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1

Bödeker’s effective theory: From Langevin dynamics to Dyson-Schwinger equations

NASA Astrophysics Data System (ADS)

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|˜g2T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bödeker 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; Hernandez, Andres; Schmidt, Michael G.

2009-10-01

2

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (?=T) and rotational (?=R) current densities j_{lm}^{?}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, ?_{T} and ?_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters ? (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states. PMID:25493790

Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O

2014-11-01

3

NASA Astrophysics Data System (ADS)

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (? =T ) and rotational (? =R ) current densities jlm ?(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, ?T and ?R, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters ? (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Elizondo-Aguilera, L. F.; Zubieta Rico, P. F.; Ruiz-Estrada, H.; Alarcón-Waess, O.

2014-11-01

4

Langevin equations from time series

NASA Astrophysics Data System (ADS)

We discuss the link between the approach to obtain the drift and diffusion of one-dimensional Langevin equations from time series, and Pope and Ching’s relationship for stationary signals. The two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels. The analysis provides a useful indication for the correct application of Pope and Ching’s relationship to obtain stochastic differential equations from time series and shows its validity, in a generalized sense, for nondifferentiable processes originating from Langevin equations.

Racca, E.; Porporato, A.

2005-02-01

5

Localized solution of a simple nonlinear quantum Langevin equation

A simple nonlinear quantum Langevin equation is introduced as phenomenological equation for quantum brownian motion. Easy calculations yield a unique localized wave function in the stationary regime. The given example may encourage more general use of nonlinear quantum Langevin equations for damped quantum systems, e.g. in measurement theory, in heavy ion physics, etc.

L. Diósi

1988-01-01

6

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

7

NASA Astrophysics Data System (ADS)

Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ?(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t-?, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ?, and the chain length N. Interestingly, the exponent ? is robust to be 1/2 against the change of these parameters, although the friction kernel ?(t) shows nontrivial dependence on time. In addition, we find that the starting time of the power-law region t1 scales with ?-1, with ? = 4?2/?0 where ?0 is the zero-frequency friction which decreases rapidly with increasing bead mass. On the other hand, the ending time t2 is not sensitive to varying ? or ?0, but it increases with N rapidly before it reaches a constant for N larger than some threshold value. Our work may provide a unified strategy starting from the microscopic level to understand the anomalous subdiffusive behavior regarding large scale conformational change of polymers or proteins.

Li, Ping; Dong, Yunhong; Zhao, Nanrong; Hou, Zhonghuai

2014-04-01

8

Langevin equation path integral ground state.

We propose a Langevin equation path integral ground state (LePIGS) approach for the calculation of ground state (zero temperature) properties of molecular systems. The approach is based on a modification of the finite temperature path integral Langevin equation (PILE) method (J. Chem. Phys. 2010, 133, 124104) to the case of open Feynman paths. Such open paths are necessary for a ground state formulation. We illustrate the applicability of the method using model systems and the weakly bound water-parahydrogen dimer. We show that the method can lead to converged zero point energies and structural properties. PMID:23738885

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

2013-08-15

9

A generalized Langevin equation for dealing with nonadditive fluctuations

NASA Astrophysics Data System (ADS)

A suitable extension of the Mori memory-function formalism to the non-Hermitian case allows a "multiplicative" process to be described by a Langevin equation of non-Markoffian nature. This generalized Langevin equation is then shown to provide for the variable of interest the same autocorrelation function as the well-known theoretical approach developed by Kubo, the stochastic Liouville equation (SLE) theory. It is shown, furthermore, that the present approach does not disregard the influence of the variable of interest on the time evolution of its thermal bath. The stochastic process under study can also be described by a Fokker-Planck-like equation, which results in a Gaussian equilibrium distribution for the variable of interest. The main flaw of the SLE theory, that resulting in an uncorrect equilibrium distribution, is therefore completely eliminated.

Grigolini, Paolo

1982-02-01

10

Generalized nonlinear Langevin equation for a rotor

NASA Astrophysics Data System (ADS)

A pendulum (rotor) coupled to a bath of harmonic oscillators is set up as a model for the dynamics of strongly coupled systems. The oscillators can be eliminated from the equation of motion for the rotor, except for initial conditions. The resulting Langevin equation is exact. Numerical solutions are provided for the power spectra of velocity and angular correlation functions of the pendulum for a broad range of the strength of the coupling starting from a weak coupling (hindered rotor) to the strong-coupling (``free'' rotor) limit, using both the rotor equation of motion and the full molecular dynamics.

Kemeny, G.; Mahanti, S. D.; Gales, Joel M.

1986-03-01

11

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

12

Computing generalized Langevin equations and generalized Fokker–Planck equations

The Mori–Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker–Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori–Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems. PMID:19549838

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-01-01

13

Scaling of ballistic deposition from a Langevin equation

NASA Astrophysics Data System (ADS)

An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions.

Haselwandter, Christoph A.; Vvedensky, Dimitri D.

2006-04-01

14

Scaling of ballistic deposition from a Langevin equation.

An exact lattice Langevin equation is derived for the ballistic deposition model of surface growth. The continuum limit of this equation is dominated by the Kardar-Parisi-Zhang (KPZ) equation at all length and time scales. For a one-dimensional substrate the solution of the exact lattice Langevin equation yields the KPZ scaling exponents without any extrapolation. For a two-dimensional substrate the scaling exponents are different from those found from computer simulations. This discrepancy is discussed in relation to analytic approaches to the KPZ equation in higher dimensions. PMID:16711773

Haselwandter, Christoph A; Vvedensky, Dimitri D

2006-04-01

15

A path integral approach to the Langevin equation

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

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

2015-01-07

16

Dynamics of Langevin Simulation

This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite step-size algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo.

A. S. Kronfeld

1992-05-08

17

Langevin Theory of Anomalous Brownian Motion Made Simple

ERIC Educational Resources Information Center

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…

Tothova, Jana; Vasziova, Gabriela; Glod, Lukas; Lisy, Vladimir

2011-01-01

18

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

19

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

2014-08-01

20

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

21

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

22

Diffusion and memory effects for stochastic processes and fractional Langevin equations

NASA Astrophysics Data System (ADS)

We consider the diffusion processes defined by stochastic differential equations when the noise is correlated. A functional method based on the Dyson expansion for the evolution operator, associated to the stochastic continuity equation, is proposed to obtain the Fokker-Planck equation, after averaging over the stochastic process. In the white noise limit the standard result, corresponding to the Stratonovich interpretation of the non-linear Langevin equation, is recovered. When the noise is correlated the averaged operator series cannot be summed, unless a family of time-dependent operators commutes. In the case of a linear equation, the constraints are easily worked out. The process defined by a linear Langevin equation with additive noise is Gaussian and the probability density function of its fluctuating component satisfies a Fokker-Planck equation with a time-dependent diffusion coefficient. The same result holds for a linear Langevin equation with a fractional time derivative (defined according to Caputo, Elasticità e Dissipazione, Zanichelli, Bologna, 1969). In the generic linear or non-linear case approximate equations for small noise amplitude are obtained. For small correlation time the evolution equations further simplify in agreement with some previous alternative derivations. The results are illustrated by the linear oscillator with coloured noise and the fractional Wiener process, where the numerical simulation for the probability density and its moments is compared with the analytical solution.

Bazzani, Armando; Bassi, Gabriele; Turchetti, Giorgio

2003-06-01

23

Langevin equation for the extended Rayleigh model with an asymmetric bath

In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and\\/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions

Alexander V. Plyukhin; Jeremy Schofield

2004-01-01

24

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

25

Scaled Langevin equation for complex systems: New linear scaling relation for weight factor

A set of scaled Langevin equations is proposed to study a long time tail of correlation functions for two model systems (Type I and Type II). Each system is composed of elements which are grouped into clusters according to dynamical activations for external forces. The clusters in Type I are characterized by linear scaling rules in repetitive operations, whereas the

S. Fujita; S. S. Lee; J. Koyama

1997-01-01

26

Gallas, Maria Haase Â· Introduction: (i) The North Atlantic Oscillation (NAO). (ii) The Langevin equation, Springer 1983 #12;)()()( )(reference)()()( ,,1)},({ 0 000 tnXtnXnXtt tnXtnXnX NnnX tM t --+= --+= = l K t t tnNtnNnN nnN l K --+= = #12;( )2 refjoint )( ),( ),|,( ),( )( 1 ),,( :analysisError Np p

Harting, Jens

27

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

28

NASA Astrophysics Data System (ADS)

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.

Brett, Tobias; Galla, Tobias

2014-03-01

29

Variable time-stepping in the pathwise numerical solution of the chemical Langevin equation

NASA Astrophysics Data System (ADS)

Stochastic modeling is essential for an accurate description of the biochemical network dynamics at the level of a single cell. Biochemically reacting systems often evolve on multiple time-scales, thus their stochastic mathematical models manifest stiffness. Stochastic models which, in addition, are stiff and computationally very challenging, therefore the need for developing effective and accurate numerical methods for approximating their solution. An important stochastic model of well-stirred biochemical systems is the chemical Langevin Equation. The chemical Langevin equation is a system of stochastic differential equation with multidimensional non-commutative noise. This model is valid in the regime of large molecular populations, far from the thermodynamic limit. In this paper, we propose a variable time-stepping strategy for the numerical solution of a general chemical Langevin equation, which applies for any level of randomness in the system. Our variable stepsize method allows arbitrary values of the time-step. Numerical results on several models arising in applications show significant improvement in accuracy and efficiency of the proposed adaptive scheme over the existing methods, the strategies based on halving/doubling of the stepsize and the fixed step-size ones.

Ilie, Silvana

2012-12-01

30

Applications of the generalized Langevin equation: Towards a realistic description of the baths

NASA Astrophysics Data System (ADS)

The generalized Langevin equation (GLE) method, as developed previously [L. Stella et al., Phys. Rev. B 89, 134303 (2014), 10.1103/PhysRevB.89.134303], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalizes toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.

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

2015-01-01

31

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump {r_reversible} pump, Stokes {r_reversible} signal, and Raman coherence {r_reversible} idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K. [Department of Physics, Montana State University, Bozeman, Montana 59717, USA (United States); Department of Physics, University of Queensland, St. Lucia, Queensland 4072, (Australia); Directed Energy Solutions, 532 Fox Run Circle, Colorado Springs, Colorado 80921, USA (United States)

2003-07-01

32

A path-integral Langevin equation treatment of low-temperature doped helium clusters

NASA Astrophysics Data System (ADS)

We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.

Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas

2012-06-01

33

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

34

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

35

Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

NASA Astrophysics Data System (ADS)

abstract-type="normal"> A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard ``fluid'' one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

Kanekar, A.; Schekochihin, A. A.; Dorland, W.; Loureiro, N. F.

2015-01-01

36

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review

T. D. Frank

2008-01-01

37

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and

T. D. Frank

2008-01-01

38

Generalized Langevin Equation Description of Stochastic Oscillations of General Relativistic Disks

NASA Astrophysics Data System (ADS)

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and Kerr cases. The power spectral distribution of the luminosity is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.

Leung, Chun Sing; Mocanu, Gabriela; Harko, Tiberiu

2014-11-01

39

NASA Astrophysics Data System (ADS)

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela

2014-05-01

40

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.

Sandev, Trifce, E-mail: trifce.sandev@drs.gov.mk [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of)] [Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Metzler, Ralf, E-mail: rmetzler@uni-potsdam.de [Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm (Germany) [Institute for Physics and Astronomy, University of Potsdam, D-14776 Potsdam-Golm (Germany); Department of Physics, Tampere University of Technology, FI-33101 Tampere (Finland); Tomovski, Živorad, E-mail: tomovski@pmf.ukim.mk [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)] [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)

2014-02-15

41

NASA Astrophysics Data System (ADS)

We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.

Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad

2014-02-01

42

We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei (AGN) may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.

Tiberiu Harko; Chun Sing Leung; Gabriela Mocanu

2014-05-12

43

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

44

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

NASA Astrophysics Data System (ADS)

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.

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

2011-08-01

45

NASA Astrophysics Data System (ADS)

The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1+m2 Wiener processes, whereas the standard approach uses 2m1+m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch.

Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.

2010-04-01

46

We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells. PMID:24580195

Grebenkov, Denis S; Vahabi, Mahsa

2014-01-01

47

NASA Astrophysics Data System (ADS)

It is found that the mean square log-returns calculated from the high-frequency one-day moving average of US and Taiwan stocks with the time internal ? show ballistic behavior \\theta \\tau^{\\alpha_1} with the exponent \\alpha_1 \\approx 2 for small ? and show diffusion-like behavior D \\tau^{\\alpha_2} with the exponent \\alpha_2 \\approx 1 for large ?. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, ? and D can be considered, respectively, as the temperature-like and diffusivity-like kinetic parameters of the market, and they can be used to characterize the behavior of the market.

Ma, Wen-Jong; Wang, Shih-Chieh; Chen, Chi-Ning; Hu, Chin-Kun

2013-06-01

48

An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.

Kim, Min-Geun; Jang, Hong-Lae [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Cho, Seonho, E-mail: secho@snu.ac.kr [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)

2013-05-01

49

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

50

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

51

NASA Astrophysics Data System (ADS)

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.

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

2013-09-01

52

NASA Astrophysics Data System (ADS)

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? for some ? < 1 until the terminal relaxation time ? of the polymer. Beyond time ? the motion of the tagged monomer becomes diffusive. Classical 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 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.

Panja, Debabrata

2010-06-01

53

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

54

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

55

We utilize a multiscale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin equation for protein dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal-mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free-energy landscape of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with nuclear magnetic resonance relaxation experiments. Fundamental to this approach is the inclusion of internal dissipation, which is absent in any rigid-body hydrodynamical modeling scheme. PMID:25356856

Copperman, J; Guenza, M G

2014-11-20

56

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

57

NASA Astrophysics Data System (ADS)

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

Miller, Steven David

1999-10-01

58

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

59

Why the Langevin-Debye theory of molecular polarisation fails in gas phase

The classical polarization formula of Langevin, which holds in the solid\\/liquid state, does not satisfy many experimental facts in gas phase, especially in diluted gas mixtures. The new formulation of the molecular polarization in gas phase is obtained on phenomenological grounds analysing the motion that polar molecules undergo under an electric field. It is shown that the polarization amplitude in

M. Michelini

60

Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

NASA Astrophysics Data System (ADS)

Many analyses based on the time-dependent Ginzburg-Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken into account correctly. We use the fluctuation-dissipation theorem in order to establish the appropriate size of the Langevin terms, and thus ensure the required consistency. Fluctuations of the electromagnetic potential are essential, even when we evaluate quantities that do not directly depend on it. Our method can be cast in gauge-invariant form. We perform numerous tests, and all the results are in agreement with statistical mechanics. We apply our method to evaluate paraconductivity of a superconducting wire. The Aslamazov-Larkin result is recovered as a limiting situation. Our method is numerically stable and the nonlinear term is easily included. We attempt a comparison between our numerical results and the available experimental data. Within an appropriate range of currents, phase slips occur, but we found no evidence for thermally activated phase slips. We studied the behavior of a moderate constriction. A constriction pins and enhances the occurrence of phase slips.

Berger, Jorge

2007-05-01

61

Second-Order Langevin Equation in Quantized Hamilton Dynamics Eric M. HEATWOLE and Oleg V. PREZHDO

are then propagated using the Heisenberg equation of motion (EOM). In general, the use of the Heisenberg EOM results effects in molecular conductance.37,38) The QHD-2 EOM are simple, computationally inexpensive, and closely

62

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

63

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.

Stephen Pankavich; Zeina Shreif; Yinglong Miao; Peter Ortoleva

2010-03-08

64

NASA Astrophysics Data System (ADS)

The dynamics of fission of excited nuclei has been studied by solving four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. The projection of the total spin of the compound nucleus to the symmetry axis, K, was considered as the fourth dimension in Langevin dynamical calculations. The average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy have been calculated in a wide range of fissile parameter for compound nuclei 162Yb, 172Yb, 215Fr, 224Th, 248Cf, 260Rf and results compared with the experimental data. Calculations were performed with a constant dissipation coefficient of K, ?K (MeV zs)-1/2, and with a non-constant dissipation coefficient. Comparison of the theoretical results for the average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy with the experimental data showed that the results of four-dimensional Langevin equations with a non-constant dissipation coefficient are in better agreement with the experimental data. Furthermore, the difference between the results of two models for compound nuclei with low fissile parameter is low whereas, for heavy compound nuclei, is high.

Eslamizadeh, H.

2014-12-01

65

NASA Astrophysics Data System (ADS)

A new attempt of calculation for the total reaction cross sections (?R) has been carried out within the isospindependent Boltzmann-Langevin equation in the intermediate energy heavy-ion collision of isotopes of C. The ?R of both stable and exotic nuclei are reproduced rather well. The incident energy and isospin dependencies of ?R have been investigated. It is found that the isospin effect is comparatively remarkable at intermediate energy. It is also found that 15-18C are neutron skin nuclei but for 19C and 20C we cannot draw a conclusion whether they have halo structures.

Chen, Yu; Zhang, Feng-Shou; Su, Jun

2009-11-01

66

Equational Theories for Inductive Types

This paper provides characterisations of the equational theory of the per model of a typed lambda calculus with inductive types. The characterisation may be cast as a full abstraction result; in other words we show that the equations between terms valid in this model coincides with a certain syntactically defined equivalence relation. Along the way we give other characterisations of

Ralph Loader

1997-01-01

67

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

68

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

69

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

70

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

71

theory of partial differential equations a. zagaris Theory of Partial Differential Equations (155010) (Some) Prerequisites & (Numerous) Remarks antonios zagaris | university of twente Guidelines://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2006.) 1 #12;theory of partial differential equations a. zagaris

Al Hanbali, Ahmad

72

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

73

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

74

Scattering equations and string theory amplitudes

NASA Astrophysics Data System (ADS)

Scattering equations for tree-level amplitudes are viewed in the context of string theory. To this end we are led to define a new dual model whose amplitudes coincide with string theory in both the small and large ?' limit, computed algebraically on the surface of solutions to the scattering equations. Because it has support only on the scattering equations, it can be solved exactly, yielding a simple resummed model for ?' corrections to all orders. We use the same idea to generalize scattering equations to amplitudes with fermions and any mixture of scalars, gluons, and fermions. In all cases checked we find exact agreement with known results.

Bjerrum-Bohr, N. Emil J.; Damgaard, Poul Henrik; Tourkine, Piotr; Vanhove, Pierre

2014-11-01

75

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

76

Stochastic Langevin Model for Flow and Transport in Porous Media

A new stochastic Lagrangian model for fluid flow and transport in porous media is described. The fluid is represented by particles whose flow and dispersion in a continuous porous medium is governed by a Langevin equation. Changes in the properties of the fluid particles (e.g. the solute concentration) due to molecular diffusion is governed by the advection-diffusion equation. The separate treatment of advective and diffusive mixing in the stochastic model has an advantage over the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing leading to over-prediction of mixing induced effective reaction rates. The stochastic model predicts much lower reaction product concentrations in mixing induced reactions. In addition the dispersion theory predicts more stable fronts (with a higher effective fractal dimension) than the stochastic model during the growth of Rayleigh-Taylor instabilities.

Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.; Meakin, Paul

2008-07-25

77

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

78

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

79

On the Langevin approach to particle transport

NASA Astrophysics Data System (ADS)

In the Langevin description of Brownian motion, the action of the surrounding medium upon the Brownian particle is split up into a systematic friction force of Stokes type and a randomly fluctuating force, alternatively termed noise. That simple description accounts for several basic features of particle transport in a medium, making it attractive to teach at the undergraduate level, but its range of applicability is limited. The limitation is illustrated here by showing that the Langevin description fails to account realistically for the transport of a charged particle in a medium under crossed electric and magnetic fields and the ensuing Hall effect. That particular failure is rooted in the concept of the friction force rather than in the accompanying random force. It is then shown that the framework of kinetic theory offers a better account of the Hall effect. It is concluded that the Langevin description is nothing but an extension of Drude's transport model subsuming diffusion, and so it inherits basic limitations from that model. This paper thus describes the interrelationship of the Langevin approach, the Drude model and kinetic theory, in a specific transport problem of physical interest.

Bringuier, Eric

2006-03-01

80

Dynamical mean-field theory for correlated electrons by Dieter Vollhardt

by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time by Einstein in 1905 [2], the Brown- ian motion of a suspended particle is a consequence of the thermal motion]. Langevin's approach is more intuitive than Einstein's approach, and the result- ing "Langevin equation" has

Texas at Austin. University of

81

Dynamical systems theory for the Gardner equation

NASA Astrophysics Data System (ADS)

The Gardner equation ut+auux+bu2ux+?uxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=?(?), ? =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ? with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and ?. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].

Saha, Aparna; Talukdar, B.; Chatterjee, Supriya

2014-02-01

82

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

83

Langevin Dynamics of Heavy Quarks in 5D Holographic QCD models

I discuss the holographic approach to the Langevin equation describing the motion of a heavy quark propagating through the deconfined Quark-Gluon Plasma (QGP). The Langevin diffusion coefficients are directly related to the jet quenching parameter, which enters in the reconstruction of RHIC events involving heavy probes. After a brief review of the Langevin equation, I discuss the calculation of the Langevin coefficients in 5-dimensional holographic duals. Finally, I discuss the results for the jet quenching parameter in a phenomenological holographic QCD model.

Nitti, Francesco [Laboratoire APC, Universite Paris 7, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13 (France)

2011-05-23

84

Undular bore theory for the Gardner equation.

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. PMID:23031043

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

85

Fermionic covariant prolongation structure theory for supernonlinear evolution equation

NASA Astrophysics Data System (ADS)

We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schrödinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Bäcklund transformation.

Cheng, Ji-Peng; Wang, Shi-Kun; Wu, Ke; Zhao, Wei-Zhong

2010-09-01

86

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), 10.1063/1.3058436] 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

87

Combining Equational Theories Sharing NonCollapseFree Constructors

Combining Equational Theories Sharing NonÂCollapseÂFree Constructors Franz Baader 1 Cesare Tinelli, AhornstraÃ?e 55, 52074 Aachen, Germany. #12; i #12; Combining Equational Theories Sharing Non In a previous work, we describe a method to combine decision procedures for the word problem for theories

Baader, Franz

88

New applications of pseudoanalytic function theory to the Dirac equation

In the present work, we establish a simple relation between the Dirac equation with a scalar and an electromagnetic potential in a two-dimensional case and a pair of decoupled Vekua equations. In general, these Vekua equations are bicomplex. However, we show that the whole theory of pseudoanalytic functions without modifications can be applied to these equations under a certain nonrestrictive

Antonio Castañeda; Vladislav V. Kravchenko

2005-01-01

89

The Mechanism of Complex Langevin Simulations

We discuss conditions under which expectation values computed from a complex Langevin process $Z$ will converge to integral averages over a given complex valued weight function. The difficulties in proving a general result are pointed out. For complex valued polynomial actions, it is shown that for a process converging to a strongly stationary process one gets the correct answer for averages of polynomials if $c_{\\tau}(k) \\equiv E(e^{ikZ(\\tau)}) $ satisfies certain conditions. If these conditions are not satisfied, then the stochastic process is not necessarily described by a complex Fokker Planck equation. The result is illustrated with the exactly solvable complex frequency harmonic oscillator.

H. Gausterer; Sean Lee

1992-11-18

90

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

91

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

92

Theory and numerical analysis of Volterra functional equations

Theory and numerical analysis of Volterra functional equations (TU Chemnitz, 22-26 September 2008 to the situation in the numerical analysis of more general Volterra functional equations in which delays occur and integro- differential equations of Volterra type and their numerical analysis, focusing on collocation

Potts, Daniel

93

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

94

THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

95

Adaptive integral equation methods in transport theory

In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented.

Kelley, C.T. (North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics)

1992-12-01

96

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

97

Kinetic equation and clipping - two limits of wave turbulence theory

Different dynamics, described by kinetic equation and clipping method is shown as well as a role of approximate resonances in wave turbulence theory. Applications of clipping method are sketched for gravity-capillary and drift waves. Brief discussion of possible transition from continuous spectrum (= kinetic equation) to discrete spectrum (= clipping) is given at the end.

Elena Kartashova

2005-01-01

98

Wave Propagation Theory 2.1 The Wave Equation

perturbations is much smaller than the speed of sound. 2.1.1 The Nonlinear Wave Equation Retaining higher2 Wave Propagation Theory 2.1 The Wave Equation The wave equation in an ideal fluid can be derived.3) and for convenience we define the quantity c2 p S , (2.4) where c will turn out to be the speed of sound in an ideal

99

A general theory of Lie symmetries for fractional differential equations

A general theoretical approach for the determination of Lie symmetries of fractional order differential equations, with an arbitrary number of independent variables, is proposed. We prove a theorem for the existence of vector fields acting as infinitesimal generators of Lie groups of transformations which leave invariant a given equation. As an application of the theory, a symmetry reduction technique for a $(N+1)$-dimensional fractional equation is developed.

Rosario Antonio Leo; Gabriele Sicuro; Piergiulio Tempesta

2014-05-09

100

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

101

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

102

Combining Equational Theories Sharing NonCollapseFree Constructors

Combining Equational Theories Sharing NonÂCollapseÂFree Constructors Franz Baader 1# and Cesare the applicability of our combination method for decision procedures for the word problem to theories sharÂ ing nonÂcollapseÂfree constructors. This extension broadens the scope of the combination procedure considerably, for example

Baader, Franz

103

Langevin representation of laser heating in PIC simulations

An algorithm for inverse bremsstrahlung heating based on a Langevin equation, suitable for particle-in-cell (PIC) codes, is presented. We consider a quasi-neutral plasma with laser heating as described by inverse bremsstrahlung. This enables the inclusion of the heating without explicitly resolving the laser frequency and allows simulation of long time scale phenomena. Like and unlike particle collisions are included using

F. Detering; V. Yu. Bychenkov; W. Rozmus; R. Sydora; C. E. Capjack

2002-01-01

104

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

105

Generalized sensitivity theory for systems of coupled nonlinear equations

A general sensitivity theory is presented for treating problems characterized by systems of nonlinear equations with nonlinear responses. Frechet derivatives are used in both differential and variational approaches to derive appropriate adjoint equations and expressions for sensitivity functions. The two approaches are unified to from a complete operator viewpoint of sensitivity theory. Also presented is an alternative sensitivity formalism for systems of nonlinear matrix equations such as those arising from the application of numerical methods to many practical problems. This approach significantly enlarges the scope and versatility of sensitivity theory as it allows direct treatment of parameters which are purely of numerical methods origin. To demonstrate the usefulness and practical applications of both operator and matrix formalisms, a significantly nonlinear transient problem in fast reactor thermal-hydraulics is considered.

Cacuci, D.G.; Weber, C.F.; Oblow, E.M.; Marable, J.H.

1980-01-01

106

Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid

The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Ito discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor R{sub AA} and the elliptic flow v{sub 2} for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The R{sub AA} for electrons with large transverse momentum (p{sub T}>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.

Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi [Department of Physics, University of Tokyo, Tokyo 113-0033 (Japan)

2009-05-15

107

Covariant light front perturbation theory and three-particle equations

A covariant version of light front perturbation theory is obtained as a limit of the covariant time-ordered perturbation theory developed recently by the author. The graphical rules for the covariant light front perturbation theory are essentially the same as Weinberg's infinite momentum frame rules; however, they involve a redefinition of the original Weinberg variables. The new definitions guarantee that the contributions of individual diagrams to the S matrix are invariant. A set of manifestly invariant three-particle integral equations is derived. These equations are obtained from a model field theory which describes the interaction of a charged scalar particle psi with a neutral scalar particle phi according to the virtual process psiarrow-right-leftpsi+phi. The solutions of the integral equations lead to amplitudes for phi+psi..-->..phi+psi and phi+psi..-->..2phi+psi which satisfy two- and three-particle unitarity. The integral equations are free of the spurious singularity in s, the square of the invariant c.m. energy, which has been an undesirable feature of earlier relativistic three-particle equations. This singularity is known to be responsible for spurious bound state solutions.

Fuda, M.G.

1987-01-01

108

Quantization conditions and functional equations in ABJ(M) theories

The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories with consecutive ranks of gauge groups but the same Chern-Simons coupling.

Alba Grassi; Yasuyuki Hatsuda; Marcos Marino

2014-10-28

109

Stochastic Navier-Stokes equation and renormalization group theory

NASA Astrophysics Data System (ADS)

We present an application of a certain renormalization group (RNG) theory developed by Chen, Goldenfeld, and Oono to the stochastic two-dimensional Navier-Stokes equation with additive Gaussian noise and periodic boundary conditions. This article is a generalization of results of Moise and Temam which were for the deterministic equation. Because the classical RNG theory (e.g. in a famous work by Yakhot and Orszag) utilizes significantly on adding noise terms, our work could be another step towards a rigorous understanding of their method.

Blömker, Dirk; Gugg, Christoph; Maier-Paape, Stanislaus

2002-12-01

110

Semigroup theory and numerical approximation for equations in linear viscoelasticity

NASA Technical Reports Server (NTRS)

A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.

Fabiano, R. H.; Ito, K.

1990-01-01

111

Field Equations and Conservation Laws in the Nonsymmetric Gravitational Theory

The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived. Among these are the generalized Bianchi identities and the law of energy-momentum conservation. The Lagrangian density is expanded to second-order, and treated as an ``Einstein plus fields'' theory. From this, it is deduced that the energy is positive in the radiation zone.

J. Legare; J. W. Moffat

1994-12-02

112

Computationally sound implementations of equational theories against passive adversaries6

: cryptographic op- erations are modeled as algorithms manipulating bit-strings. Those models cover a large class the link between formal and cryptographic models for security protocols in the presence of passive for arbi- trary equational theories. We define a framework for comparing a cryptographic implementation

113

Computationally sound implementations of equational theories against passive adversaries$

: cryptographic op- erations are modeled as algorithms manipulating bit-strings. Those models cover a large class the link between formal and cryptographic models for security protocols in the presence of passive for arbi- trary equational theories. We define a framework for comparing a cryptographic implementation

Cortier, VÃ©ronique

114

Computationally sound implementations of equational theories against passive adversaries I

: cryptographic opÂ erations are modeled as algorithms manipulating bitÂstrings. Those models cover a large class study the link between formal and cryptographic models for security protocols in the presence of passive for arbiÂ trary equational theories. We define a framework for comparing a cryptographic implementation

115

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

116

Fractional Langevin model of memory in financial markets.

The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series. PMID:12443270

Picozzi, Sergio; West, Bruce J

2002-10-01

117

Cosmological post-Newtonian equations from nonlinear perturbation theory

We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.

Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Hwang, Jai-chan, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of)

2013-08-01

118

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 (J Math Biol, 56(6):765-792 2008). In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level—a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.

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

2015-01-01

119

On Complex Langevin Dynamics and the Evaluation of Observables

In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously established, extends this idea to cases where the action is complex-valued by complexifying the basic degrees of freedom, all observables and allowing the stochastic process to probe the complexified configuration space. We review the method for a previously studied one-dimensional toy model, the U(1) one link model. We confirm that complex Langevin dynamics only works for a certain range of parameters, misestimating observables otherwise. A curious effect is observed where all moments of the basic stochastic variable are misestimated, although these misestimated moments may be used to construct, by a Taylor series, other observables that are reproduced correctly. This suggests a subtle but not completely resolved relationship between the original complex integration measure and the higher-dimensional probability distribution in the complexified configuration space, generated by the complex Langevin process.

Amel Durakovic; Emil Cortes Andre; Anders Tranberg

2014-08-15

120

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

121

Constitutive equations from molecular network theories for polymer solutions

Summary In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by

A. S. Lodge

1968-01-01

122

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

123

Equation of state for polymer liquid crystals: Theory and experiment

NASA Astrophysics Data System (ADS)

The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entropic part of the free energy enhances the effective repulsive interactions between the chains. This configurational contribution goes as the fourth root of the direct interactions. Enhancement originates from the coupling between bending fluctuations and the compressibility of the nematic array normal to the average director. In the second part of the paper we use osmotic stress to measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl solutions. These measurements cover five orders of magnitude in DNA osmotic pressure. At high osmotic pressures the equation of state, dominated by exponentially decaying hydration repulsion, is independent of the ionic strength. At lower pressures the equation of state is dominated by fluctuation enhanced electrostatic double layer repulsion. The measured equation of state for DNA fits well with our theory for all salt concentrations. We are able to extract the strength of the direct electrostatic double layer repulsion. This is an alternative way of measuring effective charge densities along semiflexible polyelectrolytes.

Strey, H. H.; Parsegian, V. A.; Podgornik, R.

1999-01-01

124

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

125

Integral equation theory for counterion distribution in polyelectrolyte solutions

NASA Astrophysics Data System (ADS)

An integral equation theory is developed to explore the behavior of rigid and flexible polyelectolyte solutions with explicit counter ions. The theory makes predictions for the distribution of counterions around the polyion in addition to polyion-polyion correlation and polymer conformations. For rigid polyelectrolytes, the theory is to fit the scattering spectra of tobacco mosaic virus solutions. In dilute solutions, the effective charge decreases as concentration is increased. The results are consistent with the nature of TMV molecules as weak polyacids. For flexible polyelectrolytes, we have extended the previous work of one component thread model and Koyama chain model to this system. The counterion distribution is very sensitive to polyion concentration. Theoretical calculations are consistent with simulation results.

Shew, Chwen-Yang; Yethiraj, Arun

1998-03-01

126

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

127

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

128

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

129

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

130

Integrals and integral equations in linearized wing theory

NASA Technical Reports Server (NTRS)

The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed.

Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B

1951-01-01

131

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

132

Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

NASA Astrophysics Data System (ADS)

A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.

Ilgenfritz, Ernst-Michael

1986-12-01

133

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

NASA Astrophysics Data System (ADS)

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

Pi?tek, Marcin; Pietrykowski, Artur R.

2014-12-01

134

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

135

Comparison of complex Langevin and mean field methods applied to effective Polyakov line models

NASA Astrophysics Data System (ADS)

Effective Polyakov line models, derived from SU(3) gauge-matter systems at finite chemical potential, have a sign problem. In this article I solve two such models, derived from SU(3) gauge-Higgs and heavy quark theories by the relative weights method, over a range of chemical potentials where the sign problem is severe. Two values of the gauge-Higgs coupling are considered, corresponding to a heavier and a lighter scalar particle. Each model is solved via the complex Langevin method, following the approach of Aarts and James, and also by a mean field technique. It is shown that where the results of mean field and complex Langevin agree, they agree almost perfectly. Where the results of the two methods diverge, it is found that the complex Langevin evolution has a branch cut crossing problem, associated with a logarithm in the action, that was pointed out by Møllgaard and Splittorff.

Greensite, Jeff

2014-12-01

136

The Interface Between Theory and Data in Structural Equation Models

Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoretically based probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite, for representing general concepts. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling general relationships of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partially reduced form models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influences of suites of variables are often of interest.

Grace, James B.; Bollen, Kenneth A.

2006-01-01

137

Nuclear Density Functional Theory and the Equation of State

A nuclear density functional can be used to find the binding energy and shell structure of nuclei and the energy gap in superconducting nuclear matter. In this paper, we study the possible application of a nuclear density functional theory to nuclear astrophysics. From energy density functional theory, we can deduce the interaction between nucleons to find a rough estimate of the charge radius of the specific nuclei. Compared to the Finite-Range Thomas Fermi model, we include three-body forces, which might be important at densities several times that of nuclear matter density. We also add the momentum dependent interaction to take into account the effective mass of the nucleons. We study matter in the neutron star crust using the Wigner-Seitz cell method. By constructing the mass-radius relation of neutron stars and investigating lepton-rich nuclear matter in proto-neutron stars, we find that the density functional can be used to construct an equation of state of hot dense matter.

Yeunhwan Lim

2011-04-06

138

Multiscale Dynamics of Macromolecules Using Normal Mode Langevin

Proteins and other macromolecules have coupled dynamics over multiple time scales (from femtosecond to millisecond and beyond) that make resolving molecular dynamics challenging. We present an approach based on periodically decomposing the dynamics of a macromolecule into slow and fast modes based on a scalable coarse-grained normal mode analysis. A Langevin equation is used to propagate the slowest degrees of freedom while minimizing the nearly instantaneous degrees of freedom. We present numerical results showing that time steps of up to 1000 fs can be used, with real speedups of up to 200 times over plain molecular dynamics. We present results of successfully folding the Fip35 mutant of WW domain. PMID:19908376

Izaguirre, J. A.; Sweet, C. R.; Pande, V. S.

2014-01-01

139

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

140

On the Essential Role of Kinetic Theory in Numerical Methods for Fluid-Dynamic Equations

The essential role of kinetic theory in the numerical methods for the Navier-Stokes equations (compressible and incompressible) is discussed. The easy theory of characteristics for kinetic equations brings about drastic simplification of approximate Riemann solver employed in various shock-capturing schemes. The lattice Boltzmann method is shown to essentially solve an artificial compressibility PDE system. The asymptotic behavior of solution of

Taku Ohwada; Pietro Asinari

2008-01-01

141

Ordinary differential equations, transport theory and Sobolev spaces

Summary We obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions.

R. J. DiPerna; P. L. Lions

1989-01-01

142

Further studies in aesthetic field theory. II: Equations for e alphai

In a previous paper (Muraskin, 1973), we obtained a bounded particle in `aesthetic' field theory. The field equations there are implied by a set of equations for a system of basis vector variables, e alphai . In this paper, we propose a simpler set of field equations for e alphai . We find that a bounded particle solution to the

M. Muraskin; B. Ring

1973-01-01

143

The theory of relaxation oscillations for Hutchinson's equation

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

2011-06-30

144

Generalized gradient flow equation and its application to super Yang-Mills theory

NASA Astrophysics Data System (ADS)

We generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of the gradient flow equation. It can be shown that the super gauge symmetry is preserved in the gradient flow. Furthermore, choosing an appropriate modification term to damp the gauge degrees of freedom, we obtain a gradient flow equation which is closed within the Wess-Zumino gauge.

Kikuchi, Kengo; Onogi, Tetsuya

2014-11-01

145

Symmetries of generating functionals of Langevin processes with colored multiplicative noise

NASA Astrophysics Data System (ADS)

We present a comprehensive study of the symmetries of the generating functionals of generic Langevin processes with multiplicative colored noise. We treat both Martin-Siggia-Rose-Janssen-De Dominicis and supersymmetric formalisms. We summarize the relations between observables that they imply including fluctuation relations, fluctuation-dissipation theorems, and Schwinger-Dyson equations. Newtonian dynamics and their invariances follow in the vanishing friction limit.

Aron, Camille; Biroli, Giulio; Cugliandolo, Leticia F.

2010-11-01

146

An elastic fluid-saturated porous medium is modeled as a bundle of parallel cylindrical tubes aligned in a direction parallel to the fluid movement. The pore space is filled with viscous compressible liquid. A cell model and the theory of transient pipe flow are used to derive one-dimensional governing equations in such media. All macroscopic constants in these equations are defined

Jan A. Ko?odziej; Mariusz Kaczmarek

1992-01-01

147

Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation

The nonlinear Schr\\"{o}dinger-Helmholtz (SH) equation in $N$ space dimensions with $2\\sigma$ nonlinear power was proposed as a regularization of the classical nonlinear Schr\\"{o}dinger (NLS) equation. It was shown that the SH equation has a larger regime ($1\\le\\sigmaHelmholtz equation is viewed as a perturbed system of the classical NLS equation, we apply modulation theory to the classical critical case ($\\sigma=1,\\:N=2$) and show that the regularization prevents the formation of singularities of the NLS equation. Our theoretical results are supported by numerical simulations

Yanping Cao; Ziad H. Musslimani; Edriss S. Titi

2008-11-23

148

The source term of the field equation in the 5D STM theory of gravitation

NASA Astrophysics Data System (ADS)

The need is shown for a source term in the field equation of the Wesson 5D STM theory of gravity if it is required that the Wesson theory extend to the Einstein theory of general relativity when the rest-mass of a typical particle equals a constant. A possible form of the source term is proposed.

Ma, Guang-Wen

1991-07-01

149

The source term of the field equation in the 5D STM theory of gravitation.

NASA Astrophysics Data System (ADS)

There is a need of a source term (5)Tij in the field equation of the Wesson 5D STM theory of gravity if one requires that the Wesson theory goes over to the Einstein theory of general relativity when the rest-mass m of a typical particle equals to a constant. A possible form of (5)Tij is proposed.

Guang-Wen, Ma

1991-07-01

150

We show here the global, in time, regularity of the three dimensional viscous Camassa-Holm (Lagrangian Averaged Navier-Stokes-alpha) equations. We also provide estimates, in terms of the physical parameters of the equations, for the Hausdorff and fractal dimensions of their global attractor. In analogy with the Kolmogorov theory of turbulence, we define a small spatial scale, \\ell_{\\epsilon}, as the scale at which the balance occurs in the mean rates of nonlinear transport of energy and viscous dissipation of energy. Furthermore, we show that the number of degrees of freedom in the long-time behavior of the solutions to these equations is bounded from above by (L/\\ell_{epsilon})^3, where L is a typical large spatial scale (e.g., the size of the domain). This estimate suggests that the Landau-Lifshitz classical theory of turbulence is suitable for interpreting the solutions of the NS-alpha equations. Hence, one may consider these equations as a closure model for the Reynolds averaged Navier-Stokes equations (NSE). We study this approach, further, in other related papers. Finally, we discuss the relation of the NS-alpha model to the NSE by proving a convergence theorem, that as the length scale alpha tends to zero a subsequence of solutions of the NS-alpha equations converges to a weak solution of the three dimensional NSE.

C. Foias; D. D. Holm; E. S. Titi

2001-03-23

151

Proofs by Induction in Equational Theories with Constructors

We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to proofs of algebraic summation

Gérard P. Huet; Jean-marie Hullot

1980-01-01

152

EQUATIONS OF MOTION THEORY FOR ELECTRON AFFINITIES Jack SIMONS

the equations of motion (EOM) point of view that McKoy and co-workers had applied to electronic excitations. His objective was to achieve computationally tractable working equations for an EOM-based method for directly is an infinitesimal fraction of the total energy. EOM methods such as the author developed in the 1970s offer a route

Simons, Jack

153

Generalized Lorentz-Dirac equation for a strongly coupled gauge theory.

We derive a semiclassical equation of motion for a "composite" quark in strongly coupled large-N_{c} N = 4 super Yang-Mills theory, making use of the anti-de Sitter space/conformal field theory correspondence. The resulting nonlinear equation incorporates radiation damping, and reduces to the standard Lorentz-Dirac equation for external forces that are small on the scale of the quark Compton wavelength, but has no self-accelerating or preaccelerating solutions. From this equation one can read off a nonstandard dispersion relation for the quark, as well as a Lorentz-covariant formula for its radiation rate. PMID:19658995

Chernicoff, Mariano; García, J Antonio; Güijosa, Alberto

2009-06-19

154

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

155

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

Denicol, G. S. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Koide, T. [Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany); Rischke, D. H. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany)

2010-10-15

156

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

157

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

158

An integral equation theory for polymer solutions: Explicit inclusion of the solvent molecules

An integral equation theory for polymer solutions: Explicit inclusion of the solvent molecules calculations and molecular dynamics MD simulations were performed on athermal solutions of linear polymers. Unlike most previous treatments of polymer solutions, we explicitly included the solvent molecules

Utah, University of

159

New Langevin and Gradient Thermostats for Rigid Body Dynamics

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is ...

Davidchack, R L; Tretyakov, M V

2014-01-01

160

A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF

A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF REINFORCED RANDOM WALKS Howard A also give some intuitive argumentswhich demonstrate the possibility of the existence of aggregation and elucidating remarks. 1 #12;2 REACTION DIFFUSION EQUATIONS I. Introduction. In order to understand

161

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 = (2axn)/(1 + xn2) ? 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

162

1. Theory for Liquid Thermal Conductivity I ) Polynomial equation (HC_THLEQN)

1. Theory for Liquid Thermal Conductivity I ) Polynomial equation (HC_THLEQN) Polynomial equation thermal conductivity. 6/1 38.0 )1( r r L T TA - = (2) where L = thermal conductivity of the liquid, W and Liquids", 5th ed. McGraw-Hill, New York #12;2. KDB Routines for Liquid Thermal Conductivity Calculation

Hong, Deog Ki

163

1. Theory for Liquid Viscosity I ) Polynomial equation (HC_VSLEQN)

1. Theory for Liquid Viscosity I ) Polynomial equation (HC_VSLEQN) Polynomial equation is used for liquid viscosity. 2 /ln DTCTTBAVSL +++= (1) where, T is Kelvin and VSL is cP. II ) Przezdziecki - = (2) where =L liquid viscosity, cP =V liquid molar volume, cm3 /mol and cfPfPc c TTTPM V E /58

Hong, Deog Ki

164

A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law of thermodynamics could be consistently applied to transient nonequilibrium processes. We find out a general equality representing the energy balance relation for the system, and further

Hao Ge

2009-01-01

165

Atomic and Molecular Quantum Theory Course Number: C561 7 The time-independent Schrodinger Equation

and Molecular Quantum Theory Course Number: C561 6. Eq. (7.7) is a first order differential equation in time, the complex number i which is not present for the first order rate equation.) 7. The time-independent SchrÂ¨odinger Equation is Eq. (7.8): H(x) = E(x) - Â¯h2 2m 2 x2 (x) + V (x) = E(x) (7.13) is a second order differential

Iyengar, Srinivasan S.

166

Consistent Langevin terms in the numeric treatment of superconducting wires

NASA Astrophysics Data System (ADS)

In order to take thermal fluctuations into account, Schmid added a Langevin term to the time-dependent Ginzburg-Landau equations. This addition was incorrect in two respects: (i) the size of this term contained a spurious factor and (ii) it ignored the influence of fluctuations of the electromagnetic potential A. For a 1D wire A can be gauged out of the problem and it might seem that its fluctuations are irrelevant. This is not the case, because the transformed order parameter does not behave as a “canonical” variable. In a recent study, based on the fluctuation-dissipation theorem, we investigated the influence that the fluctuations of A have on equilibrium and transport properties. It seems that this influence is strongest when the length of the wire is of the order of the coherence length. We also found the deviation from the Aslamazov-Larkin result near Tc and the influence of fluctuations and constrictions on phase slips. We have extended our formalism to the case of gapped superconductors, which obey a generalized form of the Ginzburg-Landau equations.

Berger, Jorge

2008-02-01

167

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

168

Three-particle equations for a model field theory

NASA Astrophysics Data System (ADS)

An analysis is carried out of an extension of the Lee model which describes the interaction of three fermions, V, N, and W, with a scalar boson ? through the virtual processes V?N+? and W?V+?. It is shown that the amplitudes for the physical processes V+?-->V+? and V+?-->N+2? can be obtained from the solution of three-particle equations which differ from those of the Amado-Lovelace type as a result of the presence of the absorption channel V+?-->W-->V+?. The techniques used to derive the equations are not peculiar to the model, since they rely mainly on unitarity and analyticity in the subenergy and total energy variables, and hence they can be applied to realistic systems. [NUCLEAR REACTIONS Modified three-particle equations for V-? sector of extended Lee model.

Fuda, Michael G.

1984-04-01

169

In the paper we study the damped half-linear partial differential equationdiv(A(x)??u?p?2?u)+?b?(x),??u?p?2?u?+c(x)|u|p?2u=0. Using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations. Using careful radialization we improve several known oscillation criteria.

Robert Marík

2008-01-01

170

Dirac theory in spacetime algebra: I. The generalized bivector Dirac equation

This paper formulates the standard Dirac theory without resorting to spinor fields. Spinor fields mix bivectors and vectors which have different properties in spacetime algebra. Instead the Dirac field is formulated as a generalized bivector field. All the usual results of the standard Dirac theory fall out naturally and simply. The plane-wave solutions to the Dirac equation are given and

William P. Joyce

2001-01-01

171

Equations of motion in scalar-tensor theories of gravity: A covariant multipolar approach

NASA Astrophysics Data System (ADS)

We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson—Papapetrou—Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies.

Obukhov, Yuri N.; Puetzfeld, Dirk

2014-11-01

172

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

173

Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory

NASA Astrophysics Data System (ADS)

The sigma model renormalization group formalism is manifestly background independent and is a possible way of obtaining a background independent string field theory. An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds and loop variable techniques are used to make the equation gauge invariant. The equations are quadratic in fields as in open string field theory. Some explicit examples are given and results are also given for curved space time. In contrast to BRST string field theory, the gauge transformations are not modified by the interactions. As in the Dirac-Born-Infeld action for massless fields, the interactions for massive fields can also be written in terms of gauge invariant field strengths.

Sathiapalan, B.

2014-06-01

174

Three-particle equations for a model field theory

An analysis is carried out of an extension of the Lee model which describes the interaction of three fermions, V, N, and W, with a scalar boson theta through the virtual processes Varrow-right-leftN+theta and Warrow-right-leftV+theta. It is shown that the amplitudes for the physical processes V+theta..-->..V+theta and V+theta..-->..N+2theta can be obtained from the solution of three-particle equations which differ from those of the Amado-Lovelace type as a result of the presence of the absorption channel V+theta..-->..W..-->..V+theta. The techniques used to derive the equations are not peculiar to the model, since they rely mainly on unitarity and analyticity in the subenergy and total energy variables, and hence they can be applied to realistic systems.

Fuda, M.G.

1984-04-01

175

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

176

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

This research is an extension of the author's article \\cite{zar}, 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 \\cite{zar}, \\cite{zari} 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" or "restructuring" (the name suggested by the author). 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.

Farkhat Zaripov

2014-10-10

177

Equation-of-motion coupled cluster perturbation theory revisited

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.

Eriksen, Janus J., E-mail: janusje@chem.au.dk; Jørgensen, Poul; Olsen, Jeppe [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark)] [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark); Gauss, Jürgen [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)] [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)

2014-05-07

178

Equation-of-motion coupled cluster perturbation theory revisited

NASA Astrophysics Data System (ADS)

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.

Eriksen, Janus J.; Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen

2014-05-01

179

Computationally sound implementations of equational theories against passive adversaries

: cryptographic operations are modeled as algorithms manipulating bit-strings. Those models cover a large class cortier@loria.fr Abstract. In this paper we study the link between formal and cryptographic models in cryptographic pi calculi. We present a soundness criterion, which for many theories is not only sufficient

Cortier, VÃ©ronique

180

Topological field theories in n-dimensional spacetimes and Cartan's equations

Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first and second structure equations together with first and second Bianchi identities are treated as the equations of motion for a field theory. In opposition to that paper, the current approach involves also auxiliary fields and holds for arbitrary n-dimensional spacetimes. Dirac's canonical analysis for the actions is detailedly carried out in the generic case and it is shown that these action principles define topological field theories, as mentioned. The current formalism is a generic framework to construct geometric theories with local degrees of freedom by introducing additional constraints on the various fields involved that destroy the topological character of the original theory. The latter idea is implemented in two-dimensional spacetimes where gravity coupled to matter fields is constructed out, which has indeed local excitations.

Cuesta, Vladimir; Vergara, Jose David [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, 70-543, Ciudad de Mexico (Mexico); Montesinos, Merced; Velazquez, Mercedes [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Instituto Politecnico Nacional 2508, San Pedro Zacatenco, 07360, Gustavo A. Madero, Ciudad de Mexico (Mexico)

2008-09-15

181

Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach.

Based on a given time series, the data-driven Langevin equation (dLE) estimates the drift and the diffusion field of the dynamics, which are then employed to reproduce the essential statistical and dynamical features of the original time series. Because the propagation of the dLE requires only local information, the input data are neither required to be Boltzmann weighted nor to be a continuous trajectory. Similar to a Markov state model, the dLE approach therefore holds the promise of predicting the long-time dynamics of a biomolecular system from relatively short trajectories which can be run in parallel. The practical applicability of the approach is shown to be mainly limited by the initial sampling of the system's conformational space obtained from the short trajectories. Adopting extensive molecular dynamics simulations of the unfolding and refolding of a short peptide helix, it is shown that the dLE approach is able to describe microsecond conformational dynamics from a few hundred nanosecond trajectories. In particular, the dLE quantitatively reproduces the free energy landscape and the associated conformational dynamics along the chosen five-dimensional reaction coordinate. PMID:25554123

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

2014-12-28

182

Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach

NASA Astrophysics Data System (ADS)

Based on a given time series, the data-driven Langevin equation (dLE) estimates the drift and the diffusion field of the dynamics, which are then employed to reproduce the essential statistical and dynamical features of the original time series. Because the propagation of the dLE requires only local information, the input data are neither required to be Boltzmann weighted nor to be a continuous trajectory. Similar to a Markov state model, the dLE approach therefore holds the promise of predicting the long-time dynamics of a biomolecular system from relatively short trajectories which can be run in parallel. The practical applicability of the approach is shown to be mainly limited by the initial sampling of the system's conformational space obtained from the short trajectories. Adopting extensive molecular dynamics simulations of the unfolding and refolding of a short peptide helix, it is shown that the dLE approach is able to describe microsecond conformational dynamics from a few hundred nanosecond trajectories. In particular, the dLE quantitatively reproduces the free energy landscape and the associated conformational dynamics along the chosen five-dimensional reaction coordinate.

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

2014-12-01

183

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

NASA Astrophysics Data System (ADS)

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the { c, h, ?} parametrization. The evolution of the orientation degree of freedom ( K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k s = 0.25 and k s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z 2/ A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, < n pre( M)>, and between, this multiplicity and the kinetic energy of fission fragments, < n pre( E k )>, are also presented.

Anischenko, Yu. A.; Adeev, G. D.

2012-08-01

184

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {l_brace}c, h, {alpha}{r_brace} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k{sub s} 0.25 and k{sub s} = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k{sub s} in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z{sup 2}/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k{sub s} with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, Left-Pointing-Angle-Bracket n{sub pre}(M) Right-Pointing-Angle-Bracket , and between, this multiplicity and the kinetic energy of fission fragments, Left-Pointing-Angle-Bracket n{sub pre}(E{sub k}) Right-Pointing-Angle-Bracket , are also presented.

Anischenko, Yu. A., E-mail: yuri.anischenko@gmail.com; Adeev, G. D. [Omsk State University (Russian Federation)

2012-08-15

185

Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory

Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.

Aupic, Jana; Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si [Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ašker?eva 5, SI-1000 Ljubljana (Slovenia)] [Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ašker?eva 5, SI-1000 Ljubljana (Slovenia)

2014-05-14

186

We construct a class of numerical schemes for the Liouville equation of geometric optics coupled with the Geometric Theory of Diffractions to simulate the high frequency linear waves with a discontinuous index of refraction. In this work [S. Jin, X. Wen, A Hamiltonian-preserving scheme for the Liouville equation of geometric optics with partial transmissions and reflections, SIAM J. Numer. Anal. 44 (2006) 1801-1828], a Hamiltonian-preserving scheme for the Liouville equation was constructed to capture partial transmissions and reflections at the interfaces. This scheme is extended by incorporating diffraction terms derived from Geometric Theory of Diffraction into the numerical flux in order to capture diffraction at the interface. We give such a scheme for curved interfaces. This scheme is proved to be positive under a suitable time step constraint. Numerical experiments show that it can capture diffraction phenomena without fully resolving the wave length of the original wave equation.

Jin Shi [Department of Mathematical Sciences, Tsinghua University, Beijing 100084 (China); Department of Mathematics, University of Wisconsin, Madison, WI 53706 (United States)], E-mail: jin@math.wisc.edu; Yin Dongsheng [Department of Mathematical Sciences and the Center for Advanced Study, Tsinghua University, Beijing 100084 (China)], E-mail: dyin@math.tsinghua.edu.cn

2008-06-01

187

Extracting the cosmological constant from the Wheeler DeWitt equation in a modified gravity theory

We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem. A generalization to a f(R) theory is taken under examination. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. We use a zeta function regularization to handle with

Remo Garattini; Viale Marconi

2008-01-01

188

Toward a gauge theory for evolution equations on vector-valued spaces

We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.

Cardanobile, Stefano [Bernstein Center for Computational Neuroscience, Hansastrasse 9A, D-79104 Freiburg (Germany); Mugnolo, Delio [Institut fuer Analysis, Universitaet Ulm, Helmholtzstrasse 18, D-89081 Ulm (Germany)

2009-10-15

189

Derivation of the Euler equations in Thomas-Fermi theories of a hot nuclear system

NASA Astrophysics Data System (ADS)

The variational extreme condition with respect to statistical distribution of nucleons in momentum space is applied to derive the Euler equation of the nuclear density profile. The resultant Euler equation of the nuclear density profile is proven to be identical with that obtained in the usual Thomas-Fermi theories of a hot nuclear system where the variation is made with respect to the nuclear density profile. A Fermi-Dirac-type distribution appears as a result of variation in the present approach, while it is used as a given expression in obtaining the variation of the nuclear density profile in the usual Thomas-Fermi theories.

Wang, Cheng-Shing

1992-03-01

190

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

191

Inverse-scattering theory at a fixed energy for the Klein-Gordon equation

NASA Astrophysics Data System (ADS)

The inverse-scattering theory at a fixed energy for the scattering of a particle by a potential in the Schrödinger equation formulated by Alam and Malik, which is based on the earlier work of Hooshyar and Razavy, is extended, in this paper, to the scattering of spinless particles at relativistic energies governed by the Klein-Gordon equation. The differential equation is replaced by a set of difference equations. This reduces the inverse-scattering problem to solving a continued fraction equation. The solution provides the values of the potential at a number of points which are equal to (one plus the number of partial waves). The theory is tested for three widely different complex potentials, one of which is relevant to pion-nucleus scattering. The points of the potentials determined from the inverse-scattering formalism are in accord with the actual ones in all three cases. Since the Klein-Gordon equation is effectively a Schrödinger equation with an energy-dependent potential, the method may, in the appropriate cases, be suitable for the latter case.

Shehadeh, Z. F.; Alam, M. M.; Malik, F. B.

1999-02-01

192

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

193

NASA Technical Reports Server (NTRS)

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.; Kunisch, K.

1982-01-01

194

A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF

A SYSTEM OF REACTION DIFFUSION EQUATIONS ARISING IN THE THEORY OF REINFORCED RANDOM WALKS Howard A of aggregation (piecewise constant) solutions. 1991 Mathematics Subject Classification. 35K50, 35M10, 35R25, 92C45. Key words and phrases. chemotaxis, reactionÂdiffusion systems, reinforced random walks. This work

195

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

196

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

197

The factorized Helmholtz equation - The construction of direct and inverse wave propagation theories

The development of both direct and indirect analytical wave propagation theories is discussed, with particular emphasis on the principal scalar Helmholtz equation. A factorization analysis is presented which provides a microscopic description of backward and forward Helmholtz wave propagation in a transversely inhomogeneous environment. The theoretical analysis is applied to a wide range of physical phenomena and functional methods including:

L. Fishman; J. J. McCoy

1983-01-01

198

HEAT TRANSPORT AND THE BOLTZMANN EQUATION IN THE THEORY OF THERMAL BOUNDARY RESISTANCE

conductance related in the works of Wagner et al. [14] and Challis et al. [15] will exist even if the thermalL-167 HEAT TRANSPORT AND THE BOLTZMANN EQUATION IN THE THEORY OF THERMAL BOUNDARY RESISTANCE N stationnaire Ã travers une plaque mÃ©tallique en contact avec l'hÃ©lium liquide, et Ã©tudions les variations

Boyer, Edmond

199

Role of secondary instability theory and parabolized stability equations in transition modeling

NASA Technical Reports Server (NTRS)

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

1993-01-01

200

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

NASA Astrophysics Data System (ADS)

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 178W, 188Pt, 200Pb, 213Fr, 224Th, and 251Es. 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.

Chaudhuri, Gargi; Pal, Santanu

2002-05-01

201

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

202

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

203

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

204

Splines and the Galerkin method for solving the integral equations of scattering theory

NASA Astrophysics Data System (ADS)

This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado-Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.

Brannigan, M.; Eyre, D.

1983-06-01

205

Kinetics and Boltzmann kinetic equation for fluctuation Cooper pairs

NASA Astrophysics Data System (ADS)

The Boltzmann equation for excess Cooper pairs above Tc is derived in the framework of the time-dependent Ginzburg-Landau (TDGL) theory using Langevin’s approach of the stochastic differential equation. The Newton dynamic equation for the momentum-dependent drift velocity is obtained and the effective drag force is determined by the energy-dependent lifetime of the metastable Cooper pairs. The Newton equation gives just the Drude mobility for the fixed momentum of Cooper pairs. It is shown that the comparison with the well-known result for Aslamazov-Larkin paraconductivity and BCS treatment of the excess Hall effect can give the final determination of all the coefficients of TDGL theory. As a result the intuitive arguments used for an interpretation of the experimental data for fluctuation kinetics are successively introduced. The presented simple picture of the degenerated Bose gas in ? approximation near the Bose-Einstein condensation temperature can be used for analysis of fluctuation conductivity for the cases of high frequency and external magnetic field for layered and bulk superconductors. The work of the Boltzmann equation is illustrated by frequency-dependent Aslamazov-Larkin conductivity in nanowires, in the two-dimensional case and in the case of strong electric field where the TDGL equation is solved directly. There are also derived explicit formulas for the current in the case of arbitrary time dependence of electric field up to the THz range, the distribution of fluctuation Cooper pairs for nonparabolic dispersion, the influence of the energy cut-off, and the self-consistent equation for the reduced temperature. The general theory is illustrated by formulas for fluctuation conductivity in nanowires and nanostructured superconductors.

Mishonov, Todor M.; Pachov, Georgi V.; Genchev, Ivan N.; Atanasova, Liliya A.; Damianov, Damian Ch.

2003-08-01

206

NASA Astrophysics Data System (ADS)

The reduced scalar Helmholtz equation for a transversely inhomogeneous half-space sup-plemented with an outgoing radiation condition and an appropriate boundary condition on the initial-value plane defines a direct acoustic propagation model. This elliptic formulation admits a factorization and is subsequently equivalent to a first-order Weyl pseudo-differ-ential equation which is recognized as an extended parabolic propagation model. Perturbation treatments of the appropriate Weyl composition equation result in a systematic devel-opment of approximate wave theories while exact inversions for several nontrivial profiles provide for an analysis of strong refractive and diffractive effects. The analysis, in a natural manner, provides the basis for the formulation and exact solution of an arbitrary-dimensional nonlinear inverse problem appropriate for ocean acoustic, seismic, and optical studies- Moreover, the n-dimensional reduced scalar Helmholtz equation for the transversely inhomogeneous medium is naturally related to parabolic propagation models through (1) the above mentioned n-dimensional extended parabolic (Weyl pseudo-differential) equation and (2) an imbedding in an (n + 1)-dimensional parabolic (SchrOdinger) equation. The first relationship provides the basis for the parabolic-based Hamiltonian phase space path integral representation of the half-space propagator. The second relationship provides the basis for the elliptic-based path integral representations associated with Feynman/Fradkin, Feynman/Garrod, and Feynman/Dewitt-Morette. The path integrals allow for a global perspective of the transition from elliptic to parabolic wave theory in addition to providing a unifying framework in the direct and inverse formulations for dynamical approximations, resolution of the square root operator, and the concepts of an underlying stochastic process and free motion on curved spaces. The wave equation and path integral analysis provides for computational algorithms while foreshadowing the extension to (1) the vector formulation appropriate for elastic media, (2) the bilinear formulation appropriate for acoustic field coherence, and (3) the stochastic formulation appropriate for wave propagation in random media.

Fishman, Louis; McCoy, John J.

1983-09-01

207

From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation

We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two point correlation function of the sine-Gordon theory is related to the generating function of the height distribution of the KPZ field with droplet initial conditions, i.e. the directed polymer free energy with two endpoints fixed. As shown recently, the latter can be expressed as a Fredholm determinant which in the large time separation limit converges to the GUE Tracy-Widom cumulative distribution. Possible applications and extensions are discussed.

Pasquale Calabrese; Marton Kormos; Pierre Le Doussal

2014-05-11

208

Application of Equation-Of Coupled-Cluster Theory to Photodetachment Cross Section Calculations

NASA Astrophysics Data System (ADS)

Photodetachment cross sections of atomic anions have been calculated with equation-of-motion coupled-cluster (EOM-CC) theory. Two techniques have been examined. One of them treats the photodetached electron as a plane wave, and the transition moment integral is evaluated with the Dyson orbital obtained from EOMIP-CC calculations. In the other technique, the EOM-EE method is utilized to calculate the oscillator strengths for photodetachment processes within the framework of moment theory. The results of these calculations are compared with experimental results, and the pros and cons of the two techniques are discussed.

Ichino, Takatoshi; Stanton, John F.

2012-06-01

209

Using condition of relativistic invariance, group theory and Clifford algebra the component Lorentz invariance generalized Dirac equation for a particle with arbitrary mass and spin is suggested, where In the case of half-integral spin particles, this equation is reduced to the sets of two-component independent matrix equations. It is shown that the relativistic scalar and integral spin particles are described by component equation.

I. I. Guseinov

2012-06-06

210

Stochastic quantization of real-time thermal field theory

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.

Aguiar, T. C. de; Svaiter, N. F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rua Dr. Xavier Sigaud 150, Rio de Janeiro 22290-180, Rio de Janeiro (Brazil); Menezes, G. [Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, Sao Paulo 01140-070, Sao Paulo (Brazil)

2010-10-15

211

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

212

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

213

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

214

The Einstein-Maxwell Equations, Extremal Kahler Metrics, and Seiberg-Witten Theory

The Einstein-Maxwell equations on a smooth compact 4-manifold are reformulated as a purely Riemannian variational problem analogous to Calabi's variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is used to show that these two problems are in fact intimately related. Extremal Kahler metrics are then used to probe the limits of Seiberg-Witten curvature estimates. The article then concludes with a brief survey of some recent results on extremal Kahler metrics.

Claude LeBrun

2008-03-26

215

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

216

Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures

Most of the work on the combination of unification algorithms for the union of disjoint equational theories has been restricted to algorithms that compute finite complete sets of unifiers.Thus the developed combination methods usually cannot be used to combine decision procedures,i.e., algorithms that just decide solvability of unification problems without computing unifiers.In this paper we describe a combination algorithm for

Franz Baader; Klaus U. Schulz

1996-01-01

217

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

218

Reconstruction and Convergence in Quantum $K$-Theory via Difference Equations

We prove that the big quantum $K$-ring can be reconstructed from the small $J$-function provided that the topological $K$-ring is generated by line bundles, using difference equations. We also discuss convergence properties in quantum $K$-theory. We show polynomiality of quantum products in $t$ and $e^t$ and prove that our reconstruction is convergent provided that the initial data are convergent.

Iritani, Hiroshi; Tonita, Valentin

2013-01-01

219

Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities. PMID:25097751

Liao, David; Tlsty, Thea D

2014-08-01

220

Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities. PMID:25097751

Liao, David; Tlsty, Thea D.

2014-01-01

221

Chemical Master versus Chemical Langevin for First-Order Reaction Networks

Chemical Master versus Chemical Langevin for First-Order Reaction Networks Desmond J. Higham Raya in computational cell biology, and in this case, the interactions are typically first-order. The Chemical Langevin effectively. In this work, we obtain expressions for the first and second moments of the Chemical Langevin

Mottram, Nigel

222

For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. We verify numerically for the shell model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.

Takeshi Matsumoto; Michio Otsuki; Ooshida Takeshi; Susumu Goto; Akio Nakahara

2014-06-30

223

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

224

Fluids of hard natural and Gaussian ellipsoids: A comparative study by integral equation theories.

The hard Gaussian overlap (HGO) model for ellipsoids is compared to the hard ellipsoid of revolution (HER) model, in the isotropic fluid phase and within the framework of the Percus-Yevick (PY) and hypernetted chain (HNC) integral equation theories. The former model is often used in place of the latter in many approximate theories. Since the HGO model slightly overestimates the contact distance when the two ellipsoids are perpendicular to each other, it leads to small differences in the Mayer function of the two models, but nearly none in the integrals of these functions and particularly for the second virial coefficients. However, it leads to notable differences in the pair correlation functions, as obtained by the Percus-Yevick and the hypernetted chain theories, especially at high densities. The prediction of the stability of the isotropic phase with respect to orientational order, at high densities, is notably influenced by these small differences. Both theories predict that, for same aspect ratios, the HGO model overestimates the ordering, when compared to the HER model. This explains why the PY approximation predicts ordering for the HGO model with aspect ratio of 1:3, while it does not for the HER model, in accordance with the very first integral equation results obtained for this system, and at variance with many opposite claims from subsequent publications that used the HGO model in place of the HER model. PMID:19026063

Perera, Aurélien

2008-11-21

225

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

226

Modular anomaly equations in =2* theories and their large- N limit

NASA Astrophysics Data System (ADS)

We propose a modular anomaly equation for the prepotential of the =2* super Yang-Mills theory on ?4 with gauge group U( N) in the presence of an ?-background. We then study the behavior of the prepotential in a large- N limit, in which N goes to infinity with the gauge coupling constant kept fixed. In this regime instantons are not suppressed. We focus on two representative choices of gauge theory vacua, where the vacuum expectation values of the scalar fields are distributed either homogeneously or according to the Wigner semi-circle law. In both cases we derive an all-instanton exact formula for the prepotential. As an application, we show that the gauge theory partition function on 4 at large N localizes around a Wigner distribution for the vacuum expectation values leading to a very simple expression in which the instanton contribution becomes independent of the coupling constant.

Billó, M.; Frau, M.; Fucito, F.; Lerda, A.; Morales, J. F.; Poghossian, R.; Ricci Pacifici, D.

2014-10-01

227

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 analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.

Mattia Bruno; Michele Caselle; Marco Panero; Roberto Pellegrini

2014-09-29

228

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

229

NASA Technical Reports Server (NTRS)

One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.

Weatherford, Charles A.

1993-01-01

230

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

231

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

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry. PMID:25375609

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

2014-10-01

232

Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.

Buividovich, P. V. [ITEP, Bolshaya Cheremushkinskaya 25, 117218 Moscow (Russian Federation); JINR, Joliot-Curie 6, 141980 Dubna, Moscow region (Russian Federation)

2011-02-15

233

Equation of State of a Relativistic Theory from a Moving Frame

NASA Astrophysics Data System (ADS)

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 computing the expectation value of the off-diagonal components T0k of the energy-momentum tensor in the 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 0.9Tc-20Tc. At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of T0k 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.

Giusti, Leonardo; Pepe, Michele

2014-07-01

234

Weisskopf-Wigner decay theory for the energy-driven stochastic Schrödinger equation

NASA Astrophysics Data System (ADS)

We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schrödinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schrödinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects. In addition, elegant stochastic-theoretic methods suggested by Diósi are used to rederive the principal results, without the assumptions needed to linearize the stochastic equation, and to give analogous results for the Rabi oscillations of a two-level system.

Adler, Stephen L.

2003-01-01

235

One parameter family of master equations for logistic growth and BCM theory

NASA Astrophysics Data System (ADS)

We propose a one parameter family of master equations, for the evolution of a population, having the logistic equation as mean field limit. The parameter ? determines the relative weight of linear versus nonlinear terms in the population number n ? N entering the loss term. By varying ? from 0 to 1 the equilibrium distribution changes from maximum growth to almost extinction. The former is a Gaussian centered at n = N, the latter is a power law peaked at n = 1. A bimodal distribution is observed in the transition region. When N grows and tends to ?, keeping the value of ? fixed, the distribution tends to a Gaussian centered at n = N whose limit is a delta function corresponding to the stable equilibrium of the mean field equation. The choice of the master equation in this family depends on the equilibrium distribution for finite values of N. The presence of an absorbing state for n = 0 does not change this picture since the extinction mean time grows exponentially fast with N. As a consequence for ? close to zero extinction is not observed, whereas when ? approaches 1 the relaxation to a power law is observed before extinction occurs. We extend this approach to a well known model of synaptic plasticity, the so called BCM theory in the case of a single neuron with one or two synapses.

De Oliveira, L. R.; Castellani, C.; Turchetti, G.

2015-02-01

236

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

237

Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density

NASA Technical Reports Server (NTRS)

The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.

Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.

1988-01-01

238

Elasticity theory equations and fracture condition for materials of varying moduli

Many massive rocks and composite materials belong to the class of materials of varying moduli with definite distinct deformation and strength properties under tension and compression. The results of experiments indicate that the difference between the properties of materials of different moduli is not limited to tension and compression cases but can also appear clearly for any change in the form of the state of stress. Elasticity theory equations are constructed here to describe the strain of materials of varying moduli as well as the dependence of the strength properties on the form of the state of strain. Tests were done on coal, limestone, diabase and cement and results are shown. Using the dependencies obtained, Poisson's ratio and the elastic modulus can be calculated for these rocks. The equations and conditions of fracture proposed, are written in a simple invariant form.

Oleinikov, A.I.

1986-11-01

239

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

240

WKB theory of wave tunneling for Hermitian vector systems of integral equations

A general theory of wave tunneling in one dimension for Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium, and without regard to specific models gives a proper account to the forward and backward nature of the waves. Energy conservation in the WKB approximation can be obtained for general linear systems by a consistent treatment of the vector polarization and by the use of modified Furry rules, which are similar to those used by Heading for second order differential equations. Operational graphical rules are developed to construct global wave solutions and to determine the direction of energy flow for spatially disconnected roots. In principle these rules could be applied to systems with arbitrary mode complexity. Coupling coefficients for wave tunneling problems with up to four interacting modes are calculated explicitly. 23 refs., 9 figs.

Kull, H.J.; Kashuba, R.J.; Berk, H.L.

1988-01-01

241

WKB theory of wave tunneling for Hermitian and nearly Hermitian vector systems of integral equations

A general theory of wave tunneling in one dimension for Hermitian and nearly Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium and properly accounts for the forward and backward nature of the waves without regard to specific models. Energy conservation in the WKB approximation can be obtained for general Hermitian systems by the use of modified Furry rules that are similar to those used by Heading for second-order differential equations. Wave energy absorption can then be calculated perturbatively using the conservation properties of the dominant Hermitian operator. Operational graphical rules are developed to construct global wave solutions and to determine the direction of energy flow for spatially disconnected roots. In principle, these rules could be applied to systems with arbitrary mode complexity. Coupling coefficients for wave tunneling problems with up to four interacting modes are calculated explicitly.

Kull, H.J.; Kashuba, R.J.; Berk, H.L. (Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (US))

1989-11-01

242

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.

R. Giachetti; V. Grecchi

2009-05-13

243

On loop equations in KdV exactly solvable string theory

In this paper, the non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation ({bar P}, Q) = Q, where {bar P} generates scale transformations. In general the end of the half-line (the wall) is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of (P,Q) = 1. Detailed arguments are given for the (2,2m {minus} 1) models while generalization to the other (p,q) minimal models and c = 1 is briefly addressed.

Dalley, S. (Princeton Univ., NJ (United States). Joseph Henry Labs.)

1992-05-10

244

A review is presented of the fundamental equations of point, perfect incompressible fluid and wave dynamics in the Fantappie-Arcidiacono theory of projective relativity, also known as De Sitter relativity. Compared to the original works, some deductions have been simplified and the physical meaning of the equations has been analyzed in greater depth.

Leonardo Chiatti

2009-01-23

245

It has been shown that the derivative nonlinear Schroedinger equation, concerned with wave propagation in plasmas, can be associated with a modified Zakharov-Shabat inverse scattering problem. An operator formula is produced for the most general system of equations solvable by this method and a perturbation theory developed capable of determining the variation in the scattering data to first order. The

R. K. Dodd; H. C. Morris; J. Eagleton

1980-01-01

246

Thin airfoil theory based on approximate solution of the transonic flow equation

NASA Technical Reports Server (NTRS)

A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

Spreiter, John R; Alksne, Alberta Y

1958-01-01

247

Thin airfoil theory based on approximate solution of the transonic flow equation

NASA Technical Reports Server (NTRS)

A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.

Spreiter, John R; Alksne, Alberta Y

1957-01-01

248

Analysis of High-Pressure Equation of State for Solids Based on the Lattice Potential Theory

NASA Astrophysics Data System (ADS)

A two-parameter high-pressure equation of state (EOS) is derived on the basis of the lattice potential theory using the concept of a short-range force constant as introduced by Born and Huang. The application of the EOS to some solids is presented and compared with the Birch-Murnaghan (BM) third-order EOS, the BM fourth-order EOS, and the Vinet EOS. A comparison of the results provides a crucial test for the EOSs used in this article.

Liu, Quan; Niu, Zhong-Ming

2012-12-01

249

Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The inter-particle interactions in the system were taken from the Asakura-Oosawa model, for colloid-polymer mixtures, for which the phase diagram is known. In the current model version the colloid particles were made active using the Vicsek model for self-propelling particles. The resultant active system was studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model based activity facilitates phase separation, thus broadening the coexistence region.

Subir K. Das; Sergei Egorov; Benjamin Trefz; Peter Virnau; Kurt Binder

2014-05-15

250

Cosmological models with viscous fluid and time- dependent equation of state in Wesson's theory

NASA Astrophysics Data System (ADS)

Assuming the time-dependent equation of state p=?(t)?, five dimensional cosmological models with viscous fluid for an open universe (k=-1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys. 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this theory, i.e. the mass scale factor A(t) which characterizes the rest mass of a typical particle is evolving with cosmic time just as the spatial scale factor R(t). It is further found that rest mass is approximately constant in the present universe.

Khadekar, G. S.; Avachar, G. R.

2007-07-01

251

Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation

NASA Technical Reports Server (NTRS)

Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.

Spreiter, John R.; Alksne, Alberta Y.

1959-01-01

252

Stochastic theory of an optical vortex in nonlinear media

NASA Astrophysics Data System (ADS)

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.

Kuratsuji, Hiroshi

2013-07-01

253

Statistical-mechanical theory of a new analytical equation of state

NASA Astrophysics Data System (ADS)

We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks-Chandler-Andersen decomposition of the potential and the Carnahan-Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule-Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p-v-T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases. As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is incorrect. Limited testing on the polyatomic gases CH4, N2, and CO2 suggests that the results for spherical molecules (CH4) may be as good as for the noble gases, nearly as good for slightly nonspherical molecules (N2), but poor at high densities for nonspherical molecules (CO2). In all cases, however, the results are accurate up to the critical density. Except for the eight-parameter empirical Benedict-Webb-Rubin equation, this appears to be the most accurate analytical equation of state proposed to date.

Song, Yuhua; Mason, E. A.

1989-12-01

254

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

255

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

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

Beraudo, A

2014-01-01

256

SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS

In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the friction and diffusion coefficients are computed from first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators.

J. QIANG; R. RYNE; S. HABIB

2000-05-01

257

LE DERNIER THEOR`EME DE FERMAT PHILIPPE LANGEVIN

`ere modification : octobre 2004. 2. Prologue Au milieu du xviie si`ecle, le toulousain Pierre de Fermat consigneLE DERNIER THÂ´EOR`EME DE FERMAT PHILIPPE LANGEVIN RÂ´esumÂ´e. Pour les Â« f^etes de la science Â» de- plines scientifiques, l'Â´etude des nombres, sur les sentiers du dernier thÂ´eor`eme de Fermat. Le texte

Faccanoni, Gloria

258

A kinetic theory solution method for the Navier-Stokes equations

NASA Astrophysics Data System (ADS)

The kinetic-theory-based solution methods for the Euler equations proposed by Pullin and Reitz are here extended to provide new finite volume numerical methods for the solution of the unsteady Navier-Stokes equations. Two approaches have been taken. In the first, the equilibrium interface method (EIM), the forward- and backward-flowing molecular fluxes between two cells are assumed to come into kinetic equilibrium at the interface between the cells. Once the resulting equilibrium states at all cell interfaces are known, the evaluation of the Navier-Stokes fluxes is straightforward. In the second method, standard kinetic theory is used to evaluate the artificial dissipation terms which appear in Pullin's Euler solver. These terms are subtracted from the fluxes and the Navier Stokes dissipative fluxes are added in. The new methods have been tested in a 1D steady flow to yield a solution for the interior structure of a shock wave and in a 2D unsteady boundary layer flow. The 1D solutions are shown to be remarkably accurate for cell sizes large compared to the length scale of the gradients in the flow and to converge to the exact solutions as the cell size is decreased. The steady-state solutions obtained with EIM agree with those of other methods, yet require a considerably reduced computational effort.

Macrossan, M. N.; Oliver, R. I.

1993-08-01

259

Layzer-Irvine equation for scalar-tensor theories: A test of modified gravity N-body simulations

NASA Astrophysics Data System (ADS)

The Layzer-Irvine equation describes energy conservation for a pressure less fluid interacting though quasi-Newtonian gravity in an expanding Universe. We here derive a Layzer-Irvine equation for scalar field theories where the scalar field is coupled to the matter fields, and show applications of this equation by applying it to N-body simulations of modified gravity theories. There it can be used as both a dynamical test of the accuracy of the solution and the numerical implementation when solving the equation of motion. We also present an equation that can be used as a new static test for an arbitrary matter distribution. This allows us to test the N-body scalar field solver using a matter distribution which resembles what we actually encounter in numerical simulations.

Winther, Hans A.

2013-08-01

260

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

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained. PMID:11863612

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

2002-02-01

261

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

NASA Astrophysics Data System (ADS)

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

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

2002-02-01

262

A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.

B. A. Kashiwa; W. B. VanderHeyden

2000-12-01

263

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 computing the expectation value of the off-diagonal components T(0k) of the energy-momentum tensor in the 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 0.9T(c)-20T(c). At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, 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. PMID:25083632

Giusti, Leonardo; Pepe, Michele

2014-07-18

264

It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Ho?ava-Lifshitz(HL) theory.

Tu, Fei-Quan; Chen, Yi-Xin, E-mail: fqtuzju@foxmail.com, E-mail: yxchen@zimp.zju.edu.cn [Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027 (China)

2013-05-01

265

Five-dimensional cosmological model with a time-dependent equation of state in Wesson's theory

NASA Astrophysics Data System (ADS)

Exact solution for a homogeneous cosmological model in 5D space-time-mass gravity theory proposed by Wesson (Astron. Astrophys. 119:145, 1983) is obtained by assuming the time-dependent equation of state. The behavior of the solution is discussed for the two cases k<0 and k=0. It is found that the observed constancy of the rest mass of an isolated particle in the present era may be interpreted as a consequence of the decreasing rate of change of rest mass with time. Moreover, a spontaneous compactification-like phenomenon of an extra dimension takes place in the case of k=0. It is also found that with decrease in extra space the observable three-dimensional space entropy increases, thus accounting for the large value of entropy observable at present.

Khadekar, G. S.; Avachar, G. R.

2007-12-01

266

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

267

Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, H{phi}=(-{delta}+V){phi}=-({phi}{sub n+1}+{phi}{sub n-1}-2{phi}{sub n})+V{sub n}{phi}{sub n}. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sub {sigma}{sup 2}}{yields}{sub l-{sigma}{sup 2}}} < or approx. t{sup -3/2} for any fixed {sigma}>(5/2) and any t>0, where P{sub a.c.}(H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sup 1}{yields}{sub l{sup {infinity}}}} < or approx. t{sup -1/3}, which are sharp for the discrete Schroedinger operators even for V=0.

Pelinovsky, D. E. [Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1 (Canada); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, Kansas 66045-7523 (United States)

2008-11-15

268

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

269

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

270

We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10(-2). With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format. PMID:25591336

Godtliebsen, Ian H; Hansen, Mads Bøttger; Christiansen, Ove

2015-01-14

271

NASA Astrophysics Data System (ADS)

We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10-2. With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format.

Godtliebsen, Ian H.; Hansen, Mads Bøttger; Christiansen, Ove

2015-01-01

272

A systematic theory is given for a general class of scalar waves by introducing a surface Green’s function, which is a 2×2 matrix function governed by boundary equations, transferred onto two reference boundary planes enclosing the real boundary inside. It is subjected to several symmetries, including a relation eventually leading to optical relations. Governing equations of statistical surface Green’s functions

K. Furutsu

1985-01-01

273

Solvation effects on chemical shifts by embedded cluster integral equation theory.

The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of N-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute-solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute-solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent's charge distribution. PMID:25377116

Frach, Roland; Kast, Stefan M

2014-12-11

274

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

275

Theory of Partial Differential Equations (155010) Exercises WC #1 (Week 46) 2011.11.18

satisfies equation (4). 03. Consider the first order partial differential equation ux + exuy = 1. (5) (a procedure for first order, linear equations as outlined in the lecture. i. Write down the characteristic) Apply the transformation procedure for first order, linear equations as outlined (step by step

Al Hanbali, Ahmad

276

The problem of finding periodic solutions of the matrix Riccati equations of linear control theory is interpreted geometrically as a problem of finding periodic orbits of certain one-parameter transformation groups on Grassmann manifolds. For certain control problems the vector fields which generate these groups can be written as a sum of two commuting vector fields, one a gradient vector field,

Robert Hermann; Clyde Martin

1981-01-01

277

This article proposes a new approach for computing a semi-explicit form of the solution to a class of Hamilton-Jacobi (HJ) partial differential equations (PDEs), using control techniques based on viability theory. We characterize the epigraph of the value function solving the HJ PDE as a capture basin of a target through an auxiliary dynamical system, called ??characteristic system??. The properties

Christian G. Claudel; Alexandre M. Bayen

2010-01-01

278

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

279

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

280

Perturbation theory based equation of state for polar molecular fluids: I. Pure fluids

NASA Astrophysics Data System (ADS)

Based on the thermodynamic perturbation theory an equation of state (EOS) for molecular fluids has been formulated which can be used for many fluid species in geological systems. The EOS takes into account four substance specific parameters. These are the molecular dipole moment, the molar polarizability and the two parameters of the Lennard-Jones potential. For many fluids these parameters can be evaluated directly or indirectly from experimental measurements. In the absence of direct experimental determinations, as a first approximation, for a pure fluid the parameters of the Lennard-Jones potential can be evaluated using the critical temperature and the critical density if for polar molecules in addition the dipole moment is known with reasonable accuracy. The EOS with its model potential has the appropriate asymptotic behaviour at high pressures and temperatures and can be used to calculate both vapor-liquid equilibria and thermodynamic properties of single phase fluids up to at least 10 GPa and 2000 K. Currently, parameters for 98 inorganic and organic compounds are available. In this article the EOS for pure fluids is presented. In a further communication the EOS is extended to fluid mixtures (Churakov and Gottschalk, 2003).

Churakov, S. V.; Gottschalk, M.

2003-07-01

281

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.

282

NASA Astrophysics Data System (ADS)

Do stochastic Schrödinger equations, also known as unravelings, have a physical interpretation? In the Markovian limit, where the system on average obeys a master equation, the answer is yes. Markovian stochastic Schrödinger equations generate quantum trajectories for the system state conditioned on continuously monitoring the bath. For a given master equation, there are many different unravelings, corresponding to different sorts of measurement on the bath. In this paper we address the non-Markovian case, and in particular the sort of stochastic Schrödinger equation introduced by Strunz, Diósi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum-measurement theory approach, we rederive their unraveling that involves complex-valued Gaussian noise. We also derive an unraveling involving real-valued Gaussian noise. We show that in the Markovian limit, these two unravelings correspond to heterodyne and homodyne detection, respectively. Although we use quantum-measurement theory to define these unravelings, we conclude that the stochastic evolution of the system state is not a true quantum trajectory, as the identity of the state through time is a fiction.

Gambetta, Jay; Wiseman, H. M.

2002-07-01

283

Stability theory for difference approximations of some dispersive shallow water equations

Modeling of thin film flows Â§ Shallow water equations with surface tension Â§ Related models 1: phase transition Â§ Related models 2: water waves 2 Stability of difference approximations for shallow water eqs: shallow water equations I General model: Navier-Stokes (NS) equations with a free surface Â§ Unknowns

d'OrlÃ©ans, UniversitÃ©

284

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

N. V. Krylov; B. L. Rozovskii

1982-01-01

285

In this article we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory that can be applied to open quantum systems without requiring a particular form of the interactions. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a c...

Kelly, Aaron; Markland, Thomas E

2015-01-01

286

Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.

Giacometti, Achille, E-mail: achille.giacometti@unive.it [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia (Italy)] [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia (Italy); Gögelein, Christoph, E-mail: christoph.goegelein@ds.mpg.de [Max-Planck-Institute for Dynamics and Self-Organization, Göttingen (Germany)] [Max-Planck-Institute for Dynamics and Self-Organization, Göttingen (Germany); Lado, Fred, E-mail: lado@ncsu.edu [Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 (United States)] [Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 (United States); Sciortino, Francesco [Dipartimento di Fisica and CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma (Italy)] [Dipartimento di Fisica and CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma (Italy); Ferrari, Silvano, E-mail: silvano.ferrari@tuwien.ac.at [Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wiedner Hauptstraße 8-10/136, A-1040 Wien (Austria)] [Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wiedner Hauptstraße 8-10/136, A-1040 Wien (Austria); Pastore, Giorgio, E-mail: pastore@ts.infn.it [Dipartimento di Fisica dell’ Università di Trieste and CNR-IOM, Strada Costiera 11, 34151 Trieste (Italy)] [Dipartimento di Fisica dell’ Università di Trieste and CNR-IOM, Strada Costiera 11, 34151 Trieste (Italy)

2014-03-07

287

NASA Astrophysics Data System (ADS)

Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.

Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano; Pastore, Giorgio

2014-03-01

288

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. PMID:19256946

Ruban, V P

2008-12-01

289

Numerical Simulations of PT-Symmetric Quantum Field Theories

Many non-Hermitian but PT-symmetric theories are known to have a real positive spectrum. Since the action is complex for there theories, Monte Carlo methods do not apply. In this paper the first field-theoretic method for numerical simulations of PT-symmetric Hamiltonians is presented. The method is the complex Langevin equation, which has been used previously to study complex Hamiltonians in statistical physics and in Minkowski space. We compute the equal-time one-point and two-point Green's functions in zero and one dimension, where comparisons to known results can be made. The method should also be applicable in four-dimensional space-time. Our approach may also give insight into how to formulate a probabilistic interpretation of PT-symmetric theories.

Claude Bernard; Van M. Savage

2001-06-15

290

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

291

The solution of the equation XA + AX T = 0 and its application to the theory of orbits

describe how to find the general solution of the matrix equation XA+AXT=0, with A?Cn×n, which allows us to determine the dimension of its solution space. This result has immediate applications in the theory of congruence orbits of matrices in Cn×n, because the set {XA+AXT:X?Cn×n} is the tangent space at A to the congruence orbit of A. Hence, the codimension of

Fernando De Terán; Froilán M. Dopico

2011-01-01

292

A review of the present status of the application of Lie-group theory to the solution of first-order ordinary differential equations (ODEs) is given. A code written in the MACSYMA language is presented which finds and solves first-order DOEs invariant under group with infinitesimal generation of the form U = A(x)B(y)delta\\/sub x\\/ + C(x)D(y)delta\\/sub y\\/. An algorithm is given by which

1979-01-01

293

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

294

NASA Astrophysics Data System (ADS)

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree-Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.

Hahn, Y. K.

2014-12-01

295

2D/1D approximations to the 3D neutron transport equation. I: Theory

A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)

Kelley, B. W.; Larsen, E. W. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109 (United States)

2013-07-01

296

Generalized Langevin models of molecular dynamics simulations with applications to ion channels

NASA Astrophysics Data System (ADS)

We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as "distributional molecular dynamics," and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.

Gordon, Dan; Krishnamurthy, Vikram; Chung, Shin-Ho

2009-10-01

297

Interpretation of quantum Hall effect from angular momentum theory and Dirac equation

It is found that when suitable modifications to the g values are made, the effective charge of a particle is determined by eeff =(1\\/2)ge, which enters in the Dirac equation to yield the fractional charges. The calculated values of the fractional charges agree with the data on fractional charge deduced from the quantum Hall effect. Therefore, the Dirac equation can

Keshav Shrivastava

2007-01-01

298

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

299

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

300

Ising field theory: Quadratic difference equations for the n-point Green's functions on the lattice

For the two-dimensional Ising model at arbitrary temperature, we present a system of quadratic difference equations involving the correlations of n order variables and that of n-2 order and 2 disorder variables. With suitable boundary conditions these equations specify the correlations.

Barry McCoy; Jacques Perk; Tai Wu

1981-01-01

301

The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can actually occur.

Walter Bergweiler; Alexandre Eremenko

2009-08-31

302

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

303

NASA Astrophysics Data System (ADS)

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.

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

2010-11-01

304

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Rubinstein, Robert; Zhou, Ye

1996-01-01

305

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

306

Lie and Morse Theory for Periodic Orbits of Vector Fields and Matrix Riccati Equations, II

In this paper, elementary techniques from linear algebra and elementary properties of the Grassmann manifolds are used to prove the existence of periodic orbits and to study the equilibrium structure of Riccati differential equations.

Robert Hermann; Clyde Martin

1983-01-01

307

Scattering theory for the Dirac equation of Hartree type in 2+1 dimensions

Consider a scattering problem for the Dirac equation with a nonlocal term including the Hartree type in two dimensions. We show the existence of scattering operators for small data in the subcritical and critical Sobolev spaces.

Shuji Machihara; Kimitoshi Tsutaya

2009-01-01

308

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

309

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

AND J. SABIN 1. Introduction The time-dependent Hartree equation i tu = - x + w |u|2 u, (t, x) R Ã? Rd equations of the previous form: i tu1 = -x + w N k=1 |uk|2 u1, ... i tuN = -x + w N k=1 |uk|2 uN , uj(0 to Frank, Lieb, Seiringer and the first author of this article. Contents 1. Introduction 2 2. Main results

Recanati, Catherine

310

Structural analysis of differential-algebraic equation systems—theory and applications

The choice of a feasible numerical method for the solution of a Differential-Algebraic Equation (DAE) model of general type F(z,z,u) = 0 requires knowledge about its solvability, index, number and type of dynamic degrees of freedom as well as the set of equations to be satisfied by consistent initial conditions. Furthermore, a set of design quantities has to be specified.

J. Unger; A. Kröner; W. Marquardt

1995-01-01

311

NASA Astrophysics Data System (ADS)

Two recent papers [V. Yakhot, Phys. Rev. E 63, 026307, (2001) and R. J. Hill, J. Fluid Mech. 434, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of dynamic equations for structure functions of arbitrary order in turbulence. These equations are not closed. Yakhot proposed a ``mean-field theory'' to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments, and for its behavior for intermediate amplitudes. At high Reynolds numbers, some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure, as well as on other aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.

Kurien, Susan; Sreenivasan, Katepalli R.

2001-11-01

312

Two recent papers [V. Yakhot, Phys. Rev. E 63, 026307, (2001) and R. J. Hill, J. Fluid Mech. 434, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of dynamic equations for structure functions of arbitrary order in turbulence. These equations are not closed. Yakhot proposed a "mean-field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and expressions for the peak in the probability density function of transverse velocity increments, and for its behavior for intermediate amplitudes. At high Reynolds numbers, some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure, as well as on other aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory. PMID:11736089

Kurien, S; Sreenivasan, K R

2001-11-01

313

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

314

NASA Astrophysics Data System (ADS)

In this paper, we continue investigations on the solution methods for the generalized Percus-Yevick equations for the pair correlation functions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In this paper, a translational invariance approximation is used to reduce the number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a polymer consisting of N beads (monomers). The behavior of an isolated polymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of universality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end distance distribution functions, intermediate distribution functions, chemical potentials, the density distributions, and various expansion factors of the polymer chain are computed from the solutions of the integral equations in the case of coiled, ideal, and collapsed states of the polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T)-B(?¯)], where B(T) is the second virial coefficient and ?¯ is a modified ? temperature. The values of these exponents approach those from the known theories of polymer collapse as the chain length becomes long and the ratio of bond length to bead radius becomes large.

Gan, Hin Hark; Eu, Byung Chan

1994-04-01

315

Diffuse optical tomography through solving a system of quadratic equations: theory and simulations

NASA Astrophysics Data System (ADS)

This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.

Kanmani, B.; Vasu, R. M.

2006-02-01

316

The tap density of a granular powder is often linked to the flowability via the 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 the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are 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 environmental temperature are grouped into this parameter that weighs the pace of the 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). PMID:25589375

Hao, Tian

2015-02-11

317

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

318

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

319

NASA Astrophysics Data System (ADS)

Many properties of solutions to linear differential equations with unbounded operator coefficients (their boundedness, almost periodicity, stability) are closely connected with the corresponding properties of the differential operator defining the equation and acting in an appropriate function space. The structure of the spectrum of this operator and whether it is invertible, correct, and Fredholm depend on the dimension of the kernel of the operator, the codimension of its range, and the existence of complemented subspaces. The notion of a state of a linear relation (multivalued linear operator) is introduced, and is associated with some properties of the kernel and range. A linear difference operator (difference relation) is assigned to the differential operator under consideration (or the corresponding equation), the sets of their states are proved to be the same, and necessary and sufficient conditions for them to have the Fredholm property are found. Criteria for the almost periodicity at infinity of solutions of differential equations are derived. In the proof of the main results, the property of exponential dichotomy of a family of evolution operators and the spectral theory of linear relations are heavily used. Bibliography: 98 titles.

Baskakov, Anatoly G.

2013-02-01

320

Equation-of-state spinning fluids in the Einstein-Cartan theory

NASA Technical Reports Server (NTRS)

The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.

Ray, John R.; Smalley, Larry L.

1987-01-01

321

We present the recent works \\cite{trisetyarso2011} on the application of Darboux transformation on one-dimensional Dirac equation related to the field of Quantum Information and Computation (QIC). The representation of physical system in one-dimensional equation and its transformation due to the Bagrov, Baldiotti, Gitman, and Shamshutdinova (BBGS)-Darboux transformation showing the possibility admitting the concept of relativity and the trade-off of concurrent condition of quantum and classical physics play into the area of QIC. The applications in cavity quantum electrodynamics and on the proposal of quantum transistor are presented.

Agung Trisetyarso

2014-11-23

322

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

323

611: Electromagnetic Theory II Special relativity; Lorentz covariance of Maxwell equations

611: Electromagnetic Theory II CONTENTS Â· Special relativity; Lorentz covariance of Maxwell Â· Action principle for electromagnetism; energy-momentum tensor Â· Electromagnetic waves; waveguides Electromagnetic Fields 42 3.1 Description in terms of potentials

Pope, Christopher

324

611: Electromagnetic Theory II Special relativity; Lorentz covariance of Maxwell equations

611: Electromagnetic Theory II CONTENTS #15; Special relativity; Lorentz covariance of Maxwell particles #15; Action principle for electromagnetism; energy-momentum tensor #15; Electromagnetic waves Electromagnetic Fields 38 3.1 Description in terms of potentials

Pope, Christopher

325

611: Electromagnetic Theory II . Special relativity; Lorentz covariance of Maxwell equations

611: Electromagnetic Theory II CONTENTS . Special relativity; Lorentz covariance of Maxwell . Action principle for electromagnetism; energyÂmomentum tensor . Electromagnetic waves; waveguides Electromagnetic Fields 42 3.1 Description in terms of potentials

Pope, Christopher

326

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. PMID:25362323

Huš, Matej; Munaò, Gianmarco; Urbic, Tomaz

2014-10-28

327

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

328

Hypersingular integral equations not needed in the impedance problem in scattering theory

We propose a new approach to the analysis of the impedance problem for the Helmholtz equation in the exterior of a body (obstacle) in two and three dimensions. This approach can be called ‘method of interior boundaries’, because an additional boundary is introduced inside the scattering body. An appropriate boundary condition is specified on the additional boundary. The solution of

P. A. Krutitskii

2003-01-01

329

NASA Astrophysics Data System (ADS)

In Part I of this work, we derived a general equation of motion, based only on the special theory of relativity and energy conservation. This equation, turned out to be that of Newton, in the case the motion is driven by a weak gravitational field, with a velocity small as compared to the velocity of light. Thus in Part I we found -(GM_0/(r_0)^2)(1-(v_0)^2/(c_0)^2)=v_0dv_0/dr0 (written by the author, in the local frame of reference) here r0 is the distance of the object to the center of celestial object of mass M_0, v0 its velocity, as referred to the local observer; G is the universal constant of gravitation, and c0 the velocity of light in empty space. The above equation is written for the local observer; we should as well be able to write it, as seen by the distant observer. Thus, as we have discussed, the rest mass of an object in a gravitational field (in fact in any field the object in hand enters into interaction), is decreased as much as its binding energy in the field; a mass deficiency conversely, via quantum mechanics, yields (on the contrary to what the general theory of relativity predicts), the stretching of its size, as well as the weakening of its internal energy [1]. Henceforth we are not in the need of the Â"principle of equivalenceÂ" assumed by the general theory of relativity, in order to predict the occurrences dealt with this theory [2]. Our approach then, as viewed by the distant observer, yields -(GM_0/r^2)e^-?_0(1-2e^2?_0(v^2/(c_0)^2))=vdv/dr; ?_0r=GM_0/(r(c_0)^2); here r is the distance of the object to the center of celestial object of mass M_0, and v its velocity, as referred to the distant observer. The frame drawn by the above equation allows us to derive the essential findings of the general theory of relativity, i.e. the bending of light through its passage nearby a celestial body, and the precession of the perihelion of the planets. Thus light is deflected exactly twice of what is classically predicted, whereas we predict for Mercury, a precession of the perihelion about 1.3Einstein predicted; the difference in question is experimentally indiscernible in the case of Mercury, but it should become more important, in a stronger field. Following our approach we further undertake the behavior of an object thrown with a very high speed from a celestial body; this amazingly evokes the inflationary behavior of the universe, at the very beginning. [1] T. Yarman, Invariances Based on Mass And Charge Variation, Manufactured by Wave Mechanics, Making up The Rules of Universal Matter Architecture, Chimica Acta Turcica, Vol 27, 1999. [2] T. Yarman, A Novel Approach to The End Results of the General Theory of Relativity and to Bound Muon Decay Rate Retardation, DAMOP 2001 Meeting, APS, May 16 -19, 2001, London, Ontario, Canada.

Yarman, Tolga

2003-04-01

330

General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of “effective” particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

Doktorov, Alexander B.; Kipriyanov, Alexey A. [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090 (Russian Federation)] [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090 (Russian Federation)

2014-05-14

331

Scattering theory for the fourth-order Schrödinger equation in low dimensions

NASA Astrophysics Data System (ADS)

We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial dimensions (1 ? n ? 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 791-822), we utilize a strategy from Kenig and Merle (2006 Invent. Math. 166 645-75) to compensate for the absence of a Morawetz-type estimate, then we use a new virial-type ingredient to finish the proof.

Pausader, Benoit; Xia, Suxia

2013-08-01

332

ERIC Educational Resources Information Center

One model that is potentially useful in the rehabilitation field is the Consumer-Directed Theory of Empowerment (CDTE; Kosciulek, 1999a). However, additional empirical data are needed to further develop and critically evaluate the CDTE. To accomplish this task, the purpose of this study was to test the hypothesized structural model CDTE in a…

Kosciulek, John F.

2005-01-01

333

The passing rate of the Medical Licensing Examination has been variable, which probably originated from the difference in the difficulty of items and/or difference in the ability level of examinees. We tried to explain the origin of the difference using the test equating method based on the item response theory. The number of items and examinees were 500, 3,647 in 2003 and 550, 3,879 in 2004. Common item nonequivalent group design was used for 30 common items. Item and ability parameters were calculated by three parametric logistic models using ICL. Scale transformation and true score equating were executed using ST and PIE. The mean of difficulty index of the year 2003 was -0.957 (SD 2.628) and that of 2004 after equating was -1.456 (SD 3.399). The mean of discrimination index of year 2003 was 0.487 (SD 0.242) and that of 2004 was 0.363 (SD 0.193). The mean of ability parameter of year 2003 was 0.00617 (SD 0.96605) and that of year 2004 was 0.94636 (SD 1.32960). The difference of the equated true score at the same ability level was high at the range of score of 200-350. The reason for the difference in passing rates over two consecutive years was due to the fact that the Examination in 2004 was easier and the abilities of the examinees in 2004 were higher. In addition, the passing rates of examinees with score of 270-294 in 2003, and those with 322-343 in 2004, were affected by the examination year. PMID:19223994

Yim, Mi Kyoung; Huh, Sun

2006-01-01

334

NASA Astrophysics Data System (ADS)

In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.

Planková, Barbora; Hrubý, Jan; Vinš, Václav

2013-04-01

335

Theory of warm ionized gases: equation of state and kinetic Schottky anomaly

Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed.

Capolupo, Antonio; Illuminati, Fabrizio

2013-01-01

336

Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.

Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments. PMID:24229140

Capolupo, A; Giampaolo, S M; Illuminati, F

2013-10-01

337

Calculation of scattering with the light-cone two-body equation in ?3 theories

NASA Astrophysics Data System (ADS)

The analysis of the light-cone two-body bound-state equation is extended to the scattering problem. The rotational invariance is violated in the light-cone quantization method when the Fock space is truncated for practical calculations. Using a simple scalar field model, we investigate the explicit rotation dependence of the two-body scattering phase shifts in the light-cone quantization approach. We find the regions of coupling constant and c.m. momentum where the rotation dependence in the phase shift is negligible. We also make a connection of our analysis with the light-cone scattering formalism recently presented by Fuda.

Ji, Chueng-Ryong; Surya, Yohanes

1992-10-01

338

Reconstruction and Convergence in Quantum $K$-Theory via Difference Equations

We give a new reconstruction method of big quantum $K$-ring based on the $q$-difference module structure in quantum $K$-theory. The $q$-difference structure yields commuting linear operators $A_{i,\\rm com}$ on the $K$-group as many as the Picard number of the target manifold. The genus-zero quantum $K$-theory can be reconstructed from the $q$-difference structure at the origin $t=0$ if the $K$-group is generated by a single element under the actions of $A_{i,\\rm com}$. This method allows us to prove the convergence of the big quantum $K$-rings of certain manifolds, including the projective spaces and the complete flag manifold $\\operatorname{Fl}_3$.

Hiroshi Iritani; Todor Milanov; Valentin Tonita

2013-09-15

339

Integrable Structure of Conformal Field Theory II.Q-operator and DDV equation

: This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory.\\u000a We show here how to construct the operators ${\\\\bf Q}_{\\\\pm}(\\\\lambda)$ which act in the highest weight Virasoro module and commute\\u000a for different values of the parameter ?. These operators appear to be the CFT analogs of the Q -

Vladimir V. Bazhanov; Sergei L. Lukyanov; Alexander B. Zamolodchikov

1997-01-01

340

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

341

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

342

arXiv:quantph/9804051v1 Quantum Langevin equations for semiconductor light-emitting devices

the semiconductor QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula for the Fano factor parameters of LEDs. Key ingredients are non-radiative processes, carrier-number dependence of the radiative and non-radiative lifetimes, and multimodeness of LEDs. The formula is applicable to the actual cases

Shimizu, Akira

343

NASA Astrophysics Data System (ADS)

We present several approaches for deriving the coarse-grained continuous Langevin equation (or Edwards-Wilkinson equation) from a random deposition with surface relaxation (RDSR) model. First we introduce a novel procedure to divide the first transition moment into the three fundamental processes involved: deposition, diffusion and volume conservation. We show how the diffusion process is related to the antisymmetric contribution and the volume conservation process is related to the symmetric contribution, which renormalizes to zero in the coarse-grained limit. In another approach, we find the coefficients of the continuous Langevin equation, by regularizing the discrete Langevin equation. Finally, in a third approach, we derive these coefficients from the set of test functions supported by the stationary probability density function (SPDF) of the discrete model. The applicability of the approaches used to other discrete random deposition models with instantaneous relaxation to a neighboring site is discussed.

Buceta, R. C.; Hansmann, D.; von Haeften, B.

2014-12-01

344

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

345

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

346

Equation of state of two-dimensional Yang-Mills theory

NASA Astrophysics Data System (ADS)

We study the pressure, P , of SU (N ) gauge theory on a two-dimensional torus as a function of area, A =l /t . We find a crossover scale that separates the system on a large circle from a system on a small circle at any finite temperature. The crossover scale approaches zero with increasing N and the crossover becomes a first-order transition as N ?? and l ?0 with the limiting value of 2/P l (N -1 )t depending on the fixed value of N l .

Karthik, Nikhil; Narayanan, Rajamani

2014-12-01

347

The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.

Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D.; Parker, G.A.; Redmon, M.J.; Schmalz, T.G.; Secrest, D.; Walker, R.B.

1980-07-01

348

The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.

Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester, W.A. Jr.; Light, J.C.; McLenithan, K.D.; Parker, G.A.; Redmon, M.J.; Schmalz, T.G.; Secrest, D.; Walker, R.B.

1981-06-01

349

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

350

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

351

Perturbation theory based equation of state for polar molecular fluids: II. Fluid mixtures

NASA Astrophysics Data System (ADS)

The equation of state (EOS) for 98 pure organic and inorganic fluids formulated by Churakov and Gottschalk (2003) is extended to complex fluid mixtures. For the calculation of the thermodynamic properties of mixtures, theoretical combining rules from statistical mechanics are used. These mixing rules do not involve any empirical parameters. The properties of the fluid mixtures are directly derived from those of the pure constituents. As an example we show that the EOS describes accurately the thermodynamic relations in the H 2O-CO 2 binary at high pressures and temperatures. At subcritical conditions the EOS is able to reproduce accurately the phase relations within mixtures of non-polar fluids. In particular the EOS predicts phase separations within various fluid mixtures of polar and non-polar molecules.

Churakov, S. V.; Gottschalk, M.

2003-07-01

352

The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

NASA Astrophysics Data System (ADS)

We construct the Lax-pair, the classical monodromy matrix and the corresponding solution of the Yang-Baxter equation, for a two-parameter deformation of the Principal chiral model for a simple group. This deformation includes as a one-parameter subset, a class of integrable gauged WZW-type theories interpolating between the WZW model and the non-Abelian T-dual of the principal chiral model. We derive in full detail the Yangian algebra using two independent methods: by computing the algebra of the non-local charges and alternatively through an expansion of the Maillet brackets for the monodromy matrix. As a byproduct, we also provide a detailed general proof of the Serre relations for the Yangian symmetry.

Itsios, Georgios; Sfetsos, Konstantinos; Siampos, Konstantinos; Torrielli, Alessandro

2014-12-01

353

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

354

NASA Astrophysics Data System (ADS)

We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green’s functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.

Feng, Qingguo; Oppeneer, P. M.

2012-02-01

355

NASA Astrophysics Data System (ADS)

We present in this paper a general analytical solution to the integral equations of liquid state theories (Born-Green-Yvon, hyper-netted-chain, and Percus-Yevick Equations) at low-density limit for potentials with a hard core. For the specific case of the Lennard-Jones potential with a hard core, we have derived an analytical function for the radial distribution function at high temperature and low density. We have noted that this function has two humps which is the characteristic feature of the radial distribution function at low densities. In addition, this function has been used to calculate the third virial coefficient for such a fluid exactly. We see that for the especial case of Lennard-Jones fluid with a hard core, which its radial distribution function has explicitly been calculated at high temperatures, the correct behavior of the third virial coefficient with temperature is obtained. The magnitude of hard-core diameter has significant effect on the thermodynamic properties of fluid: for instance, when the diameter changes only by a few percent the third virial coefficient may change more than 100%. The hard-core diameter decreases when temperature increases. The reduction is less than 20%. For the supercritical fluid, the calculated compression factor and internal energy are in good agreement with those obtained from the simulation for the Lennard-Jones fluid.

Khanpour, Mehrdad; Parsafar, G. A.; Najafi, B.

2004-05-01

356

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- n bar 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

357

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

358

The notion of error in Langevin dynamics. I. Linear analysis Bimal Mishra and Tamar Schlicka)

for the averages of the potential, kinetic, and total energy; and various limiting cases e.g., timestep and damping by analyzing the behavior of selected implicit and explicit finite-difference algorithms for the Langevin-dependent perturbative damping and perturbative frequency functions. Interesting differences in the asymptotic behavior

Schlick, Tamar

359

Generalized Langevin models of molecular dynamics simulations with applications to ion channels

Generalized Langevin models of molecular dynamics simulations with applications to ion channels Dan present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile

Krishnamurthy, Vikram

360

The augmented Langevin approach described in a previous article is applied to the problem of introducing multiplicative noise and nonlinear dissipation into an arbitrary Hamiltonian system in a thermodynamically consistent way, so that a canonical equilibrium distribution is approached asymptotically at long times. This approach leads to a general nonlinear fluctuation-dissipation relation which, for a given form of the multiplicative

John D. Ramshaw; Katja Lindenberg

1986-01-01

361

Lattice model theory of the equation of state covering the gas, liquid, and solid phases

NASA Technical Reports Server (NTRS)

The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.

Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.

1975-01-01

362

Polymer field-theory simulations on graphics processing units

NASA Astrophysics Data System (ADS)

We report the first CUDA™ graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic polymer systems. Our implementation is suitable both for self-consistent field theory (mean-field) solutions of the field equations, and for fully fluctuating simulations using the complex Langevin approach. Running on NVIDIA® Tesla T20 series GPUs, we find double-precision speedups of up to 30× compared to single-core serial calculations on a recent reference CPU, while single-precision calculations proceed up to 60× faster than those on the single CPU core. Due to intensive communications overhead, an MPI implementation running on 64 CPU cores remains two times slower than a single GPU.

Delaney, Kris T.; Fredrickson, Glenn H.

2013-09-01

363

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

364

A generalized nodal finite element formalism is presented, which covers virtually all known finite difference approximations to the discrete ordinates equations in slab geometry. This paper (hereafter referred to as Part II) presents the theory of the so-called “discontinuous moment methods”, which include such well-known methods as the “linear discontinuous” scheme. It is the sequel of a first paper (Part

J. P. Hennart; E. del Valle

1995-01-01

365

A generalized nodal finite element formalism is presented, which covers virtually all known finite difference approximations to the discrete ordinates equations in slab geometry. This paper (Part I) presents the theory of the so-called “continuous moment methods”, which include such well-known methods as the “diamond difference” and the “characteristic” schemes. In a second paper (hereafter referred to as Part II),

J. P. Hennart; E. del Valle

1995-01-01

366

electromagnetism as it is for quantum mechanics and other fields. Not only does it allow one to apply, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory tech- niques, however, have difficulties when applied to Maxwell's equations for small

367

Constant pressure and temperature discrete-time Langevin molecular dynamics.

We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. PMID:25416875

Grønbech-Jensen, Niels; Farago, Oded

2014-11-21

368

Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation

We investigate some unusual behaviour observed while performing molecular dynamics simulations with the DL_POLY_4.03 code. Under the standard Langevin thermostat, atoms appear to be thermalised to different temperatures, depending on their mass and on the total number of particles in the system. We find that an imposed constraint whereby no thermal noise acts on the centre of mass of the system is the cause of the unexpected behaviour. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. The effect of the constraint can be considerable for small systems with disparate masses. By removing the constraint the Langevin thermostat may be restored to its intended behaviour and this has been implemented as an option in DL_POLY_4.05. SMK was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

Stinson, Jake L.; Kathmann, Shawn M.; Ford, Ian J.

2014-11-17

369

The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the\\u000a approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at larger\\u000a chemical potential by comparison with the world line method. While complex Langevin works for larger ?, we find that it fails for smaller ?, in

Gert Aarts; Frank A. James

2010-01-01

370

Using a set of general methods developed by Krotov [A. I. Konnov and V. A. Krotov, Automation and Remote Control, {\\bf 60}, 1427 (1999)], we extend the capabilities of Optimal Control Theory to the Nonlinear Schr\\"odinger Equation (NLSE). The paper begins with a general review of the Krotov approach to optimization. Although the linearized version of the method is sufficient for the linear Schr\\"odinger equation, the full flexibility of the general method is required for treatment of the nonlinear Schr\\"odinger equation. Formal equations for the optimization of the NLSE, as well as a concrete algorithm are presented. As an illustration, we consider a Bose-Einstein condensate initially at rest in a harmonic trap. A phase develops across the BEC when an optical lattice potential is turned on. The goal is to counter this effect and keep the phase flat by adjusting the trap strength. The problem is formulated in the language of Optimal Control Theory (OCT) and solved using the above methodology. To our knowledge, this is the first rigorous application of OCT to the Nonlinear Schr\\"odinger equation, a capability that is bound to have numerous other applications.

Shlomo E. Sklarz; David J. Tannor

2002-09-09

371

NASA Astrophysics Data System (ADS)

In this paper, the (G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann—Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota—Satsuma coupled KdV equations and the time-fractional fifth-order Sawada—Kotera equation. As a result, some new exact solutions for them are successfully established.

Zheng, Bin

2012-11-01

372

Robust and efficient configurational molecular sampling via Langevin dynamics

NASA Astrophysics Data System (ADS)

A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation). The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep.

Leimkuhler, Benedict; Matthews, Charles

2013-05-01

373

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

374

The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables it reduces to a pair of decoupled bicomplex Vekua-type equations [8]. Using the technique developed for complex Vekua equations a system of exact solutions for the bicomplex equation is conctructed under additional conditions, in particular when the electromagnetic potential is absent and the scalar potential is a function of one Cartesian variable. Introducing a transmutation operator relating the involved bicomplex Vekua equation with the Cauchy-Riemann equation we prove the expansion and the Runge approximation theorems corresponding to the constructed family of solutions.

Hugo M. Campos; Vladislav V. Kravchenko; Luis M. Mendez

2011-11-17

375

In previous paper we have shown that there is a special kind of nonlinear\\u000aelectrodynamics - Curvilinear Wave Electrodynamics (CWED), whose equations are\\u000amathematically equivalent to the equations of quantum electrodynamics. The\\u000apurpose of the present paper is to show that in framework of CWED the known\\u000asolutions of the nonlinear electromagnetic equations can be considered as the\\u000aapproximate solutions

Alexander G. Kyriakos

2005-01-01

376

Kinematic matrix theory and universalities in self-propellers and active swimmers.

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers. PMID:25019773

Nourhani, Amir; Lammert, Paul E; Borhan, Ali; Crespi, Vincent H

2014-06-01

377

Kinematic matrix theory and universalities in self-propellers and active swimmers

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix", from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.

Amir Nourhani; Paul E. Lammert; Ali Borhan; Vincent H. Crespi

2014-09-10

378

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the

Alexander Dubkov; Bernardo Spagnol

2005-01-01

379

NSDL National Science Digital Library

This activity is designed to help building student understanding of how scientific theories can change over time. Science theories change in the face of new evidence. However, when new explanatory frameworks, or theories, are proposed to explain scientific phenomena, there is often a lengthy period during which groups of scientists use different competing theories to explain the same phenomena. During the activity, students are introduced to the geocentric and heliocentric models, students compare the two models, and then observe the time it took to change the theory underpinning the heliocentric model. This activity is part of the "Swift: Eyes through Time" collection that is available on the Teacher's Domain website.

380

The Henderson-Hasselbalch equation is probably the most famous equation in biology but is more descriptive than mechanistic. The traditional approach to acid-base assessment using the Henderson-Hasselbalch equation provides a clinically useful and accurate method when plasma protein concentrations are within the reference range. The simplified strong ion approach is a mechanistic acid-base model that can provide new insight into complicated acid-base disturbances. The simplified strong ion approach should be used to evaluate acid-base balance whenever plasma protein concentrations are abnormal. PMID:24980723

Constable, Peter D

2014-07-01

381

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

382

Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out. {copyright} {ital 1999} {ital The American Physical Society}

Frenkel, A.L.; Indireshkumar, K. [Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350 (United States)] [Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350 (United States)

1999-10-01

383

Progress in complex Langevin simulations of full QCD at non-zero density

NASA Astrophysics Data System (ADS)

Progress in the application of the complex Langevin method to full QCD at non-zero chemical potential is reported. The method evades the sign problem which makes naive simulations at non-zero density impossible. The procedure 'gauge cooling' is used to stabilize the simulations at small enough lattice spacings. The method allows simulations also at high densities, all the way up to saturation. Simulations in a systematic hopping parameter expansion are also performed and good convergence is observed, validating the full as well as the expanded simulations.

Sexty, Dénes

2014-11-01

384

First results of the (n,?) EXILL campaigns at the Institut Laue Langevin using EXOGAM and FATIMA

NASA Astrophysics Data System (ADS)

At the PF1B cold neutron beam line at the Institut Laue Langevin the EXILL array consisting of EXOGAM, GASP and LOHENGRIN detectors was used to perform (n,?) measurements under very high coincidence rates. About ten different reactions were then measured in autumn 2012. In spring 2013 the EXOGAM array was combined with 16 LaBr3(Ce) scintillators in the FATIMA@EXILL campaign for the measurement of lifetimes using the generalised centroid difference method. We report on the properties of both set-ups and present first results on Pt isotopes from both campaigns.

Jolie, J.; Régis, J.-M.; Wilmsen, D.; Ahmed, S.; Pfeiffer, M.; Saed-Samii, N.; Warr, N.; Blanc, A.; Jentschel, M.; Köster, U.; Mutti, P.; Soldner, T.; Simpson, G.; de France, G.; Urban, W.; Bruce, A. M.; Roberts, O. J.; Fraile, L. M.; Paziy, V.; Ignatov, A.; Ilieva, S.; Kröll, Th; Scheck, M.; Thürauf, M.; Ivanova, D.; Kisyov, S.; Lalkovski, S.; Podolyak, Zs; Regan, P. H.; Korten, W.; Habs, D.; Thirolf, P. G.; Ur, C. A.

2014-09-01

385

New source for ultracold neutrons at the Institut Laue-Langevin

NASA Astrophysics Data System (ADS)

A new intense superthermal source for ultracold neutrons (UCN) was installed at a dedicated beam line at the Institut Laue-Langevin. Incident neutrons with a wavelength of 0.89 nm are converted to UCN in a 5-liter volume filled with superfluid He4 at a temperature of about 0.7 K. The UCN can be extracted to room temperature experiments. We present the cryogenic setup of the source, a characterization of the cold neutron beam, and UCN production measurements, where a UCN density in the production volume of at least 55 per cm3 was determined.

Piegsa, F. M.; Fertl, M.; Ivanov, S. N.; Kreuz, M.; Leung, K. K. H.; Schmidt-Wellenburg, P.; Soldner, T.; Zimmer, O.

2014-07-01

386

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

387

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

388

NASA Astrophysics Data System (ADS)

In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.

Doktorov, A. B.

2014-09-01

389

In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed. PMID:25217901

Doktorov, A B

2014-09-14

390

A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered.

Uma, B.; Radhakrishnan, R.; Eckmann, D.M.

2014-01-01

391

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data. PMID:23185059

Sukoriansky, Semion; Galperin, Boris

2013-01-13

392

Time evolution of the onsager regression variables: A microscopic theory

NASA Astrophysics Data System (ADS)

We derive a general exact expression obeyed by the Onsager regression variables for an arbitrary nonlinear markovian Langevin equation. In some approximations, we get a microscopic corroboration of the ansatz introduced by Hurley and Garrod to generalize the Onsager theorem. This is done explicitly for the nonlinear Zwanzig model.

Del Río-Correa, J. L.; Hernández-Machado, A.

1987-06-01

393

Thermal equilibrium properties of surface hopping with an implicit Langevin bath

NASA Astrophysics Data System (ADS)

The ability of fewest switches surface hopping (FSSH) approach, where the classical degrees of freedom are coupled to an implicit Langevin bath, to establish and maintain an appropriate thermal equilibrium was evaluated in the context of a three site model for electron transfer. The electron transfer model consisted of three coupled diabatic states that each depends harmonically on the collective bath coordinate. This results in three states with increasing energy in the adiabatic representation. The adiabatic populations and distributions of the collective solvent coordinate were monitored during the course of 250 ns FSSH-Langevin (FSSH-L) simulations performed at a broad range of temperatures and for three different nonadiabatic coupling strengths. The agreement between the FSSH-L simulations and numerically exact results for the adiabatic population ratios and solvent coordinate distributions was generally favorable. The FSSH-L method produces a correct Boltzmann distribution of the solvent coordinate on each of the adiabats, but the integrated populations are slightly incorrect because FSSH does not rigorously obey detailed balance. The overall agreement is better at high temperatures and for high nonadiabatic coupling, which agrees with a previously reported analytical and simulation analysis [J. R. Schmidt, P. V. Parandekar, and J. C. Tully, J. Chem. Phys. 129, 044104 (2008)] on a two-level system coupled to a classical bath.

Sherman, M. C.; Corcelli, S. A.

2015-01-01

394

Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics

We report a serious problem associated with a number of current implementations of Andersen and Langevin dynamics algorithms. When long simulations are run in many segments, it is sometimes possible to have a repeating sequence of pseudorandom numbers enter the calcuation. We show that, if the sequence repeats rapidly, the resulting artifacts can quickly denature biomolecules and are then easily detectable. However, if the sequence repeats less frequently, the artifacts become subtle and easily overlooked. We derive a formula for the underlying cause of artifacts in the case of the Langevin thermostat, and find it vanishes slowly as the inverse square root of the number of time steps per simulation segment. Numerous examples of simulation artifacts are presented, including dissociation of a tetrameric protein after 110 ns of dynamics, reductions in atomic fluctuations for a small protein in implicit solvent, altered thermodynamic properties of a box of water molecules, and changes in the transition free energies between dihedral angle conformations. Finally, in the case of strong thermocoupling, we link the observed artifacts to previous work in nonlinear dynamics and show that it is possible to drive a 20-residue, implicitly solvated protein into periodic trajectories if the thermostat is not used properly. Our findings should help other investigators re-evaluate simulations that may have been corrupted and obtain more accurate results. PMID:19180249

Cerutti, David S.; Duke, Robert; Freddolino, Peter L.; Fan, Hao; Lybrand, Terry P.

2008-01-01

395

Two-pulse solutions in the fifth-order KdV equation : rigorous theory and numerical approximations

We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg--de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhood of two-pulse solutions. Second, we prove structural stability of embedded eigenvalues of negative Krein signature in a linearized KdV equation. Combined with stability analysis in Pontryagin spaces, this result completes the proof of spectral stability of the corresponding two-pulse solutions. Eigenvalues of the linearized problem are approximated numerically in exponentially weighted spaces where embedded eigenvalues are isolated from the continuous spectrum. Approximations of eigenvalues and full numerical simulations of the fifth-order KdV equation confirm stability of two-pulse solutions related to the minima of the effective interaction potential and instability of two-pulse solutions related to the maxima points.

Marina Chugunova; Dmitry Pelinovsky

2006-05-23

396

A generalized nodal finite element formalism is presented, which covers virtually all known finite difference approximations to the discrete ordinates equations in slab geometry. This paper (hereafter referred to as Part II) presents the theory of the so-called discontinuous moment methods, which include such well-known methods as the linear discontinuous scheme. It is the sequel of a first paper (Part I) where continuous moment methods were presented. Corresponding numerical results for all the schemes of both parts will be presented in a third paper (Part III).

Hennart, J.P. [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas de la UNAM (Mexico); Valle, E. del

1995-04-01

397

NASA Astrophysics Data System (ADS)

We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional, bounded, multiply connected domain {? = ?_1 backslash overline{?}_2, overline?_2subset ?_1} . We prove that this problem has a solution if the flux {{F}} of the boundary value through ?? 2 is nonnegative (inflow condition). The proof of the main result uses the Bernoulli law for a weak solution to the Euler equations and the one-sided maximum principle for the total head pressure corresponding to this solution.

Korobkov, Mikhail V.; Pileckas, Konstantin; Russo, Remigio

2013-01-01

398

We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetry energy increases, while at energies of order 300 and 800 MeV, it is almost independent of L. This is a feature of the optical limit Glauber theory in which an exponential dependence of the reaction cross section on the neutron skin thickness remains when the total proton-neutron cross section is small enough.

K. Iida; K. Oyamatsu; B. Abu-Ibrahim; A. Kohama

2011-07-05

399

A generalized nodal finite element formalism is presented, which covers virtually all known finit difference approximation to the discrete ordinates equations in slab geometry. This paper (Part 1) presents the theory of the so called {open_quotes}continuous moment methods{close_quotes}, which include such well-known methods as the {open_quotes}diamond difference{close_quotes} and the {open_quotes}characteristic{close_quotes} schemes. In a second paper (hereafter referred to as Part II), the authors will present the theory of the {open_quotes}discontinuous moment methods{close_quotes}, consisting in particular of the {open_quotes}linear discontinuous{close_quotes} scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III). 12 refs.

Hennart, J.P.; Valle, E. del

1995-04-01

400

A Theory of Matter Wave Detection

From a microscopic model describing the detection process for matter waves, we derive a quantum theory of matter wave detection. We use perturbation theory to calculate the short-time approximation to the detection rate of matter waves and a Langevin-type calculation to obtain the long-time correction. In both instances we show that the detection rate can be related to the flux of the matter waves through a detector medium.

Whitlock, Nicholas K.; Barnett, Stephen M.; Jeffers, John [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Cresser, James D. [Physics Department, Macquarie University, NSW 2109 (Australia)

2004-11-15

401

Chaos theory was appeared as a scientific discipline at 1960's with Edward Lorenz, who has studied to model meteorological systems with Lorenz Equations in computer environment by using the data he collected to estimate the weather forecast. In these days, Chaos theory has successful applications in the fields such as secure communication, automatic control systems, laser physics and financial modeling.

Songül GÜNDÜZ

402

Hypersingular boundary integral equations (HBIE) have been studied very intensively in recent years especially because of their application for precise computations of potential gradient and stresses on the boundary. One free term which in general does not vanish for non-smooth boundary points with adjacent curved boundary parts has been omitted in previous formulations of HBIE. This paper demonstrates the presence

V. Manti?; F. París

1995-01-01

403

The positive purely imaginary roots of four equations, taking in complex confluent hypergeometric functions, are studied numerically. The first of them involves the Kummer function only, the second is stated through two Kummer and two Tricomi ones, the third is written by two complex Kummer and four real Bessel and Neumann functions, and the fourth - in terms of four

Mariana Nikolova Georgieva-Grosse; Georgi Nikolov Georgiev

2010-01-01

404

NASA Astrophysics Data System (ADS)

While free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal Lévy walks rather than Gaussian random walks with perturbations.

Kleinert, Hagen

2012-10-01

405

We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric tensor on reduced dimensions is negligible it becomes a pure antisymmetric tensor.

Pei Wang

2007-05-09

406

A wide range of questionnaires for measuring depression are available. Item Response Theory models can help to evaluate the questionnaires exceeding the boundaries of Classical Test Theory and provide an opportunity to equate the questionnaires. In this study after checking for unidimensionality, a General Partial Credit Model was applied to data from two different depression scales [Patient Health Questionnaire (PHQ-9) and ICD-10-Symptom Rating (ISR)] obtained in clinical settings from a consecutive sample, including 4517 observations from a total of 2999 inpatients and outpatients of a psychosomatic clinic. The precision of each questionnaire was compared and the model was used to transform scores based on the assumed underlying latent trait. Both instruments were constructed to measure the same construct and their estimates of depression severity are highly correlated. Our analysis showed that the predicted scores provided by the conversion tables are similar to the observed scores in a validation sample. The PHQ-9 and ISR depression scales measure depression severity across a broad range with similar precision. While the PHQ-9 shows advantages in measuring low or high depression severity, the ISR is more parsimonious and also suitable for clinical purposes. Furthermore, the equation tables derived in this study enhance the comparability of studies using either one of the instruments, but due to substantial statistical spread the comparison of individual scores is imprecise. PMID:22021205

Fischer, H Felix; Tritt, Karin; Klapp, Burghard F; Fliege, Herbert

2011-12-01

407

Two-pulse solutions in the fifth-order KdV equation : rigorous theory and numerical approximations

We revisit existence and stability of two-pulse solutions in the fifth-order Korteweg--de Vries (KdV) equation with two new results. First, we modify the Petviashvili method of successive iterations for numerical (spectral) approximations of pulses and prove convergence of iterations in a neighborhood of two-pulse solutions. Second, we prove structural stability of embedded eigenvalues of negative Krein signature in a linearized

Marina Chugunova; Dmitry Pelinovsky

2006-01-01

408

This paper presents an application of new discrete path integral solutions recently introduced for Fokker-Planck dynamics with the aim to compare their relative efficacy in giving precise numerical results. The basic idea used in the derivation of these solutions is to model a complex Fokker-Planck equation with a general drift coefficient by a linear (Ornstein-Uhlenbeck) process, which is solved exactly,

A. N. Drozdov; J. J. Brey

1998-01-01

409

NASA Technical Reports Server (NTRS)

A technique to deduce the virtual temperature from the combined use of the equations of fluid dynamics, observed wind and observed radiances is described. The wind information could come from ground-based sensitivity very high frequency (VHF) Doppler radars and/or from space-borne Doppler lidars. The radiometers are also assumed to be either space-borne and/or ground-based. From traditional radiometric techniques the vertical structure of the temperature can be estimated only crudely. While it has been known for quite some time that the virtual temperature could be deduced from wind information only, such techniques had to assume the infallibility of certain diagnostic relations. The proposed technique is an extension of the Gal-Chen technique. It is assumed that due to modeling uncertainties the equations of fluid dynamics are satisfied only in the least square sense. The retrieved temperature, however, is constrained to reproduce the observed radiances. It is shown that the combined use of the three sources of information (wind, radiances and fluid dynamical equations) can result in a unique determination of the vertical temperature structure with spatial and temporal resolution comparable to that of the observed wind.

Tzvi, G. C.

1986-01-01

410

The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. The new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces. PMID:25596368

Dahms, Rainer N

2015-05-01

411

Particle abundance in a thermal plasma: quantum kinetics vs. Boltzmann equation

We study the abundance of a particle species in a thermalized plasma by introducing a quantum kinetic description based on the non-equilibrium effective action. A stochastic interpretation of quantum kinetics in terms of a Langevin equation emerges naturally. We consider a particle species that is stable in the vacuum and interacts with \\emph{heavier} particles that constitute a thermal bath in equilibrium and define of a fully renormalized single particle distribution function. The distribution function thermalizes on a time scale determined by the \\emph{quasiparticle} relaxation rate. The equilibrium distribution function depends on the full spectral density and features off-shell contributions to the particle abundance. A model of a bosonic field $\\Phi$ in interaction with two \\emph{heavier} bosonic fields is studied. We find substantial departures from the Bose-Einstein result both in the high temperature and the low temperature but high momentum region. In the latter the abundance is exponentially suppressed but larger than the Bose-Einstein result. We obtain the Boltzmann equation in renormalized perturbation theory and highlight the origin of the differences. We argue that the corrections to the abundance of cold dark matter candidates are observationally negligible and that recombination erases any possible spectral distortions of the CMB. However we expect that the enhancement at high temperature may be important for baryogenesis.

D. Boyanovsky; K. Davey; C. M. Ho

2004-11-02

412

A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II

We have performed three QM/Langevin-MD simulations for oxygen-evolving complex (OEC) and surrounding residues, which are different configurations of the oxidation numbers on Mn atoms in the Mn{sub 4}O{sub 5}Ca cluster. By analyzing these trajectories, we have observed sensitivity of the change to the configuration of Mn oxidation state on O atoms of carboxyl on three amino acids, Glu354, Ala344, and Glu333. The distances from Mn to O atoms in residues contacting with the Mn{sub 4}O{sub 5}Ca cluster were analyzed for the three trajectories. We found the good correlation of the distances among the simulations. However, the distances with Glu354, Ala344, and Glu333 have not shown the correlation. These residues can be sensitive index of the changes of Mn oxidation numbers.

Uchida, Waka; Kimura, Yoshiro; Wakabayashi, Masamitsu [Department of Biomolecular Engineering, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama 226-8503 (Japan); Hatakeyama, Makoto; Ogata, Koji; Nakamura, Shinichiro [RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Yokojima, Satoshi [Tokyo University of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan and RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)

2013-12-10

413

A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II

NASA Astrophysics Data System (ADS)

We have performed three QM/Langevin-MD simulations for oxygen-evolving complex (OEC) and surrounding residues, which are different configurations of the oxidation numbers on Mn atoms in the Mn4O5Ca cluster. By analyzing these trajectories, we have observed sensitivity of the change to the configuration of Mn oxidation state on O atoms of carboxyl on three amino acids, Glu354, Ala344, and Glu333. The distances from Mn to O atoms in residues contacting with the Mn4O5Ca cluster were analyzed for the three trajectories. We found the good correlation of the distances among the simulations. However, the distances with Glu354, Ala344, and Glu333 have not shown the correlation. These residues can be sensitive index of the changes of Mn oxidation numbers.

Uchida, Waka; Kimura, Yoshiro; Hatakeyama, Makoto; Wakabayashi, Masamitsu; Yokojima, Satoshi; Ogata, Koji; Nakamura, Shinichiro

2013-12-01

414

Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be successfully corrected by scaling each eigenvalue in the appropriate propagation matrix by the least-squares fitted slope of the blocked vs nonblocked eigenvalue spectra. The RTB responses for each test system were dominated by small eigenvalue overdamped Langevin modes. The large eigenvalue members of each response dissipated within the first 5 ps, after which the long time response was dominated by a modest set of low energy, overdamped normal modes, that were characterized by highly cooperative, functionally relevant displacements. The response assuming that the system is in the overdamped limit was compared to the full phase space Langevin dynamics results. The responses after the first 5 ps were nearly identical, confirming that the inertial components were significant only in the initial stages of the relaxation. Since the propagator matrix in the overdamped formulation is real-symmetric and does not require the inertial component in the propagator, the computation time and memory footprint was reduced by 1 order of magnitude. PMID:22924611

Manson, Anthony C; Coalson, Rob D

2012-10-11

415

Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires one to modify the basic relation between dissipation and time reversal and to include a contribution arising from the noncausal character of the reverse process. We then propose a new definition of the quantity measuring the irreversibility of a path in a nonequilibrium stationary state, which can also be regarded as the trajectory-dependent total entropy production. This leads to an extension of the second law, which takes a simple form in the long-time limit. As an illustration, we apply the general approach to linear systems that are both analytically tractable and experimentally relevant. PMID:24856682

Munakata, T; Rosinberg, M L

2014-05-01

416

Advantage of suppressed non-Langevin recombination in low mobility organic solar cells

Photovoltaic performance in relation to charge transport is studied in efficient (7.6%) organic solar cells (PTB7:PC{sub 71}BM). Both electron and hole mobilities are experimentally measured in efficient solar cells using the resistance dependent photovoltage technique, while the inapplicability of classical techniques, such as space charge limited current and photogenerated charge extraction by linearly increasing voltage is discussed. Limits in the short-circuit current originate from optical losses, while charge transport is shown not to be a limiting process. Efficient charge extraction without recombination can be achieved with a mobility of charge carriers much lower than previously expected. The presence of dispersive transport with strongly distributed mobilities in high efficiency solar cells is demonstrated. Reduced non-Langevin recombination is shown to be beneficial for solar cells with imbalanced, low, and dispersive electron and hole mobilities.

Stolterfoht, Martin; Armin, Ardalan; Pandey, Ajay K.; Burn, Paul L.; Meredith, Paul; Pivrikas, Almantas, E-mail: almantas.pivrikas@uq.edu.au [Centre for Organic Photonics and Electronics (COPE), School of Chemistry and Molecular Biosciences and School of Mathematics and Physics, The University of Queensland, Brisbane 4072 (Australia); Philippa, Bronson; White, Ronald D. [School of Engineering and Physical Sciences, James Cook University, Townsville 4811 (Australia)

2014-07-07

417

Existence Theorems for Some Quadratic Integral Equations

Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs

Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed

1998-01-01

418

The Kinetic Theory Molecular Dynamics Method

NASA Astrophysics Data System (ADS)

We are interested in simulating plasmas under thermonuclear burn conditions relevant to NIF. As such, we have recently developed the Kinetic Theory Molecular Dynamics (KTMD) method, which takes advantage of the fact that the plasma electrons are typically moderately degenerate and weakly coupled, whereas the ions are classical and moderately to strongly coupled. The basic approach of KTMD is to describe the fully non-equilibrium electron dynamics with an appropriate kinetic equation while leaving the ion dynamics to MD. The current version of KTMD self-consistently follows the time evolution of a Fermi gas via the time-dependent, fully nonlinear Wigner-Poisson system. Our approach, its associated implementation, and preliminary physics benchmarking results, such as nonlinear plasma waves and instabilities, will be presented. We describe a Langevin approach designed to mitigate numerical errors causing the Fermi distribution to relax towards a Maxwellian during long simulations. Ideas for extending the current capability, such as extending the mean-field approach by including collisions and quantum mechanical smearing, will be outlined.

Fichtl, Chris; Murillo, Michael; Graziani, Frank

2011-11-01

419

NASA Astrophysics Data System (ADS)

This paper presents an application of new discrete path integral solutions recently introduced for Fokker-Planck dynamics with the aim to compare their relative efficacy in giving precise numerical results. The basic idea used in the derivation of these solutions is to model a complex Fokker-Planck equation with a general drift coefficient by a linear (Ornstein-Uhlenbeck) process, which is solved exactly, and to then employ an iterative technique to quantify what is missing from the reference description. We reexamine and analyze two different approaches to realize the above strategy. These are an operator decoupling technique and a power series expansion method. Both approaches allow one to construct higher-order propagators valid to any desired precision in a time increment ?. Their use in a path integral means that many fewer time steps N are required to achieve a given accuracy for a given net increment t=N?. Our comparison also includes results from standard path integral representations. The relative efficacy of the various different methods is illustrated by means of two problems, namely, the dynamics of an overdamped Brownian particle in a potential field and the Kramers model of chemical reaction. The former process can be modeled by a one-dimensional Fokker-Planck equation for the position coordinate only, while the latter is governed by a two-dimensional Fokker-Planck equation where the relaxation over velocity is taken into account. The numerical applications clearly demonstrate that the new representations are superior in the sense that they yield much more accurate results with less computational effort than the best alternative path integral method now in use.

Drozdov, A. N.; Brey, J. J.

1998-01-01

420

Calculation of scattering with the light-cone two-body equation in. phi. sup 3 theories

The analysis of the light-cone two-body bound-state equation is extended to the scattering problem. The rotational invariance is violated in the light-cone quantization method when the Fock space is truncated for practical calculations. Using a simple scalar field model, we investigate the explicit rotation dependence of the two-body scattering phase shifts in the light-cone quantization approach. We find the regions of coupling constant and c.m. momentum where the rotation dependence in the phase shift is negligible. We also make a connection of our analysis with the light-cone scattering formalism recently presented by Fuda.

Ji, C. (Department of Physics, North Carolina State University, Raleigh, North Carolina 27695 (United States)); Surya, Y. (Department of Physics, The College of William and Mary, Williamsburg, Virginia 23185 (United States))

1992-10-15

421

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

Wu Shuangqing

2009-01-01

422

The fundamental equation of the metabolic theory of ecology (MTE) indicates that most of the variation in metabolic rate are a consequence of variation in organismal size and environmental temperature. Although evolution is thought to minimize energy costs of nutrient transport, its effects on metabolic rate via adaptation, acclimatization or acclimation are considered small, and restricted mostly to variation in the scaling constant, b(0). This contrasts strongly with many conclusions of evolutionary physiology and life-history theory, making closer examination of the fundamental equation an important task for evolutionary biologists. Here we do so using scorpions as model organisms. First, we investigate the implications for the fundamental equation of metabolic rate variation and its temperature dependence in the scorpion Uroplectes carinatus following laboratory acclimation. During 22 days of acclimation at 25 degrees C metabolic rates declined significantly (from 127.4 to 78.2 microW; P = 0.0001) whereas mean body mass remained constant (367.9-369.1 mg; P = 0.999). In field-fresh scorpions, metabolic rate-temperature (MRT) relationships varied substantially within and among individuals, and therefore had low repeatability values (tau = 0.02) and no significant among-individual variation (P = 0.181). However, acclimation resulted in a decline in within-individual variation of MRT slopes which subsequently revealed significant differences among individuals (P = 0.0031) and resulted in a fourfold increase in repeatability values (tau = 0.08). These results highlight the fact that MRT relationships can show substantial, directional variation within individuals over time. Using a randomization model we demonstrate that the reduction in metabolic rate with acclimation while body mass remains constant causes a decline both in the value of the mass-scaling exponent and the coefficient of determination. Furthermore, interspecific comparisons of activation energy, E, demonstrated significant variation in scorpions (0.09-1.14 eV), with a mean value of 0.77 eV, significantly higher than the 0.6-0.7 eV predicted by the fundamental equation. Our results add to a growing body of work questioning both the theoretical basis and empirical support for the MTE, and suggest that alternative models of metabolic rate variation incorporating explicit consideration of life history evolution deserve further scrutiny. PMID:17584252

Terblanche, J S; Janion, C; Chown, S L

2007-07-01

423

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Bardhan, J. P.; Mathematics and Computer Science

2008-10-14

424

An inverse scattering problem for a quantized scalar field ${\\bm \\phi}$ obeying a linear Klein-Gordon equation $(\\square + m^2 + V) {\\bm \\phi} = J \\mbox{in $\\mathbb{R} \\times \\mathbb{R}^3$}$ is considered, where $V$ is a repulsive external potential and $J$ an external source $J$. We prove that the scattering operator $\\mathscr{S}= \\mathscr{S}(V,J)$ associated with ${\\bm \\phi}$ uniquely determines $V$. Assuming that $J$ is of the form $J(t,x)=j(t)\\rho(x)$, $(t,x) \\in \\mathbb{R} \\times \\mathbb{R}^3$, we represent $\\rho$ (resp. $j$) in terms of $j$ (resp. $\\rho$) and $\\mathscr{S}$.

Hironobu Sasaki; Akito Suzuki

2011-01-01

425

Under hypernetted chain (HNC) approximation, effective ion pair interaction potentials for the warm dense matter are extracted by using available radial distribution functions (RDFs). The effective ion pair potentials extracted from first-principles simulation results are found containing the short-ranged attraction (SRA) component for both warm dense helium and beryllium plasmas. The SRA potentials can be well represented by Gaussian functions in both cases and then the extracted effective ion potentials are well fitted. As an application, the well fitted potentials are used to describe ion-ion interactions in classical molecular dynamics simulations. The yield RDFs are in excellent agreement with those computed by HNC equations and first-principles simulations, respectively.

Ye Jingxin; Zhao Bin; Zheng Jian [CAS Key Laboratory of Basic Plasma Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China) and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2011-03-15

426

epl draft Crossover behavior of stock returns and mean square displace- ments of particles governed-average of US and Taiwan stocks with the time internal show ballistic behavior 1 with the exponent 1 2 that fluctuations in stocks are not completely random. In 1966, King found that changes in prices of different

427

NASA Astrophysics Data System (ADS)

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

Landau, Arie

2013-07-01

428

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper (Khalili et al. J. Phys. Chem. B 2005, 109, 13785), was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala10 polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala10 polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain–side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time. PMID:16852728

Khalili, Mey; Liwo, Adam; Jagielska, Anna; Scheraga, Harold A.

2008-01-01

429

In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

NONE

1998-11-01

430

Neutral Equations of Mixed Type

In this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. In Chapter 2, we extend...

Lamb, Charles

2012-12-31

431

NASA Astrophysics Data System (ADS)

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.

Wu, Wei; Wang, Jin

2014-09-01

432

Equations For Rotary Transformers

NASA Technical Reports Server (NTRS)

Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

1988-01-01

433

SuperADAM: Upgraded polarized neutron reflectometer at the Institut Laue-Langevin

A new neutron reflectometer SuperADAM has recently been built and commissioned at the Institut Laue-Langevin, Grenoble, France. It replaces the previous neutron reflectometer ADAM. The new instrument uses a solid state polarizer/wavelength filter providing a highly polarized (up to 98.6%) monochromatic neutron flux of 8 Multiplication-Sign 10{sup 4} n cm{sup -2} s{sup -1} with monochromatization {Delta}{lambda}/{lambda}= 0.7% and angular divergence {Delta}{alpha}= 0.2 mrad. The instrument includes both single and position sensitive detectors. The position sensitive detector allows simultaneous measurement of specular reflection and off-specular scattering. Polarization analysis for both specular reflection and off-specular scattering is achieved using either mirror analyzers or a {sup 3}He spin filter cell. High efficiency detectors, low background, and high flux provides a dynamic range of up to seven decades in reflectivity. Detailed specifications and the instrument capabilities are illustrated with examples of recently collected data in the fields of thin film magnetism and thin polymer films.

Devishvili, A.; Zhernenkov, K. [Department of Physics and Astronomy, Ruhr-Universitaet Bochum, 44780 Bochum (Germany); Institut Laue-Langevin, BP 156, 38042 Grenoble (France); Dennison, A. J. C. [Institut Laue-Langevin, BP 156, 38042 Grenoble (France); Division for Materials Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala (Sweden); Toperverg, B. P. [Department of Physics and Astronomy, Ruhr-Universitaet Bochum, 44780 Bochum (Germany); Petersburg Nuclear Physics Institute, 188300 Gatchina (Russian Federation); Wolff, M.; Hjoervarsson, B. [Division for Materials Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala (Sweden); Zabel, H. [Department of Physics and Astronomy, Ruhr-Universitaet Bochum, 44780 Bochum (Germany)

2013-02-15

434

Examination of a Langevin-Type Transducer Using a LiNbO3 Single Crystal

NASA Astrophysics Data System (ADS)

We are aiming at developing a Langevin longitudinal transducer without a bolt using a single crystal. The Z plate of the LiNbO3 single crystal was used as a piezoelectric material. We selected epoxy resin for bonding a piezoelectric disc (10 mm?) and stainless blocks (12.5 mm in length) as trial samples. The resonant frequency is about 94 kHz and the Q factor is about 1000. The material constants of the adhesive were derived for the finite element method (FEM) analysis. We measured the marked decrease in the Q factor due to temperature rise. It became clear that the measurement for high-voltage operation by continuous wave was limited within 4 cm/s of the edge surface velocity. We drove transducers using a burst signal and suppressed the temperature rise of the transducer. This method extended the measurement limitation to 40 cm/s. To clarify the problems of this transducer, the relationship between the bonding layer and the resonance resistance, and the stress in the bonding layer were determined using FEM. A thin crystal disc was also found to decrease the resonance resistance using FEM.

Okuda, Takatoshi; Wakatsuki, Noboru

2002-05-01

435

Relaxation processes in proteins range in time from picoseconds to seconds. Correspondingly, biological electron transfer (ET) could be controlled by slow protein relaxation. We used the Langevin stochastic approach to describe this type of ET dynamics. Two different types of kinetic behavior were revealed, namely: oscillating ET (that could occur at picoseconds) and monotonically relaxing ET. On a longer time scale, the ET dynamics can include two different kinetic components. The faster one reflects the initial, nonadiabatic ET, whereas the slower one is governed by the medium relaxation. We derived a simple relation between the relative extents of these components, the change in the free energy (DeltaG), and the energy of the slow reorganization Lambda. The rate of ET was found to be determined by slow relaxation at -DeltaG < or = Lambda. The application of the developed approach to experimental data on ET in the bacterial photosynthetic reaction centers allowed a quantitative description of the oscillating features in the primary charge separation and yielded values of Lambda for the slower low-exothermic ET reactions. In all cases but one, the obtained estimates of Lambda varied in the range of 70-100 meV. Because the vast majority of the biological ET reactions are only slightly exothermic (DeltaG > or = -100 meV), the relaxationally controlled ET is likely to prevail in proteins. PMID:11222272

Cherepanov, D A; Krishtalik, L I; Mulkidjanian, A Y

2001-01-01

436

ThALES—three axis low energy spectroscopy at the Institut Laue Langevin

NASA Astrophysics Data System (ADS)

Building on the strength of the present cold neutron three-axis spectrometer IN14, but using state-of-the-art neutron optics, we conceived the next generation three-axis instrument for low energy spectroscopy (ThALES) at the Institut Laue-Langevin (ILL). The main aims of the new instrument are: (i) to increase the overall data collection rate by rebuilding the neutron optics of the primary spectrometer achieving a higher incident neutron flux as well as by multiplexing the analyser-detector system, (ii) to provide an efficient and easy-to-use polarized neutron option, (iii) to extend the incident neutron range towards higher energies bridging the gap with thermal instruments, and (iv) to be able to use high-field magnets—such as the currently available 15 T cryomagnet—under all possible experimental conditions, i.e. in a wider range of incident energies. The expected increase in count rate by at least one order of magnitude allows for new experiments such as high pressure experiments on small sample sizes or investigations of magnetic excitations in thin films. Polarized inelastic neutron measurements should equal count rates of the present IN14 in unpolarized mode. The implementation of various optical elements enhances the flexibility of the instrument and allows trading momentum resolution for high neutron intensity.

Boehm, M.; Hiess, A.; Kulda, J.; Roux, S.; Saroun, J.

2008-03-01

437

Nonlinear gyrokinetic equations

Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

1983-03-01

438

Differential Equations Textbook

NSDL National Science Digital Library

This is a free textbook which covers material for an introductory course on differential equations with some partial differential equations material, though it assumes knowledge of matrix theory. It includes a section on computing Fourier series of polynomials. It also includes a link to the freely available student solutions manual.

Trench, William F.

2014-04-04

439

Excitability in a stochastic differential equation model for calcium puffs

NASA Astrophysics Data System (ADS)

Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.

Rüdiger, S.

2014-06-01

440

Heavy dense QCD and nuclear matter from an effective lattice theory

NASA Astrophysics Data System (ADS)

A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, ?, whose action is correct to ? n u m with n + m = 4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state in the limit of heavy baryons. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as a gap between the onset of isospin and baryon condensation.

Langelage, Jens; Neuman, Mathias; Philipsen, Owe

2014-09-01

441

Invariance of tautological equations II

NASA Astrophysics Data System (ADS)

The aim of Part II is to explore the technique of invariance of tautological equations in the realm of Gromov-Witten theory. The relationship between Gromov-Witten theory and the tautological rings of the moduli of curves is studied from Givental's point of view via deformation theory of semisimple axiomatic Gromov-Witten theory.

Lee, Y.-P.; Lee, With Appendix A. By Y. Iwao; Y.-P

2009-04-01

442

Computation of rare transitions in the barotropic quasi-geostrophic equations

NASA Astrophysics Data System (ADS)

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 action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.

Laurie, Jason; Bouchet, Freddy

2015-01-01

443

Modelling by Differential Equations

ERIC Educational Resources Information Center

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

Chaachoua, Hamid; Saglam, Ayse

2006-01-01

444

NASA Astrophysics Data System (ADS)

Radial and triplet correlation functions of the reference hard sphere system are determined at several solid densities by canonical Monte Carlo (MC) simulations. These customized data are used to extend the second order thermodynamic perturbation theory (TPT) to the solid phase of flexible hard chain systems. In order to test the accuracy of the TPT equation of state (EOS) for hard chains, MC simulations are carried out for systems of chain length 4 to 15. Several simulations are performed in the isobaric-isothermal ensemble to obtain the high-density EOS of hard chains in the fluid and solid phases. To determine solid-fluid equilibrium (SFE), Helmholtz free energies of solid crystals at a reference density are determined in a series of canonical MC simulations. As the chain length increases, asymptotic behaviors are observed in the coexistence pressure and densities of fluid and solid phases. It is found that the accuracy of TPT for EOS and SFE in systems of hard chains greatly improves by extending it to second order.

Alavi, Farzad; Feyzi, Farzaneh

2013-01-01

445

NASA Astrophysics Data System (ADS)

Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H-, and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, ?. Standard basis sets that are optimized for not-complex-scaled calculations (? = 0) are not sufficiently flexible to describe the ?-dependence of the wave functions even when heavily augmented by additional sets.

Bravaya, Ksenia B.; Zuev, Dmitry; Epifanovsky, Evgeny; Krylov, Anna I.

2013-03-01

446

Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H{sup -}, and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, {theta}. Standard basis sets that are optimized for not-complex-scaled calculations ({theta} = 0) are not sufficiently flexible to describe the {theta}-dependence of the wave functions even when heavily augmented by additional sets.

Bravaya, Ksenia B.; Zuev, Dmitry; Epifanovsky, Evgeny; Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)

2013-03-28

447

On use of the Amber potential with the Langevin dipole method.

Inclusion of solvent effects in biomolecular simulations is most ideally done using explicit methods, as they are able to capture the heterogeneous environment typical of biomolecules and systems involving them (e.g., proteins at solid interfaces). Common explicit methods based on molecular solvent models (e.g., TIP and SPC models) and molecular dynamic or Monte Carlo simulation are computationally expensive and are, therefore, not well-suited to situations where many simulations are required (e.g., in the ab initio structure prediction or design contexts). In such cases, more coarse-grained explicit approaches such as the Langevin dipole (LD) method of Warshel and co-workers are more appropriate. The recent incarnations of the LD method appear to produce good solvation free energy estimates. These incarnations use charges and solute structures obtained from high-level quantum mechanics simulations. As such an approach is clearly not possible for larger solutes or when many structures are to be considered, an alternative must be sought. One possibility is to use structures and charges derived from an existing analytical potential model-we report on such a coupling here with the Amber potential model. The accuracy and computational performance of this hybrid approach, which we term LD-Amber to distinguish it from previous incarnations of the LD method, was assessed by comparing results obtained from the approach with those from experiment and other theoretical methods for the solvation of 18 amino acid analogues and the alanine dipeptide. This comparison shows that the LD-Amber approach can yield results in line with experiment both qualitatively and quantitatively and is as accurate as other explicit methods while being computationally much cheaper. PMID:17550281

Mijajlovic, Milan; Biggs, Mark J

2007-07-01

448

Critical dynamics of self-gravitating Langevin particles and bacterial populations.

We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [P. H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index n similar to polytropic stars in astrophysics. At the critical index n_{3}=d(d-2) (where d>or=2 is the dimension of space), there exists a critical temperature Theta_{c} (for a given mass) or a critical mass M_{c} (for a given temperature). For Theta>Theta_{c} or M

Sire, Clément; Chavanis, Pierre-Henri

2008-12-01

449

NSDL National Science Digital Library

This lesson includes a theory-evaluation activity. A set of five scenarios (theories for how diverse life came into existence on Earth) is divided evenly throughout the class, so each student is asked to evaluate one theory. Students then come together in groups of five, so that all theories are represented in each group, where they are compared and evaluated. Each group reports to the entire class for further discussion and clarifications.

Kimmel, Michael

450

Liouville equation and schottky problem

An Ansatz for the Poincaré metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a nonchiral analogous of the higher genus relationships (KP equation) arising within the framework of Schottky's problem solution. This approach connects uniformization (Fuchsian groups) and moduli space theories with KP hierarchy. Besides its mathematical interest, the Ansatz

Marco Matone; G. Galilei

1995-01-01

451

NASA Astrophysics Data System (ADS)

Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in Paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughly Arrhenius form. The two-barrier (local cage and long range collective elastic) description results in a rich dynamic behavior including apparent Arrhenius, narrow crossover, and deeply supercooled regimes, and multiple characteristic or crossover times and temperatures of clear physical meaning. Application of the theory to nonpolar molecules, alcohols, rare gases, and liquids metals is carried out. Overall, the agreement with experiment is quite good for the temperature dependence of the alpha time, plateau shear modulus, and Boson-like peak frequency for van der Waals liquids, though less so for hydrogen-bonding molecules. The theory predicts multiple growing length scales upon cooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics. Calculations of the growth with cooling of an activation volume, which is strongly correlated with a measure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic, entropy crisis, dynamic facilitation, and other approaches are performed, and a fundamental basis for empirically extracted crossover temperatures is established. The present work sets the stage for addressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.

Mirigian, Stephen; Schweizer, Kenneth S.

2014-05-01

452

NASA Astrophysics Data System (ADS)

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

Mirigian, Stephen; Schweizer, Kenneth S.

2014-05-01

453

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time. PMID:24852549

Mirigian, Stephen; Schweizer, Kenneth S

2014-05-21

454

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transient localization length, and a growing microscopic jump length. Alpha relaxation time calculations are in good agreement with recent experiments and simulations on dense fluids and suspensions of hard spheres. Comparisons of the theory with elastic models and entropy crisis ideas are explored. The present work provides a foundation for constructing a quasi-universal, fit-parameter-free theory for relaxation in thermal molecular liquids over 14 orders of magnitude in time.

Mirigian, Stephen [University of Illinois, Urbana-Champaign] [University of Illinois, Urbana-Champaign; Schweizer, Kenneth [University of Illinois] [University of Illinois

2014-01-01

455

A population equation with diffusion

In this paper we discuss a population equation with diffusion. It is different from the equation proposed, for example, in [K.J. Engel, R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, 2000] or in [J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, 1996] so far as it combines diffusion with delay. We explain the origin of this

G. Fragnelli; L. Tonetto

2004-01-01

456

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

University, Bozeman, Montana 59717, USA T. C. Ralph and A. G. White Department of Physics, University of Queensland, St. Lucia, Queensland 4072, Australia J. K. Brasseur Directed Energy Solutions, 532 Fox Run

White, Andrew G.