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1

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

SciTech Connect

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (); G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: ()]. In this work we provide a complementary, more analytic approach based on Dyson-Schwinger equations. Using methods known from stochastic quantitation, we recast Boedeker's Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson-Schwinger equations are derived.

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

2009-10-15

2

Numerical Solutions of the Complex Langevin Equations in Polymer Field Theory  

Microsoft Academic Search

Using a diblock copolymer melt as a model system, we show that complex Langevin (CL) simulations constitute a practical method for sampling the complex weights in field theory models of polymeric fluids. Prior work has primarily focused on numerical methods for obtaining mean-field solutions—the deterministic limit of the theory. This study is the first to go beyond Euler- Maruyama integration

Erin M. Lennon; George O. Mohler; Hector D. Ceniceros; Glenn H. Fredrickson

2008-01-01

3

Langevin equations for fluctuating surfaces  

NASA Astrophysics Data System (ADS)

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

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

2005-11-01

4

Einstein-Langevin equations from running coupling constants  

SciTech Connect

The Einstein-Langevin equations take into account the back reaction of quantum matter fields on the background geometry. We present a derivation of these equations to lowest order in a covariant expansion in powers of the curvature. For massless fields, the equations are completely determined by the running coupling constants of the theory. {copyright} {ital 1997} {ital The American Physical Society}

Lombardo, F.C.; Mazzitelli, F.D. [Departamento de Fisica and IAFE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires- Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)

1997-03-01

5

Langevin equation approach to reactor noise analysis: stochastic transport equation  

Microsoft Academic Search

This paper is concerned with an application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density, as well as in the detector outputs, in nuclear reactors. The Langevin equation in this case is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the

A. Z. Akcasu; A. M. Stolle

1991-01-01

6

Langevin Equation for Slow Degrees of Freedom of Hamiltonian Systems  

Microsoft Academic Search

\\u000a A way is sketched to derive a Langevin equation for the slow degrees of freedom of a Hamiltonian system whose fast ones are\\u000a mixing Anosov. It uses the Anosov-Kasuga adiabatic invariant, martingale theory, Ruelle’s formula for weakly non-autonomous\\u000a SRB measures, and large deviation theory.

R. S. MacKay

7

Nuclear fission with a Langevin equation  

Microsoft Academic Search

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

David Boilley; Eric Suraud; Abe Yasuhisa; Sakir Ayik

1993-01-01

8

Computing ergodic limits for Langevin equations  

NASA Astrophysics Data System (ADS)

To evaluate averages with respect to the invariant law for Langevin-type equations, one has to integrate a system over long time intervals, especially when dissipation is small. This is a challenging problem from the computational point of view. Since coefficients of the Langevin equations are typically not globally Lipschitz, the difficulties are redoubled. In the nonglobal Lipschitz case we observe an exploding behavior of some approximate trajectories due to many usual numerical methods. In [G.N. Milstein, M.V. Tretyakov, Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients, SIAM J. Numer. Anal. 43 (2005) 1139 1154] we propose and justify a concept which, in principle, allows us to apply any numerical method to stochastic differential equations with nonglobally Lipschitz coefficients. Here quasi-symplectic integrators from [G.N. Milstein, M.V. Tretyakov, Quasi-symplectic methods for Langevin-type equations, IMA J. Numer. Anal. 23 (2003) 593 626] (they are the most appropriate methods for solving Langevin-type equations, especially when damping is small) and the concept of [G.N. Milstein, M.V. Tretyakov, Numerical integration of stochastic differential equations with nonglobally Lipschitz coefficients, SIAM J. Numer. Anal. 43 (2005) 1139 1154] are applied for calculation of ergodic limits. Special attention is paid to the case when the invariant measure is known (e.g., when this measure is Gibbsian). Some computer experiments with three model problems (Van der Pol’s equation with additive noise, one-dimensional arrays of oscillators in thermal equilibrium, and a physical pendulum with linear friction and additive noise) are presented.

Milstein, G. N.; Tretyakov, M. V.

2007-05-01

9

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

10

Fractional dynamics from the ordinary Langevin equation.  

PubMed

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

Stanislavsky, A A

2003-02-27

11

Fractional dynamics from the ordinary Langevin equation  

NASA Astrophysics Data System (ADS)

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

Stanislavsky, A. A.

2003-02-01

12

Presentation of solutions of impulsive fractional Langevin equations and existence results. Impulsive fractional Langevin equations  

NASA Astrophysics Data System (ADS)

In this paper, a class of impulsive fractional Langevin equations is firstly offered. Formula of solutions involving Mittag-Leffler functions and impulsive terms of such equations are successively derived by studying the corresponding linear Langevin equations with two different fractional derivatives. Meanwhile, existence results of solutions are established by utilizing boundedness, continuity, monotonicity and nonnegative of Mittag-Leffler functions and fixed point methods. Further, other existence results of nonlinear impulsive problems are also presented. Finally, an example is given to illustrate our theoretical results.

Wang, J.; Fec?kan, M.; Zhou, Y.

2013-09-01

13

Langevin equation as a stochastic differential equation in nuclear physics  

SciTech Connect

Two kinds of stochastic integrals, Ito integral and Stratonovich integral, are applied for solving Langevin equation. In the case of the simplified Langevin equation for over-damped motion, the fission rate obtained with Stratonovich integral is significantly larger than that with Ito integral. On the other hand, in the case where the random force acts on the momentum variables, the two integrals give essentially the same results. The condition for the difference with two integrals to appear is discussed. The proper treatment of the double stochastic integral is necessary to obtain a high numerical accuracy.

Asano, T.; Wada, T.; Ohta, M. [Department of Physics, Konan University, 8-9-1 Okamoto, Kobe 658-8501 (Japan); Takigawa, N. [Department of Physics, Tohoku University, Sendai, 980-8578 (Japan)

2007-02-26

14

Computing generalized Langevin equations and generalized Fokker-Planck equations  

PubMed Central

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

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-01-01

15

Foundations of quantum mechanics: The Langevin equations for QM  

NASA Astrophysics Data System (ADS)

Stochastic derivations of the Schrödinger equation are always developed on very general and abstract grounds. Thus, one is never enlightened which specific stochastic process corresponds to some particular quantum mechanical system, that is, given the physical system—expressed by the potential function, which fluctuation structure one should impose on a Langevin equation in order to arrive at results identical to those comming from the solutions of the Schrödinger equation. We show, from first principles, how to write the Langevin stochastic equations for any particular quantum system. We also show the relation between these Langevin equations and those proposed by Bohm in 1952. We present numerical simulations of the Langevin equations for some quantum mechanical problems and compare them with the usual analytic solutions to show the adequacy of our approach. The model also allows us to address important topics on the interpretation of quantum mechanics.

Olavo, L. S. F.; Lapas, L. C.; Figueiredo, A.

2012-05-01

16

Langevin theory of anomalous Brownian motion made simple  

NASA Astrophysics Data System (ADS)

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

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

2011-05-01

17

Waveform characteristics of deep low-frequency earthquakes: time-series evolution based on the theory of the KM2O-Langevin equation  

NASA Astrophysics Data System (ADS)

Since the 1970s, deep low-frequency earthquakes (DLF) with depths ranging 20-40 km have been observed just beneath the Japan Island Arc. Almost all of these earthquakes are recognized up to now have had magnitudes less than 2.5, so that we have little information concerning DLF. Employing the theory of KM2O-Langevin equations, we develop a new method to represent the characteristics of the coda parts of DLF, and propose a new concept of `average dissipation spectrum'. The new averaging algorithm for the KM2O-Langevin matrix function was applied in the analysis of DLF (M: 1.0), which occurred in Akita prefecture on 2001 July 11, and we succeeded in separating the characteristics of the source vibration system and the source excitation process into the averaged dissipation term and the fluctuation term, respectively. The gaps between the arrival times of the fluctuation term's peaks at three stations near the epicentre are slightly different than the gaps between the S-wave arrival times. Assuming a homogenous crust structure with an S-wave velocity of 4.3 km s-1 and assuming the depth of the second source to be the same as that of the hypocentre, the second source lies about 1.5 km, N 56°E of the hypocentre. We estimate the common characteristics of this DLF successfully by using the `average dissipation spectrum', which is made up of typical frequencies, ?k, attenuation factors, Qk and amplitude factors, Ak. The common elements of (?k~ 1.5, Qk~-0.3) and (?k~ 3.25, Qk~-0.45) among all stations indicate the characteristics of the source dynamics of the Akita DLF. The major parts of the coda waves of DLF satisfy the stationary property, and the causality values for the linear and odd-degree non-linear transformations are relatively higher than those for the even-degree non-linear transformations. These characteristics are quite different from the characteristics of tectonic earthquakes. This quantitative property is common among all DLF.

Takeo, Minoru; Ueda, Hiroko; Okabe, Yasunori; Matsuura, Masaya

2006-04-01

18

Stochastic Resonance in a Linear Fractional Langevin Equation  

NASA Astrophysics Data System (ADS)

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.

Zhong, Suchuan; Wei, Kun; Gao, Shilong; Ma, Hong

2013-03-01

19

Diffusion described with quantum Langevin equation in tilted periodic potential  

NASA Astrophysics Data System (ADS)

In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.

Duan, Hong-Guang; Liang, Xian-Ting

2012-11-01

20

Numerical simulation of the Langevin equation for skewed turbulence  

SciTech Connect

In this paper the authors present a numerical method for the generalized Langevin equation of motion with skewed random forcing for the case of homogeneous, skewed turbulence. The authors begin by showing how the analytic solution to the Langevin equation for this case can be used to determine the relationship between the particle velocity moments and the properties of the skewed random force. They then present a numerical method that uses simple probability distribution functions to simulate the effect of the random force. The numerical solution is shown to be exact in the limit of infinitesimal time steps, and to be within acceptable error limits when practical time steps are used.

Ermak, D.L. [Lawrence Livermore National Lab., CA (United States); Nasstrom, J.S. [EG and G Energy Measurements Inc., Pleasanton, CA (United States)

1994-12-01

21

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

22

Modeling enzymatic reactions via chemical Langevin-Levy equation  

Microsoft Academic Search

Chemical Langevin Equation (CLE) describes a useful approximation in stochastic modeling of chemical reactions. CLE-based ?-leaping algoritm updates the quantities of every molecule in a reaction system with a period of ?, firing every reaction in the system so many times that the concentration of each molecule can be assumed to remain in the current concentration state. Substituting the Brownian

Mustafa A. Altinkaya; Ercan E. Kuruoglu

2012-01-01

23

An adaptive stepsize method for the chemical Langevin equation.  

PubMed

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes. PMID:22583271

Ilie, Silvana; Teslya, Alexandra

2012-05-14

24

Different diffusive regimes, generalized Langevin and diffusion equations  

NASA Astrophysics Data System (ADS)

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time.

Tateishi, A. A.; Lenzi, E. K.; da Silva, L. R.; Ribeiro, H. V.; Picoli, S., Jr.; Mendes, R. S.

2012-01-01

25

Different diffusive regimes, generalized Langevin and diffusion equations.  

PubMed

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time. PMID:22400552

Tateishi, A A; Lenzi, E K; da Silva, L R; Ribeiro, H V; Picoli, S; Mendes, R S

2012-01-27

26

Fluctuation-dissipation relation for nonlinear Langevin equations  

NASA Astrophysics Data System (ADS)

It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion.

Kumaran, V.

2011-04-01

27

Langevin Theory of Anomalous Brownian Motion Made Simple  

ERIC Educational Resources Information Center

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

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

2011-01-01

28

Coulomb blockade in a SET transistor and a single tunnel junction: Langevin equation approach  

NASA Astrophysics Data System (ADS)

We developed a formalism, based on a quantum Langevin equation, which allows one to describe charging effects in systems of normal tunnel junctions in the strong tunneling regime and to obtain simple analytical expressions for the /IV curves covering a wide range of temperatures and bias voltages. We fabricated and investigated experimentally several low resistive SET transistors. Good agreement between the experiment and the theory is observed. We also applied our theory to single tunnel junctions embedded in an external electromagnetic environment with a linear effective impedance ZS(?) and found a remarkably good agreement with recent experimental data for such systems.

Chouvaev, D.; Kuzmin, L.; Golubev, D.; Zaikin, A.

2000-07-01

29

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator  

NASA Astrophysics Data System (ADS)

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

Figueiredo Camargo, R.; Capelas de Oliveira, E.; Vaz, J.

2009-12-01

30

Extension to the quantum Langevin equation in the incoherent hopping regime  

SciTech Connect

An extension to the quantum Langevin equation is derived, that is valid in the incoherent hopping regime, and which allows one to incorporate quantum tunneling events. This is achieved by the inclusion of additional stochastic variables in the Langevin equation representing the tunneling events. A systematic derivation of this extension and of its regime of validity is presented. The study is motivated by efforts to determine the error in reading the state of a superconducting quantum bit.

Green, Andrew G. [School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY16 9XP (United Kingdom)

2006-04-01

31

From Langevin to generalized Langevin equations for the nonequilibrium Rouse model.  

PubMed

We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects. PMID:23496497

Maes, Christian; Thomas, Simi R

2013-02-28

32

The basis for, and some limitations of, the Langevin equation in atmospheric relative dispersion modelling  

NASA Astrophysics Data System (ADS)

The use of the Langevin equation to model turbulent dispersion, particularly in the atmosphere, is examined. The essential feature of the Langevin equation is that fluid particle accelerations are uncorrelated, a good approximation in high Reynolds number three-dimensional turbulence. It thus satisfies all the wellknown inertial range scaling laws. An important consequence of these laws is the equivalence of conditioned one-particle dispersion and relative dispersion. Relative dispersion on global scales is not well represented by the Langevin model, at least in part because motion on these scales is quasi-two-dimensional. On smaller scales, the well-known lack of an upper limit to the scale of turbulent kinetic energy throws doubt on the applicability of the Langevin equation in toto, although a three-dimensional inertial range stage of dispersion may be reasonably well represented. Use of the Langevin equation to directly model relative velocities results in a Gaussian probability density for particle separation. This is unrealistic and leads to an incorrect representation of concentration fluctuations. However, a relative dispersion model based on an appropriate combination of a pair of Langevin equations does realistically model concentration fluctuations.

Sawford, B. L.

33

Comparison of reflection boundary conditions for langevin equation modeling of convective boundary layer dispersion  

SciTech Connect

Lagrangian stochastic modeling based on the Langevin equation has been shown to be useful for simulating vertical dispersion of trace material in the convective boundary layer or CBL. This modeling approach can account for the effects of the long velocity correlation time scales, skewed vertical velocity distributions, and vertically inhomogeneous turbulent properties found in the CBL. It has been recognized that Langevin equation models assuming skewed but homogenous velocity statistics can capture the important aspects of diffusion from sources in the CBL, especially elevated sources. We compare three reflection boundary conditions using two different Langevin-equation-based numerical models for vertical dispersion in skewed, homogeneous turbulence. One model, described by Ermak and Nasstrom (1995) is based on a Langevin equation with a skewed random force and a linear deterministic force. The second model, used by Hurley and Physick (1993) is based on a Langevin equation with a Gaussian random force and a non-linear deterministic force. The reflection boundary conditions are all based on the approach described by Thompson and Montgomery (1994).

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

1997-04-01

34

Study of fission dynamics with the three-dimensional Langevin equations  

NASA Astrophysics Data System (ADS)

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei 210Po and 224Th formed in the fusion-fission reactions 4He + 206Pb , 16O + 208Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.

Eslamizadeh, H.

2011-11-01

35

Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics.  

PubMed

This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions. PMID:17994991

Yeomans-Reyna, L; Chávez-Rojo, M A; Ramírez-González, P E; Juárez-Maldonado, R; Chávez-Páez, M; Medina-Noyola, M

2007-10-22

36

Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics  

NASA Astrophysics Data System (ADS)

This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.

Yeomans-Reyna, L.; Chávez-Rojo, M. A.; Ramírez-González, P. E.; Juárez-Maldonado, R.; Chávez-Páez, M.; Medina-Noyola, M.

2007-10-01

37

Perturbative and non-perturbative aspects non-Abelian Boltzmann-Langevin equation  

NASA Astrophysics Data System (ADS)

We study the Boltzmann-Langevin equation which describes the dynamics of hot Yang-Mills fields with typical momenta of order of the magnetic screening scale g2T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/g)-1. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g2T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann-Langevin equation.

Bödeker, Dietrich

2002-12-01

38

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

PubMed

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. PMID:23267474

Ilie, Silvana

2012-12-21

39

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

40

Anomalous diffusion: exact solution of the generalized Langevin equation for harmonically bounded particle.  

PubMed

We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed. PMID:16486220

Viñales, A D; Despósito, M A

2006-01-12

41

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

42

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

43

Stochastic resonance in the fractional Langevin equation driven by multiplicative noise and periodically modulated noise  

NASA Astrophysics Data System (ADS)

First we study the time and frequency characteristics of fractional calculus, which reflect the memory and gain properties of fractional-order systems. Then, the fractional Langevin equation driven by multiplicative colored noise and periodically modulated noise is investigated in the over-damped case. Using the moment equation method, the exact analytical expression of the output amplitude is derived. Numerical results indicate that the output amplitude presents stochastic resonance driven by periodically modulated noise. For low frequency signal, the higher the system order is, the bigger the resonance intensity will be; while the result of high frequency signal is quite the contrary. This is consistent with the frequency characteristics of fractional calculus.

Yu, Tao; Zhang, Lu; Luo, Mao-Kang

2013-10-01

44

Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.  

PubMed

We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results. PMID:23829723

Brett, Tobias; Galla, Tobias

2013-06-18

45

Generalized Langevin theory for gas-solid processes: Continuum elastic treatment of surface lattice dynamics  

Microsoft Academic Search

Model studies of the systematics of elementary atom-solid energy exchange processes are presented. The studies are based on the generalized Langevin equation (GLE) classical trajectory method [S. A. Adelman and J. D. Doll, J. Chem. Phys. 64, 2375 (1976)] and on a full isotropic continuum elastic treatment of both bulk and surface solid atom velocity response functions ? (t). Within

Alain C. Diebold; S. A. Adelman; Chung Y. Mou

1979-01-01

46

Generalized Langevin theory for gas–solid processes: Continuum elastic treatment of surface lattice dynamics  

Microsoft Academic Search

Model studies of the systematics of elementary atom–solid energy exchange processes are presented. The studies are based on the generalized Langevin equation (GLE) classical trajectory method [S. A. Adelman and J. D. Doll, J. Chem. Phys. 64, 2375 (1976)] and on a full isotropic continuum elastic treatment of both bulk and surface solid atom velocity response functions ? (t). Within

Alain C. Diebold; S. A. Adelman; Chung Y. Mou

1979-01-01

47

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

48

Laws of large numbers and langevin approximations for stochastic neural field equations.  

PubMed

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

Riedler, Martin G; Buckwar, Evelyn

2013-01-23

49

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

50

Higher-order Time Integration of Coulomb Collisions in a Plasma Using Langevin Equations  

NASA Astrophysics Data System (ADS)

We examine the extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler O(?t^1/2)-order time integration to the next higher [Milstein-O(?t)] order. In one common Langevin-equation approach, the angular scattering step is treated with a combination of near-Cartesian stochastic velocity-direction kicks, in a unit-vector frame that is rotated so that at the beginning of each timestep, one axis is aligned with the velocity direction. We find that in such schemes, the angular component of the collisional scattering cannot be extended beyond the Euler order. Instead, the extension to higher order proceeds through a formulation of the angular scattering directly as stochastic differential equations in the two fixed-frame spherical coordinates. Such an algorithm involves generation of random numbers that sample the joint distribution function of both the (Gaussian) random coordinate displacements and of double stochastic ``area integrals.'' The sampling of the area integrals can be made using simple but highly accurate approximations to results on ``Levy-area'' processes. Implications for particle simulation of Coulomb collisions in plasmas are discussed.

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

2011-11-01

51

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

52

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

NASA Astrophysics Data System (ADS)

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

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

2011-08-01

53

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

54

Generalized Langevin equation with a three parameter Mittag-Leffler noise  

NASA Astrophysics Data System (ADS)

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the Laplace transform method. The asymptotic behavior of the particle in the short and long time limits are found by using the Tauberian theorems. It is shown that for large times the particle motion is subdiffusive for ?-1

Sandev, Trifce; Tomovski, Živorad; Dubbeldam, Johan L. A.

2011-10-01

55

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

56

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

NASA Astrophysics Data System (ADS)

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

Kantorovich, L.

2008-09-01

57

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

PubMed Central

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

2010-01-01

58

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

59

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

60

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

PubMed

The temporal behavior of the mean-square displacement and the velocity autocorrelation function of a particle subjected to a periodic force in a harmonic potential well is investigated for viscoelastic media using the generalized Langevin equation. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise, by an internal Mittag-Leffler noise with a finite memory time, and by an additive external noise. It is shown that the presence of a multiplicative noise has a profound effect on the behavior of the autocorrelation functions. Particularly, for correlation functions the model predicts a crossover between two different asymptotic power-law regimes. Moreover, a dependence of the correlation function on the frequency of the external periodic forcing occurs that gives a simple criterion to discern the multiplicative noise in future experiments. It is established that additive external and internal noises cause qualitatively different dependences of the autocorrelation functions on the external forcing and also on the time lag. The influence of the memory time of the internal noise on the dynamics of the system is also discussed. PMID:21797326

Mankin, R; Laas, K; Sauga, A

2011-06-20

61

Fisher information metric for the Langevin equation and least informative models of continuous stochastic dynamics  

NASA Astrophysics Data System (ADS)

The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology.

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

2013-09-01

62

Temperature-driven irreversible generalized Langevin equation can capture the nonequilibrium dynamics of two dissipated coupled oscillators  

NASA Astrophysics Data System (ADS)

Kawai and Komatsuzaki [J. Chem. Phys.10.1063/1.3561065 134, 114523 (2011)] recently derived the nonequilibrium generalized Langevin equation (GLE) for a nonstationary system using the projection operator technique. In the limit when the environment is slowly changing (that is, a quasi-equilibrium bath), it should reduce to the irreversible GLE approach (iGLE) [J. Chem. Phys.10.1063/1.480160 111, 7701 (1999)]. Kawai and Komatsuzaki, however, found that the driven harmonic oscillator, an example of a nonequilibrium system does not obey the iGLE presumably because it did not quite satisfy the limiting conditions of the latter. Notwithstanding the lack of a massive quasi-equilibrium bath (one of the conditions under which the iGLE had been derived earlier), we found that the temperature-driven iGLE (T-iGLE) [J. Chem. Phys.10.1063/1.2743032 126, 244506 (2007)] can reproduce the nonequilibrium dynamics of a driven dissipated pair of harmonic oscillators. It requires a choice of the function representing the coupling between the oscillator coordinate and the bath and shows that the T-iGLE representation is consistent with the projection operator formalism if only dominant bath modes are taken into account. Moreover, we also show that the more readily applicable phenomenological iGLE model is recoverable from the Kawai and Komatsuzaki model beyond the adiabatic limit used in the original T-iGLE theory.

Popov, Alexander V.; Hernandez, Rigoberto

2013-09-01

63

Automatic seismic wave arrival detection and picking with stationary analysis: Application of the KM2O-Langevin equations  

NASA Astrophysics Data System (ADS)

An automatic detection and a precise picking of the arrival times of seismic waves using digital seismograms are important for earthquake early detection systems. Here we suggest a new method for detecting and picking Pand S-wave signals automatically. Compared to methods currently in use, our method requires fewer assumption with properties of the data time series. We divide a record into intervals of equal lengths and check the "local and weak stationarity" of each interval using the theory of the KM2O-Langevin equations. The intervals are stationary when these include only background noise, but the stationarity breaks abruptly when a seismic signal arrives and the intervals include both the background noise and the P-wave. This break of stationarity makes us possible to detect P-wave arrival. We expand the method for picking of S-waves. We applied our method to earthquake data from Hi-net Japan, and 90% of P-wave auto-picks were found to be within 0.1 s of the corresponding manual picks, and 70% of S-wave picks were within 0.1 s of the manual picks. This means that our method is accurate enough to use as a part of the seismic early detection system.

Nakamula, S.; Takeo, M.; Okabe, Y.; Matsuura, M.

2007-06-01

64

Study of fission dynamics of 215Fr and 213Fr produced in fusion reactions with three-dimensional Langevin equations  

NASA Astrophysics Data System (ADS)

A stochastic approach that treats fission dynamics on the basis of three-dimensional Langevin equations was used to calculate the average pre-scission neutron multiplicities, fission probabilities, mass and energy distribution of fission fragments, and the dependences of the multiplicities of pre-scission neutrons on the masses of fission fragments and their kinetic energies for compound nuclei 213Fr and 215Fr. In these calculations, dissipation was generated through the chaos weighted wall and window friction formula. Comparison of the theoretical results with the experimental data showed that three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula make it possible to satisfactorily reproduce the experimental data.

Eslamizadeh, H.

2013-09-01

65

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

66

Exact Solutions and Monte Carlo Simulations of Self-Consistent Langevin Equations:. a Case Study for the Collective Dynamics of STOCK Prices  

NASA Astrophysics Data System (ADS)

In a case study, the exact solution of a self-consistent Langevin equation associated with a nonlinear Fokker-Planck equation is derived. On the basis of this solution, a Monte Carlo simulation scheme for the Langevin equation is proposed. The case study addresses a generalized geometric Brownian walk that describes the collective dynamics of a large set of interacting stocks. Numerical results obtained from the Monte Carlo simulation are compared with analytical solutions derived from the nonlinear Fokker-Planck equation. The power of the Monte Carlo simulation is demonstrated for situations in which analytical solutions are not available.

Frank, T. D.

67

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

Microsoft Academic Search

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

Patrice Koehl; Marc Delarue

2010-01-01

68

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

NASA Astrophysics Data System (ADS)

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

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

2013-03-01

69

Stochastic Description of Traffic Breakdown: Langevin Approach  

Microsoft Academic Search

From probabilistic point of view we investigate a quite classical dynamical system given by stochastic differential equations, i. e. ordinary differential\\u000a equations driven by multiplicative noise. Based on this Langevin approach the probability density distributions of vehicular\\u000a velocities as well as headway distances are calculated and discussed.\\u000a \\u000a Our work is a continuation of a stochastic theory of freeway traffic based

R. Mahnke; J. Kaupužs; J. Tolmacheva

70

Exact exponential function solution of the generalized Langevin equation for autocorrelation functions of many-body systems.  

PubMed

We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected. PMID:22463264

Barocchi, Fabrizio; Bafile, Ubaldo; Sampoli, Marco

2012-02-17

71

Notes on the Langevin model for turbulent diffusion of ``marked`` particles  

SciTech Connect

Three models for scalar diffusion in turbulent flow (eddy diffusivity, random displacement, and on the Langevin equation) are briefly described. These models random velocity increment based Fokker-Planck equation is introduced as are then examined in more detail in the reverse order. The Fokker-Planck equation is the Eulerian equivalent of the Lagrangian Langevin equation, and the derivation of e outlined. The procedure for obtaining the deterministic and stochastic components of the Langevin equation from Kolmogorov`s 1941 inertial range theory and the Fokker-Planck equation is described. it is noted that a unique form of the Langevin equation can be determined for diffusion in one dimension but not in two or three. The Langevin equation for vertical diffusion in the non-Gaussian convective boundary layer is presented and successively simplified for Gaussian inhomogeneous turbulence and Gaussian homogeneous turbulence in turn. The Langevin equation for Gaussian inhomogeneous turbulence is mathematically transformed into the random displacement model. It is shown how the Fokker-Planck equation for the random displacement model is identical in form to the partial differential equation for the eddy diffusivity model. It is noted that the Langevin model is applicable in two cases in which the other two are not valid: (1) very close in time and distance to the point of scalar release and (2) the non-Gaussian convective boundary layer. The two- and three-dimensional cases are considered in Part III.

Rodean, H.C.

1994-01-26

72

Langevin model for reactive transport in porous media  

NASA Astrophysics Data System (ADS)

Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)10.1103/PhysRevLett.101.044502]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing.

Tartakovsky, Alexandre M.

2010-08-01

73

Langevin model for reactive transport in porous media.  

PubMed

Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing. PMID:20866900

Tartakovsky, Alexandre M

2010-08-05

74

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

2008-07-22

75

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

SciTech Connect

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

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

2009-12-15

76

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: a one-dimensional generalized Langevin equation treatment.  

PubMed

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t) identical with x(0)x(t). We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)]. PMID:16351313

Debnath, Pallavi; Min, Wei; Xie, X Sunney; Cherayil, Binny J

2005-11-22

77

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

78

Anomaly equations and intersection theory  

NASA Astrophysics Data System (ADS)

Six-dimensional supergravity theories with mathcal{N} = (1, 0) supersymmetry must satisfy anomaly equations. These equations come from demanding the cancellation of gravitational, gauge and mixed anomalies. The anomaly equations have implications for the geometrical data of Calabi-Yau threefolds, since F-theory compactified on an elliptically fibered Calabi-Yau threefold with a section generates a consistent six-dimensional mathcal{N} = (1, 0) supergravity theory. In this paper, we show that the anomaly equations can be summarized by three intersection theory identities. In the process we also identify the geometric counterpart of the anomaly coefficients — in particular, those of the abelian gauge groups — that govern the low-energy dynamics of the theory. We discuss the results in the context of investigating string universality in six dimensions.

Park, Daniel S.

2012-01-01

79

Langevin's `Twin Paradox' paper revisited  

Microsoft Academic Search

An in-depth and mathematically-detailed analysis of Langevin's popular 1911\\u000aarticle on the special theory of relativity is presented. For the reader's\\u000aconvenience, English translations of large parts of the original French text\\u000aare given. The self-contradictory nature of many of Langevin's assertions is\\u000apointed out. Of special interest is the analysis of the exchange of light\\u000asignals between the travelling

J. H. Field

2008-01-01

80

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

PubMed

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. PMID:12188698

Kim, Joohyun; Keyes, T

2002-06-12

81

Balancing of partially-observed stochastic differential equations  

Microsoft Academic Search

We study Balanced Truncation for stochastic dif- ferential equations. In doing so, we adopt ideas from large deviations theory and discuss notions of controllability and obervability for dissipative Hamiltonian systems with degener- ate noise term, also known as Langevin equations. For partially- observed Langevin equations, we illustrate model reduction by balanced truncation with an example from molecular dynamics and discuss

Carsten Hartmann; Christof Schütte

2008-01-01

82

Generalized Langevin theory for many-body problems in chemical dynamics: Gas-surface collisions, vibrational energy relaxation in solids, and recombination reactions in liquids  

NASA Astrophysics Data System (ADS)

Model classical trajectory simulations of gas-solid inelastic collisions, vibrational energy relaxation of a diatom in a solid, and atomic recombination reactions in a liquid are presented. These simulations are first applications of the molecular timescale generalized Langevin equation (MTGLE) theory [S. A. Adelman, Adv, Chem. Phys. 44, 143 (1980)] for condensed phase energy transfer and chemical reaction processes. The main conclusions of these model studies are as follows: (i) The MTGLE theory often provides computationally practical methods for condensed phase chemical problems. These methods are applicable with equal ease to both solid and liquid state processes. (ii) The equivalent harmonic chain heatbath modeling for reducing many-body chemical problems to effective few-body problems often converges rapidly. This rapid convergence is found for both short (subpicosecond) timescale processes (gas-solid collisions) and long (nanosecond) timescale processes (vibrational energy relaxation). (iii) The simplest harmonic chain model (heatbath replaced by a single fictitious atom) is often found to yield a qualitatively correct description of heatbath influence on both solid and liquid state processes. (iv) The MTGLE parameters ?e0 (chemical system Einstein frequency) and ?2c1 (chemical system/heatbath coupling constant) are the quantities which often determine the gross magnitude of heatbath influence on condensed phase chemical processes. For both solid and liquid state processes ?e0 determines the effective vibrational frequencies (normal modes) of the chemical system and ?2c1 determines the gross efficiency of chemical system/heatbath energy transfer. For liquid state processes ?e0 also determines the frequency of oscillations in the solvent cage, and ?2c1 also determines rigidity of the solvent cage. (?2c1=0 means the cage is perfectly rigid).

Brooks, C. L.; Berkowitz, M.; Adelman, S. A.

1980-11-01

83

Relativistic Langevin dynamics in expanding media  

NASA Astrophysics Data System (ADS)

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.

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

2013-09-01

84

Modeling Chaotic Evolution with Nonlinear Langevin Dynamics  

NASA Astrophysics Data System (ADS)

In order to statistically describe chaotic time series numerically or experimentally observed, we propose a new approach to statistically model the observed data. This is carried out by first introducing temporally coarse-grained quantities. Then we derive a set of nonlinear Langevin equations of motion for these quantities by employing the projection-operator method developed in nonequilibrium statistical mechanics to treat systems near thermal equilibrium. This set of equations simulates the observed time series. We apply the present approach to a time series generated by the Rössler model of chaos. Comparing power spectra from Langevin equations of motion with those from the Rössler model, we find that the modeled Langevin dynamics simulates the original observed time series quite well.

Tao, T.; Fujisaka, H.

2000-11-01

85

The Boltzmann equation from quantum field theory  

NASA Astrophysics Data System (ADS)

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.

Drewes, Marco; Mendizabal, Sebastián; Weniger, Christoph

2013-01-01

86

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

87

Localised distributions and criteria for correctness in complex Langevin dynamics  

NASA Astrophysics Data System (ADS)

Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker-Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected.

Aarts, Gert; Giudice, Pietro; Seiler, Erhard

2013-10-01

88

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

89

Stochastic Langevin Model for Flow and Transport in Porous Media  

SciTech Connect

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

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

2008-07-25

90

Deducibility Constraints, Equational Theory and Electronic Money  

Microsoft Academic Search

The starting point of this work is a case study (from France Télécom) of an electronic purse protocol. The goal was to prove\\u000a that the protocol is secure or that there is an attack. Modeling the protocol requires algebraic properties of a fragment\\u000a of arithmetic, typically containing modular exponentiation. The usual equational theories described in papers on security\\u000a protocols are

Sergiu Bursuc; Hubert Comon-lundh; Stéphanie Delaune

2007-01-01

91

Electronic Journal of Qualitative Theory of Differential Equations  

NSDL National Science Digital Library

Created by the Bolyai Institute at the University of Szeged, the "Electronic Journal of Qualitative Theory of Differential Equations" publishes peer-reviewed articles related to "the qualitative theory (stability, periodicity, soundness, etc.) of differential equations (ODE's, PDE's, integral equations, functional differential equations, etc.) and their applications." Proceedings of conferences are also available in the journal.

Burton, T. A. (Theodore Allen), 1935-; Hatvani, L.; Makay, G.; Vajda, R.

2009-03-26

92

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

93

Scattering theory of close-coupling equations  

SciTech Connect

The scattering theory implied by the close-coupling equations is studied using a Lippmann-Schwinger formalism. The new results derived can be summarized as follows: An alternative form of the equations that ensures there are no spurious solutions in the scattering region can be constructed, and moreover there is an infinite number of such forms. The Neumann- (perturbation-) series expansion diverges in general for most energies for both the old and new forms. The Born limit nevertheless holds and can be recovered by appropriate rearrangement of the Neumann series. The original integral formulation may give convergent scattering amplitudes despite the lack of uniqueness of the solutions. The conditions under which this happens are examined.

Stelbovics, A.T. (School of Mathematical, Murdoch University, Perth, Western Australia, Australia 6150 (Australia) Physical Sciences, Murdoch University, Perth, Western Australia, Australia 6150 (Australia))

1990-03-01

94

Fundamental equations for species-area theory  

PubMed Central

Species-area theory is an important concept in ecology. However, debates still surround the species-area relationship (SAR) or endemics-area relationship (EAR) and their relations to expected extinction rates. In this paper, I introduce the concept of overlap-area relationship (OAR) to link SAR and EAR. Two fundamental equations are derived from the relationship between the area and species number in a limited whole area A: 1) the sum of species number in area a and species number, here defined as endemics, in area A ? a is the total species number in area A; 2) the number of species common to both areas a and A ? a (overlapping species) equals the species number in area a minus the endemics number in area a. Thus, we should carefully consider the total area on which EAR depends, when estimating extinction rate based on SAR.

Pan, Xubin

2013-01-01

95

Twistor Theory and the Einstein Equations  

NASA Astrophysics Data System (ADS)

R. Penrose (in Advances in twistor theory, pp. 168-176, and in Cosmology and gravitation; Nato advanced study institute series, pp. 287-316 (1980). New York: Plenum Press) has argued that the goal of twistor theory with regard to the vacuum Einstein equations ought to consist of some kind of unification of twistor-theoretic descriptions of anti-self-dual (a.s.d.) and self-dual (s.d.) space-times. S.d. space-times currently possess a description only in terms of dual twistor space, however, rather than twistor space. In this paper, suggestions due to Penrose for providing a purely twistor space description of s.d. space-times are investigated. It is shown how the points of certain s.d. space-times define mappings on twistor space and the geometry of these mappings is studied. The families of mappings for two particular s.d. space-times are presented explicitly.

Law, P. R.

1985-05-01

96

Intermediate dynamics between Newton and Langevin.  

PubMed

A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlation between the system degrees of freedom and the heat-bath degrees of freedom for the asymptotic long-time behavior of the system dynamics. As two test beds we investigate (i) the anomalous energy relaxation of free non-Markovian Brownian motion that is driven by a harmonic velocity noise and (ii) the phenomenon of a net directed acceleration in noise-induced transport of an inertial rocking Brownian motor. PMID:17280042

Bao, Jing-Dong; Zhuo, Yi-Zhong; Oliveira, Fernando A; Hänggi, Peter

2006-12-20

97

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

98

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

99

Data driven Langevin modeling of biomolecular dynamics.  

PubMed

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

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

2013-05-28

100

Combining Equational Tree Automata over AC and ACI Theories  

Microsoft Academic Search

In this paper, we study combining equational tree automata in two dierent senses: (1) whether decidability results about equational tree automata over disjoint theoriesE1 andE2 imply similar decidability results in the combined theory E1(E2; (2) checking emptiness of a lan- guage obtained from the Boolean combination of regular equational tree languages. We present a negative result for the first problem.

Joe Hendrix; Hitoshi Ohsaki

2008-01-01

101

On Pokrovskii's anisotropic gap equations in superconductivity theory  

NASA Astrophysics Data System (ADS)

An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.

Yang, Yisong

2003-11-01

102

Filtration theory using computer simulations  

SciTech Connect

We have used commercially available fluid dynamics codes based on Navier-Stokes theory and the Langevin particle equation of motion to compute the particle capture efficiency and pressure drop through selected two- and three- dimensional fiber arrays. The approach we used was to first compute the air velocity vector field throughout a defined region containing the fiber matrix. The particle capture in the fiber matrix is then computed by superimposing the Langevin particle equation of motion over the flow velocity field. Using the Langevin equation combines the particle Brownian motion, inertia and interception mechanisms in a single equation. In contrast, most previous investigations treat the different capture mechanisms separately. We have computed the particle capture efficiency and the pressure drop through one, 2-D and two, 3-D fiber matrix elements.

Bergman, W.; Corey, I.

1997-01-01

103

Behavioral Momentum Theory: Equations and Applications  

ERIC Educational Resources Information Center

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

Nevin, John A.; Shahan, Timothy A.

2011-01-01

104

On the equation of state in effective quark theories  

SciTech Connect

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

Bentz, Wolfgang; Lawley, Sarah; Thomas, Anthony

2008-09-01

105

Electron transfer dynamics: Zusman equation versus exact theory  

SciTech Connect

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

Shi Qiang; Chen Liping; Nan Guangjun [Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China); Xu Ruixue [Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China); Yan Yijing [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong)

2009-04-28

106

Interlaced branching equations in the theory of non-linear equations  

SciTech Connect

Necessary conditions for inheriting the interlacing property of a non-linear equation by the branching system are obtained. The case when the pair of linear operators interlacing the equation consists of projections or parametric families of linear operators is considered. New conditions are presented which allow one to reduce the number of the equations in the branching system and extend the range of applications of the method of successive approximations in the branching theory of non-linear equations. Solutions depending on free parameters belonging to certain hypersurfaces in Euclidean spaces are considered. The results obtained add to and extend earlier results on the applications of group analysis in branching theory.

Sidorov, N A; Abdullin, V R [Institute of Systems Dynamics and Control Theory Siberian Branch of the Russian Academy of Sciences, Irkutsk (Russian Federation)

2001-08-31

107

The Lamé equation in shell membrane theory  

NASA Astrophysics Data System (ADS)

A classical nonlinear shell membrane system has recently been demonstrated to have underlying integrable structure. Here, a wide class of corresponding parallel membranes is shown to be generated via a Schrödinger equation of Lamé type. This class is characterized by the existence of a multiplicity of stress distributions for a given membrane geometry. A variety of viable membrane geometries such as generalized Dupin cyclides are constructed explicitly together with the associated one-parameter families of stress resultants. A Lax pair which encapsulates both the Gauss-Mainardi-Codazzi and constrained equilibrium equations is also recorded.

Schief, W. K.; Szereszewski, A.; Rogers, C.

2007-07-01

108

The Lamé equation in shell membrane theory  

Microsoft Academic Search

A classical nonlinear shell membrane system has recently been demonstrated to have underlying integrable structure. Here, a wide class of corresponding parallel membranes is shown to be generated via a Schrödinger equation of Lamé type. This class is characterized by the existence of a multiplicity of stress distributions for a given membrane geometry. A variety of viable membrane geometries such

W. K. Schief; A. Szereszewski; C. Rogers

2007-01-01

109

Advancing operations management theory using exploratory structural equation modelling techniques  

Microsoft Academic Search

The structural equation modelling (SEM) technique has been touted as a useful tool for tightening links between theoretical and empirical operations management (OM) research. Despite SEM's increasing prominence in the field, leading scholars continue to call for a deeper infusion of theory into empirical OM research. To strengthen ties between theory and analysis in OM research, this study evaluates previous

Nicholas Roberts; Jason Bennett Thatcher; Varun Grover

2010-01-01

110

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

111

A Langevin approach to stock market fluctuations and crashes  

Microsoft Academic Search

:   We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on\\u000a an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize\\u000a the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an “up-down”\\u000a symmetry breaking term

Jean-Philippe Bouchaud; Rama Cont

1998-01-01

112

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

113

Measurement theory and stochastic differential equations in quantum mechanics  

NASA Astrophysics Data System (ADS)

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.

Barchielli, Alberto

1986-09-01

114

Wick Equation, the Infinite-Momentum Frame, and Perturbation Theory  

Microsoft Academic Search

The eigenvalues of the Wick equation in the weak-binding limit are found in perturbation theory employing two different approaches: (1) a covariant approach using an integral representation for the Bethe-Salpeter wave function and (2) quantization in the infinite-momentum frame using the technique of Kogut and Soper. The eigenvalues agree to order alpha3lnalpha.

G. Feldman; T. Fulton; J. Townsend

1973-01-01

115

Modern Integral Equation Techniques for Quantum Reactive Scattering Theory  

Microsoft Academic Search

Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H\\/D + H_2 to H _2\\/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the

Scott Michael Auerbach

1993-01-01

116

Basic equations, theory and principle of computational stock market (III)—basic theories  

Microsoft Academic Search

By basic equations, two basic theories are presented: 1. Theory of stock' s value ?* (t) = ?*(0) exp(ar*2 t); 2. Theory of conservation of stock' s energy. Let stock' s energy ? be defined as a quadratic function of stock' s price\\u000a ? and its derivative\\u000a $$\\\\dot v,\\\\phi = {\\\\rm A}v^2 + Bv\\\\dot v + C\\\\dot v^2 + Dv$$

Yun Tian-quan

2000-01-01

117

Coherent structures theory for the generalized Kuramoto-Sivashinsky equation  

NASA Astrophysics Data System (ADS)

We examine coherent structures interaction and formation of bound states in active-dispersive-dissipative nonlinear media. A prototype for such media is a simple weakly nonlinear model, the generalized Kuramoto-Sivashinsky (gKS) equation, that retains the fundamental mechanisms of any nonlinear process involving wave evolution, namely, a dominant nonlinearity, instability, stability and dispersion. We develop a weak interaction theory for the solitary pulses of the gKS equation by representing the solution as a superposition of the pulses and an overlap function. We derive a linearized equation for the overlap function in the vicinity of each pulse and project the dynamics of this function onto the discrete part of the spectrum of the linearized interaction operator. This leads to a coupled system of ordinary differential equations describing the evolution of the locations of the pulses. By analyzing this system, we prove a criterion for the existence of a countable infinite or finite number of bound states, depending on the strength of the dispersive term in the equation. The theoretical findings are corroborated by computations of the full equation.

Tseluiko, D.; Saprykin, S.; Kalliadasis, S.

2010-03-01

118

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

SciTech Connect

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

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

2009-05-15

119

Fluctuation theory of starlight polarization  

NASA Astrophysics Data System (ADS)

The average and the variance of absolute polarization of starlight are calculated as a function of distance based on the fluctuation theory of Langevin's scheme. The computed curves from the theory agree with the sample observational data. It estimates a correlation length of 225 pc and a fluctuating angle of 22.5 deg for the fluctuation of interstellar magnetic field for the observation direction within an l(II) range of 60-90 deg around the galactic equator.

Nee, S. F.

1980-04-01

120

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

121

Self-guided Langevin dynamics simulation method  

NASA Astrophysics Data System (ADS)

This work presents a self-guided Langevin dynamics simulation method. The guiding force is calculated as a local average of the friction forces during a self-guided Langevin dynamics simulation. Three parameters, the local average time, tL, the guiding factor, ?, and the collision frequency, ?, control a self-guided Langevin dynamics simulation. It is demonstrated through three model systems that this simulation method has an enhanced conformational search ability while has little alteration in conformational distribution when the guiding factor is chosen within the limit of ??<1 ps -1. This method is well suited for simulation studies where extensive conformational searching is required.

Wu, Xiongwu; Brooks, Bernard R.

2003-11-01

122

Comparison of Langevin and Markov channel noise models for neuronal signal generation  

NASA Astrophysics Data System (ADS)

The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either Na+ and K+ , or only K+ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas, and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and nonspiking membranes. Even with increasing numbers of channels, the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels.

Sengupta, B.; Laughlin, S. B.; Niven, J. E.

2010-01-01

123

Multireference equation-of-motion coupled cluster theory.  

PubMed

A generalization of the equation-of-motion coupled cluster theory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, H? = e(-T) H?e(T), in a compact multireference configuration interaction space, which involves configurations with at most single virtual orbital substitution. The latter effects are thus state-specific and this allows us to obtain multiple electronic states in the spirit of the equation-of-motion coupled cluster approach. A crucial aspect of this formulation is the use of the amplitudes of the generalized normal-ordered transformed Hamiltonian H? as the residual equations for determining the internally contracted cluster amplitudes without any projection onto the excited configurations. These residuals have been termed as the many-body residuals. These equations are formally non-singular and thus allow us to solve for all amplitudes without discarding any, in contrast to other internally contracted approaches. This is desirable to ensure transferability of dynamical correlation from the parent state to the target states. Preliminary results involving the low-lying electronic states of C(2), O(2), and the excitation spectra of three transition metal atoms, e.g., Fe, Cr, and Mn, including hundreds of excited states, illustrate the potential of our approach. PMID:23205981

Datta, Dipayan; Nooijen, Marcel

2012-11-28

124

Langevin thermostat for rigid body dynamics.  

PubMed

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

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

2009-06-21

125

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

126

Two-temperature Langevin dynamics in a parabolic potential.  

PubMed

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the stationary regime the system is described by a nontrivial particle position distribution, P(x,y), which we determine explicitly. We show that this distribution corresponds to a nonequilibrium stationary state, characterized by the presence of space-dependent particle currents which exhibit a nonzero rotor. Theoretical results are confirmed by the numerical simulations. PMID:23848650

Dotsenko, Victor; Macio?ek, Anna; Vasilyev, Oleg; Oshanin, Gleb

2013-06-19

127

Solving Multiscale Polymer Field Theory Simulations with Lattice Boltzmann Equation  

NASA Astrophysics Data System (ADS)

A new Lattice Boltzmann (LB) approach is introduced to solve for the modified diffusion equations in polymer field theory. This method bridges two desired properties from different numerical techniques, namely: (i) it is robust and stable as the pseudo-spectral method, and (ii) it is flexible and allows for grid refinement and arbitrary boundary conditions. While the LB method is not as accurate as the pseudo-spectral method, full self-consistent field theoretic (SCFT) simulations of block copolymers on graphoepitaxial templates yield indistinguishable results from pseudo-spectral calculations. Furthermore, we were able to achieve speedups of about 100x compared to single CPU core implementations by using graphics processing units (GPUs). We expect this method to be very useful in truly multi-scale studies where small length scale details have to be resolved, such as in strongly segregating block copolymer blends, nanoparticle-polymer interfaces, or polymer wetting phenomena.

Chen, Hsieh; Kim, Yongjoo; Alexander-Katz, Alfredo

2013-03-01

128

Mean-field theories of random advection  

NASA Astrophysics Data System (ADS)

Two mean-field theories of random advection are formulated for the purpose of predicting the probability density function (PDF) of a randomly advected passive scalar, subject to an imposed mean scalar gradient. One theory is a generalization of the mean-field analysis used by Holzer and Pumir [Phys. Rev. E 47, 202 (1993)] to derive the phenomenological model of Pumir, Shraiman, and Siggia [Phys. Rev. Lett. 66, 2984 (1991)] governing PDF shape in the imposed-gradient configuration. The other theory involves a Langevin equation representing concentration time history within a fluid element. Predicted PDF shapes are compared to results of advection simulations by Holzer and Pumir. Both theories reproduce gross trends, but the Langevin theory provides the better representation of detailed features of the PDF's. An analogy is noted between the two theories and two widely used engineering models of turbulent mixing.

Kerstein, Alan R.; McMurtry, Patrick A.

1994-01-01

129

The equation of deviation in a conformally invariant theory of gravitation and electromagnetism  

Microsoft Academic Search

The equation of deviation is derived for a conformally invariant theory of gravitation and electromagnetism in which scale is generated by a topological constraint. Compared with its counterpart in the Einstein-Maxwell theory, the equation contains some extra terms proportional to the electromagnetic potential indicating the existence of linear and nonlinear Bohm-Aharonov effects. These are present also in the related theories

Y. Q. Cai; G. Papini

1988-01-01

130

Applications of the Characteristic Theory to the Madelung-de Broglie-Bohm System of Partial Differential Equations: The Guiding Equation as the Characteristic Velocity  

Microsoft Academic Search

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

Javier González; Xavier Giménez; Josep Maria Bofill

131

Electron transfer dynamics: Zusman equation versus exact theory  

Microsoft Academic Search

The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature

Qiang Shi; Liping Chen; Guangjun Nan; Ruixue Xu; Yijing Yan

2009-01-01

132

Complex Langevin simulation of chiral symmetry restoration at finite baryonic density  

NASA Astrophysics Data System (ADS)

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

Ilgenfritz, Ernst-Michael

1986-12-01

133

Dynamics of the Langevin model subjected to colored noise: Functional-integral method  

Microsoft Academic Search

We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is

Hideo Hasegawa

2008-01-01

134

Bifurcations in Boltzmann-Langevin one body dynamics for fermionic systems  

NASA Astrophysics Data System (ADS)

We investigate the occurrence of bifurcations in the dynamical trajectories depicting central nuclear collisions at Fermi energies. The quantitative description of the reaction dynamics is obtained within a new transport model, based on the solution of the Boltzmann-Langevin equation in three dimensions, with a broad applicability for dissipative fermionic dynamics.

Napolitani, P.; Colonna, M.

2013-10-01

135

Theory of submanifolds, associativity equations in 2D topological quantum field theories, and Frobenius manifolds  

NASA Astrophysics Data System (ADS)

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of flat torsionless potential submanifolds. We show that all flat torsionless potential submanifolds in pseudo-Euclidean spaces bear natural structures of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set of the Weingarten operators of the submanifolds). We prove that each N-dimensional Frobenius manifold can be locally represented as a flat torsionless potential submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction, this submanifold is uniquely determined up to motions. Moreover, we consider a nonlinear system that is a natural generalization of the associativity equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this system is integrable by the inverse scattering method.

Mokhov, O. I.

2007-08-01

136

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

137

Integral equation theory for the structure of DNA solutions  

NASA Astrophysics Data System (ADS)

The static structure of solutions of DNA fragments is investigated using integral equation theory. The solution is modeled as a four-component system with DNA molecules, bound counterions, free counterions, and coions, all of which are treated explicitly. Each DNA fragment is modeled as a shish-kebab chain with three kinds of sites, i.e., charged sites, neutralized (protonated) sites, and sites with bound counterions. The partial structure factors are obtained using a generalization of the polymer reference interaction model. The undetermined parameters in the model, namely the fraction of protonated and bound sites, are obtained by fitting theoretical predictions for the polymer-polymer and polymer-counterions structure factors to experimental data. It is found that a large majority of counterions is localized near the DNA molecules due to counterions binding and protonation. The bound counterions make a dominant contribution to the total scattering from counterion species. The best fit is obtained when each DNA molecule contains about 22% protonated sites and 53% counterion occupied sites, i.e., the effective DNA charge fraction is about 0.25. This DNA charge fraction is consistent with electrospray ionization and DNA titration experiments.

Shew, Chwen-Yang; Yethiraj, Arun

2002-03-01

138

Ordinary differential equations, transport theory and Sobolev spaces  

Microsoft Academic Search

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

R. J. DiPerna; P. L. Lions

1989-01-01

139

Stability theory of the orbit-averaged Boltzmann equation  

Microsoft Academic Search

Consideration is given to the relation between the thermal runaway predicted in models of the collisional evolution of stellar systems and the onset of linear instability in equilibrium solutions of the Boltzmann equation obtained by averaging over the stellar orbits. The orbit-averaged Boltzmann equation is obtained by instantaneously averaging, over orbits of fixed energy and angular momentum, the Boltzmann equation

J. R. Ipser; H. E. Kandrup

1980-01-01

140

On boundary layer and interior equations for higher-order theories of plates  

NASA Astrophysics Data System (ADS)

Several shear-deformation plate theories of symmetric laminated plates with transversely isotropic layers are reviewed and the governing equations of these theories are then recast into two equations: one for the interior of the domain and the other for the edge-zone or the boundary layer. For the first time it is shown that the governing equations of the third-order shear-deformation theory of Reddy result in a sixth-order interior equation and a second-order edge-zone equation. It is also demonstrated that in bending and stability problems, and under certain conditions in dynamic problems, the contribution of the edge-zone equation is identically zero for a simply-supported plate. The pure-shear frequencies of a plate according to different theories are determined and compared.

Nosier, Asghar; Reddy, J. N.

141

Diffusion in the special theory of relativity.  

PubMed

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion. PMID:20364950

Herrmann, Joachim

2009-11-11

142

Open problems in the theory of the Navier-Stokes equations for viscous incompressible flow  

Microsoft Academic Search

The Navier-Stokes equations occupy a central position in the study of nonlinear partial differential equations, dynamical systems, and modem scientific computation, as well as classical fluid dynamics. Because of the complexity and variety of fluid dynamical phenomena, and the simplicity and exactitude of the governing equations, a very special depth and beauty is expected in the mathematical theory. Thus, it

JOHN G. HEYWOOD

143

Theory of the interplay of luminescence and vibrational relaxation: A master-equation approach  

Microsoft Academic Search

A theory is developed to describe the interplay of vibrational relaxation and luminescence occurring simultaneously in a molecule, in terms of a master equation involving true sinks of probability. Specifically, the basic equation is the Montroll-Shuler equation augmented by the addition of sink terms which can be nonlinear as well as linear in the vibrational energy. These terms describe radiative

V. Seshadri; V. M. Kenkre

1978-01-01

144

Construction of a Langevin model from time series with a periodical correlation function: Application to wind speed data  

NASA Astrophysics Data System (ADS)

A Langevin-type equation for stochastic processes with a periodical correlation function is introduced. A procedure of reconstruction of the equation from time series is proposed and verified on simulated data. The method is applied to geophysical time series–hourly time series of wind speed measured in northern Italy–constructing the macroscopic model of the phenomenon.

Czechowski, Zbigniew; Telesca, Luciano

2013-11-01

145

Temporal breakdown and Borel resummation in the complex Langevin method  

NASA Astrophysics Data System (ADS)

We reexamine the Parisi-Klauder conjecture for complex e?4 measures with a Wick rotation angle 0??/2??/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?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?? 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 tc. The breakdown time tc 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.

Duncan, A.; Niedermaier, M.

2013-02-01

146

Fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation  

NASA Astrophysics Data System (ADS)

The fermionic covariant prolongation structure theory is investigated. We extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining the prolongation structure. Furthermore, we investigate a (2+1)-dimensional super nonlinear Schrödinger equation and analyze its integrability by means of this prolongation structure technique. We derive its Lax representation and Bäcklund transformation. Moreover, we present a solution of this multidimensional super integrable equation.

Yan, Zhao-Wen; Li, Min-Li; Wu, Ke; Zhao, Wei-Zhong

2013-03-01

147

Cartan's equations define a topological field theory of the BF type  

SciTech Connect

Cartan's first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields T{sup I} and R{sub J}{sup I}. From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the BF type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einstein's equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the BF type is also present in the first-order formalism for general relativity.

Cuesta, Vladimir; Montesinos, Merced [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Avenida Instituto Politecnico Nacional 2508, San Pedro Zacatenco, 07360, Gustavo A. Madero, Mexico City (Mexico)

2007-11-15

148

Controlling one-dimensional Langevin dynamics on the lattice  

SciTech Connect

Stochastic evolutions of classical field theories have recently become popular in the study of problems such as the determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain high precision results from numerical calculations, a careful accounting of spacetime discreteness effects is essential, as well as the development of schemes to systematically improve convergence to the continuum. With a kink-bearing {phi}{sup 4} field theory as the application arena, we present such an analysis for a (1+1)-dimensional Langevin system. Analytical predictions and results from high resolution numerical solutions are found to be in excellent agreement. {copyright} {ital 1999} {ital The American Physical Society}

Bettencourt, L.M. [T-6/T-11, Theoretical Division, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Habib, S. [T-8, Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Lythe, G. [CNLS, Theoretical Division, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

1999-11-01

149

Scaling theory for homogenization of the Maxwell equations  

NASA Astrophysics Data System (ADS)

The wide application of composite materials is a distinctive feature of modern technologies. This encourages scientists dealing with radio physics and optics, to search for new type of artificial materials. Recently such investigations have shifted in the field of materials with weak spatial dispersion: chiral, omega materials, artificial magnets, etc. By weak spatial dispersion we mean that the constitutive relations are still local but constitutive parameters depend upon a wavenumber k. It is the dependence that is responsible for non-encountered-in-nature properties of the materials such as chirality [a first order in (ka) effect] or artificial magnetism [a second order in (ka effect)]. Here a is a typical size of an inclusion. Certainly, all these effects are small enough unless there is a resonance interaction of electromagnetic wave with an inclusion. Near the resonance frequency the effects are significant and perturbation theory in (ka) fails. Nevertheless it is convenient to describe the effects in terms of orders in (ka), understanding this as a matter of classification. In spite of physical clarity of the classification the constitutive relations are treated in terms of multipole expansion. The multipoles naturally appear at field expansion in (d/R) where d is the source size and R is the distance between the source and recorder. Such an expansion is useful in 'molecular optics' approximation where d very much less than r, with r to be a mean distance between the 'molecules.' Though the 'molecular optics' ceases to be a good approximation if we deal with composites where d approximately equals r, the mean current in the right hand side of the Maxwell equations is still expressed through multipoles (see Fig. 1). Below we consider the reasons justifying this sight on things even if we are working beyond the 'molecular optics' approximation. To repel an accusation in abstract contemplation let us consider examples of the 'multipole' media. Permeable composites made of non-permeable ingredients are well known. The simplest example is a composite loaded with highly conducting spherical inclusions. Due to eddy currents there appears a magnetic moment of the inclusion and the composite exhibits properties of diamagnetic. The inclusions of more complicated structure can exhibit resonant excitation resulting in induced magnetic moment. Examples of such inclusions are open rings, dielectric spheres, helix and bi-helix. In this case depending upon the relation between the working and resonant frequencies we can observe both diamagnetism or paramagnetism. Q-medium is more smart system. As the system of identical dielectric spheres is a permeable material, the system of different in size spheres may be non-permeable. The concentrations and radii may be chosen so that one part of spheres is excited in diamagnetic mode and the other in paramagnetic. Such a system is described by its quadrupole moment (see Fig. 1). Putting quantum mechanics apart we shall consider a classical composite material. The adjective 'classical' means that the scale of inhomogeneity is large enough to describe the reply of material on electromagnetic disturbance in terms of local constitutive equations Di equals (epsilon) ((omega) ,r)Ej ji equals (sigma) ((omega) ,r)Ej where (epsilon) ((omega) ,r), (sigma) ((omega) ,r) are local permittivity and conductivity.

Vinogradov, Alexei P.

1997-11-01

150

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

151

Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach.  

PubMed

We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates. PMID:16606044

Cheng, X Z; Jalil, M B A; Lee, Hwee Kuan; Okabe, Yutaka

2006-02-17

152

The equation of deviation in a conformally invariant theory of gravitation and electromagnetism  

NASA Astrophysics Data System (ADS)

The equation of deviation is derived for a conformally invariant theory of gravitation and electromagnetism in which scale is generated by a topological constraint. Compared with its counterpart in the Einstein-Maxwell theory, the equation contains some extra terms proportional to the electromagnetic potential indicating the existence of linear and nonlinear Bohm-Aharonov effects. These are present also in the related theories of Weyl and Dirac. From the same equation one can derive an expression for the quantization of geometry which further illustrates the topological mechanism for the genesis of scale. As a by-product, the magnitudes of some Einstein-Maxwell corrections in Weber-type experiments are estimated.

Cai, Y. Q.; Papini, G.

1988-03-01

153

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

NASA Astrophysics Data System (ADS)

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-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. Supported in part by the Danish Natural Science Research Council and the SARC Foundation.

Brustein, Ram; Roland, Kaj

1992-03-01

154

The Yang-Baxter Equation in Knot Theory  

Microsoft Academic Search

The role played by the Yang-Baxter equation in generating knot invariants using the method of statistical mechanics is reexamined and elucidated. The formulation of knot invariants is made precise with the introduction of piecewise-linear lattices and enhanced vertex and interaction-round-a-face (IRF) models with strictly local weights. It is shown that the Yang-Baxter equation and the need of using its solution

F. Y. Wu

1993-01-01

155

Quantum theory of rotational isomerism and Hill equation  

SciTech Connect

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

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

2012-06-15

156

Order Preservation Between Brownian Particles Modeled By Langevin Dynamics  

NASA Astrophysics Data System (ADS)

We studied the dynamics of two overdamped Brownian particles in an elongational force gradient following their release from some initial separation. Using a modified one-dimensional Langevin equation, we computed the probability that the particles maintain their order as a function of time. The probability approaches unity when the work required to bring the particles together against the force gradient greatly exceeds the thermal energy, kBT. The time window within which the particles are most likely to reverse their order is given by the time to diffuse the initial separation. We apply our theoretical model to the dynamics of DNA monomers approaching the vertex of the Taylor cone in an electrospray ionization mass spectrometer. The likelihood of preserving the sequential order is estimated to be 95% when the neighboring monomers of a stretched polymer are cleaved within 10 nm of the vertex. The implications of these results to a DNA sequencing strategy will be discussed.

Maulbetsch, William; Poole, William; Bush, Joseph; Stein, Derek

2013-03-01

157

Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory  

SciTech Connect

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

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

2010-10-15

158

Workshop/School on Stochastic Partial Differential Equations: Theory and Applications.  

National Technical Information Service (NTIS)

The workshop/school on Stochastic Partial Differential Equations: Theory and Applications was held January 3 through January 7, 1996 in Los Angeles. The event was organized and hosted by the University of Southern California. Funding was provided by ONR (...

B. Rozovskii R. Carmona

1996-01-01

159

Dual conformal constraints and infrared equations from global residue theorems in SYM theory  

Microsoft Academic Search

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed employing\\u000a the recently proposed Grassmannian integral in super Yang-Mills theory. Examples for infrared equations have been shown to be implied by global residue theorems in the\\u000a Grassmannian picture.\\u000a \\u000a \\u000a Both dual conformal

Johannes Brödel; Song He

2010-01-01

160

Flow equation approach to the linear response theory of superconductors  

NASA Astrophysics Data System (ADS)

We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions, we reproduce the standard response kernel of the BCS superconductor. We next generalize this nonperturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.

Zapalska, M.; Doma?ski, T.

2011-11-01

161

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

162

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

163

Dyson Schwinger Equations: From Hopf algebras to Number Theory  

Microsoft Academic Search

We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative results for the short-distance singular sector of a renormalizable quantum field theory. We focus on the short-distance behaviour and thus discuss renormalized Green functions $G_R(\\\\alpha,L)$ which

Dirk Kreimer

2006-01-01

164

Some aspects of the theory of time and band limited operators associated with Lame's equation  

Microsoft Academic Search

The thesis has three chapters. In Chapter 1, it introduces the Gegenbauer functions and their fundamental properties. Following Grunbaum, it proves that the partial Gram matrix for Gegenbauer's equation admits a commuting tridiagonal matrix. Chapter 2 discusses the rudiments of the theory of the Weierstrass P-function and associated functions, and investigates in some detail the Sturm-Liouville problem for Lame's equation.

Perline

1984-01-01

165

Quantum field scattering theory for the nonlinear Schrodinger equation with repulsive coupling  

SciTech Connect

The author constructs nonstationary quantum field scattering theory for the nonlinear Schroedinger equation with repulsion. Local fields are introduced through the quantum Gel'fandLevitan-Marchenko equations and the equivalence of the field problem to a set of N-particle quantum-mechanical problems with two-body delta-functional potential (coordinate Bethe ansatz) is not used.

Khamitov, I.M.

1985-11-01

166

Angular Pseudomomentum Theory for the Generalized Nonlinear Schrodinger Equation in Discrete Rotational Symmetry Media  

Microsoft Academic Search

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schrodinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schrodinger equation with a nonlinearity depending on the modulus of the eld. We provide a rigorous proof of a set of mathematical results justifying that these solitons

M.-A. Garc; A. Ferrando; M. Zacar; J. Vijande; L. D. Carr

167

Group foliation of the Lamé equations of the classical dynamical theory of elasticity  

Microsoft Academic Search

We perform the group foliation of the system of Lamé equations of the classical dynamical theory of elasticity for an infinite\\u000a subgroup contained in a normal divisor of the main group. The resolving system of this foliation includes the following two\\u000a classical systems of mathematical physics: the system of equations of vortex-free acoustics and the system of Maxwell equations,\\u000a which

Yu. A. Chirkunov

2009-01-01

168

Scattering Theory for the Coupled Klein-Gordon-Schrodinger Equations in Two Space Dimensions  

Microsoft Academic Search

We study the scattering theory for the coupled Klein- Gordon-Schrodinger equation with the Yukawa type interaction in two space dimensions.The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the

Akihiro Shimomura

2003-01-01

169

ZM theory II: Hamilton's and Lagrange's equations of motion  

Microsoft Academic Search

We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The derivation may provide a simple understanding of the conventions that are used in defining the relationship between independent and dependent variables

Yaneer Bar-Yam

2006-01-01

170

Item Response Theory Test Equating in Health Sciences Education  

ERIC Educational Resources Information Center

|In the context of health sciences education, and education in general, the knowledge or ability of one or several subjects in a specific area is frequently compared using different forms of a test, or by means of different instruments aimed at measuring this knowledge or ability. In such cases, test scores must be equated so that they can be…

Guilera, Georgina; Gomez, Juana

2008-01-01

171

Item Response Theory Test Equating in Health Sciences Education  

ERIC Educational Resources Information Center

In the context of health sciences education, and education in general, the knowledge or ability of one or several subjects in a specific area is frequently compared using different forms of a test, or by means of different instruments aimed at measuring this knowledge or ability. In such cases, test scores must be equated so that they can be…

Guilera, Georgina; Gomez, Juana

2008-01-01

172

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

173

The Yang-Baxter Equation in Knot Theory  

NASA Astrophysics Data System (ADS)

The role played by the Yang-Baxter equation in generating knot invariants using the method of statistical mechanics is reexamined and elucidated. The formulation of knot invariants is made precise with the introduction of piecewise-linear lattices and enhanced vertex and interaction-round-a-face (IRF) models with strictly local weights. It is shown that the Yang-Baxter equation and the need of using its solution in the infinite rapidity limit arise naturally in the realization of invariances under Reidemeister moves III. It is also shown that it is essential for the vertex models be charge-conserving, and that the construction of knot invariants from IRF models follows directly from the vertex model formulation.

Wu, F. Y.

174

Classical field theory for a non-Hermitian Schrödinger equation with position-dependent masses  

NASA Astrophysics Data System (ADS)

A linear one-dimensional Schrödinger equation, defined by means of a non-Hermitian Hamiltonian characterized by position-dependent masses, was proposed lately. Herein we present an exact classical field theory for this equation, showing the need for an extra field ?(x,t), in addition to the usual one, ?(x,t), similar to what was done recently in the analysis of a class of nonlinear quantum equations. These generalizations of the Schrödinger equation depend on an index q, in such a way that the standard case is recovered in the limit q?1. Particularly, the field ?(x,t) becomes ?*(x,t) only when q?1 and satisfies a similar Schrödinger equation for the Hermitian conjugate of the Hamiltonian operator. In terms of these two fields one may define a probability density following a standard continuity equation, leading to the preservation of probability in Cartesian space. Simple applications are performed by solving the equations for the two fields.

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

2013-09-01

175

From Naive Mean Field Theory to the TAP Equations  

Microsoft Academic Search

IntroductionMean field (MF) methods provide tractable approximations for thecomputation of high dimensional sums and integrals in probabilisticmodels. By neglecting certain dependencies between random variables,a closed set of equations for the expected values of these variables isderived which often can be solved in a time that only grows polynomiallyin the number of variables. The method has its origin in StatisticalPhysics where

Manfred Opper; Ole Winther

2001-01-01

176

Quantum non-Markovian Langevin formalism for heavy ion reactions near the Coulomb barrier  

Microsoft Academic Search

The generalized Langevin approach is suggested to describe the capture inside of the Coulomb barrier of two heavy nuclei at bombarding energies near the barrier. The equations of motion for the relative distance (collective coordinate) between two interacting nuclei are consistent with the generalized quantum fluctuation-dissipation relations. The analytical expressions are derived for the time-dependent non-Markovian microscopic transport coefficients for

V. V. Sargsyan; N. V. Antonenko; Z. Kanokov; G. G. Adamian

2008-01-01

177

Equation of state for polymer liquid crystals: Theory and experiment  

Microsoft Academic Search

The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entropic part

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

1999-01-01

178

Complete Cut-Free Tableaux for Equational Simple Type Theory  

Microsoft Academic Search

We present a cut-free tableau system for a version of Church's simple type theory with primitive equality. The system is formulated with an abstract normalization operator that completely hides the details of lambda con- version. We prove completeness of the system relative to Henkin models. The proof constructs Henkin models using the novel notion of a value sys- tem. 1I

Chad E. Brown; Gert Smolka

2009-01-01

179

Theory of differential equations in discontinuous piecewise-defined functions  

Microsoft Academic Search

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

I. Herrera

2007-01-01

180

Equations of motion in gravity theories with nonminimal coupling: A loophole to detect torsion macroscopically?  

NASA Astrophysics Data System (ADS)

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

Puetzfeld, Dirk; Obukhov, Yuri N.

2013-09-01

181

Fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid  

NASA Astrophysics Data System (ADS)

We have derived fourth-order perturbative equations in Lagrangian perturbation theory for a cosmological dust fluid. These equations are derived under the supposition of Newtonian cosmology in the Friedmann-Lemaître-Robertson-Walker Universe model. Even if we consider the longitudinal mode in the first-order perturbation, the transverse mode appears in the third-order perturbation. Furthermore, in this case, six longitudinal-mode equations and four transverse-mode equations appear in the fourth-order perturbation. The application of the fourth-order perturbation leads to a precise prediction of the large-scale structure.

Tatekawa, Takayuki

2013-01-01

182

Theory of inert gas-condensing vapor thermoacoustics: transport equations.  

PubMed

The preceding paper [J. Acoust. Soc. Am. 112, 1414-1422 (2002)] derives the propagation equation for sound in an inert gas-condensing vapor mixture in a wet-walled pore with an imposed temperature gradient. In this paper the mass, enthalpy, heat, and work transport equations necessary to describe the steady-state operation of a wet-walled thermoacoustic refrigerator are derived and presented in a form suitable for numerical evaluation. The requirement that the refrigerator operate in the steady state imposes zero mass flux for each species through a cross section. This in turn leads to the evaluation of the mass flux of vapor in the system. The vapor transport and heat transport are shown to work in parallel to produce additional cooling power in the wet refrigerator. An idealized calculation of the coefficient of performance (COP) of a wet-walled thermoacoustic refrigerator is derived and evaluated for a refrigeration system. The results of this calculation indicate that the wet-walled system can improve the performance of thermoacoustic refrigerators. Several experimental and practical questions and problems that must be addressed before a practical device can be designed and tested are described. PMID:12398450

Slaton, William V; Raspet, Richard; Hickey, Craig J; Hiller, Robert A

2002-10-01

183

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

SciTech Connect

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

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

2008-09-15

184

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

185

Approximate equations obtained using a refined theory for calculation of natural frequencies of vibration for longitudinally reinforced cylindrical shells  

Microsoft Academic Search

The approximate equations and computational formulas presented below are derived taking into account the discrete placement of ribs on the basis of the refined theory of ribbed shells using the S.P. Timoshenko model. They are no more complicated that the complicated that the corresponding equations and formulas obtained on the basis of the theory of structurally orthotropic shells. Analogous equations

V. A. Zarutskii

1995-01-01

186

Complex-Distance Potential Theory and Hyperbolic Equations  

Microsoft Academic Search

An extension of potential theory in R^n is obtained by continuing the\\u000aEuclidean distance function holomorphically to C^n. The resulting Newtonian\\u000apotential is generated by an extended source distribution D(z) in C^n whose\\u000arestriction to R^n is the delta function. This provides a natural model for\\u000aextended particles in physics. In C^n, interpreted as complex spacetime, D(z)\\u000aacts as a

Gerald Kaiser

1999-01-01

187

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

188

Aqueous interaction site integral-equation theory that exactly takes into account intramolecular correlations  

NASA Astrophysics Data System (ADS)

We report the development of a formally exact integral equation for the three-dimensional hydration structure around molecular solutes of arbitrary complexity. A distinctive feature of our theory--termed aqueous interaction site (AXIS) integral-equation theory--is that it fully takes into account the intramolecular structural correlations of solvent water, which has been missing in the previous integral-equation theories such as the three-dimensional reference interaction site model (3D-RISM) theory. With a simplifying approximation in which the intermolecular bridge function is neglected, an illustrative application of the AXIS theory is made on the equilibrium oxygen and hydrogen distributions of solvent water surrounding a solute water molecule at ambient and supercritical conditions. We demonstrate through a comparison with molecular dynamics simulation results that the inclusion of the exact intramolecular correlations improves upon the 3D-RISM theory in describing the water distribution around molecular solute, in particular near the surface region of the solute molecule, though there still remain quantitative differences from the simulation results. To further improve the quantitative accuracy of the theory, one needs to incorporate the intermolecular bridge function, and a possible formulation for the approximate bridge function is suggested based on the angular decomposition.

Chong, Song-Ho; Ham, Sihyun

2012-10-01

189

Determination of a general solution of three-dimensional Lamé equations of elasticity theory  

Microsoft Academic Search

We integrate the Lam equation and find new solutions in the case of three-dimensional elasticity theory, which are expressed\\u000a in terms of harmonic functions. We prove that the solution obtained involves only three independent functions. In a curvilinear\\u000a orthogonal coordinate system, a general solution of the Lam equation is expressed in terms of three harmonic functions.

V. P. Revenko

2006-01-01

190

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

191

Proposal for a conformal field theory interpretation of Watts' differential equation for percolation  

NASA Astrophysics Data System (ADS)

G M T Watts established that in two-dimensional critical percolation the crossing probability ?hv satisfies a fifth-order differential equation which includes another one of third order whose independent solutions describe the physically relevant quantities 1,?h,?hv. We will show that this differential equation can be derived from a level three null vector condition for a rational c = -24 conformal field theory and motivate how this solution may be fitted into known properties of percolation.

Flohr, Michael; Müller-Lohmann, Annekathrin

2005-12-01

192

Spectral equation-of-state theory for dense, partially ionized matter  

NASA Astrophysics Data System (ADS)

The Schrödinger equation is solved in time and space to implement a finite-temperature equation-of-state theory for dense, partially ionized matter. The time-dependent calculation generates a spectrum of quantum states. Eigenfunctions are calculated from a knowledge of the spectrum and used to calculate the electronic pressure and energy. Results are given for Be and LiD and compared with results from the INFERNO model [D. A. Liberman, Phys. Rev. B 20, 4981 (1979)].

Ritchie, Burke

2005-07-01

193

Spectral Equations-Of-State Theory for Dense, Partially Ionized Matter  

SciTech Connect

The Schroedinger equation is solved in time and space to implement a finite-temperature equation-of-state theory for dense, partially ionized matter. The time-dependent calculation generates a spectrum of quantum states. Eigenfunctions are calculated from a knowledge of the spectrum and used to calculate the electronic pressure and energy. Results are given for LID and compared with results from the INFERNO model.

Ritchie, A B

2004-05-14

194

Spectral equation-of-state theory for dense, partially ionized matter  

SciTech Connect

The Schroedinger equation is solved in time and space to implement a finite-temperature equation-of-state theory for dense, partially ionized matter. The time-dependent calculation generates a spectrum of quantum states. Eigenfunctions are calculated from a knowledge of the spectrum and used to calculate the electronic pressure and energy. Results are given for Be and LiD and compared with results from the INFERNO model [D. A. Liberman, Phys. Rev. B 20, 4981 (1979)].

Ritchie, Burke [University of California, Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)

2005-07-15

195

Second-order elliptic integro-differential equations: viscosity solutions' theory revisited  

Microsoft Academic Search

The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen–Ishii's lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The proof of this

Guy Barlesand; Cyril Imbert

2008-01-01

196

Introduction to the theory of functional differential equations and their applications. Group approach  

Microsoft Academic Search

In this work, we give an introduction to the theory of nonlinear functional differential equations of pointwise type on a\\u000a finite interval, semi-axis, or axis. This approach is based on the formalism using group peculiarities of such differential\\u000a equations. For the main boundary-value problem and the Euler-Lagrange boundary-value problem, we consider the existence and\\u000a uniqueness of the solution, the continuous

Levon Andreevich Beklaryan

2006-01-01

197

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

198

Analogues of generalized hydrodynamic potentials in the theory of Lamé and Maxwell equations  

Microsoft Academic Search

For a certain class of orthogonal coordinates we simultaneously obtain representations of the general solutions of Lamé and Maxwell systems of equations in terms of generalized scalar potentials which are analogues of generalized potentials of the theory of gas dynamics fields defined by us earlier. We compare representations obtained in this way with known Hertz, Whittaker, Debye, Bateman, and Morse-Feshbach

N. V. Saltanov

1990-01-01

199

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

SciTech Connect

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

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

2011-05-23

200

Scattering theory for the Klein-Gordon equation with nondecreasing potentials  

SciTech Connect

The Klein-Gordon equation is considered in the case of nondecreasing potentials. The energy inner product is nonpositive on a subspace of infinite dimension, not consisting entirely of eigenvectors of the associated operator. A scattering theory for this case is developed and asymptotic completeness for generalized Moeller operators is proven.

Cruz, Maximino; Arredondo R, Juan H. [Departamento de Matematicas, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco, 186. Col. Vicentina, C.P. 09340, Del. Iztapalapa, Mexico D.F. (Mexico)

2008-11-15

201

Convergence problems associated with the iteration of adjoint equations in nuclear reactor theory  

Microsoft Academic Search

Convergence problems associated with the iteration of adjoint equations based on two-group neutron diffusion theory approximations in slab geometry are considered. For this purpose first-order variational techniques are adopted to minimise numerical errors involved. The importance of deriving the adjoint source from a breeding ratio is illustrated. The results obtained are consistent with the expected improvement in accuracy.

E. Ngcobo

2003-01-01

202

Relativistic kinetic theory of electromagnetic waves in equilibrium magnetized plasma. General dispersion equations  

Microsoft Academic Search

The relativistic kinetic theory of parallel propagating electromagnetic waves in a magnetized equilibrium plasma is presented. On the basis of relativistic Vlasov-Maxwell equations, a general explicit dispersion relation is derived by a correct analytical continuation for all complex frequencies of electromagnetic waves.

M. Lazar; R. Schlickeiser

2003-01-01

203

Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory  

ERIC Educational Resources Information Center

|This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

Muthen, Bengt; Asparouhov, Tihomir

2012-01-01

204

Deposition of Colloidal Particles on Homogeneous Surfaces: Integral-Equation Theory and Monte Carlo Simulation  

Microsoft Academic Search

Deposition of large particles such as colloidal or bio-particles on a solid surface is usually modeled by the random sequential adsorption (RSA). The model was previously described by the integral-equation theory whose validity was proved by Monte Carlo simulation. This work generalized the model to include the concentration effect of added particles on the surface. The fraction of particles inserted

Panu Danwanichakul

2009-01-01

205

Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory  

ERIC Educational Resources Information Center

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed…

Muthen, Bengt; Asparouhov, Tihomir

2012-01-01

206

Bayesian Structural Equation Modeling: A More Flexible Representation of Substantive Theory  

Microsoft Academic Search

This article proposes a new approach to factor analysis and structural equation modeling using Bayesian analysis. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors. It is argued that this produces an analysis that better reflects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to

Bengt Muthén; Tihomir Asparouhov

2012-01-01

207

WKB Theory of Wave Tunneling for Hermitian Vector Systems of Integral Equations.  

National Technical Information Service (NTIS)

A general theory of wave tunneling in one dimension for Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium, and without regard to specific models gives a proper...

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

1988-01-01

208

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

SciTech Connect

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

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

2012-08-15

209

Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory  

SciTech Connect

Coulomb gauge Yang-Mills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The Ward-Takahashi identity arising from this non-standard transform is shown to be automatically satisfied by the equations of motion.

Watson, P.; Reinhardt, H. [Institut fuer Theoretische Physik, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

2007-02-27

210

IRTEQ: Windows Application that Implements Item Response Theory Scaling and Equating  

ERIC Educational Resources Information Center

|This article provides a brief description of a Windows application called IRTEQ. IRTEQ employs an intuitive, user-friendly graphic user interface that can rescale one test form to another by using various item response theory (IRT) scaling methods. It supports various IRT models for test forms. It can also equate test scores on the scale of one…

Han, Kyung T.

2009-01-01

211

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

212

Dryson equations, Ward identities, and the infrared behavior of Yang-Mills theories. [Schwinger-Dyson equations, Slavnov-Taylor identities  

SciTech Connect

It was shown using the Schwinger-Dyson equations and the Slavnov-Taylor identities of Yang-Mills theory that no inconsistency arises if the gluon propagator behaves like (1/p/sup 2/)/sup 2/ for small p/sup 2/. To see whether the theory actually contains such singular long range behavior, a nonperturbative closed set of equations was formulated by neglecting the transverse parts of GAMMA and GAMMA/sub 4/ in the Schwinger-Dyson equations. This simplification preserves all the symmetries of the theory and allows the possibility for a singular low-momentum behavior of the gluon propagator. The justification for neglecting GAMMA/sup (T)/ and GAMMA/sub 4//sup (T)/ is not evident but it is expected that the present study of the resulting equations will elucidate this simplification, which leads to a closed set of equations.

Baker, M.

1979-01-01

213

Coherent backscattering in nonlinear atomic media: Quantum Langevin approach  

NASA Astrophysics Data System (ADS)

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.

Grémaud, Benoît; Wellens, Thomas; Delande, Dominique; Miniatura, Christian

2006-09-01

214

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

215

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

SciTech Connect

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

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

2012-08-15

216

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

SciTech Connect

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

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

2011-01-15

217

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

NASA Astrophysics Data System (ADS)

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

Akyol, M.; Papadopoulos, G.

2012-07-01

218

Angular distribution of fission fragments of excited compound nuclei in multidimensional Langevin dynamics  

SciTech Connect

Angular distributions of fission fragments were calculated within a multidimensional approach to the fission dynamics of excited nuclei, and the results of these calculations are presented. The evolution of the shape parameters of a fissile nucleus was described by the set of three-dimensional Langevin equations for collective coordinates introduced on the basis of the (c, h, a) parametrization. The evolution of the orientation degree of freedom (K mode, K being the projection of the total angular momentum on the symmetry axis of the nucleus under study) was described with the aid of the Langevin equation in an overdampedmode. The coupled Langevin equations for the shape and K-mode collective coordinates were integrated simultaneously. The friction parameter for the K mode was set to 0.077 (MeV Multiplication-Sign 10{sup -21} s){sup -1/2}, which is the estimate obtained previously for this quantity in calculating angular distributions of excited compound nuclei with allowance for the effects of the orientation degree of freedom. The developed model was used to analyze the anisotropy of angular distribution of fission fragments in {sup 16}O+{sup 208}Pb, {sup 16}O+{sup 232}Th, and {sup 16}O + {sup 238}U reactions over a broad interval of projectile-ion energies. The results of the calculations show that the developedmodel, usedwith the above value of the friction parameter for theK mode, leads to a rather good description of experimental data on the anisotropy of angular distributions of fission fragments. The effect of the dimensionality of the dynamicalmodel used to describe the evolution of the shape of a fissile nucleus on the results obtained by calculating the anisotropy of angular distributions is discussed.

Gegechkori, A. E., E-mail: gecktor@gmail.com; Adeev, G. D. [Omsk State University (Russian Federation)

2011-01-15

219

Solutions of Dirac's equation in Bianchi type I spacetime in teleparallel gravity theory  

NASA Astrophysics Data System (ADS)

Different from the Einstein's general relativity which describes gravity through the curvature of a spacetime, teleparallel gravity theory depicts gravity through the Weitzenbock torsion of the spacetime. This leads to different expressions of the dynamical equations of fundamental fields, including Dirac fields, in both theories. Here we derive two types of solutions of the Dirac's equations for the case of isotropic Bianchi type I spacetime. The first is an oscillatory solution, i.e. the time dependence of the solution is chosen to be sinusoidal. Here we derive the general form of space coordinate dependent part of the solution. The second type of solution is a solution where the space coordinate part of solution is chosen to be sinusoidal. Here we derive the time dependence of the solution for the case of exponential scale factor.

Triyanta; Supardi; Zen, F. P.

2013-09-01

220

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

221

Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion  

Microsoft Academic Search

In constructions of analytical solutions to open string field theories pure\\u000agauge configurations parameterized by wedge states play an essential role.\\u000aThese pure gauge configurations are constructed as perturbation expansions and\\u000ato guaranty that these configurations are asymptotical solutions to equations\\u000aof motions one needs to study convergence of the perturbation expansions. We\\u000ademonstrate that for the large parameter of

I. Ya. Aref'eva; Roman V. Gorbachev; Dmitry A. Grigoryev; Pavel N. Khromov; Maxim V. Maltsev; P. B. Medvedev

2009-01-01

222

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

223

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

224

Solution of Two-Dimensional Laplace Equation By Multipole Theory Method  

Microsoft Academic Search

A new approach, the multipole theory (MT) method, is presented for calculating two-dimensional (2-D) Laplace equation boundary-value problem. By the mathematical deduction, the generalized MT series formula and its applied laws are derived. The numerical analysis procedure and application of the MT method in electromagnetic engineering have been discussed. In order to verify the accuracy of this method, the MT

Q. Zheng; D. Hou; F. Xie; W. Lin

1999-01-01

225

Physical theories in Galilean space-time and the origin of Schroedinger-like equations  

SciTech Connect

A method to develop physical theories of free particles in space-time with the Galilean metric is presented. The method is based on a Principle of Analyticity and a Principle of Relativity, and uses the Galilei group of the metric. The first principle requires that state functions describing the particles are analytic and the second principle demands that dynamical equations for these functions are Galilean invariant. It is shown that the method can be used to formally derive Schroedinger-like equations and to determine modifications of the Galilei group of the metric that are necessary to fullfil the requirements of analyticity and Galilean invariance. The obtained results shed a new light on the origin of Schroedinger's equation of non-relativistic quantum mechanics.

Musielak, Z.E. [Department of Physics, University of Texas at Arlington, Science Hall, Rm 108, Arlington, TX 76019 (United States)], E-mail: zmusielak@uta.edu; Fry, J.L. [Department of Physics, University of Texas at Arlington, Science Hall, Rm 108, Arlington, TX 76019 (United States)

2009-02-15

226

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

227

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

SciTech Connect

Based on ideas proposed by Massoudi and Rajagopal (M-R), we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells (RBCs) suspended in plasma, where the plasma behaves as a linearly viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.

Massoudi, Mehrdad; Antaki, J.F.

2008-09-12

228

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

SciTech Connect

Based on ideas proposed by Massoudi and Rajagopal #2;M-R#3;, we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells #2;RBCs#3; suspended in plasma, where the plasma behaves as a linearly viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.

Massoudi, M.; Antaki, J.

2008-01-01

229

Kinetic Theory of Jet Dynamics in the Stochastic Barotropic and 2D Navier-Stokes Equations  

NASA Astrophysics Data System (ADS)

We discuss the dynamics of zonal (or unidirectional) jets for barotropic flows forced by Gaussian stochastic fields with white in time correlation functions. This problem contains the stochastic dynamics of 2D Navier-Stokes equation as a special case. We consider the limit of weak forces and dissipation, when there is a time scale separation between the inertial time scale (fast) and the spin-up or spin-down time (large) needed to reach an average energy balance. In this limit, we show that an adiabatic reduction (or stochastic averaging) of the dynamics can be performed. We then obtain a kinetic equation that describes the slow evolution of zonal jets over a very long time scale, where the effect of non-zonal turbulence has been integrated out. The main theoretical difficulty, achieved in this work, is to analyze the stationary distribution of a Lyapunov equation that describes quasi-Gaussian fluctuations around each zonal jet, in the inertial limit. This is necessary to prove that there is no ultraviolet divergence at leading order, in such a way that the asymptotic expansion is self-consistent. We obtain at leading order a Fokker-Planck equation, associated to a stochastic kinetic equation, that describes the slow jet dynamics. Its deterministic part is related to well known phenomenological theories (for instance Stochastic Structural Stability Theory) and to quasi-linear approximations, whereas the stochastic part allows to go beyond the computation of the most probable zonal jet. We argue that the effect of the stochastic part may be of huge importance when, as for instance in the proximity of phase transitions, more than one attractor of the dynamics is present.

Bouchet, Freddy; Nardini, Cesare; Tangarife, Tomás

2013-09-01

230

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

231

Force-Annihilation Conditions for Variable-Coefficient Lanchester-Type Equations of Modern Warfare, I. Mathematical Theory.  

National Technical Information Service (NTIS)

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type square-law attrition equations for combat between two homogeneous f...

C. Comstock J. G. Taylor

1976-01-01

232

The relationship between the solutions of the parabolic equation method and first Rytov approximation in stochastic wave propagation theory  

NASA Astrophysics Data System (ADS)

The source of the curious exact agreement between the predictions of the disparate approaches of weak and strong fluctuation theory for the mutual coherence functions of plane and spherical wave propagation is identified. It is found that the linear approximation of the Ricatti equation that results within the Rytov method reduces to the parabolic equation of strong fluctuation theory only for the plane and spherical wave cases. Such a reduction does not prevail for the general beam wave case.

Manning, R. M.

233

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

PubMed

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. PMID:22803522

Yang, Lei; Devi, Murali; Jang, Seogjoo

2012-07-14

234

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

235

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

236

Solution of 1-D multi-group time-dependent diffusion equations using the coupled reactors theory  

Microsoft Academic Search

A new method to solve time-dependent multi-group diffusion equations is presented using multi-point kinetics equations of the coupled reactors theory. The usual improved quasi-static method is generalized such that the fission sources for each core or node obtained from multi-point kinetics equations are used as amplitude functions for each node instead of a single amplitude function. Coupling coefficients between nodes

Y. Nagaya; K. Kobayashi

1995-01-01

237

Renormalization-group theory for the phase-field crystal equation.  

PubMed

We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time. PMID:16907101

Athreya, Badrinarayan P; Goldenfeld, Nigel; Dantzig, Jonathan A

2006-07-17

238

Additional global internal contraction in variations of multireference equation of motion coupled cluster theory  

NASA Astrophysics Data System (ADS)

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

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

2013-04-01

239

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

NASA Astrophysics Data System (ADS)

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 × 10-4 to 1.347 × 103 g/cm3 and up to 5 × 107 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

2013-09-01

240

Seiberg-Witten equations and non-commutative spectral curves in Liouville theory  

NASA Astrophysics Data System (ADS)

We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.

Chekhov, Leonid; Eynard, Bertrand; Ribault, Sylvain

2013-02-01

241

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

NASA Astrophysics Data System (ADS)

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

Kast, Stefan M.; Tomazic, Daniel

2012-11-01

242

Stochastic quantization of real-time thermal field theory  

SciTech Connect

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

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

2010-10-15

243

Stochastic quantization of real-time thermal field theory  

NASA Astrophysics Data System (ADS)

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

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

2010-10-01

244

Continuum regularization of gauge theory with fermions  

SciTech Connect

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

Chan, H.S.

1987-03-01

245

The Lippmann-Schwinger equation in electron-molecule scattering theory and the many-body Brillouin-Wigner expansion  

NASA Astrophysics Data System (ADS)

The Lippmann-Schwinger equation for the scattering of electrons by atoms and molecules is investigated from the perspective of Brillouin-Wigner perturbation theory. It is shown that the solution of the Lippmann-Schwinger can be obtained from many-body Brillouin-Wigner methods for bound-state problems. In particular, the equations of many-body Brillouin-Wigner coupled cluster theory for bound-state systems can be shown to lead directly to equations for the amplitudes for electron-molecule scattering processes.

Huba?, Ivan; Masarik, Jozef; Wilson, Stephen

2011-10-01

246

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise.  

PubMed

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed. PMID:21950847

Uma, B; Swaminathan, T N; Ayyaswamy, P S; Eckmann, D M; Radhakrishnan, R

2011-09-21

247

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise  

PubMed Central

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

Uma, B.; Swaminathan, T. N.; Ayyaswamy, P. S.; Eckmann, D. M.; Radhakrishnan, R.

2011-01-01

248

Spectra and dynamics in the b800 antenna: comparing hierarchical equations, redfield and förster theories.  

PubMed

We model the spectra (absorption and circular dichroism) and excitation dynamics in the B800 ring of the LH2 antenna complex from Rs. molischianum using different theoretical approaches, i.e., Förster theory, standard and modified versions of the Redfield theory, and the more versatile nonperturbative approach based on hierarchically coupled equations for the reduced density operator. We demonstrate that, although excitations in the B800 ring are localized due to disorder, thermal effects, and phonons, there are still sizable excitonic effects producing shift, narrowing, and asymmetry of the spectra. Moreover, the excitation dynamics reveals the presence of long-lived (up to 1 ps) non-oscillatory coherences between the exciton states maintained due to nonsecular population-to-coherence transfers. The sub-ps decay of the coherences is followed by slow motion of the excitation around the ring, producing equilibration of the site populations with a time constant of about 3-4 ps, which is slower than the B800 ? B850 transfer. The exact solution obtained with the hierarchical equations is compared with other approaches, thus illustrating limitations of the Förster and Redfield pictures. PMID:23531197

Novoderezhkin, Vladimir; van Grondelle, Rienk

2013-04-11

249

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

PubMed

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

Muthén, Bengt; Asparouhov, Tihomir

2012-09-01

250

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

251

On the derivation of the Wheeler-Dewitt equation in the heterotic superstring theory  

SciTech Connect

It has been shown by Pollock that the Wheeler-DeWitt equation for the wave function of the Universe [psi] cannot be derived for the D-dimensional, heterotic superstring theory, when higher-derivative terms [alpha][prime][ital R][sup 2] are included in the effective Lagrangian [ital L], because they occur as the Euler-number density [ital R][sup 2][sub E]. This means that [ital L] cannot be written in the standard Hamiltonian form, and hence that macroscopic quantum mechanics does not exist at this level of approximation. It was further conjectured that the solution to this difficulty is to take into account the effect of the terms [alpha][prime][sup 3][ital R][sup 4], an expression for which has been obtained by Gross and Witten, and by Freeman et al. In this paper, this conjecture is proved, but it is pointed out that the theory must first be reduced to a lower dimensionality [ital D] [lt] D. When this is done, the reduced term [ital R][sup 2] is no longer proportional to [ital R][sup 2][sub E], because of additional contributions arising from the dimensional reduction of [ital R][sup 4]. The Wheeler-DeWitt equation can now be derived in the form of a Schrodinger equation, in particular when [ital D] = 4 (and [ital R][sup 2][sub E] is a total divergence which can be discarded), and quantum mechanics can be set up in the usual way. In the light of these results, it is argued that the non-locality of quantum mechanics is related to the cosmological horizon problem.

Pollack, M.D. (L.D. Landau Inst. for Theoretical Physics, Academy of Sciences of the USSR, Ulitsa Kosygina 2, Moscow 117940 (USSR))

1992-07-10

252

The Theme of Love in the Novels of André Langevin  

Microsoft Academic Search

The thesis presents an analysis of the much ignored yet essential theme of love in the novels of André Langevin. Love between man and God proves ineffectual while that love between man and others as well as the love between man and woman, although being characterized by several intrinsic limitations, are none the less beneficial to the Langevinian characters in

Margaret Ena McInnes

1969-01-01

253

Langevin simulation of the Gross-Neveu spectrum.  

National Technical Information Service (NTIS)

We study the order parameter of Chiral symmetry, and fermion and boson masses in the Gross-Neveu model as a function of the flavour number N and of the Langevin time step (epsilon) in the scaling region. The 1/N dependence of the (epsilon)=0 value of the ...

R. Lacaze A. Morel B. Petersson

1989-01-01

254

Exponential Convergence of Langevin Diffusions and Their Discrete Approximations  

Microsoft Academic Search

In this paper we consider a continous time method of approximating a givendistribution ? using the Langevin diffusion dL t = dW t +12 r log ?(L t )dt:We find conditions under which this diffusion converges exponentially quicklyto ? or does not: in one dimension, these are essentially that for distributionswith exponential tails of the form ?(x) \\/ exp(\\\\Gammafljxjfi), 0

G. O. Roberts; R. L. Tweedie; Colorado State

1997-01-01

255

Improved Langevin Approach to Spinodal Decomposition in the Chiral Transition  

SciTech Connect

We use an improved Langevin description that incorporates both additive and multiplicative noise terms to study the dynamics of phase ordering. We perform real-time lattice simulations to investigate the role played by different contributions to the dissipation and noise. Lattice-size independence is assured by the use of appropriate lattice counterterms.

Fraga, Eduardo S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, C.P. 68528, 21941-972 Rio de Janeiro, RJ (Brazil); Krein, Gastao [Instituto de Fisica Teorica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900 Sao Paulo, SP (Brazil); Ramos, Rudnei O. [Departamento de Fisica Teorica, Universidade do Estado do Rio de Janeiro, 20550-013 Rio de Janeiro, RJ Brazil (Brazil)

2006-02-11

256

Langevin dynamics of polymeric manifolds in melts  

NASA Astrophysics Data System (ADS)

The Martin-Siggia-Rose generating functional (MSR-GF) technique is used for treating the polymeric D-dimensional-manifold melt dynamics. The one- (test-) manifold dynamics and the collective dynamics are considered separately. The test-manifold dynamics is obtained by integrating out the melt collective variables. This is done within the dynamic random-phase approximation (RPA). The resulting effective-action functional of the test manifold is treated by making use of the self-consistent Hartree approximation. As a consequence, the generalized Rouse equation of the test manifold is derived, and its static and dynamic properties are studied. By making use the MSR-GF technique, the fluctuations around the RPA of the collective variables - mass density and response-field density - are investigated. As a result, the equations for the correlation and response functions are derived. The memory kernel can be specified for the ideal glass transition as a sum of all `water-melon' diagrams.

Rostiashvili, V. G.; Rehkopf, M.; Vilgis, T. A.

1999-03-01

257

On Pfaff's equations of motion in dynamics; Applications to satellite theory  

Microsoft Academic Search

In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the

R. Broucke

1978-01-01

258

Continuum regularization of quantum field theory  

SciTech Connect

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

Bern, Z.

1986-04-01

259

Dynamics of the Langevin model subjected to colored noise: Functional-integral method  

NASA Astrophysics Data System (ADS)

We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is examined with relevance to a recent controversy on the stationary subthreshold voltage distribution of an integrate-and-fire model including stochastic excitatory and inhibitory synapses and a noisy input. We have studied the stationary probability distribution and dynamical responses to time-dependent (pulse and sinusoidal) inputs of the linear Langevin model. Model calculations have shown that results of the FIM are in good agreement with those of direct simulations (DSs). A comparison is made among various approximate analytic solutions such as the universal colored noise approximation (UCNA). It has been pointed out that dynamical responses to pulse and sinusoidal inputs calculated by the UCNA are rather different from those of DS and the FIM, although they yield the same stationary distribution.

Hasegawa, Hideo

2008-05-01

260

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

261

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory.  

PubMed

We approach the perturbative solution to the diffusion equation for the case of absorbing inclusions embedded in a heterogeneous scattering medium by using general properties of the radiative transfer equation and the solution of the Fredholm equation of the second kind given by the Neumann series. The terms of the Neumann series are used to obtain the expression of the moments of the generalized temporal point-spread function derived in transport theory. The moments are calculated independently by using Monte Carlo simulations for validation of the theory. While the mixed moments are correctly derived from the theory by using the solution of the diffusion equation in the geometry of interest, in order to obtain the self moments we should reframe the problem in transport theory and use a suitable solution of the radiative transfer equation for the calculation of the multiple integrals of the corresponding Neumann series. Since the rigorous theory leads to impractical formulas, in order to simplify and speed up the calculation of the self moments, we propose a heuristic method based on the calculation of only a single integral and some scaling parameters. We also propose simple quadrature rules for the calculation of the mixed moments for speeding up the computation of perturbations due to multiple defects. The theory can be developed in the continuous-wave domain, the time domain, and the frequency domain. In a companion paper [J. Opt. Soc. Am. A23, 2119 (2006)] we discuss the conditions of applicability of the theory in practical cases found in diffuse optical imaging of biological tissues. PMID:16912737

Sassaroli, Angelo; Martelli, Fabrizio; Fantini, Sergio

2006-09-01

262

Anharmonic Vibrational MØLLER-PLESSET Perturbation Theories Using the Dyson Equation  

NASA Astrophysics Data System (ADS)

We have developed new second-order diagrammatic perturbation theories for the anharmonic vibrational structure of molecules and solids in the Møller-Plesset partitioning of the Hamiltonian which we refer to as XVMP2. XVMP2 uses the size-extensive vibrational self-consistent field (XVSCF) methods for the reference wave function. In lieu of calculating the total energies of excited vibrational states, XVMP2 calculates frequencies directly using the Dyson equation for the single-particle vibrational Green's function and a truncated diagrammatic sum for the Dyson self-energy. This method enables XVMP2 to predict accurate anharmonic frequencies even for methods affected by strong anharmonic resonance without any matrix diagonalization step.

Hermes, Matthew R.; Hirata, So

2013-06-01

263

Stochastic theory of an optical vortex in nonlinear media.  

PubMed

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

Kuratsuji, Hiroshi

2013-07-08

264

Violation of the continuity equation in the Krieger-Li-Iafrate approximation for current-density functional theory  

NASA Astrophysics Data System (ADS)

We show that the exchange-correlation scalar and vector potentials obtained from the optimized effective potential (OEP) equations and from the Krieger-Li-Iafrate (KLI) approximation for the current-density functional theory (CDFT) change under a gauge transformation such that the energy functional remains invariant. This alone does not assure, however, the theory’s compliance with the continuity equation. Using the model of a quantum ring with a broken angular symmetry which is penetrated by a magnetic flux we demonstrate that the physical current density calculated with the exact-exchange CDFT in the KLI approximation violates the continuity condition. In contrast, the current found from a solution of the full OEP equations satisfies this condition. We argue that the continuity violation stems from the fact that the KLI potentials are not (in general) the exact functional derivatives of a gauge-invariant exchange-correlation functional.

Siegmund, Marc; Pankratov, Oleg

2011-01-01

265

Landau transport equations in a slave-boson mean-field theory of the t-J model  

Microsoft Academic Search

In this paper we generalize slave-boson mean-field theory for t-J model to the time-dependent regime, and derive transport equations for t-J model, both in the normal and superconducting states. By eliminating the boson and constraint fields exactly at zero temperature in the linear-response regime we obtain a set of transport equations for physical electrons which have the same form as

Tai-Kai Ng

2004-01-01

266

An Equation of State for Gases at Extremely High Pressures and Temperatures from the Hydrodynamic Theory of Detonation  

Microsoft Academic Search

The hydrodynamic theory of detonation is derived in a convenient form for practical utility by employing the general equation of state pv=nRT+?(T, v)p. Two methods of solution of the general equations based on measured detonation velocity are discussed. In method (a) the detailed form of ?(T, v) is unspecified. It is therefore, in principle, at least, a general solution. However,

Melvin A. Cook

1947-01-01

267

Dynamic flight stability of hovering model insects: theory versus simulation using equations of motion coupled with Navier–Stokes equations  

Microsoft Academic Search

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate\\u000a theory and computed by numerical simulation. The theory is based on the averaged model (which assumes that the frequency of\\u000a wingbeat is sufficiently higher than that of the body motion, so that the flapping wings’ degrees of freedom relative to the

Yan-Lai Zhang; Mao Sun

2010-01-01

268

Prediction of the homogeneous droplet nucleation by the density gradient theory and PC-SAFT equation of state  

NASA Astrophysics Data System (ADS)

We combined the density gradient theory (DGT) with the PC-SAFT and Peng-Robinson equations of state to model the homogeneous droplet nucleation and compared it to the classical nucleation theory (CNT) and experimental data. We also consider the effect of capillary waves on the surface tension. DGT predicts nucleation rates smaller than the CNT and slightly improves the temperature-dependent deviation of the predicted and experimental nucleation rates.

Planková, Barbora; Hrubý, Jan; Vinš, Václav

2013-05-01

269

Quantum non-Markovian Langevin formalism for heavy ion reactions near the Coulomb barrier  

SciTech Connect

The generalized Langevin approach is suggested to describe the capture inside of the Coulomb barrier of two heavy nuclei at bombarding energies near the barrier. The equations of motion for the relative distance (collective coordinate) between two interacting nuclei are consistent with the generalized quantum fluctuation-dissipation relations. The analytical expressions are derived for the time-dependent non-Markovian microscopic transport coefficients for the stable and unstable collective modes. The calculated results show that the quantum effects in the diffusion process increase with increasing friction or/and decreasing temperature. The capture probability inside of the Coulomb barrier is enhanced by the quantum noise at low energies near the barrier. An increase of the passing probability with dissipation is found at sub-barrier energies.

Sargsyan, V. V.; Antonenko, N. V. [Joint Institute for Nuclear Research, RU-141980 Dubna (Russian Federation); Kanokov, Z. [Joint Institute for Nuclear Research, RU-141980 Dubna (Russian Federation); National University, 700174 Tashkent (Uzbekistan); Adamian, G. G. [Joint Institute for Nuclear Research, RU-141980 Dubna (Russian Federation); Institute of Nuclear Physics, 702132 Tashkent (Uzbekistan)

2008-02-15

270

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

SciTech Connect

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

J. QIANG; R. RYNE; S. HABIB

2000-05-01

271

Ambient space formulations and statistical mechanics of holonomically constrained Langevin systems  

NASA Astrophysics Data System (ADS)

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

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

2011-11-01

272

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

2002-12-19

273

On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion  

Microsoft Academic Search

Differential equations governing the time evolution of distribution functions for Brownian motion in the full phase space were first derived independently by Klein and Kramers. From these so-called Fokker-Planck equations one may derive the reduced differential equations in coordinate space known as Smoluchowski equations. Many such derivations have previously been reported, but these either involved unnecessary assumptions or approximations, or

Gerald Wilemski

1976-01-01

274

The Sasao-Okubo-Saito equations by Hamilton theory. First results.  

NASA Astrophysics Data System (ADS)

A canonical formulation of the rotational motion for an elastic Earth model has been developed. From the canonical equations for the precessional and nutational motions in an inertial frame, the equations in an Earth fixed frame are deduced. The linearized equations obtained for polar motion and liquid core motion are equivalents to the Sasao-Okubo-Saito equations.

Romero, P.; Sevilla, M. J.

275

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

Microsoft Academic Search

An analytic approximate solution of New Kinematic Model with the boundary conditions is developed for the incompressible packing condition in Pebble Bed Reactors. It is based on velocity description of the packing density in the hopper. The packing structure can be presented with a jamming phenomenon from flow types. The gravity-driven macroscopic motions are governed not only by the geometry

Kyoung Lee; Zhijian Wang; Robin Gardner

2010-01-01

276

A Patient Satisfaction Theory and Its Robustness Across Gender in Emergency Departments: A Multigroup Structural Equation Modeling Investigation  

Microsoft Academic Search

This investigation tested the patient-centered Primary Provider Theory of Patient Satisfaction across gender in national random samples of emergency patients. Using multigroup structural equation modeling, the results supported the model's robustness. Physician service, waiting time, and nursing satisfaction explained 48%, 41%, and 11% of overall satisfaction plus 92% and 93% of female and male satisfaction, respectively. Unit increases in physician

Stephen J. Aragon; Sabina B. Gesell

2003-01-01

277

On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity  

Microsoft Academic Search

In the present report, we investigate the formulation, for the numerical evaluation of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity. Some simple formulas are given for the numerical solution of the general case of the multidimensional singular integrals. Moreover a numerical technique is also established for the numerical solution of some special cases

E. G. Ladopoulos

1988-01-01

278

Molecular origin of the hydrophobic effect: Analysis using the angle-dependent integral equation theory  

NASA Astrophysics Data System (ADS)

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is ~1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.

Kinoshita, Masahiro

2008-01-01

279

Loop Variables and Gauge Invariant Exact Renormalization Group Equations for Closed String Theory  

NASA Astrophysics Data System (ADS)

We formulate the Exact Renormalization Group on the string worldsheet for closed string backgrounds. The same techniques that were used for open strings are used here. There are some subtleties. One is that holomorphic factorization of the closed string vertex operators does not hold in the presence of a cutoff on the Euclidean worldsheet. This introduces extra terms in the Lagrangian at the cutoff scale and they turn out to be crucial for implementing gauge invariance. This naive generalization from open string to closed string requires a massive graviton and the gauge symmetry is Abelian, just as in open string theory. Interestingly, it turns out that if one introduces a nondynamical background metric (as in background field formalism) and combines a gauge transformation on the field with a transformation on the coordinates and background metric, the graviton can be massless. Some examples of background coordinate covariant equations are worked out explicitly. A preliminary discussion of massive modes, massive gauge transformations and the role of worldsheet regulator terms is given. Some of the gauge transformations can be given a geometric meaning if space-time is assumed to be complex at some level.

Sathiapalan, B.

2013-09-01

280

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

SciTech Connect

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

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

1993-09-01

281

Multinomial diffusion equation.  

PubMed

We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N??, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails. PMID:21797338

Balter, Ariel; Tartakovsky, Alexandre M

2011-06-24

282

Multinomial diffusion equation  

NASA Astrophysics Data System (ADS)

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

Balter, Ariel; Tartakovsky, Alexandre M.

2011-06-01

283

Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism  

SciTech Connect

Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance--invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green's functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.

Watson, P.; Reinhardt, H. [Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

2007-02-15

284

Prediction of viscosity of mixed electrolyte solutions based on the Eyring's absolute rate theory and the equations of Patwardhan and Kumar  

Microsoft Academic Search

The mixing behavior of viscosities of electrolyte solutions at constant ionic strength has been studied for the first time using the Eyring's absolute rate theory and the equations of Patwardhan and Kumar. Coupling of the Eyring's theory with the equations of Patwardhan and Kumar yields simple mixing behavior of viscosities of electrolyte solutions at constant ionic strength, and thus permits

Yu-Feng Hu

2004-01-01

285

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

286

Langevin description of speckle dynamics in nonlinear disordered media.  

PubMed

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies Omega below some Omega(max), provided that the nonlinearity exceeds some Omega-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of 1/Omega(max). PMID:12636619

Skipetrov, S E

2003-01-06

287

Restricted primitive model of dianions and counterions within the mean spherical approximation: Integral equation and thermodynamic perturbation theory  

NASA Astrophysics Data System (ADS)

We present an analytical integral equation theory for dimers modeled as hard-sphere tangentially connected anions and cationic hard-sphere monomeric counterions embedded in a continuum dielectric medium. Each hard-sphere segment on the dimer and hard-sphere counterion is univalent with unit diameters. The model was formulated in the context of the two-density Ornstein-Zernike integral equation theory within the mean spherical approximation. Analytical algebraic solutions for the model were obtained except for one parameter which requires simple numerical computation. The contact values of the radial distribution functions, internal energy, Helmholtz energy, and osmotic pressure of the system were derived analytically as a function of density and Bjerrum length via the energy route. Radial distribution functions beyond contact predicted by the theory were calculated numerically using the Perram algorithm. Thermodynamic perturbation theory was used to predict the osmotic pressure of longer chains using the dimer thermodynamic and structural properties as a reference system. Predictions from the theory compared well with computer simulation data reported in the literature although no significant improvement over the monomer reference system was found.

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

2000-10-01

288

Body Quantum Scattering Theory in Two Hilbert Spaces: Body Integral Equations  

Microsoft Academic Search

.   Scattering for a nonrelativistic system of distinguishable and spinless particles interacting via short-range pair potentials is considered. Half-on-shell integral\\u000a equations (the CG equations) are proposed, the solutions of which determine approximate scattering amplitudes that converge\\u000a to the exact scattering amplitude. It is proved, under mild Hölder integrability assumptions, that these apparently singular\\u000a equations actually have a compact kernel for

C. Chandler; A. G. Gibson

1998-01-01

289

M5-branes in the ABJM theory and the Nahm equation  

NASA Astrophysics Data System (ADS)

We explicitly construct two classes of the BPS solutions in the Aharony-Bergman-Jafferis-Maldacena action—the funnel type solutions and the ’t Hooft-Polyakov type solutions—and study their physical properties as the M2-M5 bound state. Furthermore, we give a one-to-one correspondence between the solutions of the BPS equation and the ones of an extended Nahm equation which includes the Nahm equation. This enables us to construct infinitely many conserved quantities from the Lax form of the Nahm equation.

Nosaka, Tomoki; Terashima, Seiji

2012-12-01

290

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

291

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

292

Radial distribution function for hard spheres from scaled particle theory, and an improved equation of state  

Microsoft Academic Search

Previous applications of scaled particle theory have been limited to the calculation of thermodynamic properties of fluids rather than structure. In the present paper, the theory is expanded so that it is capable of yielding the radial distribution function. The method is first illustrated by applying it to one- dimensional fluids of hard rods where, as in other theories, the

H. Reiss; R. V. Casberg

1974-01-01

293

A density functional theory for vapor-liquid interfaces using the PCP-SAFT equation of state  

NASA Astrophysics Data System (ADS)

A Helmholtz energy functional for inhomogeneous fluid phases based on the perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state is proposed. The model is supplemented with a capillary wave contribution to the surface tension to account for long-wavelength fluctuations of a vapor-liquid interface. The functional for the dispersive attraction is based on a nonlocal perturbation theory for chain fluids and the difference of the perturbation theory to the dispersion term of the PCP-SAFT equation of state is treated with a local density approximation. This approach suggested by Gloor et al. [Fluid Phase Equilib. 194, 521 (2002)] leads to full compatibility with the PCP-SAFT equation of state. Several levels of approximation are compared for the nonlocal functional of the dispersive attractions. A first-order non-mean-field description is found to be superior to a mean-field treatment, whereas the inclusion of a second-order perturbation term does not contribute significantly to the results. The proposed functional gives excellent results for the surface tension of nonpolar or only moderately polar fluids, such as alkanes, aromatic substances, ethers, and ethanoates. A local density approximation for the polar interactions is sufficient for carbon dioxide as a strongly quadrupolar compound. The surface tension of acetone, as an archetype dipolar fluid, is overestimated, suggesting that a nonisotropic orientational distribution function across an interface should for strong dipolar substances be accounted for.

Gross, Joachim

2009-11-01

294

Mixed quantum classical rate theory for dissipative systems  

NASA Astrophysics Data System (ADS)

Numerically exact solutions for the quantum rate of potential barrier crossing in dissipative systems are only possible for highly idealized systems. It is, therefore, of interest to develop approximate theories of more general applicability. In this paper we formulate a mixed quantum classical thermodynamical rate theory for dissipative systems. The theory consists of two parts. The evaluation of a thermal flux and the computation of the classically evolved product projection operator. Since the dividing surface is perpendicular to the unstable normal mode of the dissipative system, we reformulate the theory in terms of the unstable normal mode and a collective bath mode. The influence functional for the thermal flux matrix elements in this representation is derived. The classical mechanics are reformulated in terms of the same two degrees of freedom. The one-dimensional Langevin equation for the system coordinate is replaced by a coupled set of Langevin equations for the unstable normal mode and the collective bath mode. The resulting rate expression is given in the continuum limit, so that computation of the rate does not necessitate a discretization of the bath modes. To overcome the necessity of computing a multidimensional Fourier transform of the matrix elements of the thermal flux operator, we adapt, as in previous studies, a method of Creswick [Mod. Phys. Lett. B 9, 693 (1995)], by which only a one-dimensional Fourier transform is needed. This transform is computed by quadrature. The resulting theory is tested against the landmark numerical results of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] obtained for barrier crossing in a symmetric double well potential. We find that mixed quantum classical rate theory (MQCLT) provides a substantial improvement over our previous quantum transition state theory as well as centroid transition state theory computations and is in overall good agreement with the exact results.

Liao, Jie-Lou; Pollak, Eli

2002-02-01

295

Correlation Theory of Quantized Electromagnetic Fields. I. Dynamical Equations and Conservation Laws  

Microsoft Academic Search

Dynamical equations are derived, which describe the space-time development of second-order coherence tensors of a quantized electromagnetic field in vacuo. With the help of these equations, laws for the conservation of correlations are obtained. Some new non-negative-definiteness conditions which the coherence tensors obey are also established.

C. L. Mehta; E. Wolf

1967-01-01

296

Adomian's method for Hammerstein integral equations arising from chemical reactor theory  

Microsoft Academic Search

An ordinary differential equation with a parameter in the boundary conditions describes the steady state in an adiabatic tubular chemical reactor. In this paper, the problem is considered as a Hammerstein integral equation and solutions are obtained using Adomian's decomposition method.

N. M. Madbouly; D. F. McGhee; G. F. Roach

2001-01-01

297

Nonlocal Theory of Radiation-Matter Interaction: Boundary-Condition-Less Treatment of Maxwell Equations  

Microsoft Academic Search

Based on the separability with respect to position variables of the susceptibility for a finite system, we have developed a formulation which solves Schrödinger and Maxwell equations selfconsistently. The case of linear response is described in detail. As a manifestation of the selfconsistency between the two equations, the appearance of radiative damping rate with correct magnitude has been demonstrated for

Kikuo Cho

1991-01-01

298

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

ERIC Educational Resources Information Center

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

Koutsoyiannis, Demetris

2012-01-01

299

Reconciling theory and practice: a revised pole equation for w-cdma cell powers  

Microsoft Academic Search

The performance evaluation of w-cdma networks is intri- cate as cells are strongly coupled through interference. Pole equations have been developed as a simple tool to analyze cell capacity. Numerous scientific contributions have been made on their basis. In the established forms, the pole equations rely on strong assumptions such as homogeneous traffic, uniform users, and constant downlink orthogonality factor.

Hans-florian Geerdes; Andreas Eisenblätter

2007-01-01

300

An Investigation of Factors Affecting Test Equating in Latent Trait Theory.  

ERIC Educational Resources Information Center

Studied five factors that can affect the equating of scores from two tests onto a common score scale through the simulation and equating of 4,860 item data sets. Findings indicate three statistically significant two-way interactions for common item length and test length, item difficulty standard deviation and item distribution type, and item…

Sunathong, Surintorn; Schumacker, Randall E.; Beyerlein, Michael M.

2000-01-01

301

Application of a temperature-dependent liquid-drop model to dynamical Langevin calculations of fission-fragment distributions of excited nuclei  

NASA Astrophysics Data System (ADS)

A stochastic approach to fission dynamics based on three-dimensional Langevin equations was applied to calculation of the mass-energy and angular distributions of fission fragments. The dependence of the mass-energy distribution parameters on the angular momentum and the anisotropy of the fission-fragment angular distribution on excitation energy have been studied in a wide range of the fissility parameter. A temperature-dependent finite-range liquid-drop model was used in a consistent way to calculate the functional of the Helmholtz free energy and level-density parameter. The modified one-body mechanism of nuclear dissipation (the so-called surface-plus-window dissipation) was used to determine the dissipative forces in Langevin equations. The evaporation of light prescission particles was taken into account on the basis of a statistical model combined with Langevin dynamics. The calculated parameters of the mass-energy distribution and their angular dependencies are in good quantitative agreement with the available experimental data at the value of the reduction coefficient of the contribution from the wall formula equal to 0.25. Analysis of the anisotropy of the fission-fragment angular distribution performed with the saddle-point transition state model and scission-point transition state model indicates that it is necessary to take into account the dynamical aspects of the fission-fragment angular distribution formation.

Ryabov, E. G.; Karpov, A. V.; Nadtochy, P. N.; Adeev, G. D.

2008-10-01

302

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

303

Interfacial Behavior in Polyelectrolyte Blends: Hybrid Liquid-State Integral Equation and Self-Consistent Field Theory Study  

NASA Astrophysics Data System (ADS)

Polyelectrolytes and electrolyte solutions are known to demonstrate a rich array of phase behaviors due to the effects of long-ranged interactions inherent in Coulombic attractions and repulsions. While there is a wealth of literature examining these materials to provide some physical insight into their thermodynamics, all of these methods make strong approximations with regards to the nature of the ionic component. In this investigation we develop a hybrid liquid-state integral equation and self-consistent field theory numerical theory, and systematically demonstrate the ramifications on local ion structure on the overall thermodynamics of segregated polymer blends. We show effects on phase separation such as suppression due to hard sphere interactions and enhancement due to ion cohesion that are not described using traditional Poisson-Boltzmann mean-field theory.

Sing, Charles E.; Zwanikken, Jos W.; de la Cruz, Monica Olvera

2013-10-01

304

Correctness of certain integral equation theories for core-softened fluids  

NASA Astrophysics Data System (ADS)

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

Huš, Matej; Zalar, Matja; Urbic, Tomaz

2013-06-01

305

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

306

Statistical Theory of the Fracture of Fragile Bodies. Part 2: The Integral Equation Method.  

National Technical Information Service (NTIS)

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams ...

P. Kittl

1984-01-01

307

Solving the Schroedinger equation with use of 1/N perturbation theory  

SciTech Connect

The large N expansion provides a powerful new tool for solving the Schroedinger equation. In this paper, we present simple recursion formulas which facilitate the calculation. We do some numerical calculations which illustrate the speed and accuracy of the technique

Mlodinow, L.D.; Shatz, M.P.

1984-04-01

308

The Generalized Gravity Equation, Monopolistic Competition, and the Factor-Proportions Theory in International Trade  

Microsoft Academic Search

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

Jeffrey H Bergstrand

1989-01-01

309

Functional equations for path-dependent phase factors in Yang-Mills theories  

Microsoft Academic Search

We introduce a gauge-covariant functional derivative for path-dependent quantities, and use it to analyze the behavior of the phase matrix Phiy,x(Gamma)=PGammaexp[-?xyA(x).dx], under variations of the contour Gamma. We give a general formula for Phiy+deltay,x+deltax(Gamma') for a varied path in terms of Phiy,x(Gamma), and analyze a gauge-covariant version of the functional wave equation (or ``string equation'') for Phi derived by Nambu

Loyal Durand; Eduardo Mendel

1979-01-01

310

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

Microsoft Academic Search

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

Victor S. L'vov; Oleksii Rudenko

2008-01-01

311

A Mean-field statistical theory for the nonlinear Schrodinger equation  

Microsoft Academic Search

A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrodinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such equations consists of a deterministic coherent structure coupled with fine-scale, random fluctuations, or radiation. The model is derived from equilibrium statistical mechanics by using a

Richard Jordan; Bruce Turkington; Craig L. Zirbel

1999-01-01

312

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

SciTech Connect

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

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

2010-12-14

313

The equations of motion of slowly moving particles in the general theory of relativity  

Microsoft Academic Search

Summary  The equations of motion of slowly moving particles in a harmonic co-ordinate system are obtained up to an accuracy of the\\u000a 9th order inc\\u000a -1, wherec is the velocity of light. This is done for the twoparticle case, and is an extension of the familiar Einstein, Infeld and\\u000a Hoffmann (EIH) equations of motion, which hold up to an accuracy of

M. Carmeli

1965-01-01

314

Interplay of cooperativity and entanglements in polymer melt dynamics: insights from theory and simulations  

NASA Astrophysics Data System (ADS)

Dynamical heterogeneities in polymer melts generate cooperative ?motion, which results in subdiffusive center-of-mass mean-square ?displacement at times shorter than the longest Rouse relaxation time. ?This behavior is described by our Generalized Langevin Equation ?for cooperative dynamics, which is found to be in agreement with data ?from simulations and from Neuron Spin Echo experiments. We present a ?study of the interplay between cooperative dynamics and polymer ?confinement due to the presence of entanglements. Semiflexibility, ?which is specific to the chemical structure of the polymer, and ?intermolecular interactions, which generate dynamical cooperativity ?and entanglements and are functions of the degree of polymerization, ?are explicitly included in the theory.

Guenza, Marina; Lyubimov, Ivan

2010-03-01

315

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

2012-03-30

316

Langevin Molecular Dynamics of Driven Magnetic Flux Lines  

NASA Astrophysics Data System (ADS)

The characterization of type-II superconducting materials and their technological applications in external magnetic fields require a thorough understanding of the stationary and dynamical properties of vortex matter. The competition of repulsive interactions and attractive material defects renders the physics of externally driven magnetic flux lines very rich. We study the non-equilibrium steady states as well as transient relaxation properties of driven vortex lines in the presence of randomly distributed point pinning centers. We model the vortices as interacting elastic lines and employ a Langevin Molecular Dynamics (LMD) algorithm to extract steady-state and non-stationary time-dependent behavior. We compare the efficiency and accuracy of LMD to previously obtained Metropolis Monte Carlo steady-state force-velocity and gyration radius data. In future work we intend investigate the transient two-time height-height correlation and response functions.

Dobramysl, Ulrich; Pleimling, Michel; Täuber, Uwe C.

2011-10-01

317

Complex Langevin: etiology and diagnostics of its main problem  

NASA Astrophysics Data System (ADS)

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

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

2011-10-01

318

Initial-Value Methods for Integral Equations Arising in Theories of the Solar Atmosphere.  

National Technical Information Service (NTIS)

A computationally useful initial-value theory for determining the intensity of radiation emerging normal to the surface of the atmosphere for comparison with observed profiles is discussed. In this theory the emergent intensity E is the solution of an ini...

H. Kagiwada R. Kalaba S. Ueno

1968-01-01

319

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

320

Determination of critical exponents and equation of state by field theory method  

Microsoft Academic Search

Path integrals have played a fundamental role in emphasizing the profound analogies between Quantum Field Theory (QFT), and Classical as well as Quantum Statistical Physics. Ideas coming from Statistical Physics have then led to a deeper understanding of Quantum Field Theory and open the way for a wealth of non-perturbative methods. Conversely QFT methods are become essential for the description

Jean Zinn-Justin; Service de Physique Theorique

1998-01-01

321

AdS/CFT connection between Boltzmann and Einstein equations: Kinetic theory and pure gravity in AdS space  

SciTech Connect

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

Iyer, Ramakrishnan [Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484 (United States); Mukhopadhyay, Ayan [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019 (India)

2010-04-15

322

Comparisons Between Integral Equation Theory and Molecular Dynamics Simulations for Atomistic Models of Polyethylene Liquids  

SciTech Connect

Molecular dynamics (MD) simulations were performed on dense liquids of polyethylene chains of 24 and 66 united atom CH{sub 2} units. A series of models was studied ranging in atomistic detail from coarse-grained, freely-jointed, tangent site chains to realistic, overlapping site models subjected to bond angle restrictions and torsional potentials. These same models were also treated with the self-consistent, polymer reference interaction site model (PRISM) theory. The intramolecular and total structure factors, as well as, the intermolecular radial distribution functions g(r) and direct correlation functions C(r) were obtained from theory and simulation. Angular correlation functions were also simulation obtained from the MD simulations. Comparisons between theory and reveal that PRISM theory works well for computing the intermolecular structure of coarse-grained chain models, but systematically underpredicts the extent of intermolecular packing as more atomistic details are introduced into the model. A consequence of g(r) having insufficient structure is that the theory yields an isothermal compressibility that progressively becomes larger, relative to the simulations, as overlapping the PRISM sites and angular restrictions are introduced into the model. We found that theory could be considerably improved by adding a tail function to C(r) beyond the effective hard core diameter. The range of this tail function was determined by requiring the theory to yield the correct compressibility.

Curro, John G.; Webb III, Edmund B.; Grest, Gary S.; Weinhold, Jeffrey D.; Putz, Mathias; McCoy, John D.

1999-07-21

323

Comparisons between integral equation theory and molecular dynamics simulations for realistic models of polyethylene liquids  

SciTech Connect

Molecular dynamics (MD) simulations were performed on dense liquids of polyethylene chains of 24 and 66 united atom CH{sub 2} units. A series of models was studied ranging in atomistic detail from coarse-grained, freely-jointed, tangent site chains to realistic, overlapping site models subjected to bond angle restrictions and torsional potentials. These same models were also treated with the self-consistent, polymer reference interaction site model (PRISM) theory. The intramolecular and total structure factors, as well as, the intermolecular radial distribution functions g(r) and direct correlation functions C(r) were obtained from theory and simulation. Angular correlation functions were also obtained from the MD simulations. Comparisons between theory and simulation reveal that PRISM theory works well for computing the intermolecular structure of coarse-grained chain models, but systematically underpredicts the extent of intermolecular packing, and overpredicts the compressibility, as more realistic details are introduced into the model. We found that the PRISM theory could be considerably improved by adding a tail function to C(r) beyond the effective hard core diameter. The range of this tail function was determined by requiring the theory to yield the correct compressibility. The intermolecular radial distribution functions from this modified PRISM theory were in excellent agreement with g(r){close_quote}s obtained from the simulations. {copyright} {ital 1999 American Institute of Physics.}

Curro, J.G.; Webb, E.B. III,; Grest, G.S.; Weinhold, J.D. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Puetz, M. [Center for Microengineered Materials, University of New Mexico, Albuquerque, New Mexico 87106 (United States); McCoy, J.D. [Department of Materials and Metallurgical Engineering, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87185 (United States)

1999-11-01

324

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

325

Toward the theory of stochastic condensation in clouds. Part 1: A general kinetic equation  

SciTech Connect

In order to understand the mechanisms of formation of broad size spectra of cloud droplets and to develop a basis for the parameterization of cloud microphysical and optical properties, the authors derive a general kinetic equation of stochastic condensation that is applicable for various relationships between the supersaturation relaxation time {tau}{sub f} and the timescale of turbulence {tau}{sub i}. Supersaturation is considered as a nonconservative variable, and thus additional covariances and a turbulent diffusion coefficient tensor that is dependent on the supersaturation relaxation time, k{sub ij}({tau}{sub f}), are introduced into the kinetic equation. This equation can be used in cloud models with explicit microphysics or can serve as a basis for development of parameterizations for bulk cloud models and general circulation models.

Khvorostyanov, V.I.; Curry, J.A.

1999-12-01

326

Critical dynamics in systems controlled by fractional kinetic equations  

NASA Astrophysics Data System (ADS)

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

Batalov, Lev; Batalova, Anastasia

2013-02-01

327

Multi-zone TAP-reactors theory and application: I. The global transfer matrix equation  

Microsoft Academic Search

A general theory of single-pulse state-defining experiments for a multi-zone TAP (temporal analysis of products) reactor, is developed using the Laplace transform formalism; the theory gives explicit expressions for the moments of the outlet flux, series expansions for the transient values of this flux, and offers an efficient means to compute the actual profiles of gas concentration in the reactor

D. Constales; G. S. Yablonsky; G. B. Marin; J. T. Gleaves

2001-01-01

328

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

329

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations  

SciTech Connect

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs.

Tanimura, Shogo (Nagoya Univ. (Japan))

1992-12-01

330

A quantitative theory of vegetation patterns based on plant structure and the non-local F-KPP equation  

NASA Astrophysics Data System (ADS)

The theory of vegetation patterns presented rests on two hypotheses: (i) the self-organization hypothesis that attributes their cause to interactions intrinsic to vegetation dynamics; (ii) the complementary self-assembly hypothesis that attributes their large spatial scale to the proximity of their dynamical conditions with a critical point. A non-local version of the F-KPP equation allows us to formulate these hypotheses in terms of individual plant properties. Both general and parsimonious, this formulation is strictly quantitative. It only relies on structural parameters that can be measured with precision in the field. Quantitative interpretation of observations and of the predictions provided by the theory is illustrated by an analysis of the periodic patterns found in some Sub-Sahelian regions.

Lefever, René; Turner, John W.

2012-11-01

331

A modified repulsive bridge correction to accurate evaluation of solvation free energy in integral equation theory for molecular liquids  

NASA Astrophysics Data System (ADS)

Integral equation theory for molecular liquids is one of the powerful frameworks to evaluate solvation free energy (SFE). Different from molecular simulation methods, the theory computes SFE in an analytical manner. In particular, the correction method proposed by Kovalenko and Hirata [Chem. Phys. Lett. 290, 237 (1998); and J. Chem. Phys. 113, 2793 (2000)] is quite efficient in the accurate evaluation of SFE. However, the application has been limited to aqueous solution systems. In the present study, an improved method is proposed that is applicable to a wide range of solution systems. The SFE of a variety of solute molecules in chloroform and benzene solvents is evaluated. A key is the adequate treatment of excluded volume in SFE calculation. By utilizing the information of chemical bonds in the solvent molecule, the accurate computation of SFE is achieved.

Kido, Kentaro; Yokogawa, Daisuke; Sato, Hirofumi

2012-07-01

332

Equation of hydrostatic equilibrium in the theory of a planetary figure  

SciTech Connect

A numerical method is developed for solving the equation of hydrostatic equilibrium with allowance for corrections for the asphericity of the planet. Radial density distributions are found for a set of polytropes with indices of from 1 to 2 in planets with the parameters of Jupiter, Saturn, Uranus, and Neptune.

Bobrov, A.M.; Vasil'ev, P.P.; Zharkov, V.N.; Trubitsyn, V.P.

1978-07-01

333

ACCURACY AND SCOPE OF VARIATIONAL AND DIFFERENCE SOLUTIONS OF THE DIFFUSION EQUATIONS OF REACTOR THEORY  

Microsoft Academic Search

A comparison is made of the accuracy of variational and difference ; solutions of the one-group diffusion equation. For reactors with a few regions ; there is little practical difference in the solutions for the fluxes and ; laplacians as given by the two methods. The variational method can easily be ; used with a hand machine, and when programmed

R. T. Ackroyd; M. A. Perks

1959-01-01

334

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

335

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

Microsoft Academic Search

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

Ling Chen; Lianxing Wen; Tianyu Zheng

2005-01-01

336

High Order Perturbation Theory for Helmholtz\\/Schrodinger Equations via a Separable Preconditioner  

Microsoft Academic Search

A numerical procedure is suggested for the solution of multidimensional inhomogeneous Helmholtz\\/Schrodinger equations. The procedure is based on coordinate-space (grid) representations in which all the coupling terms (V ˆ ) between different degrees of freedom are local (diagonal) and therefore the remaining differential (nonlocal) terms are separable. This separability leads to an efficient (sparse) representation of an approximate Green's opera-

Ilya Vorobeichik; Uri Peskin

1997-01-01

337

High Order Perturbation Theory for Helmholtz\\/Schrodinger Equations via a  

Microsoft Academic Search

A numerical procedure is suggested for the solution of multidimensional inhomogeneous Helmholtz\\/Schrodinger equations. The procedure is based on coordinate-space (grid) representations in which all the coupling terms (V ˆ ) between different degrees of freedom are local (diagonal) and therefore the remaining differential (nonlocal) terms are separable. This separability leads to an efficient (sparse) representation of an approximate Green's opera-

Separable Preconditioner; Ake Edlund; Ilya Vorobeichik; Uri Peskin

338

Theory and phenomenology of the gluon propagator from the Dyson-Schwinger equation in QCD  

Microsoft Academic Search

A new solution is found for the Dyson-Schwinger equation for the gluon propagator in the axial gauge. Unlike previously found ones this propagator does not display a 1\\/k4 pole as k --> 0 but has a very soft singularity in this region. Thus it represents a gluon which is not confining but rather confined since in configuration space the propagator

J. R. Cudell; D. A. Ross

1991-01-01

339

Theory of SNAP devices: basic equations and comparison with the experiment.  

PubMed

A SNAP (Surface Nanoscale Axial Photonics) device consists of an optical fiber with introduced nanoscale effective radius variation, which is coupled to transverse input/output waveguides. The input waveguides excite whispering gallery modes circulating near the fiber surface and slowly propagating along the fiber axis. In this paper, the theory of SNAP devices is developed and applied to the analysis of transmission amplitudes of simplest SNAP models exhibiting a variety of asymmetric Fano resonances and also to the experimental characterization of a SNAP bottle microresonator and to a chain of 10 coupled microresonators. Excellent agreement between the theory and the experiment is demonstrated. PMID:23037403

Sumetsky, M

2012-09-24

340

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

341

On the equivalence of the first and second order equations for gauge theories  

Microsoft Academic Search

We prove that every solution to the SU(2) Yang-Mills equations, invariant under the lifting to the principle bundle of the action of the group, O(3), of rotations about a fixed line in R4, with locally bounded and globally square integrable curvature is either self-dual or anti-self dual. In other words we prove, under the above assumptions, that every critical point

Clifford Henry Taubes

1980-01-01

342

The Geometry of the Master Equation and Topological Quantum Field Theory  

Microsoft Academic Search

In Batalin-Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some

M. Alexandrov; A. Schwarz; O. Zaboronsky; M. Kontsevich

1997-01-01

343

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

344

Simplified Derivation of the Fokker-Planck Equation.  

ERIC Educational Resources Information Center

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

Siegman, A. E.

1979-01-01

345

Topological Theory of Entanglement: A Polymer Chain and a Fixed Barrier. I. Diffusion Equation  

Microsoft Academic Search

A statistical mechanical theory of entanglement is developed, based on the topology of loops. As the simplest example of entangling systems, a system composed of a polymer chain and a fixed barrier is studied in the present and in the two following papers. First, Gauss linking coefficient T is given for simple-square-lattice chains, and it is transformed, basing on the

Kazuyoshi Iwata

1974-01-01

346

B.R.S. algebras. Analysis of the consistency equations in gauge theory  

Microsoft Academic Search

We compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms. By using the appropriate cohomological and algebraic methods, we do it for all dimensions of spacetime and all structure groups with reductive Lie algebras.

M. Dubois-Violette; M. Talon; C.-M. Viallet

1985-01-01

347

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

348

Energy and equations of motion in a tentative theory of gravity with a privileged reference frame  

Microsoft Academic Search

Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as in special relativity was expressed in terms of these distorted local standards, and was found to imply geodesic motion. Here, the formulation of

Mayeul Arminjon

2007-01-01

349

Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity  

NASA Astrophysics Data System (ADS)

We consider Bose-Einstein condensation of photons in an optical cavity filled with dye molecules that are excited by laser light. By using the Schwinger-Keldysh formalism we derive a Langevin field equation that describes the dynamics of the photon gas and, in particular, its equilibrium properties and relaxation towards equilibrium. Furthermore we show that the finite lifetime effects of the photons are captured in a single dimensionless damping parameter that depends on the power of the external laser pumping the dye. Finally, as applications of our theory we determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases.

de Leeuw, A.-W.; Stoof, H. T. C.; Duine, R. A.

2013-09-01

350

Explaining the Conversion to Organic Farming of Farmers of the Obwalden Canton, Switzerland - Extension of the Theory of Planned Behavior within a Structural Equation Modeling Approach  

Microsoft Academic Search

Farmers' decisions about conversion to organic farming are analyzed with a structural equation model. The Theory of Planned Behavior (ToPB), one of the prominent theories in the social psychology, is used as the theoretical basis of this study. Though ToPB is a well-defined theory, it is static rather than procedural and cannot model the individual decision-making as a process. Therefore,

Aysel Tutkun; Bernard Lehmann; Peter Schmidt

2006-01-01

351

Evaluation of minor hysteresis loops using Langevin transforms in modified inverse Jiles-Atherton model  

NASA Astrophysics Data System (ADS)

In this paper, we present a Langevin transforms model which evaluates accurately minor hysteresis loops for the modified inverse Jiles-Atherton model by using appropriate expressions in order to improve minor hysteresis loops characteristics. The parameters of minor hysteresis loops are then related to the parameters of the major hysteresis loop according to each level of maximal induction by using Langevin transforms expressions. The stochastic optimization method "simulated annealing" is used for the determination of the Langevin transforms coefficients. This model needs only two experimental tests to generate all hysteresis loops. The validity of the Langevin transforms model is justified by comparison of calculated minor hysteresis loops to measured ones and good agreements are obtained with better results than the exponential transforms model (Hamimid et al., 2011 [4]).

Hamimid, M.; Mimoune, S. M.; Feliachi, M.

2013-11-01

352

One-dimensional Langevin models of fluid particle acceleration in developed turbulence  

NASA Astrophysics Data System (ADS)

We make a comparative analysis of some recent one-dimensional Langevin models of the acceleration of a Lagrangian fluid particle in developed turbulent flow. The class of models characterized by random intensities of noises (RIN models) provides a fit to the recent experimental data on the acceleration statistics. We review the model by Laval, Dubrulle, and Nazarenko (LDN) formulated in terms of temporal velocity derivative in the rapid distortion theory approach, and propose its extension due to the RIN framework. The fit of the contribution to fourth-order moment of the acceleration is found to be better than in the other stochastic models. We study the acceleration probability density function conditional on velocity fluctuations implied by the RIN approach to the LDN-type model. The shapes of the conditional distributions and the conditional acceleration variance have been found in a good agreement with the recent experimental data by Mordant, Crawford, and Bodenschatz [Physica D (to be published), e-print physics/0303003].

Aringazin, A. K.; Mazhitov, M. I.

2004-02-01

353

Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes  

SciTech Connect

We present a fully quantal version of the Langevin model for the total rate of exoergic ion-molecule reactions or inelastic processes. The model, which is derived from a rigorous multichannel quantum-defect formulation of bimolecular processes, agrees with the classical Langevin model at sufficiently high temperatures. It also gives an analytic description of ion-molecule reactions and inelastic processes in the ultracold regime where the quantum nature of the relative motion between the reactants becomes important.

Gao Bo [Department of Physics and Astronomy, Mailstop 111, University of Toledo, Toledo, Ohio 43606 (United States)

2011-06-15

354

Analytical Energy Gradients for Excited-State Coupled-Cluster Methods: Automated Algebraic Derivation of First Derivatives for Equation-of-Motion Coupled-Cluster and Similarity Transformed Equation-of-Motion Coupled-Cluster Theories  

Microsoft Academic Search

The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the

Mark Wladyslawski; Marcel Nooijen

2005-01-01

355

Asymmetric Langevin dynamics for the ferromagnetic spherical model  

NASA Astrophysics Data System (ADS)

The present work pursues the investigation of the role of spatial asymmetry and irreversibility on the dynamical properties of spin systems. We consider the ferromagnetic spherical model with asymmetric linear Langevin dynamics. Such an asymmetric dynamics is irreversible, i.e., breaks detailed balance, because the principle of action and reaction is violated. The fluctuation-dissipation theorem therefore no longer holds. The stationary state is however still Gibbsian, i.e., the weights of configurations are given by the Boltzmann factor corresponding to the ferromagnetic Hamiltonian. The model is exactly solvable in any dimension, enabling an analytical evaluation of time-dependent observables. We show the existence of two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite but less than unity and varies continuously with the asymmetry, and a regime of strong violation where the fluctuation-dissipation ratio vanishes asymptotically. This phenomenon was first uncovered in the asymmetric kinetic Ising chain. The present results suggest that this novel kind of dynamical transition in nonequilibrium stationary states might be quite general. We also perform a systematic analysis of several regimes of interest, either stationary or transient, in various dimensions and in the different phases of the model.

Godrèche, C.; Luck, J. M.

2013-05-01

356

Langevin dynamics studies of unsaturated phospholipids in a membrane environment.  

PubMed Central

Computer simulations of three unsaturated phospholipids in a membrane environment have been carried out using Langevin dynamics and a mean-field based on the Marcelja model. The applicability of the mean-field to model unsaturated lipids was judged by comparison to available experimental NMR data. The results show that the mean-field methodology and the parameters developed for saturated lipids are applicable in simulations of unsaturated molecules, indicating that these simulations have good predictive capabilities. Single molecule simulations, each 100 ns in length, of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-elaidoyl-sn-glycero-3-phosphocholine (PEPC), and 1-palmitoyl-2-isolinoleoyl-sn-glycero-3-phosphocholine (PiLPC) reveal similarities between PEPC and DPPC. The presence of the trans double bond in PEPC has a minimum impact on the structural and dynamic properties of the molecule, which is probably the reason that isolated trans double bonds are rare in biological lipids. POPC exhibits different behavior, especially in the calculated average interchain distances, because of the cis double bond. The position of the two double bonds in PiLPC imparts special properties to the molecule.

Pearce, L L; Harvey, S C

1993-01-01

357

Theory of periodic solutions of the stationary Landau-Lifshitz equation  

SciTech Connect

In the phenomenological approach, quasi-one-dimensional structures in a magnet of a definite symmetry are described by solutions of the stationary Landau-Lifshitz equation or, equivalently, by the solutions of a variational problem with Lagrangian L whose actual form is determined by the requirement of invariance with respect to the symmetry group of the paramagnetic phase of the given magnet. In the present note, the methods of the variational calculus in the large are used to estimate the number of possible magnetic phases with periodic superstructure corresponding to a given free energy functional of the magnet.

Bar'yakhtar, V.G.; Leonov, I.A.; Soboleva, T.K.

1987-04-01

358

Fluids of linearly fused Lennard-Jones sites: Comparison between simulations and integral equation theories  

Microsoft Academic Search

The structural and thermodynamic properties of model molecular fluids of linear aggregates of Lennard-Jones sites was investigated using molecular dynamics simulation, reference interaction site model (RISM), and hypernetted-chain theory (HNC). This paper presents molecules of two, three, and five sites, and of aspect ratios 1.5, 2, and 3, respectively. The emphasis is given here to the numerical solution of HNC

A. Perera; F. Sokolic; M. Moreau

1992-01-01

359

Equations of state of mixtures: Density functional theory (DFT) simulations and experiments on Sandia's z machine  

NASA Astrophysics Data System (ADS)

Mixtures of materials are expected to behave quite differently from their isolated constituents, particularly when the constituents atomic numbers differ significantly. To investigate the mixture behavior, we performed density functional theory (DFT) calculations on xenon/hydrogen (deuterium) mixtures. Since the DFT simulations treat electrons and nuclei generically, simulations of pure and mix systems are expected to be of comparable accuracy, and we present a method to simulate mixtures at constant pressure, an approach that makes comparisons between different mix models straightforward.

Magyar, Rudolph

2012-03-01

360

Hierarchical equations of motion: A fundamental theory for quantum open systems  

NASA Astrophysics Data System (ADS)

As a powerful alternative to the influence functional path integral formalism, HEOM has been exploited in the study of various systems. In this talk, I will present some recent advancement on the HEOM-based nonlinear/nonequilibrium response theory and efficient implementation methods. Numerical demonstrations include coherent two-dimensional spectroscopy signals of light-harvesting model systems, and transport current noise spectrums through Anderson model quantum dots, operated in high-order co-tunneling regime.

Yan, Yijing

2012-02-01

361

Elongational viscosity of LDPE with various structures: employing a new evolution equation in MSF theory  

Microsoft Academic Search

Molecular stress function theory with new strain energy function is used to analyze transient extensional viscosity data of\\u000a seven low-density polyethylene (LDPE) melts with various molecular structures as published by Stadler et al. (Rheol Acta 48:479–490,\\u000a 2009) Pivokonsky et al. (J Non Newton Fluid Mech 135:58–67, 2006) and Wagner et al. (J Rheol 47(3):779–793, 2003). The new strain energy function

Mahdi Abbasi; Nadereh Golshan Ebrahimi; Mahdi Nadali; Masood Khabazian Esfahani

362

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

SciTech Connect

The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the Quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's ({beta} = 0; {gamma} = 1/2) method, leading to a robust numerical behavior and energy conservation. In its current form, the method only allows for wave propagations supported by the less compliant of the two meshes across a heterogeneous boundary, which requires the use of overdamped dynamics to avoid spurious heating due to reflected vibrations. We have applied the method to two independent crystallographic systems characterized by different interatomic potentials (Al and Ta) and have measured thermal expansion in order to quantify the vibrational entropy loss due to homogenization. We rationalize the results in terms of system size, mesh coarseness, and nodal cluster diameter within the framework of the quasiharmonic approximation. For Al, we find that the entropy loss introduced by mesh coarsening varies linearly with the element size, and that volumetric effects are not critical in driving the anharmonic behavior of the simulated systems. In Ta, the anomalies of the interatomic potential employed result in negative and zero thermal expansion at low and high temperatures, respectively.

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

2009-05-08

363

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

364

Fokker-Planck equation for lattice deposition models  

NASA Astrophysics Data System (ADS)

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

Baggio, Chiara; Vardavas, Raffaele; Vvedensky, Dimitri D.

2001-10-01

365

Finite element methods for Navier-Stokes equations: Theory and algorithms  

NASA Astrophysics Data System (ADS)

The mathematical basis of FEMs for incompressible steady interior flow problems is examined in a text (a revised and expanded version of the work of Girault and Raviart, 1979) intended for a postgraduate course in numerical analysis. Chapters are devoted to the mathematical foundation of the Stokes problem, results obtained with a standard FEM approximation, the numerical solution of the Stokes problem in primitive variables, incompressible mixed FEMs for solving the Stokes problem, and the theory and approximation of the Navier-Stokes problem.

Girault, Vivette; Raviart, Pierre-Arnaud

366

An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach  

NASA Astrophysics Data System (ADS)

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

Feng, Qingguo; Oppeneer, P. M.

2012-02-01

367

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

368

Vectorial algorithm for the computation of light propagation equation based on Huygens' principle using the scalar theory of diffraction  

NASA Astrophysics Data System (ADS)

In digital holography, computation of holograms is often reduced to calculations of fast Fourier transforms if the distance between the object plane and the hologram plane is large enough. Two classical approximations for solving this problem include a binomial series expansion of the distance and an elimination of the so-called inclination factor. We present here a vectorial algorithm which computes the discrete form of the light propagation equation obtained by the Huygens' principle for a bidimensional object. None of the approximations mentioned above have been used. This enables the computation of a diffraction pattern at any distance compatible with the scalar theory of diffraction. This vectorial algorithm has been implemented on workstations, on a Convex C-220 and on a Cray YMP computer. We focus our attention on the computing granularity of the problem and we present processing times and the associated performances for bidimensional images. Various holograms are computed and compared with those obtained by two traditional methods, namely, Fresnel transforms and the resolution of the rigorous scalar diffraction equation using discrete convolutions. We then consider the 3D case and modifications are proposed in order to parallelize this algorithm.

Morucci, Stephane; Noirard, Pierre; Grossetie, Jean-Claude

1996-03-01

369

Regularized and renormalized Bethe-Salpeter equations: Some aspects of irreducibility and asymptotic completeness in renormalizable theories  

NASA Astrophysics Data System (ADS)

Results on the links between 2-particle irreducibility and asymptotic completeness are presented in the framework of a renormalized Bethe-Salpeter formalism, introduced recently by J. Bros from an axiomatic viewpoint, for the most simple class of renormalizable theories. These results, which involve the renormalized 2-particle irreducible kernel G (i.e. from the perturbative viewpoint the sum of renormalized Feynman amplitudes of 2-particle irreducible graphs in the channel considered), complement the general quasi-equivalence previously established by Bros for regularized (non-renormalized) Bethe-Salpeter kernels. On the one hand, a formal derivation of (2-particle) asymptotic completeness from the irreducibility of G is given. On the other hand, the links between regularized and renormalized kernels are investigated. This analysis provides in particular a converse derivation (up to some assumptions) of the 2-particle irreducibility of G from asymptotic completeness. As a byproduct, it also provides a more explicit justification of previous heuristic derivations by K. Symanzik of integral equations between F and various differences of values of G, and a simple alternative derivation of the recently proposed “renormalized” Bethe-Salpeter equation.

Iagolnitzer, D.

1985-09-01

370

Dyson-Schwinger equations approach to the large-N limit: Model systems and string representation of Yang-Mills theory  

SciTech Connect

Simple model systems like the O(N) sigma model, the Gross-Neveu model, and the random matrix model are solved at N..-->..infinity using Dyson-Schwinger equations and the fact that the Hartree-Fock approximation is exact at N..-->..infinity. The complete string equations of the U(infinity) lattice gauge theory are presented. These must include both string rearrangement and splitting. Comparison is made with the ''continuum'' equations of Makeenko and Migdal which are structurally different. The difference is ascribed to inequivalent regularization procedures in the treatment of string splitting or rearrangement at intersections.

Wadia, S.R.

1981-08-15

371

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

372

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate  

NASA Astrophysics Data System (ADS)

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's Langevin equation in 6 N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6 N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6 N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.

Xing, Xiusan

2010-12-01

373

Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space  

SciTech Connect

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

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

2010-06-01

374

The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems  

PubMed Central

We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the “Langevin Hull”, can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work.

Vardeman, Charles F.; Stocker, Kelsey M.; Gezelter, J. Daniel

2011-01-01

375

The possibility of using the thermal equation of absorption from the theory of volume filling of micropores for calculation of holding capacity of busofit in thermal vacuum desorption  

Microsoft Academic Search

An experimental study was carried out to investigate thermal desorption of organic solvents from activated carbon fiber materials (ACFM) of the busofit type in the temperature range of 29 423 K. Comparison of experimental and calculated holding capacities of ACFM has shown that the thermal equation of absorption from the theory of volume filling of micropores can be used for

A. F. Dolidovich; G. S. Akhremkova; T. V. Tumysheva

1997-01-01

376

Solvation free energies of non-polar and polar solutes reproduced by a combination of extended scaled particle theory and the Poisson-Boltzmann equation  

Microsoft Academic Search

A hybrid approach using extended scaled particle theory and the Poisson-Boltzmann (PB) equation is proposed for calculating the solvation free energy of a solute with partial charges in dilute aqueous solution. The applicability of this method is demonstrated by taking a series of the normal alcohols and normal alkanes. The solvation free energy of normal alkanes, which has been studied

Masayuki Irisa; Takuya Takahashi; Kuniaki Nagayama; Fumio Hirata

1995-01-01

377

Estimation of applicability of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in isotropic polycrystalline p-silicon  

Microsoft Academic Search

A condition is formulated for application of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in an isotropic silicon polycrystal, where holes are scattered both by a disordered system of potential barriers formed on crystallite surfaces and by a disordered lattice of silicon atoms characterized by local ordering. The total specific resistance of

A. G. Moiseev

2009-01-01

378

Field equations, equations of motion, and energy functionals for thick shells of revolution with arbitrary curvature and variable thickness from a three-dimensional theory  

Microsoft Academic Search

Summary  This work uses tensor calculus to derive a complete set of three-dimensional field equations well-suited for determining the\\u000a behavior of thick shells of revolution having arbitrary curvature and variable thickness. The material is assumed to be homogeneous,\\u000a isotropic and linearly elastic. The equations are expressed in terms of coordinates tangent and normal to the shell middle\\u000a surface. The relationships are

J.-H. Kang

2007-01-01

379

Analytical integral equation theory for a restricted primitive model of polyelectrolytes and counterions within the mean spherical approximation. I. Thermodynamic properties  

NASA Astrophysics Data System (ADS)

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

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

1999-09-01

380

Laser flash photolysis and integral equation theory to investigate reactions of dilute solutes with oxygen in supercritical fluids  

SciTech Connect

The absolute reactivity of triplet benzophenone ({sup 3}BP) and benzyl free radical (PhCH{sub 2}) toward molecular oxygen (O{sub 2}) in supercritical CO{sub 2} and CHF{sub 3} has been measured by laser flash photolysis (LFP). The transient reactants may be considered to be infinitely dilute solutes reacting with a gaseous cosolvent in a supercritical fluid mixture. Both reactants were found to undergo kinetically controlled reactivity with O{sub 2} and the measured bimolecular rate constants (k{sub hi}) were found to decrease with a decrease in solvent density at reduced pressures between 1.0 and 2.5. These results are consistent with solute reactivity with a `nonattractive` cosolvent. The results are compared with those previously obtained for the reaction of {sup 3}BP with an `attractive` cosolvent, 1,4-cyclohexadiene, in supercritical CO{sub 2} and CHF{sub 3}, in which enhanced {sup 3}BP reactivity was observed due to preferential cosolvent/solute solvation. Integral equation theory has also been applied to model these ternary systems, and the results indicate how the strengths of local solvation forces can influence kinetically controlled reactions in supercritical fluids. 36 refs., 8 figs., 3 tabs.

Roberts, C.B. [Auburn Univ., AL (United States); Zhang, J.; Chateauneuf, J.E.; Brennecke, J.F. [Univ. of Notre Dame, IN (United States)

1995-06-21

381

A Floating Random-Walk Algorithm based on Iterative Perturbation Theory: Solution of the Maxwell-Helmholtz Equation  

NASA Astrophysics Data System (ADS)

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

Chatterjee, Kausik; Le Coz, Yannick

2002-10-01

382

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

NASA Astrophysics Data System (ADS)

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.

Shew, Chwen-Yang; Do, Changwoo; Hong, Kunlun; Liu, Yun; Porcar, Lionel; Smith, Gregory S.; Chen, Wei-Ren

2012-07-01

383

THE INTEGRAL EQUATION APPROACH TO KINEMATIC DYNAMO THEORY AND ITS APPLICATION TO DYNAMO EXPERIMENTS IN CYLINDRICAL GEOMETRY  

Microsoft Academic Search

ments Abstract. The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed to an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting uid and to its boundary. This integral equation approach is applied to simulate kinematic dynamos within cylindrical geometry including the

M. Xu; F. Stefani; G. Gerbeth

2009-01-01

384

NUMERICAL SOLUTION OF TWO-DIMENSIONAL POISSON EQUATION: THEORY AND APPLICATION TO ELECTROSTATIC-ION-ENGINE ANALYSIS  

Microsoft Academic Search

The Poisson equation is solved for mixed boundary conditions by a method ; of successive approximations in which the differential equation is replaced by ; finite difference equations. Properties of the resulting matrix are studied. ; The Cyclic Chebyshev Semi-Iterative Method is described, and detailed ; calculations of ion trajectories are given. Also included is a numerical ; example, solved

V. Hamza; E. A. Richley

1962-01-01

385

Velocity autocorrelation functions of dusty particles obtained by the Langevin dynamics  

Microsoft Academic Search

Velocity autocorrelation functions of dusty particles obtained based on the Langevin dynamics simulations are investigated. The potential of interaction between dust particles is the Yukawa potential. Autocorrelation function decay times are analyzed for different coupling, screening and friction parameters. It is shown that at the same ? and ? but different ? the autocorrelation function and oscillations on it (at

T. S. Ramazanov; K. N. Dzhumagulova; A. N. Jumabekov

386

A Langevin approach to the Log–Gauss–Pareto composite statistical structure  

NASA Astrophysics Data System (ADS)

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.

Eliazar, Iddo I.; Cohen, Morrel H.

2012-11-01

387

(G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics  

NASA Astrophysics Data System (ADS)

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

Zheng, Bin

2012-11-01

388

Moving Finite-Element method: an introduction to its theory and application to conservation-law equations  

SciTech Connect

This report introduces engineers to the specific adaptive mesh method known as the Moving Finite Element (MFE) method. An elementary introduction to some basic mathematical concepts is given in support of the MFE method. The mathematics and physics of basic conservation laws are discussed. The basic discretization procedure of MFE is developed around a one-dimensional scalar partial differential equation. The necessary numerical methods of implicit, stiff ordinary differential equations are introduced. Two nonlinear wave equation examples are given: Burgers' equation (scalar) and the Euler equations (system) of gas dynamics. Brief conclusions are drawn.

Berry, R.A.

1982-04-01

389

Spatial decomposition of solvation free energy based on the 3D integral equation theory of molecular liquid: application to miniproteins.  

PubMed

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

Yamazaki, Takeshi; Kovalenko, Andriy

2010-12-17

390

Single particle dynamics of many-body systems described by Vlasov-Fokker-Planck equations  

NASA Astrophysics Data System (ADS)

Using Langevin equations we describe the random walk of single particles that belong to particle systems satisfying Vlasov-Fokker-Planck equations. In doing so, we show that Haissinski distributions of bunched particles in electron storage rings can be derived from a particle dynamics model.

Frank, T. D.

2003-12-01

391

Theory of physical aging in polymer glasses  

NASA Astrophysics Data System (ADS)

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

Chen, Kang; Schweizer, Kenneth S.

2008-09-01

392

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

393

Initial-Value Technique for Singularly Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations Arising in Chemical Reactor Theory  

Microsoft Academic Search

An initial-value technique is presented for solving singularly perturbed two-point boundary-value problems for linear and semilinear second-order ordinary differential equations arising in chemical reactor theory. In this technique, the required approximate solution is obtained by combining solutions of two terminal-value problems and one initial-value problem which are obtained from the original boundary-value problem through asymptotic expansion procedures. Error estimates for

S. Natesan; N. Ramanujam

1998-01-01

394

The possibility of using the thermal equation of absorption from the theory of volume filling of micropores for calculation of holding capacity of busofit in thermal vacuum desorption  

NASA Astrophysics Data System (ADS)

An experimental study was carried out to investigate thermal desorption of organic solvents from activated carbon fiber materials (ACFM) of the busofit type in the temperature range of 29 423 K. Comparison of experimental and calculated holding capacities of ACFM has shown that the thermal equation of absorption from the theory of volume filling of micropores can be used for estimation of the holding capacity.

Dolidovich, A. F.; Akhremkova, G. S.; Tumysheva, T. V.

1997-01-01

395

The possibility of using the thermal equation of absorption from the theory of volume filling of micropores for calculation of holding capacity of busofit in thermal vacuum desorption  

Microsoft Academic Search

An experimental study was carried out to investigate thermal desorption of organic solvents from activated carbon fiber materials\\u000a (ACFM) of the busofit type in the temperature range of 29–423 K. Comparison of experimental and calculated holding capacities\\u000a of ACFM has shown that the thermal equation of absorption from the theory of volume filling of micropores can be used for\\u000a estimation

A. F. Dolidovich; G. S. Akhremkova; T. V. Tumysheva

1997-01-01

396

Estimating the Gibbs energy of hydration from molecular dynamics trajectories obtained by integral equations of the theory of liquids in the RISM approximation  

Microsoft Academic Search

A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used\\u000a to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected\\u000a as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach\\u000a for the excess

D. A. Tikhonov; E. V. Sobolev

2011-01-01

397

Design of Experiment for Measurement of Langevin Function  

NASA Astrophysics Data System (ADS)

The presented study focuses on a confrontation of the theory of regression models and theory of experiment with the real situation of determining properties of magnetic (nano)materials. Their magnetic properties can be deduced by measuring their magnetization, being the fundamental magnetic quantity of an arbitrary (nano)material. The results of the magnetization measurements determine the unknown parameters of a known nonlinear function that characterizes the (nano)material under investigation. Knowledge of the values of the uknkown parameters enables to decide whether the (nano)material is suitable or not for a particular application. Thus, in this work, we present a possible approach how to estimate the unknown parameters of the nonlinear function by the regression models, taking into account a relevant linearization criterion. Then, we suggest an appropriate design for the measurement to get better estimators of the parameters.

Tu?ek, P.; Tu?ková, M.; Fišerová, E.; Tu?ek, J.; Kubá?ek, L.

2012-01-01

398

Analyses of {pi}{sup {+-}-40}Ca Elastic Scattering Data in the Delta Resonance Region using Inverse Scattering Theory and the Klein-Gordon Equation  

SciTech Connect

The elastic scattering cross sections for {pi}{sup +} by {sup 40}Ca have been analyzed, for the first time, using the Klein-Gordon (KG) equation that incorporates the Coulomb interaction between the charged pions and targets explicitly for the incident energies of 163.3 and 180 MeV. The nuclear part of the potentials is determined using an inverse scattering theory as a guide. Our results are then compared to those where the Coulomb potential has not been explicitly included in the KG equation but its effect is studied by modifying the incident kinetic energy following the prescription of Stricker. Our calculations that include the Coulomb potential in the KG equation reproduce the results using the Stricker prescription for {pi}{sup +}. The Stricker method is then used to calculate {pi}{sup -} scattering. In all cases, the data have been well accounted for.

Shehadeh, Zuhair F. [Physics Department, Taif University, P.O. Box 888, Taif (Saudi Arabia); Scott, Jeremy S.; Malik, F. Bary [Physics Department, Southern Illinois University at Carbondale, Illinois, 62901 (United States)

2011-10-27

399

An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: Applications to atomic-orbital based coupled-cluster theory  

NASA Astrophysics Data System (ADS)

The conjugate residual with optimal trial vectors (CROP) algorithm is developed. In this algorithm, the optimal trial vectors of the iterations are used as basis vectors in the iterative subspace. For linear equations and nonlinear equations with a small-to-medium nonlinearity, the iterative subspace may be truncated to a three-dimensional subspace with no or little loss of convergence rate, and the norm of the residual decreases in each iteration. The efficiency of the algorithm is demonstrated by solving the equations of coupled-cluster theory with single and double excitations in the atomic orbital basis. By performing calculations on H2O with various bond lengths, the algorithm is tested for varying degrees of nonlinearity. In general, the CROP algorithm with a three-dimensional subspace exhibits fast and stable convergence and outperforms the standard direct inversion in iterative subspace method.

Zió?kowski, Marcin; Weijo, Ville; Jørgensen, Poul; Olsen, Jeppe

2008-05-01

400

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

Microsoft Academic Search

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

Sergei Kopeikin; Igor Vlasov

2004-01-01

401

Theory and Parallel Implementation of an Adaptive Finite Element Method for the Coupled Stokes and Navier-Lame Equations  

Microsoft Academic Search

Abstract We use the finite element method to compute the displacement of an elastic object im- mersed into a viscous incompressible flow. The mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. The solution to the coupled problem is produced by first solving the Stokes equation and then by using

Anton Olofsson

2008-01-01

402

Calculations of the anisotropy of the fission fragment angular distribution and neutron emission multiplicities prescission from Langevin dynamics  

SciTech Connect

The anisotropy of the fission fragment angular distribution defined at the saddle point and the neutron multiplicities emitted prior to scission for fissioning nuclei {sup 224}Th, {sup 229}Np, {sup 248}Cf, and {sup 254}Fm are calculated simultaneously by using a set of realistic coupled two-dimensional Langevin equations, where the (c,h,{alpha}=0) nuclear parametrization is employed. In comparison with the one-dimensional stochastic model without neck variation, our two-dimensional model produces results that are in better agreement with the experimental data, and the one-dimensional model is available only for low excitation energies. Indeed, to determine the temperature of the nucleus at the saddle point, we investigate the neutron emission during nucleus oscillation around the saddle point for different friction mechanisms. It is shown that the neutrons emitted during the saddle oscillation cause the temperature of a fissioning nuclear system at the saddle point to decrease and influence the fission fragment angular distribution.

Jia Ying; Bao Jingdong [Department of Physics, Beijing Normal University, Beijing 100875 (China)

2007-03-15

403

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

404

Macroscopic transport equations  

Microsoft Academic Search

The macroscopic transport equations, necessary for the description of plasmas as fluids are derived in a way which emphasizes their origin in the kinetic theory. The equations of conservation of mass, of momentum, and of energy, are obtained from a general transport equation, and are identified with the hierarchy of moments of the Boltzmann equation. The approximations inherent in the

J. A. Bittencourt

1979-01-01

405

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusions: New Set of Equations for the Growth and Ultimate Extrudate Swelling Ratios under the Free States  

NASA Astrophysics Data System (ADS)

A new dynamic theory of die swell for entangled polymeric liquids in a steady simple shear flow is proposed which can be used to predict the correlation of the time-dependent and time-independent extrudate swelling behaviors to the molecular parameters of polymers and the operational variables. The theory is based on the O-W-F constitutive equation and the free recovery from Poioeuille flow with different ratios. Experiments show that the magnitudes of the simple shear in the steady simple shear flow may be resolved into the free recoil resulting from the recoverable elastic strains and the viscous heating resulting from the unrecoverable viscoelastic strains. For distinguishing the recoil from the viscous heating, a partition function and two exponential fractions of conformation for the recoil and the viscous heating were defined. Thus the instantaneous, delayed and ultimate recoverable strain, and recoil in the free recovery were correlated to the partition function, the fraction of recoverable conformation, the molecular parameters, and the operational variables. Also the dynamics of the growth equation on the delayed viscoelastic strain and the delayed recoil in free state were deduced. After introducing the condition of uniform two dimensional extensions, the definition of swell ratio and the operational variables into the above correlation expressions and growth equations, then the correlations of the delayed extrudate swelling effect and the ultimate extrudate swelling effects to the molecular parameters and the operational variables were derived. Finally, two new sets of equations on the growth variables and ultimate extrudate swelling ratios under the dynamic and equilibrium states were also deduced from this dynamic theory of die swell. The first set of equations on the ultimate extrudate swelling ratio under the free and equilibrium states was verified by HDPE experimental data at two temperatures and different operational variables. The second set of equations on the growth extrudate swelling ratios under free and dynamic states was verified by PBD experimental data with different molecular weights and different operational variables. An excellent agreement is obtained, which shows that the two sets of equations for the growth and ultimate extrudate swelling ratios can be used directly to predict the correlation of extrudate swelling ratios to the molecular parameters and the operational variables.

Zhu, Chang-wei; Song, Ming-shi; Hu, Gui-xian; Wu, Da-ming; Zhao, Jing

2007-10-01

406

The Langevin\\/implicit-Euler\\/normal-mode scheme for molecular dynamics at large time steps  

Microsoft Academic Search

As molecular dynamics simulations continue to provide important insights into biomolecular structure and function, a growing demand for increasing the time span of the simulations is emerging. Our focus here is developing a new algorithm, LIN (Langevin\\/implicit-Euler\\/normal mode), that combines normal-mode and implicit-integration techniques, for large time step biomolecular applications. In the normal-mode phase of LIN, we solve an approximate

Guihua Zhang; Tamar Schlick

1994-01-01

407

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

408

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

409

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

410

Phase-Space Reconstruction: a Path Towards the Next Generation of Nonlinear Differential Equation Based Models and Its Implications Towards Non-Uniform Sampling Theory  

SciTech Connect

This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.

Charles R. Tolle; Mark Pengitore

2009-08-01

411

Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids  

NASA Astrophysics Data System (ADS)

We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers.

Jadrich, Ryan; Schweizer, Kenneth

2013-03-01

412

Convolution equations and the transport equation  

Microsoft Academic Search

\\u000a In this chapter the factorization theory developed in the previous chapters is applied to solve a linear transport equation.\\u000a It is known that the transport equation may be transformed into a Wiener-Hopf integral equation with an operator-valued kernel\\u000a function (see [40]). An equation of the latter type can be solved explicitly if a canonical factorization of its symbol is\\u000a available

Harm Bart; Marinus A. Kaashoek; André C. M. Ran

413

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

414

On the Flux Problem in the Theory of Steady Navier-Stokes Equations with Nonhomogeneous Boundary Conditions  

NASA Astrophysics Data System (ADS)

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

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

2013-01-01

415

Localization length of stationary states in the nonlinear Schrödinger equation  

NASA Astrophysics Data System (ADS)

For the nonlinear Schrödinger equation (NLSE), in the presence of disorder, exponentially localized stationary states are found. We demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the “white noise” random potential, and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust.

Iomin, Alexander; Fishman, Shmuel

2007-11-01

416

Localization length of stationary states in the nonlinear Schrödinger equation.  

PubMed

For the nonlinear Schrödinger equation (NLSE), in the presence of disorder, exponentially localized stationary states are found. We demonstrate analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the "white noise" random potential, and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust. PMID:18233782

Iomin, Alexander; Fishman, Shmuel

2007-11-29

417

Periodic Solutions and Rogue Wave Type Extended Compactons in the Nonlinear Schrodinger Equation and \\\\phi^{4} Theories  

Microsoft Academic Search

By employing a mapping to classical anharmonic oscillators, we explore a class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1 dimensions and, by extension, asymptotically in general dimensions. We discuss a possible way for creating approximate rogue wave like solutions to the NLSE by truncating exact solutions at their nodes and stitching them with other solutions to the

Patrick Johnson; Daniel Cole; Zohar Nussinov

2010-01-01

418

An Approach to Transport in Heterogeneous Porous Media Using the Truncated Temporal Moment Equations: Theory and Numerical Validation  

Microsoft Academic Search

In the last decade, the characterization of transport in porous media has benefited largely from numerical advances in applied mathematics and from the increasing power of computers. However, the resolution of a transport problem often remains cumbersome, mostly because of the time-dependence of the equations and the numerical stability constraints imposed by their discretization. To avoid these difficulties, another approach

Frédérick Delay; Gilles Porel; Olivier Banton

1998-01-01

419

Simulation of an atomistic dynamic field theory for monatomic liquids: freezing and glass formation.  

PubMed

We examine a phase field crystal model for simple liquid-solid systems consisting of a free energy functional related to the Ramakrishnan-Yussouff free energy of classical density functional theory and an equation of motion capable of describing long-time-scale behavior in the deeply supercooled regime. The thermodynamics and dynamics of freezing and glass formation in this model system are studied through large-scale three-dimensional Langevin simulations. At low cooling rates bcc crystals are formed by nucleation and growth from the melt. At large cooling rates no clear glass transition is observed, but a kinetically driven first-order transition from supercooled liquid to a disordered glasslike solid does occur. Despite the peculiarities of the transition, the structure and properties of the resulting disordered solid are shown to strongly resemble those of a typical glass. Consequences of pseudocritical behavior and heterogeneity near the liquid spinodal are also discussed. PMID:18643271

Berry, Joel; Elder, K R; Grant, Martin

2008-06-09

420

Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory  

Microsoft Academic Search

Summary.    Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such\\u000a equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity\\u000a waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on\\u000a large lakes or the

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

2008-01-01

421

Exact integral operator form of the Wigner distribution-function equation in many-body quantum transport theory  

Microsoft Academic Search

A formal derivation of a generalized equation of a Wigner distribution function including all many-body effects and all scattering mechanisms is given. The result is given in integral operator form suitable for application to the numerical modeling of quantum tunneling and quantum interference solid state devices. In the absence of scattering and many-body effects, the result reduces to the “noninteracting-particle”

F. A. Buot

1990-01-01

422

A unified formulation for the three-dimensional shallow water equations using orthogonal co-ordinates: theory and application  

Microsoft Academic Search

In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and

Herman W. J. Kernkamp; Henri A. H. Petit; Herman Gerritsen; Erik D. de Goede

2005-01-01

423

The extension of Buckley-Feuring solutions for non-polynomial fuzzy partial differential equations. Application to microeconomics utility theory  

Microsoft Academic Search

This paper presents the natural extension of Buckley-Feuring method proposed in for solving fuzzy partial differential equations (FPDE) in a nonpolynomial relation, such as the operator phi(Dx1,Dx2), which maps to the quotient between both partials. The new assumptions and conditions proceedings from this consideration given in this document, have been developed for a concrete application: a new method for building

D. Galvez; J. L. Pino

2009-01-01

424

A unified formulation for the three-dimensional shallow water equations using orthogonal co-ordinates: theory and application  

Microsoft Academic Search

In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems\\u000a and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal\\u000a co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same\\u000a for the three- and

Herman W. J. Kernkamp; Henri A. H. Petit; Herman Gerritsen; Erik D. de Goede

2005-01-01

425

Using Structural Equation Modeling to Validate the Theory of Planned Behavior as a Model for Predicting Student Cheating  

ERIC Educational Resources Information Center

|The purpose of this paper is to validate the use of a modified Theory of Planned Behavior (TPB) for predicting undergraduate student cheating. Specifically, we administered a survey assessing how the TPB relates to cheating along with a measure of moral reasoning (DIT- 2) to 527 undergraduate students across three institutions; and analyzed the…

Mayhew, Matthew J.; Hubbard, Steven M.; Finelli, Cynthia J.; Harding, Trevor S.; Carpenter, Donald D.

2009-01-01

426

Understanding Physical Activity Behavior of Type 2 Diabetics Using the Theory of Planned Behavior and Structural Equation Modeling  

Microsoft Academic Search

Understanding patient factors related to physical activity behavior is important in the management of Type 2 Diabetes. This study applied the Theory of Planned Behavior model to understand physical activity behavior among sampled Type 2 diabetics in Kenya. The study was conducted within the diabetic clinic at Kisii Level 5 Hospital and adopted sequential mixed methods design beginning with qualitative

D. O. Omondi; G. M. Mbagaya; L. O. A. Othuon

2010-01-01

427

A new approach to the equation of state of silicate melts: An application of the theory of hard sphere mixtures  

NASA Astrophysics Data System (ADS)

A comparison of compressional properties of silicate solids, glasses, and liquids reveals the following fundamental differences: (1) Liquids have much smaller bulk moduli than solids and glasses and the bulk moduli of various silicate melts have a narrow range of values; (2) Liquids do not follow the Birch's law of corresponding state as opposed to solids and glasses; (3) The Grüneisen parameter increases with increasing pressure for liquids but decreases for solids; (4) The radial distribution functions of liquids show that the interatomic distances in liquids do not change upon compression as much as solids do. The last observation indicates that the compression of silicate melts occurs mostly through the geometrical arrangement of various units whose sizes do not change much with compression, i.e., the entropic mechanism of compression plays a dominant role over the internal energy contribution. All of the other three observations listed above can be explained by this point of view. In order to account for the role of the entropic contribution, we propose a new equation of state for multi-component silicate melts based on the hard sphere mixture model of a liquid. We assign a hard sphere for each cation species that moves in the liquid freely except for the volume occupied by other spheres. The geometrical arrangement of these spheres gives the entropic contribution to compression, while the Columbic attraction between all ions provides the internal energy contribution to compression. We calibrate the equation of state using the experimental data on room-pressure density and room-pressure bulk modulus of liquids. The effective size of a hard sphere for each component in silicate melts is determined. The temperature and volume dependencies of sphere diameters are also included in the model in order to explain the experimental data especially the melt density data at high pressures. All compressional properties of a silicate melt can be calculated using the calibrated sphere diameters. This equation of state provides a unified explanation for most of compressional behaviors of silicate melts and the experimental observations cited above including the uniformly small bulk moduli of silicate melts as well as the pressure dependence of Grüneisen parameters. With additional data to better constrain the key parameters, this equation of state will serve as a first step toward the unified equation of state for silicate melts.

Jing, Zhicheng; Karato, Shun-ichiro

2011-11-01

428

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium  

PubMed Central

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature.

Uma, B.; Eckmann, D.M.; Ayyaswamy, P.S.; Radhakrishnan, R.

2012-01-01

429

Langevin simulation approach to a two-dimensional coupled flashing ratchet  

NASA Astrophysics Data System (ADS)

We study the directed motion of a Brownian particle moving in a two-dimensional coupled flashing ratchet driven by Gaussian white noise. The temperature dependence of the current is evaluated numerically in terms of Langevin simulation and discussed by means of a heuristic analytical ad hoc approximation. The current can be enhanced or reversed due to the coupling effects between two degrees of freedom. Our results show that the noise is rectified even in the absence of a true activation energy barrier and the two-dimensional ratchet current does not vanish as the temperature approaches infinity.

Bao, Jing-Dong; Zhuo, Yi-Zhong

1998-03-01

430

Statistical Transport Theory for Turbulent Particle Dispersion  

NASA Astrophysics Data System (ADS)

A statistical transport theory for turbulent particle dispersion is formulated having general applicability to inhomogeneous turbulent flows. The new theory avoids the practical difficulties associated with defining a Lagrangian particle velocity autocorrelation function in the classical approach and circumvents the principle computational disadvantages associated with conventional Lagrangian stochastic discrete -particle techniques. Exploiting the concepts of statistical mechanics, groups of physical particles are represented by phase space distribution functions. In particular, a computational parcel representing a group of discrete physical particles is characterized by probability density functions (pdf) in configuration space and velocity space. Evolution of the first and second moments of these phase space distribution functions is described in a Lagrangian frame. The mean of each pdf is determined by tracking a parcel through a sequence of stochastic eddy interactions. A variance propagation theorem is fashioned from a direct attack on the linearized Lagrangian particle equation of motion (Langevin's equation) for sequential stochastic eddy interactions. Convolution of the parcel pdfs produces the probable instantaneous distribution in physical particle position and velocity. Using Gaussian pdfs, the validity of the new theory was established for dispersed particles in nonreacting and reacting turbulent flows by demonstrating favorable comparison with experiment and with predictions using the conventional stochastic direct modeling method. To improve efficiency, a memory function truncation criteria was developed for the variance propagation theorem demonstrating significant computational savings. In addition, pdf shape sensitivity was examined for uniform and isosceles triangle pdfs revealing that for the same sample size, uniform pdfs yielded highly irregular distributions whereas triangular pdfs yielded distributions virtually indistinguishable from those predicted using Gaussian pdfs. The resulting theoretical construction contributed by this dissertation offers unparalleled economy in pursuing large scale computation of turbulent particle dispersion.

Litchford, Ron J.

431

An analytical theory of the buoyancy-Kolmogorov subrange transition in turbulent flows with stable stratification.  

PubMed

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

Sukoriansky, Semion; Galperin, Boris

2013-01-13

432

Fluid-fluid phase separation of nonadditive hard-sphere mixtures as predicted by integral-equation theories  

Microsoft Academic Search

We investigate the existence of a fluid–fluid phase separation in binary mixtures of equal-size hard spheres with positively nonadditive diameters [i.e., d11=d22?d, d12=(1+?)d with ?>0]. An integral-equation approach is used to evaluate both thermodynamics and structure of many symmetric (equal to equimolar) mixtures (with ?=0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 1) and some asymmetric cases. We present the results obtained

Domenico Gazzillo; S. Marta

1991-01-01

433

Superconformal field theory and SUSY N=1 KdV hierarchy I: vertex operators and Yang-Baxter equation  

NASA Astrophysics Data System (ADS)

The supersymmetry invariant integrable structure of two-dimensional superconformal field theory is considered. The classical limit of the corresponding infinite family of integrals of motion (IM) coincide with the family of IM of SUSY N=1 KdV hierarchy. The quantum version of the monodromy matrix, generating quantum IM, associated with the SUSY N=1 KdV is constructed via vertex operator representation of the quantum R-matrix. The possible applications to the perturbed superconformal models are discussed.

Kulish, Petr P.; Zeitlin, Anton M.

2004-09-01

434

Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance  

Microsoft Academic Search

In Einstein's gravitational theory, the spacetime is Riemannian, that is, it has vanishing torsion and vanishing nonmetricity (covariant derivative of the metric). In the gauging of the general affine group A(4, R) and of its subgroup GL(4, R) in four dimensions, energy-momentum and hypermomentum currents of matter are canonically coupled to the coframe and to the connection of a metric-affine

Friedrich W. Hehl; J. Dermott McCrea; Eckehard W. Mielke; Yuval Ne'eman

1995-01-01

435

Interfacial tension of nonassociating pure substances and binary mixtures by density functional theory combined with Peng-Robinson equation of state.  

PubMed

We develop a density functional theory and investigate the interfacial tension of several pure substances N(2), CO(2), H(2)S, normal alkanes from C(1) to nC(10), and binary mixtures C(1)/C(3), C(1)/nC(5), C(1)/nC(7), C(1)/nC(10), CO(2)/nC(4), N(2)/nC(5), N(2)/nC(6), N(2)/nC(8), N(2)/nC(10), nC(6)/nC(7), nC(6)/nC(8), and nC(6)/nC(10). The theory is combined with the semiempirical Peng-Robinson equation of state (PR-EOS). The weighted density approximation (WDA) is adopted to extend the bulk excess Helmholtz free energy to the inhomogeneous interface. Besides, a supplementary term, quadratic density expansion (QDE), is introduced to account for the long-range characteristic of intermolecular dispersion attractions, which cannot be accurately described by the WDA. In the bulk limit, the QDE vanishes and the theory is reduced to the PR-EOS. For pure substances, the potential expansion parameter is the only adjustable parameter in the QDE and determined by using a single measured interfacial tension at the lowest temperature examined. Then without any parameter adjustment, we faithfully predict the interfacial tensions of pure substances and mixtures over a wide range of conditions. PMID:19388737

Li, Zhidong; Firoozabadi, Abbas

2009-04-21

436

Interfacial tension of nonassociating pure substances and binary mixtures by density functional theory combined with Peng-Robinson equation of state  

NASA Astrophysics Data System (ADS)

We develop a density functional theory and investigate the interfacial tension of several pure substances N2, CO2, H2S, normal alkanes from C1 to nC10, and binary mixtures C1/C3, C1/nC5, C1/nC7, C1/nC10, CO2/nC4, N2/nC5, N2/nC6, N2/nC8, N2/nC10, nC6/nC7, nC6/nC8, and nC6/nC10. The theory is combined with the semiempirical Peng-Robinson equation of state (PR-EOS). The weighted density approximation (WDA) is adopted to extend the bulk excess Helmholtz free energy to the inhomogeneous interface. Besides, a supplementary term, quadratic density expansion (QDE), is introduced to account for the long-range characteristic of intermolecular dispersion attractions, which cannot be accurately described by the WDA. In the bulk limit, the QDE vanishes and the theory is reduced to the PR-EOS. For pure substances, the potential expansion parameter is the only adjustable parameter in the QDE and determined by using a single measured interfacial tension at the lowest temperature examined. Then without any parameter adjustment, we faithfully predict the interfacial tensions of pure substances and mixtures over a wide range of conditions.

Li, Zhidong; Firoozabadi, Abbas

2009-04-01

437

Monte Carlo algorithms for lattice gauge theory  

SciTech Connect

Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations.

Creutz, M.

1987-05-01

438

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks.  

PubMed

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(?), with the minimum anisotropy occurring at approximately the magic angle (?(MA)), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle ? progresses from 0° to 90°. The corresponding diffusion ellipsoids are prolate for ??(MA). Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed. PMID:23030954

Powell, Sean K; Momot, Konstantin I

2012-09-17

439

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling  

NASA Astrophysics Data System (ADS)

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

Wu, Xiongwu; Hodoscek, Milan; Brooks, Bernard R.

2012-07-01

440

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks  

NASA Astrophysics Data System (ADS)

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(?), with the minimum anisotropy occurring at approximately the magic angle (?MA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle ? progresses from 0? to 90?. The corresponding diffusion ellipsoids are prolate for ??MA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Powell, Sean K.; Momot, Konstantin I.

2012-09-01

441

Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics  

PubMed Central

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

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

2008-01-01

442

Extraction of effective ion pair interactions in warm dense beryllium and helium plasmas within integral equation theory  

SciTech Connect

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

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

2011-03-15

443

Anatomy of a controversy: Application of the Langevin technique to the analysis of the Californium-252 Source-Driven Noise Analysis method for subcriticality determination  

SciTech Connect

The expressions for the power spectral density of the noise equivalent sources have been calculated explicitly for the (a) stochastic transport equation, (b) the one-speed transport equaton, (c) the one-speed P{sub 1} equations, (d) the one-speed diffusion equation and (e) the point kinetic equation. The stochastic nature of Fick's law in (d) has been emphasized. The Langevin technique has been applied at various levels of approximation to the interpretation of the Californium-252 Source-Driven Noise Analysis (CSDNA) experiment for determining the reactivity in subcritical media. The origin of the controversy surrounding this method has been explained. The foundations of the CSDNA method as a viable experimental technique to infer subcriticality from a measured ratio of power spectral densities of the outputs of two neutron detectors and a third external source detector has been examined by solving the one-speed stochastic diffusion equation for a point external Californium-252 source and two detectors in an infinite medium. The expression relating reactivity to the measured ratio of PSDs was found to depend implicitly on k itself. Through a numerical analysis fo this expression, the authors have demonstrated that for a colinear detector-source-detector configuration for neutron detectors far from the source, the expression for the subcritical multiplication factor becomes essentially insensitive to k, hence, demonstrating some possibility for the viability of this technique. However, under more realistic experimental conditions, i.e., for finite systems in which diffusion theroy is not applicable, the measurement of the subcritical multiplication factor from a single measured ratio of PSDs, without extensive transport calculations, remains doubtful.

Stolle, A.M.

1991-01-01

444

Hot nuclei -- Landau theory, thermal fluctuations and dissipation  

SciTech Connect

The basic ideas and theoretical methods used in the description of hot nuclei are reviewed. In particular, a macroscopic approach to shape transitions is discussed in the framework of the Landau theory in which the quadrupole shape degrees of freedom play the role of the order parameters. This theory describes the universal features of the nuclear shape evolution with temperature and spin. A unified description of fluctuations in all five quadrupole degrees of freedom is introduced and plays an important role in the calculation of physical observables. A macroscopic approach to the giant dipole resonance (GDR) in hot nuclei is developed. With all parameters fixed by the zero temperature nuclear properties, the theory predicts both the GDR cross-section and angular anisotropy of the {gamma}-rays in very good agreement with recent experiments. The intrinsic shape fluctuations are the main cause for the resonance broadening at higher temperatures, while the orientation fluctuations are responsible for the observed attenuation in the angular anisotropy. Dissipation at finite temperature is discussed in the framework of a Langevin-like equation describing the time-dependent shape fluctuations. Non-adiabatic effects may cause motional narrowing of the resonance.

Alhassid, Y.

1990-12-31

445

Hot nuclei -- Landau theory, thermal fluctuations and dissipation  

SciTech Connect

The basic ideas and theoretical methods used in the description of hot nuclei are reviewed. In particular, a macroscopic approach to shape transitions is discussed in the framework of the Landau theory in which the quadrupole shape degrees of freedom play the role of the order parameters. This theory describes the universal features of the nuclear shape evolution with temperature and spin. A unified description of fluctuations in all five quadrupole degrees of freedom is introduced and plays an important role in the calculation of physical observables. A macroscopic approach to the giant dipole resonance (GDR) in hot nuclei is developed. With all parameters fixed by the zero temperature nuclear properties, the theory predicts both the GDR cross-section and angular anisotropy of the {gamma}-rays in very good agreement with recent experiments. The intrinsic shape fluctuations are the main cause for the resonance broadening at higher temperatures, while the orientation fluctuations are responsible for the observed attenuation in the angular anisotropy. Dissipation at finite temperature is discussed in the framework of a Langevin-like equation describing the time-dependent shape fluctuations. Non-adiabatic effects may cause motional narrowing of the resonance.

Alhassid, Y.

1990-01-01

446

On the higher order corrections to the Fokker Planck equation  

NASA Astrophysics Data System (ADS)

The Rayleigh model of nonlinear Brownian motion is revisited in which the heavy particle of mass M interacts with ideal gas molecules of mass m?M via instantaneous collisions. Using the van Kampen method of expansion of the master equation, nonlinear corrections to the Fokker Planck equation are obtained up to sixth order in the small parameter ?=m/M, improving earlier results. The role and origin of non-Gaussian statistics of the random force in the corresponding Langevin equation are also discussed.

Plyukhin, A. V.

2005-06-01

447

Excitons in Potassium Bromide: A Study using Embedded Time-dependent Density Functional Theory and Equation-of-Motion Coupled Cluster Methods  

SciTech Connect

We present a study of the electronic excitations in insulating materials using an embedded- cluster method. The excited states of the embedded cluster are studied systematically using time-dependent density functional theory (TDDFT) and high-level equation-of-motion coupled cluster (EOMCC) methods. In particular, we have used EOMCC models with singles and doubles (EOMCCSD) and two approaches which account for the e®ect of triply excited con¯gurations in non-iterative and iterative fashions. We present calculations of the lowest surface excitations of the well-studied potassium bromide (KBr) system and compare our results with experiment. The bulk-surface exciton shift is also calculated at the TDDFT level and compared with experiment.

Govind, Niranjan; Sushko, Petr V.; Hess, Wayne P.; Valiev, Marat; Kowalski, Karol

2009-03-05

448

Similarity transformed coupled cluster response (ST-CCR) theory--a time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach.  

PubMed

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism. PMID:23822296

Landau, Arie

2013-07-01