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1

Generalized Langevin theory for inhomogeneous fluids: The equations of motion  

NASA Astrophysics Data System (ADS)

We use the generalized Langevin approach to study the dynamical correlations in an inhomogeneous system. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor, and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamiclike quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low-density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We also indicate how the resulting general set of equations would simplify for systems in which the inhomogeneity is unidirectional, e.g., a liquid-vapor interface.

Grant, Martin; Desai, Rashmi C.

1982-05-01

2

Distance fluctuation of a single molecule in Lennard-Jones liquid based on generalized Langevin equation and mode coupling theory  

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

3

Langevin equation path integral ground state.  

PubMed

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

4

Simple derivations of generalized linear and nonlinear Langevin equations  

Microsoft Academic Search

With the aid of a single operator identity, the derivation of the Mori generalized linear Langevin equation is simplified and a new generalized nonlinear Langevin equation is obtained. The flexibility of the method is stressed which allows the derivation of various generalized nonlinear Langevin equations that can be used as bases for devising approximation schemes such as the mode coupling

K. Kawasaki

1973-01-01

5

Quantum theory of open systems based on stochastic differential equations of generalized Langevin (non-Wiener) type  

SciTech Connect

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

6

The generalized Schrödinge-Langevin equation  

NASA Astrophysics Data System (ADS)

In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinge-Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation.

Bargueño, Pedro; Miret-Artés, Salvador

2014-07-01

7

Generalized Langevin Theory for Inhomogeneous Fluids.  

NASA Astrophysics Data System (ADS)

This thesis presents a molecular theory of the dynamics of inhomogeneous fluids. Dynamical correlations in a nonuniform system are studied through the generalized Langevin approach. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamic-like quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We apply this formalism to several problems. We study the correlation of currents orthogonal to a diffuse planar, liquid-vapour, interface, introducing new nonlocal elastic moduli and new nonlocal, frequency dependent, viscosities. Novel symmetry breaking contributions are obtained, which are related to the Young-Laplace equation for pressure balance. The normal modes, associated with the symmetry breaking interface in the liquid-vapour system, are analyzed, taking into account the nonlocal nature of the diffuse planar interface. We obtain the classical dispersion relation for capillary waves, observed in light scattering experiments, from an adiabatic (molecular) approach. We consider the 'capillary wave model' (CWM) of the equilibrium liquid-vapour interface. CWM is reformulated to be consistent with capillary waves; corrections to the standard CWM results, due to self-consistent long range coupling, are obtained for finite surface area and nonzero gravitational acceleration. Finally, we obtain the Landau-Lifshitz theory of fluctuating hydrodynamics from the general molecular equations of motion. Our derivation yields, in a natural way, a nonlocal driving force which has been shown to be useful in the study of spinodal decomposition, in the early time regime.

Grant, Martin Garth

8

Langevin equations for competitive growth models.  

PubMed

Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension ? and the nonlinear coefficient ? of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p?0. The superposition of those scaling factors gives ?~p(2) for random deposition with surface relaxation (RDSR) as the CD, and ?~p, ?~p(3/2) for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p dependence of ?, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients. PMID:22400575

Silveira, F A; Aarão Reis, F D A

2012-01-01

9

Langevin equations for competitive growth models  

NASA Astrophysics Data System (ADS)

Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension ? and the nonlinear coefficient ? of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p?0. The superposition of those scaling factors gives ?˜p2 for random deposition with surface relaxation (RDSR) as the CD, and ?˜p, ?˜p3/2 for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p dependence of ?, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients.

Silveira, F. A.; Aarão Reis, F. D. A.

2012-01-01

10

Probability Density Function Method for Langevin Equations with Colored Noise  

SciTech Connect

We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.

Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.

2013-04-05

11

Scaling of ballistic deposition from a Langevin equation.  

PubMed

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

12

Comment on ``Langevin equation for the squeezing of light by means of a parametric oscillator''  

NASA Astrophysics Data System (ADS)

We comment on statements made about quantum representation theory in the paper by T. W. Marshall and E. Santos [Phys. Rev. A 41, 1582 (1990)]. Results are presented which show that correct results can be obtained from Langevin equations derived from the positive-P representation, even when those obtained by truncation of the Wigner time-evolution equation give incorrect results.

Kinsler, P.; Drummond, P. D.

1991-12-01

13

Langevin equation approach to diffusion magnetic resonance imaging  

NASA Astrophysics Data System (ADS)

The normal phase diffusion problem in magnetic resonance imaging (MRI) is treated by means of the Langevin equation for the phase variable using only the properties of the characteristic function of Gaussian random variables. The calculation may be simply extended to anomalous diffusion using a fractional generalization of the Langevin equation proposed by Lutz [E. Lutz, Phys. Rev. E 64, 051106 (2001)] pertaining to the fractional Brownian motion of a free particle coupled to a fractal heat bath. The results compare favorably with diffusion-weighted experiments acquired in human neuronal tissue using a 3 T MRI scanner.

Cooke, Jennie M.; Kalmykov, Yuri P.; Coffey, William T.; Kerskens, Christian M.

2009-12-01

14

Langevin models of turbulence: Renormalization group, distant interaction algorithms or rapid distortion theory?  

NASA Astrophysics Data System (ADS)

A new dynamical turbulence model is validated by comparisons of its numerical simulations with fully resolved, direct numerical simulations (DNS) of the Navier-Stokes equations in three-dimensional, isotropic, homogeneous conditions. In this model the small-scale velocities are computed using a Langevin, linear, inhomogeneous, stochastic equation that is derived from a quasi-linear approximation of the Navier-Stokes equations, in the spirit of rapid distortion theory (RDT). The values of the turbulent viscosity involved in our Langevin model are compared with a theoretical prescription based on the renormalization group and the distant interaction algorithms (DSTA) model. We show that the empirical turbulent viscosities derived from simulations of the Langevin model are in good quantitative agreement with the DSTA predictions. Finally, Langevin simulations are compared with DNS and large eddy simulations based on the eddy-damped quasi-normal Markovian closure. The Langevin RDT model is able to reproduce the correct spectrum shape, intermittency statistics, and coherent flow structures for both the resolved and the largest sub-grid scales. It also predicts the evolution of the resolved scales better than the alternative models.

Laval, J.-P.; Dubrulle, B.; McWilliams, J. C.

2003-05-01

15

Solving the generalized Langevin equation with the algebraically correlated noise  

NASA Astrophysics Data System (ADS)

We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.

Srokowski, T.; P?oszajczak, M.

1998-04-01

16

Numerical study of the Langevin theory for fixed-energy sandpiles  

NASA Astrophysics Data System (ADS)

The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles and other self-organizing systems, is studied numerically. The equation is similar to the Reggeon field theory, describing generic systems with absorbing states, but it is coupled linearly to a second conserved and static (nondiffusive) field. It has been claimed to represent a different universality class, including different discrete models: the Manna as well as other sandpiles, reaction-diffusion systems, etc. In order to integrate the equation, and surpass the difficulties associated with its singular noise, we follow a numerical technique introduced by Dickman. Our results coincide remarkably well with those of discrete models claimed to belong to this universality class, in one, two, and three dimensions. This provides a strong backing for the Langevin theory of stochastic sandpiles, and to the very existence of this meagerly understood universality class.

Ramasco, José J.; Muñoz, Miguel A.; da Silva Santos, Constantino A.

2004-04-01

17

Quantum probability distributions in the early Universe. II. The quantum Langevin equation  

NASA Astrophysics Data System (ADS)

In this paper, we construct a stochastic differential equation for the quantum evolution of the large-scale or coarse-grained (>causal horizon) scalar field (inflaton) in de Sitter space that is valid to all orders in ?. This quantum Langevin equation is the equivalent of the Wigner equation for quantum probability distributions. We show that in general quantum fluctuations are associated with multicomponent multiplicative non-Gaussian Markovian noise. However, to order ? this noise becomes simple white noise. This is the origin behind the observations of Linde, Starobinsky, and Vilenkin that the large-scale quantum evolution of the inflaton is similar to Brownian motion. In addition, we show that Starobinsky's Langevin equation arises from our quantum Langevin equation as an order-?-slow-rolling approximation. Finally we compute the random-number distribution associated with noise of the quantum Langevin equation. We conclude that the Wigner description based on quasiprobability distributions is probably more useful computationally than the quantum Langevin equation.

Graziani, F. R.

1988-08-01

18

LETTER: Generalized Langevin equation formulation for anomalous polymer dynamics  

NASA Astrophysics Data System (ADS)

For reproducing the anomalous—i.e., sub-diffusive or super-diffusive—behavior in some stochastic dynamical systems, the generalized Langevin equation (GLE) has gained considerable popularity in recent years. Motivated by the question of whether or not a system with anomalous dynamics can have the GLE formulation, here I consider polymer physics, where sub-diffusive behavior is commonplace. I provide an exact derivation of the GLE for phantom Rouse polymers, and by identifying the polymeric response to local strains, I argue the case for a GLE formulation for self-avoiding polymers and polymer translocation through a narrow pore in a membrane. Instances in polymer physics where the anomalous dynamics corresponds to the GLE thus seem to be fairly common.

Panja, Debabrata

2010-02-01

19

V-Langevin equations, continuous time random walks and fractional diffusion  

Microsoft Academic Search

The following question is addressed: under what conditions can a strange diffusive process, defined by a semi-dynamical V-Langevin equation or its associated hybrid kinetic equation (HKE), be described by an equivalent purely stochastic process, defined by a continuous time random walk (CTRW) or by a fractional differential equation (FDE)? More specifically, does there exist a class of V-Langevin equations with

Radu Balescu

2007-01-01

20

Description of quantum noise by a Langevin equation  

NASA Technical Reports Server (NTRS)

General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.

Metiu, H.; Schon, G.

1984-01-01

21

Particles dispersed in a dilute gas. II. From the Langevin equation to a more general kinetic approach  

NASA Astrophysics Data System (ADS)

In the attempt to solve the age-old problem of unifying Langevin, Fokker-Planck and Boltzmann theories for test particles in a dilute gas, the Uhlenbeck and Ornstein's theory relating Langevin and Fokker-Planck equations is critically analyzed. Agreement and discrepancies between such theory and the results following from the Boltzmann one are also examined. It is concluded that the currently assumed form of the fluctuating-force autocorrelation function, which is extremely successful for Brownian particles in dense fluids, cannot generally guarantee an accurate (or acceptable) relaxation law for the mean square velocity components of generic test particles in dilute gases. This difficulty can be overcome in the framework of a more general kinetic approach which is shown to consistently include Langevin, Fokker-Planck, and Boltzmann theories. The advantages of such approach in interpreting experimental results are particularly evident when the test particles move in a (homogeneous) gas in non-equilibrium conditions and when correlations exist between test- and gas-particle velocities.

Ferrari, Leonardo

2014-01-01

22

Generalized Langevin dynamics simulation: numerical integration and application of the generalized Langevin equation with an exponential model for the friction kernel  

NASA Astrophysics Data System (ADS)

An efficient procedure is introduced for a generalized Langevin dynamics simulation when the exponential model is taken for the friction kernel. The leap frog algorithm is used for numerical integration of the generalized Langevin equation. Simulation with this model has been performed on a cyclic undecapeptide, cyclosporin A (CPA). By comparison with the results obtained from previous simulations, the method proves to be reliable and efficient in the simulation of CPA.

Wan, Shun Zhou; Wang, Cun Xin; Shi, Yun Yu

23

Nonstationary Langevin equation: Statistical properties and application to explain effects observed in cardiological time series  

NASA Astrophysics Data System (ADS)

Using the Langevin equation we develop the model of a stochastic process subject to a given time-dependent regulatory mechanism. The effects of this nonstationarity on the statistical properties of the time series, i.e., on global and conditional probability densities and on the moments of the distribution, are derived. Application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the Langevin equation for time series of heart rate.

Kirchner, Jens; Meyer, Wolfgang; Elsholz, Markus; Hensel, Bernhard

2007-08-01

24

A combined quasi-continuum/Langevin equation approach to study the self-diffusion dynamics of confined fluids.  

PubMed

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

25

A dynamical interpretation of fusion-fission reactions using four-dimensional Langevin equations  

NASA Astrophysics Data System (ADS)

Four-dimensional Langevin equations have been applied to calculate the neutron multiplicity and evaporation residue cross section for hot nuclei. The projection of the total spin of the compound nucleus to the symmetry axis, K, is the fourth dimension in Langevin dynamical calculations. The relaxation time of the K as a function of the dynamical parameters is investigated. Calculations were performed for the 18O+192Os and 19F+169Tm reactions with a non-constant dissipation coefficient for the K coordinate. The obtained results based on four-dimensional Langevin equations with a non-constant dissipation coefficient in comparison with calculations based on a constant dissipation coefficient (?K = 0.077(MeVzs)-1/2) are in better agreement with the experimental data. The difference between the two models for the evaporation residue cross section is high, whereas for neutron multiplicity, the discrepancy is low.

Naderi, D.

2013-12-01

26

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

NASA Astrophysics Data System (ADS)

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

Sadhukhan, Jhilam; Pal, Santanu

2009-06-01

27

Uses and abuses of the Langevin equation for chemical reactions in condensed phases  

NASA Astrophysics Data System (ADS)

The Langevin and Fokker-Planck equations are useful in the description of many classical and quantum mechanical systems. However, these equations are justifiable from molecular considerations under very restricted conditions. These conditions include weak coupling, Brownian motion, and systems with special Hamiltonians. The application of these equations to chemical reactions in condensed phases is fraught with peril, particularly for fluid systems. We examine the molecular derivations of these equations and describe the conditions under which they are justifiable. It is, of course, possible that the equations are useful under other conditions.

Oppenheim, Irwin; Orsky, Alex

1991-12-01

28

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

29

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

Microsoft Academic Search

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

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

2008-01-01

30

Langevin equation modeling of convective boundary layer dispersion assuming homogeneous, skewed turbulence  

SciTech Connect

Vertical dispersion of material in the convective boundary layer, CBL, is dramatically different than in natural or stable boundary layers, as has been shown by field and laboratory experiments. Lagrangian stochastic modeling based on the Langevin equation has been shown to be useful for simulating vertical dispersion in the CBL. This modeling approach can account for the effects of the long Lagrangian time scales (associated with large-scale turbulent structures), skewed vertical velocity distributions, and vertically inhomogeneous turbulent properties found in the CBL. It has been recognized that simplified Langevin equation models that assume skewed but homogeneous velocity statistics can capture the important aspects of dispersion from sources the the CBL. The assumption of homogeneous turbulence has a significant practical advantage, specifically, longer time steps can be used in numerical simulations. In this paper, we compare two Langevin equations models that use the homogeneous turbulence assumption. We also compare and evaluate three reflection boundary conditions, the method for determining a new velocity for a particle that encounters a boundary. Model results are evaluated using data from Willis and Deardorff`s laboratory experiments for three different source heights.

Hasstrom, J.S.; Ermak, D.L.

1997-10-01

31

Solving the Langevin equation with stochastic algebraically correlated noise  

NASA Astrophysics Data System (ADS)

The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.

P?oszajczak, M.; Srokowski, T.

1997-05-01

32

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

PubMed

We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package. PMID:22713049

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

2012-06-14

33

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)] 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)], an open-source molecular simulation package.

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

2012-06-01

34

Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation  

NASA Astrophysics Data System (ADS)

The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.

Srokowski, T.

2001-09-01

35

Anomalous diffusion in nonhomogeneous media: Time-subordinated Langevin equation approach  

NASA Astrophysics Data System (ADS)

Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Lévy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process subordinated to a random time: it separately takes into account effects related to the medium structure and the memory. Density distributions and moments are derived from the solutions of the corresponding Langevin equation and compared with the numerical calculations for the exact problem. Both subdiffusion and enhanced diffusion are predicted. Distribution of the process satisfies the fractional Fokker-Planck equation.

Srokowski, Tomasz

2014-03-01

36

Stochastic Processes with Distributed Delays: Chemical Langevin Equation and Linear-Noise Approximation  

NASA Astrophysics Data System (ADS)

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.

Brett, Tobias; Galla, Tobias

2013-06-01

37

Implicit numerical schemes for the stochastic Liouville equation in Langevin form.  

PubMed

We present and numerically test implicit as well as explicit numerical schemes for solving the Stochastic Liouville Equation in Langevin form. It is found that implicit schemes provide significant gain in robustness, for example, when nonsecular Hamiltonian terms cannot be ignored in electron and nuclear spin resonance. Implicit schemes open up several spectroscopic relaxation problems for direct interpretation using the Stochastic Liouville Equation. To illustrate the proposed numerical schemes, studies are presented for an electron paramagnetic resonance problem involving a coordinated copper complex and a fluorescence problem. PMID:21503297

Håkansson, Pär; Nair, Prasanth B

2011-05-28

38

Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions  

SciTech Connect

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

39

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

PubMed Central

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.

2013-01-01

40

Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel.  

PubMed

Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel. PMID:23901960

Baczewski, Andrew D; Bond, Stephen D

2013-07-28

41

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

SciTech Connect

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

42

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks  

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

43

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations  

NASA Astrophysics Data System (ADS)

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, 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 of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

Lucarini, V.; Faranda, D.; Willeit, M.

2012-01-01

44

Accelerating the convergence of path integral dynamics with a generalized Langevin equation  

NASA Astrophysics Data System (ADS)

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

Ceriotti, Michele; Manolopoulos, David E.; Parrinello, Michele

2011-02-01

45

Analytical solution of the generalized Langevin equation with hydrodynamic interactions: subdiffusion of heavy tracers.  

PubMed

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

46

Accelerating the convergence of path integral dynamics with a generalized Langevin equation.  

PubMed

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water. PMID:21361524

Ceriotti, Michele; Manolopoulos, David E; Parrinello, Michele

2011-02-28

47

Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach  

NASA Astrophysics Data System (ADS)

We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway “waterwheel” modes) and investigate the signature of these in the Raman signals.

Lü, Jing-Tao; Brandbyge, Mads; Hedegård, Per; Todorov, Tchavdar N.; Dundas, Daniel

2012-06-01

48

Crossover behavior of stock returns and mean square displacements of particles governed by the Langevin equation  

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

49

Adjoint design sensitivity analysis of reduced atomic systems using generalized Langevin equation for lattice structures  

SciTech Connect

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

50

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

PubMed

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

51

Analysis of porosity distribution of large-scale porous media and their reconstruction by Langevin equation  

NASA Astrophysics Data System (ADS)

Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs ?(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=?(h+?h)-?(h) is a stationary and Markov process, characterized by a Markov length scale hM. The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y0,h0) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured.

Jafari, G. Reza; Sahimi, Muhammad; Rasaei, M. Reza; Tabar, M. Reza Rahimi

2011-02-01

52

Analysis of porosity distribution of large-scale porous media and their reconstruction by Langevin equation.  

PubMed

Several methods have been developed in the past for analyzing the porosity and other types of well logs for large-scale porous media, such as oil reservoirs, as well as their permeability distributions. We developed a method for analyzing the porosity logs ?(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=?(h+?h)-?(h) is a stationary and Markov process, characterized by a Markov length scale h(M). The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y(0),h(0)) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured. PMID:21405908

Jafari, G Reza; Sahimi, Muhammad; Rasaei, M Reza; Tabar, M Reza Rahimi

2011-02-01

53

Generalized Langevin equation: An efficient approach to nonequilibrium molecular dynamics of open systems  

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

54

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

NASA Astrophysics Data System (ADS)

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.

Koehl, Patrice; Delarue, Marc

2010-02-01

55

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

PubMed

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

2010-02-14

56

Generalized Langevin equation with multiplicative noise: Temporal behavior of the autocorrelation functions  

NASA Astrophysics Data System (ADS)

The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed.

Mankin, R.; Laas, K.; Sauga, A.

2011-06-01

57

Use of a Modified Langevin Equation to Describe Turbulent Dispersion of Fluid Particles in a Channel Flow  

Microsoft Academic Search

A stochastic method to represent the positions and velocities of fluid particles in a nonhomogeneous turbulence was pursued.\\u000a Spatially varying Lagrangian time scales obtained from direct numerical simulations of turbulent flow in a channel and spatially\\u000a varying joint Gaussian forcing functions were incorporated into a Langevin equation. The model was tested by comparing calculations\\u000a of the dispersions and velocities of

Yoichi Mito; Thomas J. Hanratty

2002-01-01

58

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.  

NASA Astrophysics Data System (ADS)

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Frank, T. D.

2008-02-01

59

Classical Noise IV: Langevin Methods  

Microsoft Academic Search

A Langevin theory for linear and nonlinear, stationary and nonstationary, processes is developed and compared with Markoff methods. For short correlation times tauc, we find the Markoff process that is a good approximation to the Langevin process for Deltat>tauc. Conversely, given the diffusion coefficients Dn of a Markoff process, we find the moments (to all orders) of the Langevin forces

Melvin Lax

1966-01-01

60

Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues.  

PubMed

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. PMID:24952517

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

2014-06-21

61

Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues  

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

62

Field theories and exact stochastic equations for interacting particle systems  

SciTech Connect

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

Andreanov, Alexei; Lefevre, Alexandre [Service de Physique Theorique, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Biroli, Giulio [Service de Physique de l'Etat Condense, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Bouchaud, Jean-Philippe [Service de Physique de l'Etat Condense, Orme des Merisiers-CEA Saclay, 91191 Gif sur Yvette Cedex (France); Science and Finance, Capital Fund Management, 6 Boulevard Haussmann, 75009 Paris (France)

2006-09-15

63

Augmented Langevin evaluation of imaginary-time Feynman path integrals  

NASA Astrophysics Data System (ADS)

An alternative formulation of the stochastic representation of the Feynman path-integral theory is introduced. Stationary (imaginary-time) paths are generated as solutions of suitable Zwanzig-Ramshaw augmented Langevin equations. The required equilibrium distribution is obtained for a freely chosen functional form of the fluctuations and its associated dissipative term, in the presence of a generalized reversible drift. The method is both theoretically and numerically advantageous with respect to the standard Langevin and hybrid algorithms.

Badii, R.; Broggi, G.

1990-11-01

64

Event-driven Langevin simulations of hard spheres  

NASA Astrophysics Data System (ADS)

The blossoming of interest in colloids and nanoparticles has given renewed impulse to the study of hard-body systems. In particular, hard spheres have become a real test system for theories and experiments. It is therefore necessary to study the complex dynamics of such systems in presence of a solvent; disregarding hydrodynamic interactions, the simplest model is the Langevin equation. Unfortunately, standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during an integration time step. This is not the case for hard-body systems, where there is no clear-cut distinction between the correlation time of the noise and the time scale of the interactions. Starting first from a splitting of the Fokker-Plank operator associated with the Langevin dynamics, and then from an approximation of the two-body Green's function, we introduce and test two algorithms for the simulation of the Langevin dynamics of hard spheres.

Scala, A.

2012-08-01

65

Stochastic langevin model for flow and transport in porous media.  

PubMed

We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies. PMID:18764333

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

2008-07-25

66

Langevin evolution of disoriented chiral condensate  

NASA Astrophysics Data System (ADS)

As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilibrium behavior of the quantum field theory of pions and ? fields over a wide range of temperatures. Finally, we estimate the viscosity ?(T), which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting ?(T) is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics.

Bettencourt, Luís. M. A.; Rajagopal, Krishna; Steele, James V.

2001-10-01

67

Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications  

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

68

Self-assembly of nanocomponents into composite structures: derivation and simulation of Langevin equations.  

PubMed

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. PMID:19466829

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

2009-05-21

69

Self-assembly of nanocomponents into composite structures: Derivation and simulation of Langevin equations  

NASA Astrophysics Data System (ADS)

The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.

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

2009-05-01

70

A LES-Langevin model for turbulence  

NASA Astrophysics Data System (ADS)

We propose a new model of turbulence for use in large-eddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddy-viscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scales, including the turbulent force, and a generalized Langevin equation integrated on a twice-finer grid. We compare the full model with several approximations. In the first one, the friction operator of the Langevin equation is simply replaced by an empirical constant, of the order of the resolved scale correlation time. In the second approximation, the integration is replaced by a condition of instantaneous adjustment to the stochastic force. In this approximation, our model becomes equivalent to the velocity-estimation model of Domaradzki et al. [1-3]. In the isotropic, homogeneous situations we study, both approximations provide satisfactory results, at a reduced computational cost. The model is finally validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow.

Laval, J.-P.; Dubrulle, B.

2006-02-01

71

Generalized Langevin equation approach to higher-order classical response: Second-order-response time-resolved Raman experiment in CS2  

NASA Astrophysics Data System (ADS)

A simple, systematic generalized Langevin equation approach for calculating classical nonlinear response functions is formulated and discussed. The two-time Poisson brackets appearing at second and higher order are rendered tractable by a physically motivated approximation. The method is used to calculate the fifth order (second order response) Raman response of liquid CS2. Agreement with simulation is good, but the simplicity of the theoretical expression suggests that the path to obtaining qualitatively new information about liquids with the fifth order experiment is uncertain. Further applications of the basic approach are suggested.

Kim, Joohyun; Keyes, T.

2002-06-01

72

A LES-Langevin model for turbulence  

NASA Astrophysics Data System (ADS)

The rationale for Large Eddy Simulation is rooted in our inability to handle all degrees of freedom (N˜10^16 for Re˜10^7). ``Deterministic'' models based on eddy-viscosity seek to reproduce the intensification of the energy transport. However, they fail to reproduce backward energy transfer (backscatter) from small to large scale, which is an essentiel feature of the turbulence near wall or in boundary layer. To capture this backscatter, ``stochastic'' strategies have been developed. In the present talk, we shall discuss such a strategy, based on a Rapid Distorsion Theory (RDT). Specifically, we first divide the small scale contribution to the Reynolds Stress Tensor in two parts: a turbulent viscosity and the pseudo-Lamb vector, representing the nonlinear cross terms of resolved and sub-grid scales. We then estimate the dynamics of small-scale motion by the RDT applied to Navier-Stockes equation. We use this to model the cross term evolution by a Langevin equation, in which the random force is provided by sub-grid pressure terms. Our LES model is thus made of a truncated Navier-Stockes equation including the turbulent force and a generalized Langevin equation for the latter, integrated on a twice-finer grid. The backscatter is automatically included in our stochastic model of the pseudo-Lamb vector. We apply this model to the case of homogeneous isotropic turbulence and turbulent channel flow.

Dolganov, Rostislav; Dubrulle, Bérengère; Laval, Jean-Philippe

2006-11-01

73

Localised distributions and criteria for correctness in complex Langevin dynamics  

SciTech Connect

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

74

From shape to randomness: A classification of Langevin stochasticity  

NASA Astrophysics Data System (ADS)

The Langevin equation-perhaps the most elemental stochastic differential equation in the physical sciences-describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output-based on the shape of the Langevin equation’s potential field.

Eliazar, Iddo; Cohen, Morrel H.

2013-01-01

75

Moment Equation Approach to Neoclassical Transport Theory.  

National Technical Information Service (NTIS)

The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory ...

S. P. Hirshman

1977-01-01

76

Soliton Perturbation Theory for the Kawahara Equation  

NASA Astrophysics Data System (ADS)

The Kawahara equation is studied along with its perturbation terms. The adiabatic dynamics of the soliton amplitude and the velocity of the soliton is obtained by the aid of soliton perturbation theory.

Biswas, Anjan; Zerrad, Essaid

77

Invariant recording of elasticity theory equations  

NASA Astrophysics Data System (ADS)

An invariant (with respect to rotations) formalization of equations of linear and nonlinear elasticity theory is proposed. An equation of state (in the form of a convex generating potential) for various crystallographic systems is written. An algebraic approach is used, which does not require any geometric constructions related to the analysis of symmetry in crystals.

Selivanova, S. V.

2008-09-01

78

Relativistic Langevin dynamics in expanding media.  

PubMed

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

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

2013-09-01

79

Nonlinear quantum equations: Classical field theory  

SciTech Connect

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

80

Degenerate KAM theory for partial differential equations  

NASA Astrophysics Data System (ADS)

This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given.

Bambusi, D.; Berti, M.; Magistrelli, E.

81

Wong's equations in Yang-Mills theory  

NASA Astrophysics Data System (ADS)

Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semi-simple Lie group are derived. The equations obtained are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations, we obtain Wong's equations in a pure Yang-Mills gauge theory with Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures performed in a finite-dimensional dynamical system and the reduction procedure in Yang-Mills gauge fields.

Storchak, Sergey N.

2014-03-01

82

Langevin Picture of Lévy Walks and Their Extensions  

NASA Astrophysics Data System (ADS)

In this paper we derive Langevin picture of Lévy walks. Applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled Lévy walk. Next, we introduce extensions of Levy walks, in which jump sizes are some functions of waiting times. We prove that under proper scaling conditions, such generalized Lévy walks converge in distribution to the appropriate limiting processes. We also derive the corresponding fractional diffusion equations and investigate behavior of the mean square displacements of the limiting processes, showing that different coupling functions lead to various types of anomalous diffusion.

Magdziarz, Marcin; Szczotka, W?adys?aw; ?ebrowski, Piotr

2012-04-01

83

Entropy production in linear Langevin systems  

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

84

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

85

Undular bore theory for the Gardner equation  

NASA Astrophysics Data System (ADS)

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

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

2012-09-01

86

Solving Kepler's equation via Smale's -theory  

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

87

Complete Sets of Reductions for Some Equational Theories  

Microsoft Academic Search

An extenston of the Knuth-Bendix algorithm for finding complete sets of reductions is described. The extension is intended to handle equational theories which can be split into two parts, R and T, such that each equation m R can be construed as a reduction and T represents an equational theory for which a finite, complete umficat~on algorithm ~s known. The

Gerald E. Peterson; Mark E. Stickel

1981-01-01

88

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

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

89

Analysis of multifrequency langevin composite ultrasonic transducers.  

PubMed

The multimode coupled vibration of Langevin composite ultrasonic transducers with conical metal mass of large cross-section is analyzed. The coupled resonance and anti-resonance frequency equations are derived and the effective electromechanical coupling coefficient is analyzed. The effect of the geometrical dimensions on the resonance frequency, the anti-resonance frequency, and the effective electromechanical coupling coefficient is studied. It is illustrated that when the radial dimension is large compared with the longitudinal dimension, the vibration of the Langevin transducer becomes a multifrequency multimode coupled vibration. Numerical methods are used to simulate the coupled vibration; the simulated results are in good agreement with those from the analytical results. Some Langevin transducers of large cross-section are designed and manufactured and their resonance frequencies are measured. It can be seen that the resonance frequencies obtained from the coupled resonance frequency equations are in good agreement with the measured results. It is expected that by properly choosing the dimensions, multifrequency Langevin transducers can be designed and used in ultrasonic cleaning, ultrasonic sonochemistry, and other applications. PMID:19812002

Lin, Shuyu

2009-09-01

90

Standard Error of an Equating by Item Response Theory  

Microsoft Academic Search

A formula is derived for the asymptotic standard error of a true-score equating by item response theory. The equating method is applicable when th two tests to be equated are administered to different groups along with an anchor test. Numerical standard errors are shown for an actual equating (1) comparing the standard errors of IRT, linear, e and equipercentile methods

Frederic M. Lord

1982-01-01

91

Equivalence of Potential Theory and Ideal Adsorbed Solution (IAS) Theory Treatments of the Dubinin-Radushkevich Equation.  

National Technical Information Service (NTIS)

Multicomponent potential theory-based adsorption equilibria equations are derived using the IAS theory of Myers and Prausnitz. It is shown that both IAS and the potential theory lead to the same multicomponent equations when the potential theory equations...

D. T. Croft

1997-01-01

92

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

93

Thermodynamic restrictions on the constitutive equations of electromagnetic theory  

NASA Technical Reports Server (NTRS)

Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences

Coleman, B. D.; Dill, E. H.

1971-01-01

94

Heavy Flavor Suppression: Boltzmann vs Langevin  

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

95

Perturbation Theory for the - Benjamin-Ono Equation.  

National Technical Information Service (NTIS)

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

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

1998-01-01

96

Implicit Renewal Theory and Tails of Solutions of Random Equations  

Microsoft Academic Search

For the solutions of certain random equations, or equivalently the stationary solutions of certain random recurrences, the distribution tails are evaluated by renewal-theoretic methods. Six such equations, including one arising in queueing theory, are studied in detail. Implications in extreme-value theory are discussed by way of an illustration from economics.

Charles M. Goldie

1991-01-01

97

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

NASA Astrophysics Data System (ADS)

The relativistic diffusion process of heavy quarks is formulated on the basis of the relativistic Langevin equation in Itô discretization scheme. The drag force inside the quark-gluon plasma (QGP) is parametrized according to the formula for the strongly coupled plasma obtained by the anti-de-Sitter space/conformal field theory (AdS/CFT) correspondence. The diffusion dynamics of charm and bottom quarks in QGP is described by combining the Langevin simulation under the background matter described by the relativistic hydrodynamics. Theoretical calculations of the nuclear modification factor RAA and the elliptic flow v2 for the single electrons from the charm and bottom decays are compared with the experimental data from the relativistic heavy-ion collisions. The RAA for electrons with large transverse momentum (pT>3 GeV) indicates that the drag force from the QGP is as strong as the AdS/CFT prediction.

Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi

2009-05-01

98

Test Equating: Mean, Linear, Equipercentile, and Item Response Theory.  

ERIC Educational Resources Information Center

This paper discusses the four major types of test equating: (1) mean; (2) linear; (3) equipercentile; and (4) item response theory. The single-group, equivalent-group, and anchor-test data collection designs are presented as methods used for test equating. Issues related to assumptions and equating error are also addressed. The advantages and…

Felan, George D.

99

Standard Error of an Equating by Item Response Theory.  

National Technical Information Service (NTIS)

A formula is derived for the asymptotic standard error of a true-score equating by item response theory. The equating method is applicable when the two tests to be equated are administered to different groups along with an 'anchor test.' Numerical standar...

F. M. Lord

1981-01-01

100

Langevin stabilization of molecular dynamics  

NASA Astrophysics Data System (ADS)

In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brünger-Brooks-Karplus-Molly (BBK-M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK-M uses the popular Brünger-Brooks-Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps-1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK-M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein-DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK-M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps-1 is used the dynamics are not significantly distorted.

Izaguirre, Jesús A.; Catarello, Daniel P.; Wozniak, Justin M.; Skeel, Robert D.

2001-02-01

101

On extremals of the entropy production by ‘Langevin–Kramers’ dynamics  

NASA Astrophysics Data System (ADS)

We refer as ‘Langevin–Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin–Kramers models differs from the now well-understood case of Langevin–Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge–Ampère–Kantorovich optimal mass-transport equations.

Muratore-Ginanneschi, Paolo

2014-05-01

102

Augmented Langevin approach to fluctuations in nonlinear irrversible proceses  

SciTech Connect

A Fokker-Planck equation derived from statistical mechanics by M. S. Green (J. Chem. Phys. 20:1281 (1952)) has been used by Grabert et al. (Phys. Rev. A 21:2136 (1980)) to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker--Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker--Planck equation as that of Grabert et al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker--Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.

Ramshaw, J.D.

1985-02-01

103

Langevin processes, agent models and socio-economic systems  

Microsoft Academic Search

We review some approaches to the understanding of fluctuations of financial asset prices. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalize the approach to stochastic equations that model interacting agents. The agent models recently

Peter Richmond; Lorenzo Sabatelli

2004-01-01

104

Functional Equation in the Theory of Fluids.  

National Technical Information Service (NTIS)

Two functional equations of the form (psi squared)(s) - E(s)(phi squared) = V(s), where s is a complex variable and E(s) and V(s) are given even polynomials, are solved for the even entire functions. Psi and phi which are required to behave like cosh(alph...

J. L. Lebowitz O. Penrose

1971-01-01

105

Poisson vertex algebras in the theory of Hamiltonian equations  

Microsoft Academic Search

.  We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian\\u000a partial differential equations. Such an equation is called integrable if it can be included in an infinite hierarchy of compatible\\u000a Hamiltonian equations, which admit an infinite sequence of linearly independent integrals of motion in involution. The construction\\u000a of a hierarchy

Aliaa Barakat; Alberto De Sole; Victor G. Kac

2009-01-01

106

Data driven Langevin modeling of biomolecular dynamics  

NASA Astrophysics Data System (ADS)

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

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

2013-05-01

107

Bogomol'nyi equations in gauge theories.  

National Technical Information Service (NTIS)

By imposing self-duality conditions, we obtain the explicit form in which gauge theories spontaneously breakdown in the Bogomol'nyi. In this context, we reconsider the Abelian Higgs and Maxwell-Chern-Simons Higgs models. On the same footing, we find a top...

M. S. Cunha H. R. Christiansen C. A. S. Almeida

1997-01-01

108

Master-equation theory of semiconductor lasers  

SciTech Connect

A master-equation approach to the semiconductor laser is derived. Projection-operator techniques are used to eliminate the fast motion occurring in the system, leading to a description of the system in terms of numbers of electrons and holes, with a fully quantum-mechanical description of the field. The output light statistics are calculated and compared with that appearing elsewhere [Y. Yamamoto and S. Machida, Phys. Rev. A 35, 5114 (1987)].

Gardiner, C.W.; Eschmann, A. [Physics Department, University of Waikato, Hamilton (New Zealand)] [Physics Department, University of Waikato, Hamilton (New Zealand)

1995-06-01

109

Applications of Langevin and Molecular Dynamics methods  

SciTech Connect

Computer simulation of complex nonlinear and disordered phenomena from materials science is rapidly becoming an active and new area serving as guide for experiments and for testing of theoretical concepts. This is especially true when novel massively parallel computer systems and techniques are used on these problems. In particular the Langevin dynamics simulation technique has proven useful in situations where the time evolution of a system in contact with a heat bath is to be studied. The traditional way to study systems in contact with a heat bath has been via the Monte Carlo method. While this method has indeed been used successfully in many applications, it has difficulty addressing true dynamical questions. Large systems of coupled stochastic ODEs (or Langevin equations) are commonly the end result of a theoretical description of higher dimensional nonlinear systems in contact with a heat bath. The coupling is often local in nature, because it reflects local interactions formulated on a lattice, the lattice for example represents the underlying discreteness of a substrate of atoms or discrete k-values in Fourier space. The fundamental unit of parallelism thus has a direct analog in the physical system the authors are interested in. In these lecture notes the authors will illustrate the use of Langevin stochastic simulation techniques on a number of nonlinear problems from materials science and condensed matter physics that have attracted attention in recent years. First, the authors will review the idea behind the fluctuation-dissipation theorem which forms that basis for the numerical Langevin stochastic simulation scheme. The authors then show applications of the technique to various problems from condensed matter and materials science.

Lomdahl, P.S.

1994-12-31

110

Applications of Langevin and Molecular Dynamics methods  

NASA Astrophysics Data System (ADS)

Computer simulation of complex nonlinear and disordered phenomena from materials science is rapidly becoming an active and new area serving as a guide for experiments and for testing of theoretical concepts. This is especially true when novel massively parallel computer systems and techniques are used on these problems. In particular the Langevin dynamics simulation technique has proven useful in situations where the time evolution of a system in contact with a heat bath is to be studied. The traditional way to study systems in contact with a heat bath has been via the Monte Carlo method. While this method has indeed been used successfully in many applications, it has difficulty addressing true dynamical questions. Large systems of coupled stochastic ODE's (or Langevin equations) are commonly the end result of a theoretical description of higher dimensional nonlinear systems in contact with a heat bath. The coupling is often local in nature, because it reflects local interactions formulated on a lattice, the lattice for example represents the underlying discreteness of a substrate of atoms or discrete k-values in Fourier space. The fundamental unit of parallelism thus has a direct analog in the physical system the authors are interested in. In these lecture notes the authors illustrate the use of Langevin stochastic simulation techniques on a number of nonlinear problems from materials science and condensed matter physics that have attracted attention in recent years. First, the authors review the idea behind the fluctuation-dissipation theorem which forms that basis for the numerical Langevin stochastic simulation scheme. The authors then show applications of the technique to various problems from condensed matter and materials science.

Lomdahl, P. S.

111

The Boltzmann equation in classical Yang-Mills theory  

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

112

Extended Thermodynamics: a Theory of Symmetric Hyperbolic Field Equations  

NASA Astrophysics Data System (ADS)

Extended thermodynamics is based on a set of equations of balance which are supplemented by local and instantaneous constitutive equations so that the field equations are quasi-linear first order differential equations. If the constitutive functions are subject to the requirements of the entropy principle, one may write them in symmetric hyperbolic form by a suitable choice of fields. The kinetic theory of gases, or the moment theories based on the Boltzmann equation provide an explicit example for extended thermodynamics. The theory proves its usefulness and practicality in the successful treatment of light scattering in rarefied gases. This presentation is based upon the book [1] of which the author of this paper is a co-author. For more details about the motivation and exploitation of the basic principles the interested reader is referred to that reference. It would seem that extended thermodynamics is worthy of the attention of mathematicians. It may offer them a non-trivial field of study concerning hyperbolic equations, if ever they get tired of the Burgers equation. Physicists may prefer to appreciate the success of extended thermodynamics in light scattering and to work on the open problems concerning the modification of the Navier-Stokes-Fourier theory in rarefied gases as predicted by extended thermodynamics of 13, 14, and more moments.

Müller, Ingo

2008-12-01

113

Einstein equations and MOND theory from Debye entropic gravity  

NASA Astrophysics Data System (ADS)

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.; Rezazadeh Sarab, K.

2012-10-01

114

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

115

Role of pumping statistics in laser dynamics: Quantum Langevin approach  

Microsoft Academic Search

We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a

Claus Benkert; M. O. Scully; J. Bergou; L. Davidovich; M. Hillery; M. Orszag

1990-01-01

116

Modified Friedmann equation from nonminimally coupled theories of gravity  

NASA Astrophysics Data System (ADS)

In this work we study how nonminimally coupled theories of gravity modify the usual Friedmann equation, and develop two methods to treat these. The ambiguity in the form of the Lagrangian density of a perfect fluid is emphasized, and the impact of different dominant matter species is assessed. The cosmological constant problem is also discussed.

Bertolami, Orfeu; Páramos, Jorge

2014-02-01

117

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

118

Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers  

Microsoft Academic Search

A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric

C. Henry; H. HENRY

1986-01-01

119

Langevin approach for stochastic Hodgkin-Huxley dynamics with discretization of channel open fraction  

NASA Astrophysics Data System (ADS)

The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.

Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

2013-12-01

120

Equation of State and Integral Equation Theory for Hard Sphere and Hard-Sphere Chain Fluids  

Microsoft Academic Search

The development of an accurate equation of state based on molecular thermodynamics for simple and complex fluids is important to chemical process design. In this dissertation we study the thermodynamic and intermolecular structural properties of hard sphere and hard-sphere chain fluids. These are theoretically challenging problems, the solution of which are useful for perturbation theory of more realistic potential models.

Jaeeon Chang

1994-01-01

121

Tutorial on Optimization Theory and Difference and Differential Equations  

NSDL National Science Digital Library

This online tutorial is intended for college students taking an early course in mathematical optimization or linear differential equations. Although it is written by a professor of economics, little economic theory is presented. This keeps the material centered on the mathematical aspects of optimization and differential equations, which have a wide range of scientific applications. The text is very well organized and is accompanied by illustrative figures. No prerequisites to the tutorial are listed; however, a fairly strong background in undergraduate calculus would probably be useful.

122

A theory of open systems based on stochastic differential equations  

NASA Astrophysics Data System (ADS)

For a model of an open quantum system—a concentrated ensemble consisting of similar atoms and interacting with a one-dimensional quantum vacuum environment with a zero photon density—quantum stochastic differential equations of a non-Wiener type of the general form have been obtained; based on the equations, kinetic equations describing a wide class of physical systems are derived. The distinctive feature of such systems is effects of suppression of collective spontaneous emission and stabilization of the excited state. For the open classical system exposed to the action of noise in the form of a Levy process of the general non-Gaussian kind, kinetic equations of the Fokker-Planck type with fractional derivatives have been obtained based on classical non-Wiener stochastic differential equations. This emphasizes the common base of the developed theory for different types of open systems, which is expressed in using the mathematical formalism of stochastic differential equations of the general non-Wiener type.

Basharov, A. M.

2014-04-01

123

Hessian polyhedra, invariant theory and Appell hypergeometric partial differential equations  

Microsoft Academic Search

It is well-known that Klein's lectures on the icosahedron and the solution of equations of fifth degree is one of the most important and influential books of 19th-century mathematics. In the present paper, we will give the complex counterpart of Klein's book, i.e., a story about complex regular polyhedra. We will show that the following four apparently disjoint theories: the

Lei Yang

2004-01-01

124

Theory of a ring laser. [electromagnetic field and wave equations  

NASA Technical Reports Server (NTRS)

Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.

Menegozzi, L. N.; Lamb, W. E., Jr.

1973-01-01

125

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

Microsoft Academic Search

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

2006-01-01

126

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

127

Global solutions of hyperbolic equations of gauge theories  

NASA Astrophysics Data System (ADS)

The Cauchy problem for the classical Lorentzian-signature equations of gauge theories, Yang-Mills fields, and associated fields is examined, summarizing and expanding the results of Choquet-Bruhat and Christodoulou (1981) and Choquet-Bruhat and Segal (1982). The global existence theorem for the solutions is obtained by conformal mapping of Minkowski space-time onto the Einstein cylinder and by the method of a priori estimates, and the combined results are shown to lead to the asymptotic decay properties of the solutions on Minkowski space-time.

Choquet-Bruhat, Y.

128

A moment equation reformulation of Rayleigh - Ritz theory  

NASA Astrophysics Data System (ADS)

We present a moment equation Rayleigh - Ritz (RR) variational theory for the ground-state energy. An extended Fourier transform space can be defined through the moment equation corresponding to a given Schrödinger Hamiltonian. Within this extended space, we can implement a variational ansatz with respects to configurations of the form 0305-4470/29/14/030/img1 in which the energy-dependent functions 0305-4470/29/14/030/img2: (i) satisfy the momentum space Schrödinger equation; (ii) are uniquely prescribed; (iii) are (most likely) non-integrable; and (iv) yield the 0305-4470/29/14/030/img3 physical solution for physical E and 0305-4470/29/14/030/img4 values. On the basis of this representation, one can minimize the energy expectation value 0305-4470/29/14/030/img5 with respects to the E and missing moment variables, 0305-4470/29/14/030/img4. The proposed approach is in sharp contrast to traditional configuration-space RR implementations in which the selection of a variational basis is not manifest a priori, particularly for problems of spatial dimension greater than one. The analysis of one- and two-dimension problems is presented.

Handy, Carlos R.

1996-07-01

129

Universal theory of dynamical chaos in nonlinear dissipative systems of differential equations  

NASA Astrophysics Data System (ADS)

A new universal theory of dynamical chaos in nonlinear dissipative systems of differential equations including ordinary and partial, autonomous and non-autonomous differential equations and differential equations with delay arguments is presented in this paper. Four corner-stones lie in the foundation of this theory: the Feigenbaum's theory of period doubling bifurcations in one-dimensional mappings, the Sharkovskii's theory of bifurcations of cycles of an arbitrary period up to the cycle of period three in one-dimensional mappings, the Magnitskii's theory of rotor type singular points of two-dimensional non-autonomous systems of differential equations as a bridge between one-dimensional mappings and differential equations and the theory of homoclinic cascade of bifurcations of stable cycles in nonlinear differential equations. All propositions of the theory are strictly proved and illustrated by numerous analytical and computing examples.

Magnitskii, Nikolai A.

2008-03-01

130

Nonlocal continuum theory: A hierarchy of balance equations  

Microsoft Academic Search

The generalized Cauchy equations of motion are reviewed and differences in order of magnitude in equation terms are shown. By expanding the neighborhood around the material point a hierarchy of equations of motion is obtained. This set of equations follows as a matter of course by equating terms of the same order of magnitude. The stress tensor is symmetric, regardless

G. D. C. Kuiken

1981-01-01

131

Time scales in rotating unstable Langevin-type dynamics.  

PubMed

In this Rapid Communication we propose a different and general characterization of rotating, unstable Langevin-type dynamics in the presence of an external force in the context of two dynamical representations x and y, using the passage time distribution. Here y is the transformed space of coordinates obtained by means of a time-dependent rotation matrix. The Langevin dynamics in the new y space defines an interesting concept of external force and internal noise due to rotation. The theory is applied to the characterization of rotational unstable systems of two (such as the laser system) and three variables, and stimulates its application in other fields, for instance, in plasma physics. PMID:11735880

Jiménez-Aquino, J I; Romero-Bastida, M

2001-11-01

132

New explicit solutions of Einstein equations in the framework of GAP Theory  

NASA Astrophysics Data System (ADS)

The presented paper develops a new method for solving Einstein equations explicitly. Not only the solutions are new but also the mathematical framework of their construction which is given by a nonstandard function theory built over nonstandard algebras (in the following denoted as GAPs) and will be called here as ``GAP Theory.'' It is shown that the GAP theory succeeds in regions, where group theory fails: the group structure is too small to solve Einstein equations explicitly.

Starkl, Reinhard

2007-12-01

133

Modern integral equation techniques for quantum reactive scattering theory  

SciTech Connect

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

134

Ambient-temperature passive magnetic bearings: Theory and design equations  

SciTech Connect

Research has been underway at the Lawrence Livermore National Laboratory to build a theoretical and experimental base for the design of ambient-temperature passive magnetic bearings for a variety of possible applications. in the approach taken the limitations imposed by Earnshaw`s theorem with respect to the stability of passive magnetic bearing systems employing axially symmetric permanent-magnet elements are overcome by employing special combinations of elements, as follows: Levitating and restoring forces are provided by combinations of permanent-magnet-excited elements chosen to provide positive stiffnesses (negative force derivatives) for selected displacements (i.e., those involving translations or angular displacement of the axis of rotation). As dictated by Eamshaw`s theorem, any bearing system thus constructed will be statically unstable for at least one of the remaining possible displacements. Stabilization against this displacement is accomplished by using periodic arrays (`Halbach arrays`) of permanent magnets to induce currents in close-packed inductively loaded circuits, thereby producing negative force derivatives stabilizing the system while in rotation. Disengaging mechanical elements stabilize the system when at rest and when below a low critical speed. The paper discusses theory and equations needed for the design of such systems.

Post, R.F.; Ryutov, D.D.

1997-12-30

135

The theory of relaxation oscillations for Hutchinson's equation  

SciTech Connect

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

136

Approximate equations of the theory of liquids in the statistical thermodynamics of classical liquid systems  

Microsoft Academic Search

This review presents the fundamentals of the method of integral equations of the theory of liquids. One of the central problems of the theory, the definition of bridge-functionals, is analyzed. Some applications of the method of integral equations to simple liquid systems are discussed, and the problem of description of complex polyatomic classical systems is considered.

Gari N Sarkisov

1999-01-01

137

Diffusion in the special theory of relativity  

NASA Astrophysics Data System (ADS)

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Herrmann, Joachim

2009-11-01

138

Langevin description of gauged scalar fields in a thermal bath  

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

139

Liouvillian propagators, Riccati equation and differential Galois theory  

NASA Astrophysics Data System (ADS)

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

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

140

Functional Equations in Asymptotical Problems of Queueing Theory  

Microsoft Academic Search

The investigation of communication systems with a large number of devices sometimes leads to initial-boundary problems for functional equations. In this work we consider several classes of such problems for differential-difference and integral-differential equations and for partial differential equations. We are interested in the global existence of solutions in the quarter-plane x > 0, t > 0; in the existence of

N. D. Vvedenskaya; Yu. M. Suhov

2004-01-01

141

Spherically Symmetric Solutions of the Einstein--Bach Equations and a Consistent Spin-2 Field Theory  

NASA Astrophysics Data System (ADS)

We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein--Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein--Bach equations.

Janda, A.

2006-12-01

142

Morse-type index theory for flows and periodic solutions for Hamiltonian equations  

Microsoft Academic Search

An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic solutions of a time-dependent (periodic in time) and asymptotically linear Hamiltonian equation.

Charles Conley; Eduard Zehnder

1984-01-01

143

Structure of Polymer Melts and Blends: Comparison of Integral Equation Theory and Computer Simulations  

Microsoft Academic Search

This review covers the most recent developments using the Polymer Reference Interaction Site Model (PRISM) integral equation theory to study polymer melts and blends. Comparisons to computer simulations are presented that have isolated the deficiencies in the theory and led to improvements including the self-consistent approach where the theory is coupled with single chain Monte Carlo simulations. Using recent simulation

David R. Heine; Gary S. Grest; John G. Curro

144

Infinite Dimensional Geometric Singular Perturbation Theory for the Maxwell--Bloch Equations  

Microsoft Academic Search

We study the Maxwell-Bloch equations governing a two-level laser in a ring cavity. For Class A lasers, these equations have two widely separated time scales and form a singularly perturbed, semilinear hyperbolic system with two distinct characteristics. We extend Fenichel's geometric singular perturbation theory (N. Fenichel, J. Di!er ential Equations, 31 (1979), pp. 53-98) to the Maxwell-Bloch equations by proving

Govind Menon; ORGY HALLER

2001-01-01

145

Existence of algebraic matrix Riccati equations arising in transport theory  

Microsoft Academic Search

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

Jonq Juang

1995-01-01

146

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

NASA Astrophysics Data System (ADS)

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

Ghoroku, Kazuo; Nakamura, Akihiro

2013-03-01

147

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

PubMed

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

148

Electron band theory and high pressure equation of state  

SciTech Connect

Calculations of the high pressure equation of state of selected materials are reviewed, in order to illustrate general trends which occur in the evolution of electronic structure with compression, and the consequences of these trends for material properties.

McMahan, A.K.

1981-07-21

149

Oscillation theory for neutral delay differential equations with variable coefficients  

NASA Astrophysics Data System (ADS)

New oscillation criteria are derived for all solutions of first order neutral delay differential equations. Our results can improve and extend several of the well known results in the literature. Some examples are given to illustrate the main results.

Ahmed, Fatima N.; Ahmad, Rokiah Rozita; Din, Ummul Khair Salma; Noorani, Mohd Salmi Md

2014-06-01

150

Equation of state for solid neon from quantum theory  

Microsoft Academic Search

The equation of state P(V,T) for solid neon is obtained from a quantum theoretical treatment using two- and three-body forces, and an anharmonic treatment for lattice vibrations and temperature effects within the Einstein approximation. Our results are in excellent agreement with experiment for the pressure and temperature range of up to 200 GPa and 900 K. The calculated equation of

P. Schwerdtfeger; Andreas Hermann

2009-01-01

151

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

152

An impulse integrator for Langevin dynamics  

NASA Astrophysics Data System (ADS)

The best simple method for Newtonian molecular dynamics is indisputably the leapfrog St&(o)uml;rmer-Verlet method. The appropriate generalization to simple Langevin dynamics is unclear. An analysis is presented comparing an 'impulse method' (kick; fluctuate; kick), the 1982 method of van Gunsteren and Berendsen, and the Br&(u)uml;nger-Brooks-Karplus (BBK) method. It is shown how the impulse method and the van Gunsteren-Berendsen methods can be implemented as efficiently as the BBK method. Other considerations suggest that the impulse method is the best basic method for simple Langevin dynamics, with the van Gunsteren-Berendsen method a close contender.

Skeel, Robert D.; Izaguirre, Jesús A.

2002-12-01

153

Stochastic regulator theory for a class of abstract wave equations  

NASA Technical Reports Server (NTRS)

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

Balakrishnan, A. V.

1991-01-01

154

Temporal breakdown and Borel resummation in the complex Langevin method  

SciTech Connect

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

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

2013-02-15

155

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

ERIC Educational Resources Information Center

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

Brossman, Bradley G.; Lee, Won-Chan

2013-01-01

156

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

PubMed

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

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

2014-01-01

157

Space-time versus world-sheet renormalization group equation in string theory.  

National Technical Information Service (NTIS)

We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-...

R. Brustein K. Roland

1991-01-01

158

Quantifying Equating Errors with Item Response Theory Methods  

Microsoft Academic Search

The purpose of this paper was to examine alterna tive techniques for quantifying the errors associated with the criterion of equating a test to itself. Data for the study came from the national standardization of the 3-R's Achievement Test. The reading and mathe matics subtests were analyzed using random samples from the Grade 4 norming group. Errors for two item

S. E. Phillips

1985-01-01

159

Semismall perturbations in the martin theory for elliptic equations  

Microsoft Academic Search

We investigate stability of Martin boundaries for positive solutions of elliptic partial differential equations. We define\\u000a a perturbation which isG\\u000a \\u000a L\\u000a D\\u000a -semismall at infinity, show that Martin boundaries are stable under this perturbation, and give sufficient conditions for\\u000a it.

Minoru Murata

1997-01-01

160

The Boltzmann Equation for a Bounded Medium I. General Theory  

Microsoft Academic Search

A general theoretical treatment is given of the linearized Boltzmann equation for flow in a bounded medium under conditions when the collision mean free path is of the order of the dimensions of the cross-section of the specimen. The approach given may be used for any type of particle; we consider gas molecules, electrons and phonons. Part 1 is concerned

S. Simons

1960-01-01

161

Application of integral equation theory to polyolefin liquids and blends  

SciTech Connect

The ability to model the packing of polymers in melts and blends is important in many polymer applications. One significant application is the development of new polymer blends. It would be exceedingly helpful to the materials chemist if molecular modeling could be employed to predict the thermodynamics and phase behavior of hypothetical polymer alloys before embarking on a time consuming and expensive synthesis program. The well known Flory-Huggins theory has been remarkably successful in describing many aspects of polymer mixing from a qualitative point of view. This theory is known, however, to suffer from several deficiencies which can be traceable to the fact that: (1) it is a lattice model requiring both monomer components to have the same volume; and (2) a mean field or random mixing approximation is made which effectively ignores chain connectivity. Because of these limitations the Flory-Huggins theory does not include packing effects and cannot be used to make quantitative molecular engineering calculations. Recently Curro and Schweizer developed a new approach for treating polymer liquids and mixtures which the authors call PRISM theory. This is an extension to polymers of the Reference Interaction Site Model (RISM Theory) developed by Chandler and Andersen to describe the statistical mechanics of small molecule liquids. The PRISM theory is a continuous space description of a polymer liquid, which includes chain connectivity and nonrandom mixing effects in a computationally tractable manner. The primary output from PRISM calculations is the average structure or packing of the amorphous liquid given by the radial distribution function denoted as g(r). This radial distribution function is employed to deduce thermodynamic or structural properties of interest. Here, the authors describe the theoretical approach and demonstrate its application to polyethylene, isotactic polypropylene, syndiotactic polypropylene, and polyisobutylene liquids and blends.

Curro, J.G.; Weinhold, J.D.

1997-11-01

162

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

163

Equation-of-motion coupled cluster perturbation theory revisited.  

PubMed

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. PMID:24811632

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

2014-05-01

164

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

NASA Astrophysics Data System (ADS)

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

Zaripov, Farkhat

2014-07-01

165

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

NASA Astrophysics Data System (ADS)

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

Zaripov, Farkhat

2014-04-01

166

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

167

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

168

Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion  

PubMed Central

We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj

Hsu, David; Hsu, Murielle

2009-01-01

169

Some aspects of field equations in generalized theories of gravity  

NASA Astrophysics Data System (ADS)

A class of theories of gravity based on a Lagrangian L=L(Rabcd,gab) which depends on the curvature and metric—but not on the derivatives of the curvature tensor—is of interest in several contexts including in the development of the paradigm that treats gravity as an emergent phenomenon. This class of models contains, as an important subset, all Lanczos-Lovelock models of gravity. I derive several identities and properties which are useful in the study of these models and clarify some of the issues that seem to have received insufficient attention in the past literature.

Padmanabhan, T.

2011-12-01

170

On the connection between the reference interaction site model integral equation theory and the partial wave expansion of the molecular Ornstein-Zernike equation  

NASA Astrophysics Data System (ADS)

We develop an integral equation theory based on the partial wave expansion of the molecular Ornstein-Zernike (OZ) equation. The theory provides a rigorous and transparent framework for multiple site treatments of molecular fluids. We examine free-energy functional and closure expressions with pilot calculations of homonuclear diatomic Lennard-Jones liquids.

Ten-No, Seiichiro; Iwata, Suehiro

1999-09-01

171

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

NASA Astrophysics Data System (ADS)

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

Nakamura, K.

2009-06-01

172

Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction  

SciTech Connect

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

173

Derivation of non-Markovian transport equations for trapped cold atoms in nonequilibrium thermal field theory  

SciTech Connect

The non-Markovian transport equations for the systems of cold Bose atoms confined by a external potential both without and with a Bose-Einstein condensate are derived in the framework of nonequilibrium thermal field theory (Thermo Field Dynamics). Our key elements are an explicit particle representation and a self-consistent renormalization condition which are essential in thermal field theory. The non-Markovian transport equation for the non-condensed system, derived at the two-loop level, is reduced in the Markovian limit to the ordinary quantum Boltzmann equation derived in the other methods. For the condensed system, we derive a new transport equation with an additional collision term which becomes important in the Landau instability.

Nakamura, Y. [Department of Electronic and Photonic Systems, Waseda University, Tokyo 169-8555 (Japan)], E-mail: nakamura@aoni.waseda.jp; Sunaga, T. [Department of Physics, Waseda University, Tokyo 169-8555 (Japan)], E-mail: tomoka@fuji.waseda.jp; Mine, M. [Waseda University Honjo Senior High School, 1136 Nishitomida, Honjo, Saitama 367-0035 (Japan)], E-mail: mine@waseda.jp; Okumura, M. [CCSE, Japan Atomic Energy Agency, 6-9-3 Higashi-Ueno, Taito-ku, Tokyo 110-0015 (Japan); CREST (JST), 4-1-8 Honcho, Kawaguchi-shi, Saitama 332-0012 (Japan)], E-mail: okumura.masahiko@jaea.go.jp; Yamanaka, Y. [Department of Electronic and Photonic Systems, Waseda University, Tokyo 169-8555 (Japan)], E-mail: yamanaka@waseda.jp

2010-02-15

174

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

NASA Astrophysics Data System (ADS)

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

2014-05-01

175

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

PubMed

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. PMID:24832290

Aupic, Jana; Urbic, Tomaz

2014-05-14

176

Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites  

NASA Astrophysics Data System (ADS)

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite’s survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

Zaburdaev, Vasily; Uppaluri, Sravanti; Pfohl, Thomas; Engstler, Markus; Friedrich, Rudolf; Stark, Holger

2011-05-01

177

The Schwinger-Dyson equation and dynamical mass generation in two-dimensional field theories  

Microsoft Academic Search

A truncated Schwinger-Dyson equation is used to investigate the dynamical generation of mass in (1 + 1)-dimensional field theories with a four-fermion interaction. An affective potential formalism is developed to clarify the nature of the approximations made to the Schwinger-Dyson kernel. The gap equation for the Gross-Neveu model is found to have solutions of the ''collapse of the wave function''

N. Dorey; R. D. Kenway

1990-01-01

178

Quantum cybernetics: a new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation  

NASA Astrophysics Data System (ADS)

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

Grössing, Gerhard

2002-04-01

179

On the structure of balance equations and extended field theories of mechanics  

Microsoft Academic Search

Summary  A new approach to thermodynamics has been proposed recently, in which, in addition to the densities of mass, momentum and\\u000a energy, the densities of momentum flux and energy flux are also taken as independent state variables. Extra equations of balance\\u000a motivated by the moment equations of the kinetic theory are postulated. In this paper, we explore the general structure of

I-Shih Liu

1986-01-01

180

Faddeev equations including three-body forces in first order perturbation theory  

Microsoft Academic Search

We propose a modification of the standard Faddeev equations which takes into account the effects of a three-body force in first order perturbation theory on the triton wave function and its binding energy. Furthermore, we report our results for the energy expectation value caused by the two-pion-exchange three-nucleon force. NUCLEAR STRUCTURE Faddeev equations, energy expectation value of the two-pion-exchange three-nucleon

A. Boemelburg; W. Gloeckle

1983-01-01

181

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

SciTech Connect

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

182

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

Microsoft Academic Search

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

183

Langevin dynamics for the transport of flexible biological macromolecules in confined geometries.  

PubMed

The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an ?-helix protein through a carbon nanotube is simulated. PMID:21241153

Peters, Michael H

2011-01-14

184

Langevin dynamics for the transport of flexible biological macromolecules in confined geometries  

NASA Astrophysics Data System (ADS)

The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an ?-helix protein through a carbon nanotube is simulated.

Peters, Michael H.

2011-01-01

185

The peridynamic equation of motion in non-local elasticity theory  

Microsoft Academic Search

During the last few years, non-local theories in solid mechanics that account for effects of long-range interactions have\\u000a become topical again. One of these theories is the so-called peridynamic modelling, introduced by Silling [1].\\u000a \\u000a The governing equation of motion is the partial integro-differential equation \\u000a \\u000a \\u000a \\u000a \\u000a $\\u000a\\\\rho \\\\left( x \\\\right)\\\\partial _t^2 u\\\\left( {x,t} \\\\right) = \\\\smallint _{\\\\mathcal{H}\\\\left( x \\\\right)} f\\\\left( {x,\\\\hat

Etienne Emmrich; Olaf Weckner

186

Climate change, theory of planned behavior and values: a structural equation model with mediation analysis  

Microsoft Academic Search

An online survey about climate change was conducted 2008\\/2009 among all university members (N = 3541). Using the Theory of\\u000a Planned Behavior and Cultural Theory within a structural equation modeling approach, one main goal was to explain climate-friendly\\u000a behavioral intentions and the underlying psychological processes comprehensively and to show the interdependencies between\\u000a both approaches. The model explained 72% of the

Aysel Tikir; Bernard Lehmann

2011-01-01

187

An improved effective-mass-theory equation for phosphorus doped in silicon  

NASA Astrophysics Data System (ADS)

A new multi-valley effective-mass-theory (EMT) equation is derived for the phosphorus doped in silicon. This equation admits solutions which agree with the measured ground state energy and the square modulus of the ground-state wavefunction |?(0)| at the donor site accurately. This avoids the use of the so-called "central-cell correction" approximation method to calculate the hyperfine constant at the donor site. Furthermore, the energy levels for the upper lying states of T2 and E can also be predicted relatively accurately. The newly derived EMT equation has applications in the characterization of semiconductor or spintronics devices.

Hui, H. T.

2013-01-01

188

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

PubMed

We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, J. Stat. Mech. (2008) P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic mode-coupling one in that a further approximation corresponding to Gaussian density fluctuations leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-nonergodic transition, as opposed to the historical mode-coupling approach. PMID:24580215

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

2014-01-01

189

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

NASA Astrophysics Data System (ADS)

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

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

2014-01-01

190

The Monte-Carlo get finished in hollow cathode theory -- a source equation is incoming!  

NASA Astrophysics Data System (ADS)

The hollow cathode effect (HCE) in glow discharge occurred rather hard bean for theoreticians. Classical local Engel and Shtenbek cathode dark space theory does not work under conditions of HCE because it is not possible to neglect inertia of electron here. The electron distribution function has many features and it is far from Maxwellian one. The absence of non-local source model from Paschen invention of a hollow cathode in 1916 till today forced to use Monte-Carlo methods. It meant an absence of any equation for a source of ionization in a hollow cathode! Time to find this equation is coming. It is an integral equation, which is derived from kinetic equation and determines a non-local dependence of ionization source on electric field through phase trajectories of electron motion. When simplification of local dependence is possible, the equation can be transformed into ordinary differential equation and then it is coincident with a continuity equation of classical Engel-Shtenbek model. In joining with field equations the source equation enables to calculate current voltage characteristics of simple glow and hollow cathode discharge and see the HCE in mathematical simulation.

Gorin, Vladimir

2008-10-01

191

Correlated continuous-time random walks—scaling limits and Langevin picture  

Microsoft Academic Search

In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor.43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces.

Marcin Magdziarz; Ralf Metzler; Wladyslaw Szczotka; Piotr Zebrowski

2012-01-01

192

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

Microsoft Academic Search

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

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

2010-01-01

193

Universal calculational recipe for solvent-mediated potential: based on a combination of integral equation theory and density functional theory  

Microsoft Academic Search

A universal formalism, which enables calculation of solvent-mediated potential (SMP) between two equal or non-equal solute particles with any shape immersed in solvent reservior consisting of atomic particle and\\/or polymer chain or their mixture, is proposed by importing a density functional theory externally into OZ equation systems. Only if size asymmetry of the solvent bath components is moderate, the present

Shiqi Zhou

2004-01-01

194

An Investigation of the Feasibility of Applying Item Response Theory to Equate Achievement Tests.  

ERIC Educational Resources Information Center

The purpose of this study was to examine the feasibility of using item response theory (IRT) methods to equate different forms of three College Board Achievement Tests (Biology, American History and Social Studies, and Mathematics Level II) and one Graduate Record Examinations Achievement Test (Advanced Biology), rather than conventional or…

Cook, Linda L.; Eignor, Daniel R.

195

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

ERIC Educational Resources Information Center

The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted.…

Brossman, Bradley Grant

2010-01-01

196

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

Microsoft Academic Search

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

Integrodifferential Equations for Systems of Leaky Aquifers and Applications 1. The Nature of Approximate Theories  

Microsoft Academic Search

The dynamics of leaky aquifers are governed by a system of integrodifferential equations derived in this paper. Alternative expressions for the memory functiolls are obtailled, and it is shown that approximate theories of leaky aquifers correspolld to several ways of approximatillg the memory fuJlctioIlS.

Ismael Herrera; Leopoldo Rodarte

1973-01-01

198

Coupling of Dynamical and Transport Equations in f(R) Theory  

NASA Astrophysics Data System (ADS)

This paper is devoted to study spherically symmetric gravitational collapse with anisotropic fluid in f(R) theory which undergoes dissipation in the form of heat flux. We develop dynamical and transport equation and finally couple them. This yields different possibilities of collapse and explosions connected with supernovae events and immense of dark energy terms arising from modifying gravity.

Sharif, M.; Rizwana Kausar, H.

199

Faddeev equations including three-body forces in first order perturbation theory  

SciTech Connect

We propose a modification of the standard Faddeev equations which takes into account the effects of a three-body force in first order perturbation theory on the triton wave function and its binding energy. Furthermore, we report our results for the energy expectation value caused by the two-pion-exchange three-nucleon force.

Boemelburg, A.; Gloeckle, W.

1983-11-01

200

Integral equation theory of hard sphere liquids on two-dimensional cylindrical surfaces  

Microsoft Academic Search

An integral equation theory has been developed to elucidate the structure of hard sphere liquids on the two dimensional (2D) surface of a cylinder. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair correlation function is reformulated as a function of two variables to account for particles packing along and around the cylinder. Both Percus–Yevick (PY) and Hypernetted

Takafumi Iwaki; Chwen-Yang Shew; Godfrey Gumbs

2006-01-01

201

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

202

Second-Order Gauge Invariant Cosmological Perturbation Theory --- Einstein Equations in Terms of Gauge Invariant Variables ---  

NASA Astrophysics Data System (ADS)

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

Nakamura, K.

2007-01-01

203

Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations  

NASA Astrophysics Data System (ADS)

This paper contains an account of A.A. Bolibrukh's results obtained in the new directions of research that arose in the analytic theory of differential equations as a consequence of his sensational counterexample to the Riemann-Hilbert problem. A survey of results of his students in developing topics first considered by Bolibrukh is also presented. The main focus is on the role of the reducibility/irreducibility of systems of linear differential equations and their monodromy representations. A brief synopsis of results on the multidimensional Riemann-Hilbert problem and on isomonodromic deformations of Fuchsian systems is presented, and the main methods in the modern analytic theory of differential equations are sketched. Bibliography: 69 titles.

Anosov, Dmitry V.; Leksin, Vladimir P.

2011-02-01

204

REVIEWS OF TOPICAL PROBLEMS: Approximate equations of the theory of liquids in the statistical thermodynamics of classical liquid systems  

Microsoft Academic Search

This review presents the fundamentals of the method of integral equations of the theory of liquids. One of the central problems of the theory, the definition of bridge-functionals, is analyzed. Some applications of the method of integral equations to simple liquid systems are discussed, and the problem of description of complex polyatomic classical systems is considered.

Gari N. Sarkisov

1999-01-01

205

Hierarchy of equations for the energy functional of the density-functional theory  

NASA Astrophysics Data System (ADS)

A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.

Nagy, Á.

1993-04-01

206

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

NASA Astrophysics Data System (ADS)

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

Toledo, Porfirio

2013-12-01

207

Communication: Integral equation theory for pair correlation functions in a crystal  

NASA Astrophysics Data System (ADS)

A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two-particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving parts are calculated using the integral equation theory of homogeneous fluids. The symmetry broken part of the direct pair correlation function is calculated from a series written in powers of order parameters and that of the total pair correlation function from the Ornstein-Zernike equation. The results found for a two-dimensional hexagonal lattice show that the method provides accurate and detailed informations about the pair correlation functions in a crystal.

Jaiswal, Anubha; Bharadwaj, Atul S.; Singh, Yashwant

2014-06-01

208

Time step rescaling recovers continuous-time dynamical properties for discrete-time langevin integration of nonequilibrium systems.  

PubMed

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

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

2014-06-19

209

Langevin processes, agent models and socio-economic systems  

NASA Astrophysics Data System (ADS)

We review some approaches to the understanding of fluctuations of financial asset prices. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalize the approach to stochastic equations that model interacting agents. The agent models recently advocated by Marsilli and Solomon are motivated. Using a simple change of variable, we show that the peer pressure model of Marsilli and the wealth dynamics model of Solomon are essentially equivalent. The methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the Boltzmann formula. There follows a brief digression on the Heston model that extends the simple model to one that, in the language of physics, exhibits a temperature this is subject to stochastic fluctuations. Mathematically the model corresponds to a Feller process. Dragulescu and Yakovenko have shown how the model yields some of the stylised features of asset prices. A more recent approach by Michael and Johnson maximised a Tsallis entropy function subject to simple constraints. They obtain a distribution function for financial returns that exhibits power law tails and which can describe the distribution of returns not only over low but also high frequencies (minute by minute) data for the Dow Jones index. We show how this approach can be developed from an agent model, where the simple Langevin process is now conditioned by local rather than global noise. Such local noise may of course be the origin of speculative frenzy or herding in the market place. The approach yields a BBGKY type hierarchy of equations for the system correlation functions. Of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a Tsallis like entropy term replaces the Boltzmann entropy term. A mean field approximation yields the results of Michael and Johnson. We show how personal income data for Brazil, the US, Germany and the UK, analyzed recently by Borgas can be qualitatively understood by this approach.

Richmond, Peter; Sabatelli, Lorenzo

2004-05-01

210

Langevin dynamics in inhomogeneous media: Re-examining the Itô-Stratonovich dilemma  

NASA Astrophysics Data System (ADS)

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly developed method for Langevin simulations to measure the probability distribution of a particle diffusing in a flat potential. Our results reveal that both the Itô and Stratonovich interpretations converge very slowly to the uniform equilibrium distribution for vanishing time step sizes. Three other conventions exhibit significantly improved accuracy: (i) the "isothermal" (Hänggi) convention, (ii) the Stratonovich convention corrected by a drift term, and (iii) a newly proposed convention employing two different effective friction coefficients representing two different averages of the friction function during the time step. We argue that the most physically accurate dynamical description is provided by the third convention, in which the particle experiences a drift originating from the dissipation instead of the fluctuation term. This feature is directly related to the fact that the drift is a result of an inertial effect that cannot be well understood in the Brownian, overdamped limit of the Langevin equation.

Farago, Oded; Grønbech-Jensen, Niels

2014-01-01

211

A Padé approximant to the inverse Langevin function  

Microsoft Academic Search

Application of the methodology of Pade approximants to a Taylor expansion of the inverse Langevin function led to an accurate analytical expression. The approximation, retaining a finite extendibility of the Langevin spring, enables a convenient analysis of experimental data and analytical manipulations of material models.

A. Cohen

1991-01-01

212

Equations of Motion of Glashow-Salam-Weinberg Theory after Spontaneous Symmetry Breaking  

NASA Astrophysics Data System (ADS)

While for quantum field theoretical calculations it is sufficient to know the Lagrangian, we give here the field equations of the unified gauge-theory of weak and electromagnetic interactions after spontaneous symmetry breaking. With this approach, inhomogeneous Lorentz conditions for the massive vector bosons Z, W[stack +/- ] are obtained.Translated AbstractBewegungsgleichungen der Glashow-Salam-Weinberg-Theorie nach spontaner SymmetriebrechungWährend es für quantenfeldtheoretische Rechnungen ausreichend ist, die Lagrangefunktion zu kennen, geben wir hier die Feldgleichungen der einheitlichen Eichtheorie der schwachen und elektromagnetischen Wechselwirkung nach spontaner Symmetriebrechung an. Auf diese Weise werden inhomogene Lorentzbedingungen für die massiven Vektorbosonen Z?, W[stack ?+/- ] erhalten.

Ebner, Dieter W.

213

Quantum-shell corrections to Thomas-Fermi-Dirac equation-of-state theory  

NASA Astrophysics Data System (ADS)

Quantum-shell corrections are made directly to the finite-temperature Thomas-Fermi-Dirac (TFD) statistical model of the atom by a partition of the electronic density into bound and free parts. The bound part is calculated using analytic basis functions whose parameters are chosen to minimize the energy and pressure. Poisson's equation is solved for the modified density. The shock Hugoniot is calculated for aluminum. Shell effects characteristic of quantum self-consistent field (QSCF) models are fully captured by the present theory. The use of a quantum decription of the bound density removes the physically spurious singularity at the origin which is present in TFD theory.

Ritchie, Burke

2004-07-01

214

Dimensional reduction of Seiberg-Witten monopole equations, N=2 noncommutative supersymmetric field theories and Young diagrams  

SciTech Connect

We investigate the Seiberg-Witten monopole equations on noncommutative (N.C.) R{sup 4} at the large N.C. parameter limit, in terms of the equivariant cohomology. In other words, N=2 supersymmetric U(1) gauge theories with a hypermultiplet on N.C.R{sup 4} are studied. It is known that after topological twisting partition functions of N>1 supersymmetric theories on N.C. R{sup 2D} are invariant under the N.C. parameter shift; then the partition functions can be calculated by its dimensional reduction. At the large N.C. parameter limit, the Seiberg-Witten monopole equations are reduced to ADHM equations with the Dirac equation reduced to the 0 dimension. The equations are equivalent to the dimensional reduction of non-Abelian U(N) Seiberg-Witten monopole equations in N{yields}{infinity}. The solutions of the equations are also interpreted as a configuration of a brane antibrane system. The theory has global symmetries under torus actions originated in space rotations and gauge symmetries. We investigate the Seiberg-Witten monopole equations reduced to the 0 dimension and the fixed point equations of the torus actions. We show that the Dirac equation reduced to the 0 dimension is automatically satisfied when the fixed point equations and the ADHM equations are satisfied. Then, we find that the Seiberg-Witten equations reduced to the 0 dimension and fixed point equations of the torus action are equivalent to just the ADHM equations with the fixed point equations. For finite N, it is known that the fixed points of the ADHM data are isolated and are classified by the Young diagrams. We also give a new proof of this statement by solving the ADHM equations and the fixed point equations concretely and by giving graphical interpretations of the field components and these equations.

Sako, Akifumi; Suzuki, Toshiya [Department of Mathematics, Faculty of Science and Technology, Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522 (Japan); Department of Physics, Faculty of Engineering, Musashi Institute of Technology 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan and Department of Physics, Faculty of Science, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610 (Japan)

2006-11-15

215

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.  

PubMed

Exact equations of motion for the microscopically defined collective density ?(x,t) and the momentum density ?(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations. PMID:24229277

Das, Shankar P; Yoshimori, Akira

2013-10-01

216

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid  

NASA Astrophysics Data System (ADS)

Exact equations of motion for the microscopically defined collective density ??(x,t) and the momentum density ?(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Das, Shankar P.; Yoshimori, Akira

2013-10-01

217

Criticality of a liquid-vapor interface from an inhomogeneous integral equation theory.  

PubMed

A microscopic theory is developed to study the liquid-vapor interfacial properties of simple fluids with ab initio treatment of the inhomogeneous two-body correlation functions, without any interpolation. It consists of the inhomogeneous Ornstein-Zernike equation coupled with the Duh-Henderson-Verlet closure and the Lovett-Mou-Buff-Wertheim equation. For the liquid-vapor interface of the Lennard-Jones fluid, we obtained the density profile and the surface tension, as well as their critical behaviour. In particular, we identified non-classical critical exponents. The theory accurately predicts the phase diagram and the interfacial properties in a very good agreement with simulations. We also showed that the method leads to true capillary-wave asymptotics in the macroscopic limit. PMID:16474878

Omelyan, Igor; Hirata, Fumio; Kovalenko, Andriy

2005-12-21

218

Extension of the Neoclassical Theory of Capillarity to Advanced Cubic Equations of State  

NASA Astrophysics Data System (ADS)

The neoclassical Redlich-Kwong (RK) theory of capillarity is extended to the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations of state. Use of the SRK and PR fluid models results in poorer predictions of interfacial tension compared to the RK model because the RK overpredicts vapor densities to a greater extent than SRK or PR, reducing the corresponding RK interfacial tension predictions to be in better agreement with accepted values. The limits of the theory applied to cubic equations are reached by proposing modified SRK and PR fluid models based on a known interfacial tension datum and knowledge of the fluid molecular structure. These modified fluid models provide improved accuracy in interfacial tension predictions of 6% (SRK) and 10% (PR) for the fluid set in this study when compared to applying the RK model (17%). These modified fluid models also provide improved predictions of bulk liquid density, but sacrifice accuracy in pressure and vapor density predictions.

Wemhoff, Aaron P.

2010-02-01

219

Exact series model of Langevin transducers with internal losses.  

PubMed

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

220

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

221

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

Microsoft Academic Search

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

J. K. Spelt; A. W. Neumann

222

Physical Foundation of a Unified Statistical Theory of Fields and the Scale-Invariant Schrödinger Equation  

Microsoft Academic Search

An invariant statistical theory of fields from cosmic to tachyonic scales is presented. The invariant wavefunction is defined as the first perturbation of action S_beta = rho_betaPhi_beta, the product of density and velocity potential. The invariant Schrödinger equation is derived, and invariant forms of Planck constant, de Broglie matter wave hypothesis, and Heisenberg uncertainty relation are presented. The field of

S. H. Sohrab

1998-01-01

223

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

Microsoft Academic Search

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

224

Constitutive Equations of StrainHardening Theory for Nonisothermal Deformation Processes  

Microsoft Academic Search

A variant of the strain-hardening theory is proposed for describing nonisothermal deformation processes. The author postulates\\u000a the dependence of parameters of the constitutive equations on stress and temperature. The influence of the loading history\\u000a on the creep rate variation is allowed for by means of a scalar function of damage level. A procedure for more specific definition\\u000a of the constitutive

N. K. Kucher

2005-01-01

225

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

Microsoft Academic Search

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

226

Dynamical equations for a Regge theory with crossing symmetry and unitarity. IV. Coupled channels  

SciTech Connect

Integral equations for construction of a crossing-symmetric unitary Regge theory are extended to allow two coupled two-body channels. As in the case of a single channel, spectral functions are represented as Watson-Sommerfeld integrals over continued partial waves. A new type of partial wave is needed to represent one of the spectral functions in a region where one channel is open and the other is closed. This leads to certain difficulties in allowing realistic Regge poles.

Warnock, R.L.

1981-04-15

227

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

NASA Astrophysics Data System (ADS)

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

Chavanis, Pierre-Henri

2013-04-01

228

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

229

The projective geometric theory of systems of second-order differential equations: straightening and symmetry theorems  

SciTech Connect

In the framework of the projective geometric theory of systems of differential equations, which is being developed by the authors, conditions which ensure that a family of graphs of solutions of a system of m second-order ordinary differential equations y-vector-ddot=f-vector(t,y-vector,y-vector-dot) with m unknown functions y{sup 1}(t),...,y{sup m}(t) can be straightened (that is, transformed into a family of straight lines) by means of a local diffeomorphism of the variables of the system which takes it to the form z-vector''=0 (straightens the system) are investigated. It is shown that the system to be straightened must be cubic with respect to the derivatives of the unknown functions. Necessary and sufficient conditions for straightening the system are found, which have the form of differential equations for the coefficients of the system or are stated in terms of symmetries of the system. For m=1 the system consists of a single equation y-ddot=f-vector(t,y,y-dot), and the tests obtained reduce to the conditions for straightening this equations which were derived by Lie in 1883. Bibliography: 34 titles.

Aminova, Asya V [Kazan State University, Kazan (Russian Federation); Aminov, Nail' A-M [Kazan State Technological University, Kazan (Russian Federation)

2010-06-29

230

BKLT equations for reactive scattering. I. Theory and application to three finite mass atom systems  

SciTech Connect

The BKLT equations for reactive scattering are considered in detail, both from a formal and computational point of view. The equations are very attractive because they do not require any matching of wave functions. It is shown how these equations may be solved for a general collinear three-finite mass atom system. Special care is taken to treat subleties in the theory arising from restrictions on the ranges of the vibrational coordinate of the various diatoms due to the skewing angle being less than 90/sup 0/. In addition, the structure of the equations is explored in detail since this has significance for their optimum solution. It is found that the structure of the equations for asymmetric systems leads to important redutions in the size of the matrix which must be inverted within the present, nonpropagative method. Other solution methods are also discussed to some extent. Finally, the method is illustrated by an application to the H+H/sub 2/ exchange reaction with the Porter--Karplus potential surface. The results obtained agree well with those obtained earlier by Diestler using a close coupling, propagation procedure.

Shima, Y.; Kouri, D.J.; Baer, M.

1983-06-01

231

Application and development of the Schwinger multichannel scattering theory and the partial differential equation theory of electron-molecule scattering  

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

232

Fluid substitution in carbonate rocks based on the Gassmann equation and Eshelby-Walsh theory  

NASA Astrophysics Data System (ADS)

Fluid substitution in carbonate rocks is more difficult than it is in clastic rocks for two reasons. Firstly, the rock physics modeling uncertainties in carbonate rocks, this is due to the difficulty of accurately acquiring the moduli of carbonate rocks' solid matrix because the experimental data on carbonate rocks have not been as thoroughly studied as silici-clastic sedimentary rocks. Secondly, due to the complex pore systems of carbonate rocks, it is very difficult to model pore geometry of carbonates, and hence hard to assess how the elastic properties change as fluid saturation changes based on the traditional Biot and Gassmann theories. In order to solve these problems, we present a new fluid substitution equation of carbonate rocks using the Gassmann equation and Eshelby-Walsh theory (GEW) in this paper. Then, the specific procedures of how to calculate the moduli of carbonate rocks' solid matrix and how to measure the effect of pore geometry in fluid substitution based on the new fluid substation equation were illustrated by experimental testing about 12 carbonate rock samples in different fluid saturation scenarios and logging data. Finally, we further compared the new fluid substitution method with the conventional Gassmann fluid substitution based on the experimental data. The results verified that the new method is more accurate and reliable in the fluid substitution of complex carbonate rocks.

Feng, Quanxiong; Jiang, Lian; Liu, Mingquan; Wan, Huan; Chen, Li; Xiao, Wei

2014-07-01

233

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

NASA Astrophysics Data System (ADS)

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.

2011-02-01

234

A Non-Linear Hydrodynamic Stability Theory with Numerical Calculations. Part 1: A Power Series Method for the Numerical Treatment of the Orr-Sommerfeld Equation.  

National Technical Information Service (NTIS)

A boundary value problem of a linear ordinary differential equation of the fourth order is solved numerically. The equation treated here has the generalized form of the Orr-Sommerfeld equation which arises from hydrodynamic stability theory. The method of...

N. Itoh

1973-01-01

235

Integral equation theory for hard spheres confined on a cylindrical surface: anisotropic packing entropically driven.  

PubMed

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube. PMID:16392516

Iwaki, Takafumi; Shew, Chwen-Yang; Gumbs, Godfrey

2005-09-22

236

Prediction of tautomer ratios by embedded-cluster integral equation theory.  

PubMed

The "embedded cluster reference interaction site model" (EC-RISM) approach combines statistical-mechanical integral equation theory and quantum-chemical calculations for predicting thermodynamic data for chemical reactions in solution. The electronic structure of the solute is determined self-consistently with the structure of the solvent that is described by 3D RISM integral equation theory. The continuous solvent-site distribution is mapped onto a set of discrete background charges ("embedded cluster") that represent an additional contribution to the molecular Hamiltonian. The EC-RISM analysis of the SAMPL2 challenge set of tautomers proceeds in three stages. Firstly, the group of compounds for which quantitative experimental free energy data was provided was taken to determine appropriate levels of quantum-chemical theory for geometry optimization and free energy prediction. Secondly, the resulting workflow was applied to the full set, allowing for chemical interpretations of the results. Thirdly, disclosure of experimental data for parts of the compounds facilitated a detailed analysis of methodical issues and suggestions for future improvements of the model. Without specifically adjusting parameters, the EC-RISM model yields the smallest value of the root mean square error for the first set (0.6 kcal mol(-1)) as well as for the full set of quantitative reaction data (2.0 kcal mol(-1)) among the SAMPL2 participants. PMID:20352296

Kast, Stefan M; Heil, Jochen; Güssregen, Stefan; Schmidt, K Friedemann

2010-04-01

237

Coherent backscattering in nonlinear atomic media: Quantum Langevin approach  

SciTech Connect

In this theoretical paper, we investigate coherence properties of the near-resonant light scattered by two atoms exposed to a strong monochromatic field. To properly incorporate saturation effects, we use a quantum Langevin approach. In contrast to the standard optical Bloch equations, this method naturally provides the inelastic spectrum of the radiated light induced by the quantum electromagnetic vacuum fluctuations. However, to get the right spectral properties of the scattered light, it is essential to correctly describe the statistical properties of these vacuum fluctuations. Because of the presence of the two atoms, these statistical properties are not Gaussian: (i) the spatial two-points correlation function displays a specklelike behavior and (ii) the three-points correlation function does not vanish. We also explain how to incorporate in a simple way propagation with a frequency-dependent scattering mean-free path, meaning that the two atoms are embedded in an average scattering dispersive medium. Finally we show that saturation-induced nonlinearities strongly modify the atomic scattering properties and, as a consequence, provide a source of decoherence in multiple scattering. This is exemplified by considering the coherent backscattering configuration where interference effects are blurred by this decoherence mechanism. This leads to a decrease of the so-called coherent backscattering enhancement factor.

Gremaud, Benoit; Delande, Dominique [Laboratoire Kastler Brossel, Universite Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05 (France); Wellens, Thomas [Laboratoire Kastler Brossel, Universite Pierre et Marie Curie, 4, place Jussieu, 75252 Paris Cedex 05 (France); Institut Non Lineaire de Nice, UMR 6618, 1361 route des Lucioles, F-06560 Valbonne (France); Miniatura, Christian [Institut Non Lineaire de Nice, UMR 6618, 1361 route des Lucioles, F-06560 Valbonne (France)

2006-09-15

238

Langevin simulation of rf collisional multipactor breakdown of gases  

NASA Astrophysics Data System (ADS)

The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed.

Conde, L.; Pérez, F.; de Lara, J.; Alfonseca, M.; Raboso, D.

2009-06-01

239

Langevin simulation of rf collisional multipactor breakdown of gases.  

PubMed

The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed. PMID:19658608

Conde, L; Pérez, F; de Lara, J; Alfonseca, M; Raboso, D

2009-06-01

240

Nonideal statistical rate theory formulation to predict evaporation rates from equations of state.  

PubMed

A method of including nonideal effects in the statistical rate theory (SRT) formulation is presented and a generic equation-of-state based SRT model was developed for predicting evaporation rates. Further, taking the Peng-Robinson equation of state as an example, vapor phase pressures at which particular evaporation rates are expected were calculated, and the predictions were found to be in excellent agreement with the experimental observations for water and octane. A high temperature range (near the critical region) where the previously existing ideal SRT model is expected to yield inaccurate results was identified and predictions (for ethane and butane) were instead made with the Peng-Robinson based SRT model to correct for fluid nonidealities at high temperatures and pressures. PMID:18954106

Kapoor, Atam; Elliott, Janet A W

2008-11-27

241

Polaronic quantum master equation theory of inelastic and coherent resonance energy transfer for soft systems  

SciTech Connect

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

242

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

243

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

244

Solvent effects on supercoiled DNA dynamics explored by Langevin dynamics simulations  

NASA Astrophysics Data System (ADS)

The dynamical effects of solvent on supercoiled DNA are explored through a simple, macroscopic energy model for DNA in the Langevin dynamics framework. Closed circular DNA is modeled by B splines, and both eleastic and electrostatic (screened Coulomb) potentials are included in the energy function. The Langevin formalism describes approximately the influence of the solvent on the motion of the solute. The collision frequency ? determines the magnitude of the friction and the variance of the random forces due to molecular collisions. Thus, as a first approximation, the Langevin equation of motion can be parametrized to capture the approximate dynamics of DNA in a viscous medium. Solvent damping is well known to alter the dynamical behavior of DNA and affect various hydrodynamic properties. This work examines these effects systematically by varying the collision frequency (viscosity) with the goal of better understanding the dynamical behavior of supercoiled DNA. By varying ? over ten orders of magnitude, we identify three distinct physical regimes of DNA behavior: (i) low ?, dominated by globally harmonic motion; (ii) intermediate ?, characterized by maximal sampling and high mobility of the DNA; and (iii) high ?, dominated by random forces, where all of the global modes are effectively frozen by extreme overdamping. These regimes are explored extensively by Langevin dynamics simulations, offering insight into hydrodynamic effects on supercoiled DNA. At low ?, the DNA exhibits small, harmonic fluctuations. Transitions to other configurational regions are more difficult to capture in finite simulations. In the intermediate ? regime, the DNA exhibits maximal sampling of the writhe. Transition times are accelerated and more readily captured in the simulations. A preferential lowering of the writhe from the value at the potential energy minimum is noted, reflecting entropic effects. Only beyond a specific value of ? in this regime do we find reasonable convergence of the translational diffusion constants and velocity autocorrelation functions. This brackets the biologically relevant regime. At high ? the DNA supercoil fluctuates about two distinct regions of configuration space, one near the tightly wound potential energy minimum, the other related to more open configurations. Transitions between the two regions are infrequent. This behavior suggests two regions of free-energy minima (potential and entropically favored) separated by a barrier. Indeed, the general dependence of the extent of configurational sampling on the collision frequency is analogous to the isomerization behavior of a particle in a bistable potential modeled by the Langevin equation of motion. This intriguing parallelism suggests a favorable viscosity medium where specific internal modes, namely, global twisting, are activated. It is possible that physiological solvent densities correspond to this region of optimal mobility for the DNA.

Ramachandran, Gomathi; Schlick, Tamar

1995-06-01

245

Phase behavior of active swimmers in depletants: molecular dynamics and integral equation theory.  

PubMed

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are 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 are made active using the Vicsek model for self-propelling particles. The resultant active system is 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. PMID:24877969

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

2014-05-16

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

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

NASA Astrophysics Data System (ADS)

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are 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 are made active using the Vicsek model for self-propelling particles. The resultant active system is 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.

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

2014-05-01

248

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

249

Optimized hierarchical equations of motion theory for Drude dissipation and efficient implementation to nonlinear spectroscopies.  

PubMed

Hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on the basis of a Pade? spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the a priori convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system. We combine the present theory with several advanced techniques such as the block hierarchical dynamics in mixed Heisenberg-Schro?dinger picture and the on-the-fly filtering algorithm for the efficient evaluation of third-order optical response functions. PMID:22047228

Ding, Jin-Jin; Xu, Jian; Hu, Jie; Xu, Rui-Xue; Yan, YiJing

2011-10-28

250

Lattice Gross-Neveu Model and the Langevin Algorithm.  

National Technical Information Service (NTIS)

The analytic solution of the Gross-Neveu model on the lattice is given including order 1/N. It is compared with a high statistics numerical simulation using the Langevin algorithm. (ERA citation 14:025875)

R. Lacaze A. Morel N. Attig B. Petersson M. Wolff

1988-01-01

251

Comparison of Equipercentile and Item Response Theory Equating When the Scaling Test Method Is Applied to a Multilevel Achievement Battery  

Microsoft Academic Search

Test publishers generally choose an anchor or scal ing test approach to the development of a growth scale for a multilevel achievement battery. Although some studies have been conducted comparing traditional equipercentile equating procedures with item response theory models using the anchor test (overlapping items) approach, to date there is no evidence on the comparability of equating procedures when the

S. E. Phillips

1983-01-01

252

Exact closed-form frequency equations for thick circular plates using a third-order shear deformation theory  

Microsoft Academic Search

This paper presents, for the first time, exact closed-form frequency equations and transverse displacement for thick circular plates with free, soft simply supported, hard simply supported and clamped boundary conditions based on Reddy's third-order shear deformation theory. Hamiltonian and minimum potential energy principles are used to extract the equations of dynamic equilibrium and natural boundary conditions of the plate. The

Sh. Hosseini-Hashemi; M. Es'Haghi; H. Rokni Damavandi Taher; M. Fadaie

2010-01-01

253

Advancing towards constitutive equations for the metal industry via the LEDS theory  

NASA Astrophysics Data System (ADS)

A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. They are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. While plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newton’s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.

Kuhlmann-Wilsdorf, Doris

2004-02-01

254

Advancing towards constitutive equations for the metal industry via the LEDS theory  

NASA Astrophysics Data System (ADS)

A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. The are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. White plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newton’s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.

Kuhlmann-Wilsdorf, Doris

2004-02-01

255

Stochastic differential equations and turbulent dispersion  

NASA Technical Reports Server (NTRS)

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Durbin, P. A.

1983-01-01

256

A langevin canonical approach to the dynamics of chiral systems: thermal averages and heat capacity.  

PubMed

A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators was developed within a coupling scheme different from the well-known spin-boson model. Thermal equilibrium values were reached at asymptotic times by solving the corresponding set of nonlinear coupled equations in a Markovian regime. In particular, phase difference thermal values (or, equivalently, the so-called coherence factor) and heat capacity through energy fluctuations were obtained and are discussed in terms of tunneling rates and asymmetries. Chirality 26:319-325, 2014. © 2014 Wiley Periodicals, Inc. PMID:24788824

Peñate-Rodríguez, Helen C; Dorta-Urra, Anais; Bargueño, Pedro; Rojas-Lorenzo, German; Miret-Artés, Salvador

2014-06-01

257

Spectral methods for the equations of classical density-functional theory: relaxation dynamics of microscopic films.  

PubMed

We propose a numerical scheme based on the Chebyshev pseudo-spectral collocation method for solving the integral and integro-differential equations of the density-functional theory and its dynamic extension. We demonstrate the exponential convergence of our scheme, which typically requires much fewer discretization points to achieve the same accuracy compared to conventional methods. This discretization scheme can also incorporate the asymptotic behavior of the density, which can be of interest in the investigation of open systems. Our scheme is complemented with a numerical continuation algorithm and an appropriate time stepping algorithm, thus constituting a complete tool for an efficient and accurate calculation of phase diagrams and dynamic phenomena. To illustrate the numerical methodology, we consider an argon-like fluid adsorbed on a Lennard-Jones planar wall. First, we obtain a set of phase diagrams corresponding to the equilibrium adsorption and compare our results obtained from different approximations to the hard sphere part of the free energy functional. Using principles from the theory of sub-critical dynamic phase field models, we formulate the time-dependent equations which describe the evolution of the adsorbed film. Through dynamic considerations we interpret the phase diagrams in terms of their stability. Simulations of various wetting and drying scenarios allow us to rationalize the dynamic behavior of the system and its relation to the equilibrium properties of wetting and drying. PMID:22462841

Yatsyshin, Petr; Savva, Nikos; Kalliadasis, Serafim

2012-03-28

258

Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations  

SciTech Connect

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

259

Minding one's P's and Q's: From the one loop effective action in quantum field theory to classical transport theory  

SciTech Connect

The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot {phi}{sup 4} theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society.

Jalilian-Marian, Jamal [Physics Department, University of Arizona, Tucson, Arizona 85721 (United States)] [Physics Department, University of Arizona, Tucson, Arizona 85721 (United States); Jeon, Sangyong [Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)] [Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Venugopalan, Raju [Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States)] [Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States); Wirstam, Jens [Institute for Theoretical Physics, University of Stockholm, Box 6730, S-113 85, Stockholm, (Sweden)] [Institute for Theoretical Physics, University of Stockholm, Box 6730, S-113 85, Stockholm, (Sweden)

2000-08-15

260

Inertial stochastic dynamics. I. Long-time-step methods for Langevin dynamics  

NASA Astrophysics Data System (ADS)

Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID (``long-time-step inertial dynamics'') method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD (``inertial Brownian dynamics'') modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.

Beard, Daniel A.; Schlick, Tamar

2000-05-01

261

Solution of the one-dimensional consolidation theory equation with a pseudospectral method  

USGS Publications Warehouse

The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.

Sepulveda, N.

1991-01-01

262

Wide range equation of state for fluid hydrogen from density functional theory  

SciTech Connect

Wide range equation of state (EOS) for liquid hydrogen is ultimately obtained by combining two kinds of density functional theory (DFT) molecular dynamics simulations, namely, first-principles molecular dynamics simulations and orbital-free molecular dynamics simulations. Specially, the present introduction of short cutoff radius pseudopotentials enables the EOS to be available in the range from 9.82 × 10{sup ?4} to 1.347 × 10{sup 3} g/cm{sup 3} and up to 5 × 10{sup 7} K. By comprehensively comparing with various attainable experimental and theoretical data, we derive the conclusion that our DFT-EOS can be readily and reliably applied to hydrodynamic simulations of the inertial confinement fusion.

Wang, Cong; Zhang, Ping [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China) [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Center for Applied Physics and Technology, Peking University, Beijing 100871 (China)

2013-09-15

263

Time-dependent density functional theory using atomic orbitals and the self-consistent Sternheimer equation  

NASA Astrophysics Data System (ADS)

We present the implementation of linear-response time-dependent density functional theory based on the self-consistent Sternheimer equation and employing a basis set of numerical pseudo-atomic orbitals. We demonstrate this method by presenting test calculations on systems of increasing size ranging from benzene to chlorophyll a, and by comparing our results with those obtained within Casida's formalism and with previous calculations. We provide a detailed assessment of the accuracy of this method, both in relation to the use of local orbitals for describing electronic excitations and to the handling of the frequency response using Padé approximants. We establish a simple criterion for estimating a priori the accuracy of the basis set in the calculation of optical spectra. We show that the computational cost of this method scales quadratically with the system size.

Hübener, Hannes; Giustino, Feliciano

2014-02-01

264

On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension  

SciTech Connect

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

265

The Bloch Equations in High-Gradient Magnetic Resonance Force Microscopy: Theory and Experiment  

NASA Astrophysics Data System (ADS)

We report theory and observations of paramagnetic resonance in a measured field gradient of 44,000 T per meter by the technique of magnetic resonance force microscopy (MRFM). Resonance was induced in a dilute solid solution of diphenylpicrylhydrazyl in polystyrene at 77 and 10 K by an amplitude-modulated microwave field. This modulated the force between resonant sample spins and a micrometer-scale SmCo magnetic tip on a force microscope cantilever. The force signals were typically of order 10 fN, and were detected above a thermal noise floor of 80 aN per root hertz at 10 K, equivalent to a magnetic moment noise of 200 ? B per root hertz of bandwidth. Resonance saturation was readily observed. Starting with the Bloch equations, we derived simple analytic expressions for the predicted cantilever signal amplitudes and T1-dependent phase lags, valid at low microwave power levels. For power levels below saturation, the data were in good agreement with the Bloch equation predictions, while above saturation the measured force increased more slowly with power than predicted. Several ESR mechanisms which might lead to non-Bloch dynamics in the MRFM environment are reviewed. Spin-relaxation mechanisms are also reviewed. A detailed description of the experimental apparatus is offered.

Dougherty, W. M.; Bruland, K. J.; Chao, S. H.; Garbini, J. L.; Jensen, S. E.; Sidles, J. A.

2000-03-01

266

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

267

Virial equation of state of water based on Wertheim's association theory.  

PubMed

Wertheim's multidensity formalism for pairwise additive molecular interaction is extended to handle nonadditive contributions and is applied to formulate an equation of state (WEOS) for the Gaussian-charge polarizable model (GCPM) of water, with cluster integrals appearing in the theory calculated via the Mayer sampling Monte Carlo method. At both sub- and supercritical temperatures, the equation of state of GCPM water obtained from WEOS converges well to Monte Carlo simulation data, and performs significantly better than the conventional virial treatment (VEOS). The critical temperature for GCPM water using a fourth-order WEOS is given to within 1.3% of the established value, compared to a 17% error shown by fifth-order VEOS; as seen in previous applications, the critical density obtained from both VEOS and WEOS significantly underestimates the true critical density for GCPM water. Examination of the magnitudes of the computed cluster diagrams at the critical density finds that negligible contributions are made by clusters in which a water molecule has both of its hydrogens involved in association interactions. PMID:23148680

Kim, Hye Min; Schultz, Andrew J; Kofke, David A

2012-12-01

268

Multidensity integral-equation theory for short diblock hard-sphere-sticky-hard-sphere chains.  

PubMed

The multidensity Ornstein-Zernike integral equation theory is applied to study a simple model of hard sphere/sticky hard sphere diblock chains. The multidensity integral equation formalism has been successfully used to model the equilibrium structure and thermodynamic properties of homonuclear chains and shorter dimer fluids; to our knowledge it has not been applied to model diblock chains. In this work, a diblock chain fluids is represented by an m-component equal molar mixture of hard spheres with species 1,2,...,mh and sticky hard spheres with species mh+1,mh+2,...,m. Each spherical particle has two attractive sites A and B except species 1 and m, which have only one site per particle. In the limit of complete association, this mixture yields a system of monodisperse diblock chains. A general solution of this model is obtained in the Percus-Yevick, Polymer Percus-Yevick and ideal chain approximations. Both structural and thermodynamic properties of this model are investigated. From this study, a microphase separation is predicted for relatively short diblock symmetric and asymmetric chains. This microphase separation is enhanced at lower temperature and higher density. When chain length increases, the phase transition changes from a microphase level to a macrophase level. The size of microdomain structure is found to be dependent on total chain length, relative ratio of block lengths, temperature, and density. PMID:20481746

Wu, Ning; Chiew, Y C

2010-04-01

269

Primer vector theory applied to the linear relative-motion equations. [for N-impulse space trajectory optimization  

NASA Technical Reports Server (NTRS)

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

Jezewski, D.

1980-01-01

270

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes  

NASA Technical Reports Server (NTRS)

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

Majda, G.

1985-01-01

271

Hybrid two-chain simulation and integral equation theory : application to polyethylene liquids.  

SciTech Connect

We present results from a hybrid simulation and integral equation approach to the calculation of polymer melt properties. The simulation consists of explicit Monte Carlo (MC) sampling of two polymer molecules, where the effect of the surrounding chains is accounted for by an HNC solvation potential. The solvation potential is determined from the Polymer Reference Interaction Site Model (PRISM) as a functional of the pair correlation function from simulation. This hybrid two-chain MC-PRISM approach was carried out on liquids of polyethylene chains of 24 and 66 CH{sub 2} units. The results are compared with MD simulation and self-consistent PRISM-PY theory under the same conditions, revealing that the two-chain calculation is close to MD, and able to overcome the defects of the PRISM-PY closure and predict more accurate structures of the liquid at both short and long range. The direct correlation function, for instance, has a tail at longer range which is consistent with MD simulation and avoids the short-range assumptions in PRISM-PY theory. As a result, the self-consistent two-chain MC-PRISM calculation predicts an isothermal compressibility closer to the MD results.

Huimin Li, David T. Wu (Colorado School of Mines Golden, CO.); Curro, John G.; McCoy, John Dwane (New Mexico Institute of Mining & Technology Socorro, NM.)

2006-02-01

272

Stochastic Gravity: Theory and Applications  

NASA Astrophysics Data System (ADS)

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein-Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out directions for further developments and applications.

Hu, Bei Lok; Verdaguer, Enric

2008-05-01

273

Theory of collision algorithms for gases and plasmas based on the boltzmann equation and the landau-fokker-planck equation  

PubMed

A time-explicit formula that describes the time evolution of velocity distribution functions of gases and plasmas is derived from the Boltzmann equation. The formula can be used to construct collision simulation algorithms. Specialization of the formula to the case of the Coulomb interaction shows that the previous method [K. Nanbu, Phys. Rev. E 55, 4642 (1997)] for a Coulomb collision simulation is a solution method of the Landau-Fokker-Planck equation in the limit of a small time step. Also, a collision simulation algorithm for multicomponent plasmas is proposed based on the time-explicit formula derived. PMID:11088258

Bobylev; Nanbu

2000-04-01

274

mathcal{N} = 1 Supersymmetric Yang-Mills Theory in It? Calculus  

NASA Astrophysics Data System (ADS)

The stochastic quantization method is applied to {cal N} = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on It? calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global {cal N} = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an ``almost Wess-Zumino gauge''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM10, the IIB matrix model is studied in this context.

Nakazawa, N.

2003-12-01

275

Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise  

NASA Astrophysics Data System (ADS)

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), 10.1103/PhysRevLett.95.130602]. 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.

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

2014-06-01

276

Magnetized plasma kinetic theory. I. Derivation of the kinetic equation for a uniform magnetized plasma  

Microsoft Academic Search

A kinetic equation for a multi-species plasma in an external uniform magnetic field is derived from the BBGKY hierarchy of equations. The equation generalizes the equation of Rostoker (1960), which assumes that the distribution function is independent of the azimuthal angle, and all previous results can be derived from it. An additional advantage is that the collision integral is obtained

M H A Hassan; C J H Watson

1977-01-01

277

Applying Structural Equation Modeling in the Context of the Theory of Reasoned Action: Some Problems and Solutions.  

ERIC Educational Resources Information Center

Problems found in the application of structural equation modeling to the theory of reasoned action are explored, and an alternative model specification is proposed that improves the fit of the data while leaving intact the structural part of the model being tested. Problems and the proposed alternative are illustrated. (SLD)

van den Putte, Bas; Hoogstraten, Johan

1997-01-01

278

Nonlinear Structural Equation Models with the Theory of Planned Behavior: Comparison of Multiple Group and Latent Product Term Analyses  

Microsoft Academic Search

Nonlinear relationships in structural equation analysis became moreinteresting for applied researchers since the implementation of nonlinearconstraints in software programs (i.e., LISREL). This article provides acomprehensive application of the expectancy × value part of the Theory of Planned Behavior (Ajzen, 1991) including interactions of latent variables.The main purpose of the study is to overcome limitations of similarprevious analyses of Baumgartner and

Jost Reinecke

2002-01-01

279

The Best of Both Worlds: Factor Analysis of Dichotomous Data Using Item Response Theory and Structural Equation Modeling  

ERIC Educational Resources Information Center

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

Glockner-Rist, Angelika; Hoijtink, Herbert

2003-01-01

280

A Practitioner's Introduction to Equating with Primers on Classical Test Theory and Item Response Theory  

ERIC Educational Resources Information Center

Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…

Ryan, Joseph; Brockmann, Frank

2009-01-01

281

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.  

PubMed

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis. PMID:12513319

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

282

Diffusion theory for transport in porous media: Transition-probability densities of diffusion processes corresponding to advection-dispersion equations  

NASA Astrophysics Data System (ADS)

Local-scale spatial averaging of pore-scale advection-diffusion equations in porous media leads to advection-dispersion equations (ADEs). While often used to describe subsurface transport, ADEs may pose special problems in the context of diffusion theory. Standard diffusion theory applies only when characteristic coefficients, velocity, porosity, and dispersion tensor, are smooth functions of space. Subsurface porous-material properties, however, naturally exhibit spatial variability. Transitions between material types are often abrupt rather than smooth, such as sand in contact with clay. In such composite porous media, characteristic coefficients in spatially averaged transport equations may be discontinuous. Although commonly called on to model transport in these cases, standard diffusion theory does not apply. Herein we develop diffusion theory for ADEs of transport in porous media. Derivation of ADEs from probabilistic assumptions yields (1) necessary conditions for convergence of diffusion processes to ADEs, even when coefficients are discontinuous, and (2) general probabilistic definitions of physical quantities, velocity, and dispersion tensor. As examples of how the new theory can be applied to theoretical and numerical problems of transport in porous media, we evaluate several random walk methods that have appeared in the water resources literature.

LaBolle, Eric M.; Quastel, Jeremy; Fogg, Graham E.

283

Exponential convergence of Langevin distributions and their discrete approximations  

Microsoft Academic Search

In this paper we consider a continuous-time method of approximating a given distribution [math] using the Langevin diffusion [math] . We find conditions under which this diffusion converges exponentially quickly to [math] or does not: in one dimension, these are essentially that for distributions with exponential tails of the form [math] , [math] , exponential convergence occurs if and only

Gareth O. Roberts; Richard L. Tweedie

1996-01-01

284

Stochastic approach to the theory of intramicellar kinetics. II. Master equation for reversible reactions  

SciTech Connect

In this paper we focus on a particular class of intramicellar kinetic processes: reversible reactions of molecularity two taking place in the interior (or perhaps the immediate vicinity) of a micellar assembly. We formulate a stochastic master equation to describe an ensemble of compartmentalized, distributed systems wherein the (only) microscopic chemical event is a photoinduced, reversible, bimolecular reaction. Then, for an initial distribution of reactants assumed to be Poissonian, we calculate and characterize the overall (macroscopic) dynamics displayed by such a system. The resulting kinetic description is compared with the behavior found previously for the simpler case of irreversible, intramicellar kinetic processes. Finally, we introduce and then investigate the notion of an ''apparent'' equilibrium constant Q for a reversible reaction taking place in a compartmentalized, distributed system and compare this quantity with the ''canonical'' equilibrium constant K obtained for the (same) reversible reaction carried out in bulk, homogeneous solution. The full behavior of Q=Q(K) is explored numerically, and we prove analytically that Qapprox.K/sup 2/ in the small K limit and that Q is independent of K in the limit of large K. The experimental consequences of the theory are dicussed in some detail.

Hatlee, M.D.; Kozak, J.J.

1981-01-15

285

Effective particle methods for Fisher–Kolmogorov equations: Theory and applications to brain tumor dynamics  

NASA Astrophysics Data System (ADS)

Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics. Here we obtain a small number of effective equations describing the dynamics of single-front and localized solutions of Fisher–Kolmogorov type equations. These solutions are parametrized by means of a minimal set of time-dependent quantities for which ordinary differential equations ruling their dynamics are found. A comparison of the finite dimensional equations and the dynamics of the full partial differential equation is made showing a very good quantitative agreement with the dynamics of the partial differential equation. We also discuss some implications of our findings for the understanding of the growth progression of certain types of primary brain tumors and discuss possible extensions of our results to related equations arising in different modeling scenarios.

Belmonte-Beitia, Juan; Calvo, Gabriel F.; Pérez-García, Víctor M.

2014-09-01

286

Augmented Langevin description of multiplicative noise and nonlinear dissipation in Hamiltonian systems  

NASA Astrophysics Data System (ADS)

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 noise (chosen on physical grounds), uniquely determines the form of the nonlinear dissipative terms needed to balance the fluctuations. In addition to the noise and dissipation terms, the augmented Langevin equation contains an additional term whose form depends on the stochastic interpretation rule used. This term vanishes when the Stratonovich rule is chosen and the noise itself is of a Hamiltonian origin. This development provides a simple phenomenological route to results previously obtained by detailed analysis of microscopic system-bath models. The procedure is illustrated by applications to a mechanical oscillator with fluctuating frequency, a classical spin in a fluctuating magnetic field, and the Brownian motion of a rigid rotor.

Ramshaw, John D.; Lindenberg, Katja

1986-10-01

287

Augmented langevin description of multiplicative noise and nonlinear dissipation in Hamiltonian systems  

SciTech Connect

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 noise (chosen on physical grounds), uniquely determines the form of the nonlinear dissipative terms needed to balance the fluctuations. In addition to the noise and dissipation terms, the augmented Langevin equation contains an addition term whose form depends on the stochastic interpretation rule used. This term vanishes when the stratonovich rule is chosen and the noise itself is of a Hamiltonian origin. This development provides a simple phenomenological route to results previously obtained by detailed analysis of microscopic system-bath models. The procedure is illustrated by applications to a mechanical oscillator with fluctuating frequency, a classical spin in a fluctuating magnetic field, and the Brownian motion of a rigid rotor.

Ramshaw, J.D.; Lindenberg, K.

1986-10-01

288

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

NASA Astrophysics Data System (ADS)

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

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

2011-06-01

289

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

PubMed Central

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

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

2011-01-01

290

Gas-kinetic theory and Boltzmann equation of share price within an equilibrium market hypothesis and ad hoc strategy  

NASA Astrophysics Data System (ADS)

Recent observations have indicated that the traditional equilibrium market hypothesis ( EMH; also known as Efficient Market Hypothesis) is unrealistic. It is shown here that it is the analog of a Boltzmann equation in physics, thus having some bad properties of mean-field approximations like a Gaussian distribution of price fluctuations. A kinetic theory for prices can be simply derived, considering in a first approach that market actors have all identical relaxation times, and solved within a Chapman-Enskog like formalism. In closing the set of equations, (i) an equation of state with a pressure and (ii) the equilibrium ( isothermal) equation for the price ( taken as the order parameter) of a stock as a function of the volume of money available are obtained.

Ausloos, M.

2000-09-01

291

The Theory of Individual Based Discrete-Time Processes  

NASA Astrophysics Data System (ADS)

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map. From the Chapman-Kolmogorov equation for the discrete-time Markov process, we derive the analogues of the Fokker-Planck equation and the Langevin equation, which are routinely employed for continuous time processes. In particular, a stochastic difference equation is derived which accurately reproduces the results found from the Markov chain model. Stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map. The proposed scheme is tested on stochastic models which have the logistic and Ricker maps as their deterministic limits.

Challenger, Joseph D.; Fanelli, Duccio; McKane, Alan J.

2014-04-01

292

The Theory of Individual Based Discrete-Time Processes  

NASA Astrophysics Data System (ADS)

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map. From the Chapman-Kolmogorov equation for the discrete-time Markov process, we derive the analogues of the Fokker-Planck equation and the Langevin equation, which are routinely employed for continuous time processes. In particular, a stochastic difference equation is derived which accurately reproduces the results found from the Markov chain model. Stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map. The proposed scheme is tested on stochastic models which have the logistic and Ricker maps as their deterministic limits.

Challenger, Joseph D.; Fanelli, Duccio; McKane, Alan J.

2014-07-01

293

A kinetic-theory approach to turbulent chemically reacting flows  

NASA Technical Reports Server (NTRS)

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

Chung, P. M.

1976-01-01

294

Yang-Mills equations of motion for the Higgs sector of SU(3)-equivariant quiver gauge theories  

SciTech Connect

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form RxSU(3)/H, with H equals either SU(2)xU(1) or U(1)xU(1). For the corresponding quiver gauge theory, we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically, we choose the gauge groups U(6) and U(8) for the space RxCP{sup 2}, as well as the gauge group U(3) for the space RxSU(3)/U(1)xU(1), and derive Yang-Mills equations for the latter one using a spin connection endowed with a nonvanishing torsion. We find that a specific value for the torsion is necessary in order to obtain nontrivial solutions of Yang-Mills equations. Finally, we take the space RxCP{sup 1}xCP{sup 2} and derive the equations of motion for the Higgs sector for the U(3m+3) gauge theory.

Rahn, Thorsten [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)

2010-07-15

295

Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers  

SciTech Connect

A theory of spontaneous emission noise is presented based on classical electromagnetic theory. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The fields of lasers and amplifiers are found by solving the wave equation by the Green's function method. The lasing mode is a resonant state associated with a pole in Green's function. In this way, noise in lasers and amplifiers is treated by a unified approach that is valid for either gain guiding or index guiding. The Langevin rate equations for the laser are derived. The theory is illustrated with applications to traveling wave and Fabry-Perot amplifiers and Fabry-Perot lasers. Several new results are found: optical amplifier noise increases inversely with quantum efficiency; spontaneous emission into the lasing mode is enhanced in lasers with low facet reflectivities; and the linewidth of a Fabry-Perot laser with a passive section decreases as the square of the fraction of the cavity optical length that is active. 27 references.

Henry, C.H.

1986-03-01

296

The General Equation of Motion via the Special Theory of Relativity and Quantum Mechanics Part i: a New Approach to Newton Equation of Motion  

NASA Astrophysics Data System (ADS)

Herein we present a whole new approach to the derivation of the Newton Equation of Motion; throughout Part II of the present work, this shall lead to the findings brought up within the frame of the general theory of relativity (such as the precession of the perihelion of the planets, and the deflection of light nearby a star). To the contrary of what had been generally achieved so far, our basis consists in supposing that the gravitational field, through the binding process, alters the "rest mass" of an object conveyed in it. In fact, the special theory of relativity already imposes such a change. Next to this theory, we use the classical Newtonian gravitational attraction, reigning between two static masses; we have previously shown however that the 1/r^2 dependency of the gravitational force is also imposed by the special theory of relativity [1]. Our metric, is (just like the one used by the general theory of relativity) altered by the gravitational field (in fact, by any field the "measurement unit" in hand interacts with); yet in our approach, this occurs via quantum mechanics. More specifically, the rest mass of an object in a gravitational field is decreased as much as its binding energy in the field. A mass deficiency conversely, via quantum mechanics, yields the stretching of the size of the object in hand, as well as the weakening of its internal energy. Henceforth we shall not need the "principle of equivalence" assumed by the general theory of relativity, in order to predict the occurrences dealt with this theory [2]. We start with the following interesting postulate, in fact nothing else but the conservation of energy, in the broader sense of the concept of "energy". Thus The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this as much as its binding energy vis-à-vis the gravitational field of concern. This yields (with the familiar notation), the interesting equation of motion ( e^-?_0(r_0)/(1-(v_0/c_0)^2)^1/2 )=Constant; ?_0(r_0)=GM_0/(r_0(c_0)^2); here M0 is the mass of the celestial body creating the gravitational field of concern; G is the universal gravitational constant; r0 points to a location picked up on the trajectory of the motion; v0 is the tangential velocity of the object at r_0, and c0 the speed of light in empty space. The above relationship tells us that the mass of the object in motion can be conceived as made of its mass brought from infinity, at the location defined by r0 on its trajectory, thus i) decreased as much as its binding energy, ii) but at the same time, increased by a Lorentz factor, due to its translational motion on the trajectory. The differentiation of this relationship leads to -(GM_0/(r_0)^2)(1-(v_0)^2/(c_0)^2)=v_0dv_0/dr0 This differential equation is the classical Newton Equation of Motion, were v0 , negligible as compared to c0 (the speed of light in empty space). [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

297

From square-well to Janus: improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model.  

PubMed

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. PMID:24606350

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

2014-03-01

298

From square-well to Janus: Improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model  

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

299

Hamiltonian structure of Dubrovin{close_quote}s equation of associativity in 2-d topological field theory  

SciTech Connect

mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}

Galvao, C.A. [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil)] [Universidade de Brasilia, Departamento de Fisica, 70.910 Brasilia DF, (Brasil); Nutku, Y. [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)] [TUeBITAK---Marmara Research Center, Research Institute for Basic Sciences, Department of Physics, 41470 Gebze (Turkey)

1996-12-01

300

Higher-order perturbation theory for the bound states of the Dirac equation with a Yukawa-type potential  

SciTech Connect

The method of calculating higher orders of perturbation theory based on perturbation of the Fock operator with a purely discrete spectrum is generalized to the case of the Dirac equation with a potential of the Yukawa type. Corrections to any order of perturbation theory in the energy of an arbitrary bound state are given as finite polynomials which are determined through recurrence relations derived from the dynamical symmetry of the unperturbed problem. We propose a modified Pade approximant method which can be used to transform a divergent perturbation series into a rapidly convergent sequence for all bound and quasistationary states of the system.

Sergeev, A.V.; Sherstyuk, A.I.

1984-05-01

301

Nonlinear equations of the gravitational field in the special theory of relativity  

NASA Astrophysics Data System (ADS)

It is proposed that the nonlinearity of the field be taken into account with the help of a method which essentially consists of the fact that the structure of the Lagrangian, expressed in terms of the potential of the field and its derivatives, is not known a priori, but is obtained from a solution of the self-action equation in phase space in which the Lagrangian is the unknown. This equation has a solution and the Lagrangian turns out to be a nonpolynomial function with respect to the field potential. The gravitational field equations following from the variational principle have a similar structure to the equations of general relativity and coincide with them in the linear approximation. The equations of other fields taking into account gravitation, as well as the equation of motion of a test particle in a gravitational field, are constructed.

Razgovorov, N. N.

1983-08-01

302

Nonlinear gravitational-field equations in the special theory of relativity  

NASA Astrophysics Data System (ADS)

A method is proposed for the consideration of field nonlinearity which is based on the fact that the structure of the Lagrangian expressed through the potential of the field and its derivatives is not prescribed beforehand but is derived as a result of the solution in phase space of the self-action equation whose unknown is the field Lagrangian. It is shown that this equation has a solution and that the Lagrangian is nonpolynomial with respect to the field potential. The gravitational-field equations which follow from the variational principle are found to be structurally similar to the general-relativity equations and coincide with them in the linear approximation. Equations of other fields with allowance for gravitation are constructed along with the equation of motion of a test particle in a gravitational field.

Razgovorov, N. N.

1983-08-01

303

Ab initio calculations of optical absorption spectra: solution of the Bethe-Salpeter equation within density matrix perturbation theory.  

PubMed

We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This procedure is equivalent to solving the statically screened Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on density functional perturbation theory. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations. PMID:21033777

Rocca, Dario; Lu, Deyu; Galli, Giulia

2010-10-28

304

Quantum-driven phase transition in ice described via an efficient Langevin approach  

NASA Astrophysics Data System (ADS)

The phase transition from ice VII to ice X under extreme pressures is an example where quantum proton delocalization coexists with classical thermal fluctuations. We investigate this transition, including quantum effects on the nuclear motion through adapted Langevin dynamics. This approach, which allows us to follow the semiclassical trajectories of protons, provides excellent agreement with experimental vibrational spectra indicating a transition pressure of about 65 GPa. Furthermore, we map the full dynamical problem onto a pressure-dependent, one-dimensional mean-field potential for the proton. By solving exactly the corresponding Schrödinger equation, we disentangle tunneling and quantum delocalization from classical thermal effects and identify the transition through the topological changes of the proton ground state and its susceptibility. The process is dominated by quantum effects even at ambient temperature and can be considered to be a paradigmatic case of a quantum-driven phase transition.

Bronstein, Yael; Depondt, Philippe; Finocchi, Fabio; Saitta, Antonino Marco

2014-06-01

305

METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS  

Microsoft Academic Search

CONTENTSIntroduction § 1. The Akhiezer function and the Zakharov-Shabat equations § 2. Commutative rings of differential operators § 3. The two-dimensional Schrödinger operator and the algebras associated with it § 4. The problem of multi-dimensional -algebraic operators Appendix 1. The Hamiltonian formalism in equations of Lax and Novikov types Appendix 2. Elliptic and rational solutions of the K-dV equations and

I M Krichever

1977-01-01

306

Application of group theory to integral-difference equations of plasma physics  

NASA Astrophysics Data System (ADS)

The Ovsyannikov method of determining the symmetry groups of differential equations was generalized to the case of integrodifferential equations. The new method is designed for the Vlasov-Maxwell equations describing plasma in zero magnetic field. In the case of single-component plasma, Taranov's result obtained indirectly was reproduced. A new result with respect to the indirect method was derived for a multi-component plasma: a complete symmetry group was defined.

Zawistowski, Jacek

307

Oscillation theory for higher order linear differential equations with entire coefficients  

Microsoft Academic Search

Sincc 1982, a considerable number of results have been proved concerning the frequency of zeros of solutions of second-order equations having entire coefficients. The proofs of these results were peculiar to second-order equations since they used techniques which hold only for second -order equations(e.g. the differential equalion for the product of two solutions). Surprisingly, we show in the present paper

Steven B. Bank; J. K. Langley

1991-01-01

308

On the Bardeen-Cooper-Schrieffer integral equation in the theory of superconductivity  

Microsoft Academic Search

The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, Tcso that, if Tc,the equation possesses a positive solution, representing the onset of the superconducting phase, while if T>Tc,the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover,

Yisong Yang

1991-01-01

309

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

SciTech Connect

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)] [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109 (United States)

2013-07-01

310

A Bimodular Theory for Finite Deformations: Comparison of Orthotropic Second-order and Exponential Stress Constitutive Equations for Articular Cartilage  

Microsoft Academic Search

Cartilaginous tissues, such as articular cartilage and the annulus fibrosus, exhibit orthotropic behavior with highly asymmetric\\u000a tensile–compressive responses. Due to this complex behavior, it is difficult to develop accurate stress constitutive equations\\u000a that are valid for finite deformations. Therefore, we have developed a bimodular theory for finite deformations of elastic\\u000a materials that allows the mechanical properties of the tissue to

Stephen M. Klisch

2006-01-01

311

Integral Equation Theory of Molecular Solvation Coupled with Quantum Mechanical\\/Molecular Mechanics Method in NWChem Package  

Microsoft Academic Search

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 consequent 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

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

2012-01-01

312

Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory  

Microsoft Academic Search

In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283–318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to

J. L. Bona; M. Chen; J.-C. Saut

2004-01-01

313

A Variant of the StrainHardening Theory Allowing for the Stress and Temperature Dependence of Parameters in Constitutive Equations  

Microsoft Academic Search

A procedure is put forward for concrete definition of constitutive relationships of the strain-hardening theory allowing for the level of damage in a material. The parameters of the equation of creep and the damage evolution relationship are assumed to be functions of stress and temperature. Efficiency of this approach is illustrated by describing creep curves for 20Kh13 and EP44 steels

N. K. Kucher

2005-01-01

314

Unified Equation of State for Supernova Cores and Neutron Stars Using the Energy-Density Functional Theory  

NASA Astrophysics Data System (ADS)

A unified equation of state (EoS) based on the nuclear energy-density functional theory is presented. This approach is particularly well-suited for describing both the homogeneous and inhomogeneous phases of dense matter at any temperature. We employ generalized Skyrme functionals fitted to essentially all experimental nuclear mass data and constrained to reproduce properties of infinite nuclear matter. Three different EoSs at T = 0 are shown here.

Fantina, A. F.; Chamel, N.; Pearson, J. M.; Goriely, S.

2013-03-01

315

L{sup p} Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space  

SciTech Connect

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

316

A study of the edge-zone equation of Mindlin-Reissner plate theory in bending of laminated rectangular plates  

Microsoft Academic Search

Summary The bending equations of the Mindlin-Reissner theory of plates laminated of transversely isotropic layers are reformulated in terms of the boundary-layer and transverse displacement functions. Analytical expressions are obtained for the primary response quantities of rectangular laminates with various boundary conditions. It is found that various edge conditions have boundary-layer effects on the primary and secondary response quantities that

A. Nosier; A. Yavari; S. Sarkani

2001-01-01

317

Potential Gradient Parametrization in a Langevin Type Dissipative Dynamics  

NASA Astrophysics Data System (ADS)

A parametrization of the conservative force in the dynamical coalescence and reseparation model is proposed. This model with one body dissipation formula, Yukawa plus exponential finite range potential, and shell effects included was recently adopted to follow Langevin trajectories for a collision of two very heavy nuclei which can end up as a compound system or reseparate. With our parametrization it is possible to speed up model calculations by a factor of 10 without loosing accuracy of trajectory integration. This can be of some importance in a case of Langevin trajectories calculation where many of them have to be traced in order to estimate probability for a process of interest, namely a fusion of two very heavy nuclei at beam energies close to the Coulomb barrier. Few examples of fusion excitation functions of heavy nuclei calculated with this faster version of the computer code are presented.

Wieloch, A.; Sosin, Z.; Blocki, J.

1999-04-01

318

Efficient Langevin simulation of coupled classical fields and fermions  

NASA Astrophysics Data System (ADS)

We introduce an efficient Langevin method to study bilinear fermionic Hamiltonians interacting with classical fields. Our approach is orders of magnitude faster than previous methods when applied to very large systems with high accuracy requirements. To demonstrate the method, we study complex noncoplanar chiral spin textures on the triangular Kondo lattice model. We also explore nonequilibrium mesoscale physics such as chiral domain coarsening and Z2 vortex annihilation.

Barros, Kipton; Kato, Yasuyuki

2013-12-01

319

A New Approach to Test Score Equating Using Item Response Theory with Fixed C-Parameters  

ERIC Educational Resources Information Center

Because parameter estimates from different calibration runs under the IRT model are linearly related, a linear equation can convert IRT parameter estimates onto another scale metric without changing the probability of a correct response (Kolen & Brennan, 1995, 2004). This study was designed to explore a new approach to finding a linear equation by…

Lee, Guemin; Fitzpatrick, Anne R.

2008-01-01

320

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

USGS Publications Warehouse

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

321

Periodic solutions of second-order nonlinear difference equations containing a small parameter. III - Perturbation theory  

NASA Technical Reports Server (NTRS)

A technique to construct a uniformly valid perturbation series solution to a particular class of nonlinear difference equations is shown. The method allows the determination of approximations to the periodic solutions to these equations. An example illustrating the technique is presented.

Mickens, R. E.

1986-01-01

322

Rayleigh-Schroedinger perturbation theory at large order for radial Klein-Gordon equations  

SciTech Connect

The relativistic hypervirial and Hellmann-Feynman theorems for the Klein-Gordon (KG) equation are used to construct Rayleigh-Schroedinger (RS) perturbation expansions to arbitrary order. The method is applied to the KG equation for a particle in an attractive Coulomb-type vector potential with perturbing vector or scalar potentials of the form [lambda][ital r][sup [ital k

McQuarrie, B.R.; Vrscay, E.R. (Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, N2L3G1 (Canada))

1993-02-01

323

An anisotropic constitutive equation for the stress tensor of blood based on mixture theory  

Microsoft Academic Search

Based on ideas proposed by Massoudi and Rajagopal M-R, we develop a model for blood using;\\u000athe theory of interacting continua, that is, the mixture theory. We first provide a brief review;\\u000aof mixture theory, and then discuss certain issues in constitutive modeling of a two-component;\\u000amixture. In the present formulation, we ignore the biochemistry of blood and assume that

Mehrdad Massoudi; James F. Antaki

2008-01-01

324

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models  

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

325

Univariate polynomial equation providing on-lattice higher-order models of thermal lattice Boltzmann theory  

NASA Astrophysics Data System (ADS)

A univariate polynomial equation is presented. It provides on-lattice higher-order models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate approximate solutions of the Boltzmann equation. We derive models approaching the complete Galilean invariant and providing accuracy of the fourth-order moment and beyond. We simulate one-dimensional thermal shock tube problems to illustrate the accuracy of our models. Moreover, we show the remarkably enhanced stability obtained by our models and our discretized equilibrium distributions.

Shim, Jae Wan

2013-01-01

326

Field transformations and the classical equation of motion in chiral perturbation theory.  

National Technical Information Service (NTIS)

The construction of effective Lagrangians commonly involves the application of the 'classical equation of motion' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework o...

S. Scherer H. Fearing

1994-01-01

327

Kinetic Theory of Inhomogeneous Bounded Plasmas. Pt. 1. The Vlasov-Poisson System of Equations.  

National Technical Information Service (NTIS)

The formal solution of the linearized Vlasov-Poisson system of equations is carried out for an inhomogeneous strong magnetized plasma column. The system considered is closely related to several experiments in magnetically confined cylindrical plasmas. A g...

C. J. Diaz

1980-01-01

328

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

SciTech Connect

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

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

2011-10-31

329

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

Microsoft Academic Search

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

330

The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory  

Microsoft Academic Search

In the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns

Michael Dütsch; Klaus Fredenhagen

2003-01-01

331

On the reduction of many-body dielectric theories to the Onsager equation  

Microsoft Academic Search

An approximate theory for the dielectric constant &egr; of a dense polar fluid was derived by Ramshaw, Schaefer, Waugh, and Deutch (RSWD). In the present article, the RSWD theory is generalized and made rigorous by another method of derivation. The result is a rigorous expression for &egr; which differs from the RSWD expression by the presence of a fluctuation term.

John D. Ramshaw

1974-01-01

332

On the reduction of many-body dielectric theories to the Onsager equation  

Microsoft Academic Search

An approximate theory for the dielectric constant ? of a dense polar fluid was derived by Ramshaw, Schaefer, Waugh, and Deutch (RSWD). In the present article, the RSWD theory is generalized and made rigorous by another method of derivation. The result is a rigorous expression for ? which differs from the RSWD expression by the presence of a fluctuation term.

John D. Ramshaw

1974-01-01

333

Integral equations and nonlocal damage theory: a numerical implementation using the BDEM  

Microsoft Academic Search

In this paper the integral equation approach is developed to describe elastic-damaging materials. An isotropic damage model\\u000a is implemented to study nonlinear structural problems involving localisation phenomena. Especially for the cases that exhibit\\u000a stress or strain concentrations, an integral approach can be recommended. Besides, the technique is able to represent well\\u000a high gradients of stress\\/strain. The governing integral equations are

V. Mallardo

2009-01-01

334

Stochastic theory of quantum vortex on a sphere.  

PubMed

A stochastic theory is presented for a quantum vortex in superfluid films coated on a two-dimensional sphere S^{2}. The starting point is the canonical equation of motion (Kirchhoff equation) for a point vortex, which is derived using the time-dependent Landau-Ginzburg theory. The vortex equation, which is equivalent to the spin equation, turns out to be the Langevin equation in presence of random forces. This is converted to the Fokker-Planck (FP) equation for the distribution function of a point vortex by using a functional integral technique. The FP equation is analyzed with special emphasis on the role of the pinning potential. By considering a typical form of the pinning potential, we address two problems: (i) The one is concerning an interplay between strength of the pinning potential and effective temperature, which discriminates the weak and strong coupling scheme to determine the solutions of the FP equation. (ii) The other is concerning a small diffusion limit, for which an asymptotic analysis is given using the functional integral to lead a compact expression of the distribution function. An extension to the vortex in nonspherical geometry is briefly discussed for the case of vortex on a plane and a pseudosphere. PMID:22587081

Kuratsuji, Hiroshi

2012-03-01

335

Reaction kinetics of CO + HO(2) --> products: ab initio transition state theory study with master equation modeling.  

PubMed

The kinetics of the reaction CO + HO2* --> CO2 + *OH was studied using a combination of ab initio electronic structure theory, transition state theory, and master equation modeling. The potential energy surface was examined with the CCSD(T) and CASPT2 methods. The classical energy barriers were found to be about 18 and 19 kcal/mol for CO + HO2* addition following the trans and cis paths, respectively. For the cis path, rate constant calculations were carried out with canonical transition state theory. For the trans path, master equation modeling was also employed to examine the pressure dependence. Special attention was paid to the hindered internal rotations of the HOOC*O adduct and transition states. The theoretical analysis shows that the overall rate coefficient is independent of pressure up to 500 atm for temperature ranging from 300 to 2500 K. On the basis of this analysis, we recommend the following rate expression for reaction R1 k(cm(3)/mol x s) = 1.57 x 10(5) T(2.18)e(-9030/T) for 300 < or = T < or = 2500 K with the uncertainty factor equal to 8, 2, and 1.7 at temperatures of 300, 1000, and 2000 K, respectively. PMID:17388389

You, Xiaoqing; Wang, Hai; Goos, Elke; Sung, Chih-Jen; Klippenstein, Stephen J

2007-05-17

336

FEMSYN - A Code System to Solve Multigroup Diffusion Theory Equations Using a Variety of Solution Techniques. Part 1: Description of Code System - Input and Sample Problems.  

National Technical Information Service (NTIS)

A modular computer code system called FEMSYN has been developed to solve the multigroup diffusion theory equations. The various methods that are incorporated in FEMSYN are (i) finite difference method (FDM) (ii) finite element method (FEM) and (iii) singl...

V. Jagannathan

1985-01-01

337

Lattice Model Theory of the Equation of State Covering the Gas, Liquid, and Solid Phases.  

National Technical Information Service (NTIS)

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. T...

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

1975-01-01

338

Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory  

SciTech Connect

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

339

Computational fixed-point theory for differential delay equations with multiple time lags  

NASA Astrophysics Data System (ADS)

We introduce a general computational fixed-point method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of periodic solutions using Newton's method applied on a finite dimensional projection, to derive a set of analytic estimates to bound the truncation error term and finally to use this explicit information to verify computationally the hypotheses of a contraction mapping theorem in a given Banach space. The fixed point so obtained gives us the desired periodic solution. We provide two applications. The first one is a proof of coexistence of three periodic solutions for a given delay equation with two time lags, and the second one provides rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags.

Kiss, Gábor; Lessard, Jean-Philippe

340

Equations of motion and conservation laws in a theory of stably stratified turbulence  

NASA Astrophysics Data System (ADS)

This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.

L'vov, Victor S.; Rudenko, Oleksii

2008-12-01

341

Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo.  

PubMed

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

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

2011-01-28

342

Einstein-Yang-Mills equations in the presence of q-stars in scalar-tensor gravitational theories  

SciTech Connect

We study Einstein-Yang-Mills equations in the presence of a gravitating nontopological soliton field configuration consisting of a Higgs doublet, in Brans-Dicke and general scalar-tensor gravitational theories. The results of General Relativity are reproduced in the {omega}{sub BD},{omega}{sub 0}{yields}{infinity} limit. The numerical solutions correspond to a soliton star with a non-Abelian gauge field. We study the effects of the coupling constant, the frequency of the Higgs field, and the Brans-Dicke field on the soliton parameters.

Prikas, Athanasios [Physics Department, National Technical University, Zografou Campus, 157 80 Athens (Greece)

2005-03-15

343

Investigating the Population Sensitivity Assumption of Item Response Theory True-Score Equating Across Two Subgroups of Examinees and Two Test Formats  

Microsoft Academic Search

Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that are commonly used in

Alina A. von Davier; Christine Wilson

2008-01-01

344

Investigating the Population Sensitivity Assumption of Item Response Theory True-Score Equating across Two Subgroups of Examinees and Two Test Formats  

ERIC Educational Resources Information Center

Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that…

von Davier, Alina A.; Wilson, Christine

2008-01-01

345

N\\/V-limit for Langevin dynamics in continuum  

Microsoft Academic Search

We construct an infinite particle\\/infinite volume Langevin dynamics on the\\u000aspace of configurations in $\\\\R^d$ having velocities as marks. The construction\\u000ais done via a limiting procedure using $N$-particle dynamics in cubes\\u000a$(-\\\\lambda,\\\\lambda]^d$ with periodic boundary conditions. A main step to this\\u000aresult is to derive an (improved) Ruelle bound for the canonical correlation\\u000afunctions of $N$-particle systems in $(-\\\\lambda,\\\\lambda]^d$

Florian Conrad; Martin Grothaus

2008-01-01

346

The method of local linear approximation in the theory of nonlinear functional-differential equations  

SciTech Connect

Conditions for the existence of solutions to the nonlinear functional-differential equation (d{sup m}x(t))/dt{sup m} + (fx)(t)=h(t), t element of R in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.

Slyusarchuk, Vasilii E [Ukranian State Academy of Water Economy (Ukraine)

2010-10-06

347

Application of perturbation theory to the solvability analysis of differential algebraic equations  

NASA Astrophysics Data System (ADS)

Linear systems of ordinary differential equations with an identically singular or rectangular matrix multiplying the derivative of the desired vector function are considered. The structure of general solutions is discussed. A special case of perturbed systems is studied by applying the Vishik-Lyusternik method.

Boichuk, A. A.; Pokutnyi, A. A.; Chistyakov, V. F.

2013-06-01

348

Theory of the iron equation of state and melting curve to very high pressures  

Microsoft Academic Search

A semiempirical equation of state for iron has been constructed by dividing the total energy into mean field, interatomic pair potential, and electronic thermal terms. The five adjustable parameters are fitted to the experimental isotherm, Hugoniot, and melting curve. Superimposing the estimated pressure and temperature conditions of the presumably pure solid iron inner core of the earth onto the calculated

D. A. Young; R. Grover

1983-01-01

349

Equations of State of Elements Based on the Generalized Fermi-Thomas Theory  

Microsoft Academic Search

The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z values.

R. P. Feynman; E. Teller

1949-01-01

350

General Aspects of Solving Helmholtz's Equation Underlying Eigenvalue and Scattering Problems in Electromagnetic Wave Theory  

Microsoft Academic Search

This paper considers conceptual aspects of different numerical methods for solving eigenvalue and scattering problems in electrodynamics. We will focus on the separation of variables method, the method of lines as a special finite-difference technique, and surface integral equation methods. It will be shown that there are interrelations between these different methods, and that it is possible to derive a

T. Rother

1999-01-01

351

Saha equation for two-temperature plasmas: Theories, experimental evidence, and interpretation  

Microsoft Academic Search

The following statement is investigated: if electrons realize an equilibrium between ionization and recombination in a two-temperature radiationless plasma, then the Saha equation can be obtained by replacing the thermodynamic temperature by the electron temperature. It is found that the statement is in general rather academic, but becomes realistic if it is confined to the higher excited states. These states

J. A. M. van der Mullen; D. A. Benoy; F. H. A. G. Fey; B. van der Sijde; J. Vlcek

1994-01-01

352

Theory of two-atom coherence in gases. I. Master equations  

Microsoft Academic Search

The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom \\

Abraham Ben-Reuven

1980-01-01

353

An Evaluation of Three Approximate Item Response Theory Models for Equating Test Scores.  

ERIC Educational Resources Information Center

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

Marco, Gary L.; And Others

354

The General Equation of Motion via the Special Theory of Relativity and Qauntum Mechanics Part II: Check against the Basic Predictions of the General Theory of Relativity  

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

355

Converted-wave moveout and conversion-point equations in layered VTI media: theory and applications  

NASA Astrophysics Data System (ADS)

We have developed improved equations for calculating the conversion point of the P-SV converted wave (C-wave) in transversely isotropic media with a vertical symmetry axis (vertical transverse isotropy (VTI)). We have also derived modified C-wave moveout equations for layered VTI media. The derived equations for the conversion-point are valid for offsets about three-times the reflector depth ( x/ z=3.0) and those for the C-wave moveout about twice the reflector depth ( x/ z=2.0). The new equations reveal some additional analytical insights into the converted-wave properties. The anisotropy has a more significant effect on the conversion point than on the move-out, and using the effective binning velocity ratio ?eff only is often insufficient to account for the anisotropic effect, even when higher-order terms are considered. Also for C-wave propagation, the anisotropy appears to affect the P-wave leg more than the S-wave leg. The ratio of the anisotropic contributions from P- and S-waves is close to the vertical velocity ratio ?0. Consequently S-wave anisotropic parameters may be recovered from converted-waves when P-wave anisotropic parameters are known. The new equations suggest that the C-wave moveout in layered VTI media over intermediate-to-far offsets is determined by the anisotropic parameter ?eff in addition to C-wave stacking velocity VC2, and the velocity ratios ?0 and ?eff. We refer to these four parameters as the C-wave "stacking velocity model". Two practical work flows are presented for determining this model: the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that although the single-scanning flow is less accurate than the double-scanning flow, it is more efficient and, in most cases, can yield sufficiently accurate results.

Li, Xiang-Yang; Yuan, Jianxin

2003-12-01

356

Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries.  

PubMed

We apply a previously proposed perturbation theory of the diffusion equation for studying light propagation through heterogeneous media in the presence of absorbing defects. The theory is based on the knowledge of (a) the geometric characteristics of a focal inclusion, (b) the mean optical path length inside the inclusion, and (c) the optical properties of the inclusion. The potential of this method is shown in the layered and slab geometries, where calculations are carried out up to the fourth order. The relative changes of intensity with respect to the unperturbed (heterogeneous) medium are predicted by the theory to within 10% for a wide range of contrasts dDeltamu(a) (up to dDeltamu(a) approximately 0.4-0.8), where d is the effective diameter of the defect and Deltamu(a) the absorption contrast between defect and local background. We also show how the method of Padé approximants can be used to extend the validity of the theory for a larger range of absorption contrasts. Finally, we study the possibility of using the proposed method for calculating the effect of a colocalized scattering and absorbing perturbation. PMID:19340125

Sassaroli, Angelo; Martelli, Fabrizio; Fantini, Sergio

2009-04-01

357

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

NASA Astrophysics Data System (ADS)

We discuss the structure of the Poincaré gauge theory of gravity (PG) that can be considered as the standard theory of gravity with torsion. We reconfirm that torsion, in the context of PG, couples only to the elementary particle spin and under no circumstances to the orbital angular momentum of test particles. We conclude that, unfortunately, the investigations of Mao et al. (2007) and March et al. (2011)-who claimed a coupling of torsion to orbital angular momentum, in particular in the context of the Gravity Probe B (GPB) experiment-do not yield any information on torsion.

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

2013-10-01

358

Stochastic Gravity: Theory and Applications  

NASA Astrophysics Data System (ADS)

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Hu, Bei Lok; Verdaguer, Enric

2004-03-01

359

Analysis of hybrid algorithms for the Navier-Stokes equations with respect to hydrodynamic stability theory  

NASA Astrophysics Data System (ADS)

Hybrid three-dimensional algorithms for the numerical integration of the incompressible Navier-Stokes equations are analyzed with respect to hydrodynamic stability in both linear and nonlinear fields. The computational schemes are mixed - spectral and finite differences - and are applied to the case of the channel flow driven by constant pressure gradient; time marching is handled with the fractional step method. Different formulations - fully explicit convective term, partially and fully implicit viscous term combined with uniform, stretched, staggered and non-staggered meshes, x-velocity splitted and non-splitted in average and perturbation component - are analyzed by monitoring the evolution in time of both small and finite amplitude perturbations of the mean flow. The results in the linear field are compared with correspondent solutions of the Orr-Sommerfeld equation; in the nonlinear field, the comparison is made with results obtained by other authors. Copyright

Passoni, Giuseppe; Alfonsi, Giancarlo; Galbiati, Massimo

2002-04-01

360

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

NASA Astrophysics Data System (ADS)

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.

2014-05-01

361

Lorentz-Invariant Equations of Motion of Point Masses in the General Theory of Relativity  

Microsoft Academic Search

After a general discussion of the problem of motion in the general theory of relativity a simple derivation of the law of motion is given for single poles of the gravitational field, which is based on a method originally developed by Mathisson. This law follows from the covariant conservation law for the matter energy-momentum tensor alone, without reference to any

Peter Havas; Joshua N. Goldberg

1962-01-01

362

Bethe ansatz equations for the classical A^{(1)}_{n} affine Toda field theories  

NASA Astrophysics Data System (ADS)

We establish a correspondence between classical A_{n}^{(1)} affine Toda field theories and An Bethe ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy functional relations of the type that appear in the context of the massive quantum integrable model.

Adamopoulou, Panagiota; Dunning, Clare

2014-05-01

363

Quantum-shell corrections to Thomas-Fermi-Dirac equation-of-state theory  

Microsoft Academic Search

Quantum-shell corrections are made directly to the finite-temperature Thomas-Fermi-Dirac (TFD) statistical model of the atom by a partition of the electronic density into bound and free parts. The bound part is calculated using analytic basis functions whose parameters are chosen to minimize the energy and pressure. Poisson's equation is solved for the modified density. The shock Hugoniot is calculated for

Burke Ritchie

2004-01-01

364

Integral equation theory for hard spheres confined on a cylindrical surface: Anisotropic packing entropically driven  

Microsoft Academic Search

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based

Takafumi Iwaki; Chwen-Yang Shew; Godfrey Gumbs

2005-01-01

365

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

NASA Technical Reports Server (NTRS)

The Rai (1984,85) patch-boundary scheme for the Euler equations is described. The integration methods used to update the interior grid points are are discussed. Stability of patch-boundary schemes and the use of these schemes in Navier-Stokes calculations are mentioned. Results for inviscid, supersonic flow over a cylinder, blast wave diffraction by ramp, and the motion of a vortex in a freestream are presented. These test cases demonstrate the quality of solutions possible with the scheme.

Rai, M. M.

1986-01-01

366

A Quantum Theory of Gravity Based on the Local-Ether Wave Equation  

Microsoft Academic Search

Suppose that the gravitational potential as well as the local ether for wave propagation associated with the Earth or the Sun is stationary in a geocentric or a heliocentric inertial frame, respectively [1]. It is postulated that under a gravitational potential, the local-ether wave equation proposed in [2] is modified as [ frac1n_gnabla ^2-fracn_gc^2fracpartial ^2 partial t^2 Psi (r,t)=fracomega _0^2c^2Psi

Ching-Chuan Su

2001-01-01

367

P3P-6 Modeling and Design of a Linear Actuator by Langevin Vibrators  

Microsoft Academic Search

A linear actuator driven by traveling wave generated by a pair of Langevin vibrators is designed. While one vibrator is assigned as the wave generator and the other one as the absorber, vibrators propel the rail to generate traveling wave so as to drive a guide mounted above. Comprehensive analysis of the Langevin vibrator and the rail is carried out

Y. Ting; J. M. Yang; C. C. Li; C. C. Yang; Y. C. Shao

2006-01-01

368

Coarse-gradient Langevin algorithms for dynamic data integration and uncertainty quantification  

Microsoft Academic Search

The main goal of this paper is to design an efficient sampling technique for dynamic data integration using the Langevin algorithms. Based on a coarse-scale model of the problem, we compute the proposals of the Langevin algorithms using the coarse-scale gradient of the target distribution. To guarantee a correct and efficient sampling, each proposal is first tested by a Metropolis

P. Dostert; Y. Efendiev; T. Y. Hou; W. Luo

2006-01-01

369

Non-Gaussian Fluctuations and Non-Markovian Effects in the Nuclear Fusion Process: Langevin Dynamics Emerging from Quantum Molecular Dynamics Simulations  

NASA Astrophysics Data System (ADS)

Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.

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

2013-07-01

370

High-pressure equations of state of krypton and xenon by a statistical mechanical theory  

Microsoft Academic Search

We present statistical mechanical calculations for krypton and xenon, employing accurate pair potentials with and without condensed-phase modifications. A unique feature of the present work is that solid- and fluid-phase thermodynamic properties are both computed within a single framework, using our recently developed hard-sphere perturbation theory. Results are applied to analyze experimental fluid, solid, and fluid–solid transition data, ranging up

Jae Hyun Kim; Taikyue Ree; Francis H. Ree

1989-01-01

371

High-pressure equations of state of krypton and xenon by a statistical mechanical theory  

Microsoft Academic Search

We present statistical mechanical calculations for krypton and xenon, employing accurate pair potentials with and without condensed-phase modifications. A unique feature of the present work is that solid- and fluid-phase thermodynamic properties are \\/ital both\\/ computed within a \\/ital single\\/ framework, using our recently developed hard-sphere perturbation theory. Results are applied to analyze experimental fluid, solid, and fluid--solid transition data,

Jae Hyun Kim; Taikyue Ree; Francis H. Ree

1989-01-01

372

On theory and application of the Helmholtz equation least squares method in inverse acoustics  

NASA Astrophysics Data System (ADS)

This paper presents a rigorous mathematical justification of the Helmholtz equation least squares (HELS) method for reconstructing acoustic radiation from an arbitrary source. It is shown that the acoustic pressure radiated from a non-spherical structure can be approximated using the spherical wavefunctions and spherical harmonics, and errors involved in this approximation are bounded. This explains why previously the HELS method could be used to produce satisfactory reconstruction of acoustic radiation from various types of structures. In the present paper, these analytical studies are further supported by experimental validation of the reconstruction of acoustic radiation from a typical filing cabinet in both exterior and interior regions.

Isakov, Victor; Wu, Sean F.

2002-08-01

373

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

PubMed

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

374

Microscopic theory of warm ionized gases: equation of state and kinetic Schottky anomaly  

NASA Astrophysics Data System (ADS)

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

2013-06-01

375

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

NASA Astrophysics Data System (ADS)

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.

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

2013-10-01

376

On boundary conditions for the diffusion equation in room-acoustic prediction: Theory, simulations, and experiments.  

PubMed

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. PMID:18177146

Jing, Yun; Xiang, Ning

2008-01-01

377

Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator  

NASA Technical Reports Server (NTRS)

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Bogdan, V. M.; Bond, V. B.

1980-01-01

378

Renormalization-group theory for the modified porous-medium equation  

NASA Astrophysics Data System (ADS)

We analyze the long-time behavior of the modified porous-medium equation ?tu=D?u1+n in d dimensions, where n is arbitrary and D=1 for ?tu>0 and D=1+? for ?tu<0. This equation describes inter alia the height of a groundwater mound during gravity-driven flow in porous media (d=2, n=1) and the propagation of strong thermal waves following an intense explosion (d=3, n=5). Using general renormalization-group (RG) arguments, we show that a radially symmetric mound exists of the form u(r,t)~t-(d?+?)f(rt-(?+?), ?), where ?==1/(2+nd) and ? and ? are ?-dependent anomalous dimensions, obeying the scaling law n??+(1-nd?)?=0. We calculate ? and ? to O(?), for general d and n, using a perturbative RG scheme. In the case of groundwater spreading, our results to O(?2) are in good agreement with numerical calculations, with a relative error in the anomalous dimension ? of about 3% when ? is 0.5.

Chen, Lin-Yuan; Goldenfeld, Nigel; Oono, Y.

1991-11-01

379

Mercedes-Benz water molecules near hydrophobic wall: Integral equation theories vs Monte Carlo simulations  

PubMed Central

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

Urbic, T.; Holovko, M. F.

2011-01-01

380

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

381

The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory  

PubMed Central

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

Allahviranloo, T.; Gerami Moazam, L.

2014-01-01

382

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model.  

PubMed

In this work, a multi-site chain model was incorporated into the polymer reference interaction site model to investigate the structure and properties of atactic polystyrene (aPS) melt and the structural correlations of dilute spherical nanoparticles dissolved in aPS melt. The theoretically calculated X-ray scattering intensities, solubility parameters and intermolecular correlation functions of aPS and its nanocomposites are found to be in agreement with the corresponding molecular simulation and experimental data. The theory was further employed to investigate the distribution functions of different size effects of aPS-nanoparticle system with consideration of the potential of mean force and depletion force. The aggregation of large nanoparticles increases with the increase of the nanoparticle-site size ratio in the infinitely dilute limit. The results show that the present theory can be used to investigate the structure of aPS melt and its nanocomposite, and give a further understanding of the filler dispersion and aggregation. All the observations indicate molecular-level details of the underlying mechanisms, providing useful information for the future design control of new aPS-nanocomposite materials with tailored properties. PMID:24952562

Xu, Qinzhi; Chen, Lan

2014-06-21

383

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model  

NASA Astrophysics Data System (ADS)

In this work, a multi-site chain model was incorporated into the polymer reference interaction site model to investigate the structure and properties of atactic polystyrene (aPS) melt and the structural correlations of dilute spherical nanoparticles dissolved in aPS melt. The theoretically calculated X-ray scattering intensities, solubility parameters and intermolecular correlation functions of aPS and its nanocomposites are found to be in agreement with the corresponding molecular simulation and experimental data. The theory was further employed to investigate the distribution functions of different size effects of aPS-nanoparticle system with consideration of the potential of mean force and depletion force. The aggregation of large nanoparticles increases with the increase of the nanoparticle-site size ratio in the infinitely dilute limit. The results show that the present theory can be used to investigate the structure of aPS melt and its nanocomposite, and give a further understanding of the filler dispersion and aggregation. All the observations indicate molecular-level details of the underlying mechanisms, providing useful information for the future design control of new aPS-nanocomposite materials with tailored properties.

Xu, Qinzhi; Chen, Lan

2014-06-01

384

Langevin dynamics simulation of polymer-assisted virus-like assembly  

NASA Astrophysics Data System (ADS)

Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.

Mahalik, J. P.; Muthukumar, M.

2012-04-01

385

Statistical mechanical theory for steady state systems. VI. Variational principles  

NASA Astrophysics Data System (ADS)

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

Attard, Phil

2006-12-01

386

Statistical mechanical theory for steady state systems. VI. Variational principles.  

PubMed

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed. PMID:17166028

Attard, Phil

2006-12-01

387

Integral Equation Theory of Molecular Solvation Coupled with Quantum Mechanical/Molecular Mechanics Method in NWChem Package  

SciTech Connect

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

388

Unified equation of state for neutron stars and supernova cores using the nuclear energy-density functional theory  

NASA Astrophysics Data System (ADS)

We present a unified approach to the equation of state (EoS) of dense matter at any temperature, based on the nuclear energy-density functional (EDF) theory. Both homogeneous and inhomogeneous phases can be treated consistently. In particular, we have constructed three different EoSs of cold catalyzed matter for a wide range of densities from ~ 105 g cm-3 to ~ 1015 g cm-3. For this purpose, we have employed generalized Skyrme functionals fitted to essentially all experimental nuclear mass data and constrained to reproduce properties of homogeneous nuclear matter as obtained from many-body calculations. We have applied these unified EoSs to compute the structure of cold isolated neutron stars (NSs).

Fantina, A. F.; Chamel, N.; Pearson, J. M.; Goriely, S.

2012-02-01

389

Chatter dynamic analysis for Van der Pol Equation with impulsive effect via the theory of flow switchability  

NASA Astrophysics Data System (ADS)

In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow's dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.

Fu, Xilin; Zheng, Shasha

2014-09-01

390

Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory.  

PubMed

An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region. PMID:24952549

Gámez, Francisco

2014-06-21

391

Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory  

NASA Astrophysics Data System (ADS)

An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.

Gámez, Francisco

2014-06-01

392

Parametrized post-Newtonian theory of reference frames, multipolar expansions and equations of motion in the N-body problem  

NASA Astrophysics Data System (ADS)

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

Kopeikin, Sergei; Vlasov, Igor

2004-11-01

393

Quadrupole terms in the Maxwell equations: Debye-Hückel theory in quadrupolarizable solvent and self-salting-out of electrolytes  

NASA Astrophysics Data System (ADS)

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

Slavchov, Radomir I.

2014-04-01

394

Lanczos-based Low-Rank Correction Method for Solving the Dyson Equation in Inhomogenous Dynamical Mean-Field Theory  

NASA Astrophysics Data System (ADS)

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

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

395

Application of extended DLVO theory. 4: Derivation of flotation rate equation from first principles  

SciTech Connect

A flotation model was developed by considering both hydrodynamic and surface forces involved in the process. The hydrodynamic forces were determined using a stream function and then used for estimating the kinetic energies that can be used for thinning the water films between bubbles and particles. The kinetic energies were compared with the energy barriers created by surface forces to determine the probability of adhesion. The surface forces considered included ion-electrostatic, London-van der Waals, and hydrophobic forces. Due to the insufficient information available on the hydrophobic forces for bubble-particle interactions, contributions from the hydrophobic force were back-calculated from the values of the flotation rate constants determined experimentally with methylated silica sphered. The results show that the hydrophobic force constants (K{sub 132}) for bubble-particle interaction are larger than those (K{sub 131}) for particle-particle interactions but smaller than that (K{sub 232}) for air bubbles interacting with each other in the absence of surfactants. The K{sub 132} values determined in the present work are close to the geometric means of K{sub 131} and K{sub 232}, suggesting that the combining rules developed for dispersion forces may be useful for hydrophobic forces. The flotation rate equation derived in the present work suggests various methods of improving flotation processes.

Yoon, R.H.; Mao, L. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Center for Coal and Minerals Processing] [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Center for Coal and Minerals Processing

1996-08-10

396

Rotating unstable Langevin-type dynamics: linear and nonlinear mean passage time distributions.  

PubMed

To characterize the decay process of linear rotating unstable Langevin-type dynamics in the presence of constant external force, through the mean passage time distribution, two theoretical descriptions are proposed: one is called the Quasideterministic (QD) approach described in the limit of long times, and the other approach is formulated for not so long times. Both theories are matrix based and formulated in two x and y dynamical representations, y being the transformed space of coordinates by means of a time-dependent rotation matrix. In the y dynamical representation the noise as well as the external force are rotational. The QD approach is studied when the dynamics is not influenced by the external force and when it is influenced by it. In the absence of this force, the theory is given for n variables and leads to the same results as those obtained in the characterization of nonrotating unstable systems; a fact that is better understood in the space of coordinates y. In the presence of the external force, the characterization is given for two variables and it is only valid for weak amplitude forces. For large amplitudes, the dynamics is almost dominated by the deterministic rotational evolution; then the QD approach is no longer valid and therefore the other approach is required. The theory in this case is general and verified for systems of two and three variables. In the case of two variables we study a laser system and use the experimental data of this system to compare with both theoretical and simulation results. In the case of three variables, the theory foresees application in other fields, for instance, in plasma physics. We also study the time characterization of the nonlinear rotating unstable systems and show in general that the nonlinear correction to the linear case is a quantity evaluated in the deterministic limit. The same laser system studied in the linear case is used as a prototype model. PMID:12513264

Jiménez-Aquino, J I; Romero-Bastida, M

2002-12-01

397

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

398

Langevin stabilization of molecular-dynamics simulations of polymers by means of quasisymplectic algorithms  

NASA Astrophysics Data System (ADS)

Algorithms for the numerical integration of Langevin equations are compared in detail from the point of view of their accuracy, numerical efficiency, and stability to assess them as potential candidates for molecular-dynamics simulations of polymeric systems. Some algorithms are symplectic in the deterministic frictionless limit and prove to stabilize long time-step integrators. They are tested against other popular algorithms. The optimal algorithm depends on the main goal: accuracy or efficiency. The former depends on the observable of interest. A recently developed quasisymplectic algorithm with great accuracy in the position evaluation exhibits better overall accuracy and stability than the other ones. On the other hand, the well-known BrünGer-Brooks-Karplus [Chem. Phys. Lett. 105, 495 (1982)] algorithm is found to be faster with limited accuracy loss but less stable. It is also found that using higher-order algorithms does not necessarily improve the accuracy. Moreover, they usually require more force evaluations per single step, thus leading to poorer performances.

Larini, L.; Mannella, R.; Leporini, D.

2007-03-01

399

Introduction to Collision Theory and to Some Astrophysical Applications  

Microsoft Academic Search

Introduction Classical theory of elastic collisions Classical motion of a particle in a potential V(r) Cross section Typical shape of the scattering angle as a function of impact - parameter Application of classical theory to ionization Rutherford formula Thomson's method for ionization of hydrogen Application of classical theory to the formation of molecules The phenomenon of orbiting Theory of Langevin

F. Masnou-Seeuws

1975-01-01

400

The correlation functions of hard-sphere chain fluids: Comparison of the Wertheim integral equation theory with the Monte Carlo simulation  

SciTech Connect

The correlation functions of homonuclear hard-sphere chain fluids are studied using the Wertheim integral equation theory for associating fluids and the Monte Carlo simulation method. The molecular model used in the simulations is the freely jointed hard-sphere chain with spheres that are tangentially connected. In the Wertheim theory, such a chain molecule is described by sticky hard spheres with two independent attraction sites on the surface of each sphere. The OZ-like equation for this associating fluid is analytically solved using the polymer-PY closure and by imposing a single bonding condition. By equating the mean chain length of this associating hard sphere fluid to the fixed length of the hard-sphere chains used in simulation, we find that the correlation functions for the chain fluids are accurately predicted. From the Wertheim theory we also obtain predictions for the overall correlation functions that include intramolecular correlations. In addition, the results for the average intermolecular correlation functions from the Wertheim theory and from the Chiew theory are compared with simulation results, and the differences between these theories are discussed.

Chang, J.; Sandler, S.I. (Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States))

1995-01-01

401

Temperature-Dependent Protein Dynamics: A Simulation-Based Probabilistic Diffusion-Vibration Langevin Description  

SciTech Connect

An enduring challenge in the understanding of internal protein motions is the effective separation and characterization of diffusive and vibrational dynamical components. To address this problem, here nanosecond molecular dynamics trajectories of myoglobin in aqueous solution, performed over a range of temperatures between 120 and 300 K, are subjected to principal component analysis, and the coordinate autocorrelation functions of the resulting principal modes are interpreted using a model combining damped Langevin vibration within potential wells and barrier-crossing diffusion between them. Both the vibrational frequency and the fraction of the mean-square fluctuation arising from vibrational motion undergo transitions with temperature at about 180 K. In contrast, the vibrational friction remains linear with temperature. The diffusional component of the mean-square fluctuation increases dramatically at the dynamical transition. The heights of the energy barriers between the potential wells are estimated, and the associated diffusion constants are calculated using Kramers' rate theory. Model functions of the frequency dependence of the frictional and diffusional quantities are obtained. The dynamic structure factor from the full molecular dynamics trajectory is well reproduced by the model. Overall, the results indicate that a global description of nanosecond temperature-dependent diffusion and vibrational internal protein dynamics can be obtained by applying the results of the present diffusion-vibration model to the vibrational motions obtained from a normal-mode analysis.

Moritsugu, K [University of Heidelberg; Smith, Jeremy C [ORNL

2006-01-01

402

A modified Poisson–Boltzmann equation in electric double layer theory for a primitive model electrolyte with size-asymmetric ions  

Microsoft Academic Search

The modified Poisson–Boltzmann theory is extended to treat a primitive model electrolyte with unequal ionic radii in the neighborhood of a uniformly charged plane wall. The linear equation indicates that the transition from a damped exponential to a damped oscillatory asymptotic behavior in the mean electrostatic potential as the concentration is increased depends in a complicated manner on the ratio

C. W. Outhwaite; L. B. Bhuiyan

1986-01-01

403

A modified Poisson-Boltzmann equation in electric double layer theory for a primitive model electrolyte with size-asymmetric ions  

Microsoft Academic Search

The modified Poisson-Boltzmann theory is extended to treat a primitive model electrolyte with unequal ionic radii in the neighborhood of a uniformly charged plane wall. The linear equation indicates that the transition from a damped exponential to a damped oscillatory asymptotic behavior in the mean electrostatic potential as the concentration is increased depends in a complicated manner on the ratio

C. W. Outhwaite; L. B. Bhuiyan

1986-01-01

404

Equations of state for energetic materials from density functional theory with van der Waals, thermal, and zero-point energy corrections  

Microsoft Academic Search

It is shown that the introduction of zero-point energy and thermal effects to density functional theory with an empirical van der Waals correction results in a significant improvement in the prediction of equilibrium volumes and isothermal equations of state for hydrostatic compressions of energetic materials at nonzero temperatures. This method can be used to predict the thermophysical properties of these

A. C. Landerville; M. W. Conroy; M. M. Budzevich; Y. Lin; C. T. White; I. I. Oleynik

2010-01-01

405

FEMSYN - A Code System to Solve Multigroup Diffusion Theory Equations Using a Variety of Solution Techniques. Part 4: SYNTHD - The Synthesis Module.  

National Technical Information Service (NTIS)

For solving the multigroup diffusion theory equations in 3-D problems in which the material properties are uniform in large segments of axial direction, the synthesis method is known to give fairly accurate results, at very low computational cost. In the ...

V. Jagannathan

1985-01-01

406

An effective rate equation approach to reaction kinetics in small volumes: Theory and application to biochemical reactions in nonequilibrium steady-state conditions  

NASA Astrophysics Data System (ADS)

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

Grima, R.

2010-07-01

407

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths  

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

408

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths.  

PubMed

Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations. PMID:23944435

Sääskilahti, K; Oksanen, J; Tulkki, J

2013-07-01

409

Development of an equation of state for electrolyte solutions by combining the statistical associating fluid theory and the mean spherical approximation for the nonprimitive model.  

PubMed

A statistical associating fluid theory to model electrolyte fluids that explicitly accounts for solvent molecules by modeling water as a dipolar square-well associating fluid is presented. Specifically the statistical associating fluid theory for potentials of variable range (SAFT-VR) is combined with integral equation theory and the generalized mean spherical approximation using the nonprimitive model to describe the long-range ion-ion, ion-dipole, and dipole-dipole interactions. Isothermal-isobaric ensemble Monte Carlo simulations have been performed in order to test the new theoretical approach. In particular, simulations are performed for different ion concentrations and different ratios of the cation, anion, and solvent segment diameters. Predictions for the thermodynamic properties from the new equation of state are compared with the computer simulation data. Additionally, results from a combination of the SAFT-VR approach with Debye-Huckel theory and the primitive model are also presented and compared to those obtained with the nonprimitive model to illustrate the advantages of the new statistical associating fluid theory for potentials of variable range plus dipole and electrolytes (SAFT-VR+DE) approach. The results show that the proposed equation of state provides a good description of the PVT properties of electrolyte fluids with different sizes of ions and solvent. PMID:17614560

Zhao, Honggang; dos Ramos, M Carolina; McCabe, Clare

2007-06-28

410

Polymer translocation through a nanopore studied by Langevin dynamics  

NASA Astrophysics Data System (ADS)

Polymer translocation through a nanopore has gained considerable attention in recent years, due to its potential application in DNA-sequencing. The design of a corresponding device requires a full understanding of the translocation dynamics. The scaling of polymer translocation time ? with polymer chain length N is an important measure of the underlying dynamics. A recent experimentootnotetextA. J. Storm et al., arXiv q-bio/0404041 (2004). has uncovered a scaling behavior ?N^1.26 that differs from the linear law observed in other experiments. To explain this newly-observed scaling behavior, we have employed Langevin dynamics simulations. Using a bead--spring model for the polymer chain and a membrane composed of one layer of hard-sphere particles, we have studied a wide range of chain lengths 20 <=N <=640, for different friction coefficients ?. A crossover scaling behavior was found for ?, which is controlled by both N and ?. We explain the measured scaling behavior from the chain conformations and instantaneous translocation velocities.

Guo, Lei

2005-03-01

411

Langevin dynamics simulations of genome packing in bacteriophage.  

PubMed

We use Langevin dynamics simulations to study the process by which a coarse-grained DNA chain is packaged within an icosahedral container. We focus our inquiry on three areas of interest in viral packing: the evolving structure of the packaged DNA condensate; the packing velocity; and the internal buildup of energy and resultant forces. Each of these areas has been studied experimentally, and we find that we can qualitatively reproduce experimental results. However, our findings also suggest that the phage genome packing process is fundamentally different than that suggested by the inverse spool model. We suggest that packing in general does not proceed in the deterministic fashion of the inverse-spool model, but rather is stochastic in character. As the chain configuration becomes compressed within the capsid, the structure, energy, and packing velocity all become dependent upon polymer dynamics. That many observed features of the packing process are rooted in condensed-phase polymer dynamics suggests that statistical mechanics, rather than mechanics, should serve as the proper theoretical basis for genome packing. Finally we suggest that, as a result of an internal protein unique to bacteriophage T7, the T7 genome may be significantly more ordered than is true for bacteriophage in general. PMID:16617089

Forrey, Christopher; Muthukumar, M

2006-07-01

412

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: a perspective of integral equation theory  

SciTech Connect

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

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

2012-01-01

413

Theories  

NSDL National Science Digital Library

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

2010-01-01

414

Obtaining Some Degree of Correspondence Between Unequatable Scores: A Comparison of Item Response Theory and Equipercentile Equating Methods.  

ERIC Educational Resources Information Center

Test scores that are not perfectly reliable cannot be strictly equated unless they are strictly parallel. This fact implies that tau equivalence can be lost if an equipercentile equating is applied to observed scores that are not strictly parallel. Thirty-six simulated data sets are produced to simulate equating tests with different difficulties…

Yen, Wendy M.

415

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

SciTech Connect

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

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

2006-02-15

416

Langevin dynamics simulation of DNA ejection from a phage.  

PubMed

We have performed Langevin dynamics simulations of a coarse-grained model of ejection of dsDNA from ?29 phage. Our simulation results show significant variations in the local ejection speed, consistent with experimental observations reported in the literature for both in vivo and in vitro systems. In efforts to understand the origin of such variations in the local speed of ejection, we have investigated the correlations between the local ejection kinetics and the packaged structures created at various motor forces and chain flexibility. At lower motor forces, the packaged DNA length is shorter with better organization. On the other hand, at higher motor forces typical of realistic situations, the DNA organization inside the capsid suffers from significant orientational disorder, but yet with long orientational correlation times. This in turn leads to lack of registry between the direction of the DNA segments just to be ejected and the direction of exit. As a result, a significant amount of momentum transfer is required locally for successful exit. Consequently, the DNA ejection temporarily slows down exhibiting pauses. This slowing down occurs at random times during the ejection process, completely determined by the particular starting conformation created by prescribed motor forces. In order to augment our inference, we have additionally investigated the ejection of chains with deliberately changed persistence length. For less inflexible chains, the demand on the occurrence of large momentum transfer for successful ejection is weaker, resulting in more uniform ejection kinetics. While being consistent with experimental observations, our results show the nonergodic nature of the ejection kinetics and call for better theoretical models to portray the kinetics of genome ejection from phages. PMID:23860871

Mahalik, J P; Hildebrandt, B; Muthukumar, M

2013-03-01

417

Initial design with L2 Monge-Kantorovich theory for the Monge-Ampère equation method in freeform surface illumination design.  

PubMed

The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L2 Monge-Kantorovich (LMK) theory. An efficient approach is proposed to find the optimal mapping of the LMK problem. The characteristics of the new approach are introduced and the limitations of the LMK theory in illumination design are presented. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design. PMID:24977868

Wu, Rengmao; Zhang, Yaqin; Sulman, Mohamed M; Zheng, Zhenrong; Benítez, Pablo; Miñano, Juan C

2014-06-30

418

Uniformly Asymptotic Frequency Domain Green's Functions for the Acoustic Equation - Theory and Applications in Two and Three Dimensions  

NASA Astrophysics Data System (ADS)

As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6]. Central to the sensitivity kernel techniques is the use of an appropriate Green's function in either two or three dimensions and a background model is assumed for the calculation of the Green's function. In some situations, the constant velocity Green's function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green's function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7]. To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green's function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green's function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications. References [1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics 64(3), pp. 888-901. [2] J. R. Ernst, A. G. Green, H. Maurer and K. Holliger. 2007, Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data. Geophysics 72, pp. J53. [3] H. Marquering, F. Dahlen and G. Nolet. 1999, Three-dimensional sensitivity kernels for finite-frequency traveltimes: The banana-doughnut paradox. Geophysical Journal International 137(3), pp. 805-815. [4] J. Tromp, C. Tape and Q. Liu. 2005, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International 160(1), pp. 195-216. [5] M. L. Buursink, T. C. Johnson, P. S. Routh and M. D. Knoll. 2008, Crosshole radar velocity tomography with finite-frequency fresnel volume sensitivities. Geophysical Journal International 172(1), pp. 1-17. [6] I. Iturbe, P. Roux, J. Virieux and B. Nicolas. 2009, Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water. J. Acoust. Soc. Am. 126(2), pp. 713-720. [7] E. Zauderer. 1971, Uniform asymptotic solutios of the reduced wave equation. Journal of Mathematical Analysis and Application 30, pp. 157-171. [8] M. J. Yedlin. 1987, Uniform asymptotic solution for the Green's function for the two-dimensional acoustic equation. J. Acoust. Soc. Am. 81(2) pp. 238-243.

Yedlin, Matthew; Virieux, Jean

2010-05-01

419

Diffusion of Single layer Clusters: Langevin Analysis and Monte Carlo Simulations^*  

NASA Astrophysics Data System (ADS)

In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius R, the cluster diffusion constant Dc is found to vary as R-1 and R-2 in studies by Wen et al. ( J. M. Wen, S. -L. Chang, J. W. Burnett, J. W. Evans and P. A. Thiel, Phys. Rev. Lett. 73), 2591 (1994). and Morgenstern et al. (K. Morgenstern, G. Rosenfeld, B. Poelsema, and G. Comsa, Phys. Rev. Lett. 74), 2058 (1995)., repectively. From an analytical continuum description of the cluster's step-like boundary, we find a single Langevin equation for the motion of the cluster boundary. From this we determine the cluster diffusion constant and the fluctuations of the shape around an assumed equilibrium circular shape. In three limiting cases this leads to the scaling of the diffusion constant with the radius as Dc ~ R^-? and the scaling of a shape fluctuations correlation function with the elapsed time as t^1/(1+? ). These three cases correspond to the three microscopic surface mass-transport mechanisms of straight steps, namely: evaporation condensation (EC) giving ?=1, terrace diffusion (TD) implying ?=2 and periphery diffusion (PD) yielding ? = 3. We thereby provide a unified treatment of the dynamics of steps and of clusters ( S. V. Khare, N. C. Bartelt, and T. L. Einstein, Phys. Rev. Lett. 75), 2148 (1995); in preparation.. To check how well the continuum results apply to real systems with finite lattice constants, we perform Monte Carlo simulations of simple lattice gas models for these three cases. We also relate the the experimentally measured diffusion coefficients of the clusters to atomic diffusion parameters. ^* This work was done in collaboration with N. C. Bartelt and T. L. Einstein and was supported in part by NSF DMR-MRG 91-03031.

Khare, S. V.

1996-03-01

420

A combined finite element-Langevin dynamics (FEM-LD) approach for analyzing the mechanical response of bio-polymer networks  

NASA Astrophysics Data System (ADS)

A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.

Lin, Yuan; Wei, X.; Qian, J.; Sze, K. Y.; Shenoy, V. B.

2014-01-01

421

Inspiralling compact binaries in scalar-tensor theories of gravity: Equations of motion to 2.5 post-Newtonian order  

NASA Astrophysics Data System (ADS)

We derive the scalar-tensor equations of motion for non-spinning compact objects, including black holes and neutron stars, to order (v/c)^5 beyond Newtonian order. We use the DIRE (Direct Integration of the Relaxed Einstein Equations) formalism [1] adapted to scalar- tensor theory, coupled with Eardley's scheme [2] for incorporating compact, quasi- stationary, self-gravitating bodies. We find that to this order of the PN approximation, binary black hole behavior in this class of theories is indistinguishable from that predicted by general relativity. Supported in part by the NSF, PHY 09-65133.[4pt] [1] A. G. Wiseman and C. M. Will, Phys. Rev. D 54, 4813 (1996); M. E. Pati and C. M. Will, Phys. Rev. D 62, 124015 (2000); ibid. 65, 104008 (2002).[0pt] [2] D. M. Eardley, Astrophys. J. Lett. 196, L59 (1975).

Mirshekari, Saeed; Will, Clifford

2012-03-01

422

Hybrid binomial Langevin-multiple mapping conditioning modeling of a reacting mixing layer  

NASA Astrophysics Data System (ADS)

A novel, stochastic, hybrid binomial Langevin-multiple mapping conditioning (MMC) model-that utilizes the strengths of each component-has been developed for inhomogeneous flows. The implementation has the advantage of naturally incorporating velocity-scalar interactions through the binomial Langevin model and using this joint probability density function (PDF) to define a reference variable for the MMC part of the model. The approach has the advantage that the difficulties encountered with the binomial Langevin model in modeling scalars with nonelementary bounds are removed. The formulation of the closure leads to locality in scalar space and permits the use of simple approaches (e.g., the modified Curl's model) for transport in the reference space. The overall closure was evaluated through application to a chemically reacting mixing layer. The results show encouraging comparisons with experimental data for the first two moments of the PDF and plausible results for higher moments at a relatively modest computational cost.

Wandel, Andrew P.; Lindstedt, R. Peter

2009-01-01

423

Nonlinear stochastic equations with multiplicative Lévy noise  

NASA Astrophysics Data System (ADS)

The Langevin equation with a multiplicative Lévy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed. The solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the Stratonovich interpretation. The problem of escaping from a potential well is analyzed numerically; predictions of different interpretations of the stochastic integral are compared.

Srokowski, Tomasz

2010-05-01

424

Problems Related to the Use of Conventional and Item Response Theory Equating Methods in Less Than Optimal Circumstances  

Microsoft Academic Search

This paper focuses on a discussion of how various equating methods are affected by (1) sampling error, (2) sample characteristics, and (3) characteristics of anchor test items. Studies that examine the effect of analytic techniques for smoothing or modeling mar ginal and bivariate frequency distributions on the ac curacy of equipercentile equating are reviewed. A need for simulation and empirical

Linda L. Cook; Nancy S. Paterson

1987-01-01

425

The Second Orthogonality Conditions in the Theory of Proper and Improper Rotations. Iv. Solution of the Trace and Secular Equations.  

National Technical Information Service (NTIS)

The equation which connects the trace of a rotation matrix and that of its square, and the secular equation for a rotation matrix, both of which are direct results of the second orthogonality conditions, are solved by purely analytic methods based on the ...

H. Gelman

1969-01-01

426

Polaron master equation theory of the quantum-dot Mollow triplet in a semiconductor cavity-QED system  

NASA Astrophysics Data System (ADS)

We present a comprehensive theoretical study of the resonance fluorescence spectra of an coherently-driven quantum dot (QD) placed inside a high-Q semiconductor cavity and interacting with an acoustic-phonon bath. We derive a quantum master equation (ME) in the polaron frame, which includes exciton-phonon and exciton-cavity coupling to all orders. This work details and extends the theory used in a recent paper [C. Roy and S. Hughes, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.247403 106, 247403 (2011)] to describe the QD Mollow triplet in the regime of semiconductor cavity QED. Here, we introduce two ME forms, Nakajima-Zwanzig and time convolutionless (TC), both to second order in the system-phonon-reservoir perturbation. In the polaron frame, these two ME forms are shown to yield equivalent population dynamics and fluorescence spectra for a continuous wave (cw) driving field. We also demonstrate that a Markov approximation is valid for computing the incoherent scattering processes, and we subsequently exploit the TC ME to explore the resonance fluorescence spectra of an exciton-driven QD. Both cavity-emitted and exciton-emitted spectra are studied, and these are found to have qualitatively different spectral features. Using a coherent driving field, the well-known characteristics of the atomic Mollow triplet are shown to be considerably modified with electron-acoustic-phonon scattering, and we highlight the key effects arising from both cavity coupling and electron-phonon coupling. Regimes of pronounced cavity feeding and anharmonic cavity QED are exemplified, and we find that the cavity coupling depends sensitively on the exciton-cavity detuning and the temperature of the phonon bath. We show how the full width at half maximum (linewidth) of the Mollow-triplet sidebands varies as a function of the square of the Rabi frequency of the cw pump. Phonon-mediated cavity coupling also contributes to the spectral broadening of the Mollow triplet, depending upon the exciton-cavity detuning and the strength of the exciton-cavity coupling rate. Finally, we calculate the fluorescence spectra for off-resonance cw driving and investigate the resulting Mollow-triplet linewidths.

Roy, C.; Hughes, S.

2012-03-01

427

Black hole perturbation in the most general scalar-tensor theory with second-order field equations: The odd-parity sector  

NASA Astrophysics Data System (ADS)

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

Kobayashi, Tsutomu; Motohashi, Hayato; Suyama, Teruaki

2012-04-01

428

Finite-temperature extension of the quasicontinuum method using Langevin dynamics: entropy losses and analysis of errors  

NASA Astrophysics Data System (ADS)

The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's (\\beta=0;\\gamma=\\case{1}{2}) method, which is parametrized to ensure overdamped dynamics. In this fashion, spurious heating due to reflected vibrations is suppressed, leading to stable canonical trajectories. To estimate the errors introduced by the QC reduction in the resulting dynamics, we have quantified the vibrational entropy losses in Al uniform meshes by calculating the thermal expansion coefficient for a number of conditions. We find that the entropic depletion introduced by coarsening varies linearly with the element size and is independent of the nodal cluster diameter. We rationalize the results in terms of the system, mesh and cluster sizes within the framework of the quasiharmonic approximation. The limitations of the method and alternatives to mitigate the errors introduced by coarsening are discussed. This work represents the first of a series of studies aimed at developing a fully non-equilibrium finite-temperature extension of QC.

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

2010-01-01

429

The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions  

SciTech Connect

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

430

Dynamic density functional theory with hydrodynamic interactions and fluctuations  

NASA Astrophysics Data System (ADS)

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

Donev, Aleksandar; Vanden-Eijnden, Eric

2014-06-01

431

The Theory of Planned Behavior (TPB) and Pre-Service Teachers' Technology Acceptance: A Validation Study Using Structural Equation Modeling  

ERIC Educational Resources Information Center

This study applies the theory of planned behavior (TPB), a theory that is commonly used in commercial settings, to the educational context to explain pre-service teachers' technology acceptance. It is also interested in examining its validity when used for this purpose. It has found evidence that the TPB is a valid model to explain pre-service…

Teo, Timothy; Tan, Lynde

2012-01-01

432

Structure of Poly(dialkylsiloxane) Melts: Comparisons of Wide Angle X-ray Scattering, Molecular Dynamics Simulations, and Integral Equation Theory  

SciTech Connect

Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.

Habenschuss, Anton {Tony} [ORNL; Tsige, Mesfin [Southern Illinois University; Curro, John G. [Sandia National Laboratories (SNL); Grest, Gary S. [Sandia National Laboratories (SNL); Nath, Shyamal [CULGI Inc, Albuquerque, NM

2007-01-01

433

Structure of Poly(dialkylsiloxane) Melts: Comparisons of Wide-Angle X-ray Scattering, Molecular Dynamics Simualations, and Integral Equation Theory  

SciTech Connect

Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.

Habenschuss, Anton {Tony} [ORNL; Tsige, Mesfin [Southern Illinois University; Curro, John G. [Sandia National Laboratories (SNL); Grest, Gary S. [Sandia National Laboratories (SNL); Nath, Shyamal [CULGI Inc, Albuquerque, NM

2007-01-01

434

Langevin-Type Models I: Diffusions with Given Stationary Distributions and their Discretizations  

Microsoft Academic Search

We describe algorithms for estimating a given measure p known up to a constant of proportionality, based on a large class of diffusions (extending the Langevin model) for which p is invariant. We show that under weak conditions one can choose from this class in such a way that the diffusions converge at exponential rate to p, and one can

O. Stramer; R. L. Tweedie

1999-01-01

435

Channel-based Langevin approach for the stochastic Hodgkin-Huxley neuron  

NASA Astrophysics Data System (ADS)

Stochasticity in ion channel gating is the major source of intrinsic neuronal noise, which can induce many important effects in neuronal dynamics. Several numerical implementations of the Langevin approach have been proposed to approximate the Markovian dynamics of the Hodgkin-Huxley neuronal model. In this work an improved channel-based Langevin approach is proposed by introducing a truncation procedure to limit the state fractions in the range of [0, 1]. The truncated fractions are put back into the state fractions in the next time step for channel noise calculation. Our simulations show that the bounded Langevin approaches combined with the restored process give better approximations to the statistics of action potentials with the Markovian method. As a result, in our approach the channel state fractions are disturbed by two terms of noise: an uncorrelated Gaussian noise and a time-correlated noise obtained from the truncated fractions. We suggest that the restoration of truncated fractions is a critical process for a bounded Langevin method.

Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

2013-01-01

436

Langevin acoustic radiation force of a high-order bessel beam on a rigid sphere  

Microsoft Academic Search

The acoustic radiation force of Langevin type resulting from the interaction of a high-order Bessel beam with a rigid immovable sphere in an ideal fluid is theoretically investigated. The analysis is based on applying the generalized Rayleigh series used in the near-field acoustic scattering problem to calculate the force. With appropriate selection of specific Bessel beam parameters, results for the

Farid G. Mitri

2009-01-01

437

Non-Gaussian fluctuations and non-Markovian effects in the nuclear fusion process: Langevin dynamics emerging from quantum molecular dynamics simulations.  

PubMed

Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function. PMID:23862995

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

2013-07-01

438

Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. II. Structure and application to hopping dynamics.  

PubMed

Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions. PMID:23927265

Jadrich, Ryan; Schweizer, Kenneth S

2013-08-01

439

Constructing a new closure theory based on the third-order Ornstein-Zernike equation and a study of the adsorption of simple fluids.  

PubMed

The third-order Ornstein-Zernike equation (OZ3) is used in the construction of a bridge functional that improves over conventional liquid-theory closures (for example, the hypernetted chain or the Percus-Yevick equations). The OZ3 connects the triplet direct correlation C((3)) to the triplet total correlation h((3)). By invoking the convolution approximation of Jackson and Feenberg, we are able to express the third-order bridge function B(3) as a functional of the indirect correlation ?. The resulting expression is generalized to higher-order bridge terms. This new closure is tested on the adsorption of Lennard-Jones fluid on planar hard surfaces by calculating the density profiles and comparing with Monte Carlo simulations. Particular attention is paid to the cases where molecular depletion on the substrate is evident. The results prove to be highly accurate and improve over conventional closures. PMID:22128951

Lee, Lloyd L

2011-11-28

440

Efficient quantum mechanical calculation of solvation free energies based on density functional theory, numerical atomic orbitals and Poisson Boltzmann equation  

NASA Astrophysics Data System (ADS)

We have successfully coupled the Kohn-Sham with Poisson-Boltzmann equations to predict the solvation free energy, where the Kohn-Sham equations were solved by implementing the flexible pseudo atomic orbitals as in S IESTA package. It was found that the calculated solvation free energy is in good agreement with experimental results for small neutral molecules, and its standard error is 1.33 kcal/mol, the correlation coefficient is 0.97. Due to its high efficiency and accuracy, the proposed model can be a promising tool for computing solvation free energies in computer aided drug design in future.

Wang, Mingliang; Wong, Chung F.; Liu, Jianhong; Zhang, Peixin

2007-07-01

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