Langevin theory of fluctuations in the discrete Boltzmann equation
NASA Astrophysics Data System (ADS)
Gross, M.; Cates, M. E.; Varnik, F.; Adhikari, R.
2011-03-01
The discrete Boltzmann equation for both the ideal and a non-ideal fluid is extended by adding Langevin noise terms in order to incorporate the effects of thermal fluctuations. After casting the fluctuating discrete Boltzmann equation in a form appropriate to the Onsager-Machlup theory of linear fluctuations, the statistical properties of the noise are determined by invoking a fluctuation-dissipation theorem at the kinetic level. By integrating the fluctuating discrete Boltzmann equation, a fluctuating lattice Boltzmann equation is obtained, which provides an efficient way to solve the equations of fluctuating hydrodynamics for ideal and non-ideal fluids. Application of the framework to a generic force-based non-ideal fluid model leads to ideal gas-type thermal noise. Simulation results indicate proper thermalization of all degrees of freedom.
Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations
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: (
NASA Astrophysics Data System (ADS)
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, Fl m ,l m(k ,t ) and Flm ,l m S(k ,t ) , are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density nl m(k ,t ) and the translational (? =T ) and rotational (? =R ) current densities jlm ?(k ,t ) . Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by Sl m ,l m(k ) . Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, ?T and ?R, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters ? (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
Langevin equations from time series
NASA Astrophysics Data System (ADS)
Racca, E.; Porporato, A.
2005-02-01
We discuss the link between the approach to obtain the drift and diffusion of one-dimensional Langevin equations from time series, and Pope and Ching’s relationship for stationary signals. The two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels. The analysis provides a useful indication for the correct application of Pope and Ching’s relationship to obtain stochastic differential equations from time series and shows its validity, in a generalized sense, for nondifferentiable processes originating from Langevin equations.
Langevin equations from time series.
Racca, E; Porporato, A
2005-02-01
We discuss the link between the approach to obtain the drift and diffusion of one-dimensional Langevin equations from time series, and Pope and Ching's relationship for stationary signals. The two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels. The analysis provides a useful indication for the correct application of Pope and Ching's relationship to obtain stochastic differential equations from time series and shows its validity, in a generalized sense, for nondifferentiable processes originating from Langevin equations. PMID:15783455
The complex chemical Langevin equation
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 CLEâ€™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 CLEâ€™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 CLEâ€™s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the â€œcomplex CLEâ€ 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.
Self-guided Langevin dynamics via generalized Langevin equation.
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. Â© 2015 Wiley Periodicals, Inc. PMID:26183423
Quantum Langevin equations for optomechanical systems
NASA Astrophysics Data System (ADS)
Barchielli, Alberto; Vacchini, Bassano
2015-08-01
We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry requirements and equipartition at equilibrium, while the environment is described by quantum Bose fields in a suitable non-Fock representation which allows for the introduction of temperature. A generic spectral density of the environment can be described by introducing its state through a suitable P-representation. Including interaction of the mechanical oscillator with a cavity mode via radiation pressure we obtain a description of a simple optomechanical system in which, besides the Langevin equations for the system, one has the exact input-output relations for the quantum noises. The whole theory is valid at arbitrarily low temperature. This allows the exact calculation of the stationary value of the mean energy of the mechanical oscillator, as well as both homodyne and heterodyne spectra. The present analysis allows in particular to study possible cooling scenarios and to obtain the exact connection between observed spectra and fluctuation spectra of the position of the mechanical oscillator.
Langevin Equation for Slow Degrees of Freedom of Hamiltonian Systems
NASA Astrophysics Data System (ADS)
MacKay, R. S.
A way is sketched to derive a Langevin equation for the slow degrees of freedom of a Hamiltonian system whose fast ones are mixing Anosov. It uses the Anosov-Kasuga adiabatic invariant, martingale theory, Ruelle's formula for weakly non-autonomous SRB measures, and large deviation theory.
Basharov, A. M.
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
Langevin and diffusion equation of turbulent fluid flow
NASA Astrophysics Data System (ADS)
Brouwers, J. J. H.
2010-08-01
A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C0, which arises from Lagrangian similarity theory. The value of C0 in high Reynolds number turbulence is 5-6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C0-1 including terms next to leading order in C0-1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O(C0-2) in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O(C0-1). The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.
Generalized Langevin equation with chaotic force
NASA Astrophysics Data System (ADS)
Shimizu, Toshihiro
1994-12-01
The generalized Langevin equation with chaotic force is investigated: ?(t) = - limit?0tdt??(t,t?)x(t?) + ƒ(t) , where ?(t,t?) = {?ƒ(t)ƒ(t?) ?}/{?x 2 ? }. The chaotic force ƒ( t) is defined by ƒ(t)= {(y n+1 - ?y? }/{?} for n? < t ? ( n + 1) ? ( n= 0,1,2,…), where yn+1 is a chaotic sequence: yn+1 = F( yn). The time evolution of x( t), which is generated by the chaotic force, is discussed. The approach of the distribution function of x to a stationary distribution is studied. It is shown that the distribution function satisfies the Fokker-Planck type equation with the memory effect in the small ? limit. The relation between the invariant density of F ( y) and the stationary distribution of x is discussed.
Langevin equation approach to reactor noise analysis: stochastic transport equation
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.
Langevin equation approach to reactor noise analysis: stochastic transport equation
Akcasu, A.Z.; Stolle, A.M. )
1991-01-01
This paper is concerned with an application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density, as well as in the detector outputs, in nuclear reactors. The Langevin equation in this case is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral density (PSD) of the NES is evaluated in nuclear engineering applications by adopting a generalization of the Shottky formula. In this paper, the authors extend calculations to include the space and velocity dependence of neutron density by starting from the stochastic transport equation and the stochastic detection rate equations within the detectors. In addition, they discuss the implementation of the Langevin equation approach at different levels of approximation and explicitly obtain the stochastic one-speed transport and one-group P{sub 1} equations by first integrating the transport equation over speed and then eliminating in the angular dependence by spherical harmonic expansion.
Probability Density Function Method for Langevin Equations with Colored Noise
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.
Simplified simulation of Boltzmann-Langevin equation
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.
Numerical simulation of the Langevin equation for skewed turbulence
Ermak, D. L.; Nasstrom, J. S.
1994-12-01
In this paper the authors present a numerical method for the generalized Langevin equation of motion with skewed random forcing for the case of homogeneous, skewed turbulence. The authors begin by showing how the analytic solution to the Langevin equation for this case can be used to determine the relationship between the particle velocity moments and the properties of the skewed random force. They then present a numerical method that uses simple probability distribution functions to simulate the effect of the random force. The numerical solution is shown to be exact in the limit of infinitesimal time steps, and to be within acceptable error limits when practical time steps are used.
Generalized Langevin equation for tracer diffusion in atomic liquids
NASA Astrophysics Data System (ADS)
Mendoza-Méndez, Patricia; López-Flores, Leticia; Vizcarra-Rendón, Alejandro; Sánchez-Díaz, Luis E.; Medina-Noyola, Magdaleno
2014-01-01
We derive the time-evolution equation that describes the Brownian motion of labeled individual tracer particles in a simple model atomic liquid (i.e., a system of N particles whose motion is governed by Newton’s second law, and interacting through spherically symmetric pairwise potentials). We base our derivation on the generalized Langevin equation formalism, and find that the resulting time evolution equation is formally identical to the generalized Langevin equation that describes the Brownian motion of individual tracer particles in a colloidal suspension in the absence of hydrodynamic interactions. This formal dynamic equivalence implies the long-time indistinguishability of some dynamic properties of both systems, such as their mean squared displacement, upon a well-defined time scaling. This prediction is tested here by comparing the results of molecular and Brownian dynamics simulations performed on the hard sphere system.
Modeling of Brownian Dynamics with DSMC Using the Langevin Equation
NASA Astrophysics Data System (ADS)
Gallis, M. A.; Rader, D. J.; Torczynski, J. R.
2001-11-01
A new method for modeling macroscopic particles in the Direct Simulation Monte Carlo (DSMC) method is presented that is based on the Langevin equation. The traditional DSMC representation of molecular transport cannot be used for simulating macroscopic particles, which follow the Brownian-motion paradigm described by the Fokker-Planck equation. In this implementation of Brownian motion in DSMC, macroscopic particles do not collide with each other but are influenced by the background gas (the background gas is not affected by their presence). Collisions between the macroscopic particles and the gas molecules are treated through a grid-based collision field. To accurately represent Brownian motion for long time steps, particle velocities and positions are calculated in a probabilistic fashion. Comparison with theory describing the diffusion of macroscopic particles indicates excellent agreement. The coupling of Brownian dynamics into DSMC creates a method that can be applied to particle transport in applications such as semiconductor-processing equipment and atmospheric aerosols. *Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.
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 ?F. 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.
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.
The generalized SchrÃ¶dingerâ€“Langevin equation
BargueÃ±o, Pedro; Miret-ArtÃ©s, Salvador
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called SchrÃ¶dingerâ€“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: â€¢We generalize the Kostin equation for arbitrary systemâ€“bath coupling. â€¢This generalization is developed both in the SchrÃ¶dinger and Bohmian formalisms. â€¢We write the generalized Kostin equation for two measurement problems. â€¢We reformulate the generalized uncertainty principle in terms of this equation.
Large Deviations for the Langevin Equation with Strong Damping
NASA Astrophysics Data System (ADS)
Cerrai, Sandra; Freidlin, Mark
2015-11-01
We study large deviations in the Langevin dynamics, with damping of order ? ^{-1} and noise of order 1, as ? downarrow 0. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then we use a weak convergence approach to large deviations and its equivalent formulation in terms of the Laplace principle, to determine the good action functional. Some applications of these results to the exit problem from a domain and to the wave front propagation for a suitable class of reaction diffusion equations are considered.
Solving the generalized Langevin equation with the algebraically correlated noise
NASA Astrophysics Data System (ADS)
Srokowski, T.; PÅ‚oszajczak, 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 LÃ©vy 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.
Generalized Phase Space Version of Langevin Equations and Associated Fokker-Planck Equations
NASA Astrophysics Data System (ADS)
Kerr, W. C.; Graham, A. J.
2000-03-01
Generic Langevin equations are usually given as first-order stochastic ordinary differential equations for the phase space variables of a system, with noise and damping terms in the equation of motion of every variable. In contrast, Langevin equations for mechanical systems with canonical position and momentum variables usually include the noise and damping forces only in the equations for the momenta. We derive Langevin equations and associated Fokker-Planck equations for mechanical systems that include noise and damping terms in the equations for all the canonical variables. The derivation is done by comparing a distinctive derivation of a Fokker-Planck equation, given by Langer(J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969)), to the usual derivation relating Langevin equations to their associated Fokker-Planck equations. The resulting equations have simple reductions to overdamped and underdamped limits. They should be useful for efficient simulation of systems in contact with a heat bath. We conclude by presenting the modification of Kramers' result(H. A. Kramers, Physica 7, 284 (1940)) for the escape rate from a metastable well, using the new form of the Fokker-Planck equation obtained here.
On the environmental modes for the generalized Langevin equation.
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. PMID:26342353
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.
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 anâ€¦
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…
Derivation of the nonlinear fluctuating hydrodynamic equation from the underdamped Langevin equation
NASA Astrophysics Data System (ADS)
Nakamura, Takenobu; Yoshimori, Akira
2009-02-01
We derive the fluctuating hydrodynamic equation for the number and momentum densities exactly from the underdamped Langevin equation. This derivation is an extension of the Kawasaki-Dean formula in the underdamped case. The steady-state probability distribution of the number and momentum densities field can be expressed by the kinetic and potential energies. In the massless limit, the obtained fluctuating hydrodynamic equation reduces to the Kawasaki-Dean equation. Moreover, the derived equation corresponds to the field equation derived from the canonical equation when the friction coefficient is zero.
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.
From Langevin to generalized Langevin equations for the nonequilibrium Rouse model
NASA Astrophysics Data System (ADS)
Maes, Christian; Thomas, Simi R.
2013-02-01
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.
Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations
NASA Astrophysics Data System (ADS)
Fainberg, V. Ya.
2006-12-01
We recall the general proof of the statement that the behavior of every holonomic nonrelativistic system can be described in terms of the Langevin equation in Euclidean (imaginary) time such that for certain initial conditions, the different stochastic correlators (after averaging over the stochastic force) coincide with the quantum mechanical correlators. The Fokker-Planck-Kolmogorov (FPK) equation that follows from this Langevin equation is equivalent to the Schrödinger equation in Euclidean time if the Hamiltonian is Hermitian, the dynamics are described by potential forces, the vacuum state is normalizable, and there is an energy gap between the vacuum state and the first excited state. These conditions are necessary for proving the limit and ergodic theorems. For three solvable models with nonlinear Langevin equations, we prove that the corresponding Schrödinger equations satisfy all the above conditions and lead to local linear FPK equations with the derivative order not exceeding two. We also briefly discuss several subtle mathematical questions of stochastic calculus.
NASA Astrophysics Data System (ADS)
Sääskilahti, K.; Oksanen, J.; Tulkki, J.
2014-04-01
Near-field and resonance effects have a strong influence on nanoscale electromagnetic energy transfer, and detailed understanding of these effects is required for the design of new, optimized nano-optical devices. We provide a comprehensive microscopic view of electromagnetic energy transfer phenomena by introducing quantum Langevin heat baths as local noise sources in the equations of motion for the thermally fluctuating electric dipoles forming dielectric bodies. The theory is, in a sense, the microscopic generalization of the well-known fluctuational electrodynamics theory and thereby provides an alternative and conceptually simple way to calculate the local emission and absorption rates from the local Langevin bath currents. We apply the model to study energy transfer between silicon carbide nanoparticles located in a microcavity formed of two mirrors and next to a surface supporting propagating surface modes. The results show that the heat current between dipoles placed in a cavity oscillates as a function of their position and separation and can be enhanced by several orders of magnitude as compared to the free-space heat current with a similar interparticle distance. The predicted enhancement can be viewed as a many-body generalization of the well-known cavity Purcell effect. Similar effects are also observed in the interparticle heat transfer between dipoles located next to a surface of a polar material supporting surface phonon polaritons.
A new approach to solve the Boltzmann Langevin equation for fermionic systems
NASA Astrophysics Data System (ADS)
Rizzo, J.; Chomaz, Ph.; Colonna, M.
2008-06-01
We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann-Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer et al. for transport codes employing the test particle method. In the new procedure, the Pauli principle is carefully checked, leading to a good reproduction of the correct fluctuations in the "continuum limit" ( hâ†’0). Accurate tests are carried out in one and two dimensional idealized systems, and finally results for a full 3D application are shown. We stress the reliability of this method, which can be easily plugged into existing transport codes using test particles, and its general applicability to systems characterized by instabilities, like for instance multifragmentation processes.
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.
Diffusion and memory effects for stochastic processes and fractional Langevin equations
NASA Astrophysics Data System (ADS)
Bazzani, Armando; Bassi, Gabriele; Turchetti, Giorgio
2003-06-01
We consider the diffusion processes defined by stochastic differential equations when the noise is correlated. A functional method based on the Dyson expansion for the evolution operator, associated to the stochastic continuity equation, is proposed to obtain the Fokker-Planck equation, after averaging over the stochastic process. In the white noise limit the standard result, corresponding to the Stratonovich interpretation of the non-linear Langevin equation, is recovered. When the noise is correlated the averaged operator series cannot be summed, unless a family of time-dependent operators commutes. In the case of a linear equation, the constraints are easily worked out. The process defined by a linear Langevin equation with additive noise is Gaussian and the probability density function of its fluctuating component satisfies a Fokker-Planck equation with a time-dependent diffusion coefficient. The same result holds for a linear Langevin equation with a fractional time derivative (defined according to Caputo, Elasticità e Dissipazione, Zanichelli, Bologna, 1969). In the generic linear or non-linear case approximate equations for small noise amplitude are obtained. For small correlation time the evolution equations further simplify in agreement with some previous alternative derivations. The results are illustrated by the linear oscillator with coloured noise and the fractional Wiener process, where the numerical simulation for the probability density and its moments is compared with the analytical solution.
Critical comparison of Kramers' fission width with the stationary width from the Langevin equation
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.
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. PMID:24697429
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.
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 Î³ -ray emission. Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and Î³ -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 Î³ -ray multiplicity, and the average kinetic energy of emitted neutrons and Î³ 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.
NASA Astrophysics Data System (ADS)
Levasseur, Laurence Perreault
2013-10-01
We present a new, recursive approach to stochastic inflation which is self-consistent and solves multiple problems that plagued a certain number of previous studies, in particular, in realistic contexts where the background spacetime is taken to be dynamical, where there is more than one field present (especially with a mass hierarchy), or where the role played by backreaction is suspected to be important. We first review the formalism of stochastic inflation as it is usually heuristically presented, that is, deriving the Langevin equations from the field equations of motion, and summarize previous results on the subject. We demonstrate where inconsistent approximations to the Langevin equations are commonly made and show how these can be avoided. This setup shares many similarities with quantum Brownian motion and out-of-equilibrium statistical quantum dynamics. We hence review how path integral techniques can be applied to the stochastic inflationary context. We show that this formalism is consistent with the standard approach. We then develop a natural perturbative expansion and use it to calculate the one-loop corrected Langevin equations.
Applications of the generalized Langevin equation: Towards a realistic description of the baths
NASA Astrophysics Data System (ADS)
Ness, H.; Stella, L.; Lorenz, C. D.; Kantorovich, L.
2015-01-01
The generalized Langevin equation (GLE) method, as developed previously [L. Stella et al., Phys. Rev. B 89, 134303 (2014), 10.1103/PhysRevB.89.134303], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalizes toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.
General Laser Intensity Langevin Equation in a Single-Mode Laser Model
NASA Astrophysics Data System (ADS)
Ke, Sheng-Zhi; Cao, Li; Wu, Da-Jin; Yao, Kai-Lun
2001-03-01
A two-dimensional single-mode laser model is investigated, with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation ?q between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing ?q, we can unify the two opposite intensity Langevin equations which correspond to the two special cases for |?q|?0 and |?q|?1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when ?q varies.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
PÅ‚oszajczak, 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.
NASA Astrophysics Data System (ADS)
ViÃ±ales, A. D.; DespÃ³sito, M. A.
2006-01-01
We study the effect of a disordered or fractal environment in the irreversible dynamics of a harmonic oscillator. Starting from a generalized Langevin equation and using Laplace analysis, we derive exact expressions for the mean values, variances, and velocity autocorrelation function of the particle in terms of generalized Mittag-Leffler functions. The long-time behaviors of these quantities are obtained and the presence of a whip-back effect is analyzed.
A Langevin equation approach to electron transfer reactions in the diabatic basis
Song Xiaogeng; Van Voorhis, Troy; Wang Haobin
2008-10-14
A linear Langevin equation that governs the population dynamics of electron transfer reactions is derived. The noise in the Langevin equation is eliminated by treating the diabatic population fluctuations as the relevant variables, leaving only the memory kernel responsible for the population relaxation. Within the memory kernel, the diabatic coupling is treated perturbatively and a second order expansion is found to give a simple closed form expression for the kernel. The accuracy of the second order truncation is maximized by performing a fixed rotation of the diabatic electronic states that minimizes the first order free energy of the system and thus minimizes the effect of the perturbation on the thermodynamics. The resulting two-hop Langevin equation (THLE) is then validated by applying it to a simple spin-boson model, where exact results exist. Excellent agreement is found in a wide parameter range, even where the perturbation is moderately strong. Results obtained in the rotated electronic basis are found to be consistently more accurate than those from the unrotated basis. These benchmark calculations also allow us to demonstrate the advantage of treating the population fluctuations instead of the populations as the relevant variables, as only the former lead to reliable results at long time. Thus, the THLE appears to provide a viable alternative to established methods - such as Ehrenfest dynamics or surface hopping--for the treatment of nonadiabatic effects in electron transfer simulations.
NASA Astrophysics Data System (ADS)
Brett, Tobias; Galla, Tobias
2013-06-01
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
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.
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.
Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach
Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K.
2003-07-01
We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump {r_reversible} pump, Stokes {r_reversible} signal, and Raman coherence {r_reversible} idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.
Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations
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
Laws of large numbers and langevin approximations for stochastic neural field equations.
Riedler, Martin G; Buckwar, Evelyn
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
A reference trajectory approach to Langevin equations in gas phase collision dynamics
NASA Astrophysics Data System (ADS)
Schatz, George C.; Moser, Mark D.
1980-09-01
In this paper, a new approach to the development of Langevin-like equations for studying gas phase collisional energy tranfer and other dynamical problems is introduced based on the use of reference trajectories to describe memory effects and nonlinear interactions. In this development, the exact equations of motion are first expressed in terms of the deviations of the coordinates and momenta from some reference trajectory values and then linearized about those values. A partitioning between fast and slow variables is then assumed, and those members of the above mentioned linearized equations which refer to the fast variables are re-expressed as integral equations. A ''local Brownian-like'' approximation is then made in the memory kernel appearing in the integral equations to reduce them to algebraic equations, and upon substitution of these into the slow variable equations of motion, we obtain Langevin-like equations for the slow variables. In these equations the interaction between slow and fast variables appears as frictionlike and random forcelike terms, and in these terms, information about nonlinear interactions and correlated motions (including recurrences) is evaluated using the reference trajectory. In order to keep the deviations from the reference trajectory small during each collision, this trajectory is best chosen as the ensemble averaged trajectory, and we find that a good approximation to this for many problems is provided by a trajectory in which all initial vibrational energies are set equal to zero. Applications of this Langevin-like approach to several models of gas phase VT collisional energy transfer show that it is capable of quantitative predictions (errors typically<20%) of the first and second (classical) moments of the final translational distributions, provided that the initial translational energy is low enough to make the collision duration long compared with typical vibrational periods, and that the initial vibrational energy is low enough to make the deviations about the reference trajectory small. Often these restrictions are not particularly severe. For example, in a collinear Kr+CO2(000) model, the average energy transfer is accurate to 5% for initial translational energies as high as 10 eV, while for a collinear He+H2 model, energy transfers accurate to 30% or better are obtained with five quanta of initial vibrational excitation in the H2. In addition, accurate results are obtained even when the average energy transfer is of different sign than that of the reference, and in spite of the fact that the width of the translational distribution is a factor of 10 or more larger than its first moment. We also demonstrate that the Langevin equation works well when the average energy transfer becomes comparable to a quantum of vibrational energy (i.e., in the nonperturbative regime) provided that the necessary time scale separations for invoking the Langevin treatment exist.
NASA Astrophysics Data System (ADS)
KazakeviÄius, 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.
A Bohmian approach to the non-Markovian non-linear SchrÃ¶dingerâ€“Langevin equation
Vargas, AndrÃ©s F.; Morales-DurÃ¡n, NicolÃ¡s; BargueÃ±o, Pedro
2015-05-15
In this work, a non-Markovian non-linear SchrÃ¶dingerâ€“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.
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
NASA Astrophysics Data System (ADS)
Grima, Ramon; Thomas, Philipp; Straube, Arthur V.
2011-08-01
The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?-3/2 for reaction systems which do not obey detailed balance and at least accurate to order ?-2 for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?-1/2 and variance estimates accurate to order ?-3/2. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
Grima, Ramon; Thomas, Philipp; Straube, Arthur V
2011-08-28
The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?(-3?2) for reaction systems which do not obey detailed balance and at least accurate to order ?(-2) for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?(-1?2) and variance estimates accurate to order ?(-3?2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules. PMID:21895155
NASA Astrophysics Data System (ADS)
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
2010-04-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1+m2 Wiener processes, whereas the standard approach uses 2m1+m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch.
Non-Gaussian statistics, classical field theory, and realizable Langevin models
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.
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.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
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
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
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.
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.
Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.
Gongadze, Ekaterina; van Rienen, Ursula; Kralj-IgliÄ, Veronika; IgliÄ, AleÅ¡
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
NASA Astrophysics Data System (ADS)
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 ?(h) (where h is the depth) and similar data that are often nonstationary stochastic series. In this method one first generates a new stationary series based on the original data, and then analyzes the resulting series. It is shown that the series based on the successive increments of the log y(h)=?(h+?h)-?(h) is a stationary and Markov process, characterized by a Markov length scale hM. The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y0,h0) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured.
Generalized Langevin equation for solids. I. Rigorous derivation and main properties
NASA Astrophysics Data System (ADS)
Kantorovich, L.
2008-09-01
We demonstrate explicitly that the derivation by Adelman and Doll (AD) [J. Chem. Phys. 64, 2375 (1976)] of the generalized Langevin equation (GLE) to describe dynamics of an extended solid system by considering its finite subsystem is inconsistent because it relies on performing statistical averages over the entire system when establishing properties of the random force. This results in the random force representing a nonstationary process opposite to one of the main assumptions made in AD that the random force corresponds to a stationary stochastic process. This invalidates the derivation of the Brownian (or Langevin) form of the GLE in AD. Here we present a different and more general approach in deriving the GLE. Our method generalizes that of AD in two main aspects: (i) the structure of the finite region can be arbitrary (e.g., anharmonic), and (ii) ways are indicated in which the method can be implemented exactly if the phonon Green’s function of the harmonic environment region surrounding the anharmonic region is known, which is, e.g., the case when the environment region represents a part of a periodic solid (the bulk or a surface). We also show that in general after the local perturbation has ceased, the system returns to thermodynamic equilibrium with the distribution function for region 1 being canonical with respect to an effective interaction between atoms, which includes instantaneous response of the surrounding region. Note that our method does not rely on the assumption made in AD that the stochastic force correlation function depends on the times difference only (i.e., the random force corresponds to a stationary random process). In fact, we demonstrate explicitly that generally this is not the case. Still, the correct GLE can be obtained, which satisfies exactly the fluctuation-dissipation theorem.
AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation
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 the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727
AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.
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 solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727
Growth-collapse and decay-surge evolutions, and geometric Langevin equations
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2006-07-01
We introduce and study an analytic model for physical systems exhibiting growth-collapse and decay-surge evolutionary patterns. We consider a generic system undergoing a smooth deterministic growth/decay evolution, which is occasionally interrupted by abrupt stochastic collapse/surge discontinuities. The deterministic evolution is governed by an arbitrary potential field. The discontinuities are multiplicative perturbations of random magnitudes, and their occurrences are state-dependent-governed by an arbitrary rate function. The combined deterministic-stochastic evolution of the system turns out to be governed by a geometric Langevin equation driven by a state-dependent noise. A statistical exploration of these growth-collapse and decay-surge systems is conducted, with a focus on two special classes of systems: scale-free systems and generalized power-law systems. For stationary scale-free systems we explicitly compute the distribution of the pre-discontinuity, post-discontinuity, and equilibrium levels. Generalized power-law systems are proved to display three possible qualitative types of behavior: (i) super-critical-in which the system eventually explodes/freezes; (ii) critical-in which the system's underlying dynamical structure is that of a geometric random walk; and, (iii) sub-critical-in which the system reaches statistical equilibrium.
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 tÎ± for some Î± < 1 until the terminal relaxation time Ï„ of the polymer. Beyond time Ï„ 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.
Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei
2013-09-28
The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology. PMID:24089743
Higher-order time integration of Coulomb collisions in a plasma using Langevin equations
NASA Astrophysics Data System (ADS)
Dimits, A. M.; Cohen, B. I.; Caflisch, R. E.; Rosin, M. S.; Ricketson, L. F.
2013-06-01
The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler-Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(?t) vs. O(?t)] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the "area-integral" terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler-Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.
Higher-order time integration of Coulomb collisions in a plasma using Langevin equations
Dimits, A.M.; Cohen, B.I.; Caflisch, R.E.; Rosin, M.S.; Ricketson, L.F.
2013-06-01
The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler–Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(?t) vs. O(?t{sup 1/2})] 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. 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.
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
Copperman, J; Guenza, M G
2015-07-23
We utilize a multiscale approach where molecular dynamic simulations are performed to obtain quantitative structural averages used as input to a coarse-grained Langevin equation for protein dynamics, which can be solved analytically. The approach describes proteins as fundamentally semiflexible objects collapsed into the free energy well representing the folded state. The normal-mode analytical solution to this Langevin equation naturally separates into global modes describing the fully anisotropic tumbling of the macromolecule as a whole and internal modes which describe local fluctuations about the folded structure. Complexity in the configurational free-energy landscape of the macromolecule leads to a renormalization of the internal modes, while the global modes provide a basis set in which the dipolar orientation and global anisotropy can be accounted for when comparing to experiments. This simple approach predicts the dynamics of both global rotational diffusion and internal motion from the picosecond to the nanosecond regime and is quantitative when compared to time correlation functions calculated from molecular dynamic simulations and in good agreement with nuclear magnetic resonance relaxation experiments. Fundamental to this approach is the inclusion of internal dissipation, which is absent in any rigid-body hydrodynamical modeling scheme. PMID:25356856
Two critical issues in Langevin simulation of gas flows
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.
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.â€™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.
Notes on the Langevin model for turbulent diffusion of ``marked`` particles
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.
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.
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.
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. PMID:26465459
NASA Astrophysics Data System (ADS)
Bouzat, SebastiÃ¡n
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.
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-BÃ©nard 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.
NASA Astrophysics Data System (ADS)
Chen, Yu; Zhang, Feng-Shou; Su, Jun
2009-11-01
A new attempt of calculation for the total reaction cross sections (ÏƒR) has been carried out within the isospindependent Boltzmann-Langevin equation in the intermediate energy heavy-ion collision of isotopes of C. The ÏƒR of both stable and exotic nuclei are reproduced rather well. The incident energy and isospin dependencies of ÏƒR have been investigated. It is found that the isospin effect is comparatively remarkable at intermediate energy. It is also found that 15-18C are neutron skin nuclei but for 19C and 20C we cannot draw a conclusion whether they have halo structures.
Langevin dynamics of the pure SU(2) deconfining transition
Fraga, E. S.; Mizher, A. J.; Krein, G.
2007-08-01
We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU(2) gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the Markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise.
Analysis of multifragmentation in a Boltzmann-Langevin approach
Zhang, F.; Suraud, E.
1995-06-01
By using the Boltzmann-Langevin equation, which incorporates dynamical fluctuations beyond usual transport theories, we simulate the {sup 40}Ca+{sup 40}Ca reaction system at different beam energies 20, 60, and 90 MeV/nucleon for different impact parameters. Dynamical fluctuations become larger and larger with increasing bombarding energy and the system can reach densities corresponding to the unstable region of the nuclear matter equation of state at energies above 60 MeV/nucleon. By coupling the Boltzmann-Langevin equation with a coalescence model in the late stages of the reaction, we obtain the distribution of the intermediate mass fragments in each event. From the correlation analysis of these fragments, we recover some trends of recent multifragmentation data. A critical behavior analysis is also provided.
NASA Astrophysics Data System (ADS)
Kalmykov, Yu. P.; Coffey, W. T.; Waldron, J. T.
1996-08-01
The correlation time of the positional autocorrelation function is calculated exactly for one-dimensional translational Brownian motion of a particle in a 2-4 double-well potential in the noninertial limit. The calculations are carried out using the method of direct conversion (by averaging) of the Langevin equation for a nonlinear stochastic system to a set of differential-recurrence relations. These, in the present problem, reduce on taking the Laplace transform, to a three-term recurrence relation. Thus the correlation time Tc of the positional autocorrelation function may be formally expressed as a sum of products of infinite continued fractions which may be represented in series form as a sum of two term products of Whittaker's parabolic cylinder functions. The sum of this series may be expressed as an integral using the integral representation of the parabolic cylinder functions and subsequently the Taylor expansion of the error function, thus yielding the exact solution for Tc. This solution is in numerical agreement with that obtained by Perico et al. [J. Chem. Phys. 98, 564 (1993)] using the first passage time approach while previous asymptotic results obtained by solving the underlying Smoluchowski equation are recovered in the limit of high barrier heights. A simple empirical formula which provides a close approximation to the exact solution for all barrier heights is also given.
Localised distributions and criteria for correctness in complex Langevin dynamics
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 Fokkerâ€“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: â€¢Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. â€¢Connection between criteria for correctness and breakdown. â€¢Solution of the Fokkerâ€“Planck equation in the case of real noise. â€¢Analytical determination of support in complexified space.
Prolongation theory. A new nonlinear Schroedinger equation
Roy, S.; Chowdhury, A.R.
1987-07-01
The authors discuss a new kind of nonlinear Schroedinger equation from the viewpoint of prolongation theory. It is shown that the equation possess a Lax pair with a 3 x 3 matrix structure. It is further demonstrated that by a multiple scale perturbation of Zakharov et al. it can be reduced to the usual KdV equation.
NASA Astrophysics Data System (ADS)
Kim, S.; Gordon, J. M.; Frank, T. D.
2015-03-01
Nonequilibrium thermodynamic state variables are derived for a stochastic limit-cycle oscillator model that has been used in motor control research to describe human rhythmic limb movements. The nonequilibrium thermodynamic state variables are regarded as counterparts to the thermodynamic state variables entropy, internal energy, and free energy of equilibrium systems. The derivation of the state variables is based on maximum entropy distributions of the Hamiltonian energy of the stochastic limit-cycle oscillators. The limit-cycle oscillator model belongs to the class of canonical-dissipative systems, on the one hand, and, on the other hand, can be cast into the form of an augmented Langevin equation. Both concepts are known as physical models for open systems. Experimental data from paced and self-paced pendulum swinging experiments are presented and estimates for the nonequilibrium thermodynamic state variables are given. Entropy and internal energy increased with increasing oscillation frequency both for the paced and self-paced conditions. Interestingly, the nonequilibrium free energy decayed when oscillation frequency was increased, which is akin to the decay of the Landau free energy when the control parameter is scaled further away from its critical value.
Theory and applications of the Vlasov equation
NASA Astrophysics Data System (ADS)
Pegoraro, Francesco; Califano, Francesco; Manfredi, Giovanni; Morrison, Philip J.
2015-03-01
Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and Applications of the Vlasov Equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of scientific results involving the Vlasov equation. In this editorial, after some introductory notes, a brief account is given of the main points addressed in these papers and of the perspectives they open.
Quantum Langevin approach for non-Markovian quantum dynamics of the spin-boson model
NASA Astrophysics Data System (ADS)
Zhou, Zheng-Yang; Chen, Mi; Yu, Ting; You, J. Q.
2016-02-01
One longstanding difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due to its crucial applications in quantum noise control and manipulation as well as its central role in developing quantum theories of open systems. Here we solve this important model by developing a non-Markovian quantum Langevin approach. By projecting the quantum Langevin equation onto the coherent states of the bath, we can derive a set of non-Markovian quantum Bloch equations containing no explicit noise variables. This special feature offers a tremendous advantage over the existing stochastic SchrÃ¶dinger equations in numerical simulations. The physical significance and generality of our approach are briefly discussed.
Behavioral momentum theory: equations and applications.
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 reinforcers are contingent on the target behavior, are noncontingent, or are even contingent on an alternative behavior. In this paper, we describe the equations that constitute the theory and address their application to issues of particular importance in applied settings. The theory provides a framework within which to consider the effects of interventions such as extinction, noncontingent reinforcement, differential reinforcement of alternative behavior, and other phenomena (e.g., resurgence). Finally, the theory predicts some counterintuitive and potentially counterproductive effects of alternative reinforcement, and can serve as an integrative guide for intervention when its terms are identified with the relevant conditions of applied settings. PMID:22219536
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+Î¼uxxx=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)=Ï†(Î¾), Î¾ =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 Ï• 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 Î¼. 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].
New Langevin and gradient thermostats for rigid body dynamics.
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
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.
Undular bore theory for the Gardner equation.
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
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.
Heavy Flavor Suppression: Boltzmann vs Langevin
NASA Astrophysics Data System (ADS)
Das, S. K.; Scardina, F.; Plumari, S.; Greco, V.
2014-05-01
The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough study of the approximations involved by Langevin equation by mean of a direct comparison with the full collisional integral within the framework of Boltzmann transport equation. We have compared the results obtained in both approaches which can differ substantially for charm quark leading to quite different values extracted for the heavy quark diffusion coefficient. In the case of bottom quark the approximation appears to be quite reasonable.
Langevin stabilization of molecular dynamics
NASA Astrophysics Data System (ADS)
Izaguirre, JesÃºs 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 BrÃ¼nger-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 BrÃ¼nger-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.
On extremals of the entropy production by ‘Langevin-Kramers’ dynamics
NASA Astrophysics Data System (ADS)
Muratore-Ginanneschi, Paolo
2014-05-01
We refer as ‘Langevin-Kramers’ dynamics to a class of stochastic differential systems exhibiting a degenerate ‘metriplectic’ structure. This means that the drift field can be decomposed into a symplectic and a gradient-like component with respect to a pseudo-metric tensor associated with random fluctuations affecting increments of only a sub-set of the degrees of freedom. Systems in this class are often encountered in applications as elementary models of Hamiltonian dynamics in a heat bath eventually relaxing to a Boltzmann steady state. Entropy production control in Langevin-Kramers models differs from the now well-understood case of Langevin-Smoluchowski dynamics for two reasons. First, the definition of entropy production stemming from fluctuation theorems specifies a cost functional which does not act coercively on all degrees of freedom of control protocols. Second, the presence of a symplectic structure imposes a non-local constraint on the class of admissible controls. Using Pontryagin control theory and restricting the attention to additive noise, we show that smooth protocols attaining extremal values of the entropy production appear generically in continuous parametric families as a consequence of a trade-off between smoothness of the admissible protocols and non-coercivity of the cost functional. Uniqueness is, however, always recovered in the over-damped limit as extremal equations reduce at leading order to the Monge-Ampère-Kantorovich optimal mass-transport equations.
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.
THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES
The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...
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 thoseâ€¦
Extended Jarzynski equality in general Langevin system
NASA Astrophysics Data System (ADS)
Sughiyama, Yuki; Ohzeki, Masayuki
2011-01-01
The Speck-Seifert equality and the Hatano-Sasa equality are known to be bases to construct stationary state thermodynamics. The well known nonequilibrium relations, the Jarzynski equality and the fluctuation theorem, share the mathematical structure with the above equalities. This hidden common property motivates us to extend the Jarzynski equality to a relation applicable in the generalized dynamical system. As a result, we find several equalities which are able to be established in this generalized system described by the Langevin equation. These results easily reproduce the Speck-Seifert equality and the Hatano-Sasa equality. We hope that our formulation gives a new insight on nonequilibrium statistical physics.
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.
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…
Laplacian growth and Whitham equations of soliton theory
NASA Astrophysics Data System (ADS)
Krichever, I.; Mineev-Weinstein, M.; Wiegmann, P.; Zabrodin, A.
2004-11-01
The Laplacian growth (the Hele-Shaw problem) of multiply-connected domains in the case of zero surface tension is proven to be equivalent to an integrable system of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.
Theory of relativistic Brownian motion: the (1+1)-dimensional case.
Dunkel, JÃ¶rn; HÃ¤nggi, 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 HÃ¤nggi-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
Filtration theory using computer simulations
Bergman, W.; Corey, I.
1997-01-01
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.
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
NASA Astrophysics Data System (ADS)
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken ??4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
Boltzmann equation in classical and quantum field theory
Jeon, Sangyong
2005-07-01
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given.
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.
Einstein equations and MOND theory from Debye entropic gravity
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.
Experimenting with Langevin lattice QCD
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.
Quantization conditions and functional equations in ABJ(M) theories
NASA Astrophysics Data System (ADS)
Grassi, Alba; Hatsuda, Yasuyuki; MariÃ±o, Marcos
2016-03-01
The partition function of ABJ(M) theories on the three-sphere can be regarded as the canonical partition function of an ideal Fermi gas with a non-trivial Hamiltonian. We propose an exact expression for the spectral determinant of this Hamiltonian, which generalizes recent results obtained in the maximally supersymmetric case. As a consequence, we find an exact WKB quantization condition determining the spectrum which is in agreement with numerical results. In addition, we investigate the factorization properties and functional equations for our conjectured spectral determinants. These functional equations relate the spectral determinants of ABJ theories to consecutive ranks of gauge groups but the same Chernâ€“Simons coupling.
NASA Astrophysics Data System (ADS)
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2013-12-01
The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10 K channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.
Translating Words into Equations: A Cognitive Load Theory Approach
ERIC Educational Resources Information Center
Pawley, Duncan; Ayres, Paul; Cooper, Martin; Sweller, John
2005-01-01
The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a…
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.
Perturbation theory of a symmetric center within Liénard equations
NASA Astrophysics Data System (ADS)
Françoise, Jean-Pierre; Xiao, Dongmei
2015-09-01
In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.
Theoretische Modellierung granularer Stroeme in duennen Roehren mit Langevin-Gleichungen
NASA Astrophysics Data System (ADS)
Riethmueller, T. L.
2008-12-01
This is the final version of the author's diploma thesis written at the Humboldt University of Berlin in 1995. The topic is the flow of granular material in narrow vertical pipes, driven by the gravity, that is described by Langevin equations. Neglecting the interactions, we can solve the resulting Fokker-Planck equation for the homogeneous case. The consideration of inelastic collisions leads to a Boltzmann equation. Assuming local equilibrium, the hydrodynamic equations lead to the extension of the Langevin equation formalism for the inhomogeneous case. For certain parameter ranges, our formalism can also be used to describe traffic flows. We applied stability analyses to the hydrodynamic equations and found critical densities for the occurrence of particle clustering. We used numerical simulations of the Langevin equations to verify our homogeneous solution as well as the critical densities.
The Fokker-Planck equation and the master equation in the theory of migration
NASA Astrophysics Data System (ADS)
Tabata, Minoru; Eshima, Nobuoki
2004-12-01
In the theory of migration two mathematical models are regarded as very important. One is described by a quasilinear partial differential equation of parabolic type called the Fokker-Planck equation. The other is described by a nonlinear integro-partial differential equation called the master equation. Both the models are employed frequently at the same time in the theory of migration. Hence we need to investigate whether the descriptions given by the models are close to each other or not. The purpose of the present paper is to mathematically prove that if the effort required in moving is large, then the models are close to each other in the following sense: the mixed problem with the periodic boundary condition for the master equation has a unique solution that is very close to a solution of that for the Fokker-Planck equation, where the effort is a sociodynamic quantity that represents a cost incurred in moving. By making use of the result of the paper, we can apply both the models to movement of human population at the same time.
Integral equation theory of solutions of rigid polyelectrolytes
NASA Astrophysics Data System (ADS)
Shew, Chwen-Yang; Yethiraj, Arun
1997-04-01
The properties of dilute and semidilute solutions of rigid polyelectrolytes are investigated using integral equation theory. The theory predicts liquidlike structure on length scales of the order of the length of the molecules in dilute solution. This structure appears at concentrations much lower than the overlap threshold concentration, and disappears when the concentration is sufficiently high. Liquidlike order reappears at higher concentrations on a lengthscale of the order of the thickness of the rods. The predictions of the theory for the static structure factor in tobacco mosaic virus solutions are in good agreement with light scattering experiments in both dilute and semidilute solutions. The theory predicts that kmax˜??, where kmax is the position of the maximum in the structure factor and ? is the concentration, with ??1/3 and 1/2 in the dilute and semidilute regimes, respectively. These values are consistent with experimental results. Predictions are also presented for rigid starlike polymers.
Langevin dynamics neglecting detailed balance condition.
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
Langevin dynamics neglecting detailed balance condition
NASA Astrophysics Data System (ADS)
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.
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 ??S, 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.
Parquet Equations for Numerical Self-Consistent Theory
NASA Astrophysics Data System (ADS)
Bickers, N. E.
In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail.
NASA Astrophysics Data System (ADS)
Fodor, Z.; Katz, S. D.; Sexty, D.; Török, C.
2015-11-01
We study lattice QCD at nonvanishing chemical potential using the complex Langevin equation. We compare the results with multiparameter reweighting both from ? =0 and phase-quenched ensembles. We find a good agreement for lattice spacings below ?0.15 fm . On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on Nt=4 , 6 and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
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.
General Dynamical Density Functional Theory for Classical Fluids
NASA Astrophysics Data System (ADS)
Goddard, Benjamin D.; Nold, Andreas; Savva, Nikos; Pavliotis, Grigorios A.; Kalliadasis, Serafim
2012-09-01
We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.
Heavy quark diffusion with relativistic Langevin dynamics in the quark-gluon fluid
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.
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.
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.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
Moreno, Miguel Vera; Arenas, Zochil GonzÃ¡lez; 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
NASA Astrophysics Data System (ADS)
Reeves, Daniel B.; Weaver, John B.
2015-11-01
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.
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.
Multireference equation-of-motion coupled cluster theory.
Datta, Dipayan; Nooijen, Marcel
2012-11-28
A generalization of the equation-of-motion coupled cluster theory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, H? = e(-T) H?e(T), in a compact multireference configuration interaction space, which involves configurations with at most single virtual orbital substitution. The latter effects are thus state-specific and this allows us to obtain multiple electronic states in the spirit of the equation-of-motion coupled cluster approach. A crucial aspect of this formulation is the use of the amplitudes of the generalized normal-ordered transformed Hamiltonian H? as the residual equations for determining the internally contracted cluster amplitudes without any projection onto the excited configurations. These residuals have been termed as the many-body residuals. These equations are formally non-singular and thus allow us to solve for all amplitudes without discarding any, in contrast to other internally contracted approaches. This is desirable to ensure transferability of dynamical correlation from the parent state to the target states. Preliminary results involving the low-lying electronic states of C(2), O(2), and the excitation spectra of three transition metal atoms, e.g., Fe, Cr, and Mn, including hundreds of excited states, illustrate the potential of our approach. PMID:23205981
Fractional Langevin model of memory in financial markets.
Picozzi, Sergio; West, Bruce J
2002-10-01
The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series. PMID:12443270
Universal theory of dynamical chaos in nonlinear dissipative systems of differential equations
NASA Astrophysics Data System (ADS)
Magnitskii, Nikolai A.
2008-03-01
A new universal theory of dynamical chaos in nonlinear dissipative systems of differential equations including ordinary and partial, autonomous and non-autonomous differential equations and differential equations with delay arguments is presented in this paper. Four corner-stones lie in the foundation of this theory: the Feigenbaum's theory of period doubling bifurcations in one-dimensional mappings, the Sharkovskii's theory of bifurcations of cycles of an arbitrary period up to the cycle of period three in one-dimensional mappings, the Magnitskii's theory of rotor type singular points of two-dimensional non-autonomous systems of differential equations as a bridge between one-dimensional mappings and differential equations and the theory of homoclinic cascade of bifurcations of stable cycles in nonlinear differential equations. All propositions of the theory are strictly proved and illustrated by numerous analytical and computing examples.
Scaling of Langevin and molecular dynamics persistence times of nonhomogeneous fluids.
Olivares-Rivas, Wilmer; Colmenares, Pedro J
2012-01-01
The existing solution for the Langevin equation of an anisotropic fluid allowed the evaluation of the position-dependent perpendicular and parallel diffusion coefficients, using molecular dynamics data. However, the time scale of the Langevin dynamics and molecular dynamics are different and an ansatz for the persistence probability relaxation time was needed. Here we show how the solution for the average persistence probability obtained from the backward Smoluchowski-Fokker-Planck equation (SE), associated to the Langevin dynamics, scales with the corresponding molecular dynamics quantity. Our SE perpendicular persistence time is evaluated in terms of simple integrals over the equilibrium local density. When properly scaled by the perpendicular diffusion coefficient, it gives a good match with that obtained from molecular dynamics. PMID:22400522
Ambient-temperature passive magnetic bearings: Theory and design equations
Post, R.F.; Ryutov, D.D.
1997-12-30
Research has been underway at the Lawrence Livermore National Laboratory to build a theoretical and experimental base for the design of ambient-temperature passive magnetic bearings for a variety of possible applications. in the approach taken the limitations imposed by Earnshaw`s theorem with respect to the stability of passive magnetic bearing systems employing axially symmetric permanent-magnet elements are overcome by employing special combinations of elements, as follows: Levitating and restoring forces are provided by combinations of permanent-magnet-excited elements chosen to provide positive stiffnesses (negative force derivatives) for selected displacements (i.e., those involving translations or angular displacement of the axis of rotation). As dictated by Eamshaw`s theorem, any bearing system thus constructed will be statically unstable for at least one of the remaining possible displacements. Stabilization against this displacement is accomplished by using periodic arrays (`Halbach arrays`) of permanent magnets to induce currents in close-packed inductively loaded circuits, thereby producing negative force derivatives stabilizing the system while in rotation. Disengaging mechanical elements stabilize the system when at rest and when below a low critical speed. The paper discusses theory and equations needed for the design of such systems.
Modern integral equation techniques for quantum reactive scattering theory
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.
Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations
NASA Astrophysics Data System (ADS)
Plastino, A. R.
Introduction Jaynes Maximum Entropy Principle General Thermostatistical Formalisms Time Dependent MaxEnt Time-Dependent Tsallis MaxEnt Solutions of the Nonlinear Fokker-Planck - Equation Tsallis Nonextensive Thermostatistics and the Vlasov-Poisson Equations Conclusions
Generalized-master-equation theory for heavy ion collisions
Tripathi, R.K.; Satpathy, L.
1980-09-01
We apply nonequilibrium quantum statistical mechanics to the description of heavy ion collisions. Starting from the Liouville-Von Neumann equation we derive via the generalized master equation, the drift and diffusion coefficients.
The theory of relaxation oscillations for Hutchinson's equation
NASA Astrophysics Data System (ADS)
Kolesov, Andrei Yu; Rozov, Nikolai Kh
2011-06-01
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.
The theory of relaxation oscillations for Hutchinson's equation
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.
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.
Note on a well-known equation in cosmological perturbation theory which is in error
Hwang, Jai-chan; Park, Chan-Gyung; Noh, Hyerim
2010-08-15
We have a well-known equation in cosmological perturbation theory which appeared only by several simple algebraic errors made in many textbooks. There have been attempts to modify Newtonian equations aiming to reproduce that incorrect equation. We clarify why such attempts are wrong, present the correct equation to try in the modification, and explain its own limitation as well. We show that any form of density perturbation equation is possible by a suitable gauge condition.
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 UniversitÃ¤t, DDR-7010 Leipzig, German Democratic Republic.
Stellar convection theory. I - The anelastic modal equations
NASA Technical Reports Server (NTRS)
Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J.-P.
1976-01-01
Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.
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 composites made of non-permeable ingredients are well known. The simplest example is a composite loaded with highly conducting spherical inclusions. Due to eddy currents there appears a magnetic moment of the inclusion and the composite exhibits properties of diamagnetic. The inclusions of more complicated structure can exhibit resonant excitation resulting in induced magnetic moment. Examples of such inclusions are open rings, dielectric spheres, helix and bi-helix. In this case depending upon the relation between the working and resonant frequencies we can observe both diamagnetism or paramagnetism. Q-medium is more smart system. As the system of identical dielectric spheres is a permeable material, the system of different in size spheres may be non-permeable. The concentrations and radii may be chosen so that one part of spheres is excited in diamagnetic mode and the other in paramagnetic. Such a system is described by its quadrupole moment (see Fig. 1). Putting quantum mechanics apart we shall consider a classical composite material. The adjective 'classical' means that the scale of inhomogeneity is large enough to describe the reply of material on electromagnetic disturbance in terms of local constitutive equations Di equals (epsilon) ((omega) ,r)Ej ji equals (sigma) ((omega) ,r)Ej where (epsilon) ((omega) ,r), (sigma) ((omega) ,r) are local permittivity and conductivity.
Temporal breakdown and Borel resummation in the complex Langevin method
Duncan, A. Niedermaier, M.
2013-02-15
We reexamine the Parisi-Klauder conjecture for complex e{sup i{theta}/2}{phi}{sup 4} measures with a Wick rotation angle 0{<=}{theta}/2{<=}{pi}/2 interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t{yields}0 asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t, including their t{yields}{infinity} equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the 'correct' result for t larger than a finite t{sub c}. The breakdown time t{sub c} increases powerlike for decreasing strength of the noise's imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure. - Highlights: Black-Right-Pointing-Pointer The Parisi-Klauder conjecture is reexamined for complex e{sup i{theta}/2}{phi}{sup 4} measures. Black-Right-Pointing-Pointer The time dependent moments are evaluated by temporal Borel resummation. Black-Right-Pointing-Pointer The results disagree with the Langevin simulations beyond a critical time t{sub c}. Black-Right-Pointing-Pointer t{sub c} increases with decreasing strength of the noise's imaginary part. Black-Right-Pointing-Pointer The technical reason for the breakdown is identified.
Schram, P P; Sitenko, A G; Trigger, S A; Zagorodny, A G
2001-01-01
Basic principles of statistical theory of dusty plasmas are formulated with regard for electron and ion absorption by dust particles. Rigorous microscopic equations are introduced and employed to derive the BBGKY hierarchy and kinetic equations. The charging processes are shown to induce a considerable modification of both microscopic and kinetic equations for plasma particles and grains. In the approximation of dominant influence of charging collisions, explicit kinetic equations are derived and applied to calculate stationary distributions of grain velocities and charges. PMID:11304361
Fedorov universal equations in the string and membrane theories
Shavokhina, N.S. )
1990-01-01
In this paper, it is shown that the equation of minimal hypersurface in the Euclidean (or pseudo-Euclidean) space can be written as the universal Fedorov matrix equation with first-order partial derivatives. Time-like minimal surfaces in the pseudo-Euclidean Minkowski space describe the free motion of relativistic strings and membranes, whereas space-like minimal surfaces describe the potential in the nonlinear Born electrostatic. All of them are imaginary images of minimal surface of the Euclidean space. Spherically symmetric surfaces are found to be all the three types, the hypercatenoid of any dimensionality and its imaginary images. The Fedorov equations provide rich information on the minimal surfaces.
Heat fluctuations for underdamped Langevin dynamics
NASA Astrophysics Data System (ADS)
Rosinberg, Martin Luc; Tarjus, Gilles; Munakata, Toyonori
2016-01-01
Fluctuation theorems play a central role in nonequilibrium physics and stochastic thermodynamics. Here we derive an integral fluctuation theorem for the dissipated heat in systems governed by an underdamped Langevin dynamics. We show that this identity may be used to predict the occurrence of extreme events leading to exponential tails in the probability distribution functions of the heat and related quantities.
Quantum theory of rotational isomerism and Hill equation
NASA Astrophysics Data System (ADS)
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.
2012-06-01
The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schrödinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schrödinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schrödinger equation spectrum the "right" points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schrödinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.
Quantum theory of rotational isomerism and Hill equation
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.
Complex Langevin simulation of quantum vortices in a Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Hayata, Tomoya; Yamamoto, Arata
2015-10-01
The ab initio simulation of quantum vortices in a Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the nonrelativistic boson field theory at finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
NASA Astrophysics Data System (ADS)
Byrd, Jason N.; Rishi, Varun; Perera, Ajith; Bartlett, Rodney J.
2015-10-01
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.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory.
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. PMID:26520494
Cartan's equations define a topological field theory of the BF type
NASA Astrophysics Data System (ADS)
Cuesta, Vladimir; Montesinos, Merced
2007-11-01
Cartanâ€™s first and second structure equations together with first and second Bianchi identities can be interpreted as equations of motion for the tetrad, the connection and a set of two-form fields TI and RJI. From this viewpoint, these equations define by themselves a field theory. Restricting the analysis to four-dimensional spacetimes (keeping gravity in mind), it is possible to give an action principle of the BF type from which these equations of motion are obtained. The action turns out to be equivalent to a linear combination of the Nieh-Yan, Pontrjagin, and Euler classes, and so the field theory defined by the action is topological. Once Einsteinâ€™s equations are added, the resulting theory is general relativity. Therefore, the current results show that the relationship between general relativity and topological field theories of the BF type is also present in the first-order formalism for general relativity.
Dynamic field theory and equations of motion in cosmology
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 Einsteinâ€™s equations in the form of the Friedmannâ€“LemaÃ®treâ€“Robertsonâ€“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 Î´Ï/Ïâ‰¤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits Î´Ï/Ïâ‰«1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stressâ€“energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einsteinâ€™s equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
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-LemaÃ®tre-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 Î´Ï / Ï â‰¤ 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits Î´Ï / Ï â‰« 1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of these equations with the bare stress-energy tensor of the baryonic matter. We explicitly work out the covariant field equations of the successive post-Friedmannian approximations of Einstein's equations in cosmology and derive equations of motion of large and small scale inhomogeneities of dark matter and dark energy. We apply these equations to derive the post-Friedmannian equations of motion of baryonic matter comprising stars, galaxies and their clusters.
Analytical approach for the Floquet theory of delay differential equations.
Simmendinger, C; Wunderlin, A; Pelster, A
1999-05-01
We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions. PMID:11969494
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.
NASA Astrophysics Data System (ADS)
Haddad, L. H.; Carr, Lincoln D.
2015-09-01
We present the theoretical and mathematical foundations of stability analysis for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination of s-wave scattering for bosons and lattice interaction places constraints on the mean-field description, and hence on vortex configurations in the Bloch-envelope function near the Dirac point. A full derivation of the relativistic linear stability equations (RLSE) is presented by two independent methods to ensure veracity of our results. Solutions of the RLSE are used to compute fluctuations and lifetimes of vortex solutions of the nonlinear Dirac equation, which include Anderson-Toulouse skyrmions with lifetime ? 4 s. Beyond vortex stabilities the RLSE provide insight into the character of collective superfluid excitations, which we find to encode several established theories of physics. In particular, the RLSE reduce to the Andreev equations, in the nonrelativistic and semiclassical limits, the Majorana equation, inside vortex cores, and the Dirac-Bogoliubov-de Gennes equations, when nearest-neighbor interactions are included. Furthermore, by tuning a mass gap, relative strengths of various spinor couplings, for the small and large quasiparticle momentum regimes, we obtain weak-strong Bardeen-Cooper-Schrieffer superconductivity, as well as fundamental wave equations such as Schrödinger, Dirac, Klein-Gordon, and Bogoliubov-de Gennes equations. Our results apply equally to a strongly spin-orbit coupled BEC in which the Laplacian contribution can be neglected.
Denicol, G. S.; Koide, T.; Rischke, D. H.
2010-10-15
We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.
Mackie, R.L.; Madden, T.R. ); Wannamaker, P.E. . Research Inst.)
1993-02-01
The authors have developed an algorithm for computing the magnetotelluric response of three-dimensional (3-D) earth models. It is a difference equation algorithm that is based on the integral forms of Maxwell's equations rather than the differential forms. This formulation does not require approximating derivatives of earth properties or electromagnetic fields, as happens when using the second-order vector diffusion equation. Rather, one must determine how averages are to be computed. Side boundary values for the H fields are obtained from putting two-dimensional (2-D) slices of the model into a larger-scale 2-D model and solving for the fields at the 3-D boundary positions. To solve the 3-D system of equations, they propagate an impedance matrix, which relates all the horizontal E fields in a layer to all the horizontal H fields in that same layer, up through the earth model. Applying a plane-wave source condition and the side boundary H field values allows them to solve for the unknown fields within the model. The results of their method compare favorably with results from previously published integral equation solutions.
Multidimensional Langevin Modeling of Nonoverdamped Dynamics.
Schaudinnus, Norbert; Bastian, Björn; Hegger, Rainer; Stock, Gerhard
2015-07-31
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. PMID:26274405
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…
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.
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
ERIC Educational Resources Information Center
Brossman, Bradley G.; Lee, Won-Chan
2013-01-01
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. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure wasâ€¦
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
ERIC Educational Resources Information Center
Brossman, Bradley G.; Lee, Won-Chan
2013-01-01
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. Three equating procedures--two observed score procedures and one true score procedure--were created and described in detail. One observed score procedure was…
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.
Langevin representation of laser heating in PIC simulations
NASA Astrophysics Data System (ADS)
Detering, F.; Bychenkov, V. Yu.; Rozmus, W.; Sydora, R.; Capjack, C. E.
2002-02-01
An algorithm for inverse bremsstrahlung heating based on a Langevin equation, suitable for particle-in-cell (PIC) codes, is presented. We consider a quasi-neutral plasma with laser heating as described by inverse bremsstrahlung. This enables the inclusion of the heating without explicitly resolving the laser frequency and allows simulation of long time scale phenomena. Like and unlike particle collisions are included using a standard Monte Carlo procedure. The evolution of the distribution function in a homogeneous plasma is examined using this model and good agreement with theoretical predictions is achieved. This simulation model is a useful tool for the investigation of the evolution of the electron distribution and electron transport in inhomogeneous plasmas.
Integral equation theory for polyelectrolyte solutions containing counterions and coions
NASA Astrophysics Data System (ADS)
Harnau, Ludger; Reineker, Peter
2000-01-01
Integral equations for equilibrium correlation functions of a three-component polyelectrolyte solution (polyions, counterions, coions) are solved numerically. Various pair correlation functions and structure factors are investigated. It is shown that added salt screens the Coulomb interaction between the negatively charged polyions. The comparison of the calculated polyion-polyion partial structure factor with experimental results of light scattering experiments on tobacco mosaic virus in a solution with added salt exhibits good agreement. Moreover, the counterion condensation on rodlike polyions is studied by means of pair correlation functions.
Spherically symmetric solutions of modified field equations in f(R) theories of gravity
Multamaeki, T.; Vilja, I.
2006-09-15
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In particular, we show that for a large class models, including e.g. the f(R)=R-{mu}{sup 4}/R model, the Schwarzschild-de Sitter metric is an exact solution of the field equations. The significance of these solutions is discussed in light of solar system constraints on f(R) theories of gravity.
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.
Some aspects of field equations in generalized theories of gravity
NASA Astrophysics Data System (ADS)
Padmanabhan, T.
2011-12-01
A class of theories of gravity based on a Lagrangian L=L(Rabcd,gab) which depends on the curvature and metric—but not on the derivatives of the curvature tensor—is of interest in several contexts including in the development of the paradigm that treats gravity as an emergent phenomenon. This class of models contains, as an important subset, all Lanczos-Lovelock models of gravity. I derive several identities and properties which are useful in the study of these models and clarify some of the issues that seem to have received insufficient attention in the past literature.
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.
The notion of error in Langevin dynamics. I. Linear analysis
NASA Astrophysics Data System (ADS)
Mishra, Bimal; Schlick, Tamar
1996-07-01
The notion of error in practical molecular and Langevin dynamics simulations of large biomolecules is far from understood because of the relatively large value of the timestep used, the short simulation length, and the low-order methods employed. We begin to examine this issue with respect to equilibrium and dynamic time-correlation functions by analyzing the behavior of selected implicit and explicit finite-difference algorithms for the Langevin equation. We derive: local stability criteria for these integrators; analytical expressions for the averages of the potential, kinetic, and total energy; and various limiting cases (e.g., timestep and damping constant approaching zero), for a system of coupled harmonic oscillators. These results are then compared to the corresponding exact solutions for the continuous problem, and their implications to molecular dynamics simulations are discussed. New concepts of practical and theoretical importance are introduced: scheme-dependent perturbative damping and perturbative frequency functions. Interesting differences in the asymptotic behavior among the algorithms become apparent through this analysis, and two symplectic algorithms, ``LIM2'' (implicit) and ``BBK'' (explicit), appear most promising on theoretical grounds. One result of theoretical interest is that for the Langevin/implicit-Euler algorithm (``LI'') there exist timesteps for which there is neither numerical damping nor shift in frequency for a harmonic oscillator. However, this idea is not practical for more complex systems because these special timesteps can account only for one frequency of the system, and a large damping constant is required. We therefore devise a more practical, delay-function approach to remove the artificial damping and frequency perturbation from LI. Indeed, a simple MD implementation for a system of coupled harmonic oscillators demonstrates very satisfactory results in comparison with the velocity-Verlet scheme. We also define a probability measure to estimate individual trajectory error. This framework might be useful in practice for estimating rare events, such as barrier crossing. To illustrate, this concept is applied to a transition-rate calculation, and transmission coefficients for the five schemes are derived.
From Jacobi problem of separation of variables to theory of quasipotential Newton equations
NASA Astrophysics Data System (ADS)
Rauch-Wojciechowski, S.
2009-08-01
Our solution to the Jacobi problem of finding separation variables for natural Hamiltonian systems H = ½ p 2 + V( q) is explained in the first part of this review. It has a form of an effective criterion that for any given potential V( q) tells whether there exist suitable separation coordinates x( q) and how to find these coordinates, so that the Hamilton-Jacobi equation of the transformed Hamiltonian is separable. The main reason for existence of such criterion is the fact that for separable potentials V( q) all integrals of motion depend quadratically on momenta and that all orthogonal separation coordinates stem from the generalized elliptic coordinates. This criterion is directly applicable to the problem of separating multidimensional stationary Schrödinger equation of quantum mechanics. Second part of this work provides a summary of theory of quasipotential, cofactor pair Newton equations ddot q = M( q) admitting n quadratic integrals of motion. This theory is a natural generalization of theory of separable potential systems ddot q = -?( q). The cofactor pair Newton equations admit a Hamilton-Poisson structure in an extended 2 n + 1 dimensional phase space and are integrable by embedding into a Liouville integrable system. Two characterizations of these systems are given: one through a Poisson pencil and another one through a set of Fundamental Equations. For a generic cofactor pair system separation variables have been found and such system have been shown to be equivalent to a Stäckel separable Hamiltonian system. The theory is illustrated by examples of driven and triangular Newton equations.
Existence of a solution to an equation arising from the theory of Mean Field Games
NASA Astrophysics Data System (ADS)
Gangbo, Wilfrid; ÅšwiÄ™ch, 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 toÂ (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved inÂ [48], and make a more rigorous connection between the master equationÂ (1.1) and the Mean Field Games equationsÂ (1.2).
Gauge theories on noncommutative ?PN 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 ?PN 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 ?PN. 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 ?P1 and ?P2 are derived from these actions. There are analogies between BPS-like equations on ?P1 and monopole equations on ?3 and BPS-like equations on ?P2 and instanton equations on ?8. We discuss solutions of these BPS-like equations.
Zwanzig-Mori projection operators and EEG dynamics: deriving a simple equation of motion
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
Implicit discretization schemes for Langevin dynamics
NASA Astrophysics Data System (ADS)
Zhang, Guihua; Schlick, Tamar
We explore here several numerical schemes for Langevin dynamics in the general implicit discretization framework of the Langevin/implicit-Euler scheme, LI. Specifically, six schemes are constructed through different discretization combinations of acceleration, velocity, and position. Among them, the explicit BBK method (LE in our notation) and LI are recovered, and the other four (all implicit) are named LIM1, LIM2, MID1, and MID2. The last two correspond, respectively, to the well-known implicit-midpoint scheme and the trapezoidal rule. LI and LIM1 are first-order accurate and have intrinsic numerical damping. LIM2, MID1, and MID2 appear to have large-timestep stability as LI but overcome numerical damping. However, numerical results reveal limitations on other grounds. From simulations on a model butane, we find that the non-damping methods give similar results when the timestep is small; however, as the timestep increases, LIM2 exhibits a pronounced rise in the potential energy and produces wider distributions for the bond lengths. MID1 and MID2 appear to be the best among those implicit schemes for Langevin dynamics in terms of reasonably reproducing distributions for bond lengths, bond angles and dihedral angles (in comparison to 1 fs timestep explicit simulations), as well as conserving the total energy reasonably. However, the minimization subproblem (due to the implicit formulation) becomes difficult when the timestep increases further. In terms of computational time, all the implicit schemes are very demanding. Nonetheless, we observe that for moderate timesteps, even when the error is large for the fast motions, it is relatively small for the slow motions. This suggests that it is possible by large timestep algorithms to capture the slow motions without resolving accurately the fast motions.
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.
Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory
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.
Toward a gauge theory for evolution equations on vector-valued spaces
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.
An improved effective-mass-theory equation for phosphorus doped in silicon
NASA Astrophysics Data System (ADS)
Hui, H. T.
2013-01-01
A new multi-valley effective-mass-theory (EMT) equation is derived for the phosphorus doped in silicon. This equation admits solutions which agree with the measured ground state energy and the square modulus of the ground-state wavefunction |Î¨(0)| at the donor site accurately. This avoids the use of the so-called "central-cell correction" approximation method to calculate the hyperfine constant at the donor site. Furthermore, the energy levels for the upper lying states of T2 and E can also be predicted relatively accurately. The newly derived EMT equation has applications in the characterization of semiconductor or spintronics devices.
Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form
NASA Astrophysics Data System (ADS)
Kim, Sunghan; Lee, Ki-Ahm
2016-03-01
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.
Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
NASA Astrophysics Data System (ADS)
Fukushima, Kenji; Tanizaki, Yuya
2015-11-01
The Lefschetz-thimble method, i.e., integration along the steepest descent cycles, is a way to avoid the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave functions on a grid using a toy model and confirm their well-localized behavior.
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.
Exact series model of Langevin transducers with internal losses.
Nishamol, P A; Ebenezer, D D
2014-03-01
An exact series method is presented to analyze classical Langevin transducers with arbitrary boundary conditions. The transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders. All three cylinders are of the same diameter. The length to diameter ratio is arbitrary. Complex piezoelectric and elastic coefficients are used to model internal losses. Solutions to the exact linearized governing equations for each cylinder include four series. Each term in each series is an exact solution to the governing equations. Bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions, respectively, are used in the series. Asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti-symmetric sets of functions. All interface and boundary conditions are satisfied in a weighted-average sense. The computed input electrical admittance, displacement, and stress in transducers are presented in tables and figures, and are in very good agreement with those obtained using atila-a finite element package for the analysis of sonar transducers. For all the transducers considered in the analysis, the maximum difference between the first three resonance frequencies calculated using the present method and atila is less than 0.03%. PMID:24606259
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.
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 proposedâ€¦
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…
The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
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.
Scattering theory for the Klein-Gordon equation with nondecreasing potentials
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.
Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge
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.
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.
Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions
NASA Astrophysics Data System (ADS)
Bikbaev, R. F.; Bobenko, A. I.; Its, A. R.
2014-02-01
Using the inverse scattering method, we study the XXZ Landau-Lifshitz equation well-known in the theory of ferromagnetism. We construct all elementary soliton-type excitations and study their interaction. We also obtain finite-gap solutions (in terms of theta functions) and select the real solutions among them.
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…
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.…
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…
The general class of the vacuum spherically symmetric equations of the general relativity theory
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.
Sivak, David A; Chodera, John D; Crooks, Gavin E
2014-06-19
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
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
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
NASA Astrophysics Data System (ADS)
HorvÃ¡th, D. X.; Sotiriadis, S.; TakÃ¡cs, 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.
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.
Equation of state for expanded fluid mercury: variational theory with many-body interaction.
Kitamura, Hikaru
2007-04-01
A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quantum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isocloric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data. PMID:17430049
Microscopic Theory of the Nuclear Equation of State and Neutron Star Structure
NASA Astrophysics Data System (ADS)
Baldo, Marcello; Burgio, Fiorella
The Bethe-Brueckner-Goldstone many-body theory of the Nuclear Equation of State is reviewed in some details. In the theory, one performs an expansion in terms of the Brueckner two-body scattering matrix and an ordering of the corresponding many-body diagrams according to the number of their hole-lines. Recent results are reported, both for symmetric and for pure neutron matter, based on realistic two-nucleon interactions. It is shown that there is strong evidence of convergence in the expansion. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. One finds that in the interior of neutron stars the onset of hyperons strongly softens the Nuclear Equation of State. As a consequence, the maximum mass of neutron stars turns out to be at the lower limit of the present phenomenological observation.
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.
Statistical-Mechanical Theory of Equations of State for Fluids and Mixtures.
NASA Astrophysics Data System (ADS)
Song, Yuhua
The theory of equation of state is one of the oldest of the unsolved problems in physics. In this thesis, we present a statistical-mechanical perturbation theory of equations of state for fluids and mixtures, employing effective hard bodies as reference systems. Unlike previous perturbation theories, we treat the second virial coefficient exactly, in order to obtain a good description of a fluid at low densities, and calculate the effective hard-body volume as a function of temperature (only). The theory can give simple analytical equations of state for simple fluids, molecular fluids, and even fluid mixtures, in any number of dimensions, if the representations of the equations of state for the reference systems are known analytically. All temperature-dependent parameters can be calculated from the intermolecular potentials. Agreement with computer-simulated results for the Lennard-Jones (12,6) fluid and some of its mixtures, and for the Kihara (12,6) core fluid for rodlike molecules is quite good, extending up to the limit of available data. For practical purposes, however, the theory is usable with much less input than the full intermolecular potential, since all temperature-dependent parameters of the equation of state that depend only on the repulsion are insensitive to the detailed shape of the intermolecular potential. They can be predicted with satisfactory accuracy from the second virial coefficient by means of scaling rules. An additional shape factor for (nonspherical) molecular fluids is needed to describe the nonsphericities of molecules or the sizes of inner hard cores, and can be found from a few reliable liquid densities. The theory is tested for a number of real systems, including as simple fluids the noble gases (except He) and CH _4, the molecular fluids N_2, O_2, F_2, CO_2, C_2H_4, C_3H_6, and CF_4, and the polar fluid H_2O. The overall agreement with experimental p-v- T data is quite remarkable. The theory includes a mean-field approximation and the resulting equation of state is analytical in the density, and can thus not be expected to be very accurate in the nonanalytical critical and two-phase regions. In particular, it yields only the "classical," or van der Waals, values of the critical exponents, the prediction of the critical constants is only fair, and of the vapor pressures is at best moderately accurate.
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.
Number-conserving master equation theory for a dilute Bose-Einstein condensate
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.
Langevin dynamics of a heavy particle and orthogonality effects
NASA Astrophysics Data System (ADS)
Thomas, Mark; Karzig, Torsten; Viola Kusminskiy, Silvia
2015-12-01
The dynamics of a classical heavy particle moving in a quantum environment is determined by a Langevin equation which encapsulates the effect of the environment-induced reaction forces on the particle. For an open quantum system, these include a Born-Oppenheimer force, a dissipative force, and a stochastic force due to shot and thermal noise. Recently, it was shown that these forces can be expressed in terms of the scattering matrix of the system by considering the classical heavy particle as a time-dependent scattering center, allowing to demonstrate interesting features of these forces when the system is driven out of equilibrium. At the same time, it is well known that small changes in a scattering potential can have a profound impact on a fermionic system due to the Anderson orthogonality catastrophe. In this work, by calculating the Loschmidt echo, we relate Anderson orthogonality effects with the mesoscopic reaction forces for an environment that can be taken out of equilibrium. In particular, we show how the decay of the Loschmidt echo is characterized by fluctuations and dissipation in the system and discuss different quench protocols.
From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
NASA Astrophysics Data System (ADS)
Calabrese, Pasquale; Kormos, Márton; Le Doussal, Pierre
2014-07-01
We unveil a remarkable connection between the sine-Gordon quantum field theory and the Kardar-Parisi-Zhang (KPZ) growth equation. We find that the non-relativistic limit of the two-point correlation function of the sine-Gordon theory is related to the generating function of the height distribution of the KPZ field with droplet initial conditions, i.e. the directed polymer free energy with two endpoints fixed. As shown recently, the latter can be expressed as a Fredholm determinant which in the large-time separation limit converges to the GUE Tracy-Widom cumulative distribution. Possible applications and extensions are discussed.
Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory
NASA Astrophysics Data System (ADS)
Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio
2012-03-01
Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.
NASA Astrophysics Data System (ADS)
Yamane, Y.; Itoh, M.
2012-10-01
Self-consistent theory of Anderson localization of two-dimensional non-interacting electrons is formulated in the context of the exact transport equation and conductivity expression derived by the present authors (YI). The irreducible scattering vertex by Vollhardt and Wölfle (VW) is used in this equation, determining the diffusion coefficient in the scattering vertex self-consistently, through Einstein relation. It predicts a similar localization length to that obtained by VW, but shows that the conductivity evaluated by the Kubo formula decays exponentially, as the system size approaches the localization length. The result is opposed to the prediction by VW, who showed different behaviour of the diffusion coefficient that is equivalent to our conductivity. Our calculation also implies that the localization may be described along with the Landau-Silin theory of Fermi liquid.
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
Physical theories in Galilean space-time and the origin of Schroedinger-like equations
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.
NASA Astrophysics Data System (ADS)
Giraldi, Filippo
2015-09-01
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.
NASA Astrophysics Data System (ADS)
Garnier, Josselin; Kalimeris, Konstantinos
2012-01-01
In this paper, a perturbation theory for the nonlinear Schrödinger equation with non-vanishing boundary conditions based on the inverse scattering transform is presented. It is applied to study the stability of the soliton propagation on a continuous-wave background. It is shown that the soliton is rather robust with respect to dispersive perturbations but it can be strongly affected by damping. In particular, it is shown that adiabatic approaches can underestimate the decay of the soliton energy.
NASA Astrophysics Data System (ADS)
Linscheid, A.; Sanna, A.; Essenberger, F.; Gross, E. K. U.
2015-07-01
We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory SpinSCDFT by extending the Hohenberg-Kohn theorem and constructing the noninteracting Kohn-Sham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham-Schlüter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.
Schwinger-Dyson equation and NJL approximation in massive gauge theory with fermions
NASA Astrophysics Data System (ADS)
Zubkov, M. A.
2015-03-01
We consider massive SU(N) gauge theory with fermions. Gauge bosons become massive due to the interaction with the scalar field, whose vacuum average provides the spontaneous breakdown of gauge symmetry. We investigate Dyson-Schwinger equation for the fermion propagator written in ladder approximation and in Landau gauge. Our analysis demonstrates that the chiral symmetry breaking in the considered theory is the strong coupling phenomenon. There are the indications that there appears the second order phase transition between chirally broken and symmetric phases of the theory at the value of coupling constant ?c =(1 + ?) × ?/3 × 1/2C2(F), where 0 < ? < 1, and ? depends on the scale, at which the fluctuations of the scalar field destroy the gauge boson mass. In the broken phase near the critical value of ? the Dyson-Schwinger equation is approximated well by the gap equation of the effective Nambu-Jona-Lasinio model with the value of cutoff around gauge boson mass M and the effective four-fermion coupling constant 4/?? M2 × 2C2(F)/N. The dynamical fermion mass m may be essentially smaller than M.
Skontorp, A.; Wang, S.S.; Shibuya, Y.
1994-12-31
In this paper, a homogenization theory is developed to determine high-temperature effective viscoelastic constitutive equations for fiber-reinforced polymer composites. The homogenization theory approximates the microstructure of a fiber composite, and determine simultaneously effective macroscopic constitutive properties of the composite and the associated microscopic strain and stress in the heterogeneous material. The time-temperature dependent homogenization theory requires that the viscoelastic constituent properties of the matrix phase at elevated temperatures, the governing equations for the composites, and the boundary conditions of the problem be Laplace transformed to a conjugate problem. The homogenized effective properties in the transformed domain are determined, using a two-scale asymptotic expansion of field variables and an averaging procedure. Field solutions in the unit cell are determined from basic and first-order governing equations with the aid of a boundary integral method (BIM). Effective viscoelastic constitutive properties of the composite at elevated temperatures are determined by an inverse transformation, as are the microscopic stress and deformation in the composite. Using this method, interactions among fibers and between the fibers and the matrix can be evaluated explicitly, resulting in accurate solutions for composites with high-volume fraction of reinforcing fibers. Examples are given for the case of a carbon-fiber reinforced thermoplastic polyamide composite in an elevated temperature environment. The homogenization predictions are in good agreement with experimental data available for the composite.
Unification of classical nucleation theories via a unified ItÃ´-Stratonovich stochastic equation.
DurÃ¡n-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-DÃ¶ring-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. DurÃ¡n-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
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation
NASA Astrophysics Data System (ADS)
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.
Three new branched chain equations of state based on Wertheim's perturbation theory
NASA Astrophysics Data System (ADS)
Marshall, Bennett D.; Chapman, Walter G.
2013-05-01
In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.
Fluids of hard natural and Gaussian ellipsoids: A comparative study by integral equation theories
NASA Astrophysics Data System (ADS)
Perera, Aurélien
2008-11-01
The hard Gaussian overlap (HGO) model for ellipsoids is compared to the hard ellipsoid of revolution (HER) model, in the isotropic fluid phase and within the framework of the Percus-Yevick (PY) and hypernetted chain (HNC) integral equation theories. The former model is often used in place of the latter in many approximate theories. Since the HGO model slightly overestimates the contact distance when the two ellipsoids are perpendicular to each other, it leads to small differences in the Mayer function of the two models, but nearly none in the integrals of these functions and particularly for the second virial coefficients. However, it leads to notable differences in the pair correlation functions, as obtained by the Percus-Yevick and the hypernetted chain theories, especially at high densities. The prediction of the stability of the isotropic phase with respect to orientational order, at high densities, is notably influenced by these small differences. Both theories predict that, for same aspect ratios, the HGO model overestimates the ordering, when compared to the HER model. This explains why the PY approximation predicts ordering for the HGO model with aspect ratio of 1:3, while it does not for the HER model, in accordance with the very first integral equation results obtained for this system, and at variance with many opposite claims from subsequent publications that used the HGO model in place of the HER model.
Interpolation between the Grover-Silbey and the generalized stochastic Liouville equation theories
Capek, V.; Barvik, I. )
1992-12-15
A projection superoperator is introduced that is able to extract (from the full nonequilibrium exciton-phonon density matrix) the bare- as well as the dressed-exciton (exciton-polaron) single-particle density matrices. Applying it to a standard model of the exciton interacting, via a linear local coupling, with harmonic phonons in a linear chain, a general theory of exciton propagation is constructed. This theory well interpolates between the standard generalized stochastic Liouville equation (GSLE) approach and the Grover-Silbey (GS) theory [M. Grover and R. Silbey, J. Chem. Phys. 54, 4843 (1971)] depending on an interpolation parameter determining details of the basis used. As this parameter (not connected with the model but depending just on our choice of the mathematical language used) can have no impact on the regime as well as the time dependence of the exciton propagation (measured by site occupation probabilities), all famous contradictions between GSLE (or stochastic Liouville equation) and GS approaches are interpreted as only formal and, in fact, seeming. This regards mainly the lack of the local [gamma][sub 0] parameters and dependence of the [gamma][sub 1] parameter on the exciton resonance integrals in the Grover-Silbey theory.
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.
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-05-21
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules. PMID:26001441
NASA Astrophysics Data System (ADS)
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-05-01
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, "electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science." Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.
Loop variables and gauge invariant exact renormalization group equations for (open) string theory II
NASA Astrophysics Data System (ADS)
Sathiapalan, B.
2013-03-01
In arXiv:1202.4298 gauge invariant interacting equations were written down for the spin 2 and spin 3 massive modes using the exact renormalization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant "field strengths" and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invariant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher-dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space-time and this is also outlined.
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.
NASA Technical Reports Server (NTRS)
Weatherford, Charles A.
1993-01-01
One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.
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 â€œPython Renormalization group equations At Two-loop for Everyoneâ€. 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, Queenâ€™s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)
Quantum theory as a description of robust experiments: Derivation of the Pauli equation
De Raedt, Hans; Katsnelson, Mikhail I.; Donker, Hylke C.; Michielsen, Kristel
2015-08-15
It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g.Â the SchrÃ¶dinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Sternâ€“Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments. - Highlights: â€¢ The Pauli equation is obtained through logical inference applied to robust experiments on a charged particle. â€¢ The concept of spin appears as an inference resulting from the treatment of two-valued data. â€¢ The same reasoning yields the quantum theoretical description of neutral magnetic particles. â€¢ Logical inference provides a framework to establish a bridge between objective knowledge gathered through experiments and their description in terms of concepts.
Field theory and weak Euler-Lagrange equation for classical particle-field systems.
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry. PMID:25375609
Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
NASA Astrophysics Data System (ADS)
Manuel, Cristina; Torres-Rincon, Juan M.
2014-10-01
We derive the relativistic chiral transport equation for massless fermions and antifermions by performing a semiclassical Foldy-Wouthuysen diagonalization of the quantum Dirac Hamiltonian. The Berry connection naturally emerges in the diagonalization process to modify the classical equations of motion of a fermion in an electromagnetic field. We also see that the fermion and antifermion dispersion relations are corrected at first order in the Planck constant by the Berry curvature, as previously derived by Son and Yamamoto for the particular case of vanishing temperature. Our approach does not require knowledge of the state of the system, and thus it can also be applied at high temperature. We provide support for our result by an alternative computation using an effective field theory for fermions and antifermions: the on-shell effective field theory. In this formalism, the off-shell fermionic modes are integrated out to generate an effective Lagrangian for the quasi-on-shell fermions/antifermions. The dispersion relation at leading order exactly matches the result from the semiclassical diagonalization. From the transport equation, we explicitly show how the axial and gauge anomalies are not modified at finite temperature and density despite the incorporation of the new dispersion relation into the distribution function.
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P. V.
2011-02-15
We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.
NASA Astrophysics Data System (ADS)
Silbermann, C. B.; Ihlemann, J.
2016-03-01
Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.
One parameter family of master equations for logistic growth and BCM theory
NASA Astrophysics Data System (ADS)
De Oliveira, L. R.; Castellani, C.; Turchetti, G.
2015-02-01
We propose a one parameter family of master equations, for the evolution of a population, having the logistic equation as mean field limit. The parameter Î± determines the relative weight of linear versus nonlinear terms in the population number n â©½ N entering the loss term. By varying Î± from 0 to 1 the equilibrium distribution changes from maximum growth to almost extinction. The former is a Gaussian centered at n = N, the latter is a power law peaked at n = 1. A bimodal distribution is observed in the transition region. When N grows and tends to âˆž, keeping the value of Î± fixed, the distribution tends to a Gaussian centered at n = N whose limit is a delta function corresponding to the stable equilibrium of the mean field equation. The choice of the master equation in this family depends on the equilibrium distribution for finite values of N. The presence of an absorbing state for n = 0 does not change this picture since the extinction mean time grows exponentially fast with N. As a consequence for Î± close to zero extinction is not observed, whereas when Î± approaches 1 the relaxation to a power law is observed before extinction occurs. We extend this approach to a well known model of synaptic plasticity, the so called BCM theory in the case of a single neuron with one or two synapses.
On loop equations in KdV exactly solvable string theory
Dalley, S. . Joseph Henry Labs.)
1992-05-10
In this paper, the non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation ({bar P}, Q) = Q, where {bar P} generates scale transformations. In general the end of the half-line (the wall) is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of (P,Q) = 1. Detailed arguments are given for the (2,2m {minus} 1) models while generalization to the other (p,q) minimal models and c = 1 is briefly addressed.
Elasticity theory equations and fracture condition for materials of varying moduli
Oleinikov, A.I.
1986-11-01
Many massive rocks and composite materials belong to the class of materials of varying moduli with definite distinct deformation and strength properties under tension and compression. The results of experiments indicate that the difference between the properties of materials of different moduli is not limited to tension and compression cases but can also appear clearly for any change in the form of the state of stress. Elasticity theory equations are constructed here to describe the strain of materials of varying moduli as well as the dependence of the strength properties on the form of the state of strain. Tests were done on coal, limestone, diabase and cement and results are shown. Using the dependencies obtained, Poisson's ratio and the elastic modulus can be calculated for these rocks. The equations and conditions of fracture proposed, are written in a simple invariant form.
WKB theory of wave tunneling for Hermitian and nearly Hermitian vector systems of integral equations
NASA Astrophysics Data System (ADS)
Kull, H. J.; Kashuba, R. J.; Berk, H. L.
1989-11-01
A general theory of wave tunneling in one dimension for Hermitian and nearly Hermitian vector systems of integral equations is presented. It describes mode conversion in terms of the general dielectric tensor of the medium and properly accounts for the forward and backward nature of the waves without regard to specific models. Energy conservation in the WKB approximation can be obtained for general Hermitian systems by the use of modified Furry rules that are similar to those used by Heading for second-order differential equations. Wave energy absorption can then be calculated perturbatively using the conservation properties of the dominant Hermitian operator. Operational graphical rules are developed to construct global wave solutions and to determine the direction of energy flow for spatially disconnected roots. In principle, these rules could be applied to systems with arbitrary mode complexity. Coupling coefficients for wave tunneling problems with up to four interacting modes are calculated explicitly.
Yang Lei; Devi, Murali; Jang, Seogjoo
2012-07-14
This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)] by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.
NASA Astrophysics Data System (ADS)
Yang, Lei; Devi, Murali; Jang, Seogjoo
2012-07-01
This work extends the theory of coherent resonance energy transfer [S. Jang, J. Chem. Phys. 131, 164101 (2009)], 10.1063/1.3247899 by including quantum mechanical inelastic effects due to modulation of donor-acceptor electronic coupling. Within the approach of the second order time local quantum master equation (QME) in the polaron picture and under the assumption that the bath degrees of freedom modulating the electronic coupling are independent of other modes, a general time evolution equation for the reduced system density operator is derived. Detailed expressions for the relaxation operators and inhomogeneous terms of the QME are then derived for three specific models of modulation in distance, axial angle, and dihedral angle, which are all approximated by harmonic oscillators. Numerical tests are conducted for a set of model parameters. Model calculation shows that the torsional modulation can make significant contribution to the relaxation and dephasing mechanisms.
Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density
NASA Technical Reports Server (NTRS)
Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.
1988-01-01
The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.
Pure gauge configurations and tachyon solutions to string field theories equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.
2009-05-01
In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.
Poisson equation for the Mercedes diagram in string theory at genus one
NASA Astrophysics Data System (ADS)
Basu, Anirban
2016-03-01
The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three-loop Feynman diagram contributes to the {D}12{{ R }}4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one- and two-loop Feynman diagrams. We calculate its contribution to the {D}12{{ R }}4 amplitude.
Renormalization-group theory for the phase-field crystal equation
NASA Astrophysics Data System (ADS)
Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.
2006-07-01
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1958-01-01
A method is presented for the approximate solution of the nonlinear equations of transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
Thin airfoil theory based on approximate solution of the transonic flow equation
NASA Technical Reports Server (NTRS)
Spreiter, John R; Alksne, Alberta Y
1957-01-01
A method is presented for the approximate solution of the nonlinear equations transonic flow theory. Solutions are found for two-dimensional flows at a Mach number of 1 and for purely subsonic and purely supersonic flows. Results are obtained in closed analytic form for a large and significant class of nonlifting airfoils. At a Mach number of 1 general expressions are given for the pressure distribution on an airfoil of specified geometry and for the shape of an airfoil having a prescribed pressure distribution. Extensive comparisons are made with available data, particularly for a Mach number of 1, and with existing solutions.
A standard basis operator equation of motion impurity solver for dynamical mean field theory
NASA Astrophysics Data System (ADS)
Li, Hengyue; Tong, Ning-Hua
2015-12-01
We present an efficient impurity solver for the dynamical mean-field theory (DMFT). It is based on the separation of bath degrees of freedom into the low energy and the high energy parts. The former is solved exactly using exact diagonalization and the latter is treated approximately using Green's function equation of motion decoupling approximation. The two parts are combined coherently under the standard basis operator formalism. The impurity solver is applied to the Anderson impurity model and, combined with DMFT, to the one-band Hubbard model. Qualitative agreement is found with other well established methods. Some promising features and possible improvements of the present solver are discussed.
Statistical-mechanical theory of a new analytical equation of state
NASA Astrophysics Data System (ADS)
Song, Yuhua; Mason, E. A.
1989-12-01
We present an analytical equation of state based on statistical-mechanical perturbation theory for hard spheres, using the Weeks-Chandler-Andersen decomposition of the potential and the Carnahan-Starling formula for the pair distribution function at contact, g(d+), but with a different algorithm for calculating the effective hard-sphere diameter. The second virial coefficient is calculated exactly. Two temperature-dependent quantities in addition to the second virial coefficient arise, an effective hard-sphere diameter or van der Waals covolume, and a scaling factor for g(d+). Both can be calculated by simple quadrature from the intermolecular potential. If the potential is not known, they can be determined from the experimental second virial coefficient because they are insensitive to the shape of the potential. Two scaling constants suffice for this purpose, the Boyle temperature and the Boyle volume. These could also be determined from analysis of a number of properties other than the second virial coefficient. Thus the second virial coefficient serves to predict the entire equation of state in terms of two scaling parameters, and hence a number of other thermodynamic properties including the Helmholtz free energy, the internal energy, the vapor pressure curve and the orthobaric liquid and vapor densities, and the Joule-Thomson inversion curve, among others. Since it is effectively a two-parameter equation, the equation of state implies a principle of corresponding states. Agreement with computer-simulated results for a Lennard-Jones (12,6) fluid, and with experimental p-v-T data on the noble gases (except He) is quite good, extending up to the limit of available data, which is ten times the critical density for the (12,6) fluid and about three times the critical density for the noble gases. As expected for a mean-field theory, the prediction of the critical constants is only fair, and of the critical exponents is incorrect. Limited testing on the polyatomic gases CH4, N2, and CO2 suggests that the results for spherical molecules (CH4) may be as good as for the noble gases, nearly as good for slightly nonspherical molecules (N2), but poor at high densities for nonspherical molecules (CO2). In all cases, however, the results are accurate up to the critical density. Except for the eight-parameter empirical Benedict-Webb-Rubin equation, this appears to be the most accurate analytical equation of state proposed to date.
Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory
NASA Astrophysics Data System (ADS)
Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; MeiÃŸner, Ulf-G.
2015-11-01
We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Î” (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.
Slender-Body Theory Based On Approximate Solution of the Transonic Flow Equation
NASA Technical Reports Server (NTRS)
Spreiter, John R.; Alksne, Alberta Y.
1959-01-01
Approximate solution of the nonlinear equations of the small disturbance theory of transonic flow are found for the pressure distribution on pointed slender bodies of revolution for flows with free-stream, Mach number 1, and for flows that are either purely subsonic or purely supersonic. These results are obtained by application of a method based on local linearization that was introduced recently in the analysis of similar problems in two-dimensional flows. The theory is developed for bodies of arbitrary shape, and specific results are given for cone-cylinders and for parabolic-arc bodies at zero angle of attack. All results are compared either with existing theoretical results or with experimental data.
Equation of state of hot and dense QCD: resummed perturbation theory confronts lattice data
NASA Astrophysics Data System (ADS)
Mogliacci, Sylvain; Andersen, Jens O.; Strickland, Michael; Su, Nan; Vuorinen, Aleksi
2013-12-01
We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak coupling expression for the pressure, motivated by dimensional reduction. Finally, we compare the exact one-loop HTLpt and resummed dimensional reduction results with state-of-the-art lattice calculations and a recent mass-expanded three-loop HTLpt calculation.
Advancing towards constitutive equations for the metal industry via the LEDS theory
NASA Astrophysics Data System (ADS)
Kuhlmann-Wilsdorf, Doris
2004-02-01
A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. The are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. White plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newtonâ€™s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.
Advancing towards constitutive equations for the metal industry via the LEDS theory
NASA Astrophysics Data System (ADS)
Kuhlmann-Wilsdorf, Doris
2004-02-01
A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. They are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. While plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newtonâ€™s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
Invariant manifold theory and its applications to nonlinear partial differential equations
NASA Astrophysics Data System (ADS)
Jin, Jiayin
The theory of invariant manifolds and foliations provides indispensable tools for the study of dynamics of nonlinear systems in finite or infinite dimensional space. As is the case here, invariant manifolds can be used to capture complex dynamics and the long term behavior of solutions and to reduce high dimensional problems to the analysis of lower dimensional structures. Invariant manifolds with invariant foliations provide a coordinate system in which systems of differential equations may be decoupled and normal forms derived. These play an important role in the study of structural stability of dynamical systems or, when a degeneracy occurs, in understanding the nature of bifurcations. This thesis is devoted to the study of the construction of invariant manifolds of solutions with certain spatial structures to some nonlinear parabolic partial differential equations. I approach these problems in two steps: the first step is to construct a manifold of states that is approximately invariant, the second step is to show the existence of a truly invariant manifold of these states near the approximately invariant one, and to determine the dynamics on this manifold. Since this approach may be applied to many different systems, I also develop it in an abstract or general way. My thesis consists of two projects, in the first project, we consider the two-dimensional mass-conserving Allen-Cahn Equation. We establish the existence of a global invariant manifold of bubble states for this equation and give the dynamics for the center of the bubble. In the second project, we consider the existence, in forward and backward time, of dynamical interior multi-spike states driven by the nonlinear Cahn-Hilliard equation. We construct invariant manifolds of interior multi-spike states for the nonlinear Cahn-Hilliard equation and then investigate the dynamics on it. An equation for the motion of the spikes is also derived. It turns out that the dynamics of interior spikes has a global character and each spike interacts with all the others and with the boundary. Moreover, we show that the speed of the interior spikes is super slow, which indicates the long time existence of dynamical multi-spike solutions in both positive and negative time. (Abstract shortened by UMI.).
Sum rule for response function in nonequilibrium Langevin systems
NASA Astrophysics Data System (ADS)
Yuge, Tatsuro
2010-11-01
We derive general properties of the linear-response functions of nonequilibrium steady states in Langevin systems. These correspond to extension of the results which were recently found in Hamiltonian systems [A. Shimizu and T. Yuge, J. Phys. Soc. Jpn. 79, 013002 (2010)10.1143/JPSJ.79.013002]. We discuss one of the properties, the sum rule for the response function, in particular detail. We show that the sum rule for the response function of the velocity holds in the underdamped case, whereas it is violated in the overdamped case. This implies that the overdamped Langevin models should be used with great care. We also investigate the relation of the sum rule to an equality on the energy dissipation in nonequilibrium Langevin systems, which was derived by Harada and Sasa.
Effective field theory during inflation: Reduced density matrix and its quantum master equation
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-07-01
We study the power spectrum of super-Hubble fluctuations of an inflatonlike scalar field, the "system," coupled to another scalar field, the "environment" during de Sitter inflation. We obtain the reduced density matrix for the inflaton fluctuations by integrating out the environmental degrees of freedom. These are considered to be massless and conformally coupled to gravity as a proxy to describe degrees of freedom that remain sub-Hubble all throughout inflation. The time evolution of the density matrix is described by a quantum master equation, which describes the decay of the vacuum state, the production of particles and correlated pairs and quantum entanglement between super and sub-Hubble degrees of freedom. The quantum master equation provides a nonperturbative resummation of secular terms from self-energy (loop) corrections to the inflaton fluctuations. In the case studied here these are Sudakov-type double logarithms which result in the decay of the power spectrum of inflaton fluctuations upon horizon crossing with a concomitant violation of scale invariance. The reduced density matrix and its quantum master equation furnish a powerful nonperturbative framework to study the effective field theory of long wavelength fluctuations by tracing short wavelength degrees of freedom.
B. A. Kashiwa; W. B. VanderHeyden
2000-12-01
A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.
Transport-level description of the sup 252 Cf-source method using the Langevin technique
Stolle, A.M.; Akcasu, A.Z. )
1991-01-01
The fluctuations in the neutron number density and detector outputs in a nuclear reactor can be analyzed conveniently by using the Langevin equation approach. This approach can be implemented at any level of approximation to describe the time evolution of the neutron population, from the most complete transport-level description to the very basic point reactor analysis of neutron number density fluctuations. In this summary, the complete space- and velocity-dependent transport-level formulation of the Langevin equation approach is applied to the analysis of the {sup 252}Cf-source-driven noise analysis (CSDNA) method, an experimental technique developed by J.T. Mihalczo at Oak Ridge National Laboratory, which makes use of noise analysis to determine the reactivity of subcritical media. From this analysis, a theoretical expression for the subcritical multiplication factor is obtained that can then be used to interpret the experimental data. Results at the transport level are in complete agreement with an independent derivation performed by Sutton and Doub, who used the probability density method to interpret the CSDNA experiment, but differed from other expressions that have appeared in the literature.
NASA Astrophysics Data System (ADS)
Eslamizadeh, H.
2016-02-01
A stochastic approach based on one- and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity, fission probability, anisotropy of fission fragment angular distribution, fission cross section and the evaporation cross section for the compound nuclei 188Pt, 227Pa and 251Es in an intermediate range of excitation energies. The chaos weighted wall and window friction formula are used in the Langevin equations. The elongation parameter, c, is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis, K, considered as the second dimension in Langevin dynamical calculations. A constant dissipation coefficient of K, Î³K = 0.077(MeV zs)â€‘1/2, is used in two-dimensional calculations to reproduce the above mentioned experimental data. Comparison of the theoretical results of the pre-scission neutron multiplicity, fission probability, fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data. Furthermore, it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K, Î³K = 0.077(MeV zs)â€‘1/2, can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus 251Es. However, a larger value of Î³K = 0.250(MeV zs)â€‘1/2 is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus 227Pa.
High-frequency Waves in Gravitational Theories with Fourth-order Derivative Equations
NASA Astrophysics Data System (ADS)
Borzeszkowski, H.-H. V.
For Einstein's gravitational equations with fourth-order corrections being proportional to the square of an elementary length l, we discuss the behaviour of high-frequency waves. It is shown that (1) only waves with lengths can generate a macroscopic avarage background (for < l, only the terms l2 are decisive such that one has the same situation as in a pure fourth-order theory without Einstein term which cannot be interpreted as gravitational theory), (2) for l the background metric is purely determined via the second-order derivative Einstein tensor (formally one obtains the same equations for the background as in the non-modified Einsteinian theory), and (3) only waves corresponding to the massless and the massive spin-two gravitons contribute to background curvature; in the geometrical-optics approximation, these both particle sorts are moving independent of each other and satisfy a conservation law for the total number of m = 0 and massive spin-two gravitons, respectively.The results obtained in this paper corroborate partly the conclusions drawn in the weak-field approximation [11, 15, 18].
PadÃ© Approximants for the Equation of State for Relativistic Hydrodynamics by Kinetic Theory
NASA Astrophysics Data System (ADS)
Tsai, Shang-Hsi; Yang, Jaw-Yen
2015-07-01
A two-point PadÃ© approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell-Boltzmann statistics and the semiclassical Fermi-Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
Coriani, Sonia; PawÅ‚owski, Filip; Olsen, Jeppe; JÃ¸rgensen, Poul
2016-01-14
Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent SchrÃ¶dinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent SchrÃ¶dinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions-from which the EOM-CC expressions are derived-are determined using projection and not using the variational principle. In a previous article [F. PawÅ‚owski, J. Olsen, and P. JÃ¸rgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations. PMID:26772549
NASA Astrophysics Data System (ADS)
Coriani, Sonia; Paw?owski, Filip; Olsen, Jeppe; Jørgensen, Poul
2016-01-01
Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions—from which the EOM-CC expressions are derived—are determined using projection and not using the variational principle. In a previous article [F. Paw?owski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.
Advances in numerical solutions to integral equations in liquid state theory
NASA Astrophysics Data System (ADS)
Howard, Jesse J.
Solvent effects play a vital role in the accurate description of the free energy profile for solution phase chemical and structural processes. The inclusion of solvent effects in any meaningful theoretical model however, has proven to be a formidable task. Generally, methods involving Poisson-Boltzmann (PB) theory and molecular dynamic (MD) simulations are used, but they either fail to accurately describe the solvent effects or require an exhaustive computation effort to overcome sampling problems. An alternative to these methods are the integral equations (IEs) of liquid state theory which have become more widely applicable due to recent advancements in the theory of interaction site fluids and the numerical methods to solve the equations. In this work a new numerical method is developed based on a Newton-type scheme coupled with Picard/MDIIS routines. To extend the range of these numerical methods to large-scale data systems, the size of the Jacobian is reduced using basis functions, and the Newton steps are calculated using a GMRes solver. The method is then applied to calculate solutions to the 3D reference interaction site model (RISM) IEs of statistical mechanics, which are derived from first principles, for a solute model of a pair of parallel graphene plates at various separations in pure water. The 3D IEs are then extended to electrostatic models using an exact treatment of the long-range Coulomb interactions for negatively charged walls and DNA duplexes in aqueous electrolyte solutions to calculate the density profiles and solution thermodynamics. It is found that the 3D-IEs provide a qualitative description of the density distributions of the solvent species when compared to MD results, but at a much reduced computational effort in comparison to MD simulations. The thermodynamics of the solvated systems are also qualitatively reproduced by the IE results. The findings of this work show the IEs to be a valuable tool for the study and prediction of solution phase phenomena and that such a theory can be effectively used to study complicated processes such as protein folding or protein-ligand binding strengths which depend on solvation effects.
Stochastic quantization of the Chern-Simons theory
Cugliandolo, L.F. ); Rossini, G.L.; Schaposnik, F.A. )
1992-11-15
The authors discuss stochastic quantization of d = 3 dimensional non-Abelian Chern-Simons theory. They demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the correct propagator. They also analyze the connection between d = 3 Chern-Simons and d = 4 topological Yang-Mills theories, showing the equivalence between the corresponding regularized partition functions. Finally, they discuss the introduction of a non-trivial kernel as an alternative regularization. 29 refs., 2 figs., 1 tab.
Fierz-Pauli equation for massive gravitons from Induced Matter theory of gravity
NASA Astrophysics Data System (ADS)
Bellini, Mauricio
2011-01-01
Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on a 4D curved spacetime which has the form of a Fierz-Pauli one. In our model the mass of gravitons mg is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz-Pauli one.
Elementary solutions of coupled model equations in the kinetic theory of gases
NASA Technical Reports Server (NTRS)
Kriese, J. T.; Siewert, C. E.; Chang, T. S.
1974-01-01
The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.
Solution of the one-dimensional consolidation theory equation with a pseudospectral method
Sepulveda, N.
1991-01-01
The one-dimensional consolidation theory equation is solved for an aquifer system using a pseudospectral method. The spatial derivatives are computed using Fast Fourier Transforms and the time derivative is solved using a fourth-order Runge-Kutta scheme. The computer model calculates compaction based on the void ratio changes accumulated during the simulated periods of time. Compactions and expansions resulting from groundwater withdrawals and recharges are simulated for two observation wells in Santa Clara Valley and two in San Joaquin Valley, California. Field data previously published are used to obtain mean values for the soil grain density and the compression index and to generate depth-dependent profiles for hydraulic conductivity and initial void ratio. The water-level plots for the wells studied were digitized and used to obtain the time dependent profiles of effective stress.
Wide range equation of state for fluid hydrogen from density functional theory
NASA Astrophysics Data System (ADS)
Wang, Cong; Zhang, Ping
2013-09-01
Wide range equation of state (EOS) for liquid hydrogen is ultimately obtained by combining two kinds of density functional theory (DFT) molecular dynamics simulations, namely, first-principles molecular dynamics simulations and orbital-free molecular dynamics simulations. Specially, the present introduction of short cutoff radius pseudopotentials enables the EOS to be available in the range from 9.82 Ã— 10-4 to 1.347 Ã— 103 g/cm3 and up to 5 Ã— 107 K. By comprehensively comparing with various attainable experimental and theoretical data, we derive the conclusion that our DFT-EOS can be readily and reliably applied to hydrodynamic simulations of the inertial confinement fusion.
Diffusion in the special theory of relativity.
Herrmann, Joachim
2009-11-01
The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the JÃ¼ttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion. PMID:20364950
NASA Astrophysics Data System (ADS)
Nakayama, A.; Sano, Y.; Yoshikawa, K.
2010-08-01
A general three-dimensional bioheat equation for local tissue heat transfer has been derived with less assumptions, exploiting a volume averaging theory commonly used in fluid-saturated porous media. The volume averaged energy equations obtained for the arterial blood, venous blood and tissue were combined together to form a single energy equation in terms of the tissue temperature alone. The resulting energy equation turns out to be remarkably simple as we define the effective thermal conductivity tensor, which accounts not only for the countercurrent heat exchange mechanism but also for the thermal dispersion mechanism. The present equation for local tissue heat transfer naturally reduces to the Weinbaum-Jiji equation for the unidirectional case.
Improved Langevin Approach to Spinodal Decomposition in the Chiral Transition
Fraga, Eduardo S.; Krein, Gastao; Ramos, Rudnei O.
2006-02-11
We use an improved Langevin description that incorporates both additive and multiplicative noise terms to study the dynamics of phase ordering. We perform real-time lattice simulations to investigate the role played by different contributions to the dissipation and noise. Lattice-size independence is assured by the use of appropriate lattice counterterms.
Complex Langevin method: When can it be trusted?
Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu
2010-03-01
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.
Pelinovsky, D. E.; Stefanov, A.
2008-11-15
Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, H{phi}=(-{delta}+V){phi}=-({phi}{sub n+1}+{phi}{sub n-1}-2{phi}{sub n})+V{sub n}{phi}{sub n}. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sub {sigma}{sup 2}}{yields}{sub l-{sigma}{sup 2}}} < or approx. t{sup -3/2} for any fixed {sigma}>(5/2) and any t>0, where P{sub a.c.}(H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sup 1}{yields}{sub l{sup {infinity}}}} < or approx. t{sup -1/3}, which are sharp for the discrete Schroedinger operators even for V=0.
Boozer, Allen H.
2015-03-15
The plasma current in ITER cannot be allowed to transfer from thermal to relativistic electron carriers. The potential for damage is too great. Before the final design is chosen for the mitigation system to prevent such a transfer, it is important that the parameters that control the physics be understood. Equations that determine these parameters and their characteristic values are derived. The mitigation benefits of the injection of impurities with the highest possible atomic number Z and the slowing plasma cooling during halo current mitigation to â‰³40â€‰ms in ITER are discussed. The highest possible Z increases the poloidal flux consumption required for each e-fold in the number of relativistic electrons and reduces the number of high energy seed electrons from which exponentiation builds. Slow cooling of the plasma during halo current mitigation also reduces the electron seed. Existing experiments could test physics elements required for mitigation but cannot carry out an integrated demonstration. ITER itself cannot carry out an integrated demonstration without excessive danger of damage unless the probability of successful mitigation is extremely high. The probability of success depends on the reliability of the theory. Equations required for a reliable Monte Carlo simulation are derived.
On the question of current conservation for the two-body Dirac equations of constraint theory
NASA Astrophysics Data System (ADS)
Lienert, Matthias
2015-08-01
The two-body Dirac (2BD) equations of constraint theory are of special interest not only in view of applications for phenomenological calculations of mesonic spectra but also because they avoid no-go theorems about relativistic interactions. Furthermore, they provide a quantum mechanical description in a manifestly Lorentz invariant way using the concept of a multi-time wave function. In this paper, we place them into the context of the multi-time formalism of Dirac, Tomonaga and Schwinger for the first time. A general physical and mathematical framework is outlined and the mechanism which permits relativistic interaction is identified. The main requirement derived from the general framework is the existence of conserved tensor currents with a positive component which can play the role of a probability density. We analyze this question for a general class of 2BD equations thoroughly and comprehensively. While the free Dirac current is not conserved, it is possible to find replacements. Improving on previous research, we achieve definite conclusions whether restrictions of the function space or of the interaction terms can guarantee the positive definiteness of the currents—and whether such restrictions are physically adequate. The consequences of the results are drawn, with respect to both applied and foundational perspectives.
The Bloch equations in high-gradient magnetic resonance force microscopy: theory and experiment.
Dougherty, W M; Bruland, K J; Chao, S H; Garbini, J L; Jensen, S E; Sidles, J A
2000-03-01
We report theory and observations of paramagnetic resonance in a measured field gradient of 44,000 T per meter by the technique of magnetic resonance force microscopy (MRFM). Resonance was induced in a dilute solid solution of diphenylpicrylhydrazyl in polystyrene at 77 and 10 K by an amplitude-modulated microwave field. This modulated the force between resonant sample spins and a micrometer-scale SmCo magnetic tip on a force microscope cantilever. The force signals were typically of order 10 fN, and were detected above a thermal noise floor of 80 aN per root hertz at 10 K, equivalent to a magnetic moment noise of 200 micro(B) per root hertz of bandwidth. Resonance saturation was readily observed. Starting with the Bloch equations, we derived simple analytic expressions for the predicted cantilever signal amplitudes and T(1)-dependent phase lags, valid at low microwave power levels. For power levels below saturation, the data were in good agreement with the Bloch equation predictions, while above saturation the measured force increased more slowly with power than predicted. Several ESR mechanisms which might lead to non-Bloch dynamics in the MRFM environment are reviewed. Spin-relaxation mechanisms are also reviewed. A detailed description of the experimental apparatus is offered. PMID:10698652
Scattering theory for the defocusing fourth-order SchrÃ¶dinger equation
NASA Astrophysics Data System (ADS)
Miao, Changxing; Zheng, Jiqiang
2016-02-01
In this paper, we study the global well-posedness and scattering theory for the defocusing fourth-order nonlinear SchrÃ¶dinger equation (FNLS) \\text{i}{{u}t}+{{Î” }2}u +\\mid u{{\\mid}p}u=0 in dimensions dâ‰¥slant 8 . We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, u\\in Ltâˆžâ‰¤ft(I;\\overset{\\centerdot}{\\mathop{H}} x{{sc}}â‰¤ft({{{R}}d}\\right)\\right) with all {{s}c}:=\\frac{d}{2}-\\frac{4}{p}â‰¥slant 1 if p is an even integer or {{s}c}\\in â‰¤ft[1,2+p\\right) otherwise, then u is global and scatters. We will give a uniform way to treat the energy-subcritical, energy-critical and energy-supercritical FNLS by making use of the strategy derived from concentration compactness ideas, and we are able to overcome the logarithmic blowup in the double Duhamel trick in dimension eight by exploiting the refined dispersive estimate which is in sharp contrast to the SchrÃ¶dinger equation.
NASA Astrophysics Data System (ADS)
Godtliebsen, Ian H.; Hansen, Mads Bøttger; Christiansen, Ove
2015-01-01
We show how the eigenvalue equations of vibrational coupled cluster response theory can be solved using a subspace projection method with Davidson update, where basis vectors are stacked tensors decomposed into canonical (CP, Candecomp/Parafac) form. In each update step, new vectors are first orthogonalized to old vectors, followed by a tensor decomposition to a prescribed threshold TCP. The algorithm can provide excitation energies and eigenvectors of similar accuracy as a full vector approach and with only a very modest increase in the number of vectors required for convergence. The algorithm is illustrated with sample calculations for formaldehyde, 1,2,5-thiadiazole, and water. Analysis of the formaldehyde and thiadiazole calculations illustrate a number of interesting features of the algorithm. For example, the tensor decomposition threshold is optimally put to rather loose values, such as TCP = 10-2. With such thresholds for the tensor decompositions, the original eigenvalue equations can still be solved accurately. It is thus possible to directly calculate vibrational wave functions in tensor decomposed format.
NASA Astrophysics Data System (ADS)
Matsumoto, Takeshi; Otsuki, Michio; Takeshi, Ooshida; Goto, Susumu; Nakahara, Akio
2014-06-01
For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005), 10.1103/PhysRevLett.95.130602]. We verify numerically for the shell-model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.
NASA Astrophysics Data System (ADS)
Lathiotakis, Nektarios N.; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I.
2014-09-01
We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.
NASA Technical Reports Server (NTRS)
Majda, G.
1985-01-01
A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.
Tu, Fei-Quan; Chen, Yi-Xin E-mail: yxchen@zimp.zju.edu.cn
2013-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed HoÅ™ava-Lifshitz(HL) theory.
Applications of Path Integral Langevin Dynamics to Weakly Bound Clusters and Biological Molecules
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Conrad; Yang, Jing; Roy, Pierre-Nicholas
2011-06-01
We present the use of path integral molecular dynamics (PIMD) in conjunction with the path integral Langevin equation thermostat for sampling systems that exhibit nuclear quantum effects, notably those at low temperatures or those consisting mainly of hydrogen or helium. To test this approach, the internal energy of doped helium clusters are compared with white-noise Langevin thermostatting and high precision path integral monte carlo (PIMC) simulations. We comment on the structural evolution of these clusters in the absence of rotation and exchange as a function of cluster size. To quantify the importance of both rotation and exchange in our PIMD simulation, we compute band origin shifts for (He)_N-CO_2 as a function of cluster size and compare to previously published experimental and theoretical shifts. A convergence study is presented to confirm the systematic error reduction introduced by increasing path integral beads for our implementation in the Molecular Modelling Toolkit (MMTK) software package. Applications to carbohydrates are explored at biological temperatures by calculating both equilibrium and dynamical properties using the methods presented. M. Ceriotti, M. Parrinello, and D. E. Manolopoulos, J Chem Phys 133, 124104. H. Li, N. Blinov, P.-N. Roy, and R. J. L. Roy, J Chem Phys 130, 144305.
Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems
Ratynskaia, S.; Regnoli, G.; Rypdal, K.; Klumov, B.; Morfill, G.
2009-10-15
Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on ''soft'' quasi-two-dimensional dusty plasma clusters. Our model does not contain external drive or plasma interactions that serve to drive the system away from thermodynamic equilibrium. The grains are confined by an external potential, interact via static Yukawa forces, and are subject to stochastic heating and dissipation from neutrals. One remarkable feature is emergence of leptokurtic probability distributions of grain displacements {xi}({tau}) on time scales {tau}<{tau}{sub {delta}}, where {tau}{sub {delta}} is the time at which the standard deviation {sigma}({tau}){identical_to}<{xi}{sup 2}({tau})>{sup 1/2} approaches the mean intergrain distance {delta}. Others are development of humps in the distributions on multiples of {delta}, anomalous Hurst exponents, and transitions from leptokurtic toward Gaussian displacement distributions on time scales {tau}>{tau}{sub {delta}}. The latter is a signature of intermittency, here interpreted as a transition from bursty transport associated with hopping on intermediate time scales to vortical flows on longer time scales. These intermittency features are quantitatively modeled by a single-particle Ito-Langevin stochastic equation with a nonlinear drift term.
NASA Astrophysics Data System (ADS)
Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.
2015-11-01
In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-02-28
The free-complement (FC) method is a general method for solving the Schrödinger equation (SE): The produced wave function has the potentially exact structure as the solution of the Schrödinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local Schrödinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local Schrödinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H(T)Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hooke's atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the world's most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the Schrödinger equation of general atoms and molecules. PMID:25725722
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Ross, John
2002-12-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.
ERIC Educational Resources Information Center
Ryan, Joseph; Brockmann, Frank
2009-01-01
Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…
NASA Astrophysics Data System (ADS)
Martynov, N. I.
2014-11-01
Boundary value problems in the plane moment and simplified moment elasticity theory of inhomogeneous isotropic media are reduced to Riemann-Hilbert boundary value problems for a quasianalytic vector. Uniquely solvable integral equations over a domain are derived. As a result, weak solutions for composite inhomogeneous elastic media can be determined straightforwardly.
ERIC Educational Resources Information Center
van den Putte, Bas; Hoogstraten, Johan
1997-01-01
Problems found in the application of structural equation modeling to the theory of reasoned action are explored, and an alternative model specification is proposed that improves the fit of the data while leaving intact the structural part of the model being tested. Problems and the proposed alternative are illustrated. (SLD)
ERIC Educational Resources Information Center
Glockner-Rist, Angelika; Hoijtink, Herbert
2003-01-01
Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problems…
ERIC Educational Resources Information Center
Glockner-Rist, Angelika; Hoijtink, Herbert
2003-01-01
Both structural equation modeling (SEM) and item response theory (IRT) can be used for factor analysis of dichotomous item responses. In this case, the measurement models of both approaches are formally equivalent. They were refined within and across different disciplines, and make complementary contributions to central measurement problemsâ€¦
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
Gambetta, Jay; Wiseman, H.M.
2003-12-01
Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.
Loop Variables and Gauge Invariant Exact Renormalization Group Equations for Closed String Theory
NASA Astrophysics Data System (ADS)
Sathiapalan, B.
2013-09-01
We formulate the Exact Renormalization Group on the string worldsheet for closed string backgrounds. The same techniques that were used for open strings are used here. There are some subtleties. One is that holomorphic factorization of the closed string vertex operators does not hold in the presence of a cutoff on the Euclidean worldsheet. This introduces extra terms in the Lagrangian at the cutoff scale and they turn out to be crucial for implementing gauge invariance. This naive generalization from open string to closed string requires a massive graviton and the gauge symmetry is Abelian, just as in open string theory. Interestingly, it turns out that if one introduces a nondynamical background metric (as in background field formalism) and combines a gauge transformation on the field with a transformation on the coordinates and background metric, the graviton can be massless. Some examples of background coordinate covariant equations are worked out explicitly. A preliminary discussion of massive modes, massive gauge transformations and the role of worldsheet regulator terms is given. Some of the gauge transformations can be given a geometric meaning if space-time is assumed to be complex at some level.
Energy dissipation and fluctuation response in driven quantum Langevin dynamics
NASA Astrophysics Data System (ADS)
Saito, Keiji
2008-09-01
Energy dissipation in a nonequilibrium steady state is studied in driven quantum Langevin systems. We study energy dissipation flow to thermal environment, and obtain a general formula for the average rate of energy dissipation using an autocorrelation function for the system variable. This leads to a general expression of the equality that connects the violation of the fluctuation-response relation to the rate of energy dissipation, the classical version of which was first studied by Harada and Sasa.
Multinomial diffusion equation
Balter, Ariel I.; Tartakovsky, Alexandre M.
2011-06-24
We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N {yields} {infinity}, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
Quantum non-Markovian Langevin formalism for heavy ion reactions near the Coulomb barrier
Sargsyan, V. V.; Antonenko, N. V.; Kanokov, Z.; Adamian, G. G.
2008-02-15
The generalized Langevin approach is suggested to describe the capture inside of the Coulomb barrier of two heavy nuclei at bombarding energies near the barrier. The equations of motion for the relative distance (collective coordinate) between two interacting nuclei are consistent with the generalized quantum fluctuation-dissipation relations. The analytical expressions are derived for the time-dependent non-Markovian microscopic transport coefficients for the stable and unstable collective modes. The calculated results show that the quantum effects in the diffusion process increase with increasing friction or/and decreasing temperature. The capture probability inside of the Coulomb barrier is enhanced by the quantum noise at low energies near the barrier. An increase of the passing probability with dissipation is found at sub-barrier energies.
Heavy-quark Langevin dynamics and single-electron spectra in nucleus-nucleus collisions
NASA Astrophysics Data System (ADS)
Beraudo, A.; Alberico, W. M.; De Pace, A.; Molinari, A.; Monteno, M.; Nardi, M.; Prino, F.
2011-01-01
The stochastic dynamics of heavy quarks in the fireball produced in heavy-ion collisions is followed through numerical simulations based on the Langevin equation. The modification of the final pT spectra (RAA) of c and b quarks, hadrons and single-electrons with respect to pp collisions is studied. The transport coefficients are evaluated treating separately the contribution of soft and hard collisions. The initial heavy-quark spectra are generated according to NLO-pQCD, accounting for nuclear effects through recent nPDFs. The evolution of the medium is obtained from the output of two hydro-codes (ideal and viscous). The heavy-quark fragmentation into hadrons and their final semileptonic decays are implemented according to up-to-date experimental data. A comparison with RHIC data for non-photonic electron spectra is given.
SELF-CONSISTENT LANGEVIN SIMULATION OF COULOMB COLLISIONS IN CHARGED-PARTICLE BEAMS
J. QIANG; R. RYNE; S. HABIB
2000-05-01
In many plasma physics and charged-particle beam dynamics problems, Coulomb collisions are modeled by a Fokker-Planck equation. In order to incorporate these collisions, we present a three-dimensional parallel Langevin simulation method using a Particle-In-Cell (PIC) approach implemented on high-performance parallel computers. We perform, for the first time, a fully self-consistent simulation, in which the friction and diffusion coefficients are computed from first principles. We employ a two-dimensional domain decomposition approach within a message passing programming paradigm along with dynamic load balancing. Object oriented programming is used to encapsulate details of the communication syntax as well as to enhance reusability and extensibility. Performance tests on the SGI Origin 2000 and the Cray T3E-900 have demonstrated good scalability. Work is in progress to apply our technique to intrabeam scattering in accelerators.
New insights into the problem with a singular drift term in the complex Langevin method
NASA Astrophysics Data System (ADS)
Nishimura, Jun; Shimasaki, Shinji
2015-07-01
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur, in general, when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works, although the standard reweighting method is hardly applicable.
Watson, P.; Reinhardt, H.
2007-02-15
Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance--invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green's functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.
Nakatsuji, Hiroshi Nakashima, Hiroyuki
2015-02-28
The free-complement (FC) method is a general method for solving the SchrÃ¶dinger equation (SE): The produced wave function has the potentially exact structure as the solution of the SchrÃ¶dinger equation. The variables included are determined either by using the variational principle (FC-VP) or by imposing the local SchrÃ¶dinger equations (FC-LSE) at the chosen set of the sampling points. The latter method, referred to as the local SchrÃ¶dinger equation (LSE) method, is integral-free and therefore applicable to any atom and molecule. The purpose of this paper is to formulate the basic theories of the LSE method and explain their basic features. First, we formulate three variants of the LSE method, the AB, HS, and H{sup T}Q methods, and explain their properties. Then, the natures of the LSE methods are clarified in some detail using the simple examples of the hydrogen atom and the Hookeâ€™s atom. Finally, the ideas obtained in this study are applied to solving the SE of the helium atom highly accurately with the FC-LSE method. The results are very encouraging: we could get the worldâ€™s most accurate energy of the helium atom within the sampling-type methodologies, which is comparable to those obtained with the FC-VP method. Thus, the FC-LSE method is an easy and yet a powerful integral-free method for solving the SchrÃ¶dinger equation of general atoms and molecules.
Langevin Formalism as the Basis for the Unification of Population Dynamics
NASA Astrophysics Data System (ADS)
de Vladar, Harold P.
2005-03-01
We are presenting a simple reformulation to population dynamics that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. The model shows that even when a population is density-dependent the dynamics of its growth rate does not depend explicitly neither on population size nor on the carrying capacity. Actually, the growth rate is uncoupled from the population size equation. The model has only two parameters: a Malthusian parameter ? and an interaction coefficient ?. Distinct values of these parameters reproduce the family of ?-logistics, the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. Stochastic perturbations to the Malthusian parameter leads to a Langevin form of stochastic differential equation consisting of a family of cubic potentials perturbed with multiplicative noise. Using these equtions, we derive the stationary Fokker Plank distribution which which shows that in the stationary dynamics, density dependent populations fluctuate around a mean size that is shifted from the carrying capacity proportionally to the noise intensity. We also study which kinds of populations are susceptible to noise induced transitions.
NASA Astrophysics Data System (ADS)
Bauke, F. C.; Lagos, R. E.
2014-01-01
We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with the experimental results.
Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
NASA Astrophysics Data System (ADS)
Zhdanov, V. M.; Stepanenko, A. A.
2016-03-01
In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.
On a generalized basis for solving the one dimensional transport equation: Theory
NASA Astrophysics Data System (ADS)
Ayyoubzadeh, Seyed Mohsen; Vosoughi, Naser
2012-03-01
The most general basis for approximating the transport equation has been studied. The application of the Gram-Schmidt procedure has been shown to unify the complete class of functions (polynomial type or non-polynomial type), applicable to this equation. The completeness of the series of functions is proved. A generalized version of the Fick's law is introduced. It is shown that the spectrum of the transport equation obtained by this method agrees with the conventional methods of obtaining the spectrum.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano
2014-03-07
Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.
Giacometti, Achille; GÃ¶gelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano; Pastore, Giorgio
2014-03-01
Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function. PMID:24606350
Can Malin's gravitational-field equations be modified to obtain a viable theory of gravity
NASA Technical Reports Server (NTRS)
Smalley, L. L.; Prestage, J.
1976-01-01
Malin's (1975) gravitational theory, which was recently shown by Lindblom and Nester (1975) to be incorrect, is modified by means of a recently proposed method for obtaining viable gravitational theories. The resulting self-consistent theory, which is in effect a Rastall-type modification of the Einstein theory, exhibits nonconservation of momentum, yet agrees with all experimental limits known to date within the post-Newtonian approximation framework.
Galvao, C.A.; Nutku, Y.
1996-12-01
mA third order Monge-Amp{grave e}re type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac{close_quote}s theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of Kac-Moody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. {copyright} {ital 1996 American Institute of Physics.}
An Investigation of Factors Affecting Test Equating in Latent Trait Theory.
ERIC Educational Resources Information Center
Sunathong, Surintorn; Schumacker, Randall E.; Beyerlein, Michael M.
2000-01-01
Studied five factors that can affect the equating of scores from two tests onto a common score scale through the simulation and equating of 4,860 item data sets. Findings indicate three statistically significant two-way interactions for common item length and test length, item difficulty standard deviation and item distribution type, and item…
Impact of Accumulated Error on Item Response Theory Pre-Equating with Mixed Format Tests
ERIC Educational Resources Information Center
Keller, Lisa A.; Keller, Robert; Cook, Robert J.; Colvin, Kimberly F.
2016-01-01
The equating of tests is an essential process in high-stakes, large-scale testing conducted over multiple forms or administrations. By adjusting for differences in difficulty and placing scores from different administrations of a test on a common scale, equating allows scores from these different forms and administrations to be directly compared…
Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice
ERIC Educational Resources Information Center
Koutsoyiannis, Demetris
2012-01-01
While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is this…
Clausius-Clapeyron Equation and Saturation Vapour Pressure: Simple Theory Reconciled with Practice
ERIC Educational Resources Information Center
Koutsoyiannis, Demetris
2012-01-01
While the Clausius-Clapeyron equation is very important as it determines the saturation vapour pressure, in practice it is replaced by empirical, typically Magnus-type, equations which are more accurate. It is shown that the reduced accuracy reflects an inconsistent assumption that the latent heat of vaporization is constant. Not only is thisâ€¦
An electric-analog simulation of elliptic partial differential equations using finite element theory
Franke, O.L.; Pinder, G.F.; Patten, E.P.
1982-01-01
Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.
NASA Technical Reports Server (NTRS)
Cheng, H. K.; Wong, Eric Y.; Dogra, V. K.
1991-01-01
Grad's thirteen-moment equations are applied to the flow behind a bow shock under the formalism of a thin shock layer. Comparison of this version of the theory with Direct Simulation Monte Carlo calculations of flows about a flat plate at finite attack angle has lent support to the approach as a useful extension of the continuum model for studying translational nonequilibrium in the shock layer. This paper reassesses the physical basis and limitations of the development with additional calculations and comparisons. The streamline correlation principle, which allows transformation of the 13-moment based system to one based on the Navier-Stokes equations, is extended to a three-dimensional formulation. The development yields a strip theory for planar lifting surfaces at finite incidences. Examples reveal that the lift-to-drag ratio is little influenced by planform geometry and varies with altitudes according to a 'bridging function' determined by correlated two-dimensional calculations.
Theory of the dynamic Biot-Allard equations and their link to the quasi-static Biot system
NASA Astrophysics Data System (ADS)
Mikeli?, Andro; Wheeler, Mary F.
2012-12-01
We undertake establishing well-posedness of the dynamic Biot-Allard equations. It is obtained using the precise properties of the dynamic permeability matrix following the homogenization derivation of the model. By taking the singular limit of the contrast coefficient, the quasi-static Biot system can be obtained from the dynamic Biot equations. These results can be used to formulate an efficient computational algorithm for solving dynamic Biot-Allard equations for subsurface flows with the characteristic reservoir time scales larger than the intrinsical characteristic time. This result appears to be completely new in the literature on Biot's theory. We conclude by showing that in the case of periodic deformable porous media the dynamic permeability has the required properties.
Langevin analysis of fission excitation functions induced by protons
NASA Astrophysics Data System (ADS)
Tian, Jian; Wang, Ning; Ye, Wei
2015-03-01
The stochastic Langevin approach to fission is applied to analyze fission excitation functions measured in p+206Pb and p+209Bi systems. A presaddle friction strength of (3-5) × 1021 s-1 is extracted by comparing theoretical predictions with experimental data. Furthermore, the small distortion of the formed compound nuclei with respect to the spherical shape under the condition of low angular momentum suggests that experimentally, populating an excited compound system via light-ion induced reactions favors a more accurate determination of presaddle friction with a fission cross section. Supported by National Nature Science Foundation of China (11075034)
Du Kai Qiu, Jinniao Tang Shanjian
2012-04-15
This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.
A kinetic-theory approach to turbulent chemically reacting flows
NASA Technical Reports Server (NTRS)
Chung, P. M.
1976-01-01
The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.
Study on Langevin model parameters of velocity in turbulent shear flows
NASA Astrophysics Data System (ADS)
Tanière, Anne; Arcen, Boris; Oesterlé, Benoît; Pozorski, Jacek
2010-11-01
This paper deals with the stochastic equation used to predict the fluctuating velocity of a fluid particle in a nonhomogeneous turbulent flow, in the frame of probability density function (PDF) approaches. It is shown that a Langevin-type equation is appropriate provided its parameters (drift and diffusion matrices) are suitably specified. By following the approach proposed in the literature for homogeneous turbulent shear flows, these parameters have been identified using data from direct numerical simulations (DNS) of both channel and pipe flows. Using statistics extracted from the computation of the channel flow, it is shown that the drift matrix of the stochastic differential equation can reasonably be assumed to be diagonal but not spherical. This behavior of the drift coefficients is confirmed by the available results for a turbulent pipe flow at low Reynolds number. Concerning the diffusion matrix, it is found that this matrix is anisotropic for low Reynolds number flows, a property which has been observed earlier for a homogeneous turbulent shear flow. The pertinence of the present estimation of the drift and diffusion tensors is assessed through different kinds of tests including the incorporation of these parameters in a purely Lagrangian, or stand-alone, PDF computation.
Híjar, Humberto
2015-02-01
We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490
Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Zhou, Ye
1996-01-01
Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.
NASA Astrophysics Data System (ADS)
Chen, Gui-Qiang; Glimm, James
2012-02-01
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in {mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the ? th -order fractional derivatives of the velocity for some ? > 0 in the space variables in L 2, which is independent of the viscosity ? > 0. Then it is shown that this key observation yields the L 2-equicontinuity in the time variable and the uniform bound in L q , for some q > 2, of the velocity independent of ? > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations in {mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of ? > 0, that is in the high Reynolds number limit.
NASA Astrophysics Data System (ADS)
Thomas, Philipp; Straube, Arthur V.; Grima, Ramon
2010-11-01
Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.
Dynamics of essential collective motions in proteins: Theory
NASA Astrophysics Data System (ADS)
Stepanova, Maria
2007-11-01
A general theoretical background is introduced for characterization of conformational motions in protein molecules, and for building reduced coarse-grained models of proteins, based on the statistical analysis of their phase trajectories. Using the projection operator technique, a system of coupled generalized Langevin equations is derived for essential collective coordinates, which are generated by principal component analysis of molecular dynamic trajectories. The number of essential degrees of freedom is not limited in the theory. An explicit analytic relation is established between the generalized Langevin equation for essential collective coordinates and that for the all-atom phase trajectory projected onto the subspace of essential collective degrees of freedom. The theory introduced is applied to identify correlated dynamic domains in a macromolecule and to construct coarse-grained models representing the conformational motions in a protein through a few interacting domains embedded in a dissipative medium. A rigorous theoretical background is provided for identification of dynamic correlated domains in a macromolecule. Examples of domain identification in protein G are given and employed to interpret NMR experiments. Challenges and potential outcomes of the theory are discussed.
NASA Astrophysics Data System (ADS)
Jiuxun, Sun; Lingcang, Cai; Qiang, Wu; Fuqian, Jing
2003-08-01
An analytic expression of radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state (EOS). The comparison with the Monte-Carlo data and the Percus-Yevick expression shows that the expression developed gives out better results. The expression is very simple that can make most perturbation theories become analytic ones, and a simple analytic EOS for the fluids with continuous exponential-six potential is established based on the Ross variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original non-analytic theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one.
Nakatsuji, Hiroshi Nakashima, Hiroyuki
2015-05-21
The SchrÃ¶dinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, â€œelectronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.â€ Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.
Hahn, Y.K.
2014-12-15
The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the continuum HF and its improvements.
A new method of deriving electrical double layer equations from electrolyte theories
NASA Astrophysics Data System (ADS)
Lozada-Cassou, Marcelo
1981-08-01
By assuming that one of the species of a liquid mixture is made of charged, planar walls of infinite extension such that its concentration tends to zero (here called the direct method), an electrical double layer theory is obtained from the Kirkwood and Poirier theory for ionic solutions. It is shown that this double layer theory is equivalent to the theory of Stillinger and Kirkwood. Another electrical double layer theory is obtained from the Kirkwood and Poirier theory by taking the limits of infinite radius and zero concentration in one of the species of a liquid mixture (here called the asymptotic method). It is shown that this theory is also equivalent to the Stillinger and Kirkwood theory and therefore the direct and the asymptotic methods are equivalent. This happens also when the hypernetted chain and mean spherical approximations are considered. Finally, the electrostatic interaction potential between a charged plate and an ion is discussed in view of its importance in the application of the direct and asymptotic methods.
Unexpected Applications of Hill's Differential Equations in Quantum Field Theory and Cosmology
NASA Astrophysics Data System (ADS)
Mostepanenko, V. M.
The effect of the exponential pair creation from vacuum by the external field periodic in time is discussed. Two prospective applications of this physical effect in quantum field theory and in inflationary cosmology are considered. Being a nontrivial example of a parametric resonance, the effect of exponential pair creation may serve as an illustration of the effectiveness of mathematics in physical theory.
One-dimensional transport equation models for sound energy propagation in long spaces: theory.
Jing, Yun; Larsen, Edward W; Xiang, Ning
2010-04-01
In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency. PMID:20370013
Equation-of-state spinning fluids in the Einstein-Cartan theory
NASA Technical Reports Server (NTRS)
Ray, John R.; Smalley, Larry L.
1987-01-01
The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.
Equations of motion and conservation laws in a theory of stably stratified turbulence
NASA Astrophysics Data System (ADS)
L'vov, Victor S.; Rudenko, Oleksii
2008-12-01
This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.
Curro, John G.; Webb III, Edmund B.; Grest, Gary S.; Weinhold, Jeffrey D.; Putz, Mathias; McCoy, John D.
1999-07-21
Molecular dynamics (MD) simulations were performed on dense liquids of polyethylene chains of 24 and 66 united atom CH{sub 2} units. A series of models was studied ranging in atomistic detail from coarse-grained, freely-jointed, tangent site chains to realistic, overlapping site models subjected to bond angle restrictions and torsional potentials. These same models were also treated with the self-consistent, polymer reference interaction site model (PRISM) theory. The intramolecular and total structure factors, as well as, the intermolecular radial distribution functions g(r) and direct correlation functions C(r) were obtained from theory and simulation. Angular correlation functions were also simulation obtained from the MD simulations. Comparisons between theory and reveal that PRISM theory works well for computing the intermolecular structure of coarse-grained chain models, but systematically underpredicts the extent of intermolecular packing as more atomistic details are introduced into the model. A consequence of g(r) having insufficient structure is that the theory yields an isothermal compressibility that progressively becomes larger, relative to the simulations, as overlapping the PRISM sites and angular restrictions are introduced into the model. We found that theory could be considerably improved by adding a tail function to C(r) beyond the effective hard core diameter. The range of this tail function was determined by requiring the theory to yield the correct compressibility.
Iyer, Ramakrishnan; Mukhopadhyay, Ayan
2010-04-15
The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.
The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method
NASA Technical Reports Server (NTRS)
Kittl, P.
1984-01-01
It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.
NASA Astrophysics Data System (ADS)
He, Zhuo-Ran; Wu, Tai-Lin; Ouyang, Qi; Tu, Yu-Hai
2012-09-01
Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its microscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively reproduces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.
Wu Shuangqing
2009-08-15
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Staeckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.
Hao, Tian
2015-02-28
The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process). PMID:25589375
NASA Astrophysics Data System (ADS)
Baskakov, Anatoly G.
2013-02-01
Many properties of solutions to linear differential equations with unbounded operator coefficients (their boundedness, almost periodicity, stability) are closely connected with the corresponding properties of the differential operator defining the equation and acting in an appropriate function space. The structure of the spectrum of this operator and whether it is invertible, correct, and Fredholm depend on the dimension of the kernel of the operator, the codimension of its range, and the existence of complemented subspaces. The notion of a state of a linear relation (multivalued linear operator) is introduced, and is associated with some properties of the kernel and range. A linear difference operator (difference relation) is assigned to the differential operator under consideration (or the corresponding equation), the sets of their states are proved to be the same, and necessary and sufficient conditions for them to have the Fredholm property are found. Criteria for the almost periodicity at infinity of solutions of differential equations are derived. In the proof of the main results, the property of exponential dichotomy of a family of evolution operators and the spectral theory of linear relations are heavily used. Bibliography: 98 titles.
An Evaluation of Three Approximate Item Response Theory Models for Equating Test Scores.
ERIC Educational Resources Information Center
Marco, Gary L.; And Others
Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…
Slyusarchuk, Vasilii E
2010-10-06
Conditions for the existence of solutions to the nonlinear functional-differential equation (d{sup m}x(t))/dt{sup m} + (fx)(t)=h(t), t element of R in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.
Equations of State of Elements Based on the Generalized Fermi-Thomas Theory
DOE R&D Accomplishments Database
Feynman, R. P.; Metropolis, N.; Teller, E.
1947-04-28
The Fermi-Thomas model has been used to derive the equation of state of matter at high pressures and at various temperatures. Calculations have been carried out both without and with the exchange terms. Discussion of similarity transformations lead to the virial theorem and to correlation of solutions for different Z-values.
Sjostrom, Travis; Crockett, Scott
2015-09-02
The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the Î±-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a newmoreÂ Â» liquid regime equation of state table for SiO2.Â«Â less
NASA Astrophysics Data System (ADS)
Sjostrom, Travis; Crockett, Scott
2015-09-01
The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 -15 g/cm 3 and with temperatures from 0.5 to 100 eV, including the ? -quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.
Sjostrom, Travis; Crockett, Scott
2015-09-02
The liquid regime equation of state of silicon dioxide SiO_{2} is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the Î±-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO_{2}.
Tanimura, Shogo )
1992-12-01
R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs.
Pernal, Katarzyna; Baerends, Evert Jan
2006-01-01
Starting from the variational equations for the natural occupation numbers and the recently proposed eigenequations for the natural spin-orbitals, we derive coupled-perturbed density-matrix equations that furnish a linear response of the one-electron reduced density matrix to a static perturbation when the total energy is a functional of the one-electron reduced density matrix. Cases when some occupation numbers achieve exactly 0 or 1 or when the total number of the particles in a system is not preserved are taken into consideration. The scheme is applied to computing static polarizabilities from two simple density-matrix functionals. The behavior of the functionals is erratic and they provide only little or no improvement over the coupled-perturbed Hartree-Fock results. PMID:16409019
Doktorov, Alexander B; Kipriyanov, Alexey A
2014-05-14
General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered. PMID:24832250
General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations
NASA Astrophysics Data System (ADS)
Doktorov, Alexander B.; Kipriyanov, Alexey A.
2014-05-01
General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.
General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations
Doktorov, Alexander B.; Kipriyanov, Alexey A.
2014-05-14
General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of “effective” particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.
Huš, Matej; Urbic, Tomaz; Munaò, Gianmarco
2014-10-28
Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.
Self-consistent rate equation theory of cluster size distribution in aggregation phenomena
NASA Astrophysics Data System (ADS)
Family, Fereydoon; Popescu, Mihail N.; Amar, Jacques G.
2002-04-01
Cluster nucleation and growth by aggregation is the central feature of many physical processes, from polymerization and gelation in polymer science, flocculation and coagulation in aerosol and colloidal chemistry, percolation and coarsening in phase transitions and critical phenomena, agglutination and cell adhesion in biology, to island nucleation and thin-film growth in materials science. Detailed information about the kinetics of aggregation is provided by the time dependent cluster size-distribution, a quantity which can be measured experimentally. While the standard Smoluchowski rate-equation approach has been in general successful in predicting average quantities like the total cluster density, it fails to account for spatial fluctuations and correlations and thus predicts size distributions that are in significant disagreement with both experiments and kinetic Monte Carlo simulations. In this work we outline a new method which takes into account such correlations. We show that by coupling a set of evolution equations for the capture-zone distributions with a set of rate-equations for the island densities one may obtain accurate predictions for the time- and size-dependent rates of monomer capture. In particular, by using this method we obtain excellent results for the capture numbers and island-size distributions in irreversible growth on both one- and two-dimensional substrates.
ERIC Educational Resources Information Center
von Davier, Alina A.; Wilson, Christine
2008-01-01
Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods thatâ€¦
ERIC Educational Resources Information Center
von Davier, Alina A.; Wilson, Christine
2008-01-01
Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that…
ERIC Educational Resources Information Center
Kosciulek, John F.
2005-01-01
One model that is potentially useful in the rehabilitation field is the Consumer-Directed Theory of Empowerment (CDTE; Kosciulek, 1999a). However, additional empirical data are needed to further develop and critically evaluate the CDTE. To accomplish this task, the purpose of this study was to test the hypothesized structural model CDTE in aâ€¦
Langevin dynamics simulation of polymer-assisted virus-like assembly
NASA Astrophysics Data System (ADS)
Mahalik, J. P.; Muthukumar, M.
2012-04-01
Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
NASA Astrophysics Data System (ADS)
Dutta, Achintya Kumar; Neese, Frank; IzsÃ¡k, RÃ³bert
2016-01-01
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm-1 (59 Î¼Hartree) for excitation energies and 6.799 cm-1 (31 Î¼Hartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation.
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2016-01-21
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel's test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm(-1) (59 ?Hartree) for excitation energies and 6.799 cm(-1) (31 ?Hartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core. PMID:26801015
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments. PMID:24229140
Jing, Yun; Xiang, Ning
2008-01-01
This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient [V. Valeau et al., J. Acoust. Soc. Am. 119, 1504-1513 (2006)] cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient [Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284-3287 (2007); A. Billon et al., Appl. Acoust. 69, (2008)] has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. PMID:18177146
Third order wave equation in Duffin-Kemmer-Petiau theory: Massive case
NASA Astrophysics Data System (ADS)
Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.
2015-11-01
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [1] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q -commutator (q is a primitive cubic root of unity) and a new set of matrices ?? instead of the original matrices ?? of the DKP algebra are introduced. It is shown that in terms of these ?? matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z ?q , where z is some complex deformation parameter entering into the definition of the ? -matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ? (x ;z ) is performed and it is shown that the solution is singular in the z ?q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Time-optimal path planning in dynamic flows using level set equations: theory and schemes
NASA Astrophysics Data System (ADS)
Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.
2014-10-01
We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.
Time-optimal path planning in dynamic flows using level set equations: theory and schemes
NASA Astrophysics Data System (ADS)
Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.
2014-09-01
We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.
Simplified Derivation of the Fokker-Planck Equation.
ERIC Educational Resources Information Center
Siegman, A. E.
1979-01-01
Presents an alternative derivation of the Fokker-Planck equation for the probability density of a random noise process, starting from the Langevin equation. The derivation makes use of the first two derivatives of the Dirac delta function. (Author/GA)
On the equation-of-motion versus in-in approach in cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Chen, Xingang; Namjoo, Mohammad Hossein; Wang, Yi
2016-01-01
In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the first-principle in-in formalism. We check this equivalence using several explicit examples, including cases with scale-invariant corrections and scale-dependent features. Motivated by the explicit proof, we show that the usual procedures in these approaches can be extended and applied to some interesting model categories beyond what has been studied in the literature so far. These include the density perturbations with strong couplings and correlated multi-field initial states.
Scattering theory for the radial H?1/2-critical wave equation with a cubic convolution
NASA Astrophysics Data System (ADS)
Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang
2015-12-01
In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ?t2 u - ?u = ± (| x | - 3 *| u | 2) u in dimensions d ? 4. We prove that if the radial solution u with life-span I obeys (u, ut) ? Lt? (I ; H?x 1 / 2 (Rd) × H?x - 1 / 2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.
The solution of fully fuzzy quadratic equation based on optimization theory.
Allahviranloo, T; Gerami Moazam, L
2014-01-01
Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE): F(X)=D, where F(X)-AX2+BX+C. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find Î» and Î¼ as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826
Republication of: Exact solutions of the field equations of the general theory of relativity
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Ehlers, Jürgen; Kundt, Wolfgang
2009-09-01
This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasi?ski) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory.
Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications
NASA Technical Reports Server (NTRS)
Rai, M. M.
1986-01-01
A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.
Perturbation theories of a discrete, integrable nonlinear Schr{umlt o}dinger equation
Cai, D.; Bishop, A.R.; Gro/nbech-Jensen, N.
1996-04-01
We rederive the discrete inverse-scattering transform (IST) perturbation results for the time evolution of the parameters of a discrete nonlinear Schr{umlt o}dinger soliton from certain mathematical identities that can be viewed as conserved quantities in the discrete, integrable nonlinear Schr{umlt o}dinger equation in (1+1) dimension. This method significantly simplifies the derivation of the IST perturbation results. We also present a specific example for which the adiabatic IST perturbation results and the collective coordinate method results exactly coincide. This is achieved by establishing a correct Lagrangian formalism for soliton parameters via transforming dynamical variables that obey a deformed Poisson structure to ones that possess a canonical Poisson structure. {copyright} {ital 1996 The American Physical Society.}
A theory of solving TAP equations for Ising models with general invariant random matrices
NASA Astrophysics Data System (ADS)
Opper, Manfred; Ã‡akmak, Burak; Winther, Ole
2016-03-01
We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the expression for the implicit memory term of the dynamics for general invariant ensembles. By subtracting these terms, that depend on magnetizations at previous time steps, the implicit memory terms cancel making the iteration dependent on a Gaussian distributed field only. The TAP magnetizations are stable fixed points if a de Almeidaâ€“Thouless stability criterion is fulfilled. We illustrate our method explicitly for coupling matrices drawn from the random orthogonal ensemble.
The Solution of Fully Fuzzy Quadratic Equation Based on Optimization Theory
Allahviranloo, T.; Gerami Moazam, L.
2014-01-01
Firstly in this paper we introduce a new concept of the 2nd power of a fuzzy number. It is exponent to production (EP) method that provides an analytical and approximate solution for fully fuzzy quadratic equation (FFQE) : F(XËœ)=DËœ, where F(XËœ)=AËœXËœ2+BËœXËœ+CËœ. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find Î» and Î¼ as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826
NASA Astrophysics Data System (ADS)
Rosinberg, M. L.; Munakata, T.; Tarjus, G.
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
NASA Astrophysics Data System (ADS)
Kumar, N.; Vijay Kumar, K.
2009-04-01
It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.
Rosinberg, M L; Munakata, T; Tarjus, G
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups. PMID:25974446
Urbic, T.; Holovko, M. F.
2011-01-01
Associative version of Henderson-Abraham-Barker theory is applied for the study of Mercedes–Benz model of water near hydrophobic surface. We calculated density profiles and adsorption coefficients using Percus-Yevick and soft mean spherical associative approximations. The results are compared with Monte Carlo simulation data. It is shown that at higher temperatures both approximations satisfactory reproduce the simulation data. For lower temperatures, soft mean spherical approximation gives good agreement at low and at high densities while in at mid range densities, the prediction is only qualitative. The formation of a depletion layer between water and hydrophobic surface was also demonstrated and studied. PMID:21992334
Solvent exchange in liquid methanol and rate theory
NASA Astrophysics Data System (ADS)
Dang, Liem X.; Schenter, Gregory K.
2016-01-01
To enhance our understanding of the solvent exchange mechanism in liquid methanol, we report a systematic study using molecular dynamics simulations. We use transition state theory, the Impey-Madden-McDonald method, the reactive flux method, and Grote-Hynes theory to compute the rate constants for this process. Solvent coupling was found to dominate, resulting in a significantly small transmission coefficient. We predict a positive activation volume for methanol exchange. The essential features of the dynamics as well as the pressure dependence are recovered from a Generalized Langevin Equation description of the dynamics. We find that the response to anharmonicity can be decomposed into two time regimes, one corresponding to short time response (<0.1 ps) and long time response (>5 ps). An effective characterization of the process is obtained from launching dynamics from the planar hypersurface corresponding to Grote-Hynes theory, resulting in improved numerical convergence of correlation functions.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory. PMID:26277155
NASA Astrophysics Data System (ADS)
Planková, Barbora; Hrubý, Jan; Vinš, Václav
2013-04-01
In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.
NASA Astrophysics Data System (ADS)
Cutler, P. H.; He, Jun; Miller, J.; Miskovsky, N. M.; Weiss, B.; Sullivan, T. E.
1993-04-01
Field emission from metallic emitters is generally described by the Fowler-Nordheim [F-N] theory, which is based on a planar model of the tip with a classical image correction. Within the free electron model and the WKB approximation, the planar tip model leads to the well-known Fowler-Nordheim equation, which predicts that a plot of log J/F 2 versus 1/F, where J is the current density and F, the field, should be a straight line within the narrow range of field strengths of typical field emission experiments, 3 - 5V/nm. This has been experimentally confirmed for conventional emitters, (i.e., electrolytically etched tips with radii ?50 nm). Field emitters fabricated with today's new techniques are much sharper with radii of curvature of the order of nm's or even the size of a single atom. Hence, the local geometry of the tip may become an important factor in the electron emission process. To investigate the effects of the shape and/or size on emission, the authors, in a recent series of papers, studied the dependence of the current-voltage characteristics on the local geometry of pointed emitters. It was found that the calculated results, plotted as log J/V 2 vs. 1/V, do not exhibit the straight line behavior predicted by the Fowler-Nordheim theory. In addition, there is a dramatic increase in the tunneling current for a fixed external bias, V, relative to the Fowler-Nordheim result for a planar model of the tip with the same bias voltage. Using the exact current integral additional results have been obtained exhibiting the effects of emitter curvature on field electron energy distributions and on electron emission in high fields and temperatures. These results continue to differ with the predictions of the Fowler-Nordheim equation for the same emitter models. Therefore, the adequacy of a ?-factor in the conventional planar model Fowler-Nordheim equation to account for emitter curvature is examined. It is demonstrated that even a ?-modified Fowler-Nordheim equation is not valid when applied to sharp emitters (r t? 10nm) and will lead to spurious results when extracting information such as work function, field values or emitting area from experimental F-N curves. The explanation for this is discussed, and an approximate analytic expression for the J(V) characteristics of a prototype sharp emitter is derived which exhibits explicitly the dependence of the current density on field, tip geometry andmaterial parameters.
NASA Astrophysics Data System (ADS)
Tokuyama, Michio
2008-07-01
A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama-Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a ? (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the ?-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.
Langevin approach with rescaled noise for stochastic channel dynamics in Hodgkin–Huxley neurons
NASA Astrophysics Data System (ADS)
Huang, Yan-Dong; Xiang, Li; Shuai, Jian-Wei
2015-12-01
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude. Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 11125419), the National Natural Science Foundation of China (Grant No. 10925525), and the Funds for the Leading Talents of Fujian Province, China.
Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory
NASA Astrophysics Data System (ADS)
Gámez, Francisco
2014-06-01
An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.
NASA Astrophysics Data System (ADS)
Yokogawa, Daisuke; Sato, Hirofumi; Imai, Takashi; Sakaki, Shigeyoshi
2009-02-01
Three dimensional (3D) hydration structure is informative to clarify the functions of hydrated waters around a protein. We develop a new approach to calculate 3D solvation structure with reasonable computational cost. In the present method, the total solvation structure is obtained using conventional one dimensional reference interaction site model (RISM) followed by integrating the 3D fragment data, which are evaluated around each atom (site) of solute. Thanks to this strategy, time-consuming 3D fast Fourier transformation, which is required in 3D-RISM theory, can be avoided and high-parallel performance is achieved. The method is applied to small molecular systems for comparison with 3D-RISM. The obtained results by the present method and by 3D-RISM show good agreement. The hydration structures for a large protein computed by the present method are also consistent with those obtained by x-ray crystallography.
Application of extended DLVO theory. 4: Derivation of flotation rate equation from first principles
Yoon, R.H.; Mao, L.
1996-08-10
A flotation model was developed by considering both hydrodynamic and surface forces involved in the process. The hydrodynamic forces were determined using a stream function and then used for estimating the kinetic energies that can be used for thinning the water films between bubbles and particles. The kinetic energies were compared with the energy barriers created by surface forces to determine the probability of adhesion. The surface forces considered included ion-electrostatic, London-van der Waals, and hydrophobic forces. Due to the insufficient information available on the hydrophobic forces for bubble-particle interactions, contributions from the hydrophobic force were back-calculated from the values of the flotation rate constants determined experimentally with methylated silica sphered. The results show that the hydrophobic force constants (K{sub 132}) for bubble-particle interaction are larger than those (K{sub 131}) for particle-particle interactions but smaller than that (K{sub 232}) for air bubbles interacting with each other in the absence of surfactants. The K{sub 132} values determined in the present work are close to the geometric means of K{sub 131} and K{sub 232}, suggesting that the combining rules developed for dispersion forces may be useful for hydrophobic forces. The flotation rate equation derived in the present work suggests various methods of improving flotation processes.
Benchmark Applications of Variations of Multireference Equation of Motion Coupled-Cluster Theory.
Huntington, Lee M J; Demel, Ond?ej; Nooijen, Marcel
2016-01-12
In this work, several variations of the multireference equation of motion (MR-EOM) methodology are investigated for the calculation of excitation spectra. These variants of MR-EOM are characterized by the following aspects: (1) the operators included in the sequence of similarity transformations of the molecular electronic Hamiltonian, (2) whether permutational symmetries (i.e., hermitization, vertex symmetry) are imposed on the final elements of the similarity-transformed Hamiltonian, (3) the size of the manifold over which the similarity-transformed Hamiltonian is diagonalized, (4) whether the two-body cumulant is included in the expressions defining the amplitudes and the elements of the transformed Hamiltonian. The MR-EOM methods are benchmarked for the calculation of the excitation energies of a test set of organic molecules. With the availability of reliable benchmark data for this test set, it is possible to gauge the relative accuracy of these approaches. We also further examine a subset of the MR-EOM methods for the calculation of the excitation energies of some transition-metal complexes. These systems prove to be particularly difficult for single-reference coupled-cluster methods. PMID:26614092
Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes
Gao Bo
2011-06-15
We present a fully quantal version of the Langevin model for the total rate of exoergic ion-molecule reactions or inelastic processes. The model, which is derived from a rigorous multichannel quantum-defect formulation of bimolecular processes, agrees with the classical Langevin model at sufficiently high temperatures. It also gives an analytic description of ion-molecule reactions and inelastic processes in the ultracold regime where the quantum nature of the relative motion between the reactants becomes important.
Langevin Dynamics Simulations of Genome Packing in Bacteriophage
Forrey, Christopher; Muthukumar, M.
2006-01-01
We use Langevin dynamics simulations to study the process by which a coarse-grained DNA chain is packaged within an icosahedral container. We focus our inquiry on three areas of interest in viral packing: the evolving structure of the packaged DNA condensate; the packing velocity; and the internal buildup of energy and resultant forces. Each of these areas has been studied experimentally, and we find that we can qualitatively reproduce experimental results. However, our findings also suggest that the phage genome packing process is fundamentally different than that suggested by the inverse spool model. We suggest that packing in general does not proceed in the deterministic fashion of the inverse-spool model, but rather is stochastic in character. As the chain configuration becomes compressed within the capsid, the structure, energy, and packing velocity all become dependent upon polymer dynamics. That many observed features of the packing process are rooted in condensed-phase polymer dynamics suggests that statistical mechanics, rather than mechanics, should serve as the proper theoretical basis for genome packing. Finally we suggest that, as a result of an internal protein unique to bacteriophage T7, the T7 genome may be significantly more ordered than is true for bacteriophage in general. PMID:16617089
NASA Astrophysics Data System (ADS)
Wong, S. K.; Chan, V. S.; Hinton, F. L.
2001-10-01
The classic solution of the linearized drift kinetic equations in neoclassical transport theory for large-aspect-ratio tokamak flux-surfaces relies on the variational principle and the choice of ``localized" distribution functions as trialfunctions.(M.N. Rosenbluth, et al., Phys. Fluids 15) (1972) 116. Somewhat unclear in this approach are the nature and the origin of the ``localization" and whether the results obtained represent the exact leading terms in an asymptotic expansion int he inverse aspect ratio. Using the method of matched asymptotic expansions, we were able to derive the leading approximations to the distribution functions and demonstrated the asymptotic exactness of the existing results. The method is also applied to the calculation of angular momentum transport(M.N. Rosenbluth, et al., Plasma Phys. and Contr. Nucl. Fusion Research, 1970, Vol. 1 (IAEA, Vienna, 1971) p. 495.) and the current driven by electron cyclotron waves.
NASA Astrophysics Data System (ADS)
Fantina, A. F.; Chamel, N.; Pearson, J. M.; Goriely, S.
2012-02-01
We present a unified approach to the equation of state (EoS) of dense matter at any temperature, based on the nuclear energy-density functional (EDF) theory. Both homogeneous and inhomogeneous phases can be treated consistently. In particular, we have constructed three different EoSs of cold catalyzed matter for a wide range of densities from ~ 105 g cm-3 to ~ 1015 g cm-3. For this purpose, we have employed generalized Skyrme functionals fitted to essentially all experimental nuclear mass data and constrained to reproduce properties of homogeneous nuclear matter as obtained from many-body calculations. We have applied these unified EoSs to compute the structure of cold isolated neutron stars (NSs).
Chuev, Gennady N.; Valiev, Marat; Fedotova, Marina V.
2012-04-10
We have developed a hybrid approach based on a combination of integral equation theory of molecular liquids and QM/MM methodology in NorthWest computational Chemistry (NWChem) software package. We have split the evaluations into conse- quent QM/MM and statistical mechanics calculations based on the one-dimensional reference interaction site model, which allows us to reduce signicantly the time of computation. The method complements QM/MM capabilities existing in the NWChem package. The accuracy of the presented method was tested through com- putation of water structure around several organic solutes and their hydration free energies. We have also evaluated the solvent effect on the conformational equilibria. The applicability and limitations of the developed approach are discussed.
NASA Astrophysics Data System (ADS)
Fu, Xilin; Zheng, Shasha
2014-09-01
In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow's dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.
Theory of coupled translational-rotational glassy dynamics in dense fluids of uniaxial particles.
Zhang, Rui; Schweizer, Kenneth S
2009-07-01
The naïve mode coupling theory (NMCT) for ideal kinetic arrest and the nonlinear Langevin equation theory of activated single-particle barrier hopping dynamics are generalized to treat the coupled center-of-mass (CM) translational and rotational motions of uniaxial hard objects in the glassy fluid regime. The key dynamical variables are the time-dependent displacements of the particle center-of-mass and orientational angle. The NMCT predicts a kinetic arrest diagram with three dynamical states: ergodic fluid, plastic glass, and fully nonergodic double glass, the boundaries of which meet at a "triple point" corresponding to a most difficult to vitrify diatomic of aspect ratio approximately 1.43. The relative roles of rotation and translation in determining ideal kinetic arrest are explored by examining three limits of the theory corresponding to nonrotating, pure rotation, and rotationally ergodic models. The ideal kinetic arrest boundaries represent a crossover to activated dynamics described by two coupled stochastic nonlinear Langevin equations for translational and rotational motions. The fundamental quantity is a dynamic free-energy surface, which for small aspect ratios in the high-volume fraction regime exhibits two saddle points reflecting a two-step activated dynamics where relatively rapid rotational dynamics coexists with slower CM translational motions. For large-enough aspect ratios, the dynamic free-energy surface has one saddle point which corresponds to a system-specific coordinated translation-rotation motion. The entropic barriers as a function of the relative amount of rotation versus translation are determined. PMID:19658708
NASA Astrophysics Data System (ADS)
Chavanis, Pierre-Henri
2008-10-01
We developed a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic Smoluchowski equation governing the evolution of the fluctuating density field of Brownian particles, we determine the expression of the correlation function of the density fluctuations around a spatially homogeneous equilibrium distribution. In the stable regime, we find that the temporal correlation function of the Fourier components of density fluctuations decays exponentially rapidly, with the same rate as the one characterizing the damping of a perturbation governed by the deterministic mean field Smoluchowski equation (without noise). On the other hand, the amplitude of the spatial correlation function in Fourier space diverges at the critical point T=Tc (or at the instability threshold k=km) implying that the mean field approximation breaks down close to the critical point, and that the phase transition from the homogeneous phase to the inhomogeneous phase occurs sooner. By contrast, the correlations of the velocity fluctuations remain finite at the critical point (or at the instability threshold). We give explicit examples for the Brownian Mean Field (BMF) model and for Brownian particles interacting via the gravitational potential and via the attractive Yukawa potential. We also introduce a stochastic model of chemotaxis for bacterial populations generalizing the deterministic mean field Keller-Segel model by taking into account fluctuations and memory effects.
NASA Astrophysics Data System (ADS)
Fleming, Sean
2014-07-01
In soft collinear effective theory (SCET) the interaction between high energy quarks moving in opposite directions involving momentum transfer much smaller than the center-of-mass energy is described by the Glauber interaction operator which has two-dimensional Coulomb-like behavior. Here, we determine this n- n bar collinear Glauber interaction operator and consider its renormalization properties at one loop. At this order a rapidity divergence appears which gives rise to an infrared divergent (IR) rapidity anomalous dimension commonly called the gluon Regge trajectory. We then go on to consider the forward quark scattering cross section in SCET. The emission of real soft gluons from the Glauber interaction gives rise to the Lipatov vertex. Squaring and adding the real and virtual amplitudes results in a cancelation of IR divergences, however the rapidity divergence remains. We introduce a rapidity counter-term to cancel the rapidity divergence, and derive a rapidity renormalization group equation which is the Balitsky-Fadin-Kuraev-Lipatov Equation. This connects Glauber interactions with the emergence of Regge behavior in SCET.
Szyma?ski, S
2009-12-28
The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra. PMID:20059076
Finite-Temperature Non-equilibrium Quasicontinuum Method based on Langevin Dynamics
Marian, J; Venturini, G; Hansen, B; Knap, J; Ortiz, M; Campbell, G
2009-05-08
The concurrent bridging of molecular dynamics and continuum thermodynamics presents a number of challenges, mostly associated with energy transmission and changes in the constitutive description of a material across domain boundaries. In this paper, we propose a framework for simulating coarse dynamic systems in the canonical ensemble using the Quasicontinuum method (QC). The equations of motion are expressed in reduced QC coordinates and are strictly derived from dissipative Lagrangian mechanics. The derivation naturally leads to a classical Langevin implementation where the timescale is governed by vibrations emanating from the finest length scale occurring in the computational cell. The equations of motion are integrated explicitly via Newmark's ({beta} = 0; {gamma} = 1/2) method, leading to a robust numerical behavior and energy conservation. In its current form, the method only allows for wave propagations supported by the less compliant of the two meshes across a heterogeneous boundary, which requires the use of overdamped dynamics to avoid spurious heating due to reflected vibrations. We have applied the method to two independent crystallographic systems characterized by different interatomic potentials (Al and Ta) and have measured thermal expansion in order to quantify the vibrational entropy loss due to homogenization. We rationalize the results in terms of system size, mesh coarseness, and nodal cluster diameter within the framework of the quasiharmonic approximation. For Al, we find that the entropy loss introduced by mesh coarsening varies linearly with the element size, and that volumetric effects are not critical in driving the anharmonic behavior of the simulated systems. In Ta, the anomalies of the interatomic potential employed result in negative and zero thermal expansion at low and high temperatures, respectively.
NASA Astrophysics Data System (ADS)
Sääskilahti, K.; Oksanen, J.; Tulkki, J.
2013-07-01
Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys.JSTPBS0022-471510.1007/s10955-006-9235-3 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.
Sääskilahti, K; Oksanen, J; Tulkki, J
2013-07-01
Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations. PMID:23944435
Lattice model theory of the equation of state covering the gas, liquid, and solid phases
NASA Technical Reports Server (NTRS)
Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.
1975-01-01
The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.
Bavarian, Niloofar; Flay, Brian R.; Ketcham, Patricia L.; Smit, Ellen; Kodama, Cathy; Martin, Melissa; Saltz, Robert F.
2014-01-01
Objective To test a theory-driven model of health behavior to predict the illicit use of prescription stimulants (IUPS) among college students. Participants A probability sample of 554 students from one university located in California (response rate = 90.52%). Methods Students completed a paper-based survey developed with guidance from the Theory of Triadic Influence. We first assessed normality of measures and checked for multicollinearity. A single structural equation model of frequency of IUPS in college was then tested using constructs from the theoryâ€™s three streams of influence (i.e., intrapersonal, social situation/context, and sociocultural environment) and four levels of causation (i.e., ultimate causes, distal influences, proximal predictors, and immediate precursors). Results Approximately 18% of students reported engaging in IUPS during college, with frequency of use ranging from never to 40 or more times per academic term. The model tested had strong fit and the majority of paths specified within and across streams were significant at the p<.01 level. Additionally, 46% of the variance in IUPS frequency was explained by the tested model. Conclusions Results suggest the utility of the TTI as an integrative model of health behavior, specifically in predicting IUPS, and provide insight on the need for multifaceted prevention and intervention efforts. PMID:24647369
NASA Astrophysics Data System (ADS)
Sun, Jiu-xun; Wu, Qiang; Cai, Lingcang; Jing, Fuqian
2007-11-01
The analytic expressions for equation of state and thermodynamic properties have been derived for the exp-6 fluids, by using the Ross variational perturbation theory and the analytic Percus-Yevick (PY) expression of radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are fast. The comparison of the numerical results with the computer simulations shows that the precision of the analytic Ross theory is equivalent to the non-analytic modified Weeks-Chandler-Anderson (mWCA) theory, and is slightly better than the complicated optimized reference hypernetted chain (RHNC) theory.
NASA Astrophysics Data System (ADS)
Martín, C. P.; Sánchez-Ruiz, D.
2000-04-01
The one-loop renormalization of a general chiral gauge theory without scalar and Majorana fields is fully worked out within Breitenlohner and Maison dimensional renormalization scheme. The coefficients of the anomalous terms introduced in the Slavnov-Taylor equations by the minimal subtraction algorithm are calculated and the asymmetric counterterms needed to restore the BRS symmetry, if the anomaly cancellation conditions are met, are computed. The renormalization group equation and its coefficients are worked out in the anomaly free case. The computations draw heavily from the existence of action principles and BRS cohomology theory.
Quantitative test of general theories of the intrinsic laser linewidth
NASA Astrophysics Data System (ADS)
Cerjan, Alexander; Pick, Adi; Chong, Y. D.; Johnson, Steven G.; Douglas Stone, A.
2015-11-01
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and thus includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations ($\\alpha$ factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.
NASA Astrophysics Data System (ADS)
Xing, Xiusan
2010-12-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's Langevin equation in 6 N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6 N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6 N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.
Chen, Wei-Ren; Do, Changwoo; Hong, Kunlun; Liu, Yun; Porcar, L.; Shew, Chwen-Yang; Smith, Greg
2012-01-01
We present small angle neutron scattering (SANS) measurements of deuterium oxide (D2O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.
Shew, Chwen-Yang; Do, Changwoo; Hong, Kunlun; Liu, Yun; Porcar, Lionel; Smith, Gregory S; Chen, Wei-Ren
2012-07-14
We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect. PMID:22803562
Palmer, David S; Mišin, Maksim; Fedorov, Maxim V; Llinas, Antonio
2015-09-01
We report a method to predict physicochemical properties of druglike molecules using a classical statistical mechanics based solvent model combined with machine learning. The RISM-MOL-INF method introduced here provides an accurate technique to characterize solvation and desolvation processes based on solute-solvent correlation functions computed by the 1D reference interaction site model of the integral equation theory of molecular liquids. These functions can be obtained in a matter of minutes for most small organic and druglike molecules using existing software (RISM-MOL) (Sergiievskyi, V. P.; Hackbusch, W.; Fedorov, M. V. J. Comput. Chem. 2011, 32, 1982-1992). Predictions of caco-2 cell permeability and hydration free energy obtained using the RISM-MOL-INF method are shown to be more accurate than the state-of-the-art tools for benchmark data sets. Due to the importance of solvation and desolvation effects in biological systems, it is anticipated that the RISM-MOL-INF approach will find many applications in biophysical and biomedical property prediction. PMID:26212723
Zhao, Honggang; dos Ramos, M Carolina; McCabe, Clare
2007-06-28
A statistical associating fluid theory to model electrolyte fluids that explicitly accounts for solvent molecules by modeling water as a dipolar square-well associating fluid is presented. Specifically the statistical associating fluid theory for potentials of variable range (SAFT-VR) is combined with integral equation theory and the generalized mean spherical approximation using the nonprimitive model to describe the long-range ion-ion, ion-dipole, and dipole-dipole interactions. Isothermal-isobaric ensemble Monte Carlo simulations have been performed in order to test the new theoretical approach. In particular, simulations are performed for different ion concentrations and different ratios of the cation, anion, and solvent segment diameters. Predictions for the thermodynamic properties from the new equation of state are compared with the computer simulation data. Additionally, results from a combination of the SAFT-VR approach with Debye-Huckel theory and the primitive model are also presented and compared to those obtained with the nonprimitive model to illustrate the advantages of the new statistical associating fluid theory for potentials of variable range plus dipole and electrolytes (SAFT-VR+DE) approach. The results show that the proposed equation of state provides a good description of the PVT properties of electrolyte fluids with different sizes of ions and solvent. PMID:17614560
The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems.
Vardeman, Charles F; Stocker, Kelsey M; Gezelter, J Daniel
2011-04-12
We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015
The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems
Vardeman, Charles F.; Stocker, Kelsey M.; Gezelter, J. Daniel
2011-01-01
We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the “Langevin Hull”, can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015
ERIC Educational Resources Information Center
Yen, Wendy M.
Test scores that are not perfectly reliable cannot be strictly equated unless they are strictly parallel. This fact implies that tau equivalence can be lost if an equipercentile equating is applied to observed scores that are not strictly parallel. Thirty-six simulated data sets are produced to simulate equating tests with different difficulties…
NASA Astrophysics Data System (ADS)
Yedlin, Matthew; Virieux, Jean
2010-05-01
As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6]. Central to the sensitivity kernel techniques is the use of an appropriate Green's function in either two or three dimensions and a background model is assumed for the calculation of the Green's function. In some situations, the constant velocity Green's function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green's function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7]. To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green's function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green's function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications. References [1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics 64(3), pp. 888-901. [2] J. R. Ernst, A. G. Green, H. Maurer and K. Holliger. 2007, Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data. Geophysics 72, pp. J53. [3] H. Marquering, F. Dahlen and G. Nolet. 1999, Three-dimensional sensitivity kernels for finite-frequency traveltimes: The banana-doughnut paradox. Geophysical Journal International 137(3), pp. 805-815. [4] J. Tromp, C. Tape and Q. Liu. 2005, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International 160(1), pp. 195-216. [5] M. L. Buursink, T. C. Johnson, P. S. Routh and M. D. Knoll. 2008, Crosshole radar velocity tomography with finite-frequency fresnel volume sensitivities. Geophysical Journal International 172(1), pp. 1-17. [6] I. Iturbe, P. Roux, J. Virieux and B. Nicolas. 2009, Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water. J. Acoust. Soc. Am. 126(2), pp. 713-720. [7] E. Zauderer. 1971, Uniform asymptotic solutios of the reduced wave equation. Journal of Mathematical Analysis and Application 30, pp. 157-171. [8] M. J. Yedlin. 1987, Uniform asymptotic solution for the Green's function for the two-dimensional acoustic equation. J. Acoust. Soc. Am. 81(2) pp. 238-243.
Banik, Sarmistha; Hempel, Matthias; Bandyopadhyay, Debades
2014-10-01
We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of ?s. We have developed two variants of hyperonic EoS tables: in the np?? case the repulsive hyperon-hyperon interaction mediated by the strange ? meson is taken into account, and in the np? case it is not. The EoS tables for the two cases encompass a wide range of densities (10{sup –12} to ?1 fm{sup –3}), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of ? hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, ?-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M {sub ?} maximum mass neutron star for the np?? case, whereas that for the np? case is 1.95 M {sub ?}. The np?? EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M {sub ?} neutron stars.
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, JÃ¼rgen; Krylov, Anna I
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results. PMID:26277122
NASA Astrophysics Data System (ADS)
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.
2015-08-01
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Penc, K. Research Institute for Solid State Physics of the Hungarian Academy of Sciences, P.O.B. 49, H-1525 Budapest ); Zawadowski, A. Research Institute for Solid State Physics of the Hungarian Academy of Sciences, P.O.B. 49, H-1525 Budapest )
1994-10-15
The orbital Kondo effect is treated in a model where, additional to the conduction band, there are localized orbitals close to the Fermi energy. If the hopping between the conduction band and the localized heavy orbitals depends on the occupation of the atomic orbitals in the conduction band, then orbital Kondo correlation occurs. The noncommutative nature of the coupling required for the Kondo effect is formally due to the form factors associated with the assisted hopping, which in the momentum representation depends on the momenta of the conduction electrons involved. The leading logarithmic vertex corrections are due to the local Coulomb interaction between the electrons on the heavy orbital and in the conduction band. The renormalized vertex functions are obtained as a solution of a closed set of differential equations and they show power behavior. The amplitude of large renormalization is determined by an infrared cutoff due to finite energy and dispersion of the heavy particles. The enhanced assisted hopping rate results in mass enhancement and attractive interaction in the conduction band. The superconductivity transition temperature calculated is largest for the intermediate mass enhancement, [ital m][sup *]/[ital m][approx]2--3. For larger mass enhancement the small one-particle weight ([ital Z]) in the Green's function reduces the transition temperature, which may be characteristic for other models as well. The theory is developed for different one-dimensional and square-lattice models, but the applicability is not limited to them. In the one-dimensional case charge- and spin-density susceptibilities are also discussed. Good candidates for the heavy orbital are [ital f] bands in the heavy fermionic systems and nonbonding oxygen orbitals in high-temperature superconductors and different flatbands in the quasi-one-dimensional organic conductors.
Meng, Da; Zheng, Bin; Lin, Guang; Sushko, Maria L.
2014-08-29
We have developed efficient numerical algorithms for the solution of 3D steady-state Poisson-Nernst-Planck equations (PNP) with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by finite difference scheme and solved iteratively by Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Algebraic multigrid method is then applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed which reduces computational complexity from O(N2) to O(NlogN) where N is the number of grid points. Integrals involving Dirac delta function are evaluated directly by coordinate transformation which yields more accurate result compared to applying numerical quadrature to an approximated delta function. Numerical results for ion and electron transport in solid electrolyte for Li ion batteries are shown to be in good agreement with the experimental data and the results from previous studies.
Effects of atomic coherences and injected field on the dynamics of generalized Lorenz-Haken equation
NASA Astrophysics Data System (ADS)
Deng, X. L.; Ma, H. Q.; Chen, B. D.; Huang, H. B.
2001-11-01
Considering the atomic coherences and injected classical field, we derived the generalized Lorenz-Haken equation (GLHE) by using the technique of quantum Langevin operator. The dynamics of this equation is then studied numerically, and the results show that the atomic coherences and injected field can inhibit the chaos of the field in the cavity.
Interpretation of surface diffusion data with Langevin simulations: a quantitative assessment.
Diamant, M; Rahav, S; Ferrando, R; Alexandrowicz, G
2015-04-01
Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions between the substrate and adsorbate atoms, neglecting correlations in the motion of the two species. The effect of this simplification on the accuracy of observables extracted using Langevin simulations was previously unquantified. Here we report a numerical study aimed at assessing the validity of this approach. We compared experimentally accessible observables which were calculated using a Langevin simulation with those obtained from explicit molecular dynamics simulations. Our results show that within the range of parameters we explored Langevin simulations provide a good alternative for calculating the diffusion procress, i.e. the effect of correlations is too small to be observed within the numerical accuracy of this study and most likely would not have a significant effect on the interpretation of experimental data. Our comparison of the two numerical approaches also demonstrates the effect temperature dependent friction has on the calculated observables, illustrating the importance of accounting for such a temperature dependence when interpreting experimental data. PMID:25743627
Spectral Decomposition of a Fokker-Planck Equation at Criticality
NASA Astrophysics Data System (ADS)
Bologna, M.; Beig, M. T.; Svenkeson, A.; Grigolini, P.; West, B. J.
2015-07-01
The mean field for a complex network consisting of a large but finite number of random two-state elements, , has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to . In the limiting case , the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When , the inverse power law is truncated by an exponential decay with rate , the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker-Planck equation and its equivalent Schrödinger equation representation.
Theory of relativistic Brownian motion: the (1+3) -dimensional case.
Dunkel, Jörn; Hänggi, Peter
2005-09-01
A theory for (1+3) -dimensional relativistic Brownian motion under the influence of external force fields is put forward. Starting out from a set of relativistically covariant, but multiplicative Langevin equations we describe the relativistic stochastic dynamics of a forced Brownian particle. The corresponding Fokker-Planck equations are studied in the laboratory frame coordinates. In particular, the stochastic integration prescription--i.e., the discretization rule dilemma--is elucidated (prepoint discretization rule versus midpoint discretization rule versus postpoint discretization rule). Remarkably, within our relativistic scheme we find that the postpoint rule (or the transport form) yields the only Fokker-Planck dynamics from which the relativistic Maxwell-Boltzmann statistics is recovered as the stationary solution. The relativistic velocity effects become distinctly more pronounced by going from one to three spatial dimensions. Moreover, we present numerical results for the asymptotic mean-square displacement of a free relativistic Brownian particle moving in 1+3 dimensions. PMID:16241514
Polymer field-theory simulations on graphics processing units
NASA Astrophysics Data System (ADS)
Delaney, Kris T.; Fredrickson, Glenn H.
2013-09-01
We report the first CUDA™ graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic polymer systems. Our implementation is suitable both for self-consistent field theory (mean-field) solutions of the field equations, and for fully fluctuating simulations using the complex Langevin approach. Running on NVIDIA® Tesla T20 series GPUs, we find double-precision speedups of up to 30× compared to single-core serial calculations on a recent reference CPU, while single-precision calculations proceed up to 60× faster than those on the single CPU core. Due to intensive communications overhead, an MPI implementation running on 64 CPU cores remains two times slower than a single GPU.
Frenkel, A.L.; Indireshkumar, K.
1999-10-01
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out. {copyright} {ital 1999} {ital The American Physical Society}
Beklaryan, Leva A
2011-03-31
A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.
Wen, Kai; Sakata, Fumihiko; Li, Zhu-Xia; Wu, Xi-Zhen; Zhang, Ying-Xun; Zhou, Shan-Gui
2013-07-01
Macroscopic parameters as well as precise information on the random force characterizing the Langevin-type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function. PMID:23862995
Theory for non-equilibrium statistical mechanics.
Attard, Phil
2006-08-21
This paper reviews a new theory for non-equilibrium statistical mechanics. This gives the non-equilibrium analogue of the Boltzmann probability distribution, and the generalization of entropy to dynamic states. It is shown that this so-called second entropy is maximized in the steady state, in contrast to the rate of production of the conventional entropy, which is not an extremum. The relationships of the new theory to Onsager's regression hypothesis, Prigogine's minimal entropy production theorem, the Langevin equation, the formula of Green and Kubo, the Kawasaki distribution, and the non-equilibrium fluctuation and work theorems, are discussed. The theory is worked through in full detail for the case of steady heat flow down an imposed temperature gradient. A Monte Carlo algorithm based upon the steady state probability density is summarized, and results for the thermal conductivity of a Lennard-Jones fluid are shown to be in agreement with known values. Also discussed is the generalization to non-equilibrium mechanical work, and to non-equilibrium quantum statistical mechanics. As examples of the new theory two general applications are briefly explored: a non-equilibrium version of the second law of thermodynamics, and the origin and evolution of life. PMID:16883388
2015-01-01
Reduced Langevin recombination has been observed in organic solar cells (OSCs) for many years, but its origin is still unclear. A recent work by Burke et al. (Adv. Energy Mater.2015, 5, 1500123-1) was inspired by this reduced Langevin recombination, and they proposed an equilibrium model of charge-transfer (CT) states that correlates the open-circuit voltage of OSCs with experimentally available device parameters. In this work, we extend Burke et al.â€™s CT model further and for the first time directly correlate the reduced Langevin recombination with the energetic and dynamic behavior of the CT state. Recombination through CT states leads in a straightforward manner to a decrease in the Langevin reduction factor with increasing temperature, without explicit consideration of the temperature dependence of the mobility. To verify the correlation between the CT states and reduced Langevin recombination, we incorporated this CT model and the reduced Langevin model into drift-diffusion simulations of a bilayer OSC. The simulations not only successfully reproduced realistic currentâ€“voltage (Jâ€“V) characteristics of the bilayer OSC, but also demonstrate that the two models consistently lead to same value of the apparent Langevin reduction factor. PMID:26640611
Liao, David; Tlsty, Thea D.
2014-01-01
The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752
Choi, Eunsong; Yethiraj, Arun
2015-07-23
We study the conformational properties of polymers in room temperature ionic liquids using theory and simulations of a coarse-grained model. Atomistic simulations have shown that single poly(ethylene oxide) (PEO) molecules in the ionic liquid 1-butyl 3-methyl imidazolium tetrafluoroborate ([BMIM][BF4]) are expanded at room temperature (i.e., the radius of gyration, Rg), scales with molecular weight, Mw, as Rg ? Mw(0.9), instead of the expected self-avoiding walk behavior. The simulations were restricted to fairly short chains, however, which might not be in the true scaling regime. In this work, we investigate a coarse-grained model for the behavior of PEO in [BMIM][BF4]. We use existing force fields for PEO and [BMIM][BF4] and Lorentz–Berthelot mixing rules for the cross interactions. The coarse-grained model predicts that PEO collapses in the ionic liquid. We also present an integral equation theory for the structure of the ionic liquid and the conformation properties of the polymer. The theory is in excellent agreement with the simulation results. We conclude that the properties of polymers in ionic liquids are unusually sensitive to the details of the intermolecular interactions. The integral equation theory is sufficiently accurate to be a useful guide to computational work. PMID:25310685
Doktorov, A B
2014-09-14
In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed. PMID:25217901
NASA Astrophysics Data System (ADS)
Doktorov, A. B.
2014-09-01
In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.
Doktorov, A. B.
2014-09-14
In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.
Constant pressure and temperature discrete-time Langevin molecular dynamics
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Constant pressure and temperature discrete-time Langevin molecular dynamics.
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. PMID:25416875
A study of Kramers' turnover theory in the presence of exponential memory friction.
Ianconescu, Reuven; Pollak, Eli
2015-09-14
Originally, the challenge of solving Kramers' turnover theory was limited to Ohmic friction, or equivalently, motion of the escaping particle governed by a Langevin equation. Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)] (MM) presented a solution valid for Ohmic friction. The turnover theory was derived more generally and for memory friction by Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] (PGH). Mel'nikov proceeded to also provide finite barrier corrections to his theory [Phys. Rev. E 48, 3271 (1993)]. Finite barrier corrections were derived only recently within the framework of PGH theory [E. Pollak and R. Ianconescu, J. Chem. Phys. 140, 154108 (2014)]. A comprehensive comparison between MM and PGH theories including finite barrier corrections and using Ohmic friction showed that the two methods gave quantitatively similar results and were in quantitative agreement with numerical simulation data. In the present paper, we extend the study of the turnover theories to exponential memory friction. By comparing with numerical simulation, we find that PGH theory is rather accurate, even in the strong friction long memory time limit, while MM theory fails. However, inclusion of finite barrier corrections to PGH theory leads to failure in this limit. The long memory time invalidates the fundamental assumption that consecutive traversals of the well are independent of each other. Why PGH theory without finite barrier corrections remains accurate is a puzzle. PMID:26374015
A study of Kramers' turnover theory in the presence of exponential memory friction
NASA Astrophysics Data System (ADS)
Ianconescu, Reuven; Pollak, Eli
2015-09-01
Originally, the challenge of solving Kramers' turnover theory was limited to Ohmic friction, or equivalently, motion of the escaping particle governed by a Langevin equation. Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)] (MM) presented a solution valid for Ohmic friction. The turnover theory was derived more generally and for memory friction by Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] (PGH). Mel'nikov proceeded to also provide finite barrier corrections to his theory [Phys. Rev. E 48, 3271 (1993)]. Finite barrier corrections were derived only recently within the framework of PGH theory [E. Pollak and R. Ianconescu, J. Chem. Phys. 140, 154108 (2014)]. A comprehensive comparison between MM and PGH theories including finite barrier corrections and using Ohmic friction showed that the two methods gave quantitatively similar results and were in quantitative agreement with numerical simulation data. In the present paper, we extend the study of the turnover theories to exponential memory friction. By comparing with numerical simulation, we find that PGH theory is rather accurate, even in the strong friction long memory time limit, while MM theory fails. However, inclusion of finite barrier corrections to PGH theory leads to failure in this limit. The long memory time invalidates the fundamental assumption that consecutive traversals of the well are independent of each other. Why PGH theory without finite barrier corrections remains accurate is a puzzle.
Jia Ying; Bao Jingdong
2007-03-15
The anisotropy of the fission fragment angular distribution defined at the saddle point and the neutron multiplicities emitted prior to scission for fissioning nuclei {sup 224}Th, {sup 229}Np, {sup 248}Cf, and {sup 254}Fm are calculated simultaneously by using a set of realistic coupled two-dimensional Langevin equations, where the (c,h,{alpha}=0) nuclear parametrization is employed. In comparison with the one-dimensional stochastic model without neck variation, our two-dimensional model produces results that are in better agreement with the experimental data, and the one-dimensional model is available only for low excitation energies. Indeed, to determine the temperature of the nucleus at the saddle point, we investigate the neutron emission during nucleus oscillation around the saddle point for different friction mechanisms. It is shown that the neutrons emitted during the saddle oscillation cause the temperature of a fissioning nuclear system at the saddle point to decrease and influence the fission fragment angular distribution.
NASA Astrophysics Data System (ADS)
VinÅ¡, VÃ¡clav; PlankovÃ¡, Barbora; HrubÃ½, Jan; CelnÃ½, David
2014-03-01
The density gradient theory (GT) combined with a SAFT-type (Statistical Associating Fluid Theory) equation of state has been used for modeling the surface tension of associating fluids represented by a series of six alkanols ranging from methanol to 1-pentanol. The effect of nonzero dipole moment of the selected alkanols on the predicted surface tension was investigated in this study. Results of the GT + non-polar Perturbed Chain (PC) SAFT equation of state were compared to predictions of GT combined with the PC-polar-SAFT, i.e. PCP-SAFT, equation. Both GT + PC-SAFT and GT + PCP-SAFT give reasonable prediction of the surface tension for pure alkanols. Results of both models are comparable as no significant difference in the modeled saturation properties and in the predicted surface tension using GT was found. Consideration of dipolar molecules of selected alkanols using PCP-SAFT had only minor effect on the predicted properties compared to the non-polar PC-SAFT model.
NASA Astrophysics Data System (ADS)
Franke, Robert
1997-01-01
The one-electron Dirac equation is solved in an iterative manner starting with the solution of the Schrödinger equation. The method is applied in a basis of atom-centred Gaussian-type functions to the ground state of selected hydrogen-like ions up to Eka Pt 109+ and the heavy quasi-molecules Th 2179+, NiPb 109+ and Th 3269+ (in D ?h and D 3h symmetry). An overall 8-figure accuracy in the absolute relativistic energies is achieved. The iterative procedure converges better than linearly for light systems and linearly for systems containing nuclear charges greater than Z 2˜ 40.
A screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator
NASA Astrophysics Data System (ADS)
Chu, Xiangcheng; Wang, Jiawei; Yuan, Songmei; Li, Longtu; Cui, Hongchao
2014-06-01
A novel screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator, with an assembly comprised a threaded shaft, is presented. The bolt-clamped Langevin vibrator consists of 4 chips of PZT ceramics and generates more energy with a certain input power. The threads of the stator multiply the linear force and position resolution, and the threaded rod is rotated directly to achieve linear movement without additional mechanical conversion. The actuator was designed and optimized using the Finite Element Method (FEM), and a prototype was fabricated. At 300 Vp-p, the maximum thrust force, velocity, and efficiency were approximately 4.2 N, 9.5 mm s-1, and 5.6%, respectively.
A screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator.
Chu, Xiangcheng; Wang, Jiawei; Yuan, Songmei; Li, Longtu; Cui, Hongchao
2014-06-01
A novel screw-thread-type ultrasonic actuator based on a Langevin piezoelectric vibrator, with an assembly comprised a threaded shaft, is presented. The bolt-clamped Langevin vibrator consists of 4 chips of PZT ceramics and generates more energy with a certain input power. The threads of the stator multiply the linear force and position resolution, and the threaded rod is rotated directly to achieve linear movement without additional mechanical conversion. The actuator was designed and optimized using the Finite Element Method (FEM), and a prototype was fabricated. At 300 Vp-p, the maximum thrust force, velocity, and efficiency were approximately 4.2 N, 9.5 mmâ€‰s(-1), and 5.6%, respectively. PMID:24985842
Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation
Stinson, Jake L.; Kathmann, Shawn M.; Ford, Ian J.
2014-11-17
We investigate some unusual behaviour observed while performing molecular dynamics simulations with the DL_POLY_4.03 code. Under the standard Langevin thermostat, atoms appear to be thermalised to different temperatures, depending on their mass and on the total number of particles in the system. We find that an imposed constraint whereby no thermal noise acts on the centre of mass of the system is the cause of the unexpected behaviour. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. The effect of the constraint can be considerable for small systems with disparate masses. By removing the constraint the Langevin thermostat may be restored to its intended behaviour and this has been implemented as an option in DL_POLY_4.05. SMK was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward. PMID:26323089
Charles R. Tolle; Mark Pengitore
2009-08-01
This paper explores the overlaps between the Control communityâ€™s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communitiesâ€™ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannonâ€™s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauerâ€™s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Peronaâ€™s method.
NASA Astrophysics Data System (ADS)
Bona, G.; Chen, J. A.; Saut, Jing Ping
2002-08-01
Considered herein are a number of variants of the classical Boussinesq system and their higher-order generalizations. Such equations were first derived by Boussinesq to describe the two-way propagation of small-amplitude, long wavelength, gravity waves on the surface of water in a canal. These systems arise also when modeling the propagation of long-crested waves on large lakes or the ocean and in other contexts. Depending on the modeling of dispersion, the resulting system may or may not have a linearization about the rest state which is well posed. Even when well posed, the linearized system may exhibit a lack of conservation of energy that is at odds with its status as an approximation to the Euler equations. In the present script, we derive a four-parameter family of Boussinesq systems from the two-dimensional Euler equations for free-surface flow and formulate criteria to help decide which of these equations one might choose in a given modeling situation. The analysis of the systems according to these criteria is initiated.
The way from microscopic many-particle theory to macroscopic hydrodynamics
NASA Astrophysics Data System (ADS)
Haussmann, Rudolf
2016-03-01
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokkerâ€“Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term.
The way from microscopic many-particle theory to macroscopic hydrodynamics.
Haussmann, Rudolf
2016-03-23
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena. We specify the densities of the conserved quantities as the relevant hydrodynamic variables and apply the methods of non-equilibrium statistical mechanics with projection operator techniques. As a result we obtain time-evolution equations for the hydrodynamic variables with three kinds of terms on the right-hand sides: reversible, dissipative and fluctuating terms. In their original form these equations are completely exact and contain nonlocal terms in space and time which describe nonlocal memory effects. Applying a few approximations the nonlocal properties and the memory effects are removed. As a result we find the well known hydrodynamic equations of a normal fluid with Gaussian fluctuating forces. In the following we investigate if and how the time-inversion invariance is broken and how the second law of thermodynamics comes about. Furthermore, we show that the hydrodynamic equations with fluctuating forces are equivalent to stochastic Langevin equations and the related Fokker-Planck equation. Finally, we investigate the fluctuation theorem and find a modification by an additional term. PMID:26902659
The influence of piezoceramic stack location on nonlinear behavior of Langevin transducers.
Mathieson, Andrew; Cardoni, Andrea; Cerisola, Niccolò; Lucas, Margaret
2013-06-01
Power ultrasonic applications such as cutting, welding, and sonochemistry often use Langevin transducers to generate power ultrasound. Traditionally, it has been proposed that the piezoceramic stack of a Langevin transducer should be located in the nodal plane of the longitudinal mode of vibration, ensuring that the piezoceramic elements are positioned under a uniform stress during transducer operation, maximizing element efficiency and minimizing piezoceramic aging. However, this general design rule is often partially broken during the design phase if features such as a support flange or multiple piezoceramic stacks are incorporated into the transducer architecture. Meanwhile, it has also been well documented in the literature that power ultrasonic devices driven at high excitation levels exhibit nonlinear behaviors similar to those observed in Duffing-type systems, such as resonant frequency shifts, the jump phenomenon, and hysteretic regions. This study investigates three Langevin transducers with different piezoceramic stack locations by characterizing their linear and nonlinear vibrational responses to understand how the stack location influences nonlinear behavior. PMID:25004475
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Kundt, Wolfgang
2014-03-01
This is an English translation of a paper by Pascual Jordan and Wolfgang Kundt, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 3 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1, 2 and 4 of the series have already been reprinted, part 5 will be printed as a Golden Oldie in near future.) This third paper shows how solutions of the Einstein-Maxwell equations with null Maxwell field can be incorporated into the scheme of geometrodynamics. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Charles Misner.
NASA Astrophysics Data System (ADS)
Govind, N.; Sushko, P. V.; Hess, W. P.; Valiev, M.; Kowalski, K.
2009-03-01
We present a study of the lowest surface and bulk excitations of the well-studied potassium bromide (KBr) system using an embedded cluster method. The excited states of the embedded cluster are studied systematically using time-dependent density functional theory (TDDFT) and high-level equation-of-motion coupled cluster (EOMCC) methods. In particular, we have used EOMCC models with singles and doubles (EOMCCSD) and two approaches which account for the effect of triply excited configurations in non-iterative and iterative fashions. We compare and contrast the results between these theories as well as compare our results with experiment. The bulk-surface exciton shift is also calculated at the TDDFT level and compared with experiment.
NASA Astrophysics Data System (ADS)
Tikhonov, D. A.; Sobolev, E. V.
2011-04-01
A method of integral equations of the theory of liquids in the reference interaction site model (RISM) approximation is used to estimate the Gibbs energy averaged over equilibrium trajectories computed by molecular mechanics. Peptide oxytocin is selected as the object of interest. The Gibbs energy is calculated using all chemical potential formulas introduced in the RISM approach for the excess chemical potential of solvation and is compared with estimates by the generalized Born model. Some formulas are shown to give the wrong sign of Gibbs energy changes when peptide passes from the gas phase into water environment; the other formulas give overestimated Gibbs energy changes with the right sign. Note that allowance for the repulsive correction in the approximate analytical expressions for the Gibbs energy derived by thermodynamic perturbation theory is not a remedy.
Pandit, S.G.
1994-12-31
Iterative schemes converging monotonically and uniformly to the unique solution of nonlinear Volterra integral equation are developed, under various monotonicity and convexity (concavity) conditions on the kernel. The rate of convergence of the schemes is quadratic or higher, and hence rapid. An application to problem arising in connection with the boundary-layer flow past a half plane is given, and examples illustrating the results are presented.
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Mohammadian, Majid
2008-04-01
We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under-compressive shock waves which are not uniquely determined by a standard entropy criterion but must be characterized by a kinetic relation. Building on earlier work by LeFloch and collaborators, we investigate the numerical approximation of these models by high-order finite difference schemes, and uncover several new features of the kinetic function associated with physically motivated second and third-order regularization terms, especially viscosity and capillarity terms. On one hand, the role of the equivalent equation associated with a finite difference scheme is discussed. We conjecture here and demonstrate numerically that the (numerical) kinetic function associated with a scheme approaches the (analytic) kinetic function associated with the given model - especially since its equivalent equation approaches the regularized model at a higher order. On the other hand, we demonstrate numerically that a kinetic function can be associated with the thin liquid film model and the generalized Camassa-Holm model. Finally, we investigate to what extent a kinetic function can be associated with the equations of van der Waals fluids, whose flux-function admits two inflection points.
Dynamic density functional theory with hydrodynamic interactions and fluctuations
NASA Astrophysics Data System (ADS)
Donev, Aleksandar; Vanden-Eijnden, Eric
2014-06-01
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
Dynamic density functional theory with hydrodynamic interactions and fluctuations
Donev, Aleksandar Vanden-Eijnden, Eric
2014-06-21
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. LÃ¶wen, â€œDynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,â€ Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, â€œA reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,â€ J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
NASA Astrophysics Data System (ADS)
Kernkamp, Herman W. J.; Petit, Henri A. H.; Gerritsen, Herman; de Goede, Erik D.
2005-12-01
In this paper, the formulations of the primitive equations for shallow water flow in various horizontal co-ordinate systems and the associated finite difference grid options used in shallow water flow modelling are reviewed. It is observed that horizontal co-ordinate transformations do not affect the chosen co-ordinate system and representation in the vertical, and are the same for the three- and two-dimensional cases. A systematic derivation of the equations in tensor notation is presented, resulting in a unified formulation for the shallow water equations that covers all orthogonal horizontal grid types of practical interest. This includes spherical curvilinear orthogonal co-ordinate systems on the globe. Computational efficiency can be achieved in a single computer code. Furthermore, a single numerical algorithmic code implementation satisfies. All co-ordinate system specific metrics are determined as part of a computer-aided model grid design, which supports all four orthogonal grid types. Existing intuitive grid design and visual interpretation is conserved by appropriate conformal mappings, which conserve spherical orthogonality in planar representation. A spherical curvilinear co-ordinate solution of wind driven steady channel flow applying a strongly distorted grid is shown to give good agreement with a regular spherical co-ordinate model approach and the solution based on a Î²-plane approximation. Especially designed spherical curvilinear boundary fitted model grids are shown for typhoon surge propagation in the South China Sea and for ocean-driven flows through Malacca Straits. By using spherical curvilinear grids the number of grid points in these single model grid applications is reduced by a factor of 50-100 in comparison with regular spherical grids that have the same horizontal resolution in the area of interest. The spherical curvilinear approach combines the advantages of the various grid approaches, while the overall computational effort remains acceptable for very large model domains.
NASA Astrophysics Data System (ADS)
Jordan, Pascual; Ehlers, Jürgen; Sachs, Rainer K.
2013-12-01
This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.
NASA Astrophysics Data System (ADS)
Kononets, Y. V.
2010-05-01
An algebraic block-diagonalization of the Dirac Hamiltonian in a time-independent external field reveals a charge-index conservation law which forbids the physical phenomena of the Klein paradox type and guarantees a single-particle nature of the Dirac equation in strong external fields. Simultaneously, the method defines simpler quantum-mechanical objects—paulions and antipaulions, whose 2-component wave functions determine the Dirac electron states through exact operator relations. Based on algebraic symmetry, the presented theory leads to a new understanding of the Dirac equation physics, including new insight into the Dirac measurements and a consistent scheme of relativistic quantum mechanics of electron in the paulion representation. Along with analysis of the mathematical anatomy of the Klein paradox falsity, a complete set of paradox-free eigenfunctions for the Klein problem is obtained and investigated via stationary solutions of the Pauli-like equations with respective paulion Hamiltonians. It is shown that the physically correct Dirac states in the Klein zone are characterized by the total particle reflection from the potential step and satisfy the fundamental charge-index conservation law.
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.
Dahms, Rainer N.
2014-12-31
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phasemoreÂ Â» components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.Â«Â less
The stochastic radiative transfer equation: Quantum damping, Kirchoffs law and NLTE
NASA Astrophysics Data System (ADS)
Graziani, Frank
2006-05-01
A method based on the theory of quantum damping is presented, for deriving a self consistent but approximate form of the quantum transport for photons interacting with a fully ionized electron plasma. Specifically, we propose in this paper a technique of approximately including the effects of background plasma on a photon distribution function without directly solving any kinetic equations for the plasma itself. The result is a quantum Langevin equation for the photon number operator; the quantum radiative transfer equation. A dissipation term appears which is the imaginary part of the dielectric function for an electron gas with photon mediated electron electron interactions due to absorption and re-emission. It depends only on the initial state of the plasma. A quantum noise operator also appears as a result of spontaneous emission of photons from the electron plasma. The thermal expectation value of this noise operator yields the emissivity which is exactly of the form of the Kirchoff Planck relation. This non-zero thermal expectation value is a direct consequence of a fluctuation dissipation relation (FDR).
NASA Astrophysics Data System (ADS)
Ye, Jingxin; Zhao, Bin; Zheng, Jian
2011-03-01
Under hypernetted chain (HNC) approximation, effective ion pair interaction potentials for the warm dense matter are extracted by using available radial distribution functions (RDFs). The effective ion pair potentials extracted from first-principles simulation results are found containing the short-ranged attraction (SRA) component for both warm dense helium and beryllium plasmas. The SRA potentials can be well represented by Gaussian functions in both cases and then the extracted effective ion potentials are well fitted. As an application, the well fitted potentials are used to describe ion-ion interactions in classical molecular dynamics simulations. The yield RDFs are in excellent agreement with those computed by HNC equations and first-principles simulations, respectively.
Ye Jingxin; Zhao Bin; Zheng Jian
2011-03-15
Under hypernetted chain (HNC) approximation, effective ion pair interaction potentials for the warm dense matter are extracted by using available radial distribution functions (RDFs). The effective ion pair potentials extracted from first-principles simulation results are found containing the short-ranged attraction (SRA) component for both warm dense helium and beryllium plasmas. The SRA potentials can be well represented by Gaussian functions in both cases and then the extracted effective ion potentials are well fitted. As an application, the well fitted potentials are used to describe ion-ion interactions in classical molecular dynamics simulations. The yield RDFs are in excellent agreement with those computed by HNC equations and first-principles simulations, respectively.
Jadrich, Ryan; Schweizer, Kenneth S
2013-08-01
Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions. PMID:23927265
Nonlinear Langevin model for the early-stage dynamics of electrospinning jets
NASA Astrophysics Data System (ADS)
Lauricella, Marco; Pontrelli, Giuseppe; Pisignano, Dario; Succi, Sauro
2015-09-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
Off-equilibrium Langevin dynamics of the discrete nonlinear SchrÃ¶dinger chain
NASA Astrophysics Data System (ADS)
Iubini, S.; Lepri, S.; Livi, R.; Politi, A.
2013-08-01
We introduce suitable Langevin thermostats which are able to control both the temperature and the chemical potential of a one-dimensional lattice of nonlinear SchrÃ¶dinger oscillators. The resulting nonequilibrium stationary states are then investigated in the limit of low temperatures and large particle densities, where the dynamics can be mapped onto that of a coupled-rotor chain with an external torque. As a result, an effective kinetic definition of temperature can be introduced and compared with the general microcanonical (global) definition.
Lisin, E. A.; Lisina, I. I.; Vaulina, O. S.; Petrov, O. F.
2015-03-15
Solution of the inverse Langevin problem is presented for open dissipative systems with anisotropic interparticle interaction. Possibility of applying this solution for experimental determining the anisotropic interaction forces between dust particles in complex plasmas with ion flow is considered. For this purpose, we have tested the method on the results of numerical simulation of chain structures of particles with quasidipole-dipole interaction, similar to the one occurring due to effects of ion focusing in gas discharges. Influence of charge spatial inhomogeneity and fluctuations on the results of recovery is also discussed.
A Unified Proof of the Harada-Sasa Equality for Underdamped and Overdamped Langevin Systems
NASA Astrophysics Data System (ADS)
Yamada, Kazuo; Yoshimori, Akira
2014-05-01
A new expression of the Harada-Sasa equality is derived by multiple-scale analysis. The new expression unifies the equality for the underdamped and overdamped Langevin models in special cases. In addition, the expression shows that the equality is available in a new time region, which differs from that in the underdamped or overdamped model. The expression is obtained by the expansion of the fluctuation response relation (FRR) violation in the underdamped model in powers of ? = m/?, where ? is the friction coefficient and m is the mass of a Brownian particle. The violation of the FRR is in agreement with the energy dissipation rate up to the second order of ?.
Kinematic matrix theory and universalities in self-propellers and active swimmers.
Nourhani, Amir; Lammert, Paul E; Borhan, Ali; Crespi, Vincent H
2014-06-01
We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers. PMID:25019773
Kinematic matrix theory and universalities in self-propellers and active swimmers
NASA Astrophysics Data System (ADS)
Nourhani, Amir; Lammert, Paul E.; Borhan, Ali; Crespi, Vincent H.
2014-06-01
We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales. Active fluctuations and hydrodynamic interactions can be expressed as an additive composition of separate self-propellers.
DOE R&D Accomplishments Database
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
Uma, B.; Radhakrishnan, R.; Eckmann, D.M.
2014-01-01
A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered. PMID:25621317
Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling
NASA Astrophysics Data System (ADS)
Wu, Xiongwu; Hodoscek, Milan; Brooks, Bernard R.
2012-07-01
This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.
Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions.
Chavanis, Pierre-Henri; Sire, Clément
2004-01-01
We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. This is a basic model of stochastic particles in interaction. The equilibrium states correspond to polytropic configurations similar to stellar polytropes and polytropic stars. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-friction limit and reduce the problem to the study of the nonlinear Smoluchowacute;ski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function of D and n, and determine their stability by using turning point arguments and analytical methods. When no equilibrium state exists, we investigate self-similar solutions of the nonlinear Smoluchowski-Poisson system describing the collapse. Our stability analysis of polytropic spheres can be used to settle the generalized thermodynamical stability of self-gravitating Langevin particles as well as the nonlinear dynamical stability of stellar polytropes, polytropic stars and polytropic vortices. Our study also has applications concerning the chemotactic aggregation of bacterial populations. PMID:14995676
Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks
NASA Astrophysics Data System (ADS)
Powell, Sean K.; Momot, Konstantin I.
2012-09-01
In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(?), with the minimum anisotropy occurring at approximately the magic angle (?MA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle ? progresses from 0? to 90?. The corresponding diffusion ellipsoids are prolate for ??MA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.
Thermal equilibrium properties of surface hopping with an implicit Langevin bath
Sherman, M. C.; Corcelli, S. A.
2015-01-14
The ability of fewest switches surface hopping (FSSH) approach, where the classical degrees of freedom are coupled to an implicit Langevin bath, to establish and maintain an appropriate thermal equilibrium was evaluated in the context of a three site model for electron transfer. The electron transfer model consisted of three coupled diabatic states that each depends harmonically on the collective bath coordinate. This results in three states with increasing energy in the adiabatic representation. The adiabatic populations and distributions of the collective solvent coordinate were monitored during the course of 250 ns FSSH-Langevin (FSSH-L) simulations performed at a broad range of temperatures and for three different nonadiabatic coupling strengths. The agreement between the FSSH-L simulations and numerically exact results for the adiabatic population ratios and solvent coordinate distributions was generally favorable. The FSSH-L method produces a correct Boltzmann distribution of the solvent coordinate on each of the adiabats, but the integrated populations are slightly incorrect because FSSH does not rigorously obey detailed balance. The overall agreement is better at high temperatures and for high nonadiabatic coupling, which agrees with a previously reported analytical and simulation analysis [J. R. Schmidt, P. V. Parandekar, and J. C. Tully, J. Chem. Phys. 129, 044104 (2008)] on a two-level system coupled to a classical bath.
Oliveira, M B; Llovell, F; Coutinho, J A P; Vega, L F
2012-08-01
In this work, the soft statistical associating fluid theory (soft-SAFT) equation of state (EoS) has been used to provide an accurate thermodynamic characterization of the pyridinium-based family of ionic liquids (ILs) with the bis(trifluoromethylsulfonyl)imide anion [NTf(2)](-). On the basis of recent molecular simulation studies for this family, a simple molecular model was proposed within the soft-SAFT EoS framework. The chain length value was transferred from the equivalent imidazolium-based ILs family, while the dispersive energy and the molecular parameters describing the cation-anion interactions were set to constant values for all of the compounds. With these assumptions, an appropriate set of molecular parameters was found for each compound fitting to experimental temperature-density data at atmospheric pressure. Correlations for the nonconstant parameters (describing the volume of the IL) with the molecular weight were established, allowing the prediction of the parameters for other pyridiniums not included in the fitting. Then, the suitability of the proposed model and its optimized parameters were tested by predicting high-pressure densities and second-order thermodynamic derivative properties such as isothermal compressibilities of selected [NTf(2)] pyridinium ILs, in a large range of thermodynamic conditions. The surface tension was also provided using the density gradient theory coupled to the soft-SAFT equation. Finally, the soft-SAFT EoS was applied to describe the phase behavior of several binary mixtures of [NTf(2)] pyridinium ILs with carbon dioxide, sulfur dioxide, and water. In all cases, a temperature-independent binary parameter was enough to reach quantitative agreement with the experimental data. The description of the solubility of CO(2) in these ILs also allowed identification of a relation between the binary parameter and the molecular weight of the ionic liquid, allowing the prediction of the CO(2) + C(12)py[NTf(2)] mixture. The good agreement with the experimental data shows the excellent ability of the soft-SAFT EoS to describe the thermophysical properties of ILs as well as their phase behavior. Results prove that this equation of state can be a valuable tool to assist the design of ILs (in what concerns cation and anion selection) in order to obtain ILs with the desired properties and, consequently, enhancing their potential industrial applications. PMID:22712755
Stolle, A.M.
1991-01-01
The expressions for the power spectral density of the noise equivalent sources have been calculated explicitly for the (a) stochastic transport equation, (b) the one-speed transport equaton, (c) the one-speed P{sub 1} equations, (d) the one-speed diffusion equation and (e) the point kinetic equation. The stochastic nature of Fick's law in (d) has been emphasized. The Langevin technique has been applied at various levels of approximation to the interpretation of the Californium-252 Source-Driven Noise Analysis (CSDNA) experiment for determining the reactivity in subcritical media. The origin of the controversy surrounding this method has been explained. The foundations of the CSDNA method as a viable experimental technique to infer subcriticality from a measured ratio of power spectral densities of the outputs of two neutron detectors and a third external source detector has been examined by solving the one-speed stochastic diffusion equation for a point external Californium-252 source and two detectors in an infinite medium. The expression relating reactivity to the measured ratio of PSDs was found to depend implicitly on k itself. Through a numerical analysis fo this expression, the authors have demonstrated that for a colinear detector-source-detector configuration for neutron detectors far from the source, the expression for the subcritical multiplication factor becomes essentially insensitive to k, hence, demonstrating some possibility for the viability of this technique. However, under more realistic experimental conditions, i.e., for finite systems in which diffusion theroy is not applicable, the measurement of the subcritical multiplication factor from a single measured ratio of PSDs, without extensive transport calculations, remains doubtful.
Sukoriansky, Semion; Galperin, Boris
2013-01-13
The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data. PMID:23185059