, J.

2014-04-01

32

NASA Astrophysics Data System (ADS)

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mössbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscopies. Following the summary of the advantage and limitation of the stochastic theory, we then derive a quantum Fokker-Planck equation and a quantum master equation from a system-bath Hamiltonian with a suitable spectral distribution producing a nearly Markovian random perturbation. By introducing auxiliary parameters that play a role as stochastic variables in an expression for reduced density matrix, we obtain the stochastic Liouville equation including temperature correction terms. The auxiliary parameters may also be interpreted as a random noise that allows us to derive a quantum Langevin equation for non-Markovian noise at any temperature. The results afford a basis for clarifying the relationship between the stochastic and dynamical approaches. Analytical as well as numerical calculations are given as examples and discussed.

Tanimura, Yoshitaka

2006-08-01

33

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

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

Ramon Grima; Philipp Thomas; Arthur V. Straube

2011-01-01

34

Langevin equations for quasi-linear wave-particle interaction. F. Castejn and S. Eguilior

, present Montecarlo codes that arte based on the estimation of the particle trajectories (see e. g. [5 the trajectories of single particles using Langevin equations. Moreover, there is a correspondence between FLangevin equations for quasi-linear wave-particle interaction. F. CastejÃ³n and S. Eguilior

35

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. PMID:23556711

Sanghi, T; Aluru, N R

2013-03-28

36

Critical comparison of Kramers' fission width with the stationary width from the Langevin equation

It is shown that Kramers' fission width, originally derived for a system with constant inertia, can be extended to systems with a deformation-dependent collective inertia, which is the case for nuclear fission. The predictions of Kramers' width for systems with variable inertia are found to be in very good agreement with the stationary fission widths obtained by solving the corresponding Langevin equations.

Sadhukhan, Jhilam; Pal, Santanu [Physics Group, Variable Energy Cyclotron Centre, 1/AF Bidhan Nagar, Kolkata 700 064 (India)

2009-06-15

37

Langevin equation with stochastic damping - Possible application to critical binary fluid

NASA Technical Reports Server (NTRS)

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.

Jasnow, D.; Gerjuoy, E.

1975-01-01

38

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. PMID:24697429

Brett, Tobias; Galla, Tobias

2014-03-28

39

We consider Levy flights subject to external force fields. This anomalous\\u000atransport process is described by two approaches, a Langevin equation with Levy\\u000anoise and the corresponding generalized Fokker-Planck equation containing a\\u000afractional derivative in space. The cases of free flights, constant force and\\u000alinear Hookean force are analyzed in detail, and we corroborate our findings\\u000awith results from numerical

Sune Jespersen; Hans C. Fogedby

1999-01-01

40

Critique of the Brownian approximation to the generalized Langevin equation in lattice dynamics

We consider the classical motion of a harmonic lattice in which only those atoms in a certain subset of the lattice (primary zone) may interact with an external force. The formally exact generalized Langevin equation (GLE) for the primary zone is an appropriate description of the dynamics. We examine a previously proposed Brownian, or frictional damping, approximation that reduces the GLE to a set of coupled ordinary Langevin equations for the primary atoms. It is shown that the solution of these equations can contain undamped motion if there is more than one atom in the primary zone. Such motion is explicitly demonstrated for a model that has been used to describe energy transfer in atom--surface collisions. The inability of the standard Brownian approximation to yield an acceptable, physically meaningful result for primary zones comprising more than one atom suggests that the Brownian approximation may introduce other spurious dynamical effects. Further work on damping of correlated motion in lattices is needed.

Diestler, D.J.; Riley, M.E.

1985-10-01

41

New Kinematic Model in comparing with Langevin equation and Fokker Planck Equation

NASA Astrophysics Data System (ADS)

An analytic approximate solution of New Kinematic Model with the boundary conditions is developed for the incompressible packing condition in Pebble Bed Reactors. It is based on velocity description of the packing density in the hopper. The packing structure can be presented with a jamming phenomenon from flow types. The gravity-driven macroscopic motions are governed not only by the geometry and external boundary conditions of silos and hoppers, but by flow prosperities of granular materials, such as friction, viscosity and porosity. The analytical formulas for the quasi-linear diffusion and convection coefficients of the velocity profile are obtained. Since it was found that the New Kinematic Model is dependent upon the granular packing density distribution, we are motivated to study the Langevin equation with friction under the influence of the Gravitational field. We also discuss the relation with the Fokker Planck Equation using Detailed balance and Metropolis-Hastings Algorithm. Markov chain Monte Carlo methods are shown to be a non-Maxwellian distribution function with the mean velocity of the field particles having an effective temperature.

Lee, Kyoung; Wang, Zhijian; Gardner, Robin

2010-03-01

42

Brownian motion and anomalous diffusion revisited via a fractional Langevin equation

In this paper we revisit 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 in 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 back-flow, i.e. the added mass and the Basset memory drag. We provide 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} for long times, which indeed is more realistic. Finally, the mean squared displacement is shown to maintain, for sufficiently long times, the linear behaviour which is typical of normal diffusion, with the same diffusion coefficient of the classical case. However, the Basset history force induces a retarding effect in the establishing of the linear behaviour, which in some cases could appear as a manifestation of anomalous diffusion to be correctly interpreted in experimental measurements.

Francesco Mainardi; Antonio Mura; Francesco Tampieri

2010-04-20

43

Non-Gaussian statistics, classical eld theory, and realizable Langevin models John A. Krommes

Non-Gaussian statistics, classical #12;eld theory, and realizable Langevin models John A. Krommes work of Martin, Siggia, and Rose [Phys. Rev. A 8, 423 (1973)] on the functional approach to classical of products of random variables. The relationship of that GLE to renormalized #12;eld theories with non

44

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. PMID:23829723

Brett, Tobias; Galla, Tobias

2013-06-21

45

Anomalous diffusion in nonhomogeneous media: time-subordinated Langevin equation approach.

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. PMID:24730774

Srokowski, Tomasz

2014-03-01

46

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.

Kwok, Sau Fa, E-mail: kwok@dfi.uem.br

2012-08-15

47

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

2013-01-01

48

NASA Astrophysics Data System (ADS)

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

49

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. PMID:23901960

Baczewski, Andrew D; Bond, Stephen D

2013-07-28

50

Non-Gaussian statistics, classical field theory, and realizable Langevin models

The direct-interaction approximation (DIA) to the fourth-order statistic Z {approximately}{l_angle}{lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (``spurious vertices``) is described. It is shown how to derive an improved representation, that realizes cumulants through O({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z{sub DIA}{sup M} to Z{sub DIA} is derived. Both Z{sub DIA} and Z{sub DIA}{sup M} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example.

Krommes, J.A.

1995-11-01

51

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?(-3?2) for reaction systems which do not obey detailed balance and at least accurate to order ?(-2) for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?(-1?2) and variance estimates accurate to order ?(-3?2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules. PMID:21895155

Grima, Ramon; Thomas, Philipp; Straube, Arthur V

2011-08-28

52

Tracer dispersion simulation in low wind speed conditions with a new 2D Langevin equation system

NASA Astrophysics Data System (ADS)

The simulation of atmospheric dispersion in low wind speed conditions (LW) is still recognised as a challenge for modellers. Recently, a new system of two coupled Langevin equations that explicitly accounts for meandering has been proposed. It is based on the study of turbulence and dispersion properties in LW. The new system was implemented in the Lagrangian stochastic particle models LAMBDA and GRAL. In this paper we present simulations with this new approach applying it to the tracer experiments carried out in LW by Idaho National Engineering Laboratory (INEL, USA) in 1974 and by the Graz University of Technology and CNR-Torino near Graz in 2003. To assess the improvement obtained with the present model with respect to previous models not taking into account the meandering effect, the simulations for the INEL experiments were also performed with the old version of LAMBDA. The results of the comparisons clearly indicate that the new approach improves the simulation results.

Anfossi, D.; Alessandrini, S.; Trini Castelli, S.; Ferrero, E.; Oettl, D.; Degrazia, G.

53

NASA Technical Reports Server (NTRS)

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.

Aronowitz, S.; Chang, S.

1980-01-01

54

NASA Technical Reports Server (NTRS)

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.

Aronowitz. Sheldon

1980-01-01

55

Reducing stochasticity in the North Atlantic Oscillation index with coupled Langevin equations time series routinely used to define the index characterizing the North Atlantic Oscillation NAO , well The North Atlantic Oscillation NAO is increasingly be- coming the focus of much attention in climate

Gallas, Jason

56

Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.

Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles. PMID:21613667

Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Igli?, Veronika; Igli?, Aleš

2011-06-01

57

Generalized Langevin equation for solids. I. Rigorous derivation and main properties

NASA Astrophysics Data System (ADS)

We demonstrate explicitly that the derivation by Adelman and Doll (AD) [J. Chem. Phys. 64, 2375 (1976)] of the generalized Langevin equation (GLE) to describe dynamics of an extended solid system by considering its finite subsystem is inconsistent because it relies on performing statistical averages over the entire system when establishing properties of the random force. This results in the random force representing a nonstationary process opposite to one of the main assumptions made in AD that the random force corresponds to a stationary stochastic process. This invalidates the derivation of the Brownian (or Langevin) form of the GLE in AD. Here we present a different and more general approach in deriving the GLE. Our method generalizes that of AD in two main aspects: (i) the structure of the finite region can be arbitrary (e.g., anharmonic), and (ii) ways are indicated in which the method can be implemented exactly if the phonon Green’s function of the harmonic environment region surrounding the anharmonic region is known, which is, e.g., the case when the environment region represents a part of a periodic solid (the bulk or a surface). We also show that in general after the local perturbation has ceased, the system returns to thermodynamic equilibrium with the distribution function for region 1 being canonical with respect to an effective interaction between atoms, which includes instantaneous response of the surrounding region. Note that our method does not rely on the assumption made in AD that the stochastic force correlation function depends on the times difference only (i.e., the random force corresponds to a stationary random process). In fact, we demonstrate explicitly that generally this is not the case. Still, the correct GLE can be obtained, which satisfies exactly the fluctuation-dissipation theorem.

Kantorovich, L.

2008-09-01

58

NASA Astrophysics Data System (ADS)

The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.

Stella, L.; Lorenz, C. D.; Kantorovich, L.

2014-04-01

59

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

Koehl, Patrice; Delarue, Marc

2010-01-01

60

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. PMID:24125251

Popov, Alexander V; Hernandez, Rigoberto

2013-09-01

61

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 $t^\\alpha$ for some $\\alphaClassical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a {\\it unified} Generalized Langevin Equation (GLE) scheme, and therefore, are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.

Debabrata Panja

2010-04-06

62

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. PMID:21797326

Mankin, R; Laas, K; Sauga, A

2011-06-01

63

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. PMID:24089743

Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

2013-09-28

64

Higher-order time integration of Coulomb collisions in a plasma using Langevin equations

NASA Astrophysics Data System (ADS)

The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler-Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(?t) vs. O(?t)] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the "area-integral" terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler-Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.

Dimits, A. M.; Cohen, B. I.; Caflisch, R. E.; Rosin, M. S.; Ricketson, L. F.

2013-06-01

65

Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches

We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20-9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5-95 percent. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modelling of the dynamics of large protein complexes.

Jakob Schluttig; Denitsa Alamanova; Volkhard Helms; Ulrich S. Schwarz

2008-09-17

66

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.

Luis M. A. Bettencourt

2000-05-25

67

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of

Yoshitaka Tanimura

2006-01-01

68

Complex Langevin Simulation of the Coherent States Formulation of Polymer Field Theory

NASA Astrophysics Data System (ADS)

In 1969, Edwards and Freed adapted the ``coherent state'' methods employed in the second quantization formalism of quantum many-body theory to study polymer networks. Since its introduction into polymer science, this formalism has been largely neglected and to our knowledge, has never been applied as a basis for numerical simulations, even for linear polymers. However, in contrast to the Edwards auxiliary-field framework, this alternative polymer field theory has several attractive features, including an action or effective Hamiltonian with an explicit, finite-order, and semi-local polynomial character. We thus revisited the CS formalism and show that these characteristics have advantages both for analytical and numerical studies of linear polymers at equilibrium. For this purpose, we developed a new Complex Langevin sampling scheme that allows for simulations within the CS formalism with stable and efficient numerical characteristics. We anticipate that this methodology will facilitate efficient simulations of a wide range of systems, including complicated branched and networked polymers and liquid crystalline polymers.

Man, Xingkun; Delaney, Kris; Orland, Henri; Fredrickson, Glenn

2013-03-01

69

NASA Astrophysics Data System (ADS)

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, ?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.

Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas

2014-06-01

70

Publisher?s Note: Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory [Phys. Rev. A 75, 013820 (2007)] C. H. Raymond Ooi, Qingqing Sun, M. Suhail Zubairy, and Marlan O. Scully #1;Received 1...Publisher?s Note: Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory [Phys. Rev. A 75, 013820 (2007)] C. H. Raymond Ooi, Qingqing Sun, M. Suhail Zubairy, and Marlan O. Scully #1;Received 1...

Ooi, C. H. Raymond; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.

2007-01-01

71

Field theories and exact stochastic equations for interacting particle systems

NASA Astrophysics Data System (ADS)

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the “imaginary” Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.

Andreanov, Alexei; Biroli, Giulio; Bouchaud, Jean-Philippe; Lefèvre, Alexandre

2006-09-01

72

Field theories and exact stochastic equations for interacting particle systems.

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the "imaginary" Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit. PMID:17025576

Andreanov, Alexei; Biroli, Giulio; Bouchaud, Jean-Philippe; Lefèvre, Alexandre

2006-09-01

73

The Langevin equation on Lie algebras: Maxwell-Boltzmann is not always the equilibrium

We give a geometric formulation of the Fokker-Planck-Kramer equations for a particle moving on a Lie algebra under the influence of a dissipative and a random force. Special cases of interest are fluid mechanics, the Stochastic Loewner equation and the rigid body. We find that the Boltzmann distribution, although a static solution, is not normalizable when the algebra is not unimodular. This is because the invariant measure of integration in momentum space is not the standard one. We solve the special case of the upper half-plane (hyperboloid) explicitly: there is another equilibrium solution to the Fokker-Planck equation, which is integrable. It breaks rotation invariance.

Rajeev, S.G. [Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627 (United States); Department of Mathematics, University of Rochester, Rochester, NY 14627 (United States)], E-mail: rajeev@pas.rochester.edu

2009-12-15

74

We describe a tracer in a bath of soft Brownian colloids by a particle coupled to the density field of the other bath particles. From the Dean equation, we derive an exact equation for the evolution of the whole system, and show that the density field evolution can be linearized in the limit of a dense bath. This linearized Dean equation with a tracer taken apart is validated by the reproduction of previous results on the mean-field liquid structure and transport properties. Then, the tracer is submitted to an external force and we compute the density profile around it, its mobility and its diffusion coefficient. Our results exhibit effects such as bias enhanced diffusion that are very similar to those observed in the opposite limit of a hard core lattice gas, indicating the robustness of these effects. Our predictions are successfully tested against molecular dynamics simulations.

Vincent Démery; Hugo Jacquin; Olivier Bénichou

2014-01-21

75

NASA Astrophysics Data System (ADS)

We describe a tracer in a bath of soft Brownian colloids by a particle coupled to the density field of the other bath particles. From the Dean equation, we derive an exact equation for the evolution of the whole system, and show that the density field evolution can be linearized in the limit of a dense bath. This linearized Dean equation with a tracer taken apart is validated by the reproduction of previous results on the mean-field liquid structure and transport properties. Then, the tracer is submitted to an external force and we compute the density profile around it, its mobility and its diffusion coefficient. Our results exhibit effects such as bias enhanced diffusion that are very similar to those observed in the opposite limit of a hard core lattice gas, indicating the robustness of these effects. Our predictions are successfully tested against Brownian dynamics simulations.

Démery, Vincent; Bénichou, Olivier; Jacquin, Hugo

2014-05-01

76

NASA Astrophysics Data System (ADS)

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.

Pankavich, S.; Shreif, Z.; Miao, Y.; Ortoleva, P.

2009-05-01

77

Theory of fractional functional differential equations

In this paper, the basic theory for the initial value problems for fractional functional differential equations is considered, extending the corresponding theory of ordinary functional differential equations.

V. Lakshmikantham

2008-01-01

78

We present a largely analytical theory for two-photon correlations G((2)) between Stokes (s) and anti-Stokes (a) photon pairs from an extended medium (amplifier) composed of double-Lambda atoms in counterpropagating geometry. We generalize...

Ooi, C. H. Raymond; Scully, Marlan O.; Sun, Qingqing; Zubairy, M. Suhail

2007-01-01

79

Twistor theory and differential equations

NASA Astrophysics Data System (ADS)

This is an elementary and self-contained review of twistor theory as a geometric tool for solving nonlinear differential equations. Solutions to soliton equations such as KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon arise from holomorphic vector bundles over T{\\bb C}{\\bb P}^1 . A different framework is provided for the dispersionless analogues of soliton equations, such as dispersionless KP or SU(?) Toda system in 2+1 dimensions. Their solutions correspond to deformations of (parts of) T{\\bb C}{\\bb P}^1 , and ultimately to Einstein-Weyl curved geometries generalizing the flat Minkowski space. A number of exercises are included and the necessary facts about vector bundles over the Riemann sphere are summarized in the appendix.

Dunajski, Maciej

2009-10-01

80

Theory of Brownian motion with the Alder-Wainwright effect

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, the authors obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. The authors interested in whether or not it can be measured experimentally.

Okabe, Y.

1986-12-01

81

Quantum Langevin model for nonequilibrium condensation

NASA Astrophysics Data System (ADS)

We develop a quantum model for nonequilibrium Bose-Einstein condensation of photons and polaritons in planar microcavity devices. The model builds on laser theory and includes the spatial dynamics of the cavity field, a saturation mechanism, and some frequency dependence of the gain: quantum Langevin equations are written for a cavity field coupled to a continuous distribution of externally pumped two-level emitters with a well-defined frequency. As an example of application, the method is used to study the linearized quantum fluctuations around a steady-state condensed state. In the good-cavity regime, an effective equation for the cavity field only is proposed in terms of a stochastic Gross-Pitaevskii equation. Perspectives in view of a full quantum simulation of the nonequilibrium condensation process are finally sketched.

Chiocchetta, Alessio; Carusotto, Iacopo

2014-08-01

82

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...

Lucarini, Valerio; Willeit, Matteo

2011-01-01

83

Localised distributions and criteria for correctness in complex Langevin dynamics

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.

Aarts, Gert, E-mail: g.aarts@swan.ac.uk [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom)] [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)] [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)] [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)

2013-10-15

84

On the theory of Brownian motion with the Alder-Wainwright effect

NASA Astrophysics Data System (ADS)

The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.

Okabe, Yasunori

1986-12-01

85

Relativistic Langevin dynamics in expanding media.

We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann-Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the prepoint (Ito) and postpoint (Hänggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions. PMID:24125244

He, Min; van Hees, Hendrik; Gossiaux, Pol B; Fries, Rainer J; Rapp, Ralf

2013-09-01

86

Entropy theory for derivation of infiltration equations

NASA Astrophysics Data System (ADS)

An entropy theory is formulated for modeling the potential rate of infiltration in unsaturated soils. The theory is composed of six parts: (1) Shannon entropy, (2) principle of maximum entropy (POME), (3) specification of information on infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, (5) derivation of the probability distribution of infiltration, and (6) derivation of infiltration equations. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two-term, Green-Ampt, Overton, and Holtan equations, and the determination of the least biased probability distributions of these infiltration equations and their entropies. The theory leads to the expression of parameters of the derived infiltration equations in terms of measurable quantities (or information), called constraints, and in this sense these equations are rendered nonparametric. Furthermore, parameters of these infiltration equations can be expressed in terms of three measurable quantities: initial infiltration, steady infiltration, and soil moisture retention capacity. Using parameters so obtained, infiltration rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the rates computed using parameters of these equations obtained by calibration. It is found that infiltration parameter values yielded by the entropy theory are good approximations.

Singh, Vijay P.

2010-03-01

87

Entropy production in linear Langevin systems

NASA Astrophysics Data System (ADS)

We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem.

Landi, Gabriel T.; Tomé, Tânia; de Oliveira, Mário J.

2013-10-01

88

Symmetry of Differential Equations and Quantum Theory

NASA Astrophysics Data System (ADS)

The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.

Yerchuck, Dmitri; Dovlatova, Alla; Alexandrov, Andrey

2014-03-01

89

Localised distributions and criteria for correctness in complex Langevin dynamics

NASA Astrophysics Data System (ADS)

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.

Aarts, Gert; Giudice, Pietro; Seiler, Erhard

2013-10-01

90

Langevin's `Twin Paradox' paper revisited

An in-depth and mathematically-detailed analysis of Langevin's popular 1911 article on the special theory of relativity is presented. For the reader's convenience, English translations of large parts of the original French text are given. The self-contradictory nature of many of Langevin's assertions is pointed out. Of special interest is the analysis of the exchange of light signals between the travelling and stay-at-home twins in Langevin's thought experiment, in which antinomies are found in the conventional relativistic treatment. Their resolution shows that the physical basis of the differential aging effect in the experiment is not `length contraction', as in the conventional interpretation, but instead the application of the correct relative velocity transformation formula. The spurious nature of the correlated `length contraction' and `relativity of simultaneity' effects of conventional special relativity is also demonstrated. In consequence, an argument given, claiming to demonstrate that an upper limit of $c$ on the speed of any physical signal is required by causality, is invalid. Its conclusion is also in contradiction with astronomical observations and the results of a recent experiment.

J. H. Field

2008-11-21

91

Boltzmann-Langevin transport model for heavy-ion collisions

Heavy-ion collisions at intermediate energies exhibit catastrophic phenomena which requires descriptions based on stochastic transport models. First, the Boltzmann-Langevin model, which provides an example of such stochastic approaches, is briefly described. Then, a projection method for obtaining numerical solutions of the Boltzmann-Langevin equation is discussed. Finally, some applications of the model to heavy-ion collisions are presented.

Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States)]|[Joint Institute for Heavy-Ion Research, Oak Ridge, TN (United States)

1994-06-01

92

Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

Langevin model corresponding to the Fokker-Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.

Hellinger, Petr, E-mail: Petr.Hellinger@ig.cas.c [Astronomical Institute, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Atmospheric Physics, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Travnicek, Pavel M. [Astronomical Institute, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Atmospheric Physics, AS CR, Bocni II/1401, 14131 Prague 4 (Czech Republic); Institute of Geophysics and Planetary Physics, UCLA, Los Angeles 90095-1567 (United States)

2010-07-20

93

Errors in genetic theory equations.

This study addresses the consequences of eliminating terms such as x(2) and x(3) from genetic equations when the variable x is known to be small. This paper indicates logically that to assign such terms a value of 0.0 requires knowing the magnitude of the coefficients for each of these terms as well as the magnitude of all other terms in a given expression. Since most genetic expressions of interest involve several unknowns, the elimination of these terms appears difficult to justify in most situations. The effects of the elimination of a single term from an expression in a classical plant breeding paper were investigated as a simple exemplifying case. In the example, the simplified equation for change in population mean with selection sometimes greatly overestimated the response to selection and in some cases also altered conclusions as to best procedure. Though simplified equations are usually much more tractable and interpretable, the bias which is introduced into the research results and the potential for propagation of such biases in subsequent studies indicates that no term can be uncritically ignored in a genetic equation. The obvious alternatives are (1) do not simplify by eliminating terms, (2) perform a complete error analysis, or (3) restrict the range of values for variables so that terms can be justifiably eliminated in the error analysis. PMID:24247451

Rowe, D E

1985-12-01

94

Basic theory of fractional differential equations

In this paper, the basic theory for the initial value problem of fractional differential equations involving Riemann–Liouville differential operators is discussed employing the classical approach. The theory of inequalities, local existence, extremal solutions, comparison result and global existence of solutions are considered.

V. Lakshmikantham; A. S. Vatsala

2008-01-01

95

Difierential equations and conformal fleld theories

We discuss the recent results of the author on the existence of systems of difierential equations for chiral genus-zero and genus-one correlation functions in conformal fleld theories. Two-dimensional conformal fleld theories form a particular class of nontopolog- ical quantum fleld theories which have now been formulated and studied rigor- ously using various methods from difierent branches of mathematics. In physics,

Yi-Zhi Huang

96

Nonlinear quantum equations: Classical field theory

NASA Astrophysics Data System (ADS)

An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q ? 1. The main characteristic of this field theory consists on the fact that besides the usual ? (x,t), a new field ? (x,t) needs to be introduced in the Lagrangian, as well. The field ? (x,t), which is defined by means of an additional equation, becomes ? ^{*}(x,t) only when q ? 1. The solutions for the fields ? (x,t) and ? (x,t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E2 = p2c2 + m2c4, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

Rego-Monteiro, M. A.; Nobre, F. D.

2013-10-01

97

Heavy Flavor Suppression, Flow and Azimuthal Correlation: Boltzmann vs Langevin

NASA Astrophysics Data System (ADS)

The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough comparison in terms of nuclear suppression, RAA, elliptic flow, v2, and cbar c back to back correlation between the Langevin equation and the full collisional Boltzmann collision integral within the framework of Boltzmann transport equation. We have shown that the Langevin dynamics overestimates the interaction and even for a fixed RAA the full two-body collision integral shows that the elliptic flow is larger with respect to that predicted by a Langevin dynamics. Furthermore we have found that Boltzmann approach gives rise to a larger spreading of cbar c correlation in comparison with the Langevin approach.

Scardina, F.; Das, S. K.; Plumari, S.; Perricone, D.; Greco, V.

2014-09-01

98

Brownian motion from Boltzmann's equation.

NASA Technical Reports Server (NTRS)

Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

Montgomery, D.

1971-01-01

99

Langevin model of the rotational diffusion of molecules

NASA Astrophysics Data System (ADS)

Globular molecules in dense gases, liquids, and orientationally disordered crystals experience an incessant fluctuating torque of rather weak magnitude. In gases and liquids the fluctuating torque perturbs the otherwise free rotational motion which becomes diffusive. We treat the rotational diffusion within the Langevin model where the molecules are driven by a stochastic torque and hindered by a friction term. The Langevin equation for molecules with one, two, and three angular degrees of freedom is solved numerically and the dipole and Raman correlation functions are extracted. In the one-dimensional case we compare with the exact solution of the Langevin equation, in two and three dimensions with earlier work and with experimental results.

Gerling, Rainer; Hüller, Alfred

1980-09-01

100

Nonlinear quantum equations: Classical field theory

An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)

2013-10-15

101

Adaptive gauge cooling for complex Langevin dynamics

In the case of nonabelian gauge theories with a complex weight, a controlled exploration of the complexified configuration space during a complex Langevin process requires the use of SL(N,C) gauge cooling, in order to minimize the distance from SU(N). Here we show that adaptive gauge cooling can lead to an efficient implementation of this idea. First results for SU(3) Yang-Mills theory in the presence of a nonzero theta-term are presented as well.

Lorenzo Bongiovanni; Gert Aarts; Erhard Seiler; Denes Sexty; Ion-Olimpiu Stamatescu

2013-11-05

102

Renormalization group equations in resonance chiral theory

The use of the equations of motion and meson field redefinitions allows the development of a simplified resonance chiral theory lagrangian: terms including resonance fields and a large number of derivatives can be reduced into corresponding O(p2) resonance operators, containing the lowest possible number of derivatives. This is shown by means of the explicit computation of the pion vector form-factor up to next-to-leading order in 1/Nc. The study of the renormalization group equations for the corresponding couplings demonstrates the existence of an infrared fixed point in the resonance theory. The possibility of developing a perturbative 1/Nc expansion in the slow running region around the fixed point is shown here.

J. J. Sanz-Cillero

2009-05-22

103

Heavy Flavor Suppression: Boltzmann vs Langevin

NASA Astrophysics Data System (ADS)

The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable.

Das, S. K.; Scardina, F.; Plumari, S.; Greco, V.

2014-05-01

104

Explicit Solutions for a Riccati Equation from Transport Theory

Explicit Solutions for a Riccati Equation from Transport Theory Volker Mehrmann # Hongguo Xu solution of a particuÂ lar nonÂsymmetric Riccati equation arising in transport theory. The formulas demonstrate the properties of the new methods. Keywords. nonÂsymmetric Riccati equation, secular equation

Xu, Hongguo

105

Explicit Solutions for a Riccati Equation from Transport Theory

Explicit Solutions for a Riccati Equation from Transport Theory Volker Mehrmann Hongguo Xu January of a particu- lar non-symmetric Riccati equation arising in transport theory. The formulas are based demonstrate the properties of the new methods. Keywords. non-symmetric Riccati equation, secular equation

Xu, Hongguo

106

Undular bore theory for the Gardner equation

NASA Astrophysics Data System (ADS)

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2012-09-01

107

Solving Kepler's equation via Smale's -theory

NASA Astrophysics Data System (ADS)

We obtain an approximate solution of Kepler's equation for any and . Our solution is guaranteed, via Smale's -theory, to converge to the actual solution through Newton's method at quadratic speed, i.e. the -th iteration produces a value such that . The formula provided for is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near and , where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region if only rational functions are allowed in each branch.

Avendano, Martín; Martín-Molina, Verónica; Ortigas-Galindo, Jorge

2014-05-01

108

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Meng, Yu

2012-01-01

109

Nucleation theory using equations of state

NASA Astrophysics Data System (ADS)

Various equations of state (EOS) have been used with the most general Gibbsian form (P-form) of classical nucleation theory ( CNT) to see if any improvement could be realized in predicted rates for vapor-to-liquid nucleation. The standard or S-form of CNT relies on the assumption of an incompressible liquid droplet. With the use of realistic EOSs, this assumption is no longer needed. The P-form results for water and heavy water were made using the highly accurate IAPWS-95 EOS and the CREOS. The P-form successfully predicted the temperature (T) supersaturation (S ) dependence of the nucleation rate, although the absolute value was in error by roughly a factor of 100. The results for methanol and ethanol using a less accurate CPHB EOS showed little improvement over the S-form results. Gradient theory (GT), a form of density functional theory (DFT), was applied to water and alcohols using the CPHB EOS. The water results showed an improved T dependence, but the S dependence was slightly poorer compared to the S-form of CNT. The methanol and ethanol results were improved by several orders of magnitude in the predicted rates. GT and P-form CNT were also found to be in good agreement with a single high T molecular dynamics rate for TIP4P water. The P-form of binary nucleation theory was studied for a fictitious water-ethanol system whose properties were generated from DFT and a mean-field EOS for a hard sphere Yukawa fluid. The P-form was not successful in removing the unphysical behavior predicted by binary CNT in its simplest form. The DFT results were greatly superior to all forms of classical theory.

Obeidat, Abdalla A.

110

Constant pressure molecular dynamics simulation: The Langevin piston method

A new method for performing molecular dynamics simulations under constant pressure is presented. In the method, which is based on the extended system formalism introduced by Andersen, the deterministic equations of motion for the piston degree of freedom are replaced by a Langevin equation; a suitable choice of collision frequency then eliminates the unphysical ‘‘ringing’’ of the volume associated with

Scott E. Feller; Yuhong Zhang; Richard W. Pastor; Bernard R. Brooks

1995-01-01

111

Solving Kepler's equation via Smale's $?$-theory

We obtain an approximate solution $\\tilde{E}=\\tilde{E}(e,M)$ of Kepler's equation $E-e\\sin(E)=M$ for any $e\\in[0,1)$ and $M\\in[0,\\pi]$. Our solution is guaranteed, via Smale's $\\alpha$-theory, to converge to the actual solution $E$ through Newton's method at quadratic speed, i.e. the $n$-th iteration produces a value $E_n$ such that $|E_n-E|\\leq (\\frac12)^{2^n-1}|\\tilde{E}-E|$. The formula provided for $\\tilde{E}$ is a piecewise rational function with conditions defined by polynomial inequalities, except for a small region near $e=1$ and $M=0$, where a single cubic root is used. We also show that the root operation is unavoidable, by proving that no approximate solution can be computed in the entire region $[0,1)\\times[0,\\pi]$ if only rational functions are allowed in each branch.

Martin Avendano; Verónica Martín-Molina; Jorge Ortigas-Galindo

2014-01-19

112

Electronic Journal of Qualitative Theory of Differential Equations

NSDL National Science Digital Library

The Electronic Journal of Qualitative Theory of Differential Equations (EJQDTE) publishes peer-reviewed articles related to "the qualitative theory (stability, periodicity, soundness, etc.) of differential equations (ODE's, PDE's, integral equations, functional differential equations, etc.) and their applications." Proceedings of conferences are also available in the journal. Every three to four years, the EJQDTQ will publish the proceedings of the Colloquium of Qualitative Theory of Differential Equations organized by the Bolyai Institute. Journal volumes from 1998 and 1999 are currently available at the site.

1998-01-01

113

Data driven Langevin modeling of biomolecular dynamics.

Based on a given time series, the data-driven Langevin equation proposed by Hegger and Stock [J. Chem. Phys. 130, 034106 (2009)] aims to construct a low-dimensional dynamical model of the system. Adopting various simple model problems of biomolecular dynamics, this work presents a systematic study of the theoretical virtues and limitations as well as of the practical applicability and performance of the method. As the method requires only local information, the input data need not to be Boltzmann weighted in order to warrant that the Langevin model yields correct Boltzmann-distributed results. Moreover, a delay embedding of the state vector allows for the treatment of memory effects. The robustness of the modeling with respect to wrongly chosen model parameters or low sampling is discussed, as well as the treatment of inertial effects. Given sufficiently sampled input data, the Langevin modeling is shown to successfully recover the correct statistics (such as the probability distribution) and the dynamics (such as the position autocorrelation function) of all considered problems. PMID:23742453

Schaudinnus, Norbert; Rzepiela, Andrzej J; Hegger, Rainer; Stock, Gerhard

2013-05-28

114

Data driven Langevin modeling of biomolecular dynamics

NASA Astrophysics Data System (ADS)

Based on a given time series, the data-driven Langevin equation proposed by Hegger and Stock [J. Chem. Phys. 130, 034106 (2009)] aims to construct a low-dimensional dynamical model of the system. Adopting various simple model problems of biomolecular dynamics, this work presents a systematic study of the theoretical virtues and limitations as well as of the practical applicability and performance of the method. As the method requires only local information, the input data need not to be Boltzmann weighted in order to warrant that the Langevin model yields correct Boltzmann-distributed results. Moreover, a delay embedding of the state vector allows for the treatment of memory effects. The robustness of the modeling with respect to wrongly chosen model parameters or low sampling is discussed, as well as the treatment of inertial effects. Given sufficiently sampled input data, the Langevin modeling is shown to successfully recover the correct statistics (such as the probability distribution) and the dynamics (such as the position autocorrelation function) of all considered problems.

Schaudinnus, Norbert; Rzepiela, Andrzej J.; Hegger, Rainer; Stock, Gerhard

2013-05-01

115

Applications of Langevin and Molecular Dynamics methods

Computer simulation of complex nonlinear and disordered phenomena from materials science is rapidly becoming an active and new area serving as 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 ODEs (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 will 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 will 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.

Lomdahl, P.S.

1994-12-31

116

JOURNAL OF MATHEMATICAL PHYSICS 52, 083303 (2011) Diffusive behavior from a quantum master equation

of Langevin or Fokker-Planck equations in classical probability theory describing a dynamical system underJOURNAL OF MATHEMATICAL PHYSICS 52, 083303 (2011) Diffusive behavior from a quantum master equation dynamics and leading to a translation invariant master or Boltzmann-type equation, e.g., as the result

Maes, Christian

117

Perturbation Theory for the - Benjamin-Ono Equation.

National Technical Information Service (NTIS)

We develop a perturbation theory for the Benjamin-Ono (BO) equation. This perturbation theory is based on the Inverse Scattering Transform for the BO equation which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. W...

D. J. Kaup, T. I. Lakoba, Y. Matsuno

1998-01-01

118

On a relativistic Fokker-Planck equation in kinetic theory

On a relativistic Fokker-Planck equation in kinetic theory JosÂ´e Antonio AlcÂ´antara FÂ´elix Simone Fokker-Planck equation that has been recently proposed in the phys- ical literature is studied mean-field models are introduced. One is obtained by coupling the relativistic Fokker-Planck equation

119

The Master-Equation Formulation of Chromatography Theory

De Clerk et al. have recently proposed that if chromatography theory were based on a master equation rather than a Fokker-Planck equation, asymmetries could readily arise [Separation Sci., 1, 443(1966)]. It is shown here that the master-equation description of an infinitely long homogeneous column also leads to a Gaussian limiting distribution.

George H. Weiss

1967-01-01

120

arXiv:0812.2858v2[math-ph]13Jan2009 Diffusive behavior from a quantum master equation

equations take the place of Langevin or Fokker-Planck equations in classical probability theory describingarXiv:0812.2858v2[math-ph]13Jan2009 Diffusive behavior from a quantum master equation Jeremy Clark1 a microscopic dynamics and leading to a master or Boltzmann-type equation, e.g. as the result of a weak coupling

Maes, Christian

121

Localised distributions in complex Langevin dynamics

NASA Astrophysics Data System (ADS)

Complex Langevin dynamics can be used to perform 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 and relate the results to the recently derived criteria for correctness. We demonstrate analytically that if the distribution has support only on a strip in the complexified configuration space, correct results are expected.

Giudice, P.; Aarts, G.; Seiler, E.

122

Langevin agglomeration of nanoparticles interacting via a central potential

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is

Lorenzo Isella; Yannis Drossinos

2010-01-01

123

On the equations of motion in scalar-tensor theories

We work out the equations of motion for extended test bodies for a large class of scalar-tensor theories of gravitation. Our aim is to shed more light on the discussion of the so-called Jordan and Einstein formulation of these theories. The results obtained provide the framework to experimentally test which metric is physical in scalar-tensor theories.

Yuri N. Obukhov; Dirk Puetzfeld

2014-04-28

124

Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

NASA Astrophysics Data System (ADS)

We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez. In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level -- a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.

Joubaud, R.; Pavliotis, G. A.; Stoltz, G.

2014-09-01

125

On the equation of state in effective quark theories

We discuss the saturation mechanism for the nuclear matter equation of state in a chiral effective quark theory. The importance of the scalar polarizability of the nucleon is emphasized. The phase transition to color superconducting quark matter is also discussed.

Bentz, Wolfgang; Lawley, Sarah; Thomas, Anthony

2008-09-01

126

Behavioral Momentum Theory: Equations and Applications

ERIC Educational Resources Information Center

Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…

Nevin, John A.; Shahan, Timothy A.

2011-01-01

127

Some remarks on Lefschetz thimbles and complex Langevin dynamics

NASA Astrophysics Data System (ADS)

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.

Aarts, Gert; Bongiovanni, Lorenzo; Seiler, Erhard; Sexty, Dénes

2014-10-01

128

Item Response Theory Equating Using Bayesian Informative Priors.

ERIC Educational Resources Information Center

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

de la Torre, Jimmy; Patz, Richard J.

129

Scaling theory for homogenization of the Maxwell equations.

A scaling theory for homogenization of the Maxwell equations is developed upon the representation of any field as a sum of its dipole, quadrupole, and magnetic dipole moments. This representation is exact and is connected neither with multipole expansion nor with the Helmholtz theorem. A chain of hierarchical equations is derived to calculate the moments. It is shown that the resulting macroscopic fields are governed by the homogenized Maxwell equations. Generally, these fields differ from the mean values of microscopic fields. PMID:11969844

Vinogradov, A P; Aivazyan, A V

1999-07-01

130

NASA Astrophysics Data System (ADS)

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.

Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

2013-12-01

131

Hitchin's Equations and M-Theory Phenomenology

Phenomenological compactifications of M-theory involve 7-manifolds with G_2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills theory on a three-manifold Q_3. We give a general discussion of compactifications of 7d Yang-Mills theory in terms of Higgs bundles on Q_3. We show they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T^*Q_3. We explain the dictionary with ALE fibrations over Q_3 and conjecture that these configurations have G_2 holonomy. We further develop tools to study the low energy effective theory of such a model. We show that the naive massless spectrum is corrected by instanton effects. Taking the instanton effects into account, we find that the massless spectrum and many of the interactions can be computed with Morse theoretic methods.

Tony Pantev; Martijn Wijnholt

2009-05-13

132

Unification in a Combination of Equational Theories: an Efficient Algorithm

An algorithm is presented for solving equations in a combination of arbitrary theories with disjoint sets of function symbols. It is an extension of [3] in which the problem was treated for the combination of an arbitrary and a simple theory. The algorithm consists in a set of transformation rules that simplify a unification problem until a solved form is

Alexandre Boudet

1990-01-01

133

Langevin diffusion in holographic backgrounds with hyperscaling violation

In this note 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 construct the Langevin correlator which helps us to obtain the Langevin constants. Using the Langevin correlators we derive the densities spectral 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 $\\theta$ in the presence of velocity $v$.

Jafar Sadeghi; Fatemeh Pourasadollah

2014-03-10

134

Hamilton's equations in a non-associative quantum theory

A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some $(\\pm)$associators for the product of some four operators is offered. The possible generalization of Hamilton's equations for a non-associative quantum theory is proposed. Some arguments are given that a non-associative quantum theory can be a fundamental unifying theory.

Vladimir Dzhunushaliev

2006-02-05

135

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.

Mathieu, V; Triantafyllopoulos, D N

2014-01-01

136

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.

V. Mathieu; A. H. Mueller; D. N. Triantafyllopoulos

2014-03-05

137

NASA Astrophysics Data System (ADS)

Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ˜(R-Rc)?, where passing is sterically blocked for R ?Rc, with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.

Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.; Evans, James W.

2014-07-01

138

Langevin equations coupled through correlated noises

NASA Astrophysics Data System (ADS)

We consider the dynamics of non-interacting Brownian particles which are driven by correlated (non-independent) noise sources. In simple confining potentials the particles tend to aggregate as the noise correlation is increased. If two particles are subject to the same noise they will coalesce and remain together ever after. We show that complete aggregation of the particles can be expected even in the case of a disordered potential which does not confine the individual particle trajectories. Finally, we examine the case of correlation in the noises which depends on the separation of the two particles.

Lise, Stefano; Maritan, Amos; Swift, Michael R.

1999-07-01

139

Einstein equations and MOND theory from Debye entropic gravity

Verlinde's proposal on the entropic origin of gravity is based strongly on the assumption that the equipartition law of energy holds on the holographic screen induced by the mass distribution of the system. However, from the theory of statistical mechanics we know that the equipartition law of energy does not hold in the limit of very low temperature. Inspired by the Debye model for the equipartition law of energy in statistical thermodynamics and adopting the viewpoint that gravitational systems can be regarded as a thermodynamical system, we modify Einstein field equations. We also perform the study for Poisson equation and modified Newtonian dynamics (MOND). Interestingly enough, we find that the origin of the MOND theory can be understood from Debye entropic gravity perspective. Thus our study may fill in the gap existing in the literature understanding the theoretical origin of MOND theory. In the limit of high temperature our results reduce to their respective standard gravitational equations.

Sheykhi, A. [Center for Excellence in Astronomy and Astrophysics (CEAA-RIAAM) Maragha, P.O. Box 55134-441 (Iran, Islamic Republic of); Sarab, K. Rezazadeh, E-mail: sheykhi@uk.ac.ir, E-mail: kazem.rezazadeh.sarab@gmail.com [Department of Physics, Shahid Bahonar University, P.O. Box 76175, Kerman (Iran, Islamic Republic of)

2012-10-01

140

An alternative description of stochastic processes in nonlinear systems is considered. It is shown that among the possible forms of the Fokker-Planck and the Langevin equations (Ito, Stratonovich, and kinetic forms) the kinetic form is more natural from the point of view of the statistical theory. A new form of the master equation for one-step processes is proposed which is

Yu. L. Klimontovich

1992-01-01

141

Langevin agglomeration of nanoparticles interacting via a central potential

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the\\u000aLangevin equations of motion of a set of interacting monomers in the continuum\\u000aregime. Monomers interact via a radial, rapidly decaying intermonomer\\u000apotential. The morphology of generated clusters is analyzed through their\\u000afractal dimension $d_f$ and the cluster coordination number. The time evolution\\u000aof the cluster fractal dimension is

Lorenzo Isella; Yannis Drossinos

2010-01-01

142

INVARIANCE THEORY, THE HEAT EQUATION, ATIYAH-SINGER INDEX THEOREM

INVARIANCE THEORY, THE HEAT EQUATION, AND THE ATIYAH-SINGER INDEX THEOREM by Peter B. Gilkey Electronic reprint, copyright 1996, Peter B. Gilkey Book originally published on paper by Publish or Perish the reader to the bibliography of Berger and Berard for a more complete list of works on spectral geometry

Gilkey, Peter B

143

Translating Words into Equations: A Cognitive Load Theory Approach

ERIC Educational Resources Information Center

The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a…

Pawley, Duncan; Ayres, Paul; Cooper, Martin; Sweller, John

2005-01-01

144

Translating words into equations: a cognitive load theory approach

The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a checking method. However, after a more substantial

Duncan Pawley; Paul Ayres; Martin Cooper; John Sweller

2005-01-01

145

Control theory based airfoil design using the Euler equations

NASA Technical Reports Server (NTRS)

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Jameson, Antony; Reuther, James

1994-01-01

146

Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory

Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.

Yi-Fang Chang

2010-08-17

147

To nonlinear Schrodinger's equations through prequantum classical statistical field theory

We derive some important features of the standard quantum mechanics from a certain classical-like (hidden variable) statistical model (it was called prequantum classical statistical field theory, PCSFT). The correspondence between classical and quantum quantities is asymptotic, so we call our approach asymptotic dequantization. The approach might be seen as a kind of retain, through post-von-Neumannian formalism, to the approach of the old quantum theory of Bohr and Sommerfeld, except for the fact that (the standard) quantum mechanics is now seen as a limit of a {\\it new type} of classical statistical theory configured in an infinite-dimensional Hilbert space (over real numbers). One of unexpected consequences of PCSFT is the infinite dimension of physical space on the prequantum scale. Another important physical consequence is that PCSFT induces not only conventional linear Schr\\"odinger's equation, but also {\\it nonlinear generalizations of Schr\\"odinger's equations} that have been studied, e.g., by De Brog...

Khrennikov, A

2006-01-01

148

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.

Debashis Barik; Pulak Kumar Ghosh; Deb Shankar Ray

2006-02-23

149

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.

F. Haas; M. Marklund; G. Brodin; J. Zamanian

2009-10-27

150

J Syst Sci Complex (2010) 23: 896905 NONLINEAR LANGEVIN MODEL WITH PRODUCT

, especially when facing the difficult task of estimating small probabilities of biological events that occur accurately. Key words Langevin equation, master equation, noise, Schnakenberg model. 1 Introduction Chemical Markov process of the CME, and in obtaining the exact stationary probability Youfang CAO Â· Jie LIANG

Dai, Yang

151

On a relativistic Fokker-Planck equation in kinetic theory

A relativistic kinetic Fokker-Planck equation that has been recently proposed in the physical literature is studied. It is shown that, in contrast to other existing relativistic models, the one considered in this paper is invariant under Lorentz transformations in the absence of friction. A similar property (invariance by Galilean transformations in the absence of friction) is verified in the non-relativistic case. In the first part of the paper some fundamental mathematical properties of the relativistic Fokker-Planck equation are established. In particular, it is proved that the model is compatible with the finite propagation speed of particles in relativity. In the second part of the paper, two non-linear relativistic mean-field models are introduced. One is obtained by coupling the relativistic Fokker-Planck equation to the Maxwell equations of electrodynamics, and is therefore of interest in plasma physics. The other mean-field model couples the Fokker-Planck dynamics to a relativistic scalar theory of gravity (the Nordstr\\"om theory) and is therefore of interest in gravitational physics. In both cases the existence of steady states for all possible prescribed values of the mass is established. In the gravitational case this result is better than for the corresponding non-relativistic model, the Vlasov-Poisson-Fokker-Planck system, for which existence of steady states is known only for small mass.

José Antonio Alcántara Félix; Simone Calogero

2010-11-24

152

Item response theory test equating in health sciences education.

In the context of health sciences education, and education in general, the knowledge or ability of one or several subjects in a specific area is frequently compared using different forms of a test, or by means of different instruments aimed at measuring this knowledge or ability. In such cases, test scores must be equated so that they can be properly compared. The present article aims to explain the equating of scores within the framework of item response theory (IRT), special emphasis being placed on its application in the field of health sciences education. Although there are many data collection designs that can be used within the framework of score equating, the three most widely used designs are single group, randomly equivalent groups and non-equivalent groups with anchor test. Likewise, there are different equating procedures within IRT, such as the mean/mean and mean/sigma methods, or methods based on the characteristic curve. The equating of scores must ensure that examinees taking a test do so under the same conditions; however, the procedure is also highly useful in creating a bank of items that can be used subsequently in new tests. PMID:16847729

Guilera, Georgina; Gómez, Juana

2008-03-01

153

On Some Nonlinear Integral Equation in the (Super)String Theory

In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.

D. V. Prokhorenko

2006-11-25

154

Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model

We derive a phenomenological model of the underlying microscopic Langevin equation of the nonlinear Fokker-Planck equation, which is used to describe anomalous correlated diffusion. The resulting distribution-dependent stochastic equation is then analyzed and properties such as long-time scaling and the Hurst exponent are calculated both analytically and from simulations. Results of this microscopic theory are compared with those of fractional

Lisa Borland

1998-01-01

155

The noise spectra comparison of cavity and population inversion Langevin forces in class-A lasers

NASA Astrophysics Data System (ADS)

We have investigated the single role of cavity Langevin force on the noise spectra of class-A and -B lasers for the first time in 2012. The present aim is to consider the simultaneous effect of cavity and population inversion Langevin forces on the noise spectra of class-A lasers. The Maxwell-Bloch equations of motion are thus solved in the presence of both Langevin forces. The solutions give the fluctuations that are imposed to the cavity electric field and atomic population inversion by the Langevin forces. The noise fluxes of stimulated and spontaneous emission radiations are then calculated by using the notion of correlation function. It is demonstrated that the noise fluxes generated by the cavity Langevin force can be comparable or even larger than those produced by the population inversion Langevin force in some rates of laser pumping. The results are ultimately confirmed by illustrating the flux conservation so that the noise flux entered into laser by pumping is equal to those superimposed on the spontaneous and stimulated emission radiations.

Soleimani, A.; Jahanpanah, J.

2014-12-01

156

Controlling one-dimensional Langevin dynamics on the lattice

NASA Astrophysics Data System (ADS)

Stochastic evolutions of classical field theories have recently become popular in the study of problems such as the determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain high precision results from numerical calculations, a careful accounting of spacetime discreteness effects is essential, as well as the development of schemes to systematically improve convergence to the continuum. With a kink-bearing ?4 field theory as the application arena, we present such an analysis for a (1+1)-dimensional Langevin system. Analytical predictions and results from high resolution numerical solutions are found to be in excellent agreement.

Bettencourt, Luís M. A.; Habib, Salman; Lythe, Grant

1999-11-01

157

Fractional Langevin model of gait variability

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. PMID:16076394

West, Bruce J; Latka, Miroslaw

2005-01-01

158

We develop a general theory of self-diffusion in classical condensed systems, on the basis of a linear response method. Our theory, when applied to diffusion in solids, yields a nonlinear non-Markovian Langevin equation for an atom diffusing in a periodic potential. The memory kernel, which is expressed in terms of the dynamic structure factor of the host lattice and the

Toyonori Munakata

1985-01-01

159

Renormalized perturbation theory flow equations for the Anderson impurity model

NASA Astrophysics Data System (ADS)

We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the renormalized values of the hybridization ? and Coulomb interaction U of the model. The main difficulty in the RPT approach usually lies in the calculation of the renormalized values themselves. In the present work we show how this can be accomplished by deriving differential flow equations describing the evolution of with ?. By exploiting the fact that can be determined analytically in the limit ? ? ? we solve the flow equations numerically to obtain estimates for the renormalized parameters in the range 0 < U/ ??< 3.5.

Pandis, Vassilis

2014-11-01

160

COMBINING MCRG AND FOURIER ACCELERATED LANGEVIN ALGORITHM

We study the implementation of Monte Carlo renormalization group (MCRG) in momentum space. This technique is most efficient when used in combination with a Fourier accelerated Langevin algorithm. As a benchmark we calculate the critical exponents $\

D. ESPRIU; A. TRAVESSET

1995-05-24

161

Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy

Unified Field Equations Coupling Four Forces and Theory of Dark Matter and Dark Energy Tian Ma. Electroweak Theory VI. Unified Theory of Dark Energy and Dark Matter VII. Concluding Remarks 2 #12;References: 1. Tian Ma & Shouhong Wang, Gravitational Field Equations and Theory of Dark Matter and Dark Energy

Wang, Shouhong

162

Langevin thermostat for rigid body dynamics.

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the canonical distribution in a simulation of rigid molecules. We propose simple, quasisymplectic second-order numerical integrators and test their performance on the TIP4P model of water. We also investigate the optimal choice of thermostat parameters. PMID:19548705

Davidchack, Ruslan L; Handel, Richard; Tretyakov, M V

2009-06-21

163

Homogenization theory for periodic potentials in the Schrödinger equation

NASA Astrophysics Data System (ADS)

We use homogenization theory to derive asymptotic solutions of the Schrödinger equation for periodic potentials. This approach provides a rigorous framework in which the key concepts in solid-state physics naturally arise (Bloch waves, band gaps, effective mass, and group velocity). We solve the resulting spectral cell problem using numerical spectral methods, and validate our solution in an analytically-solvable case. Finally, we briefly discuss the convergence of our asymptotic approach and we prove that the ground-state k = 0 effective mass is never less than the ordinary inertial mass.

Náraigh, Lennon Ó.; O'Kiely, Doireann

2013-01-01

164

Equation solving program for aerodynamic lifting surface theory

NASA Technical Reports Server (NTRS)

A description of and user's manual are presented for one of a group of FORTRAN programs which, together, can be used for the analysis and design of wings in steady, subsonic flow according to a kernel function method lifting surface theory. This particular program is the one which solves the sets of simultaneous, linear, algebraic equations arising from the thin wing analysis. This program has the capability of striking out rows and columns of the aerodynamic influence matrix and rows of the associated boundary condition vectors (right hand sides). This capability significantly enhances the effectiveness of the kernel function method of lifting surface theory because studies of the convergence of solutions with the number of control points can be done with the calculation of only a single influence matrix.

Medan, R. T.; Lemmer, O. J.

1974-01-01

165

Langevin description of gauged scalar fields in a thermal bath

NASA Astrophysics Data System (ADS)

We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin-type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite-temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the nonlocal dissipation term and the Gaussian stochastic noise terms is verified. We find that the noise variables are anticorrelated at equal time. The dissipation rate for each mode is also studied, which turns out to depend on the wave number.

Miyamoto, Yuhei; Motohashi, Hayato; Suyama, Teruaki; Yokoyama, Jun'ichi

2014-04-01

166

Integral equation theory for athermal solutions of linear polymers

NASA Astrophysics Data System (ADS)

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.

Chatterjee, Avik P.

2004-12-01

167

Pictures and equations of motion in Lagrangian quantum field theory

The Heisenberg, interaction, and Schr\\"odinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are polynomial or convergent power series in field operators and their first derivatives. The general links between different time-dependent pictures of motion are derived. It is pointed that all of them admit covariant formulation, similar to the one of interaction picture. A new picture, called the momentum picture, is proposed. It is a 4-dimensional analogue of the Schr\\"odinger picture of quantum mechanics as in it the state vectors are spacetime-dependent, while the field operators are constant relative to the spacetime. The equations of motion in momentum picture are derived and partially discussed. In particular, the ones for the field operators turn to be of algebraic type. The general idea of covariant pictures of motion is presented. The equations of motion in these pictures are derived.

Bozhidar Z. Iliev

2003-02-01

168

Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit

900 1 Introduction Consider the randomly forced Burgers equation ut +uux = uxx + f ,(1Statistical Theory for the Stochastic Burgers Equation in the Inviscid Limit WEINAN E AND ERIC;STATISTICAL THEORY FOR BURGERS EQUATION 853 where f(x,t) is a zero-mean, Gaussian, statistically homogeneous

Van Den Eijnden, Eric

169

Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections) for processes described by Langevin dynamics. As we demonstrate with numerical examples as well as an exactly solvable model, our method can converge to the desired answer at a rate which is orders of magnitude faster than that achieved with direct simulations of the process in question.

O. Mazonka; C. Jarzynski; J. Blocki

1998-09-24

170

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

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

2012-02-15

171

First, we use the theory of characteristics of first order partial differential equations to derive the guiding equation directly from the Quantum Evolution Equation (QEE). After obtaining the general result, we apply it to a set of evolution equations (Schroedinger, Pauli, Klein-Gordon, Dirac) to show how the guiding equation is, actually, the characteristic velocity of the corresponding matter field equations.

Javier Gonzalez; Xavier Gimenez; Josep Maria Bofill

2007-12-12

172

Dynamical Theories Brownian Motion

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. Albert Einstein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. The period before Einstein phenomenon. I will review the theories put forward to account for it by Einstein, Smoluchowski, Langevin

Nelson, Edward

173

The connection between field-theory and the equations for material sistems

The existing field theories are based on the properties of closed exterior forms, which correspond to conservation laws for physical fields. In the present paper it is shown that closed exterior forms corresponding to field theories are obtained from the equations modelling conservation (balance) laws for material sistems (material media). The process of obtaining closed exterior forms demonstrates the connection between field-theory equations and the equations for material sistems and points to the fact that the foundations of field theories must be conditioned by the properties of equations conservation laws for material sistems.

L. I. Petrova

2007-05-02

174

Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ? (R-R(c))(?), where passing is sterically blocked for R?R(c), with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules. PMID:25083666

Wang, Chi-Jen; Ackerman, David M; Slowing, Igor I; Evans, James W

2014-07-18

175

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi-Klauder conjecture for complex e{sup i{theta}/2}{phi}{sup 4} measures with a Wick rotation angle 0{<=}{theta}/2{<=}{pi}/2 interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t{yields}0 asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t, including their t{yields}{infinity} equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the 'correct' result for t larger than a finite t{sub c}. The breakdown time t{sub c} increases powerlike for decreasing strength of the noise's imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure. - Highlights: Black-Right-Pointing-Pointer The Parisi-Klauder conjecture is reexamined for complex e{sup i{theta}/2}{phi}{sup 4} measures. Black-Right-Pointing-Pointer The time dependent moments are evaluated by temporal Borel resummation. Black-Right-Pointing-Pointer The results disagree with the Langevin simulations beyond a critical time t{sub c}. Black-Right-Pointing-Pointer t{sub c} increases with decreasing strength of the noise's imaginary part. Black-Right-Pointing-Pointer The technical reason for the breakdown is identified.

Duncan, A., E-mail: tony@dectony.phyast.pitt.edu; Niedermaier, M., E-mail: mnie@pitt.edu

2013-02-15

176

Complex Langevin simulation of quantum vortex nucleation in the Bose-Einstein condensate

The ab-initio simulation of quantum vortex nucleation in the Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the two-component boson field theory at a finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.

Hayata, Tomoya

2014-01-01

177

The Structure of Killing Spinor Equation (Heterotic) M-theory on Seven Manifolds with Fluxes

Recently much attention have been paid to compactifications of M-theory and string theory with fluxes turned on. In this paper we study the Killing spinor equations of M-theory and Heterotic M-theory on seven dimensional Riemannian manifolds with fluxes turned on. We derive the conditions on the geometry that follow from the integrability conditions of the Killing spinor equations. We then

Tibra Ali; Gerald Cleaver; John Perkins

2004-01-01

178

Quantum theory of multiwave mixing - Squeezed-vacuum model

The present paper combines a Langevin quantum-regression method with a denisty-operator approach to derive the master equation for the quantum theory of multiwave mixing in a very efficient way. The approach is quite general and is particularly valuable for analyzing complicated media such as semiconductors. It is used in the present paper to derive the quantum multiwave-mixing equations in a

Sunghyuck An; Murray Sargent III

1989-01-01

179

We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann boundary value problem with a coefficient equal to the ratio of the boundary values dispersion function, develops the theory of the half-space orthogonality of generalized singular eigenfunctions corresponding characteristic equations, which leads separation of variables. And in this two boundary value problems of the kinetic theory (diffusion light component of a binary gas and Kramers problem about isothermal slip) shows the application of the theory orthogonality eigenfunctions for analytical solutions these tasks.

A. V. Latyshev; A. D. Kurilov

2014-07-28

180

Modern integral equation techniques for quantum reactive scattering theory

Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.

Auerbach, S.M.

1993-11-01

181

Generalized-master-equation theory for heavy ion collisions

We apply nonequilibrium quantum statistical mechanics to the description of heavy ion collisions. Starting from the Liouville-Von Neumann equation we derive via the generalized master equation, the drift and diffusion coefficients.

Tripathi, R.K.; Satpathy, L.

1980-09-01

182

Kinetic theory and Lax equations for shock clustering and Burgers turbulence

, 39]. Burgers turbulence also refers to the study of Burgers equation with random forcing, but we doKinetic theory and Lax equations for shock clustering and Burgers turbulence Govind Menon1 and Ravi remarkable exact solutions for Burgers equation (f(u) = u2 /2) suggesting the complete integrability

Menon, Govind

183

THE HARTREE EQUATION FOR INFINITELY MANY I. WELL-POSEDNESS THEORY

THE HARTREE EQUATION FOR INFINITELY MANY PARTICLES I. WELL-POSEDNESS THEORY MATHIEU LEWIN AND JULIEN SABIN Abstract. We show local and global well-posedness results for the Hartree equation AND J. SABIN 1. Introduction The time-dependent Hartree equation i tu = - x + w |u|2 u, (t, x) R Ã? Rd

Recanati, Catherine

184

The theory of relaxation oscillations for Hutchinson's equation

NASA Astrophysics Data System (ADS)

Hutchinson's equation is a scalar equation with time delay which is well known in ecology. In this paper a complete asymptotic representation is constructed for a stable relaxation cycle of this equation, in the form of series in integer powers of a certain small parameter. The techniques of asymptotic integration developed on the way are then applied to analyse the question of attractors for a system of circularly interrelated Hutchinson equations. Bibliography: 8 titles.

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2011-06-01

185

Wave Propagation Theory 2.1 The Wave Equation

for conservation of mass, Euler's equation (Newton's 2nd Law), and the adiabatic equation of state are respec (the convection term) in Euler's equation, Eq. (2.2). First multiply Eq. (2.2) by and take its-components, respectively. Tensor nota- tion is used; repeated indices signify a summation (e.g., ivi = Â· v). The first term

186

Some singular integral equations in linear transport theory

Solutions to the steady-state transport equation for one speed, isotropic scattering in a half-space can be found from singular integral equations with Cauchy principal-value integrals. Galerkin methods for these equations are studied with special emphasis on sensitivity of approximation errors to choice of basis.

Mullikin, T. W.

1980-07-01

187

An Application of the Infinite Matrix Theory to Mathieu Equation

In this paper we study the infinite linear system M?X=0 equivalent to the Mathieu equation. Applying some results in summability we determine the Floquet exponents corresponding to the solutions of the differential equation. We also determine an approximation of the corresponding solutions and study the kernel of the operator represented by M?. Finally we deal with the Mathieu equation with

Bruno de Malafosse

2006-01-01

188

Langevin model for the rotational diffusion of molecules: Uniaxial rotator in an N-fold potential

NASA Astrophysics Data System (ADS)

The problem of a uniaxial rotator in an N-fold potential is described in the framework of the Langevin model. In this model the molecule is driven by a stochastic torque and hindered by a friction term. The resulting equation of motion is solved by numerical methods and in some limiting cases an analytic solution is given, too. Symmetry adapted autocorrelation functions are extracted and compared with the results of other models. To get results for the Smoluchowski diffusion-equation we used the Dianoux-Volino-formalism which was generalized and applied to the Sack-diffusion-equation. The calculated correlation functions determine the ranges of validity of the various models. In the mainly interesting region of low friction and intermediate times none of the two diffusion models can be used to replace the Langevin-model.

Gerling, Rainer W.

1981-03-01

189

On two integro-differential equations arising in particle transport theory

Two integro-differential equations arising in particle transport theory are solved explicitly using a technique involving difference equations. The physical problems to which these equations apply concern the energy-time and energy-space distributions of fast particles (neutrons, atoms, gamma -rays, etc.) as they slow down in a host medium. One of the equations involves the first-order derivative with respect to time or

M. M. R. Williams

1980-01-01

190

Liouvillian Propagators, Riccati Equation and Differential Galois Theory

In this paper a Galoisian approach to build propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schr\\"odinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As main application of this approach we solve the Ince's differential equation through Hamiltonian Algebrization procedure and Kovacic Algorithm to find the propagator for a generalized harmonic oscillator that has applications describing the process of degenerate parametric amplification in quantum optics and the description of the light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Primitivo B. Acosta-Humánez; Erwin Suazo

2013-04-21

191

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

192

Holographic Friedmann equation and N=4 supersymmetric Yang-Mills theory

NASA Astrophysics Data System (ADS)

According to the AdS/CFT correspondence, the N=4 supersymmetric Yang-Mills (SYM) theory has been studied by solving the dual supergravity. In solving the bulk Einstein equation, we find that it could be related to the 4D Friedmann equation, which is solved by using the cosmological constant and the energy density of the matter on the boundary, and they are dynamically decoupled from the SYM theory. We call this combination of the bulk Einstein equations and the 4D Friedmann equation as holographic Friedmann equations. Solving the holographic Friedmann equations, it is shown how the 4D decoupled matter and the cosmological constant control the dynamical properties of the SYM theory, quark confinement, chiral symmetry breaking, and baryon stability. From their effect on the SYM, the various kinds of matter are separated to two groups. Our results would give important information in studying the cosmological development of our universe.

Ghoroku, Kazuo; Nakamura, Akihiro

2013-03-01

193

Langevin agglomeration of nanoparticles interacting via a central potential.

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k? 15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (d(f)=2.25) , whereas at late times cluster-cluster agglomeration dominates (d(f)=1.56). Clusters are found to be compact (mean coordination number of ?5), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions. PMID:20866617

Isella, Lorenzo; Drossinos, Yannis

2010-07-01

194

Langevin agglomeration of nanoparticles interacting via a central potential

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial, rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension $d_f$ and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations, small ($k \\le 15$) and large ($k>15$) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism ($d_f = 2.25$), whereas at late times cluster-cluster agglomeration dominates ($d_f = 1.56$). Clusters are found to be compact (mean coordination number $\\sim 5$), tubular, and elongated. The local, compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as \\textit{ideal clusters} because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease of the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Lorenzo Isella; Yannis Drossinos

2010-04-26

195

Langevin agglomeration of nanoparticles interacting via a central potential

NASA Astrophysics Data System (ADS)

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k?15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (df=2.25) , whereas at late times cluster-cluster agglomeration dominates (df=1.56) . Clusters are found to be compact (mean coordination number of ˜5 ), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Isella, Lorenzo; Drossinos, Yannis

2010-07-01

196

The Basic Theory 2.1 Weierstrass Equations

with c, d = 0. Multiply both sides of the equation by c3 d2 to obtain (c2 dy)2 = (cdx)3 + (ac2 d)(cdx) + (bc3 d2 ). The change of variables y1 = c2 dy, x1 = cdx yields an equation in Weierstrass form. Later

197

The quantum probability equation: I. Bound state perturbation theory

The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are

Geoffrey C. Milward; Colin Wilkin

2000-01-01

198

Existence of algebraic matrix Riccati equations arising in transport theory

We consider the existence of positive solutions of a certain class of algebraic matrix Riccati equations with two parameters, c (0 ? c ? 1) and ? (0 ? ? ? 1). Here c denotes the fraction of scattering per collision, and ? is an angular shift. Equations of this class are induced via invariant imbedding and the shifted Gauss-Legendre

Jonq Juang

1995-01-01

199

Stellar convection theory. I - The anelastic modal equations

NASA Technical Reports Server (NTRS)

Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.

Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J.-P.

1976-01-01

200

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by\\u000aStudent's t-distribution and to use them in the Bayesian source separation\\u000amethod as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC)\\u000asampling scheme to unmix the astrophysical sources and describe the derivation\\u000adetails. In this scheme, we use the Langevin stochastic equation for\\u000atransitions, which enables

Koray Kayabol; Ercan E. Kuruoglu; José Luis Sanz; Bülent Sankur; Emanuele Salerno; Diego Herranz

2010-01-01

201

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.

Michael K. -H. Kiessling; Carlo Lancellotti

2004-01-13

202

Quantum theory of rotational isomerism and Hill equation

The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.

Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R. [I. Javakhishvili Tbilisi State University, 3, I. Chavchavadze Avenue, 0179 Tbilisi (Georgia); Chotorlishvili, L. [Institut fuer Physik, Martin-Luther Universitat Halle-Wittenberg, Heinrich-Damerow-Str. 4, 06120 Halle (Germany)

2012-06-15

203

Quantum theory of rotational isomerism and Hill equation

NASA Astrophysics Data System (ADS)

The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schrödinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schrödinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schrödinger equation spectrum the "right" points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schrödinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.

Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.

2012-06-01

204

On the Master-Equation Approach to Kinetic Theory: Linear and Nonlinear Fokker-Planck Equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's \\

Michael K.-H. Kiessling; Carlo Lancellotti

2004-01-01

205

Dynamic field theory and equations of motion in cosmology

NASA Astrophysics Data System (ADS)

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast ??/??1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits ??/??1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein’s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.

Kopeikin, Sergei M.; Petrov, Alexander N.

2014-11-01

206

Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann

The propagation of heavy quarks in the quark-gluon plasma (QGP) has been often treated within the framework of the Langevin equation (LV), i.e. assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_{HQ}/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra and consequently on nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but with a modified diffusion coefficient by about $\\sim 15-50\\%$ depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures $T\\gtrsim \\, 250\\,\\rm MeV$ the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultra-relativistic heavy-ion collisions. Finally, we have shown the possible impact of this study on $R_{AA}(p_T)$ and $v_2(p_T)$ for a realistic simulation of relativistic HIC. For larger $m_D$ the elliptic flow can be about $50\\%$ larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of $R_{AA}(p_T)$ and $v_2(p_T)$.

Santosh K. Das; Francesco Scardina; Salvatore Plumari; Vincenzo Greco

2013-12-24

207

Path and Path Deviation Equations in Kaluza-Klein Type Theories

Path and path deviation equations for charged, spinning and spinning charged objects in different versions of Kaluza-Klein (KK) theory using a modified Bazanski Lagrangian have been derived. The significance of motion in five dimensions, especially for a charged spinning object, has been examined. We have also extended the modified Bazanski approach to derive the path and path deviation equations of a test particle in a version of non-symmetric KK theory.

M. E. Kahil

2005-11-07

208

Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.

NASA Astrophysics Data System (ADS)

Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is discussed. We find no feasible expansion which has a fixed and small memory requirement, and is guaranteed to converge. We have found, however, that exploiting the time dependent picture of the ABC-DVR Green's function leads to a stable and efficient algorithm. The new method, which uses Newton interpolation polynomials to compute the time dependent wavefunction, gives a vastly improved version of the power series Green's function. We show that this approach is capable of obtaining converged reaction probabilities with very straightforward accuracy control. We use the ABC-DVR-Newton method to compute cross sections and rate constants for the initial state selected D + H_2(v = 1,j) to DH + H reaction. We obtain converged cross sections using no more than 4 Mbytes of core memory, and in as little CPU time as 10 minutes on a small workstation. With these cross sections, we calculate exact thermal rate constants for comparison with experiment. For the first time, quantitative agreement with experiment is obtained for the rotationally averaged rate constant k_{v=1}(T = 310 K) = 1.9 times 10^{-13} cm^3 sec^ {-1} molecule^{-1 }. The J-shifting approximation using accurate J = 0 reaction probabilities is tested against the exact results. It reliably predicts k_{v=1 }(T) for temperatures up to 700 K, but individual (v = 1, j)-selected rate constants are in error by as much as 41%.

Auerbach, Scott Michael

209

Birkhoff normal forms and KAM theory for Gumowski-Mira equation.

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2ax n)/(1+x n2)-xn-1, n=0,1,…, where x-1, x0?(-?,?), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions. PMID:24558333

Kulenovi?, M R S; Nurkanovi?, Z; Pilav, E

2014-01-01

210

Methods are proposed to obtain a specific form of scalar functions that belong to the tensor-nonlinear constitutive equations linking generalized stresses and finite strains in the theory of plasticity. Experimental data obtained earlier are used to assign a specific form to these functions and substantiate the applicability of the tensor-nonlinear constitutive equations to the description of the deformation of body

Yu. N. Shevchenko; N. N. Tormakhov; R. G. Terekhov

2000-01-01

211

Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

ERIC Educational Resources Information Center

The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the multidimensional item response theory (MIRT) framework. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure was…

Brossman, Bradley G.; Lee, Won-Chan

2013-01-01

212

A recent article by Langevin, Langevin, and Curnoe (2007) reported mixed results regarding the fraternal birth order effect, that is, the repeatedly observed finding that older brothers\\u000a correlate with homosexuality in later-born males. Using a fraternal birth order index computed as older brothers minus younger\\u000a brothers, Langevin et al. found that the “homoerotic” probands were born later among their brothers than

Ray Blanchard

2007-01-01

213

Effective equations and the inverse cascade theory for Kolmogorov flows

NASA Technical Reports Server (NTRS)

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.; Shu, Chi-Wang

1992-01-01

214

Stochastic regulator theory for a class of abstract wave equations

NASA Technical Reports Server (NTRS)

A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.

Balakrishnan, A. V.

1991-01-01

215

Eikonal equation of the Lorentz-violating Maxwell theory

NASA Astrophysics Data System (ADS)

We derive the eikonal equation of light wavefront in the presence of Lorentz invariance violation (LIV) from the photon sector of the standard model extension (SME). The results obtained from the equations of the E and B fields, respectively, are the same. This guarantees the self-consistency of our derivation. We adopt a simple case with only one non-zero LIV parameter as an illustration, from which we find two points. One is that, in analogy with the Hamilton-Jacobi equation, from the eikonal equation, we can derive dispersion relations which are compatible with results obtained from other approaches. The other is that the wavefront velocity is the same as the group velocity, as well as the energy flow velocity. If further we define the signal velocity v s as the front velocity, there always exists a mode with v s >1; hence causality is violated classically. Thus, our method might be useful in the analysis of Lorentz violation in QED in terms of classical causality.

Xiao, Zhi; Shao, Lijing; Ma, Bo-Qiang

2010-12-01

216

We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge's expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.

Dirk Puetzfeld; Yuri N. Obukhov

2013-01-18

217

X-ray parametric down-conversion in the Langevin regime.

We experimentally and theoretically study the coincidence count rate for down-converted x-ray photons. Because of photoionization, parametric down-conversion at x-ray wavelengths generally involves loss and the theoretical description requires a Langevin approach. By working in a transmission geometry (Laue) rather than in the Bragg geometry of previous experiments, we obtain an improvement in the signal-to-noise ratio of 12.5, and find agreement between experiment and theory. PMID:23031104

Shwartz, S; Coffee, R N; Feldkamp, J M; Feng, Y; Hastings, J B; Yin, G Y; Harris, S E

2012-07-01

218

X-Ray Parametric Down-Conversion in the Langevin Regime

NASA Astrophysics Data System (ADS)

We experimentally and theoretically study the coincidence count rate for down-converted x-ray photons. Because of photoionization, parametric down-conversion at x-ray wavelengths generally involves loss and the theoretical description requires a Langevin approach. By working in a transmission geometry (Laue) rather than in the Bragg geometry of previous experiments, we obtain an improvement in the signal-to-noise ratio of 12.5, and find agreement between experiment and theory.

Shwartz, S.; Coffee, R. N.; Feldkamp, J. M.; Feng, Y.; Hastings, J. B.; Yin, G. Y.; Harris, S. E.

2012-07-01

219

Newton-Schrödinger Equations are not derivable from General Relativity + Quantum Field Theory

In this note we show that Newton-Schr\\"odinger Equations (NSEs) [arXiv:1210.0457 and references therein] do not follow from general relativity (GR) and quantum field theory (QFT) by way of two considerations: 1) Taking the nonrelativistic limit of the semiclassical Einstein equation, the central equation of relativistic semiclassical gravity, a fully covariant theory based on GR+QFT with self-consistent backreaction of quantum matter on the spacetime dynamics; 2) Working out a model [see C. Anastopoulos and B. L. Hu, Class. Quant. Grav. 30, 165007 (2013), arXiv:1305.5231] with a matter scalar field interacting with weak gravity, in procedures analogous to the derivation of the nonrelativistic limit of quantum electrodynamics. We conclude that the coupling of classical gravity with quantum matter can only be via mean fields, there are no $N$-particle NSEs and theories based on Newton-Schr\\"odinger equations assume unknown physics.

C. Anastopoulos; B. L. Hu

2014-02-16

220

We derive multipolar equations of motion for gravitational theories with general nonminimal coupling in spacetimes admitting torsion. Our very general findings allow for the systematic testing of whole classes of theories by means of extended test bodies. One peculiar feature of certain subclasses of nonminimal theories turns out to be their sensitivity to post-Riemannian spacetime structures even in experiments without microstructured test matter.

Dirk Puetzfeld; Yuri N. Obukhov

2013-08-15

221

The quantum probability equation: I. Bound state perturbation theory

NASA Astrophysics Data System (ADS)

The partial-wave Schrödinger equation with real boundary conditions is recast as an equation for the probability density. When a small additional potential is included, the changes in the bound-state energy eigenvalues are obtained, up to third order in the perturbation, purely in terms of the perturbing potential and the unperturbed probability density. Although the approach is different, our results are equivalent to those derived by Bender (Bender C M 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p 330). Knowledge of neither the unperturbed energy spectrum nor the wavefunctions of excited states is required. Evaluations of the second-order energy shift are given for some soluble S-wave problems.

Milward, Geoffrey C.; Wilkin, Colin

2000-10-01

222

Pure gauge configurations and solutions to fermionic superstring field theory equations of motion

NASA Astrophysics Data System (ADS)

Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of nonpolynomial and cubic string field theory are discussed. To have the possibility of dealing with both GSO(+) and GSO(-) sectors in the uniform way, a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open-string field theories truncated pure gauge configurations parametrized by wedge states play an essential role. The matrix form of this parametrization for NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equations of motion on the subspace of the wedge states. The perturbation expansion is corrected by adding extra terms that are just those necessary for the equation of motion contracted with the solution itself to be satisfied.

Aref'eva, I. Ya; Gorbachev, R. V.; Medvedev, P. B.

2009-07-01

223

First-Order Equations of Motion for Heterotic String Field Theory

We consider the equations of motion of the full heterotic string field theory including both the Neveu-Schwarz and the Ramond sectors. It is shown that they can be formulated in the form of an infinite number of first-order equations for an infinite number of independent string fields. We prove that the conventional equations of motion are obtaned by solving the extra equations for the extra string fields with a certain assumptions at the linearized level. The conventional gauge transformations are also obtained from those in this first-order formulation, which is clarified by deriving some lower oder transformations explicitly.

Hiroshi Kunitomo

2014-07-03

224

Closed equations of the two-point functions for tensorial group field theory

NASA Astrophysics Data System (ADS)

In this paper, we provide the closed equations that satisfy two-point correlation functions of rank 3 and 4 tensorial group field theory. The formulation of the current problem extends the method used by Grosse and Wulkenhaar (2009 arXiv:0909.1389) to the tensor case. Ward-Takahashi identities and Schwinger-Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the three-dimensional case, the solution of this equation is given perturbatively at the second order of the coupling constant.

Ousmane Samary, Dine

2014-09-01

225

Modified equations in the theory of induced gravity. Solution to the cosmological constant problem

NASA Astrophysics Data System (ADS)

This research is an extension of the author's works, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of gravity and string theory. This work is devoted to the formation of self-consistent equations of the theory of induced gravity in the presence of matter in the form of a perfect fluid that interacts with scalar fields. The study is done to solve these equations for the case of the cosmological model. In this model time-evolving gravitational and cosmological "constants" take place which are determined by the square of scalar fields. The values of which can be matched with the observational data. The equations that describe the theory have solutions that can both match with the solutions of the standard theory of gravity as well as it can differ from it. This is due to the fact that the fundamental "constants" of the theory, such as gravitational and cosmological, can evolve over time and also depend of the coordinates. Thus, in a rather general case the theory describes the two systems (stages): Einstein and "evolving". This process is similar to the phenomenon of phase transition, where the different phases (Einstein gravity system, but with different constants) transit into each other.

Zaripov, Farkhat

2014-07-01

226

Theory of differential equations in discontinuous piecewise-defined functions

A truly general and systematic theory of finite element methods (FEM) should be formulated using, as trial and test functions, piecewise-defined functions that can be fully discontinuous across the internal boundary, which separates the elements from each other. Some of the most relevant work addressing such formu- lations is contained in the literature on discontinuous Galerkin (dG) methods and on

I. Herrera

2007-01-01

227

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts. PMID:24555448

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

228

Monitoring superparamagnetic Langevin behavior of individual SrRuO3 nanostructures

NASA Astrophysics Data System (ADS)

Patterned nanostructures on the order of 200 nm × 200 nm of the itinerant ferromagnet SrRuO3 give rise to superparamagnetic behavior below the Curie temperature (˜150K) down to a sample-dependent blocking temperature. We monitor the superparamagnetic fluctuations of an individual volume and demonstrate that the field dependence of the time-averaged magnetization is well described by the Langevin equation. On the other hand, the rate of the fluctuations suggests that the volume in which the magnetization fluctuates is smaller by more than an order of magnitude. We suggest that switching via nucleation followed by propagation gives rise to Langevin behavior of the total volume, whereas the switching rate is determined by a much smaller nucleation volume.

Sinwani, Omer; Reiner, James W.; Klein, Lior

2014-01-01

229

Irreversible Langevin samplers and variance reduction: a large deviation approach

In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e., they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose do not see their variances reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.

Luc Rey-Bellet; Kostantinos Spiliopoulos

2014-04-01

230

Exact series model of Langevin transducers with internal losses.

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%. PMID:24606259

Nishamol, P A; Ebenezer, D D

2014-03-01

231

Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory

NASA Astrophysics Data System (ADS)

Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.

Nakamura, K.

2009-06-01

232

On the Supersymmetric Dirac Equation and the Heterotic Superstring Theory

NASA Astrophysics Data System (ADS)

The supersymmetry transformations under which the four-dimensional massless Dirac equation for a two-component, spin-1/2 fermion field ? (the Weyl equation) remains invariant were obtained by Volkov and Akulov, who used the result to construct the action S = a-1 ? |W| d4x in terms of the energy-momentum tensor Tij = (1)/(2) i ? + ? (i{<->? }{}j)? , where Wij = ?ij + aTij and a is a constant. Here, we show, in the approximation Tij ? (Rij - (1)/(2) gij R)/? 2, that the terms linear, quadratic and quartic in Tij are contained in the bosonic sector of the dimensionally reduced, heterotic superstring action, including higher-derivative gravitational terms up to order R4. By comparison of coefficients, we derive the value Br 3.5 for the radius squared of the internal space in units of the Regge slope parameter ?', slightly greater than the Hagedorn radius squared B{( H)} r = 2.914. The cubic terms are also discussed.

Pollock, M. D.

233

The Langevin equation from Markovian Quantum Central Limits

This paper has been withdrawn by the author. The central result is now included in quant-ph/0309056 (as in the journal publication!). An erratum on the Heisenberg perturbation series estimate is also included therein.

John Gough

2003-12-05

234

NASA Astrophysics Data System (ADS)

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Wills, John M.; Mattsson, Ann E.

2012-02-01

235

Equilibrium dynamics of the Dean-Kawasaki equation: Mode-coupling theory and its extension

NASA Astrophysics Data System (ADS)

We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004, 10.1088/1742-5468/2008/02/P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-coupling approach.

Kim, Bongsoo; Kawasaki, Kyozi; Jacquin, Hugo; van Wijland, Frédéric

2014-01-01

236

CKN theory of singularities of weak solutions of the Navier-Stokes equations

The lectures are devoted to a complete exposition of the theory of singularities of the Navier Stokes equations solution studied by Leray, in a simple geometrical setting in which the fluid is enclosed in a container $\\O$ with periodic boundary conditions and side size $L$. The theory is due to the work of Scheffer, Caffarelli, Kohn, Nirenberg and is called here CKN-theory as it is inspired by the work of the last three authors which considerably improved the earlier estimates of Scheffer.

Giovanni Gallavotti

2005-03-16

237

Theory of Partial Differential Equations (155010) Exercises WC #8 (Week 03) 2012.01.20

the mean value property for harmonic functions in a bounded domain D R2, u(x) = 1 2R B(x,R) u(y) ds in that domain. (b) Use, instead, the representation theorem for (twice continuously differentiable) functionsTheory of Partial Differential Equations (155010) Exercises WC #8 (Week 03) 2012.01.20 01

Al Hanbali, Ahmad

238

Path Integral and Solutions of the Constraint Equations: The Case of Reducible Gauge Theories

It is shown that the BRST path integral for reducible gauge theories, with appropriate boundary conditions on the ghosts, is a solution of the constraint equations. This is done by relating the BRST path integral to the kernel of the evolution operator projected on the physical subspace.

R. Ferraro; M. Henneaux; M. Puchin

1994-05-25

239

The Boltzmann Equation in the Theory of Electrical Conduction in Metals

The motion of conduction electrons in a metal in an electric field, scattered by an irregular static potential, is considered; this model is applicable to the resistance due to lattice waves at high temperatures, and to imperfections at any temperature. In §2 the Boltzmann equation is re-derived without the customary perturbation theory, avoiding the usual necessity of averaging over phases

D A Greenwood

1958-01-01

240

DGLAP and BFKL equations in the N=4 supersymmetric gauge theory

We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions ? of

A. V. Kotikov; L. N. Lipatov

2003-01-01

241

Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge

A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.

Reinhardt, Hugo; Leder, Markus [Universitaet Tuebingen, Institut fuer Theoretische Physik, Auf der Morgenstelle 14, 72076 Tuebingen (Germany); Pawlowski, Jan M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg, Germany and ExtreMe Matter Institute EMMI, GSI, Planckstr. 1, 64291 Darmstadt (Germany); Weber, Axel [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Ciudad Universitaria, 58040 Morelia, Michoacan (Mexico)

2011-05-23

242

A Brief Introduction to Structural Equation Modeling Techniques: Theory and Application.

ERIC Educational Resources Information Center

This paper provides theoretical and practical information about using structural equation modeling (SEM) techniques. The first section discusses the theory of SEM, including five general steps: (1) model specification; (2) model identification; (3) model estimation; (4) testing model fit; and (5) model respecification. The second section applies…

Baloglu, Mustafa

243

A unified theory of zero power and power reactor noise via backward master equations

, *, Z.F. Kuang a,b , A.K. Prinja c a Department of Reactor Physics, Chalmers University of Technology neutronic fluctuations in a steady medium, and power reactor noise are treated as two separate phenomenaA unified theory of zero power and power reactor noise via backward master equations I. PaÂ´ zsit a

PÃ¡zsit, Imre

244

The Existential Theory of Equations with Rational Constraints in Free Groups is PSPACE-Complete

It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present an algorithm that works in poly- nomial space, even in the more general setting where each

Volker Diekert; Claudio Gutierrez; Christian Hagenah

2001-01-01

245

The general class of the vacuum spherically symmetric equations of the general relativity theory

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.

Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N., E-mail: Markov_Victor@mail.ru; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R. [Murmansk State Pedagogical University (Russian Federation)

2012-08-15

246

NASA Astrophysics Data System (ADS)

CONTENTSIntroduction § 1. The finite-dimensional case § 2. Stochastic semigroups in the L2-strong theory § 3. Homogeneous strongly continuous semigroups with the group of the first moments § 4. Stochastic equations of diffusion type with constant coefficients § 5. Continuous homogeneous stochastic semigroups in the presence of two moments References

Skorokhod, A. V.

1982-12-01

247

NASA Astrophysics Data System (ADS)

Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.

Nakamura, K.

2007-01-01

248

Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation

We present a simple method to derive the semiclassical equations of motion for a spinning particle in a gravitational field. We investigate the cases of classical, rotating particles (pole-dipole particles), as well as particles with intrinsic spin. We show that, starting with a simple Lagrangian, one can derive equations for the spin evolution and momentum propagation in the framework of metric theories of gravity and in theories based on a Riemann-Cartan geometry (Poincare gauge theory), without explicitly referring to matter current densities (spin and energy-momentum). Our results agree with those derived from the multipole expansion of the current densities by the conventional Papapetrou method and from the WKB analysis for elementary particles.

M. Leclerc

2005-05-04

249

Propagation equations for deformable test bodies with microstructure in extended theories of gravity

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.

Dirk Puetzfeld; Yuri N. Obukhov

2007-07-18

250

Renormalization group equations in resonance chiral theory: the pi pi vector form-factor

The use of the equations of motion and meson field redefinitions allows the simplification of the subleading operators required in the one-loop resonance chiral theory calculation of the pi pi vector form-factor. The study of the renormalization group equations of the relevant parameters shows the existence of an infrared fixed point for all the couplings. It is important to remark that this result does not rely on the high-energy form-factor constraints, which are often considered in other works. The possibility of developing a perturbative 1/Nc expansion in the slow running region around the fixed point is shown here.

J. J. Sanz-Cillero

2009-10-14

251

Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.

F. Haas; J. Zamanian; M. Marklund; G. Brodin

2009-12-23

252

(1,0) superconformal theories in six dimensions and Killing spinor equations

NASA Astrophysics Data System (ADS)

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the isotropy group of the Killing spinors. We focus on the models proposed by Samtleben et al in [11, 12] and find that there are solutions preserving 1,2, 4 and 8 supersymmetries. We also explore the solutions which preserve 4 supersymmetries and find that many models admit string and 3-brane solitons as expected from the M-brane intersection rules. The string solitons are smooth regulated by the moduli of instanton configurations.

Akyol, M.; Papadopoulos, G.

2012-07-01

253

Number-conserving master equation theory for a dilute Bose-Einstein condensate

We describe the transition of N weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and noncondensate thermalization, we derive a master equation for the condensate subsystem in the presence of the noncondensate environment under the inclusion of all two-body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of N noninteracting atoms.

Schelle, Alexej [Physikalisches Institut der Albert-Ludwigs Universitaet Freiburg, Hermann-Herder Str. 3, D-79104 Freiburg (Germany); Laboratoire Kastler-Brossel, Universite Pierre et Marie Curie-Paris 6, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France); Wellens, Thomas; Buchleitner, Andreas [Physikalisches Institut der Albert-Ludwigs Universitaet Freiburg, Hermann-Herder Str. 3, D-79104 Freiburg (Germany); Delande, Dominique [Laboratoire Kastler-Brossel, Universite Pierre et Marie Curie-Paris 6, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France)

2011-01-15

254

Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation

NASA Astrophysics Data System (ADS)

We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games.

Toledo, Porfirio

2013-12-01

255

We have developed robust and efficient numerical methods for solving integral equation theories for electrolyte solutions. These methods are hybrids of Newton-Raphson and Picard iterations and have been obtained as extended versions of the previous methods for pure solvents by solving nontrivial problems posed by the inclusion of ions. Bulk electrolytes and electrolytes near both inert and metallic surfaces are considered. The basic equations previously derived for a one-component fluid near a planar wall are extended to a multicomponent fluid. Analytical expressions for elements of the Jacobian matrices are arranged in compact form. A striking feature of the method for surface problems is that the Jacobian is determined only from bulk properties. A discussion of some special treatments that need to be considered for asymmetric anions and cations is included. These methods have been demonstrated using the full reference hypernetted-chain theory for various sizes of ions in a wide range of ionic concentrations. 19 refs., 3 tabs.

Kinoshita, M.; Berard, D.R. [Univ. of British Columbia, Vancouver (Canada)] [Univ. of British Columbia, Vancouver (Canada)

1996-03-01

256

NASA Astrophysics Data System (ADS)

Self-consistent theory of Anderson localization of two-dimensional non-interacting electrons is formulated in the context of the exact transport equation and conductivity expression derived by the present authors (YI). The irreducible scattering vertex by Vollhardt and Wölfle (VW) is used in this equation, determining the diffusion coefficient in the scattering vertex self-consistently, through Einstein relation. It predicts a similar localization length to that obtained by VW, but shows that the conductivity evaluated by the Kubo formula decays exponentially, as the system size approaches the localization length. The result is opposed to the prediction by VW, who showed different behaviour of the diffusion coefficient that is equivalent to our conductivity. Our calculation also implies that the localization may be described along with the Landau-Silin theory of Fermi liquid.

Yamane, Y.; Itoh, M.

2012-10-01

257

NASA Astrophysics Data System (ADS)

We develop a theory describing the operation of an opto-mechanical oscillator as a phonon laser using a set of coupled equations that is analogous to the standard set of laser rate equations. We show that laser-like parameters that characterize gain, stored energy, threshold, efficiency, oscillation frequency linewidth, and saturation power can be introduced for an opto-mechanical oscillator driven by photo-thermal or radiation pressure forces. We then apply the theoretical model to the experimental results for photo-thermally driven oscillations in a Si waveguide opto-mechanical resonator and show good agreement between the theory and experiments. We also consider the microscopic mechanism that transforms the energy of incoherent thermal phonons into coherent oscillations of a single phonon mode and show remarkable parallels with the three-wave parametric interactions in optics and also with opto-electronic oscillators used in microwave photonics.

Khurgin, J. B.; Pruessner, M. W.; Stievater, T. H.; Rabinovich, W. S.

2012-10-01

258

National Technical Information Service (NTIS)

A perturbative method for solving the systems of coupled differential equations arising from the Schrodinger equation is developed. First, general rules to evaluate the perturbative corrections for the propagators are given. Some simple differential equat...

G. L. Ixaru

1978-01-01

259

Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation

NASA Astrophysics Data System (ADS)

Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.

Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng

2014-05-01

260

Improved Inverse Gap Equation and Quasiparticle Theories of Odd and Even Tin Isotopes

The nuclear-structure properties of the odd and even tin isotopes are studied, making use of an improved inverse-gap-equation (IGE) method and the quasiparticle theories. The two-body nuclear force assumed is a realistic potential (or reaction matrix) renormalized for the core polarization, and two cases are considered: (a) the potential of Tabakin, and (b) the reaction matrix of Yale-Shakin. While most

R. Alzetta; T. Weber; Y. K. Gambhir; M. Gmitro; J. Sawicki; A. Rimini

1969-01-01

261

Closed String Field Theory: Quantum Action and the BV Master Equation

The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra $L_\\\\infty$, and the higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation.

Barton Zwiebach

1992-01-01

262

The theory of surface tension components and the equation of state approach

There are at present two main approaches to the calculation of solid surface tensions from contact angles: the theory of surface\\u000a tension components and the equation of state approach. These are compared on the basis of their abilities to predict both\\u000a the outcome of a specially designed contact-angle experiment and the engulfing behavior of microscopic particles at advancing\\u000a solidification fronts.

J. K. Spelt; A. W. Neumann

263

NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

We study next-to-leading corrections to the integral kernel of the BFKL equation for high-energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension ? of the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY,

A. V. Kotikov; L. N. Lipatov

2000-01-01

264

Linear response theory for hydrodynamic and kinetic equations with long-range interactions

NASA Astrophysics Data System (ADS)

We apply the linear response theory to systems with long-range interactions described by hydrodynamic equations such as the Euler, Smoluchowski, and damped Euler equations. We analytically determine the response of the system submitted to a pulse or to a step function. We compare these results with those obtained for collisionless systems described by the Vlasov equation. We show that, in the linear regime, the evolution of a collisionless system (Vlasov) with the waterbag distribution is the same as the evolution of a collision-dominated gas without dissipation (Euler). In this analogy, the maximum velocity of the waterbag distribution plays the role of the velocity of sound in the corresponding barotropic gas. When submitted to a step function, these systems exhibit permanent oscillations. Other distributions exhibit Landau damping and relax towards a steady state. We illustrate this behaviour with the Cauchy distribution which can be studied analytically. We apply our results to the HMF model and obtain a generalized Curie-Weiss law for the magnetic susceptibility. Finally, we compare the linear response theory to the initial value problem for the linearized Vlasov equation and report a case of algebraic damping of the initial perturbation.

Chavanis, Pierre-Henri

2013-04-01

265

Orientation-dependent integral equation theory for a two-dimensional model of water

NASA Astrophysics Data System (ADS)

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein-Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water's density maximum with temperature or the negative thermal expansion coefficient.

Urbi?, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

2003-03-01

266

The solids-flux theory--confirmation and extension by using partial differential equations.

The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts. PMID:18926553

Diehl, Stefan

2008-12-01

267

Prescission neutron multiplicity and fission probability from Langevin dynamics of nuclear fission

A theoretical model of one-body nuclear friction which was developed earlier, namely the chaos-weighted wall formula, is applied to a dynamical description of compound nuclear decay in the framework of the Langevin equation coupled with statistical evaporation of light particles and photons. We have used both the usual wall formula friction and its chaos-weighted version in the Langevin equation to calculate the fission probability and prescission neutron multiplicity for the compound nuclei $^{178}$W, $^{188}$Pt, $^{200}$Pb, $^{213}$Fr, $^{224}$Th, and $^{251}$Es. We have also obtained the contributions of the presaddle and postsaddle neutrons to the total prescission multiplicity. A detailed analysis of our results leads us to conclude that the chaos-weighted wall formula friction can adequately describe the fission dynamics in the presaddle region. This friction, however, turns out to be too weak to describe the postsaddle dynamics properly. This points to the need for a suitable explanation for the enhanced neutron emission in the postsaddle stage of nuclear fission.

Gargi Chaudhuri; Santanu Pal

2001-05-04

268

Stochastic differential equations and turbulent dispersion

NASA Technical Reports Server (NTRS)

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.

Durbin, P. A.

1983-01-01

269

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

270

Stochastic quantization of real-time thermal field theory

NASA Astrophysics Data System (ADS)

We use the stochastic quantization method to obtain the free scalar propagator of a finite temperature field theory formulated in the Minkowski space-time. First, we use the Markovian stochastic quantization approach to present the two-point function of the theory. Second, we assume a Langevin equation with a memory kernel and a colored noise. The convergence of the Markovian and non-Markovian stochastic processes in the asymptotic limit of the fictitious time is obtained. Our formalism can be the starting point to discuss systems at finite temperature out of equilibrium.

de Aguiar, T. C.; Svaiter, N. F.; Menezes, G.

2010-10-01

271

Fission rate in multi-dimensional Langevin calculations

Experimental data on nuclear dissipation have often been interpreted using one-dimensional model calculations of the Langevin or Fokker-Planck type. In the present work, the influence of the dimensionality of the deformation space on the time dependence of the fission process has been investigated in a systematic and quantitative way. In particular, the dependence of the transient time and the stationary value of the fission rate on the number of collective coordinates involved in Langevin calculations is investigated for the one-body and two-body dissipation mechanisms. We show that the results of Langevin-type calculations change appreciably if the deformation space is extended up to three dimensions.

Nadtochy, P. N.; Kelic, A.; Schmidt, K.-H. [GSI, Plankstr. 1, D-64291 Darmstadt (Germany)

2007-06-15

272

Continuum regularization of gauge theory with fermions

The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism.

Chan, H.S.

1987-03-01

273

Gravitational Field Equations and Theory of Dark Matter and Dark Energy

The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential $\\varphi$ are derived using the Einstein-Hilbert functional, and the scalar potential $\\varphi$ is a natural outcome of the divergence-free constraint of the variational elements. Gravitation is now described by the Riemannian metric $g_{ij}$, the scalar potential $\\varphi$ and their interactions, unified by the new gravitational field equations. Associated with the scalar potential $\\varphi$ is the scalar potential energy density $\\frac{c^4}{8\\pi G} \\Phi=\\frac{c^4}{8\\pi G} g^{ij}D_iD_j \\varphi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe. The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: $\\int_M \\Phi dM=0$. The sum of this new potential energy density $\\frac{c^4}{8\\pi G} \\Phi$ and the coupling energy between the energy-momentum tensor $T_{ij}$ and the scalar potential field $\\varphi$ gives rise to a new unified theory for dark matter and dark energy: The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies. In addition, the scalar curvature of space-time obeys $R=\\frac{8\\pi G}{c^4} T + \\Phi$. Furthermore, the new field equations resolve a few difficulties encountered by the classical Einstein field equations.

Tian Ma; Shouhong Wang

2012-06-22

274

An oscillating Langevin antenna for driving plasma turbulence simulations

NASA Astrophysics Data System (ADS)

A unique method of driving Alfvénic turbulence via an oscillating Langevin antenna is presented. This method of driving is motivated by a desire to inject energy into a finite domain numerical simulation in a manner that models the nonlinear transfer of energy from fluctuations in the turbulent cascade at scales larger than the simulation domain. The oscillating Langevin antenna is shown to capture the essential features of the larger scale turbulence and efficiently couple to the plasma, generating steady-state turbulence within one characteristic turnaround time. The antenna is also sufficiently flexible to explore both strong and weak regimes of Alfvénic plasma turbulence.

TenBarge, J. M.; Howes, G. G.; Dorland, W.; Hammett, G. W.

2014-02-01

275

PyR@TE. Renormalization group equations for general gauge theories

NASA Astrophysics Data System (ADS)

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

276

Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory

NASA Astrophysics Data System (ADS)

We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.

Manuel, Cristina; Torres-Rincon, Juan M.

2014-10-01

277

Field theory and weak Euler-Lagrange equation for classical particle-field systems

NASA Astrophysics Data System (ADS)

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.

Qin, Hong; Burby, Joshua W.; Davidson, Ronald C.

2014-10-01

278

Heavy-flavor in-medium momentum evolution: Langevin versus Boltzmann approach

NASA Astrophysics Data System (ADS)

The propagation of heavy quarks in the quark-gluon plasma was often treated within the framework of the Langevin equation (LV), i.e., assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass mD. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked (mD?T) or the mass to temperature ratio is quite large (MHQ/T? 8-10) there are significant differences in the evolution of the p spectra and consequently on the nuclear modification factor RAA(pT). However, for charm quark we find that very similar RAA(pT) between the LV and BM can be obtained, but with a modified diffusion coefficient of about ˜15%-50% depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by the single heavy quarks we see that at temperatures T ?250MeV the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultrarelativistic heavy-ion collisions (HICs). Finally, we have shown the possible impact of this study on RAA(pT) and v2(pT) for a realistic simulation of relativistic HICs. For larger mD the elliptic flow can be about 50% larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of RAA(pT) and v2(pT).

Das, Santosh K.; Scardina, Francesco; Plumari, Salvatore; Greco, Vincenzo

2014-10-01

279

Exceptional thermodynamics: The equation of state of G(2) gauge theory

We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G(2) gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytica...

Bruno, Mattia; Panero, Marco; Pellegrini, Roberto

2014-01-01

280

Cosmology in generalized Horndeski theories with second-order equations of motion

NASA Astrophysics Data System (ADS)

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background. In addition to a dark energy field ? associated with the gravitational sector, we take into account multiple scalar fields ?I (I =1,2,…,N-1) characterized by the Lagrangians P(I)(XI) with XI=???I???I. These additional scalar fields can model the perfect fluids of radiation and nonrelativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce nontrivial modifications to all the propagation speeds of N scalar fields, but the modifications to those for the matter fields ?I are generally suppressed relative to that for the dark energy field ?. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square cs12 associated with the field ? becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

Kase, Ryotaro; Tsujikawa, Shinji

2014-08-01

281

Equation of state of a relativistic theory from a moving frame

We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to compute the expectation value of the off-diagonal components T_{0k} of the energy-momentum tensor in presence of shifted boundary conditions. The entropy is thus easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9 T_c - 20 T_c. At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a byproduct we also determine the ultraviolet finite renormalization constant of T_{0k} by imposing suitable Ward identities. These findings establish this strategy as a solid, simple and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.

Leonardo Giusti; Michele Pepe

2014-03-03

282

Cosmology in generalized Horndeski theories with second-order equations of motion

We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\\chi$ associated with the gravitational sector, we take into account multiple scalar fields $\\phi_I$ ($I=1,2\\cdots,N-1$) characterized by the Lagrangians $P^{(I)}(X_I)$ with $X_I=\\partial_{\\mu}\\phi_I\\partial^{\\mu}\\phi_I$. These additional scalar fields can model the perfect fluids of radiation and non-relativistic matter. We derive propagation speeds of scalar and tensor perturbations as well as conditions for the absence of ghosts. The theories beyond Horndeski induce non-trivial modifications to all the propagation speeds of $N$ scalar fields, but the modifications to those for the matter fields $\\phi_I$ are generally suppressed relative to that for the dark energy field $\\chi$. We apply our results to the covariantized Galileon with an Einstein-Hilbert term in which partial derivatives of the Minkowski Galileon are replaced by covariant derivatives. Unlike the covariant Galileon with second-order equations of motion in general space-time, the scalar propagation speed square $c_{s1}^2$ associated with the field $\\chi$ becomes negative during the matter era for late-time tracking solutions, so the two Galileon theories can be clearly distinguished at the level of linear cosmological perturbations.

Ryotaro Kase; Shinji Tsujikawa

2014-07-03

283

Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

NASA Astrophysics Data System (ADS)

The dual fluid description for a general cutoff surface at radius r=rc outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ?, the coupled Einstein-Maxwell equations are solved up to O(?2). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density ?/s is independent of both the cutoff rc and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio ?/s is independent of the cutoff rc but dependent on the charge density of the black brane.

Niu, Chao; Tian, Yu; Wu, Xiao-Ning; Ling, Yi

2012-05-01

284

Pure gauge configurations and tachyon solutions to string field theories equations of motion

NASA Astrophysics Data System (ADS)

In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.

Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.

2009-05-01

285

(1,0) superconformal theories in six dimensions and Killing spinor equations

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the isotropy group of the Killing spinors. We focus on the models proposed by Samtleben et al in \\cite{ssw} and find that there are solutions preserving 1,2, 4 and 8 supersymmetries. We also explore the solutions which preserve 4 supersymmetries and find that many models admit string and 3-brane solitons as expected from the M-brane intersection rules. The string solitons are smooth regulated by the moduli of instanton configurations.

Akyol, Mehmet

2012-01-01

286

(1,0) superconformal theories in six dimensions and Killing spinor equations

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories in all cases. In particular, we derive the conditions on the fields imposed by the Killing spinor equations and demonstrate that these depend on the isotropy group of the Killing spinors. We focus on the models proposed by Samtleben et al in \\cite{ssw} and find that there are solutions preserving 1,2, 4 and 8 supersymmetries. We also explore the solutions which preserve 4 supersymmetries and find that many models admit string and 3-brane solitons as expected from the M-brane intersection rules. The string solitons are smooth regulated by the moduli of instanton configurations.

Mehmet Akyol; George Papadopoulos

2012-04-10

287

This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)] by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.

Yang Lei; Devi, Murali; Jang, Seogjoo [Department of Chemistry and Biochemistry, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367 (United States)

2012-07-14

288

A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has

Allan D. Pierce

2008-01-01

289

Extensions of multireference equation of motion coupled cluster theory (MR-EOMCC) [D. Datta and M. Nooijen, J. Chem. Phys. 137, 204107 (2012)] are presented that include additional correlation effects into the global, internally contracted similarity transformation, induced by the cluster operators. As a result the final uncontracted diagonalization space can be more compact than in the parent MR-EOMCC approach. A wide range of applications, including transition metal atomic excitation spectra, a large set of valence excited states of organic compounds, and potential energy surfaces of ground and excited states of butadiene, is presented to benchmark the applicability of the parent MR-EOMCC methodology and its new variations. PMID:23574209

Demel, Ond?ej; Datta, Dipayan; Nooijen, Marcel

2013-04-01

290

Communication: An exact bound on the bridge function in integral equation theories

NASA Astrophysics Data System (ADS)

We show that the formal solution of the general closure relation occurring in Ornstein-Zernike-type integral equation theories in terms of the Lambert W function leads to an exact relation between the bridge function and correlation functions, most notably to an inequality that bounds possible bridge values. The analytical results are illustrated on the example of the Lennard-Jones fluid for which the exact bridge function is known from computer simulations under various conditions. The inequality has consequences for the development of bridge function models and rationalizes numerical convergence issues.

Kast, Stefan M.; Tomazic, Daniel

2012-11-01

291

Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.

Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu [Department of Physics, Swansea University, Swansea (United Kingdom); Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Muenchen (Germany); Institut fuer Theoretische Physik, Universitaet Heidelberg and FEST, Heidelberg (Germany)

2010-03-01

292

Equation of state of hot and dense QCD: resummed perturbation theory confronts lattice data

NASA Astrophysics Data System (ADS)

We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak coupling expression for the pressure, motivated by dimensional reduction. Finally, we compare the exact one-loop HTLpt and resummed dimensional reduction results with state-of-the-art lattice calculations and a recent mass-expanded three-loop HTLpt calculation.

Mogliacci, Sylvain; Andersen, Jens O.; Strickland, Michael; Su, Nan; Vuorinen, Aleksi

2013-12-01

293

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this...

Lathiotakis, Nektarios N; Rubio, Angel; Gidopoulos, Nikitas I

2014-01-01

294

Continuum regularization of quantum field theory

Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.

Bern, Z.

1986-04-01

295

Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model

We show that the chiral partition function of two-dimensional Yang-Mills theory on the sphere can be mapped to the partition function of the homogeneous six-vertex model with domain wall boundary conditions in the ferroelectric phase. A discrete matrix model description in both cases is given by the Meixner ensemble, leading to a representation in terms of a stochastic growth model. We show that the partition function is a particular case of the z-measure on the set of Young diagrams, yielding a unitary matrix model for chiral Yang-Mills theory on the sphere and the identification of the partition function as a tau-function of the Painleve V equation. We describe the role played by generalized non-chiral Yang-Mills theory on the sphere in relating the Meixner matrix model to the Toda chain hierarchy encompassing the integrability of the six-vertex model. We also argue that the thermodynamic behaviour of the six-vertex model in the disordered and antiferroelectric phases are captured by particular q-deformations of two-dimensional Yang-Mills theory on the sphere.

Richard J. Szabo; Miguel Tierz

2011-02-17

296

Modelling platelet-blood flow interaction using the subcellular element Langevin method

In this paper, a new three-dimensional modelling approach is described for studying fluid–viscoelastic cell interaction, the subcellular element Langevin (SCEL) method, with cells modelled by subcellular elements (SCEs) and SCE cells coupled with fluid flow and substrate models by using the Langevin equation. It is demonstrated that: (i) the new method is computationally efficient, scaling as 𝒪(N) for N SCEs; (ii) cell geometry, stiffness and adhesivity can be modelled by directly relating parameters to experimentally measured values; (iii) modelling the fluid–platelet interface as a surface leads to a very good correlation with experimentally observed platelet flow interactions. Using this method, the three-dimensional motion of a viscoelastic platelet in a shear blood flow was simulated and compared with experiments on tracking platelets in a blood chamber. It is shown that the complex platelet-flipping dynamics under linear shear flows can be accurately recovered with the SCEL model when compared with the experiments. All experimental details and electronic supplementary material are archived at http://biomath.math.nd.edu/scelsupplementaryinformation/. PMID:21593027

Sweet, Christopher R.; Chatterjee, Santanu; Xu, Zhiliang; Bisordi, Katharine; Rosen, Elliot D.; Alber, Mark

2011-01-01

297

Applications of Path Integral Langevin Dynamics to Weakly Bound Clusters and Biological Molecules

NASA Astrophysics Data System (ADS)

We present the use of path integral molecular dynamics (PIMD) in conjunction with the path integral Langevin equation thermostat for sampling systems that exhibit nuclear quantum effects, notably those at low temperatures or those consisting mainly of hydrogen or helium. To test this approach, the internal energy of doped helium clusters are compared with white-noise Langevin thermostatting and high precision path integral monte carlo (PIMC) simulations. We comment on the structural evolution of these clusters in the absence of rotation and exchange as a function of cluster size. To quantify the importance of both rotation and exchange in our PIMD simulation, we compute band origin shifts for (He)_N-CO_2 as a function of cluster size and compare to previously published experimental and theoretical shifts. A convergence study is presented to confirm the systematic error reduction introduced by increasing path integral beads for our implementation in the Molecular Modelling Toolkit (MMTK) software package. Applications to carbohydrates are explored at biological temperatures by calculating both equilibrium and dynamical properties using the methods presented. M. Ceriotti, M. Parrinello, and D. E. Manolopoulos, J Chem Phys 133, 124104. H. Li, N. Blinov, P.-N. Roy, and R. J. L. Roy, J Chem Phys 130, 144305.

Ing, Christopher; Hinsen, Conrad; Yang, Jing; Roy, Pierre-Nicholas

2011-06-01

298

Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems

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}{sub {delta}}, where {tau}{sub {delta}} is the time at which the standard deviation {sigma}({tau}){identical_to}<{xi}{sup 2}({tau})>{sup 1/2} approaches the mean intergrain distance {delta}. Others are development of humps in the distributions on multiples of {delta}, anomalous Hurst exponents, and transitions from leptokurtic toward Gaussian displacement distributions on time scales {tau}>{tau}{sub {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 Ito-Langevin stochastic equation with a nonlinear drift term.

Ratynskaia, S. [Space and Plasma Physics, Royal Institute of Technology, SE-100 44 Stockholm (Sweden); Regnoli, G. [Max-Planck-Institut fuer Extraterrestrische Physik, D-85741 Garching (Germany); Space and Plasma Physics, Royal Institute of Technology, SE-100 44 Stockholm (Sweden); Rypdal, K. [Department of Physics and Technology, University of Tromsoe, N-9037 Tromsoe (Norway); Klumov, B.; Morfill, G. [Max-Planck-Institut fuer Extraterrestrische Physik, D-85741 Garching (Germany)

2009-10-15

299

NASA Astrophysics Data System (ADS)

The study presents some preliminary results of the density gradient theory (GT) combined with two different equations of state (EoS): the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT), namely its perturbed-chain (PC) modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation) or bubbles (boiling, cavitation). However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.

Vinš, Václav; Hrubý, Jan; Planková, Barbora

2012-04-01

300

Stochastic theory of an optical vortex in nonlinear media.

A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes. PMID:23944571

Kuratsuji, Hiroshi

2013-07-01

301

Bayesian structural equation modeling: a more flexible representation of substantive theory.

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a nonidentified model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling, such as with confirmatory factor analysis, and the measurement part of structural equation modeling. Two application areas are studied, cross-loadings and residual correlations in confirmatory factor analysis. An example using a full structural equation model is also presented, showing an efficient way to find model misspecification. The approach encompasses 3 elements: model testing using posterior predictive checking, model estimation, and model modification. Monte Carlo simulations and real data are analyzed using Mplus. The real-data analyses use data from Holzinger and Swineford's (1939) classic mental abilities study, Big Five personality factor data from a British survey, and science achievement data from the National Educational Longitudinal Study of 1988. PMID:22962886

Muthén, Bengt; Asparouhov, Tihomir

2012-09-01

302

Requirements for Predictive Density Functional Theory Methods for Heavy Materials Equation of State

NASA Astrophysics Data System (ADS)

The difficulties in experimentally determining the Equation of State of actinide and lanthanide materials has driven the development of many computational approaches with varying degree of empiricism and predictive power. While Density Functional Theory (DFT) based on the Schr"odinger Equation (possibly with relativistic corrections including the scalar relativistic approach) combined with local and semi-local functionals has proven to be a successful and predictive approach for many materials, it is not giving enough accuracy, or even is a complete failure, for the actinides. To remedy this failure both an improved fundamental description based on the Dirac Equation (DE) and improved functionals are needed. Based on results obtained using the appropriate fundamental approach of DFT based on the DE we discuss the performance of available semi-local functionals, the requirements for improved functionals for actinide/lanthanide materials, and the similarities in how functionals behave in transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Mattsson, Ann E.; Wills, John M.

2012-02-01

303

Classical irregular block, N=2 pure gauge theory and Mathieu equation

Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.

Marcin Piatek; Artur R. Pietrykowski

2014-07-01

304

Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model

We show that the chiral partition function of two-dimensional Yang-Mills theory on the sphere can be mapped to the partition function of the homogeneous six-vertex model with domain wall boundary conditions in the ferroelectric phase. A discrete matrix model description in both cases is given by the Meixner ensemble, leading to a representation in terms of a stochastic growth model. We show that the partition function is a particular case of the z-measure on the set of Young diagrams, yielding a unitary matrix model for chiral Yang-Mills theory on the sphere and the identification of the partition function as a tau-function of the Painleve V equation. We describe the role played by generalized non-chiral Yang-Mills theory on the sphere in relating the Meixner matrix model to the Toda chain hierarchy encompassing the integrability of the six-vertex model. We also argue that the thermodynamic behaviour of the six-vertex model in the disordered and antiferroelectric phases are captured by particular q-deformatio...

Szabo, Richard J

2011-01-01

305

Heavy flavour in nucleus-nucleus collisions at RHIC and LHC: a Langevin approach

NASA Astrophysics Data System (ADS)

A snapshot of the results for heavy-flavour observables in heavy-ion (AA) collisions at RHIC and LHC obtained with our transport calculations is displayed. The initial charm and beauty production is simulated through pQCD tools (POWHEG+PYTHIA) and is validated through the comparison with data from pp collisions. The propagation of c and b quarks in the medium formed in heavy-ion collisions is studied through a transport setup based on the relativistic Langevin equation. With respect to past works we perform a more systematic study, providing results with different choices of transport coefficients, either from weak-coupling calculations or from lattice-QCD simulations. Our findings are compared to a rich set of experimental data (D-mesons, non-photonic electrons, non-prompt J/?'s) which have meanwhile become accessible.

Beraudo, A.; De Pace, A.; Monteno, M.; Prino, F.; Alberico, W. M.; Molinari, A.; Nardi, M.

2014-03-01

306

Hierarchical equations of motion for an impurity solver in dynamical mean-field theory

NASA Astrophysics Data System (ADS)

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate evaluation of physical properties of strongly correlated electronic systems, in the framework of dynamical mean-field theory (DMFT). The HEOM method is also numerically convenient to achieve the same level of accuracy as that using the state-of-the-art numerical renormalization group impurity solver at finite temperatures. The practicality of the HEOM+DMFT method is demonstrated by its applications to the Hubbard models with Bethe and hypercubic lattice structures. We investigate the metal-insulator transition phenomena, and address the effects of temperature on the properties of strongly correlated lattice systems.

Hou, Dong; Wang, Rulin; Zheng, Xiao; Tong, NingHua; Wei, JianHua; Yan, YiJing

2014-07-01

307

Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e., ladder) approximation to the scattering kernel, the {\\it naive} Wick rotation is invalid. Our approach generates the vertex function and Bethe-Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

K. Kusaka; K. M. Simpson; A. G. Williams

1996-01-30

308

Fast multi-orbital equation of motion impurity solver for dynamical mean field theory.

We propose a fast multi-orbital impurity solver for dynamical mean field theory (DMFT). Our DMFT solver is based on the equations of motion (EOMs) for local Green's functions and is constructed by generalizing from the single-orbital case to the multi-orbital case with the inclusion of the inter-orbital hybridizations and applying a mean field approximation to the inter-orbital Coulomb interactions. The two-orbital Hubbard model is studied using this impurity solver within a large range of parameters. The Mott metal-insulator transition and the quasiparticle peak are well described. A comparison of the EOM method with the quantum Monte Carlo method is made for the two-orbital Hubbard model and good agreement is obtained. The developed method hence holds promise as a fast DMFT impurity solver in studies of strongly correlated systems. PMID:21970899

Feng, Qingguo; Oppeneer, Peter M

2011-10-26

309

Equation of motion coupled cluster theory calculations of the X-ray emission spectroscopy of water

NASA Astrophysics Data System (ADS)

The equation of motion coupled cluster theory including single and double excitations (EOM-CCSD) method is applied to study the X-ray emission spectroscopy of water. For the 1b1 orbital, a difference of about 0.7 eV is predicted between a tetrahedrally coordinated water molecule and a water molecule in which water molecules accepting hydrogen bonds are absent, and as a proton is dissociated emission from the 1b1 and 3a1 orbitals become closer in energy. The resonantly excited X-ray emission spectrum for the 4a1 orbital shows a red-shift in the bands and a reduction in intensity for the 3a1 band.

Besley, Nicholas A.

2012-07-01

310

NASA Technical Reports Server (NTRS)

Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.

Jezewski, D.

1980-01-01

311

Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems

NASA Astrophysics Data System (ADS)

The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of ( n - d) curvilinear coordinatesparametrizingthe manifold of configurations satisfying the constraints, and to compute the Lagrangian generating the unconstrained dynamics in these ( n - d) configuration coordinates. Starting from this Lagrangian an unconstrained Hamiltonian H( q, p) on 2( n- d) dimensional phase space can then typically be defined in the standard way via a Legendre transform. Furthermore, if the system is in contact with a heat bath, the associated Langevin and Fokker-Planck equations can be introduced. Provided that an appropriate fluctuation-dissipation condition is satisfied, there will be a canonical equilibrium distribution of the Gibbs form exp(-? H) with respect to the flat measure dqdp in these 2( n - d) dimensional curvilinear phase space coordinates. The existence of ( n - d) coordinates satisfying the constraints is often guaranteed locally by an implicit function theorem. Nevertheless in many examples these coordinates cannot be constructed in any tractable form, even locally, so that other approaches are of interest. In ambient space formulations the dynamics are defined in the full original n-dimensional configuration space, and associated 2 n-dimensional phase space, with some version of Lagrange multipliers introduced so that the 2( n - d) dimensional sub-manifold of phase space implied by the holonomic constraints and their time derivative, is invariant under the dynamics. In this article we review ambient space formulations, and explain that for constrained dynamics there is in fact considerable freedom in how a Hamiltonian form of the dynamics can be constructed. We then discuss and contrast the Langevin and Fokker-Planck equations and their equilibrium distributions for the different forms of ambient space dynamics.

Walter, J.; Hartmann, C.; Maddocks, J. H.

2011-11-01

312

Actinide electronic structure based on the Dirac equation and density functional theory

NASA Astrophysics Data System (ADS)

Density functional theory (DFT) provides a formally predictive basis for predicting the structural properties of actinides. Although available approximations to the exchange/correlation functional provide accurate predictions for many materials, they fail qualitatively and sometimes quantitatively when applied to actinides. Major contributors to this deficiency are an inadequate treatment of confinement physics and an incomplete treatment of relativity in the underlying equations. The development of a functional correctly incorporating confinement physics with a proper treatment of relativity would provide definitive, internally consistent predictions of actinide properties. To enable the development of such a functional and quantify the predictions of currently available functionals, we have developed an efficient first-principles electronic structure method based on the Dirac equation. Results are compared with current methods, and the implications for relativistic density functionals discussed. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Wills, John M.; Mattsson, Ann E.

2013-03-01

313

Mixing of equations of state for xenon-deuterium using density functional theory

We report on a theoretical study of equation of state (EOS) properties of fluid and dense plasma mixtures of xenon and deuterium to explore and illustrate the basic physics of the mixing of a light element with a heavy element. Accurate EOS models are crucial to achieve high-fidelity hydrodynamics simulations of many high-energy-density phenomena, for example inertial confinement fusion and strong shock waves. While the EOS is often tabulated for separate species, the equation of state for arbitrary mixtures is generally not available, requiring properties of the mixture to be approximated by combining physical properties of the pure systems. Density functional theory (DFT) at elevated-temperature is used to assess the thermodynamics of the xenon-deuterium mixture at different mass ratios. The DFT simulations are unbiased as to elemental species and therefore provide comparable accuracy when describing total energies, pressures, and other physical properties of mixtures as they do for pure systems. The study focuses on addressing the accuracy of different mixing rules in the temperature range 1000-40 000 K for pressures between 100 and 600 GPa (1-6 Mbar), thus, including the challenging warm dense matter regime of the phase diagram. We find that a mix rule taking into account pressure equilibration between the two species performs very well over the investigated range.

Magyar, Rudolph J.; Mattsson, Thomas R. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

2013-03-15

314

A semiclassical non-adiabatic theory for elementary chemical reactions

Electron Transfer (ET) reactions are modeled by the dynamics of a quantum two-level system (representing the electronic state) coupled to a thermalized bath of classical harmonic oscillators (representing the nuclei degrees of freedom). Unlike for the standard Marcus theory, the complex amplitudes of the electronic state are chosen as reaction coordinates. Then, the dynamical equations at non vanishing temperature become those of an effective Hamiltonian submitted to damping terms and their associated Langevin random forces. The advantage of this new formalism is to extend the original theory by taking into account both ionic and covalent interactions. The standard theory is recovered only when covalent interactions are neglected. Increasing these covalent interactions from zero, the energy barrier predicted by the standard theory first depresses, next vanish (or almost vanish) and for stronger covalent interactions, covalent bond formation takes place of ET. In biochemistry, the standard Marcus theory often ...

Aubry, Serge

2014-01-01

315

NASA Technical Reports Server (NTRS)

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Majda, G.

1985-01-01

316

NASA Astrophysics Data System (ADS)

We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.

Lathiotakis, Nektarios N.; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I.

2014-09-01

317

A kinetic-theory approach to turbulent chemically reacting flows

NASA Technical Reports Server (NTRS)

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

Chung, P. M.

1976-01-01

318

Multinomial diffusion equation

We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N {yields} {infinity}, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.

Balter, Ariel I.; Tartakovsky, Alexandre M.

2011-06-24

319

A time-explicit formula that describes the time evolution of velocity distribution functions of gases and plasmas is derived from the Boltzmann equation. The formula can be used to construct collision simulation algorithms. Specialization of the formula to the case of the Coulomb interaction shows that the previous method [K. Nanbu, Phys. Rev. E 55, 4642 (1997)] for a Coulomb collision

A. V. Bobylev; K. Nanbu

2000-01-01

320

ERIC Educational Resources Information Center

Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems…

Glockner-Rist, Angelika; Hoijtink, Herbert

2003-01-01

321

Perceived resource value reflects individual differences in motivation to acquire resource holding potential. The individualistic achievement (IA) trait, as measured by the Sociotropy Autonomy Scale, is a suitable measure for perceived resource value, and helps understand the social rank theory of depression. The present study aims to evaluate this suggestion using structural equation modeling analysis. A total of 199 university

Wai S. Tse; Jayne Wu; Kai-Chung Poon

2011-01-01

322

A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of gravity, the equation of motion of a classical mass point in gravitational gauge field is given by Newton's second law of motion. A relativistic form of the gravitational force on a mass point is deduced in this paper. Based on the spherical symmetric solution of the field equation and Newton's second law of motion, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity. From the study in this paper, an important qualitative conclusion on the nature of gravity is that gravity can be treated as a kind of physical interactions in flat Minkowski space-time, and the equation of motion of mass point in gravitational field can be given by Newton's second law of motion.

Ning Wu; Dahua Zhang

2005-08-01

323

NASA Astrophysics Data System (ADS)

The effects of quadrupole moments on the phase behaviour of isotropic-nematic transition are studied by using density functional theory for a system of molecules which interact via the Gay-Berne pair potential. The pair correlation functions of isotropic phase, which enter in the theory as input information, are found from the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to six have been considered. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures and quadrupole moments. The results have been compared with the available computer simulation results.

Singh, R. C.

2009-07-01

324

Perturbative analysis of the gradient flow in non-abelian gauge theories

The gradient flow in non-abelian gauge theories on R^4 is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on R^4 x [0,oo). For any matter multiplet and to all loop orders, we show that the correlation functions are finite, i.e.~do not require additional renormalization, once the theory in four dimensions is renormalized in the usual way. The flow thus maps the gauge field to a one-parameter family of smooth renormalized fields.

Lüscher, Martin

2011-01-01

325

Exploring the phase diagram of QCD with complex Langevin simulations

Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight factors and therefore potentially enable the determination of the phase diagram of QCD. Here we present results for QCD in the limit of heavy quarks and show evidence that the phase diagram can be mapped out by direct simulation. We apply adaptive step-size scaling and adaptive gauge cooling to ensure the convergence of these simulations.

Aarts, Gert; Jäger, Benjamin; Seiler, Erhard; Sexty, Denes; Stamatescu, Ion-Olimpiu

2014-01-01

326

Exploring the phase diagram of QCD with complex Langevin simulations

Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight factors and therefore potentially enable the determination of the phase diagram of QCD. Here we present results for QCD in the limit of heavy quarks and show evidence that the phase diagram can be mapped out by direct simulation. We apply adaptive step-size scaling and adaptive gauge cooling to ensure the convergence of these simulations.

Gert Aarts; Felipe Attanasio; Benjamin Jäger; Erhard Seiler; Denes Sexty; Ion-Olimpiu Stamatescu

2014-11-10

327

NASA Astrophysics Data System (ADS)

The similarity transformed equation of motion coupled cluster (STEOM-CC) method is benchmarked against CC3 and EOM-CCSDT-3 for a large test set of valence excited states of organic molecules studied by Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P. Sauer, and W. Thiel, J. Chem. Phys. 128, 134110 (2008)]. STEOM-CC is found to behave quite satisfactorily and provides significant improvement over EOM-CCSD, CASPT2 and NEVPT2 for singlet excited states, lowering standard deviations of these methods by almost a factor of 2. Triplet excited states are found to be described less accurately, however. Besides the parent version of STEOM-CC, additional variations are considered. STEOM-D includes a perturbative correction from doubly excited determinants. The novel STEOM-H ({\\omega}) approach presents a sophisticated technique to render the STEOM-CC transformed Hamiltonian hermitian. In STEOM-PT, the expensive CCSD step is replaced by many-body second-order perturbation theory (MBPT(2)), while extended STEOM (EXT-STEOM) provides access to doubly excited states. To study orbital invariance in STEOM, we investigate orbital rotation in the STEOM-ORB approach. Comparison of theses variations of STEOM for the large test set provides a comprehensive statistical basis to gauge the usefulness of these approaches.

Sous, J.; Goel, P.; Nooijen, M.

2014-03-01

328

Application of integral-equation theory to aqueous two-phase partitioning systems

A molecular-thermodynamic model is developed for representing thermodynamic properties of aqueous two-phase systems containing polymers, electrolytes, and proteins. The model is based on McMillan-Mayer solution theory and the generalized mean-spherical approximation to account for electrostatic forces between unlike ions. The Boublik-Mansoori equation of state for hard-sphere mixtures is coupled with the osmotic virial expansion truncated after the second-virial terms to account for short-range forces between molecules. Osmotic second virial coefficients are reported from low-angle laser-light scattering (LALLS) data for binary and ternary aqueous solutions containing polymers and proteins. Ion-polymer specific-interaction coefficients are determined from osmotic-pressure data for aqueous solutions containing a water-soluble polymer and an alkali chloride, phosphate or sulfate salt. When coupled with LALLS and osmotic-pressure data reported here, the model is used to predict liquid-liquid equilibria, protein partition coefficients, and electrostatic potentials between phases for both polymer-polymer and polymer-salt aqueous two-phase systems. For bovine serum albumin, lysozyme, and [alpha]-chymotrypsin, predicted partition coefficients are in excellent agreement with experiment.

Haynes, C.A.; Benitez, F.J.; Blanch, H.W.; Prausnitz, J.M. (Univ. of California, Berkeley, CA (United States))

1993-09-01

329

NASA Astrophysics Data System (ADS)

With fast computers and improved radiation-hydrodynamics simulation techniques, increasingly complex high energy-density physics systems are investigated by modeling and simulation efforts, putting unprecedented strain on the underlying Equation of State (EOS) modeling. EOS models that have been adequate in the past can fail in unexpected ways. With the aim of improving the EOS, models are often fitted to calculated data in parts of the parameter space where little or no experimental data is available. One example is the compression part of the cold curve. We show that care needs to be taken in using Density Functional Theory (DFT) codes. While being perfectly adequate for calculations in many parts of the parameter space, approximations inherent to pseudo-potential codes can limit their applicability for large compressions. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Mattsson, Ann E.; Cochrane, Kyle R.; Carpenter, John H.; Desjarlais, Michael P.

2008-03-01

330

The similarity transformed equation of motion coupled cluster (STEOM-CC) method is benchmarked against CC3 and EOM-CCSDT-3 for a large test set of valence excited states of organic molecules studied by Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P. Sauer, and W. Thiel, J. Chem. Phys. 128, 134110 (2008)]. STEOM-CC is found to behave quite satisfactorily and provides significant improvement over EOM-CCSD, CASPT2 and NEVPT2 for singlet excited states, lowering standard deviations of these methods by almost a factor of 2. Triplet excited states are found to be described less accurately, however. Besides the parent version of STEOM-CC, additional variations are considered. STEOM-D includes a perturbative correction from doubly excited determinants. The novel STEOM-H ({\\omega}) approach presents a sophisticated technique to render the STEOM-CC transformed Hamiltonian hermitian. In STEOM-PT, the expensive CCSD step is replaced by many-body second-order perturbation theory (MBPT(2)), while extended STEOM (EX...

Sous, John; Nooijen, Marcel

2014-01-01

331

NASA Astrophysics Data System (ADS)

We discuss twistor-like interpretation of the Sp(8) invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian Sp(8)/P which is the generalized space-time in this framework. The correspondence space C is SpH(8)/PH where SpH(8) is the semidirect product of Sp(8) with Heisenberg group SpHM and PH is some quasiparabolic subgroup of SpH(8). Spaces of functions on Sp(8)/P and SpH(8)/PH consist of QP closed functions on Sp(8) and QPH closed functions on SpH(8), where QP and QPH are canonical BRST operators of P and PH. The space of functions on the generalized twistor space T identifies with the SpH(8) Fock module. Although T cannot be realized as a homogeneous space, we find a nonstandard SpH(8) invariant BRST operator Q (Q2 = 0) that gives rise to an appropriate class of functions via the condition Qf = 0 equivalent to the unfolded higher-spin equations. The proposed construction is manifestly Sp(8) invariant, globally defined and coordinate independent. Its Minkowski analogue gives a version of twistor theory with both types of chiral spinors treated on equal footing. The extensions to the higher rank case with several Heisenberg groups and to the complex case are considered. A relation with Riemann theta functions, that are Q-closed, is discussed.

Gelfond, O. A.; Vasiliev, M. A.

2009-12-01

332

NASA Astrophysics Data System (ADS)

An invariant statistical theory of fields from cosmic to tachyonic scales is presented. The invariant wavefunction is defined as the first perturbation of action S_? = ?_??_?, the product of density and velocity potential. The invariant Schrödinger equation is derived, and invariant forms of Planck constant, de Broglie matter wave hypothesis, and Heisenberg uncertainty relation are presented. The field of tachyon-dynamics is identified as the physical space that is the stochastic ether of Dirac, or the "hidden thermostat" of de Broglie, and is assumed to be compressible in harmony with compressible ether of Planck. Compressibility of physical space is suggested to account for Fitzgerald-Lorentz contraction, thus providing an explanation of relativistic effects in harmony with the physical perceptions of Poincaré and Lorentz. Following the definition of Planck constant h = m_??_?c = 6.626x10-34 J-s, the definition of Boltzmann constant is introduced as k = m_??_?c = 1.381x10-23 J/K, where m_?, ?_?,?_?, and c are the photon mass, wavelength, frequency, and velocity. Parallel to the de Broglie relation ?_? = h/p_? for matter waves, the relation ?_? = k/p_? is introduced to give the frequency of matter waves. Therefore, the mass of the photon is predicted as m_? = (hk/c^3)^1/2 = 1.84278x10-41 kg.

Sohrab, S. H.

1998-03-01

333

1 Theory of Thunderstorm Dynamics Houze sections 7.4, 8.3, 8.5, Refer back to equations in Section Thunderstorms" by Klemp Â handout. A. Equations of Motion Boussinesq approximated equations (neglecting friction in thunderstorms, look at the vertical component of vorticity ^k = r ^ ^ ^ ^( ) ( ) ( )k V k Bk k V

Droegemeier, Kelvin K.

334

The algorithm of SHAFT79 is based on mass and energy balance equations for two-phase flow in a porous medium. These basic equations are formulated as Integrated Finite Difference equations. The latter formulation allows both regular and irregular discrete grid approximations of reservoir geometry. The present version of SHAFT79 solves the non-linear mass and energy equations simultaneously using an efficient linear

K. Pruess; R. C. Schroeder

1979-01-01

335

NASA Astrophysics Data System (ADS)

CONTENTS § 1. Introduction § 2. Solubility of the direct and inverse Cauchy problems § 3. The direct equation of inverse diffusion. The method of variation of constants § 4. The method of characteristics. First integrals and the Liouville equations for diffusion processes § 5. Inverse filtration equations References

Krylov, N. V.; Rozovskii, B. L.

1982-12-01

336

We have studied the structure and thermodynamic properties of isotropic three-dimensional core-softened fluid by using the second-order Ornstein-Zernike integral equations completed by the hypernetted chain and Percus-Yevick closures. The radial distribution functions are compared with those from singlet integral equations and with computer simulation data. The limits of the region of density anomaly resulting from different approximate theories are established. The obtained results show that the second-order hypernetted chain approximation can be used to describe both the structure and the density anomaly of this model fluid. Moreover, we present the results of calculations of the bridge functions.

O. Pizio; Z. Sokolowska; S. Sokolowski

2011-06-16

337

The methods of the quantum theory of fluctuations and damping are used to obtain a master equation for the density matrix of Bogolyubov-coherent excitons, photons, and biexcitons in solids. Glauber's P representation is used to derive a Fokker-Planck equation for the system of coherent quasiparticles. Conditions are found for two-photon lasing biexcitons in the case of exciton-biexciton conversion. It is shown that transition from the disordered to the ordered phase is equivalent to a phase transition of the first kind.

Moskalenko, S.A.; Rotaru, A.Kh.; Shvera, Yu.M.

1988-11-01

338

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. PMID:23937300

Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei

2013-12-12

339

NASA Astrophysics Data System (ADS)

It is demonstrated that a standard coupled-mode theory can successfully describe weakly nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this theory are in reasonable agreement with numerical simulations of the exact equations of motion for ideal planar potential free-surface flows, even for strongly nonlinear waves. In numerical experiments, self-localized groups of nearly standing water waves can exist up to hundreds of wave periods. Generalizations of the model to the three-dimensional case are also derived.

Ruban, V. P.

2008-12-01

340

In this work stochastic theory is applied to the treatment of atom--vibrotor collisions. This is an extension of a previous paper which described molecular collisions by a Pauli master equation or a Fokker--Planck equation. In this framework an energy conserving classical path model is explored, and methods for solving the equations numerically are discussed. The coefficients of the Fokker--Planck equation

S. D. Augustin; H. Rabitz

1977-01-01

341

NASA Astrophysics Data System (ADS)

A new analytical formulation is proposed to solve the diffusion equation under Approximation B in electron-photon cascade theory. The Suzuki-Trotter formula, analytical continuation of the hypergeometric function, and product integration are introduced. By using these methods the usual series solutions are obtained, and summation of the infinite series for arbitrary values of the energy E is performed by using the method of Prony's interpolation. As E --> 0, the infinite sum for the electron component turns out to be the function of K1(s, -s) used in the usual cascade theory, and a logarithmic divergence arises for the photon component. Use of Prony's method makes it possible to derive the energy spectra as well as the track length distributions and the transition curves. Our numerical results agree well with previous authors' as expected. Our analytical approach provides a general framework for solving other diffusion equations containing non-commutative operators in different contexts.

Nii, N.

1998-03-01

342

We consider a generalization of the projecting operators method for the case of Cauchy problem for systems of 1D evolution differential equations of first order with variable coefficients. It is supposed that the coefficients dependence on the only variable x is weak, that is described by a small parameter introduction. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics. For the Cauchy problem, to fix unidirectional modes, the projection operators are constructed. The method of successive approximations (perturbation theory) is developed and based on pseudodifferential operators theory. The application of these projection operators allows to obtain approximate evolution equations corresponding to the separated directed waves.

Sergey Leble; Irina Vereshchagina

2014-03-30

343

A recently developed crossover equation of state (EOS) incorporates contributions from long-wavelength density fluctuations by renormalization-group theory. This EOS can satisfactorily describe the thermodynamic properties of chain fluids both far-from and near-to the critical region; it is used here to calculate the critical locus of a mixture. Because the calculations require much computation time, especially for ternary (and higher) mixtures,

Jianwen Jiang; John M. Prausnitz

2000-01-01

344

On a class of solutions of the Einstein-Maxwell field equations in scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

In this paper we obtain a class of static cylindrically symmetric solutions of the Einstein-Maxwell field equations in the framework of scalar-tensor theories of gravity. In this context, in which both a Maxwell field and a dilaton field are sources of the stress energy, the solutions were obtained by using the Rainich conditions of general relativity, appropriately modified to take into account the presence of the scalar field.

Sobreira, A. A. R.; Marques, Geusa de A.; Fonseca-Neto, J. B.; Bezerra, V. B.

2009-05-01

345

This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.

Du Kai, E-mail: kdu@fudan.edu.cn; Qiu, Jinniao, E-mail: 071018032@fudan.edu.cn; Tang Shanjian, E-mail: sjtang@fudan.edu.cn [Fudan University, Department of Finance and Control Sciences, School of Mathematical Sciences, and Laboratory of Mathematics for Nonlinear Sciences (China)

2012-04-15

346

A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).

Nagy, A. [Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen (Hungary)

2011-09-15

347

Einstein-Weyl geometry, the dKP equation and twistor theory

It is shown that Einstein-Weyl (EW) equations in 2+1 dimensions contain the dispersionless Kadomtsev-Petviashvili (dKP) equation as a special case: If an EW structure admits a constant weighted vector then it is locally given by h = dy2 ?4dxdt?4udt2, ? = ?4uxdt, where u = u(x, y, t) satisfies the dKP equation (ut ? uux)x = uyy. Linearised solutions to

Maciej Dunajski; Lionel J. Mason; Paul Tod

2000-01-01

348

Complex Langevin: etiology and diagnostics of its main problem

NASA Astrophysics Data System (ADS)

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 sometimes it produces `convergence to the wrong limit'. In this paper we carefully revisit the formal justification of the method, identifying points at which it may fail and derive a necessary and sufficient criterion for correctness. This criterion is, however, not practical, since its application requires checking an infinite tower of identities. We propose instead a practical test involving only a check of the first few of those identities; this raises the question of the `sensitivity' of the test. This sensitivity as well as the general insights into the possible reasons of failure (the etiology) are then tested in two toy models where the correct answer is known. At least in those models the test works perfectly.

Aarts, Gert; James, Frank A.; Seiler, Erhard; Stamatescu, Ion-Olimpiu

2011-10-01

349

Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice

ERIC Educational Resources Information Center

While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…

Koutsoyiannis, Demetris

2012-01-01

350

On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves

NASA Astrophysics Data System (ADS)

Many studies of weakly nonlinear surface waves are based on so-called reduced integrodifferential equations. One of these is the widely used Zakharov four-wave equation for purely gravity waves. But the reduced equations now in use are not Hamiltonian despite the Hamiltonian structure of exact water wave equations. This is entirely due to shortcomings of their derivation. The classical method of canonical transformations, generalized to the continuous case, leads automatically to reduced equations with Hamiltonian structure. In this paper, attention is primarily paid to the Hamiltonian reduced equation describing the combined effects of four- and five-wave weakly nonlinear interactions of purely gravity waves. In this equation, for brevity called five-wave, the non-resonant quadratic, cubic and fourth-order nonlinear terms are eliminated by suitable canonical transformation. The kernels of this equation and the coefficients of the transformation are expressed in explicit form in terms of expansion coefficients of the gravity-wave Hamiltonian in integral-power series in normal variables. For capillary-gravity waves on a fluid of finite depth, expansion of the Hamiltonian in integral-power series in a normal variable with accuracy up to the fifth-order terms is also given.

Krasitskii, Vladimir P.

1994-08-01

351

An electric-analog simulation of elliptic partial differential equations using finite element theory

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

352

We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges.

L. Joukovskaya

2007-08-04

353

Einstein-Weyl geometry, the dKP equation and twistor theory

It is shown that Einstein-Weyl (EW) equations in 2+1 dimensions contain the dispersionless Kadomtsev-Petviashvili (dKP) equation as a special case: If an EW structure admits a constant weighted vector then it is locally given by $h=d y^2-4d xd t-4ud t^2, \

Maciej Dunajski; Lionel J. Mason; Paul Tod

2000-04-06

354

Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations

We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.

Frank Gronwald

1997-02-18

355

Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces.

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation. PMID:21231032

Henry, B I; Langlands, T A M; Straka, P

2010-10-22

356

Fractional Fokker-Planck Equations for Subdiffusion with Space- and Time-Dependent Forces

NASA Astrophysics Data System (ADS)

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.

Henry, B. I.; Langlands, T. A. M.; Straka, P.

2010-10-01

357

Noisy Kuramoto-Sivashinsky equation for an erosion model Kent Bkgaard Lauritsen,1,3

it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how in these cases is based on the master equation which determines the evolution of the joint probability density P

Cuerno, Rodolfo

358

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. PMID:24375394

Shen, Tonghao; Su, Neil Qiang; Wu, Anan; Xu, Xin

2014-03-01

359

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism. PMID:21090871

Thomas, Philipp; Straube, Arthur V; Grima, Ramon

2010-11-21

360

NASA Astrophysics Data System (ADS)

In the Horndeski's most general scalar-tensor theories the equations of scalar density perturbations are derived in the presence of non-relativistic matter minimally coupled to gravity. Under a quasi-static approximation on sub-horizon scales we obtain the effective gravitational coupling G associated with the growth rate of matter perturbations as well as the effective gravitational potential ? relevant to the deviation of light rays. We then apply our formulas to a number of modified gravitational models of dark energy - such as those based on f(R) theories, Brans-Dicke theories, kinetic gravity braidings, covariant Galileons, and field derivative couplings with the Einstein tensor. Our results are useful to test the large-distance modification of gravity from the future high-precision observations of large-scale structure, weak lensing, and cosmic microwave background.

de Felice, Antonio; Kobayashi, Tsutomu; Tsujikawa, Shinji

2011-12-01

361

We prove that Jormakka's classical solution of the Yang-Mills equations for the Minkowskian $\\mathbf{R}^{1,3}$ can be quantized to field maps satisfying Wightman's axioms of Constructive Quantum Field Theory and that the spectrum of the corresponding Hamilton operator is positive and bounded away from zero except for the case of the vacuum state which has vanishing energy level. By continuity this implies the existence of a mass gap for any four dimensional quantum Yang-Mills theory on the Minkoswki space, provided this theory exists. The positive mass gap result holds true at second quantization level as well, two of eights Wightman's axioms don't. The (virtual) particles corresponding to all solution fields are fermionic ghosts.

Simone Farinelli

2014-06-16

362

Critical dynamics in systems controlled by fractional kinetic equations

NASA Astrophysics Data System (ADS)

The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0

Batalov, Lev; Batalova, Anastasia

2013-02-01

363

Analysis of transport properties determined by Langevin dynamics using Green-Kubo formulae

NASA Astrophysics Data System (ADS)

Recently, the Langevin dynamics method has been applied to simulate gas flows. It is very crucial to evaluate whether the Langevin dynamics could correctly predict transport properties of gas or not. In this paper, the transport properties of Langevin velocity model and acceleration model are analyzed by using Green-Kubo formulae. For the Langevin velocity model, the time correlation functions have the exact exponent forms, and the Prandtl number for monatomic gas is predicted to be 3/2. For the Langevin acceleration model with an additional time scale, the molecular movements change from Markovian process to Non-Markovian process, and the Prandtl number could be adjusted to some extent. In the limit of equilibrium, there is a minimum about 1.298 for the Prandtl number of monatomic gas when the two time scales are equal in Langevin acceleration model. Besides theoretical analyses, molecular simulations according to the Langevin velocity model and acceleration model are performed, and the simulation results validate our analytical solutions.

Zhang, Jun; Zeng, Dandan; Fan, Jing

2014-10-01

364

A general equilibrium model of world trade with two differentiated-product industries and two factors is developed to illustrate how the gravity equation, including exporter and importer populations, as well as incomes, \\

Jeffrey H Bergstrand

1989-01-01

365

Self-affine polytopes. Applications to functional equations and matrix theory

A special kind of functional equation with compression of the argument--the affine self-similarity equation--is studied. The earlier known one-dimensional self-similarity equations are generalized to the multidimensional case of functions of several variables. A criterion for the existence and uniqueness of an L{sub p}-solution is established. Description of such equations involves classification of finite-dimensional convex self-affine compact sets. In this work properties of such objects are thoroughly analysed; in particular, a counterexample to the well-known conjecture about the structure of such bodies, which was put forward in 1991, is given. Applications of the results obtained include some facts about the convergence of products of stochastic matrices; also, criteria for the convergence of some subdivision algorithms are suggested. Bibliography: 39 titles.

Voynov, Andrey S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2011-10-31

366

Perturbation theory for Maxwell's equations with a time-dependent current source

NASA Astrophysics Data System (ADS)

Using a set of ideas discussed in the second volume of Feynman Lectures, we develop a perturbation-theoretic scheme for solving Maxwell's equations for time-dependent currents which are switched on at t = 0.

Roy, T.; Ghosh, S.; Bhattacharjee, J. K.

2011-12-01

367

Correctness of certain integral equation theories for core-softened fluids.

Integral equation approaches, based on the Ornstein-Zernike equation, provide a fast way to calculate phase diagrams and thermodynamic properties of systems as opposed to time-consuming and computationally expensive computer simulations. However, when employing integral equations it is necessary to introduce simplifications. The Ornstein-Zernike equation merely relates two unknown functions h(r) and c(r), and another relation (closer) between these two functions is needed. The later function cannot be obtained in a closed form and it is always in some approximations. Various approximations exist with each of its own advantages and disadvantages. In this work we extensively tested hyper-netted chain, Percus-Yevick, Kovalenko-Hirata, and Rogers-Young closure on an interaction model with core-softened potential. Convergence domain was established for each method. We calculated pair distribution functions, pressure, and excess energy. Results were compared with Monte Carlo simulation results and literature data from molecular dynamics simulations. PMID:23781806

Huš, Matej; Zalar, Matja; Urbic, Tomaz

2013-06-14

368

L 2-Stability Theory of the Boltzmann Equation near a Global Maxwellian

NASA Astrophysics Data System (ADS)

We present three a priori L 2-stability estimates for classical solutions to the Boltzmann equation with a cut-off inverse power law potential, when initial datum is a perturbation of a global Maxwellian. We show that L 2-stability estimates of classical solutions depend on Strichartz type estimates of perturbations and the non-positive definiteness of the linearized collision operator. Several well known classical solutions to the Boltzmann equation fit our L 2-stability framework.

Ha, Seung-Yeal; Yang, Xionfeng; Yun, Seok-Bae

2010-08-01

369

A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory

A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work, with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Juettner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.

Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A. [Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Mexico D. F. 09340 (Mexico)

2010-12-14

370

Modeling of thermal transport in practical nanostructures requires making trade-offs 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. 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, we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-B\\"uttiker fo...

Sääskilahti, K; Tulkki, J

2013-01-01

371

Closed string field theory: Quantum action and the Batalin-Vilkovisky master equation

The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L? encoding the gauge symmetry of the classical theory. The higher genus

Barton Zwiebach

1993-01-01

372

Load relaxation in aluminum: I. Theory of plastic deformation. II. Plastic equation of state

According to the theory of thermally-activated deformation, the plastic strain rate equality(dot in _p )_t = _{ - dt} = (dot in _p )_t = _{dt} will hold in a load relaxation experiment, where t = 0 is de-fined as the time at which the crosshead stops. In this theory, plastic flow is intrinsically time dependent and its rate is

Thomas H. Alden

1977-01-01

373

Simplified Derivation of the Fokker-Planck Equation.

ERIC Educational Resources Information Center

Presents an alternative derivation of the Fokker-Planck equation for the probability density of a random noise process, starting from the Langevin equation. The derivation makes use of the first two derivatives of the Dirac delta function. (Author/GA)

Siegman, A. E.

1979-01-01

374

The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Staeckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.

Wu Shuangqing [College of Physical Science and Technology, Central China Normal University, Wuhan, Hubei 430079 (China)

2009-08-15

375

Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in literature: The inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept, we obtain the tap density equations and they can be reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environment temperature are grouped into one parameter that weighs the pace of packing process. The current results, in conjunction with our previous findings, may imply that both dry(granular)and wet(colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).

Tian Hao

2014-09-05

376

The phonon instability and thermal equation of state of Mo are extensively investigated using density functional theory. The calculated phonon dispersion curves agree well with experiments. Under compression, we captured a large softening in the transverse acoustic (TA) branches of body-centred cubic Mo. When the pressure is raised to 716 GPa, the frequencies along ?-N in the TA branches soften to imaginary frequencies, indicating structural instability. For face-centred cubic Mo, the phonon calculations predicted the stability by promoting the frequencies from imaginary to real. Within quasi-harmonic approximation, we predicted the thermal equation of state and some other properties including the thermal expansion coefficient ?, product ?K(T), heat capacity C(V), entropy S, Grüneisen parameter ? and Debye temperature ?(D). The melting curves of Mo were also obtained successfully. PMID:21103579

Zeng, Zhao-Yi; Hu, Cui-E; Chen, Xiang-Rong; Zhang, Xiu-Lu; Cai, Ling-Cang; Jing, Fu-Qian

2011-01-28

377

We determine the path integral solution of a stochastic process described by a generalized Langevin equation with coordinate-dependent fluctuating forces and white spectrum. Since such equations do not permit a unique determination of the distribution function but require the Ito or Stratonovich prescription, we first pass over to the corresponding Fokker-Planck equation adopting such a prescription. By means of the

H. Haken

1976-01-01

378

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

NASA Technical Reports Server (NTRS)

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

Kittl, P.

1984-01-01

379

NASA Astrophysics Data System (ADS)

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

Huš, Matej; Munaò, Gianmarco; Urbic, Tomaz

2014-10-01

380

Load relaxation in aluminum: I. Theory of plastic deformation. II. Plastic equation of state

According to the theory of thermally-activated deformation, the plastic strain rate equality\\u000a $$(\\\\dot \\\\in _p )_t = _{ - dt} = (\\\\dot \\\\in _p )_t = _{dt} $$\\u000a will hold in a load relaxation experiment, wheret = 0 is de-fined as the time at which the crosshead stops. In this theory, plastic flow is intrinsically time dependent and\\u000a its rate

Thomas H. Alden

1977-01-01

381

Algebraic Meta-Theories and Synthesis of Equational Logics Research Programme

on second- order equational logic will provide foundations for design- ing a second-order extension: binders, metavariables, linearity, sharing, graphical structure, type dependency, substitution. Our research programme is planned in a stepwise fashion so that the various feature combina- tions can

Fiore, Marcelo

382

A wave equation migration method for receiver function imaging: 1. Theory

A wave equation-based poststack depth migration method is proposed to image the Earth's internal structure using teleseismic receiver functions. By utilizing a frequency wave number domain one-way phase screen propagator for wave field extrapolation in the migration scheme, common conversion point (CCP) stacked receiver functions are backward propagated to construct a subsurface structural image. The phase screen propagator migration method

Ling Chen; Lianxing Wen; Tianyu Zheng

2005-01-01

383

NASA Astrophysics Data System (ADS)

In this paper the main equations and correlations, describing behavior of coupled magnetoelastic waves of small amplitude in ferromagnetic micropolar media are obtained. As an example plane waves propagation along the anisotropy axis in elastic-isotropic medium is considered. The possibility of magnetoacoustic resonance, caused by the micropolar medium properties account, is shown.

Bagdasarian, Gevorg E.; Asanian, Davresh J.; Danoyan, Zaven

1995-05-01

384

The Application of a Discrete Function Theory to the Solution of the Navier-Stokes Equations

. We develop a numerical method for the Navier-Stokes equations over unbounded domains. From the analytic methods used to show\\u000a existence and uniqueness we obtain their discrete counterparts which allows us to establish a problem-adapted numerical solver\\u000a based on finite differences for functions with low regularity.

Nelson Faustino

2008-01-01

385

Cold equation of state from Thomas-Fermi-Dirac-Weizsacker theory

NASA Astrophysics Data System (ADS)

The Thomas-Fermi-Dirac (TFD) electronic structure model with the Weizsacker gradient corrections (TFD-?W) is employed to calculate the cold equation of state in the Wigner-Seitz spherical-cell approximation. We demonstrate how inclusion of the Weizsacker term removes many of the unphysical features of the TFD lattice model. Results are summarized for seven elements: 126C, 2412Mg, 5626Fe, 10847Ag, 19779Au, 20782Pb, and 23692U. Our equation of state (computed using several values of the Weizsacker coupling coefficient) is compared with previous computations and with experimental data. The Weizsacker correction substantially improves the theoretical TFD equation of state at low densities. We also calculate low-mass, equilibrium stellar models constructed from the TFD-?W equation of state for carbon. We find that for ?=1/9 the maximum radius of a carbon white dwarf star is R/Rsolar=3.9×10-2 at a mass M/Msolar=2.3×10-3.

Abrahams, Andrew M.; Shapiro, Stuart L.

1990-09-01

386

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. PMID:23944435

Sääskilahti, K; Oksanen, J; Tulkki, J

2013-07-01

387

NASA Astrophysics Data System (ADS)

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.JSTPBS0022-471510.1007/s10955-006-9235-3 125, 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.

Sääskilahti, K.; Oksanen, J.; Tulkki, J.

2013-07-01

388

Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics

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.

Marian, J; Venturini, G; Hansen, B; Knap, J; Ortiz, M; Campbell, G

2009-05-08

389

The results of the nonlinear Fokker-Planck equation formalism, which was recently derived as an asymptotic representation of the Master Equation for large system size, are compared with the exact solution of the Master Equation for the Schlögl model. As far as critical behaviour is concerned complete agreement is found. Furthermore at the first order transition points the nonlinear Fokker-Planck equation

W. Horsthemke; M. Malek-Mansour; L. Brenig

1977-01-01

390

Langevin dynamics simulations of biomolecules on graphics processors

Due to the very long timescales involved (us-s), theoretical modeling of fundamental biological processes including folding, misfolding, and mechanical unraveling of biomolecules, under physiologically relevant conditions, is challenging even for distributed computing systems. Graphics Processing Units (GPUs) are emerging as an alternative programming platform to the more traditional CPUs as they provide high raw computational power that can be utilized in a wide range of scientific applications. Using a coarse-grained Self Organized Polymer (SOP) model, we have developed and tested the GPU-based implementation of Langevin simulations for proteins (SOP-GPU program). Simultaneous calculation of forces for all particles is implemented using either the particle based or the interacting pair based parallelization, which leads to a ~30-fold acceleration compared to an optimized CPU version of the program. We assess the computational performance of an end-to-end application of the SOP-GPU program, where all steps of the algorithm are running on the GPU, by profiling the associated simulation time and memory usage for a number of small proteins, long protein fibers, and large-size protein assemblies. The SOP-GPU package can now be used in the theoretical exploration of the mechanical properties of large-size protein systems to generate the force-extension and force-indentation profiles under the experimental conditions of force application, and to relate the results of single-molecule experiments in vitro and in silico.

A. Zhmurov; R. I. Dima; Y. Kholodov; V. Barsegov

2010-03-04

391

Calibrated Langevin-dynamics simulations of intrinsically disordered proteins

NASA Astrophysics Data System (ADS)

We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of single-molecule fluorescence resonance energy transfer data on the interresidue separations for 36 pairs of residues in five IDPs: ?-, ?-, and ?-synuclein, the microtubule-associated protein ?, and prothymosin ?. We find that our CG model is able to recapitulate the average interresidue separations regardless of the choice of the hydrophobicity scale, which shows that our calibrated model can robustly capture the conformational dynamics of IDPs. We then employ our model to study the scaling of the radius of gyration with chemical distance in 11 known IDPs. We identify a strong correlation between the distance to the dividing line between folded proteins and IDPs in the mean charge and hydrophobicity space and the scaling exponent of the radius of gyration with chemical distance along the protein.

Smith, W. Wendell; Ho, Po-Yi; O'Hern, Corey S.

2014-10-01

392

Fokker-Planck equation for lattice deposition models.

An asymptotically exact Fokker-Planck equation for the height fluctuations of lattice deposition models is derived from a Van Kampen expansion of the master equation. Using an Edwards-Wilkinson-type model as an example, the solution of the equivalent Langevin equation reproduces the surface roughness and lateral height correlations obtained with kinetic Monte Carlo (KMC) simulations. Our discrete equations of motion thereby provide an exact analytic and computational alternative to KMC simulations of these models. PMID:11690075

Baggio, C; Vardavas, R; Vvedensky, D D

2001-10-01

393

NASA Astrophysics Data System (ADS)

We present an approach to compute optical absorption spectra from first principles, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator [1]. This is equivalent to solving the Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on Density Functional Perturbation Theory [1,2]. The calculation and inclusion of GW quasi-particle corrections within this framework are discussed. The efficiency and accuracy of our approach are demonstrated by computing optical spectra of solids, nanostructures and dipeptide molecules exhibiting charge transfer excitations. [4pt] [1] D.Rocca, D.Lu and G.Galli, J. Chem. Phys. 133, 164109 (2010). [0pt] [2] H. Wilson, F. Gygi and G. Galli, Phys. Rev. B , 78, 113303, (2008).

Rocca, Dario; Lu, Deyu; Nguyen, Huy-Viet; Galli, Giulia

2011-03-01

394

Decision theory on dynamic domains nabla derivatives and the Hamilton-Jacobi-Bellman equation

The time scales calculus, which includes the study of the Nabla derivatives, is an emerging key topic due to many multidisciplinary applications. We extend this calculus to approximate dynamic programming. In particular, we investigate application of the Nabla derivative, one of the fundamental dynamic derivatives of time scales. We present a Nabla-derivative based derivation and proof of the Hamilton-Jacobi-Bellman equation,

John Seiffertt; Donald C. Wunsch; Suman Sanyal

2008-01-01

395

Extension of the de Broglie-Bohm theory to the Ginzburg-Landau equation

The de Broglie-Bohm approach permits to assign well defined trajectories to particles that obey the Schroedinger equation. We extend this approach to electron pairs in a superconductor. In the stationary regime this extension is completely natural; in the general case additional postulates are required. This approach gives enlightening views for the absence of Hall effect in the stationary regime and for the formation of permanent currents.

Jorge Berger

2003-09-19

396

The QCD Equation of State - From Nuclear Physics to Perturbation Theory

In this talk, we briefly review the current understanding of the behavior of the QCD equation of state throughout the phase diagram. Special emphasis is given to regions of phenomenological interest, and a number of important open questions as well as directions of ongoing research are pointed out. These include in particular the region of low temperatures and (moderately) high densities, where at the moment we have extremely few first principles tools available.

Aleksi Vuorinen

2011-04-27

397

Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation

A model to treat the anomalous Hall effect is developed. Based on the Kubo formalism and on the Dirac equation, this model allows the simultaneous calculation of the skew-scattering and side-jump contributions to the anomalous Hall conductivity. The continuity and the consistency with the weak-relativistic limit described by the Pauli Hamiltonian is shown. For both approaches, Dirac and Pauli, the

A. Crépieux; P. Bruno

2001-01-01

398

Extension of the de Broglie-Bohm Theory to the Ginzburg-Landau Equation

NASA Astrophysics Data System (ADS)

The de Broglie-Bohm approach permits to assign well defined trajectories to particles that obey the Schroedinger equation. We extend this approach to electron pairs in a superconductor. In the stationary regime this extension is completely natural; in the general case additional postulates are required. This approach gives enlightening views for the absence of Hall effect in the stationary regime and for the formation of permanent currents.

Berger, Jorge

2004-06-01

399

Heuristic derivation of continuum kinetic equations from microscopic dynamics Kwan-tai Leung*

a Fokker-Planck equation for the fluctuating part, from which the noise term of the asso- ciated Langevin of a mean-field-type, decoupled approximation of the master equation followed by the ``naive'' continuum of the master equation in inverse powers of the volume of the coarse-graining block. While the leading order

Leung, Kwan-tai

400

Photons and Gravitons in Perturbation Theory: Derivation of Maxwell's and Einstein's Equations

The S matrix for photon and graviton processes is studied in perturbation theory, under the restriction that the only creation and annihilation operators for massless particles of spin j allowed in the interaction are those for the physical states with helicity +\\/-j. The most general covariant fields that can be constructed from such operators cannot represent real photon and graviton

Steven Weinberg

1965-01-01

401

On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B

Ever since E.Cartan in the 1920s enriched the geometric framework of general relativity (GR) by introducing a {\\it torsion} of spacetime, the question arose whether one could find a measurement technique for detecting the presence of a torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with the precession of the Moon and the Mercury and extend later their considerations to the Lageos satellite.--- A consistent theory of gravity with torsion emerged during the early 1960's as gauge theory of the Poincar\\'e group. This Poincar\\'e gauge theory of gravity incorporates as simplest viable cases the Einstein-Cartan(-Sciama-Kibble) theory (EC), the teleparallel equivalent GR|| of GR, and GR itself. So far, PG and, in particular, the existence of torsion have {\\it not} been experimentally confirmed. However, PG is to be considered as the standard theory of gravity with torsion because of its very convincing gauge structure.--- Since the early 1970s up to today, different groups have shown more or less independently that torsion couples only to the {\\it elementary particle spin} and under no circumstances to the orbital angular momentum of test particles. This is established knowledge and we reconfirm this conclusion by discussing the energy-momentum law of PG, which has same form for all versions of PG. Therefore, we conclude that, unfortunately, the investigations of Mao et al. and March et al. do not yield any information on torsion.

Friedrich W. Hehl; Yuri N. Obukhov; Dirk Puetzfeld

2013-04-09

402

Characterization of sheared colloidal aggregation using Langevin dynamics simulation.

Aggregation of colloidal particles under shear is studied in model systems using a Langevin dynamics model with an improved interparticle interaction potential. In the absence of shear, aggregates that form are characterized by compact structure at small scales and ramified structure at larger scales. This confirms the structural crossover mechanism previously suggested by Sorensen and coworkers, that colloidal aggregation occurs due to monomer addition at small scales and due to cluster-cluster aggregation at large scales. The fractal dimension of nonsheared aggregates is scale-dependent. Smaller aggregates have a higher fractal dimension than larger ones, but the radius of gyration where this crossover occurs is independent of potential well depth for sufficiently deep wells. When these aggregates are subjected to shear they become anisotropic and form extended cigar-like structures. The size of sheared anisotropic aggregates in the direction perpendicular to the shear flow is limited by shear-induced breakage because the shear force dominates interparticle attraction for sufficiently large aggregates. Anisotropic aggregates are not completely characterized by a single radius of gyration, but rather by an inertia ellipsoid. Consequently the fractal dimension is no longer an adequate metric to properly characterize them, and to identify changes in their structure from their nonsheared isotropic counterparts. We introduce a new compactness-anisotropy analysis that characterizes the structure of anisotropic aggregates and allows us to distinguish between aggregates from sheared and nonsheared systems. Finally, using the ratio of interparticle force to the shear force f_{pot,sh} we are able to characterize different outcomes of sheared aggregation as a function of dimensionless well depth and Péclet number. PMID:25019781

Markutsya, Sergiy; Fox, Rodney O; Subramaniam, Shankar

2014-06-01

403

Characterization of sheared colloidal aggregation using Langevin dynamics simulation

NASA Astrophysics Data System (ADS)

Aggregation of colloidal particles under shear is studied in model systems using a Langevin dynamics model with an improved interparticle interaction potential. In the absence of shear, aggregates that form are characterized by compact structure at small scales and ramified structure at larger scales. This confirms the structural crossover mechanism previously suggested by Sorensen and coworkers, that colloidal aggregation occurs due to monomer addition at small scales and due to cluster-cluster aggregation at large scales. The fractal dimension of nonsheared aggregates is scale-dependent. Smaller aggregates have a higher fractal dimension than larger ones, but the radius of gyration where this crossover occurs is independent of potential well depth for sufficiently deep wells. When these aggregates are subjected to shear they become anisotropic and form extended cigar-like structures. The size of sheared anisotropic aggregates in the direction perpendicular to the shear flow is limited by shear-induced breakage because the shear force dominates interparticle attraction for sufficiently large aggregates. Anisotropic aggregates are not completely characterized by a single radius of gyration, but rather by an inertia ellipsoid. Consequently the fractal dimension is no longer an adequate metric to properly characterize them, and to identify changes in their structure from their nonsheared isotropic counterparts. We introduce a new compactness-anisotropy analysis that characterizes the structure of anisotropic aggregates and allows us to distinguish between aggregates from sheared and nonsheared systems. Finally, using the ratio of interparticle force to the shear force fpot ,sh we are able to characterize different outcomes of sheared aggregation as a function of dimensionless well depth and Péclet number.

Markutsya, Sergiy; Fox, Rodney O.; Subramaniam, Shankar

2014-06-01

404

Classical irregular block, N=2 pure gauge theory and Mathieu equation

Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of a...

Piatek, Marcin

2014-01-01

405

Probing the finite density equation of state of QCD via resummed perturbation theory

In this Ph.D. thesis, the primary goal is to present a recent investigation of the finite density thermodynamics of hot and dense quark-gluon plasma. As we are interested in a temperature regime, in which naive perturbation theory is known to lose its predictive power, we clearly need to use a refined approach. To this end, we adopt a resummed perturbation theory point of view and employ two different frameworks. We first use hard-thermal-loop perturbation theory (HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical potentials, and next, inspired by dimensional reduction, resum the known four-loop weak coupling expansion for the quantity. We present and analyze our findings for various cumulants of conserved charges. This provides us with information, through correlations and fluctuations, on the degrees of freedom effectively present in the quark-gluon plasma right above the deconfinement transition. Moreover, we compare our results with state-of-the-art lattice Monte Carlo simulati...

Mogliacci, Sylvain

2014-01-01

406

Time-optimal path planning in dynamic flows using level set equations: theory and schemes

NASA Astrophysics Data System (ADS)

We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.

Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.

2014-09-01

407

Time-optimal path planning in dynamic flows using level set equations: theory and schemes

NASA Astrophysics Data System (ADS)

We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.

Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.

2014-10-01

408

Probing the finite density equation of state of QCD via resummed perturbation theory

In this Ph.D. thesis, the primary goal is to present a recent investigation of the finite density thermodynamics of hot and dense quark-gluon plasma. As we are interested in a temperature regime, in which naive perturbation theory is known to lose its predictive power, we clearly need to use a refined approach. To this end, we adopt a resummed perturbation theory point of view and employ two different frameworks. We first use hard-thermal-loop perturbation theory (HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical potentials, and next, inspired by dimensional reduction, resum the known four-loop weak coupling expansion for the quantity. We present and analyze our findings for various cumulants of conserved charges. This provides us with information, through correlations and fluctuations, on the degrees of freedom effectively present in the quark-gluon plasma right above the deconfinement transition. Moreover, we compare our results with state-of-the-art lattice Monte Carlo simulations as well as with a recent three-loop mass truncated HTLpt calculation. We obtain very good agreement between the two different perturbative schemes, as well as between them and lattice data, down to surprisingly low temperatures right above the phase transition. We also quantitatively test the convergence of an approximation, which is used in higher order loop calculations in HTLpt. This method based on expansions in mass parameters, is unavoidable beyond leading order, thus motivating our investigation. We find the ensuing convergence to be very fast, validating its use in higher order computations.

Sylvain Mogliacci

2014-07-08

409

NASA Astrophysics Data System (ADS)

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied.

Urbic, T.; Holovko, M. F.

2011-10-01

410

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes-Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied. PMID:21992334

Urbic, T; Holovko, M F

2011-10-01

411

Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes–Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied. PMID:21992334

Urbic, T.; Holovko, M. F.

2011-01-01

412

The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory

Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : F(X˜)=D˜, where F(X˜)=A˜X˜2+B˜X˜+C˜. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find ? and ? as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826

Allahviranloo, T.; Gerami Moazam, L.

2014-01-01

413

The solution of fully fuzzy quadratic equation based on optimization theory.

Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE): F(X)=D, where F(X)-AX2+BX+C. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find ? and ? as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826

Allahviranloo, T; Gerami Moazam, L

2014-01-01

414

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications

NASA Technical Reports Server (NTRS)

A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.

Rai, M. M.

1986-01-01

415

The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory

NASA Astrophysics Data System (ADS)

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.

Novello, M.; Bittencourt, E.; Salim, J. M.

2014-08-01

416

We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and QM/MM methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into conse- quent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce signicantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through com- putation of water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.

Chuev, Gennady N.; Valiev, Marat; Fedotova, Marina V.

2012-04-10

417

We present a method of DPD simulation based on a coarse-grained effective pair potential obtained from the DRISM-KH molecular theory of solvation. The theory is first used to calculate the radial distribution functions of all-atom solute monomers in all-atom solvent and then to invert them into an effective pair potential between coarse-grained beads such that their fluid without solvent accounts for molecular specificities and solvation effects in the all-atom system. Bonded interactions are sampled in relatively short MD of the all-atom system and modeled with best multi-Gaussian fit. Replacing the heuristically defined conservative force potential in DPD, the coarse-grained effective pair potential is free from the artificial restrictions on potential range and shape and on equal volume of solute and solvent blobs inherent in standard DPD. The procedure is flexible in specifying coarse-grained mapping and enormously increases computational efficiency by eliminating solvent. The method is validated on polystyrene chains of various length in toluene at finite concentrations for room and polystyrene glass transition temperature. It yields the chain elastic properties and diffusion coefficient in good agreement with experiment and all-atom MD simulations. DPD with coarse-grained effective pair potential is capable of predicting both structural and dynamic properties of polymer solutions and soft matter with high accuracy and computational efficiency. PMID:25162701

Kobryn, Alexander E; Nikoli?, Dragan; Lyubimova, Olga; Gusarov, Sergey; Kovalenko, Andriy

2014-10-16

418

NASA Astrophysics Data System (ADS)

A two-dimensional (2D) crystal formed by a system of identical atoms with a pair centrosymmetric interaction between them is considered. It is assumed that in the initial state of equilibrium atoms occupy sites of a flat translation-symmetrical mesh, and the deformed state appears as a result of their displacements in the crystal plane (longitudinal deformations) and in the direction perpendicular to it (flexural deformations). It is shown that in the continuum description an infinitely thin anisotropic film with a finite mass density, which is capable of elastic longitudinal and flexural deformations, corresponds to this crystal. In the framework of classical mechanics we derive the basic relations and equations for atomic displacements and corresponding to them equations of the elasticity theory, describing both modes of deformation of a 2D crystal in the linear approximation as well as with taking into account anharmonicities. The explicit expressions which relates moduli of linear and nonlinear elasticity of the crystal with the potential of interatomic interaction and geometrical characteristics of the flat crystal lattice are obtained.

Natsik, V. D.; Smirnov, S. N.

2013-06-01

419

NASA Astrophysics Data System (ADS)

If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient ?± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally ?±. Comparison with experimental data for ?± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ? 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy.

Slavchov, Radomir I.

2014-04-01

420

NASA Astrophysics Data System (ADS)

Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new e_cient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation. We report at least a 25-fold improvement of performance compared to explicit decomposition (such as sparse LU) of the matrix inverse. We also report that scaling relative to matrix sizes, of the low-rank correction method on the one hand and domain decomposition methods on the other, are comparable.

Carrier, Pierre; Tang, Jok M.; Saad, Yousef; Freericks, James K.

421

NASA Astrophysics Data System (ADS)

In soft collinear effective theory (SCET) the interaction between high energy quarks moving in opposite directions involving momentum transfer much smaller than the center-of-mass energy is described by the Glauber interaction operator which has two-dimensional Coulomb-like behavior. Here, we determine this n-nbar collinear Glauber interaction operator and consider its renormalization properties at one loop. At this order a rapidity divergence appears which gives rise to an infrared divergent (IR) rapidity anomalous dimension commonly called the gluon Regge trajectory. We then go on to consider the forward quark scattering cross section in SCET. The emission of real soft gluons from the Glauber interaction gives rise to the Lipatov vertex. Squaring and adding the real and virtual amplitudes results in a cancelation of IR divergences, however the rapidity divergence remains. We introduce a rapidity counter-term to cancel the rapidity divergence, and derive a rapidity renormalization group equation which is the Balitsky-Fadin-Kuraev-Lipatov Equation. This connects Glauber interactions with the emergence of Regge behavior in SCET.

Fleming, Sean

2014-07-01

422

NASA Astrophysics Data System (ADS)

Post-Newtonian relativistic theory of astronomical reference frames based on Einstein's general theory of relativity was adopted by General Assembly of the International Astronomical Union in 2000. This theory is extended in the present paper by taking into account all relativistic effects caused by the presumable existence of a scalar field and parametrized by two parameters, ? and ?, of the parametrized post-Newtonian (PPN) formalism. We use a general class of the scalar-tensor (Brans-Dicke type) theories of gravitation to work out PPN concepts of global and local reference frames for an astronomical N-body system. The global reference frame is a standard PPN coordinate system. A local reference frame is constructed in the vicinity of a weakly self-gravitating body (a sub-system of the bodies) that is a member of the astronomical N-body system. Such local inertial frame is required for unambiguous derivation of the equations of motion of the body in the field of other members of the N-body system and for construction of adequate algorithms for data analysis of various gravitational experiments conducted in ground-based laboratories and/or on board of spacecrafts in the solar system. We assume that the bodies comprising the N-body system have weak gravitational field and move slowly. At the same time we do not impose any specific limitations on the distribution of density, velocity and the equation of state of the body's matter. Scalar-tensor equations of the gravitational field are solved by making use of the post-Newtonian approximations so that the metric tensor and the scalar field are obtained as functions of the global and local coordinates. A correspondence between the local and global coordinate frames is found by making use of asymptotic expansion matching technique. This technique allows us to find a class of the post-Newtonian coordinate transformations between the frames as well as equations of translational motion of the origin of the local frame along with the law of relativistic precession of its spatial axes. These transformations depend on the PPN parameters ? and ?, generalize general relativistic transformations of the IAU 2000 resolutions, and should be used in the data processing of the solar system gravitational experiments aimed to detect the presence of the scalar field. These PPN transformations are also applicable in the precise time-keeping metrology, celestial mechanics, astrometry, geodesy and navigation. We consider a multipolar post-Newtonian expansion of the gravitational and scalar fields and construct a set of internal and external gravitational multipoles depending on the parameters ? and ?. These PPN multipoles generalize the Thorne-Blanchet-Damour multipoles defined in harmonic coordinates of general theory of relativity. The PPN multipoles of the scalar-tensor theory of gravity are split in three classes—active, conformal, and scalar multipoles. Only two of them are algebraically independent and we chose to work with the conformal and active multipoles. We derive the laws of conservations of the multipole moments and show that they must be formulated in terms of the conformal multipoles. We focus then on the law of conservation of body's linear momentum which is defined as a time derivative of the conformal dipole moment of the body in the local coordinates. We prove that the local force violating the law of conservation of the body's linear momentum depends exclusively on the active multipole moments of the body along with a few other terms which depend on the internal structure of the body and are responsible for the violation of the strong principle of equivalence (the Nordtvedt effect). The PPN translational equations of motion of extended bodies in the global coordinate frame and with all gravitational multipoles taken into account are derived from the law of conservation of the body's linear momentum supplemented by the law of motion of the origin of the local frame derived from the matching procedure. We use these equations to analyze translational motion of shperical

Kopeikin, Sergei; Vlasov, Igor

2004-11-01

423

NASA Astrophysics Data System (ADS)

The stochastic derivation of Schrödinger's equation as describing collective motions on top of a superfluid covariant non-dissipative chaotic background (aehter) leads to a particular non-linear Schrödinger equation if one considers possible vacuum dissipative effects. In this Letter the existence of specific associated nodispersive soliton-like (particle-like) solutions piloted by the surrounding field is established. These solutions can be considered as the first known possible representations of de Broglie's double solution theory.

Vigier, Jean-Pierre

1989-02-01

424

Control Theory based Shape Design for the Incompressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

A design method for shape optimization in incompressible turbulent viscous flow has been developed and validated for inverse design. The gradient information is determined using a control theory based algorithm. With such an approach, the cost of computing the gradient is negligible. An additional adjoint system must be solved which requires the cost of a single steady state flow solution. Thus, this method has an enormous advantage over traditional finite-difference based algorithms. The method of artificial compressibility is utilized to solve both the flow and adjoint systems. An algebraic turbulence model is used to compute the eddy viscosity. The method is validated using several inverse wing design test cases. In each case, the program must modify the shape of the initial wing such that its pressure distribution matches that of the target wing. Results are shown for the inversion of both finite thickness wings as well as zero thickness wings which can be considered a model of yacht sails.

Cowles, G.; Martinelli, L.

2003-12-01

425

Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations

for the Atlantic thermohaline circulation; and bifurcation delay in the case of the Lorenz model for Rayleigh delay, doubleÂ well potential, firstÂexit time, scaling laws, Lorenz model, thermohaline circulation], or in models of the Atlantic thermohaline circulation [34, 30]. Noise may enable transitions between the two

Berglund, Nils

426

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 talpha for some alpha < 1 until the terminal relaxation time tau of the polymer. Beyond time tau the motion of the tagged monomer becomes diffusive. Classical examples of anomalous

Debabrata Panja

2010-01-01

427

NASA Astrophysics Data System (ADS)

Among scientific challenges in space science we find the understanding and the managing of relativity and acceleration's effects on space satellites. Due to the high number of satellite launch every year, the question of recycling addressed by several countries in the world. Some projects focus on the rejection of satellites out of the gravity field of the earth for avoiding a sudden fall in a populated area, but other environmentally friendly projects involve trying to get these satellites for recycling purposes. We will focus on the second recycling point. The good knowledge of these effects can allow the control of all satellites orbit during their lifetime and also after. A mathematical analysis together with the optimal control point of view are here used. We will develop an existence method based on a variational formulation. Then we will use the optimal control theory for the trajectory optimal control under pollution (recycling satellites). Finally, we will focus on the possible generalization of the method with different fixed parameters.

Gobinddass, Marie-Line; Omrane, Abdennebi

428

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier-Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager-Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show, that by numerically minimizing an appropriate action functional, in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum a...

Laurie, Jason

2014-01-01

429

This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated fractional Langevin equation. Path integral representation of the process is constructed and the basic quantities are evaluated.

C. H. Eab; S. C. Lim

2014-05-04

430

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells. PMID:20649359

Grima, R

2010-07-21

431

NASA Astrophysics Data System (ADS)

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site-site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions necessary for the generic van der Waals equation of state, which in turn makes it possible to calculate the self-diffusion coefficient on the basis of the modified free volume theory of diffusion. A random distribution is assumed for minimum free volumes for monomers along the chain in the melt. More specifically, a stretched exponential is taken for the distribution function. If the exponents of the distribution function for minimum free volumes for monomers are chosen suitably for linear polymer melts of N monomers, the N dependence of the self-diffusion coefficient is N-1 for the small values of N, an exponent predicted by the Rouse theory, whereas in the range of 2.3?lnN?4.5 the N dependence smoothly crosses over to N-2, which is reminiscent of the exponent by the reptation theory. However, for lnN?4.5 the N dependence of the self-diffusion coefficient differs from N-2, but gives an N dependence, N(0theory is satisfactorily tested against experimental and simulation data on the temperature dependence of D for polyethylene and polystyrene melts.

Sabbagh, Haidar; Eu, Byung Chan

2010-06-01

432

Kinetic theory models involving the Fokker–Planck equation can be accurately discretized using a mesh support (finite elements, finite differences, finite volumes, spectral techniques, etc.). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function is related to a node that defines the associated degree of freedom.

A. Ammar; B. Mokdad; F. Chinesta; R. Keunings

2006-01-01

433

We derive a method of obtaining approximate numerical solution of linear variable-coefficient partial differential equations (PDEs) with two independent variables from Kida's optimum approximation theory. It is shown that a certain generalized filter bank implements linear PDEs. By applying generalized discrete orthogonality of Kida's optimum approximation to this filter bank, we prove that our approximate solution satisfies a given linear

Y. Kida; T. Kida

2008-01-01

434

The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.

Kawamura, Hiroyuki [Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX (United Kingdom); Tanaka, Kazuhiro [Department of Physics, Juntendo University, Inba-gun, Chiba 270-1695 (Japan)

2010-06-01

435

Theory for non-equilibrium statistical mechanics.

This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life. PMID:16883388

Attard, Phil

2006-08-21

436

Protein Folding Simulations Combining Self-Guided Langevin Dynamics and Temperature-Based Replica

Protein Folding Simulations Combining Self-Guided Langevin Dynamics and Temperature-Based Replica in this area is the development of algorithms that accelerate conformational sampling. Temperature-based replica exchange (ReX) is a commonly used protocol whereby simulations at several temperatures

437

NASA Astrophysics Data System (ADS)

We present an analytical integral equation theory for polyelectrolyte solutions modeled as linear freely-jointed tangent hard-sphere polyanionic chains and cationic hard-sphere monomeric counterions embedded in a continuum dielectric medium. Each hard-sphere segment on the polyelectrolyte chain and hard-sphere counterion are univalent with unit diameters. The model was formulated in the context of the multi density Ornstein-Zernike integral equation theory within the mean spherical approximation. Analytical solutions for the model were obtained using the ideal chain approximation. The contact values of the radial distribution functions, internal energy, Helmholtz energy, osmotic pressure, and activity coefficient of the system were derived as a function of chain length, density, and Bjerrum length via the energy route. Predictions from the theory were compared with computer simulation data reported in the literature, and very good agreement was found.

von Solms, N.; Chiew, Y. C.

1999-09-01

438

NASA Astrophysics Data System (ADS)

We have developed a novel, meshless, and fully parallelizable, floating random-walk (RW) algorithm for solving the time-harmonic Maxwell-Helmholtz equation. Traditional RW algorithms, in this application area, are constrained to materially homogeneous problem domains. This is because of the difficulty of obtaining a mathematically convenient, volumetric Green's function for domains of arbitrary material heterogeneity. In this work, the major challenge of deriving a useful expression for the volumetric, heterogeneous Green's function has been resolved by means of iterative perturbation theory. One of the possible applications we are currently investigating with this algorithm is the electromagnetic analysis of complex IC-interconnect structures. Therefore, we have initially tested our algorithm in describing skin-effect within a 2D circular conductor cross section. We report good agreement between analytical and RW skin-effect solutions, supporting our theoretical formulation. In closing, we note that this algorithm can be extended to nonlinear problems, thus leading to important applications in other areas of science and engineering.

Chatterjee, Kausik; Le Coz, Yannick

2002-10-01

439

We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair interaction forms comprising a hard core and a combination of two shoulders and/or wells. Since model pair potentials like these are of interest for discretized or coarse-grained representations of effective interactions in complex fluids (e.g., for computationally intensive inverse optimization problems), we focus here on assessing how accurately their properties can be predicted by analytical or simple numerical closures including Percus-Yevick, hypernetted chain, reference hypernetted chain, first-order mean spherical approximation, and a modified first-order mean spherical approximation. To make quantitative comparisons between the predicted and simulated radial distribution functions, we introduce a cumulative structural error metric. For equilibrium fluid state points of these models, we find that the reference hypernetted chain closure is the most accurate of the tested approximations as characterized by this metric or related thermodynamic quantities.

Kyle B. Hollingshead; Thomas M. Truskett

2014-07-30

440

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D2O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.

Chen, Wei-Ren [ORNL; Do, Changwoo [ORNL; Hong, Kunlun [ORNL; Liu, Yun [National Institute of Standards and Technology (NIST); Porcar, L. [National Institute of Standards and Technology (NIST); Shew, Chwen-Yang [City University of New York (CUNY); Smith, Greg [ORNL

2012-01-01

441

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. PMID:23862995

Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui

2013-07-01

442

Theory of physical aging in polymer glasses

NASA Astrophysics Data System (ADS)

A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the ? relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.

Chen, Kang; Schweizer, Kenneth S.

2008-09-01

443

Theory of physical aging in polymer glasses.

A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented. PMID:18851057

Chen, Kang; Schweizer, Kenneth S

2008-09-01

444

NASA Astrophysics Data System (ADS)

The acceleration of gravity, g, is calculated at the same point on the earth's surface for the cases of the equator at midday and at midnight. The calculations are for an ellipsoid of revolution of the earth around an axis projected from the plane of the equator. Values of g are calculated in terms of the Newton and electrothermodynamical theories, for the earth, sun, and the centrifugal rotation and revolution of the earth. The results are presented in tabular form for the midday and midnight cases, and calculations are conducted to verify the total differences between the two points, for the two theoretical frameworks, by means of a pendulum and a ballistic gravimeter.

Adamuti, I. A.

1982-04-01

445

Loop equation in D=4, N=4 super Yang-Mills theory and string field equation on AdS{sub 5}xS{sup 5}

We consider the loop equation in four-dimensional N=4 SYM, which is a functional differential equation for the Wilson loop W(C) and expresses the propagation and the interaction of the string C. Our W(C) consists of the scalar and the gaugino fields as well as the gauge field. The loop C is specified by six bosonic coordinates y{sup i}(s) and two fermionic coordinates {zeta}(s) and {eta}(s) besides the four-dimensional spacetime coordinates x{sup {mu}}(s). We have successfully determined, to quadratic order in {zeta} and {eta}, the parameters in W(C) and the loop differential operator so that the equation of motion of SYM can be correctly reproduced to give the nonlinear term of W(C). We extract the most singular and linear part of our loop equation and compare it with the Hamiltonian constraint of the string propagating on AdS{sub 5}xS{sup 5} background.

Hata, Hiroyuki; Miwa, Akitsugu [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)

2006-02-15

446

We propose the method of spatial decomposition analysis (SDA) based on three-dimensional integral equation (3D-IE) theory of molecular liquids to study and decompose the thermodynamics of proteins in solution into atomic level contributions. The 3D-IE theory maps the solvation thermodynamic properties, such as the solvation free energy and solvation entropy, onto the 3D space around the solute, including the excluded volume of the solute macromolecule, with the elementary volume contributions expressed in terms of the 3D total and direct correlation functions. The SDA thus breaks down the thermodynamic quantity into partial contributions of the solute fragments (functional groups or residues) by applying the proximity criterion to the 3D-IE mapping onto both the solvation shell outside the solute macromolecule and its excluded volume inside the van der Waals cores, the latter giving a major contribution to the solvation thermodynamics. This is distinct from the previous use of the proximity criterion applied to the 3D distribution functions in the solvation shell only. As SDA does not require perturbing the protein molecule to extract the contributions from the constituent residues, it can become an alternative to the computational "alanine scanning approach". For illustration, we apply SDA to four miniproteins composed of 10-28 amino acid residues (chignolin, CLN025, Trp-cage, and FSD-1) and decompose their solvation free energy into the partial contributions of each residue. The present results show that SDA is capable of detecting a change in the protein thermodynamics due to mutations and local conformational changes. Furthermore, the SDA exhibits a convincing consistency with the experimental values of the whole-residue transfer free energies from water to 1-octanol. Thus, the SDA provides a meaningful decomposition of the protein thermodynamics which can bear a comparison with experimental measurements and therefore can serve as a valuable sensitive tool to analyze the protein thermodynamics at the atomistic resolution level. We envision that the SDA may also serve as a tool for quantitative structure-activity relationships (QSAR) to correlate and predict various solute properties in a fragment-based manner. PMID:21166382

Yamazaki, Takeshi; Kovalenko, Andriy

2011-01-20

447

Bistable systems: Master equation versus Fokker-Planck modeling

Relaxation and fluctuations of nonlinear macroscopic systems, which are frequently described by means of Fokker-Planck or Langevin equations, are studied on the basis of a master equation. The problem of an approximate Fokker-Planck modeling of the dynamics is investigated. A new Fokker-Planck modeling is presented which is superior to the conventional method based on the truncated Kramers-Moyal expansion. The new

Peter Hanggi; Hermann Grabert; Peter Talkner; Harry Thomas

1984-01-01

448

NASA Astrophysics Data System (ADS)

Electrostrictive polymers, as an important category of electroactive polymers, are known to have non-linear response in terms of actuation that strongly affects their dynamic performance and limits their applications. Very few models exist in the literature, and even fewer are capable of making reliable predictions under an electric field. In this paper, electrostrictive strain of dipolar polymeric systems is discussed through constitutive equations derived from the Boltzmann statistics and Debye/Langevin formalism. Macroscopic polarization is expressed as a function of the inherent microscopic parameters of the dielectric material. Electrostrictive strain, polarization and dielectric permittivity are described well by the model in terms of dipole moment and saturation of dipole orientation, allowing the physical definition of the electrostrictive coefficient Q. Maxwell forces generated by dipolar orientation inducing surface charges are also used to explain the electrostrictive strain of polymers. The assessment of this analysis through a comparison with experimental data shows good agreement between reported values and theoretical predictions. These materials are generally used in low-frequency applications, thus the interfacial phenomena that are responsible for low saturation electric field should not be omitted so as not to underestimate or overestimate the low electric field response of the electrostrictive strain.

Capsal, Jean-Fabien; Lallart, Mickaël; Galineau, Jeremy; Cottinet, Pierre-Jean; Sebald, Gaël; Guyomar, Daniel

2012-05-01

449

NASA Astrophysics Data System (ADS)

We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of ?s. We have developed two variants of hyperonic EoS tables: in the np?phi case the repulsive hyperon-hyperon interaction mediated by the strange phi meson is taken into account, and in the np? case it is not. The EoS tables for the two cases encompass a wide range of densities (10-12 to ~1 fm-3), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of ? hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, ?-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M ? maximum mass neutron star for the np?phi case, whereas that for the np? case is 1.95 M ?. The np?phi EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M ? neutron stars.

Banik, Sarmistha; Hempel, Matthias; Bandyopadhyay, Debades

2014-10-01

450

Wave Fronts for Hamilton-Jacobi Equations:¶The General Theory for Riemann Solutions in $\\\\calR^n$

The Hamilton-Jacobi equation describes the dynamics of a hypersurface in Rn. This equation isa nonlinear conservation law and thus has discontinuous solutions. The dependent variable is asurface gradient and the discontinuity is a surface cusp. Here we investigate the intersection of cusphypersurfaces. These intersections define (n \\\\Gamma 1)-dimensional Riemann problems for the HamiltonJacobiequation. We propose the class of Hamilton-Jacobi equations

J. Glimm; H. C. Kranzer; D. Tan; F. M. Tangerman

1997-01-01

451

In previous paper we have shown that there is a special kind of nonlinear electrodynamics - Curvilinear Wave Electrodynamics (CWED), whose equations are mathematically equivalent to the equations of quantum electrodynamics. The purpose of the present paper is to show that in framework of CWED the known solutions of the nonlinear electromagnetic equations can be considered as the approximate solutions of the nonlinear equation of CWED. Another purpose of this paper is to show, that these solutions allow the description of electron-like particle of CWED as point of non-point particles, depending on mathematical approach.

Alexander G. Kyriakos

2005-03-09

452

National Technical Information Service (NTIS)

A phenomenological theory for contracting muscle based on irreversible thermodynamics and the sliding filament theory is developed. The individual cross bridges, considered as submits, are viewed as linear energy converters with constant transport coeffic...

W. J. Bornhorst, J. E. Minardi

1969-01-01

453

Dynamic density functional theory with hydrodynamic interactions and fluctuations.

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions. PMID:24952531

Donev, Aleksandar; Vanden-Eijnden, Eric

2014-06-21

454

Dynamic density functional theory with hydrodynamic interactions and fluctuations

NASA Astrophysics Data System (ADS)

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

Donev, Aleksandar; Vanden-Eijnden, Eric

2014-06-01

455

Post-Newtonian relativistic theory of astronomical reference frames based on Einstein's general theory of relativity was adopted by General Assembly of the International Astronomical Union in 2000. This theory is extended in the present paper by taking into account all relativistic effects caused by the presumable existence of a scalar field and parametrized by two parameters, ? and ?, of the

Sergei Kopeikin; Igor Vlasov

2004-01-01

456

Dynamics of density fluctuations in a non-Markovian Boltzmann- Langevin model

In the course of the past few years, the nuclear Boltzmann-Langevin (BL)model has emerged as a promising microscopic model for nuclear dynamics at intermediate energies. The BL model goes beyond the much employed Boltzmann-Uehling-Uhlenbeck (BUU) model, and hence it provides a basis for describing dynamics of density fluctuations and addressing processes exhibiting spontaneous symmetry breaking and catastrophic transformations in nuclear

Ayik

1996-01-01

457

The influence of piezoceramic stack location on nonlinear behavior of Langevin transducers.

Power ultrasonic applications such as cutting, welding, and sonochemistry often use Langevin transducers to generate power ultrasound. Traditionally, it has been proposed that the piezoceramic stack of a Langevin transducer should be located in the nodal plane of the longitudinal mode of vibration, ensuring that the piezoceramic elements are positioned under a uniform stress during transducer operation, maximizing element efficiency and minimizing piezoceramic aging. However, this general design rule is often partially broken during the design phase if features such as a support flange or multiple piezoceramic stacks are incorporated into the transducer architecture. Meanwhile, it has also been well documented in the literature that power ultrasonic devices driven at high excitation levels exhibit nonlinear behaviors similar to those observed in Duffing-type systems, such as resonant frequency shifts, the jump phenomenon, and hysteretic regions. This study investigates three Langevin transducers with different piezoceramic stack locations by characterizing their linear and nonlinear vibrational responses to understand how the stack location influences nonlinear behavior. PMID:25004475

Mathieson, Andrew; Cardoni, Andrea; Cerisola, Niccolò; Lucas, Margaret

2013-06-01

458

Langevin machine: a neural network based on stochastically justifiable sigmoidal function.

In neural networks the activation process controls the output as a nonlinear function of the input; and, this output remains bounded between limits as decided by a logistic function known as the sigmoid (S-shaped). Presently, by applying the considerations of Maxwell-Boltzmann statistics, the Langevin function is shown as the appropriate and justifiable sigmoid (instead of the conventional hyperbolic tangent function) to depict the bipolar nonlinear logic-operation enunciated by the collective stochastical response of artificial neurons under activation. That is, the graded response of a large network of 'neurons' such as Hopfield's can be stochastically justified via the proposed model. The model is consistent with the established link between the Hopfield model and the statistical mechanics. The Langevin function (in lieu of conventional hyperbolic tangent and/or exponential sigmoids) in determining nonlinear decision boundaries, in characterizing the neural networks by the Langevin machine versus the Boltzmann machine, in sharpening and annealing schedules and in the optimization of nonlinear detector performance are discussed. PMID:1742370

Neelakanta, P S; Sudhakar, R; DeGroff, D

1991-01-01

459

is the multitude of deep connections of soliton equations with di#11;erent branches of mathematics. They range from as the Harry Dym (HD) equation q t = 2(1= p (1 + q)) xxx (1.1) or equivalently #26; t = #26; 3 #26; xxx (1

Zubelli, Jorge Passamani

460

NSDL National Science Digital Library

This activity will help the students understand that science theories change in the face of new evidence, but those changes can be slow in coming. Students will observe how scientific theories change over time, Be introduced to the sophistication of the geocentric model and the time it took to change the theory underpinning the heliocentric model, Compare the heliocentric model to the geocentric model.

2010-01-01

461

NASA Astrophysics Data System (ADS)

We perform a fully relativistic analysis of odd-type linear perturbations around a static and spherically symmetric solution in the most general scalar-tensor theory with second-order field equations in four-dimensional spacetime. It is shown that, as in the case of general relativity, the quadratic action for the perturbations reduces to the one having only a single dynamical variable, from which concise formulas for no-ghost and no-gradient instability conditions are derived. Our result is applicable to all the theories of gravity with an extra scalar degree of freedom. We demonstrate how the generic formulas can be applied to some particular examples such as the Brans-Dicke theory, f(R) models, and Galileon gravity.

Kobayashi, Tsutomu; Motohashi, Hayato; Suyama, Teruaki

2012-04-01

462

A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.

Beklaryan, Leva A [Central Economics and Mathematics Institute, RAS, Moscow (Russian Federation)

2011-03-31

463

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Liao, David; Tlsty, Thea D.

2014-01-01

464

Results which have been recently obtained with the Boltzmann master equation and the FLUKA code in the analysis of heavy ion interactions at relative energies ranging from Coulomb barrier up to a few GeV/n are discussed.

Fasso, A.

2004-12-15

465

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely 'empirical' equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Liao, David; Tlsty, Thea D

2014-08-01