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Sample records for langevin equation theory

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

    SciTech Connect

    Zahlten, Claus Hernandez, Andres Schmidt, Michael G.

    2009-10-15

    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.

  2. Self-consistent generalized Langevin-equation theory for liquids of nonspherically interacting particles.

    PubMed

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

    2014-11-01

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

  3. Langevin Equation for DNA Dynamics

    NASA Astrophysics Data System (ADS)

    Grych, David; Copperman, Jeremy; Guenza, Marina

    Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

  4. The complex chemical Langevin equation

    SciTech Connect

    Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

    2014-07-14

    The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.

  5. Self-guided Langevin dynamics via generalized Langevin equation.

    PubMed

    Wu, Xiongwu; Brooks, Bernard R; Vanden-Eijnden, Eric

    2016-03-01

    Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc. PMID:26183423

  6. Second-quantized molecular time scale generalized Langevin equation theory: Coupled oscillator model

    SciTech Connect

    McDowell, H.K.

    1986-11-15

    A second-quantized, coupled oscillator model is presented which explicitly displays the structure of a second-quantized MTGLE theory. The Adelman ansatz (J. Chem Phys. 75, 5837 (1981)) for a quantum MTGLE response function is shown to generate the correct response function for the model. This result paves the way for the development of a general second-quantized MTGLE theory.

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

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

    Distance fluctuation of a single molecule, modeled as an idealized bead-spring chain, dissolved in a Lennard-Jones liquid is studied by using a multidimensional generalized Langevin equation, where the friction kernel ζ(t) is calculated from the kinetic mode coupling theory (MCT). Temporal behavior of the distance autocorrelation function shows three typical regimes of time dependence, starting with a constant, followed by a power law of t-α, and finally an exponential decay. Particular attentions are paid to the time span of the power law regime, which corresponds to anomalous subdiffusion behavior, and the MCT framework enables us to investigate thoroughly how this regime depends on microscopic details such as the bead-to-solvent mass ratio MR, chain spring frequency ω, and the chain length N. Interestingly, the exponent α is robust to be 1/2 against the change of these parameters, although the friction kernel ζ(t) shows nontrivial dependence on time. In addition, we find that the starting time of the power-law region t1 scales with Γ-1, with Γ = 4ω2/ζ0 where ζ0 is the zero-frequency friction which decreases rapidly with increasing bead mass. On the other hand, the ending time t2 is not sensitive to varying ω or ζ0, but it increases with N rapidly before it reaches a constant for N larger than some threshold value. Our work may provide a unified strategy starting from the microscopic level to understand the anomalous subdiffusive behavior regarding large scale conformational change of polymers or proteins.

  8. Langevin equation approach to reactor noise analysis: stochastic transport equation

    SciTech Connect

    Akcasu, A.Z. ); Stolle, A.M. )

    1993-01-01

    The 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 is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

  9. Critical exponent of the fractional Langevin equation.

    PubMed

    Burov, S; Barkai, E

    2008-02-22

    We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, when an external oscillating field drives the system. Physically, we explain these behaviors using a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing the underdamped, the overdamped and critical frequencies of the fractional oscillator, recently used to model single protein experiments, show behaviors vastly different from normal. PMID:18352535

  10. Probability Density Function Method for Langevin Equations with Colored Noise

    SciTech Connect

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

    2013-04-05

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

  11. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation

    PubMed Central

    Müller, Eike H.; Scheichl, Rob; Shardlow, Tony

    2015-01-01

    This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

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

    NASA Astrophysics Data System (ADS)

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

    2006-04-01

    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, θk, attenuation factors, Qk and amplitude factors, Ak. The common elements of (θk~ 1.5, Qk~-0.3) and (θk~ 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.

  13. Simplified simulation of Boltzmann-Langevin equation

    SciTech Connect

    Ayik, S.; Randrup, J.

    1994-06-01

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

  14. A path integral approach to the Langevin equation

    NASA Astrophysics Data System (ADS)

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

    2015-02-01

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

  15. Bifurcation dynamics of the tempered fractional Langevin equation.

    PubMed

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings. PMID:27586627

  16. Bifurcation dynamics of the tempered fractional Langevin equation

    NASA Astrophysics Data System (ADS)

    Zeng, Caibin; Yang, Qigui; Chen, YangQuan

    2016-08-01

    Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.

  17. Langevin equation model of dispersion in the convective boundary layer

    SciTech Connect

    Nasstrom, J S

    1998-08-01

    This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well

  18. Langevin equation approach to granular flow in a narrow pipe

    SciTech Connect

    Riethmueller, T.; Schimansky-Geier, L.; Rosenkranz, D.; Poeschel, T.

    1997-01-01

    The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.

  19. Boltzmann-Langevin theory of Coulomb drag

    NASA Astrophysics Data System (ADS)

    Chen, W.; Andreev, A. V.; Levchenko, A.

    2015-06-01

    We develop a Boltzmann-Langevin description of the Coulomb drag effect in clean double-layer systems with large interlayer separation d as compared to the average interelectron distance λF. Coulomb drag arises from density fluctuations with spatial scales of order d . At low temperatures, their characteristic frequencies exceed the intralayer equilibration rate of the electron liquid, and Coulomb drag may be treated in the collisionless approximation. As temperature is raised, the electron mean free path becomes short due to electron-electron scattering. This leads to local equilibration of electron liquid, and consequently drag is determined by hydrodynamic density modes. Our theory applies to both the collisionless and the hydrodynamic regimes, and it enables us to describe the crossover between them. We find that drag resistivity exhibits a nonmonotonic temperature dependence with multiple crossovers at distinct energy scales. At the lowest temperatures, Coulomb drag is dominated by the particle-hole continuum, whereas at higher temperatures of the collision-dominated regime it is governed by the plasmon modes. We observe that fast intralayer equilibration mediated by electron-electron collisions ultimately renders a stronger drag effect.

  20. Stochastic modeling of driver behavior by Langevin equations

    NASA Astrophysics Data System (ADS)

    Langner, Michael; Peinke, Joachim

    2015-06-01

    A procedure based on stochastic Langevin equations is presented and shows how a stochastic model of driver behavior can be estimated directly from given data. The Langevin analysis allows the separation of a given data-set into a stochastic diffusion- and a deterministic drift field. Form the drift field a potential can be derived. In particular the method is here applied on driving data from a simulator. We overcome typical problems like varying sampling rates, low noise levels, low data amounts, inefficient coordinate systems, and non-stationary situations. From the estimation of the drift- and diffusion vector-fields derived from the data, we show different ways how to set up Monte-Carlo simulations for the driver behavior.

  1. Quantum Non-Markovian Langevin Equations and Transport Coefficients

    SciTech Connect

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

    2005-12-01

    Quantum diffusion equations featuring explicitly time-dependent transport coefficients are derived from generalized non-Markovian Langevin equations. Generalized fluctuation-dissipation relations and analytic expressions for calculating the friction and diffusion coefficients in nuclear processes are obtained. The asymptotic behavior of the transport coefficients and correlation functions for a damped harmonic oscillator that is linearly coupled in momentum to a heat bath is studied. The coupling to a heat bath in momentum is responsible for the appearance of the diffusion coefficient in coordinate. The problem of regression of correlations in quantum dissipative systems is analyzed.

  2. The generalized Schrödinger–Langevin equation

    SciTech Connect

    Bargueño, Pedro; Miret-Artés, Salvador

    2014-07-15

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

  3. Langevin equation with fluctuating diffusivity: A two-state model

    NASA Astrophysics Data System (ADS)

    Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

    2016-07-01

    Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

  4. Langevin equation with fluctuating diffusivity: A two-state model.

    PubMed

    Miyaguchi, Tomoshige; Akimoto, Takuma; Yamamoto, Eiji

    2016-07-01

    Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool. PMID:27575079

  5. Reconstruction of the modified discrete Langevin equation from persistent time series.

    PubMed

    Czechowski, Zbigniew

    2016-05-01

    The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed. PMID:27249949

  6. Solving the generalized Langevin equation with the algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Srokowski, T.; Płoszajczak, M.

    1998-04-01

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

  7. Is the Langevin phase equation an efficient model for oscillating neurons?

    NASA Astrophysics Data System (ADS)

    Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru

    2009-12-01

    The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

  8. On the environmental modes for the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Kawai, Shinnosuke

    2015-09-01

    The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.

  9. Langevin Theory of Anomalous Brownian Motion Made Simple

    ERIC Educational Resources Information Center

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

    2011-01-01

    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…

  10. Fractional Langevin equation: overdamped, underdamped, and critical behaviors.

    PubMed

    Burov, S; Barkai, E

    2008-09-01

    The dynamical phase diagram of the fractional Langevin equation is investigated for a harmonically bound particle. It is shown that critical exponents mark dynamical transitions in the behavior of the system. Four different critical exponents are found. (i) alpha_{c}=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase, (ii) alpha_{R}=0.441... marks a transition to a resonance phase when an external oscillating field drives the system, and (iii) alpha_{chi_{1}}=0.527... and (iv) alpha_{chi_{2}}=0.707... mark transitions to a double-peak phase of the "loss" when such an oscillating field present. As a physical explanation we present a cage effect, where the medium induces an elastic type of friction. Phase diagrams describing over and underdamped regimes, with or without resonances, show behaviors different from normal. PMID:18850998

  11. Recovering hidden dynamical modes from the generalized Langevin equation.

    PubMed

    Kawai, Shinnosuke; Miyazaki, Yusuke

    2016-09-01

    In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection. PMID:27608984

  12. Description of quantum noise by a Langevin equation

    NASA Technical Reports Server (NTRS)

    Metiu, H.; Schon, G.

    1984-01-01

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

  13. Dynamical simulation of neutron-induced fission of uranium isotopes using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2016-04-01

    Four-dimensional Langevin equations have been suggested for the dynamical simulation of neutron-induced fission at low and medium excitation energies. The mass distribution of the fission fragments, the neutron multiplicity, and the fission cross section for the thermal and fast neutron-induced fission of 233U, 235U, and 238U is studied by considering energy dissipation of the compound nucleus through the fission using four-dimensional Langevin equations combined with a Monte Carlo simulation approach. The calculated results using this approach indicate reasonable agreement with available experimental data.

  14. Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states

    NASA Astrophysics Data System (ADS)

    Chou, Chia-Chun

    2015-11-01

    The Schrödinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.

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

    NASA Technical Reports Server (NTRS)

    Jasnow, D.; Gerjuoy, E.

    1975-01-01

    We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.

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

    SciTech Connect

    Sadhukhan, Jhilam; Pal, Santanu

    2009-06-15

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

  17. Gaussian approximations for stochastic systems with delay: Chemical Langevin equation and application to a Brusselator system

    SciTech Connect

    Brett, Tobias Galla, Tobias

    2014-03-28

    We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.

  18. Dynamics of neutron-induced fission of 235U using four-dimensional Langevin equations

    NASA Astrophysics Data System (ADS)

    Pahlavani, M. R.; Mirfathi, S. M.

    2015-08-01

    Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and γ -ray emission. Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and γ -ray multiplicity for 236U as compound nuclei that are constructed after fusion of a neutron and 235U. Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to "funny hills" parametrization. Results: Fission fragment mass distribution, neutron and γ -ray multiplicity, and the average kinetic energy of emitted neutrons and γ rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations. Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.

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

    NASA Astrophysics Data System (ADS)

    Lee, Kyoung; Wang, Zhijian; Gardner, Robin

    2010-03-01

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

  20. Solving the Langevin equation with stochastic algebraically correlated noise

    NASA Astrophysics Data System (ADS)

    Płoszajczak, M.; Srokowski, T.

    1997-05-01

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

  1. Dynamic scaling behaviors of linear fractal Langevin-type equation driven by nonconserved and conserved noise

    NASA Astrophysics Data System (ADS)

    Zhang, Zhe; Xun, Zhi-Peng; Wu, Ling; Chen, Yi-Li; Xia, Hui; Hao, Da-Peng; Tang, Gang

    2016-06-01

    In order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model, a generalized linear fractal Langevin-type equation, ∂h / ∂t =(- 1) m + 1 ν∇ mzrw h (zrw is the dynamic exponent of random walk on substrates), driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis. Corresponding dynamic scaling exponents are obtained.

  2. Entropy production in non-equilibrium systems described by the generalized Langevin equation

    NASA Astrophysics Data System (ADS)

    Sevilla, Francisco J.; Piña-Perez, Omar

    2014-03-01

    The generalized Langevin equation for a charged particle under the influence of time-dependent external fields, is employed to study the effects of non-Markovian dissipative terms in the entropy production of non-equilibrium states exhibiting non-zero mass flux. We present results for the case in which the fluctuation-dissipation relation holds. FJS and OPP acknowledge financial support from PAPIIT-IN113114 and PAEP-UNAM respectively.

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

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

    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.

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

    NASA Astrophysics Data System (ADS)

    Srokowski, T.

    2001-09-01

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

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

    PubMed Central

    2013-01-01

    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

  7. Stochastic Oscillations of General Relativistic Disks Described by a Fractional Langevin Equation with Fractional Gaussian Noise

    NASA Astrophysics Data System (ADS)

    Zhi-Yun, Wang; Pei-Jie, Chen

    2016-06-01

    A generalized Langevin equation driven by fractional Brownian motion is used to describe the vertical oscillations of general relativistic disks. By means of numerical calculation method, the displacements, velocities and luminosities of oscillating disks are explicitly obtained for different Hurst exponent H. The results show that as H increases, the energies and luminosities of oscillating disk are enhanced, and the spectral slope at high frequencies of the power spectrum density of disk luminosity is also increased. This could explain the observational features related to the Intra Day Variability of the BL Lac objects.

  8. Collective behavior of globally coupled Langevin equations with colored noise in the presence of stochastic resonance

    NASA Astrophysics Data System (ADS)

    Yang, Bo; Zhang, Xiao; Zhang, Lu; Luo, Mao-Kang

    2016-08-01

    The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.

  9. Time-local Heisenberg-Langevin equations and the driven qubit

    NASA Astrophysics Data System (ADS)

    Whalen, S. J.; Carmichael, H. J.

    2016-06-01

    The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg-Langevin equation. Extension to the driven qubit fails—except for weak excitation—due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

  10. Anomalous diffusion in nonhomogeneous media: Power spectral density of signals generated by time-subordinated nonlinear Langevin equations

    NASA Astrophysics Data System (ADS)

    Kazakevičius, R.; Ruseckas, J.

    2015-11-01

    Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker-Planck equations. In the homogeneous systems the power spectral density of the signals generated by such Langevin equations has power-law dependency on the frequency with the exponent smaller than 1. In this paper we consider nonhomogeneous systems and show that in such systems the power spectral density can have power-law behavior with the exponent equal to or larger than 1 in a wide range of intermediate frequencies.

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

  12. Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise

    SciTech Connect

    Sandev, Trifce; Metzler, Ralf; Department of Physics, Tampere University of Technology, FI-33101 Tampere ; Tomovski, Živorad

    2014-02-15

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

  13. A Bohmian approach to the non-Markovian non-linear Schrödinger–Langevin equation

    SciTech Connect

    Vargas, Andrés F.; Morales-Durán, Nicolás; Bargueño, Pedro

    2015-05-15

    In this work, a non-Markovian non-linear Schrödinger–Langevin equation is derived from the system-plus-bath approach. After analyzing in detail previous Markovian cases, Bohmian mechanics is shown to be a powerful tool for obtaining the desired generalized equation.

  14. Nonequilibrium processes from generalized Langevin equations: Realistic nanoscale systems connected to two thermal baths

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

    We extend the generalized Langevin equation (GLE) method [L. Stella, C. D. Lorenz, and L. Kantorovich, Phys. Rev. B 89, 134303 (2014), 10.1103/PhysRevB.89.134303] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nosé-Hoover thermostats). We concentrate on the steady-state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e., ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.

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

    SciTech Connect

    Krommes, J.A.

    1995-11-01

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2012-01-01

    The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, 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.

  17. Internal noise-driven generalized Langevin equation from a nonlocal continuum model.

    PubMed

    Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan

    2015-08-01

    Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases. PMID:26382386

  18. Internal noise-driven generalized Langevin equation from a nonlocal continuum model

    NASA Astrophysics Data System (ADS)

    Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan

    2015-08-01

    Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.

  19. A note on the fluctuation-dissipation relation for the generalized Langevin equation with hydrodynamic backflow

    NASA Astrophysics Data System (ADS)

    Tóthová, Jana; Lisý, Vladimír

    2016-07-01

    This paper is devoted to finding the fluctuation-dissipation relation (FDR) for the generalized Langevin equation (GLE) with the Boussinesq-Basset (BB) force in which the Stokes friction is generalized to a convolution of a memory kernel with the velocity of a Brownian particle. First, the solution of such GLE with hydrodynamic backflow is obtained. Using this solution, we find in a simple and easily controllable way the time correlation function of the thermal force driving the particles. If the GLE is used with the original BB force for pure liquids, the FDR known from the literature is corrected. It is shown that in this case the FDR contains, in addition to the known term ∼t - 3 / 2, a more slowly decaying contribution ∼t - 1 / 2.

  20. Behavior of molecules on interstellar grains - Application of the Langevin equation and iterative extended Hueckel

    NASA Technical Reports Server (NTRS)

    Aronowitz, S.; Chang, S.

    1980-01-01

    The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Hueckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (about 3-10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce - the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH greater than CH greater than CO greater than NO, when these entities were sufficiently distant. The nature of the silica grain and that of the 'cold' desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.

  1. Behavior of Molecules on Interstellar Grains: Application of the Langevin Equation and Iterative Extended Huckel

    NASA Technical Reports Server (NTRS)

    Aronowitz. Sheldon

    1980-01-01

    The Langevin equation was used to explore an adsorbate desorption mechanism. Calculations were performed using iterative extended Huckel on a silica model site with various small adsorbates, e.g., H, CH, OH, NO, CO. It was found that barriers to free traversal from one site to another are substantial (approximately 3 - 10 eV). A bootstrap desorption mechanism for some molecules in the process of forming at a site also became apparent from the calculations. The desorption mechanisms appear to be somewhat balanced by a counterforce--the attraction of sites for the newly desorbed molecule. The order of attraction to a silica grain site for the diatomic molecules considered was OH > CH > CO > NO, when these entities were sufficiently distant. The nature of the silica grain and that of the "cold" desorption mechanism, when considered together, suggest that the abundance of very small grains might be less common than anticipated.

  2. Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations

    NASA Astrophysics Data System (ADS)

    Hasegawa, Yoshihiko

    2015-04-01

    We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.

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

    SciTech Connect

    Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho

    2013-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-06-01

    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 τ show ballistic behavior \\theta \\tau^{\\alpha_1} with the exponent \\alpha_1 \\approx 2 for small τ and show diffusion-like behavior D \\tau^{\\alpha_2} with the exponent \\alpha_2 \\approx 1 for large τ. Such a crossover behavior can be well described by the mean square displacements of particles governed by the Langevin equation of motion. Thus, θ 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.

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

    NASA Astrophysics Data System (ADS)

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

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

  6. Composite generalized Langevin equation for Brownian motion in different hydrodynamic and adhesion regimes.

    PubMed

    Yu, Hsiu-Yu; Eckmann, David M; Ayyaswamy, Portonovo S; Radhakrishnan, Ravi

    2015-05-01

    We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics. PMID:26066173

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

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

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

  8. Biomolecular folding rates as understood from single-reaction-coordinate Langevin dynamics and Kramers' theory

    NASA Astrophysics Data System (ADS)

    Kabir, Md Adnan

    Langevin dynamics was used to model the folding and unfolding of simple, hairpin-like biomolecules whose ends are attached to laser-trapped beads, as occurs in optical tweezers experiments. The Langevin process was evolved numerically, using parameters motivated by real experimental systems. Folding trajectories were generated and analyzed to extract the folding rate as a function of the force applied to the beads. The observed rate was compared to the analytical predictions of Kramers' theory. Strong discrepancies were noted. The failure of the Kramers' theory was attributed to the slow dynamical response of the beads, which it does not account for. The results of this work highlight the necessity to include in the modeling the experimental systems that mediate force along the length of the biomolecule.

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

    PubMed

    Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Iglič, Veronika; Iglič, Aleš

    2011-06-01

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

  10. The Spatial Chemical Langevin and Reaction Diffusion Master Equations: Moments and Qualitative Solutions

    NASA Astrophysics Data System (ADS)

    Ghosh, Atiyo; Leier, Andre; Marquez-Lago, Tatiana

    2014-03-01

    Spatial stochastic effects are prevalent in many biological systems spanning a variety of scales, from intracellular (e.g. gene expression) to ecological (plankton aggregation). The most common ways of simulating such systems involve drawing sample paths from either the Reaction Diffusion Master Equation (RDME) or the Smoluchowski Equation, using methods such as Gillespie's Simulation Algorithm, Green's Function Reaction Dynamics and Single Particle Tracking. The simulation times of such techniques scale with the number of simulated particles, leading to much computational expense when considering large systems. The Spatial Chemical Langevin Equation (SCLE) can be simulated with fixed time intervals, independent of the number of particles, and can thus provide significant computational savings. However, very little work has been done to investigate the behavior of the SCLE. In this talk we summarize our findings on comparing the SCLE to the well-studied RDME. We use both analytical and numerical procedures to show when one should expect the moments of the SCLE to be close to the RDME, and also when they should differ.

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

    PubMed

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

    2011-02-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

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

    SciTech Connect

    Krommes, J.A.

    1996-05-01

    The direct-interaction approximation (DIA) to the fourth-order statistic {ital 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 {ital et} {ital al}. [Phys. Fluids A {bold 1}, 1844 (1989)]. It is shown that the formula for {ital Z}{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose [Phys. Rev. A {bold 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. Sci. {bold 28}, 145 (1971)] and Kraichnan [J. Fluid Mech. {bold 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 ({open_quote}{open_quote}spurious vertices{close_quote}{close_quote}) is described. It is shown how to derive an improved representation, which realizes cumulants through {ital O}({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation {ital Z}{sub DIA}{sup {ital M}} to {ital Z}{sub DIA} is derived. Both {ital Z}{sub DIA} and {ital Z}{sub DIA}{sup {ital M}} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example. {copyright} {ital 1996 The American Physical Society.}

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

    PubMed

    Koehl, Patrice; Delarue, Marc

    2010-02-14

    The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE

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

    PubMed Central

    Koehl, Patrice; Delarue, Marc

    2010-01-01

    The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on

  16. The Schrödinger-Langevin equation with and without thermal fluctuations

    NASA Astrophysics Data System (ADS)

    Katz, R.; Gossiaux, P. B.

    2016-05-01

    The Schrödinger-Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.

  17. Anomalous polymer dynamics is non-Markovian: memory effects and the generalized Langevin equation formulation

    NASA Astrophysics Data System (ADS)

    Panja, Debabrata

    2010-06-01

    Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as tα for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a unified generalized Langevin equation (GLE) scheme, and therefore are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the power-law memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels.

  18. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

    NASA Astrophysics Data System (ADS)

    Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George

    2016-05-01

    The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

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

    SciTech Connect

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

    2013-02-08

    The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler-Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the two fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt1/2)] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler-Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. Lastly, this method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.

  20. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations.

    PubMed

    Wu, Fuke; Tian, Tianhai; Rawlings, James B; Yin, George

    2016-05-01

    The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence. PMID:27155630

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

    SciTech Connect

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

    2014-06-21

    We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

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

    NASA Astrophysics Data System (ADS)

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

    2014-06-01

    We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψT, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

  3. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid.

    PubMed

    Colmenares, Pedro J; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer. PMID:20365134

  4. Molecular dynamics and analytical Langevin equation approach for the self-diffusion constant of an anisotropic fluid

    NASA Astrophysics Data System (ADS)

    Colmenares, Pedro J.; López, Floralba; Olivares-Rivas, Wilmer

    2009-12-01

    We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.

  5. Distributional behaviors of time-averaged observables in the Langevin equation with fluctuating diffusivity: Normal diffusion but anomalous fluctuations

    NASA Astrophysics Data System (ADS)

    Akimoto, Takuma; Yamamoto, Eiji

    2016-06-01

    We consider the Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously over time, in order to study fluctuations of time-averaged observables in temporally heterogeneous diffusion processes. We find that the time-averaged mean-square displacement (TMSD) can be represented by the occupation time of a state in the asymptotic limit of the measurement time and hence occupation time statistics is a powerful tool for calculating the TMSD in the model. We show that the TMSD increases linearly with time (normal diffusion) but the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges, i.e., intrinsic nonequilibrium processes. Thus, we find that temporally heterogeneous environments provide anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficients obtained by single-particle-tracking trajectories in experiments.

  6. 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)

    Frank, T. D.

    2008-02-01

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

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

    SciTech Connect

    Rodean, H.C.

    1994-01-26

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

  8. Fluctuations in reactive networks subject to extrinsic noise studied in the framework of the chemical Langevin equation

    NASA Astrophysics Data System (ADS)

    Berthoumieux, H.

    2016-07-01

    Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined.

  9. Fluctuations in reactive networks subject to extrinsic noise studied in the framework of the chemical Langevin equation.

    PubMed

    Berthoumieux, H

    2016-07-01

    Theoretical and experimental studies have shown that the fluctuations of in vivo systems break the fluctuation-dissipation theorem. One can thus ask what information is contained in the correlation functions of protein concentrations and how they relate to the response of the reactive network to a perturbation. Answers to these questions are of prime importance to extract meaningful parameters from the in vivo fluorescence correlation spectroscopy data. In this paper we study the fluctuations of the concentration of a reactive species involved in a cyclic network that is in a nonequilibrium steady state perturbed by a noisy force, taking into account both the breaking of detailed balance and extrinsic noises. Using a generic model for the network and the extrinsic noise, we derive a chemical Langevin equation that describes the dynamics of the system, we determine the expressions of the correlation functions of the concentrations, and we estimate the deviation of the fluctuation-dissipation theorem and the range of parameters in which an effective temperature can be defined. PMID:27575151

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

    NASA Astrophysics Data System (ADS)

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

    2009-05-01

    The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on 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.

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

    PubMed

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

    2009-05-21

    The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods, which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations, which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures. PMID:19466829

  12. The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

    NASA Astrophysics Data System (ADS)

    Olivares-Rivas, Wilmer; Colmenares, Pedro J.

    2016-09-01

    The non-static generalized Langevin equation and its corresponding Fokker-Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non-Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.

  13. Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

    NASA Astrophysics Data System (ADS)

    Uneyama, Takashi; Miyaguchi, Tomoshige; Akimoto, Takuma

    2015-09-01

    The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

  14. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

    PubMed

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models. PMID:26871095

  15. Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations

    NASA Astrophysics Data System (ADS)

    Bouzat, Sebastián

    2016-01-01

    One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

  16. PDF model based on Langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow

    NASA Astrophysics Data System (ADS)

    Minier, Jean-Pierre; Peirano, Eric; Chibbaro, Sergio

    2004-07-01

    The aim of the paper is to discuss the main characteristics of a complete theoretical and numerical model for turbulent polydispersed two-phase flows, pointing out some specific issues. The theoretical details of the model have already been presented [Minier and Peirano, Phys. Rep. 352, 1 (2001)]. Consequently, the present work is mainly focused on complementary aspects that are often overlooked and that require particular attention. In particular, the following points are analyzed: the necessity to add an extra term in the equation for the velocity of the fluid seen in the case of two-way coupling, the theoretical and numerical evaluations of particle averages and the fulfillment of the particle mass-continuity constraint. The theoretical model is developed within the probability density function (PDF) formalism. The important physical choice of the state vector variables is first discussed and the model is then expressed as a stochastic differential equation written in continuous time (Langevin equations) for the velocity of the fluid seen. The interests and limitations of Langevin equations, compared to the single-phase case, are reviewed. From the numerical point of view, the model corresponds to a hybrid Eulerian/Lagrangian approach where the fluid and particle phases are simulated by different methods. Important aspects of the Monte Carlo particle/mesh numerical method are emphasized. Finally, the complete model is validated and its performance is assessed by simulating a bluff-body case with an important recirculation zone and in which two-way coupling is noticeable.

  17. Two critical issues in Langevin simulation of gas flows

    NASA Astrophysics Data System (ADS)

    Zhang, Jun; Fan, Jing

    2014-12-01

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  18. Two critical issues in Langevin simulation of gas flows

    SciTech Connect

    Zhang, Jun; Fan, Jing

    2014-12-09

    A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.

  19. Localised distributions and criteria for correctness in complex Langevin dynamics

    SciTech Connect

    Aarts, Gert; Giudice, Pietro; Seiler, Erhard

    2013-10-15

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

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

    NASA Astrophysics Data System (ADS)

    Okabe, Yasunori

    1986-12-01

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

  1. Gauge cooling for the singular-drift problem in the complex Langevin method — a test in Random Matrix Theory for finite density QCD

    NASA Astrophysics Data System (ADS)

    Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji

    2016-07-01

    Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.

  2. Nonlinear quantum equations: Classical field theory

    SciTech Connect

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

    2013-10-15

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

  3. Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

    SciTech Connect

    Hellinger, Petr

    2010-07-20

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

  4. Dynamical systems theory for the Gardner equation

    NASA Astrophysics Data System (ADS)

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

    2014-02-01

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

  5. Dynamical systems theory for the Gardner equation.

    PubMed

    Saha, Aparna; Talukdar, B; Chatterjee, Supriya

    2014-02-01

    The Gardner equation u(t) + auu(x) + bu(2)u(x)+μu(xxx) = 0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u(x,t) = φ(ξ), ξ = x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013)]. PMID:25353592

  6. Graph theory and the Virasoro master equation

    SciTech Connect

    Obers, N.A.J.

    1991-01-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {l brace}g{sub metric}{r brace}, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, he defines the sine-area graphs' of SU(n), which label the conformal field theories of SU(n){sub metric}, and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}.

  7. Graph theory and the Virasoro master equation

    SciTech Connect

    Obers, N.A.J.

    1991-04-01

    A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equations is given. By studying ansaetze of the master equation, we obtain exact solutions and gain insight in the structure of large slices of affine-Virasoro space. We find an isomorphism between the constructions in the ansatz SO(n){sub diag}, which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabelled graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. We also define a class of magic'' Lie group bases in which the Virasoro master equation admits a simple metric ansatz (gmetric), whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g{sub metric} is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n){sub diag} in the Cartesian basis of SO(n), and the ansatz SU(n){sub metric} in the Pauli-like basis of SU(n). Finally, we define the sine-area graphs'' of SU(n), which label the conformal field theories of SU(n){sub metric}, and we note that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g{sub metric}. 24 figs., 4 tabs.

  8. New Langevin and gradient thermostats for rigid body dynamics

    NASA Astrophysics Data System (ADS)

    Davidchack, R. L.; Ouldridge, T. E.; Tretyakov, M. V.

    2015-04-01

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

  9. New Langevin and gradient thermostats for rigid body dynamics.

    PubMed

    Davidchack, R L; Ouldridge, T E; Tretyakov, M V

    2015-04-14

    We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator. PMID:25877569

  10. Brownian motion from Boltzmann's equation.

    NASA Technical Reports Server (NTRS)

    Montgomery, D.

    1971-01-01

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

  11. Undular bore theory for the Gardner equation.

    PubMed

    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

    We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations. PMID:23031043

  12. Solving Kepler's equation via Smale's -theory

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

  13. Comparison of Kernel Equating and Item Response Theory Equating Methods

    ERIC Educational Resources Information Center

    Meng, Yu

    2012-01-01

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

  14. Analysis of multifrequency langevin composite ultrasonic transducers.

    PubMed

    Lin, Shuyu

    2009-09-01

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

  15. Thermodynamic restrictions on the constitutive equations of electromagnetic theory

    NASA Technical Reports Server (NTRS)

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

    1971-01-01

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

  16. Ramond equations of motion in superstring field theory

    NASA Astrophysics Data System (ADS)

    Erler, Theodore; Konopka, Sebastian; Sachs, Ivo

    2015-11-01

    We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.

  17. Langevin stabilization of molecular dynamics

    NASA Astrophysics Data System (ADS)

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

    2001-02-01

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

  18. Langevin dynamics, entropic crowding, and stochastic cloaking.

    PubMed

    Eliazar, Iddo

    2011-12-01

    We consider a pack of independent probes--within a spatially inhomogeneous thermal bath consisting of a vast number of randomly moving particles--which are subjected to an external force. The stochastic dynamics of the probes are governed by Langevin's equation. The probes attain a steady state distribution which, in general, is different than the concentration of the particles in the spatially inhomogeneous thermal bath. In this paper we explore the state of "entropic crowding" in which the probes' distribution and the particles' concentration coincide--thus yielding maximal relative entropies of one with respect to the other. Entropic crowding can be attained by two scenarios which are analyzed in detail: (i) "entropically crowding thermal baths"--in which the particles crowd uniformly around the probes; (ii) "entropically crowding Langevin forces"--in which the probes crowd uniformly amongst the particles. Entropic crowding is equivalent to the optimal stochastic cloaking of the probes within the spatially inhomogeneous thermal bath. PMID:22304065

  19. THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

    EPA Science Inventory

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

  20. Behavioral Momentum Theory: Equations and Applications

    ERIC Educational Resources Information Center

    Nevin, John A.; Shahan, Timothy A.

    2011-01-01

    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…

  1. Electron transfer dynamics: Zusman equation versus exact theory.

    PubMed

    Shi, Qiang; Chen, Liping; Nan, Guangjun; Xu, Ruixue; Yan, YiJing

    2009-04-28

    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. PMID:19405605

  2. Item Response Theory Equating Using Bayesian Informative Priors.

    ERIC Educational Resources Information Center

    de la Torre, Jimmy; Patz, Richard J.

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

  3. Fokker-Planck equation of Schramm-Loewner evolution.

    PubMed

    Najafi, M N

    2015-08-01

    In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE(κ,ρc). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE(κ,ρc) traces and show that it is related to the higher-order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented. PMID:26382350

  4. Reprint of : The Boltzmann--Langevin approach: A simple quantum-mechanical derivation

    NASA Astrophysics Data System (ADS)

    Nagaev, K. E.

    2016-08-01

    We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.

  5. The Boltzmann-Langevin approach: A simple quantum-mechanical derivation

    NASA Astrophysics Data System (ADS)

    Nagaev, K. E.

    2015-11-01

    We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.

  6. Variance Reduction Using Nonreversible Langevin Samplers

    NASA Astrophysics Data System (ADS)

    Duncan, A. B.; Lelièvre, T.; Pavliotis, G. A.

    2016-05-01

    A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers [30, 37, 61, 72], introducing an appropriately chosen nonreversible component to the dynamics is beneficial, both in terms of reducing the asymptotic variance and of speeding up convergence to the target distribution. In this paper we present a detailed study of the dependence of the asymptotic variance on the deviation from reversibility. Our theoretical findings are supported by numerical simulations.

  7. Classical field theories from Hamiltonian constraint: Canonical equations of motion and local Hamilton-Jacobi theory

    NASA Astrophysics Data System (ADS)

    Zatloukal, Václav

    2016-04-01

    Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.

  8. Theory of relativistic Brownian motion: the (1+1)-dimensional case.

    PubMed

    Dunkel, Jörn; Hänggi, Peter

    2005-01-01

    We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (prepoint discretization rule) versus the Stratonovich (midpoint discretization rule) dilemma: It is found that the relativistic Langevin equation in the Hänggi-Klimontovich interpretation (with the postpoint discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented. PMID:15697675

  9. Filtration theory using computer simulations

    SciTech Connect

    Bergman, W.; Corey, I.

    1997-08-01

    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. 5 refs., 11 figs.

  10. Velocity-Field Theory, Boltzmann's Transport Equation and Geometry

    NASA Astrophysics Data System (ADS)

    Ichinose, Shoichi

    Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the velocity-field plays the central role. The matter (constituent particles) fields appear as the density and the viscosity. Fluctuation is examined, and is clearly discriminated from the quantum effect. The time variable is emergently introduced through the computational process step. The collision term, for the (velocity)**4 potential (4-body interaction), is explicitly obtained and the (statistical) fluctuation is closely explained. The present field theory model does not conserve energy and is an open-system model. (One dimensional) Navier-Stokes equation or Burger's equation, appears. In the latter part, we present a way to directly define the distribution function by use of the geometry, appearing in the mechanical dynamics, and Feynman's path-integral.

  11. Einstein equations and MOND theory from Debye entropic gravity

    SciTech Connect

    Sheykhi, A.; Sarab, K. Rezazadeh E-mail: kazem.rezazadeh.sarab@gmail.com

    2012-10-01

    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.

  12. Semigroup theory and numerical approximation for equations in linear viscoelasticity

    NASA Technical Reports Server (NTRS)

    Fabiano, R. H.; Ito, K.

    1990-01-01

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

  13. Accurate Langevin approaches to simulate Markovian channel dynamics

    NASA Astrophysics Data System (ADS)

    Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei

    2015-12-01

    The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu’s classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.

  14. Experimenting with Langevin lattice QCD

    SciTech Connect

    Gavai, R.V.; Potvin, J.; Sanielevici, S.

    1987-05-01

    We report on the status of our investigations of the effects of systematic errors upon the practical merits of Langevin updating in full lattice QCD. We formulate some rules for the safe use of this updating procedure and some observations on problems which may be common to all approximate fermion algorithms.

  15. Control theory based airfoil design using the Euler equations

    NASA Technical Reports Server (NTRS)

    Jameson, Antony; Reuther, James

    1994-01-01

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

  16. Driven Langevin systems: fluctuation theorems and faithful dynamics

    NASA Astrophysics Data System (ADS)

    Sivak, David; Chodera, John; Crooks, Gavin

    2014-03-01

    Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

  17. The Kelvin equation and self-consistent nucleation theory

    SciTech Connect

    Wilemski, G. |

    1995-07-15

    Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplify the calculation of nucleation rates for this model. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

  18. Master equation based steady-state cluster perturbation theory

    NASA Astrophysics Data System (ADS)

    Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico

    2015-09-01

    A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ρ̂S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.

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

    NASA Technical Reports Server (NTRS)

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

    1973-01-01

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

  20. Langevin dynamics neglecting detailed balance condition.

    PubMed

    Ohzeki, Masayuki; Ichiki, Akihisa

    2015-07-01

    An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann distribution involve numerical simulations under the detailed balance condition. In contrast, in the present study we formulate the Langevin dynamics, for which the corresponding Fokker-Planck operator includes an asymmetric component violating the detailed balance condition. This leads to shifts in the eigenvalues and results in the acceleration of the relaxation toward the steady state. The numerical implementation demonstrates faster convergence and shorter correlation time, and the technique of biased event sampling, Nemoto-Sasa theory, further highlights the efficacy of our method. PMID:26274123

  1. Integrals and integral equations in linearized wing theory

    NASA Technical Reports Server (NTRS)

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

    1951-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Piątek, Marcin; Pietrykowski, Artur R.

    2014-12-01

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

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

    SciTech Connect

    Akamatsu, Yukinao; Hatsuda, Tetsuo; Hirano, Tetsufumi

    2009-05-15

    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.

  4. Multiphoton-scattering theory and generalized master equations

    NASA Astrophysics Data System (ADS)

    Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio

    2015-11-01

    We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.

  5. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.

    PubMed

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436

  6. Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism

    NASA Astrophysics Data System (ADS)

    Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.

    2015-04-01

    We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

  7. Integral Equation Theory for the Conformation of Polyelectrolytes

    NASA Astrophysics Data System (ADS)

    Shew, C.-Y.; Yethiraj, A.

    1996-03-01

    The equilibrium conformation properties of polyelectrolyes are explored using the integral equation theory. The polymer molecules are modeled as freely-jointed beads that interact via a hard sphere plus screened Coulomb potential. To obtain the intramolecuar correlation function ( and hence the chain conformations) the many chain system is replaced by a single chain whose beads interact via the bare interaction plus a solvent-induced potential, which approximately accounts for the presence of the other molecules. Since this solvent induced potential is a functional of the intramolecular correlations it is obtained iteratively in a self-consistent fashion. The intramolecular correlation functions for a given solvation potential are obtained via Monte Carlo simulation of a single chain. A thread model of the polymer molecules is also investigated, in which case the single chain conformations are obtained using a variational method. The predictions of the theory for these two models are similar. For single chains ~ N^2 ( is the mean square end-to-end distance and N is the degree of polymerization) in salt free solutions, and ~ N^1.2 in high salt solutions. At high polymer concentration ~ N. The theory provides a means of interpolating between these limiting cases. An interesting feature is that there is a very sharp drop in polymer size at very low concentrations which happens because the overlap threshold concentration in polyelectrolytes solutions is very small.

  8. The Small-Mass Limit for Langevin Dynamics with Unbounded Coefficients and Positive Friction

    NASA Astrophysics Data System (ADS)

    Herzog, David P.; Hottovy, Scott; Volpe, Giovanni

    2016-05-01

    A class of Langevin stochastic differential equations is shown to converge in the small-mass limit under very weak assumptions on the coefficients defining the equation. The convergence result is applied to three physically realizable examples where the coefficients defining the Langevin equation for these examples grow unboundedly either at a boundary, such as a wall, and/or at the point at infinity. This unboundedness violates the assumptions of previous limit theorems in the literature. The main result of this paper proves convergence for such examples.

  9. Combined Néel and Brown rotational Langevin dynamics in magnetic particle imaging, sensing, and therapy

    SciTech Connect

    Reeves, Daniel B.; Weaver, John B.

    2015-11-30

    Magnetic nanoparticles have been studied intensely because of their possible uses in biomedical applications. Biosensing using the rotational freedom of particles has been used to detect biomarkers for cancer, hyperthermia therapy has been used to treat tumors, and magnetic particle imaging is a promising new imaging modality that can spatially resolve the concentration of nanoparticles. There are two mechanisms by which the magnetization of a nanoparticle can rotate, a fact that poses a challenge for applications that rely on precisely one mechanism. The challenge is exacerbated by the high sensitivity of the dominant mechanism to applied fields. Here, we demonstrate stochastic Langevin equation simulations for the combined rotation in magnetic nanoparticles exposed to oscillating applied fields typical to these applications to both highlight the existing relevant theory and quantify which mechanism should occur in various parameter ranges.

  10. Random matrix theory and the sixth Painlevé equation

    NASA Astrophysics Data System (ADS)

    Forrester, P. J.; Witte, N. S.

    2006-09-01

    A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realized by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be τ-functions for Painlevé systems, allowing for the former to be characterized as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the σ form of PVI. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at t = 0, 1, ∞ of σPVI displayed by a generalization of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the τ-function of σPVI in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to PVI.

  11. Fluctuation theory of starlight polarization

    SciTech Connect

    Nee, S.F.

    1980-04-15

    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./sup 0/5 for the fluctuation of interstellar magnetic field for the observation direction within 60/sup 0/equator.

  12. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.

    PubMed

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-14

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used. PMID:27421393

  13. A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat

    NASA Astrophysics Data System (ADS)

    Liu, Jian; Li, Dezhang; Liu, Xinzijian

    2016-07-01

    We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.

  14. Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing

    NASA Astrophysics Data System (ADS)

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

    2015-01-01

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

  15. The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory

    NASA Astrophysics Data System (ADS)

    Nakhleh, Charles W.

    2013-03-01

    This paper uses elementary techniques drawn from renormalization theory to derive the Lorentz-Dirac equation for the relativistic classical electron from the Maxwell-Lorentz equations for a classical charged particle coupled to the electromagnetic field. I show that the resulting effective theory, valid for electron motions that change over distances large compared to the classical electron radius, reduces naturally to the Landau-Lifshitz equation. No familiarity with renormalization or quantum field theory is assumed.

  16. Modern integral equation techniques for quantum reactive scattering theory

    SciTech Connect

    Auerbach, S.M.

    1993-11-01

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

  17. The theory of relaxation oscillations for Hutchinson's equation

    SciTech Connect

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2011-06-30

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

  18. Fractional Diffusion Equation, Quantum Subdynamics and EINSTEIN'S Theory of Brownian Motion

    NASA Astrophysics Data System (ADS)

    Abe, Sumiyoshi

    The fractional diffusion equation for describing the anomalous diffusion phenomenon is derived in the spirit of Einstein's 1905 theory of Brownian motion. It is shown how naturally fractional calculus appears in the theory. Then, Einstein's theory is examined in view of quantum theory. An isolated quantum system composed of the objective system and the environment is considered, and then subdynamics of the objective system is formulated. The resulting quantum master equation is found to be of the Lindblad type.

  19. Langevin description of gauged scalar fields in a thermal bath

    NASA Astrophysics Data System (ADS)

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

    2014-04-01

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

  20. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

    SciTech Connect

    He, Xiaoyi; Lou, Li-Shi Lou, Li-Shi

    1997-12-01

    In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. {copyright} {ital 1997} {ital The American Physical Society}

  1. Relation between the Rayleigh equation in diffraction theory and the equation based on Green's formula

    NASA Astrophysics Data System (ADS)

    Tatarskii, V. I.

    1995-06-01

    The steps necessary to produce the Rayleigh equation that is based on the Rayleigh hypothesis from the equation that is based on the Green's formula are shown. First a definition is given for the scattering amplitude that is true not only in the far zone of diffraction but also near the scattering surface. With this definition the Rayleigh equation coincides with the rigorous equation for the surface secondary sources that is based on Green's formula. The Rayleigh hypothesis is equivalent to substituting the far-zone expression of the scattering amplitude into this rigorous equation. In this case it turns out to be the equation not for the sources but directly for the scattering amplitude, which is the main advantage of this method. For comparing the Rayleigh equation with the initial rigorous equation, the Rayleigh equation is represented in terms of secondary sources. The kernel of this equation contains an integral that converges for positive and diverges for negative values of some parameter. It is shown that if we regularize this integral, defining it for the negative values of this parameter as an analytical continuation from the domain of positive values, this kernel becomes equal to the kernel of the initial rigorous equation. It follows that the formal perturbation series for the scattering amplitude obtained from the Rayleigh equation and from Green's equation always coincide. This means that convergence of the perturbation series is a sufficient condition

  2. A novel Generalized Langevin approach to bridge different timescales of relaxation in Protein Dynamics

    NASA Astrophysics Data System (ADS)

    Caballero Manrique, Esther; Bray, Jenelle; Guenza, Marina

    2006-03-01

    The derivation of a Generalized Langevin Equation (GLE) for the long-time dynamics of biological systems presents several challenges as hydrogen bonding, secondary and tertiary structure, Coulombic interactions, and hydrophobic effects come into play. Here we propose a novel GLE approach where the internal friction is explicitly included in the protein dynamics, allowing the distinction between hydrophobic and hydrophilic effects. The protein is described as a linear chain of beads (centered at the alpha carbons) that are connected by harmonic springs. Input for our theory is short time (ns) molecular dynamics simulations of a single protein (or complex) in solution, in this case the bacterial signal transduction protein CheY. Effective inter-bead potentials and local friction coefficients are obtained from the simulations. A comparison of the bond autocorrelation function predicted from the theory and calculated directly from the simulation affords the test of the theory in the short timescales (ns). In the long timescales (ms), the theory is tested against experimental NMR T1 relaxation values. Our results show a remarkable agreement in both cases, indicating that our GLE correctly bridges from the short- to the long-time scale of protein dynamics.

  3. Scaling theory for homogenization of the Maxwell equations

    NASA Astrophysics Data System (ADS)

    Vinogradov, Alexei P.

    1997-11-01

    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

  4. Complex Langevin simulation of chiral symmetry restoration at finite baryonic density

    NASA Astrophysics Data System (ADS)

    Ilgenfritz, Ernst-Michael

    1986-12-01

    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.

  5. Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Mafra, Carlos R.; Schlotterer, Oliver

    2015-09-01

    In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.

  6. Existence of a solution to an equation arising from the theory of Mean Field Games

    NASA Astrophysics Data System (ADS)

    Gangbo, Wilfrid; Święch, Andrzej

    2015-12-01

    We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied in [2,19,20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).

  7. Distribution theory for Schrödinger’s integral equation

    SciTech Connect

    Lange, Rutger-Jan

    2015-12-15

    Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between both forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.

  8. Distribution theory for Schrödinger's integral equation

    NASA Astrophysics Data System (ADS)

    Lange, Rutger-Jan

    2015-12-01

    Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger's equation. This paper, in contrast, investigates the integral form of Schrödinger's equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger's integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger's differential equation. This hints at a possible deeper connection between both forms of the equation. We also sketch a generalisation of Kurasov's [J. Math. Anal. Appl. 201(1), 297-323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger's integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger's differential equation. Third, we derive boundary conditions for "super-singular" potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger's integral equation is a viable tool for studying singular interactions in quantum mechanics.

  9. Quantum theory of rotational isomerism and Hill equation

    SciTech Connect

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

    2012-06-15

    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.

  10. Dynamic field theory and equations of motion in cosmology

    NASA Astrophysics Data System (ADS)

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2014-11-01

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

  11. Dynamic field theory and equations of motion in cosmology

    SciTech Connect

    Kopeikin, Sergei M.; Petrov, Alexander N.

    2014-11-15

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

  12. Approximating electronically excited states with equation-of-motion linear coupled-cluster theory

    SciTech Connect

    Byrd, Jason N. Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.

    2015-10-28

    A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order Møller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory equations and two new equation-of-motion methods based on the linear coupled-cluster doubles and linear coupled-cluster singles and doubles wavefunctions. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical equation-of-motion coupled-cluster singles and doubles state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.

  13. Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.

    NASA Astrophysics Data System (ADS)

    Auerbach, Scott Michael

    Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is

  14. Effective equations and the inverse cascade theory for Kolmogorov flows

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1993-01-01

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

  15. Effective equations and the inverse cascade theory for Kolmogorov flows

    NASA Technical Reports Server (NTRS)

    Weinan, E.; Shu, Chi-Wang

    1992-01-01

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

  16. Isothermal Langevin dynamics in systems with power-law spatially dependent friction

    NASA Astrophysics Data System (ADS)

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D (x ) ˜|x| c , at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c <0 and superdiffusion for 0 1 , the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (˜t2 ). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation.

  17. The quantum probability equation: I. Bound state perturbation theory

    NASA Astrophysics Data System (ADS)

    Milward, Geoffrey C.; Wilkin, Colin

    2000-10-01

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

  18. Equation-of-motion coupled cluster perturbation theory revisited

    SciTech Connect

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

    2014-05-07

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

  19. Application of integral equation theory to polyolefin liquids and blends

    SciTech Connect

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

    1997-11-01

    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.

  20. The application of the integral equation theory to study the hydrophobic interaction

    PubMed Central

    Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

    2014-01-01

    The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891

  1. LOGTRUE: A Computer Program for Test Equating with Item Response Theory.

    ERIC Educational Resources Information Center

    Phillips, S. E.; Anderson, A. E.

    The LOGTRUE program can be used to obtain a scale of equated raw scores for two tests with parameter estimates on a common item response theory scale. The program derives its name from the method of logistic true score equating described by Lord (1980). The method can be applied to two tests with overlapping items administered to different groups…

  2. Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

    NASA Technical Reports Server (NTRS)

    Pai, S. I.

    1973-01-01

    The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

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

    PubMed

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

    2006-02-17

    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

  4. Mapping the Monte Carlo Scheme to Langevin Dynamics: A Fokker-Planck Approach

    NASA Astrophysics Data System (ADS)

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

    2006-02-01

    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 α, unlike previous time-quantified MC methods which break down at low α, where precessional motion dominates.

  5. Formulation and closure of compressible turbulence equations in the light of kinetic theory

    NASA Technical Reports Server (NTRS)

    Tsuge, S.; Sagara, K.

    1976-01-01

    Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

  6. Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

    SciTech Connect

    A. Pletzer; L.E. Zakharov

    1999-07-01

    The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.

  7. An Extension of IRT-Based Equating to the Dichotomous Testlet Response Theory Model

    ERIC Educational Resources Information Center

    Tao, Wei; Cao, Yi

    2016-01-01

    Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

  8. On p -form theories with gauge invariant second order field equations

    NASA Astrophysics Data System (ADS)

    Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan

    2016-04-01

    We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.

  9. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-06-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  10. Error Analysis of Modified Langevin Dynamics

    NASA Astrophysics Data System (ADS)

    Redon, Stephane; Stoltz, Gabriel; Trstanova, Zofia

    2016-08-01

    We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations.

  11. Multidimensional Langevin Modeling of Nonoverdamped Dynamics

    NASA Astrophysics Data System (ADS)

    Schaudinnus, Norbert; Bastian, Björn; Hegger, Rainer; Stock, Gerhard

    2015-07-01

    Based on a given time series, data-driven Langevin modeling aims to construct a low-dimensional dynamical model of the underlying system. When dealing with physical data as provided by, e.g., all-atom molecular dynamics simulations, effects due to small damping may be important to correctly describe the statistics (e.g., the energy landscape) and the dynamics (e.g., transition times). To include these effects in a dynamical model, an algorithm that propagates a second-order Langevin scheme is derived, which facilitates the treatment of multidimensional data. Adopting extensive molecular dynamics simulations of a peptide helix, a five-dimensional model is constructed that successfully forecasts the complex structural dynamics of the system. Neglect of small damping effects, on the other hand, is shown to lead to significant errors and inconsistencies.

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

    NASA Astrophysics Data System (ADS)

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

    2009-07-01

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

  13. Sampling the isothermal-isobaric ensemble by Langevin dynamics

    NASA Astrophysics Data System (ADS)

    Gao, Xingyu; Fang, Jun; Wang, Han

    2016-03-01

    We present a new method of conducting fully flexible-cell molecular dynamics simulation in isothermal-isobaric ensemble based on Langevin equations of motion. The stochastic coupling to all particle and cell degrees of freedoms is introduced in a correct way, in the sense that the stationary configurational distribution is proved to be consistent with that of the isothermal-isobaric ensemble. In order to apply the proposed method in computer simulations, a second order symmetric numerical integration scheme is developed by Trotter's splitting of the single-step propagator. Moreover, a practical guide of choosing working parameters is suggested for user specified thermo- and baro-coupling time scales. The method and software implementation are carefully validated by a numerical example.

  14. Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites

    NASA Astrophysics Data System (ADS)

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

    2011-05-01

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

  15. The most general second-order field equations of bi-scalar-tensor theory in four dimensions

    NASA Astrophysics Data System (ADS)

    Ohashi, Seiju; Tanahashi, Norihiro; Kobayashi, Tsutomu; Yamaguchi, Masahide

    2015-07-01

    The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.

  16. Gauge theories on noncommutative ℂPN and Bogomol'nyi-Prasad-Sommerfield-like equations

    NASA Astrophysics Data System (ADS)

    Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi

    2015-11-01

    We give the Fock representation of a noncommutative ℂPN and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ℂPN. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Bogomol'nyi-Prasad-Sommerfield (BPS)-like equations on noncommutative ℂP1 and ℂP2 are derived from these actions. There are analogies between BPS-like equations on ℂP1 and monopole equations on ℝ3 and BPS-like equations on ℂP2 and instanton equations on ℝ8. We discuss solutions of these BPS-like equations.

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

    NASA Astrophysics Data System (ADS)

    Nakamura, K.

    2009-06-01

    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.

  18. Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

    NASA Astrophysics Data System (ADS)

    Wills, John M.; Mattsson, Ann E.

    2012-02-01

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

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

    PubMed Central

    Hsu, David; Hsu, Murielle

    2009-01-01

    We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation of motion that has the form of a generalized Langevin equation (GLE), which requires knowledge only of macroscopic properties. The macroscopic properties can be extracted from experimental data by one of two possible variational principles. These variational principles are our principal contribution to the formalism. Potential applications are discussed, including applications to the theory of critical phenomena in the brain, Granger causality and Kalman filters. PACS code: 87.19.lj PMID:19594920

  20. A theory of post-stall transients in axial compression systems. I - Development of equations

    NASA Technical Reports Server (NTRS)

    Moore, F. K.; Greitzer, E. M.

    1985-01-01

    An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.

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

    PubMed

    Aupic, Jana; Urbic, Tomaz

    2014-05-14

    Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected. PMID:24832290

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

    SciTech Connect

    Aupic, Jana; Urbic, Tomaz

    2014-05-14

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

  3. Dual chain perturbation theory: A new equation of state for polyatomic molecules

    NASA Astrophysics Data System (ADS)

    Marshall, Bennett D.

    2016-04-01

    In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

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

    SciTech Connect

    Cardanobile, Stefano; Mugnolo, Delio

    2009-10-15

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

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

    NASA Technical Reports Server (NTRS)

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

    1986-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2007-02-01

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

  8. On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    NASA Astrophysics Data System (ADS)

    Kravchenko, Vladislav V.

    2005-01-01

    Given a particular solution of a one-dimensional stationary Schrödinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schrödinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schrödinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schrödinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schrödinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schrödinger equation. Moreover, for an ample

  9. The Scherrer equation and the dynamical theory of X-ray diffraction.

    PubMed

    Muniz, Francisco Tiago Leitão; Miranda, Marcus Aurélio Ribeiro; Morilla Dos Santos, Cássio; Sasaki, José Marcos

    2016-05-01

    The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm. PMID:27126115

  10. Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation

    NASA Astrophysics Data System (ADS)

    Lindgren, I.; Salomonson, S.; Hedendahl, D.

    2005-03-01

    The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.

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

    SciTech Connect

    Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.

    2012-08-15

    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.

  12. Scattering theory for the Klein-Gordon equation with nondecreasing potentials

    SciTech Connect

    Cruz, Maximino; Arredondo R, Juan H.

    2008-11-15

    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.

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

    ERIC Educational Resources Information Center

    Brossman, Bradley Grant

    2010-01-01

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

  14. Asymptotic Standard Errors for Item Response Theory True Score Equating of Polytomous Items

    ERIC Educational Resources Information Center

    Cher Wong, Cheow

    2015-01-01

    Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like…

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

    SciTech Connect

    Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel

    2011-05-23

    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.

  16. The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature

    SciTech Connect

    Bertolami, O.; Gomes, C. E-mail: claudio.gomes@fc.up.pt

    2014-09-01

    We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.

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

    ERIC Educational Resources Information Center

    Muthen, Bengt; Asparouhov, Tihomir

    2012-01-01

    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…

  18. Dirac equation and optical scalars in the Einstein-Cartan theory

    NASA Astrophysics Data System (ADS)

    Timofeev, Vladimir

    2016-03-01

    The article deals with the Dirac equation in the Newman-Penrose formalism within the framework of Einstein-Cartan theory and behavior of isotropic congruence of autoparallels, i. e. a congruence of the curves along which tangent null vector transferred in parallel.

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

    ERIC Educational Resources Information Center

    Han, Kyung T.

    2009-01-01

    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…

  20. An approximation theory for nonlinear partial differential equations with applications to identification and control

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Kunisch, K.

    1982-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1993-01-01

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

  2. Initial states in integrable quantum field theory quenches from an integral equation hierarchy

    NASA Astrophysics Data System (ADS)

    Horváth, D. X.; Sotiriadis, S.; Takács, G.

    2016-01-01

    We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to most exact methods to treat integrable quantum quenches. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provides a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.

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

    NASA Astrophysics Data System (ADS)

    Nakamura, K.

    2007-01-01

    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.

  4. Langevin processes, agent models and socio-economic systems

    NASA Astrophysics Data System (ADS)

    Richmond, Peter; Sabatelli, Lorenzo

    2004-05-01

    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

  5. Langevin power curve analysis for numerical wind energy converter models with new insights on high frequency power performance

    NASA Astrophysics Data System (ADS)

    Mücke, Tanja A.; Wächter, Matthias; Milan, Patrick; Peinke, Joachim

    2015-11-01

    Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power curve for different data samplings. We show, how to get reliable results from synthetic data and verify the applicability of the method for field measurements with ultra-sonic, cup and Lidar measurements. The independence of the fixed points on site specific turbulence effects is also confirmed with the numerical model. Furthermore, we demonstrate the potential of the Langevin approach to detect failures in the conversion process and thus show the potential of the Langevin approach for a condition monitoring system.

  6. On a derivation of the Boltzmann equation in Quantum Field Theory

    NASA Astrophysics Data System (ADS)

    Leiler, Gregor

    The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.

  7. Irreversible Langevin samplers and variance reduction: a large deviations approach

    NASA Astrophysics Data System (ADS)

    Rey-Bellet, Luc; Spiliopoulos, Konstantinos

    2015-07-01

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

  8. Time Step Rescaling Recovers Continuous-Time Dynamical Properties for Discrete-Time Langevin Integration of Nonequilibrium Systems

    PubMed Central

    2015-01-01

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

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

    SciTech Connect

    Puetzfeld, Dirk; Obukhov, Yuri N.

    2007-10-15

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

  10. A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2015-10-01

    This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.

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

    NASA Astrophysics Data System (ADS)

    Toledo, Porfirio

    2013-12-01

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

  12. Theory of magnetohydrodynamic accretion of matter with an ultrahard equation of state onto a black hole

    SciTech Connect

    Chernov, S. V.

    2015-06-15

    We consider the magnetohydrodynamic theory of spherically symmetric accretion of a perfect fluid onto a Schwarzschild black hole with an ultrahard equation of state, p = μ ∼ ρ{sup 2}, where p is the pressure, μ is the total energy density, and ρ is the fluid density. An approximate analytical solution is written out. We show that one critical sonic surface that coincides with the black hole event horizon is formed instead of two critical surfaces (fast and slow magnetosonic surfaces) for a degenerate ultrahard equation of state of matter.

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

    SciTech Connect

    Schelle, Alexej; Wellens, Thomas; Buchleitner, Andreas; Delande, Dominique

    2011-01-15

    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.

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

    NASA Astrophysics Data System (ADS)

    Nagy, Á.

    1993-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

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

    SciTech Connect

    Musielak, Z.E. Fry, J.L.

    2009-02-15

    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.

  17. Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Huber, Markus Q.

    2016-04-01

    The two- and three-point functions and the four-gluon vertex of three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger equations and the three-particle irreducible effective action. Within a self-contained truncation, various effects of truncating Dyson-Schwinger equations are studied. Estimates for the errors induced by truncations are derived from comparisons between results from different equations, comparisons with lattice results, and varying higher Green functions. The results indicate that the two-loop diagrams are important in the gluon propagator, where they are explicitly calculated, but not for the vertices. Furthermore, the influence of the four-gluon vertex on lower Green functions is found to be small.

  18. Transcendental equations in the Schwinger-Keldysh nonequilibrium theory and nonvanishing correlations

    SciTech Connect

    Giraldi, Filippo

    2015-09-15

    The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green’s function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.

  19. Evolutionary game theory for physical and biological scientists. I. Training and validating population dynamics equations

    PubMed Central

    Liao, David; Tlsty, Thea D.

    2014-01-01

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

  20. A Revisiting of the -Stability Theory of the Boltzmann Equation Near Global Maxwellians

    NASA Astrophysics Data System (ADS)

    Ha, Seung-Yeal; Xiao, Qinghua

    2015-07-01

    We study the -stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the -distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in -topology. Our local-in-time -stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657-688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the -stability theory for the Boltzmann equation near a global Maxwellian. For this -stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform -stability of the Boltzmann equation.

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

    NASA Astrophysics Data System (ADS)

    Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

    2003-03-01

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

  2. Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.

    PubMed

    Durán-Olivencia, Miguel A; Lutsko, James F

    2015-09-01

    Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer. PMID:26465482

  3. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    SciTech Connect

    Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D. Kühn, Oliver

    2015-06-28

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.

  4. A Langevin model for low density pedestrian dynamics

    NASA Astrophysics Data System (ADS)

    Corbetta, Alessandro; Lee, Chung-Min; Benzi, Roberto; Muntean, Adrian; Toschi, Federico

    The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.

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

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Luo, Li-Shi

    2007-01-01

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

  6. An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

    NASA Astrophysics Data System (ADS)

    Pecina, P.

    2016-01-01

    We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

  7. Two dimensional Langevin recombination in regioregular poly(3-hexylthiophene)

    NASA Astrophysics Data System (ADS)

    Juška, Gytis; Genevičius, Kristijonas; Nekrašas, Nerijus; Sliaužys, Gytis; Österbacka, Ronald

    2009-07-01

    In this work, it is shown that recombination in regioregular poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester (RRP3HT:PCBM) bulk-heterojunction solar cells is caused by the two dimensional (2D) Langevin recombination in the lamellar structures of RRP3HT, which are formed after annealing process. Due to 2D Langevin process, bimolecular recombination coefficient is reduced in comparison with three dimensional Langevin case, and bimolecular recombination coefficient depends on the density of charge carriers n1/2. Data obtained from the different experimental techniques (charge extraction with linearly increasing voltage, integral time of flight, double injection current transients and transient absorption spectroscopy) confirms 2D Langevin recombination in RR3PHT.

  8. Isothermal Langevin dynamics in systems with power-law spatially dependent friction.

    PubMed

    Regev, Shaked; Grønbech-Jensen, Niels; Farago, Oded

    2016-07-01

    We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for c<0 and superdiffusion for 01, the diffusion equation predicts that the particles accelerate. Here we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit (〈x^{2}〉∼t^{2}). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin and is correctly captured by Langevin's equation. PMID:27575086

  9. Langevin analysis for time-nonlocal Brownian motion with algebraic memories and delay interactions

    NASA Astrophysics Data System (ADS)

    Chase, Matthew; McKetterick, Tom J.; Giuggioli, Luca; Kenkre, V. M.

    2016-04-01

    Starting from a Langevin equation with memory describing the attraction of a particle to a center, we investigate its transport and response properties corresponding to two special forms of the memory: one is algebraic, i.e., power-law, and the other involves a delay. We examine the properties of the Green function of the Langevin equation and encounter Mittag-Leffler and Lambert W-functions well-known in the literature. In the presence of white noise, we study two experimental situations, one involving the motional narrowing of spectral lines and the other the steady-state size of the particle under consideration. By comparing the results to counterparts for a simple exponential memory, we uncover instructive similarities and differences. Perhaps surprisingly, we find that the Balescu-Swenson theorem that states that non-Markoffian equations do not add anything new to the description of steady-state or equilibrium observables is violated for our system in that the saturation size of the particle in the steady-state depends on the memory function utilized. A natural generalization of the Smoluchowski equation for the time-local case is examined and found to satisfy the Balescu-Swenson theorem and describe accurately the first moment but not the second and higher moments. We also calculate two-time correlation functions for all three cases of the memory, and show how they differ from (tend to) their Markoffian counterparts at small (large) values of the difference between the two times.

  10. PyR@TE. Renormalization group equations for general gauge theories

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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