G. Menezes; N. F. Svaiter
2006-03-28
We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient.
Elizondo-Aguilera, L F; Zubieta Rico, P F; Ruiz-Estrada, H; Alarcón-Waess, O
2014-11-01
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (?=T) and rotational (?=R) current densities j_{lm}^{?}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, ?_{T} and ?_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters ? (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states. PMID:25493790
Langevin equations for fluctuating surfaces.
Chua, Alvin L-S; Haselwandter, Christoph A; Baggio, Chiara; Vvedensky, Dimitri D
2005-11-01
Exact Langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam. We consider two types of model: deposition models, where growth proceeds by the deposition and instantaneous local relaxation of particles, with no subsequent movement, and models with concurrent random deposition and surface diffusion. Starting from a Chapman-Kolmogorov equation the deposition, relaxation, and hopping rules of these models are first expressed as transition rates within a master equation for the joint height probability density function. The Kramers-Moyal-van Kampen expansion of the master equation in terms of an appropriate "largeness" parameter yields, according to a limit theorem due to Kurtz [Stoch. Proc. Appl. 6, 223 (1978)], a Fokker-Planck equation that embodies the statistical properties of the original lattice model. The statistical equivalence of this Fokker-Planck equation, solved in terms of the associated Langevin equation, and solutions of the Chapman-Kolmogorov equation, as determined by kinetic Monte Carlo (KMC) simulations of the lattice transition rules, is demonstrated by comparing the surface roughness and the lateral height correlations obtained from the two formulations for the Edwards-Wilkinson [Proc. R. Soc. London Ser. A 381, 17 (1982)] and Wolf-Villain [Europhys. Lett. 13, 389 (1990)] deposition models, and for a model with random deposition and surface diffusion. In each case, as the largeness parameter is increased, the Langevin equation converges to the surface roughness and lateral height correlations produced by KMC simulations for all times, including the crossover between different scaling regimes. We conclude by examining some of the wider implications of these results, including applications to heteroepitaxial systems and the passage to the continuum limit. PMID:16383589
The complex chemical Langevin equation
Schnoerr, David [School of Biological Sciences, University of Edinburgh (United Kingdom); School of Informatics, University of Edinburgh (United Kingdom); Sanguinetti, Guido [School of Informatics, University of Edinburgh (United Kingdom); Grima, Ramon [School of Biological Sciences, University of Edinburgh (United Kingdom)
2014-07-14
The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.
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 CLE's main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE's predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE's accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the "complex CLE" predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation. PMID:25027995
NASA Astrophysics Data System (ADS)
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-01
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments.
Kawai, Shinnosuke; Komatsuzaki, Tamiki
2009-12-14
We present a novel theory which enables us to explore the mechanism of reaction selectivity and robust functions in complex systems persisting under thermal fluctuation. The theory constructs a nonlinear coordinate transformation so that the equation of motion for the new reaction coordinate is independent of the other nonreactive coordinates in the presence of thermal fluctuation. In this article we suppose that reacting systems subject to thermal noise are described by a multidimensional Langevin equation without a priori assumption for the form of potential. The reaction coordinate is composed not only of all the coordinates and velocities associated with the system (solute) but also of the random force exerted by the environment (solvent) with friction constants. The sign of the reaction coordinate at any instantaneous moment in the region of a saddle determines the fate of the reaction, i.e., whether the reaction will proceed through to the products or go back to the reactants. By assuming the statistical properties of the random force, one can know a priori a well-defined boundary of the reaction which separates the full position-velocity space in the saddle region into mainly reactive and mainly nonreactive regions even under thermal fluctuation. The analytical expression of the reaction coordinate provides the firm foundation on the mechanism of how and why reaction proceeds in thermal fluctuating environments. PMID:20001055
Basharov, A. M., E-mail: basharov@gmail.com [National Research Centre 'Kurchatov Institute,' (Russian Federation)
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.
The generalized Schrödinger–Langevin equation
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co [Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, Distrito Capital (Colombia); Miret-Artés, Salvador, E-mail: s.miret@iff.csic.es [Instituto de Física Fundamental, CSIC, Serrano 123, 28006, Madrid (Spain)
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.
Computing generalized Langevin equations and generalized Fokker–Planck equations
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-01-01
The Mori–Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker–Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori–Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems. PMID:19549838
Langevin theory of anomalous Brownian motion made simple
NASA Astrophysics Data System (ADS)
Tóthová, Jana; Vasziová, Gabriela; Glod, Lukáš; Lisý, Vladimír
2011-05-01
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 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.
A path integral approach to the Langevin equation
NASA Astrophysics Data System (ADS)
Das, Ashok K.; Panda, Sudhakar; Santos, J. R. L.
2015-02-01
We study the Langevin equation with both a white noise and a colored noise. We construct the Lagrangian as well as the Hamiltonian for the generalized Langevin equation which leads naturally to a path integral description from first principles. This derivation clarifies the meaning of the additional fields introduced by Martin, Siggia and Rose in their functional formalism. We show that the transition amplitude, in this case, is the generating functional for correlation functions. We work out explicitly the correlation functions for the Markovian process of the Brownian motion of a free particle as well as for that of the non-Markovian process of the Brownian motion of a harmonic oscillator (Uhlenbeck-Ornstein model). The path integral description also leads to a simple derivation of the Fokker-Planck equation for the generalized Langevin equation.
Fluctuations of the expansion: The Langevin-Raychaudhuri equation
NASA Astrophysics Data System (ADS)
Borgman, Jacob
2004-09-01
We discuss a new semiclassical approach to the investigation of fluctuations of the energy-stress tensor in terms of passive fluctuations of the gravitational field. By using a Langevin version of the Raychaudhuri's equation, one can investigate the effect of stress-tensor fluctuations on the behavior of a bundle of light rays traversing various spacetimes. The gravitational source in each case will be that of a massless scalar field. A useful quantity to accomplish this analysis is the so- called expansion parameter, defined as the divergence of the tangent vector along a congruence of geodesic paths. Calculations of the variance of the expansion reveals the degree to which the image of a distant sources suffers luminosity fluctuations. In principle, this could be used as a check on the viability of certain theories (such as extra compactified dimensions), as well as a prediction of exactly what circumstances might lead to significant effects within the framework of general curved 4D models.
Stochastic Gravity and the Langevin-Raychaudhuri Equation
NASA Astrophysics Data System (ADS)
Borgman, J.; Ford, L. H.
We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.
Diffusion described with quantum Langevin equation in tilted periodic potential
NASA Astrophysics Data System (ADS)
Duan, Hong-Guang; Liang, Xian-Ting
2012-11-01
In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.
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.
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…
Harting, Jens
Coupled Langevin Equations for the North Atlantic Oscillation Pedro Lind, Alejandro Mora, Jason Gallas, Maria Haase · Introduction: (i) The North Atlantic Oscillation (NAO). (ii) The Langevin equation Atlantic region ranging from central North America to Europe and much into Northern Asia. · The NAO
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
Julian Schmidt; Alex Meistrenko; Hendrik van Hees; Carsten Greiner
2014-08-01
We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.
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.
Chiral Langevin theory for non-Abelian plasmas
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao; Yamamoto, Naoki
2014-12-01
Charged plasmas with chirality imbalance are unstable and tend to reduce the imbalance. This chiral plasma instability is, however, not captured in (anomalous) hydrodynamics for high-temperature non-Abelian plasmas. We derive a Langevin-type classical effective theory with anomalous parity-violating effects for non-Abelian plasmas that describes the chiral plasma instability at the magnetic scale. We show that the time scale of the instability is of order [g4T ln (1 /g )]-1 at weak coupling.
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
NASA Astrophysics Data System (ADS)
Schmidt, Julian; Meistrenko, Alex; van Hees, Hendrik; Xu, Zhe; Greiner, Carsten
2015-03-01
We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function, and then we study numerically the impact of time-correlated noise on the time evolution of a (1 +1 )-dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.
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.
Nasstrom, J.S.; Ermak, D.L.
1997-04-01
Lagrangian stochastic modeling based on the Langevin equation has been shown to be useful for simulating vertical dispersion of trace material in the convective boundary layer or CBL. This modeling approach can account for the effects of the long velocity correlation time scales, skewed vertical velocity distributions, and vertically inhomogeneous turbulent properties found in the CBL. It has been recognized that Langevin equation models assuming skewed but homogenous velocity statistics can capture the important aspects of diffusion from sources in the CBL, especially elevated sources. We compare three reflection boundary conditions using two different Langevin-equation-based numerical models for vertical dispersion in skewed, homogeneous turbulence. One model, described by Ermak and Nasstrom (1995) is based on a Langevin equation with a skewed random force and a linear deterministic force. The second model, used by Hurley and Physick (1993) is based on a Langevin equation with a Gaussian random force and a non-linear deterministic force. The reflection boundary conditions are all based on the approach described by Thompson and Montgomery (1994).
Langevin equation with stochastic damping - Possible application to critical binary fluid
NASA Technical Reports Server (NTRS)
Jasnow, D.; Gerjuoy, E.
1975-01-01
We solve the familiar Langevin equation with stochastic damping to represent the motion of a Brownian particle in a fluctuating medium. A connection between the damping and the random driving forces is proposed which preserves quite generally the Einstein relation between the diffusion and mobility coefficients. We present an application to the case of a Brownian particle in a critical binary mixture.
Scaled Langevin equation for complex systems: New linear scaling relation for weight factor
S. Fujita; S. S. Lee; J. Koyama
1997-01-01
A set of scaled Langevin equations is proposed to study a long time tail of correlation functions for two model systems (Type I and Type II). Each system is composed of elements which are grouped into clusters according to dynamical activations for external forces. The clusters in Type I are characterized by linear scaling rules in repetitive operations, whereas the
Study of dissipative dynamics in fission of hot nuclei using Langevin equation
Gargi Chaudhuri
2004-01-01
The fission of highly excited compound nuclei formed in heavy ion induced fusion reactions has emerged as a topic of considerable interest in the recent years. Dissipative dynamical models based on the Langevin equation were developed and were applied successfully for fission dynamics of highly excited heavy nuclei. However, Wall Friction(WF), the standard version of nuclear friction when incorporated in
Brett, Tobias, E-mail: tobias.brett@postgrad.manchester.ac.uk; Galla, Tobias, E-mail: tobias.galla@manchester.ac.uk [Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL (United Kingdom)] [Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL (United Kingdom)
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.
Svetislav Savovic; Alexandar Djordjevich
2002-01-01
The power-flow equation is approximated by the Fokker-Planck equation that is further transformed into a stochastic differential (Langevin) equation, resulting in an efficient method for the estimation of the state of mode coupling along step-index optical fibers caused by their intrinsic perturbation effects. The inherently stochastic nature of these effects is thus fully recognized mathematically. The numerical integration is based
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.
New Kinematic Model in comparing with Langevin equation and Fokker Planck Equation
NASA Astrophysics Data System (ADS)
Lee, Kyoung; Wang, Zhijian; Gardner, Robin
2010-03-01
An analytic approximate solution of New Kinematic Model with the boundary conditions is developed for the incompressible packing condition in Pebble Bed Reactors. It is based on velocity description of the packing density in the hopper. The packing structure can be presented with a jamming phenomenon from flow types. The gravity-driven macroscopic motions are governed not only by the geometry and external boundary conditions of silos and hoppers, but by flow prosperities of granular materials, such as friction, viscosity and porosity. The analytical formulas for the quasi-linear diffusion and convection coefficients of the velocity profile are obtained. Since it was found that the New Kinematic Model is dependent upon the granular packing density distribution, we are motivated to study the Langevin equation with friction under the influence of the Gravitational field. We also discuss the relation with the Fokker Planck Equation using Detailed balance and Metropolis-Hastings Algorithm. Markov chain Monte Carlo methods are shown to be a non-Maxwellian distribution function with the mean velocity of the field particles having an effective temperature.
NASA Astrophysics Data System (ADS)
Haga, Taiki
2015-01-01
We investigate a novel type of Langevin model that describes the nonequilibrium dynamics of a classical particle interacting with a spatially extended environment. In this model, a particle, which interacts with the environment through the nonlinear interaction Hamiltonian, is driven by a constant external force, and subsequently, it reaches a nontrivial nonequilibrium steady state. We derive an effective Langevin equation for the particle in the nonequilibrium steady states. Using this equation, we calculate the effective temperature defined as the ratio of the correlation function of the velocity fluctuation to the linear response function with respect to a small perturbation. As a result, it is shown that the effective temperature associated with the time scale of the particle is identical to the kinetic temperature if the time scale of the environment and that of the particle are well separated. Furthermore, a noteworthy expression, which relates the kinetic temperature with the curvature of the driving force-mean velocity curve, is derived.
Kwok, Sau Fa, E-mail: kwok@dfi.uem.br
2012-08-15
A Langevin equation with multiplicative white noise and its corresponding Fokker-Planck equation are considered in this work. From the Fokker-Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: Black-Right-Pointing-Pointer Fokker-Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. Black-Right-Pointing-Pointer Transformation of diffusion processes into the Wiener process in different prescriptions is provided. Black-Right-Pointing-Pointer The prescription parameter is associated with the growth rate for a Gompertz-type model.
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
Baczewski, Andrew D; Bond, Stephen D
2013-07-28
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel. PMID:23901960
NASA Astrophysics Data System (ADS)
Baczewski, Andrew D.; Bond, Stephen D.
2013-07-01
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive phenomena. Molecular dynamics (MD) simulations that include GLD in conjunction with external and/or pairwise forces require the development of numerical integrators that are efficient, stable, and have known convergence properties. In this article, we derive a family of extended variable integrators for the Generalized Langevin equation with a positive Prony series memory kernel. Using stability and error analysis, we identify a superlative choice of parameters and implement the corresponding numerical algorithm in the LAMMPS MD software package. Salient features of the algorithm include exact conservation of the first and second moments of the equilibrium velocity distribution in some important cases, stable behavior in the limit of conventional Langevin dynamics, and the use of a convolution-free formalism that obviates the need for explicit storage of the time history of particle velocities. Capability is demonstrated with respect to accuracy in numerous canonical examples, stability in certain limits, and an exemplary application in which the effect of a harmonic confining potential is mapped onto a memory kernel.
Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
NASA Astrophysics Data System (ADS)
Kanekar, A.; Schekochihin, A. A.; Dorland, W.; Loureiro, N. F.; Loureiro
2015-01-01
A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard ``fluid'' one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.
Tiberiu Harko; Chun Sing Leung; Gabriela Mocanu
2014-05-12
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise, which accounts for the general memory and retarded effects of the frictional force, and on the fluctuation-dissipation theorem. The presence of the memory effects influences the response of the disk to external random interactions, and modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution (PSD) of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei (AGN) may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.
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.
Internal noise driven generalized Langevin equation from a nonlocal continuum model
Saikat Sarkar; Shubhankar Roy Chowdhury; Debasish Roy; Ram Mohan Vasu
2015-03-10
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 (DOF), is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new 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 constraint equation, similar to a fluctuation dissipation theorem (FDT), is shown to statistically relate the internal noise to the other parameters in the GLE.
NASA Astrophysics Data System (ADS)
Grebenkov, Denis S.; Vahabi, Mahsa
2014-01-01
We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells.
Kim, Min-Geun; Jang, Hong-Lae [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Cho, Seonho, E-mail: secho@snu.ac.kr [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)] [National Creative Research Initiatives Center for Isogeometric Optimal Design and Department of Naval Architecture and Ocean Engineering, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-744 (Korea, Republic of)
2013-05-01
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.
Langevin Poisson-Boltzmann equation: point-like ions and water dipoles near a charged surface.
Gongadze, Ekaterina; van Rienen, Ursula; Kralj-Igli?, Veronika; Igli?, Aleš
2011-06-01
Water ordering near a charged membrane surface is important for many biological processes such as binding of ligands to a membrane or transport of ions across it. In this work, the mean-field Poisson-Boltzmann theory for point-like ions, describing an electrolyte solution in contact with a planar charged surface, is modified by including the orientational ordering of water. Water molecules are considered as Langevin dipoles, while the number density of water is assumed to be constant everywhere in the electrolyte solution. It is shown that the dielectric permittivity of an electrolyte close to a charged surface is decreased due to the increased orientational ordering of water dipoles. The dielectric permittivity close to the charged surface is additionally decreased due to the finite size of ions and dipoles. PMID:21613667
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 h(M). The coefficients of the Kramers-Moyal expansion for the conditional probability density function (PDF) P(y,h|y(0),h(0)) are then computed. The resulting PDFs satisfy a Fokker-Planck (FP) equation, which is equivalent to a Langevin equation for y(h) that provides probabilistic predictions for the porosity logs. We also show that the Hurst exponent H of the self-affine distributions, which have been used in the past to describe the porosity logs, is directly linked to the drift and diffusion coefficients that we compute for the FP equation. Also computed are the level-crossing probabilities that provide insight into identifying the high or low values of the porosity beyond the depth interval in which the data have been measured. PMID:21405908
Complex Langevin dynamics for SU(3) gauge theory in the presence of a theta term
Lorenzo Bongiovanni; Gert Aarts; Erhard Seiler; Denes Sexty
2014-11-04
One of the yet unsolved questions of QCD in the context of the Standard Model is to explain the strong CP problem. A way to look for a better understanding of it is to investigate the theory in the presence of a non-zero topological theta term. On the lattice such a term is complex: hence it introduces a sign problem which, in general, limits the applicability of standard Monte Carlo methods. Here we will discuss the approach of complex Langevin dynamics and show results for both real and imaginary values of theta. We also report on our experience with the gradient flow for real and imaginary theta.
Langevin equations and computed correlation functions for a rotating and translating asymmetric top
NASA Astrophysics Data System (ADS)
Evans, M. W.; Evans, G. J.
1986-07-01
The three-dimensional diffusion in condensed material of a rotating and translating asymmetric-top molecule is considered with use of three frames of reference: the laboratory frame (x,y,z), a rotating frame (1,2,3)', and a moving frame (1,2,3). The frame (1,2,3)' has the same origin as (x,y,z), but rotates with an angular velocity ?, the molecular angular velocity. The frame (1,2,3) is defined by the principal molecular moments of inertia, and its origin is therefore the molecular center of mass. The molecular angular velocity ? is the same in all three frames. By writing a pair of simultaneous single-molecule Langevin equations, a rotational equation in (1,2,3) and a translational equation in frame (1,2,3)', a natural description of the molecular diffusion is obtained without the need of friction cross terms. This description introduces into the analysis the center-of-mass position vector r, and the forces obtained by transforming Newton's equation into a noninertial frame, i.e., by the frame transformation (x,y,z)-->(1,2,3)' or vice versa. These are the Coriolis force 2m?×v, the centripetal force m?×(?×r), and the force m??×r. The analysis also implies the consideration of the velocity ?×r. Here v is the molecular center-of-mass linear velocity, ? the angular velocity, and r the position vector of the center of mass. It is shown by computer simulation that autocorrelation and cross-correlation functions of these terms can exist both in frame (x,y,z) and in frame (1,2,3), the moving frame. Examples are provided in the liquid state for the achiral asymmetric top dichloromethane and for the enantiomers and racemic mixture of bromochlorofluoromethane at two state points. The symmetry properties of some of the new cross-correlation functions are tabulated. Finally, experimental methods are suggested for observing cross-correlation functions such as these and for testing experimentally the detailed numerical paradigm provided by these computer simulations. Examples of one method are given with reference to the far-infrared power absorption of the tris(acetylacetonate) complexes of cobalt and chromium in the powdered crystalline state.
NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-02-01
We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.
NASA Astrophysics Data System (ADS)
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-01
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ?T, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 - 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Two critical issues in Langevin simulation of gas flows
NASA Astrophysics Data System (ADS)
Zhang, Jun; Fan, Jing
2014-12-01
A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.
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.
Langevin model for reactive transport in porous media.
Tartakovsky, Alexandre M
2010-08-01
Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing. PMID:20866900
The lattice gluon propagator in numerical stochastic perturbation theory
The lattice gluon propagator in numerical stochastic perturbation theory E.-M. Ilgenfritz1, H #12;Outline 1 Introduction 2 The Langevin equation Langevin equation for lattice QCD Perturbative Langevin equation 3 Gluon propagator and NSPT Lattice gluon propagator Perturbative gluon propagator
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.
Localised distributions and criteria for correctness in complex Langevin dynamics
Aarts, Gert, E-mail: g.aarts@swan.ac.uk [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom)] [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Giudice, Pietro, E-mail: p.giudice@uni-muenster.de [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom)] [Department of Physics, College of Science, Swansea University, Swansea (United Kingdom); Seiler, Erhard, E-mail: ehs@mppmu.mpg.de [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)] [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München (Germany)
2013-10-15
Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker–Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected. -- Highlights: •Characterisation of the equilibrium distribution sampled in complex Langevin dynamics. •Connection between criteria for correctness and breakdown. •Solution of the Fokker–Planck equation in the case of real noise. •Analytical determination of support in complexified space.
Ooi, C. H. Raymond; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.
2007-01-01
February 2007; published 6 February 2007#2; DOI: 10.1103/PhysRevA.75.029902 PACS number#1;s#2;: 42.50.Dv, 42.50.Gy, 42.50.Lc, 03.67.Mn, 99.10.Fg This paper was published online on 31 January 2007 without all of the author?s corrections incorporated...Publisher?s Note: Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory [Phys. Rev. A 75, 013820 (2007)] C. H. Raymond Ooi, Qingqing Sun, M. Suhail Zubairy, and Marlan O. Scully #1;Received 1...
Al Hanbali, Ahmad
theory of partial differential equations a. zagaris Theory of Partial Differential Equations (155010) (Some) Prerequisites & (Numerous) Remarks antonios zagaris | university of twente Guidelines://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2006.) 1 #12;theory of partial differential equations a. zagaris
Polynomial equations for rational conformal field theories
Gregory Moore; Nathan Seiberg
1988-01-01
Duality of the conformal blocks of a rational conformal field theory defines matrices which may be used to construct representations of all monodromies and modular transformations in the theory. These duality matrices satisfy a finite number of independent polynomial equations, which imply constraints on monodromies allowed in rational conformal field theories. The equations include a key identity needed to prove
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.
Relativistic Langevin dynamics in expanding media.
He, Min; van Hees, Hendrik; Gossiaux, Pol B; Fries, Rainer J; Rapp, Ralf
2013-09-01
We study the consequences of different realizations of diffusion processes in relativistic Langevin simulations. We elaborate on the Ito-Stratonovich dilemma by showing how microscopically calculated transport coefficients as obtained from a Boltzmann-Fokker-Planck equation can be implemented to lead to an unambiguous realization of the Langevin process. Pertinent examples within the prepoint (Ito) and postpoint (Hänggi-Klimontovich) Langevin prescriptions are worked out explicitly. Deviations from this implementation are shown to generate variants of the Boltzmann distribution as the stationary (equilibrium) solutions. Finally, we explicitly verify how the Lorentz invariance of the Langevin process is maintained in the presence of an expanding medium, including the case of an "elliptic flow" transmitted to a Brownian test particle. This is particularly relevant for using heavy-flavor diffusion as a quantitative tool to diagnose transport properties of QCD matter as created in ultrarelativistic heavy-ion collisions. PMID:24125244
Entropy theory for derivation of infiltration equations
NASA Astrophysics Data System (ADS)
Singh, Vijay P.
2010-03-01
An entropy theory is formulated for modeling the potential rate of infiltration in unsaturated soils. The theory is composed of six parts: (1) Shannon entropy, (2) principle of maximum entropy (POME), (3) specification of information on infiltration in terms of constraints, (4) maximization of entropy in accordance with POME, (5) derivation of the probability distribution of infiltration, and (6) derivation of infiltration equations. The theory is illustrated with the derivation of six infiltration equations commonly used in hydrology, watershed management, and agricultural irrigation, including Horton, Kostiakov, Philip two-term, Green-Ampt, Overton, and Holtan equations, and the determination of the least biased probability distributions of these infiltration equations and their entropies. The theory leads to the expression of parameters of the derived infiltration equations in terms of measurable quantities (or information), called constraints, and in this sense these equations are rendered nonparametric. Furthermore, parameters of these infiltration equations can be expressed in terms of three measurable quantities: initial infiltration, steady infiltration, and soil moisture retention capacity. Using parameters so obtained, infiltration rates are computed using these six infiltration equations and are compared with field experimental observations reported in the hydrologic literature as well as the rates computed using parameters of these equations obtained by calibration. It is found that infiltration parameter values yielded by the entropy theory are good approximations.
Langevin's `Twin Paradox' paper revisited
J. H. Field
2008-11-21
An in-depth and mathematically-detailed analysis of Langevin's popular 1911 article on the special theory of relativity is presented. For the reader's convenience, English translations of large parts of the original French text are given. The self-contradictory nature of many of Langevin's assertions is pointed out. Of special interest is the analysis of the exchange of light signals between the travelling and stay-at-home twins in Langevin's thought experiment, in which antinomies are found in the conventional relativistic treatment. Their resolution shows that the physical basis of the differential aging effect in the experiment is not `length contraction', as in the conventional interpretation, but instead the application of the correct relative velocity transformation formula. The spurious nature of the correlated `length contraction' and `relativity of simultaneity' effects of conventional special relativity is also demonstrated. In consequence, an argument given, claiming to demonstrate that an upper limit of $c$ on the speed of any physical signal is required by causality, is invalid. Its conclusion is also in contradiction with astronomical observations and the results of a recent experiment.
Boltzmann-Langevin transport model for heavy-ion collisions
Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States)]|[Joint Institute for Heavy-Ion Research, Oak Ridge, TN (United States)
1994-06-01
Heavy-ion collisions at intermediate energies exhibit catastrophic phenomena which requires descriptions based on stochastic transport models. First, the Boltzmann-Langevin model, which provides an example of such stochastic approaches, is briefly described. Then, a projection method for obtaining numerical solutions of the Boltzmann-Langevin equation is discussed. Finally, some applications of the model to heavy-ion collisions are presented.
Symmetry of Differential Equations and Quantum Theory
NASA Astrophysics Data System (ADS)
Yerchuck, Dmitri; Dovlatova, Alla; Alexandrov, Andrey
2014-03-01
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.
Deducibility constraints, equational theory and electronic money #
Comon-Lundh, Hubert
Deducibility constraints, equational theory and electronic money # Sergiu Bursuc 1 , Hubert Comon, France Abstract. The starting point of this work is a case study (from France Tâ??elâ??ecom) of an electronic by the RNTL project PROUV â?? E and POS â?? E. #12; perfect cryptography case. The extension to several equational
Analysis of multifrequency langevin composite ultrasonic transducers
Shuyu Lin
2009-01-01
The multimode coupled vibration of Langevin composite ultrasonic transducers with conical metal mass of large cross-section is analyzed. The coupled resonance and anti- resonance frequency equations are derived and the effective electromechanical coupling coefficient is analyzed. The effect of the geometrical dimensions on the resonance frequency, the anti-resonance frequency, and the effective electromechanical coupling coefficient is studied. It is illustrated
Brownian motion from Boltzmann's equation.
NASA Technical Reports Server (NTRS)
Montgomery, D.
1971-01-01
Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.
a Comment on Topological Field Theory Quantization and Stochastic Processes
L. F. Cugliandolo; G. Lozano; H. Montani; F. A. Schaposnik
1990-01-01
We discuss the relation between different quantization approaches to topological field theories by deriving a connection between Bogomol'nyi and Langevin equations for stochastic processes which evolve towards an equilibrium state governed by the topological charge.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Wong's equations in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Storchak, Sergey N.
2014-04-01
Wong's equations for the finite-dimensional dynamical system representing the motion of a scalar particle on a compact Riemannian manifold with a given free isometric smooth action of a compact semi-simple Lie group are derived. The equations obtained are written in terms of dependent coordinates which are typically used in an implicit description of the local dynamics given on the orbit space of the principal fiber bundle. Using these equations, we obtain Wong's equations in a pure Yang-Mills gauge theory with Coulomb gauge fixing. This result is based on the existing analogy between the reduction procedures performed in a finite-dimensional dynamical system and the reduction procedure in Yang-Mills gauge fields.
On the Langevin approach to particle transport
NASA Astrophysics Data System (ADS)
Bringuier, Eric
2006-03-01
In the Langevin description of Brownian motion, the action of the surrounding medium upon the Brownian particle is split up into a systematic friction force of Stokes type and a randomly fluctuating force, alternatively termed noise. That simple description accounts for several basic features of particle transport in a medium, making it attractive to teach at the undergraduate level, but its range of applicability is limited. The limitation is illustrated here by showing that the Langevin description fails to account realistically for the transport of a charged particle in a medium under crossed electric and magnetic fields and the ensuing Hall effect. That particular failure is rooted in the concept of the friction force rather than in the accompanying random force. It is then shown that the framework of kinetic theory offers a better account of the Hall effect. It is concluded that the Langevin description is nothing but an extension of Drude's transport model subsuming diffusion, and so it inherits basic limitations from that model. This paper thus describes the interrelationship of the Langevin approach, the Drude model and kinetic theory, in a specific transport problem of physical interest.
Dynamical mean-field theory for correlated electrons by Dieter Vollhardt
Texas at Austin. University of
by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time by Einstein in 1905 [2], the Brown- ian motion of a suspended particle is a consequence of the thermal motion]. Langevin's approach is more intuitive than Einstein's approach, and the result- ing "Langevin equation" has
Smith, Hart F.
Contents Ordinary Differential Equations 1 Existence and Uniqueness Theory Theorem for Nonlinear Real Scalar Equations . . . . . . . . . . 15 Continuation of Solutions . . . . . . . . . . . . . 20 Continuity and Differentiability of Solutions . . . . . . . . . . . . . . . . . . . . . 21
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+?uxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=?(?), ? =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ? with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and ?. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].
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.
Fermionic covariant prolongation structure theory for supernonlinear evolution equation
Cheng Jipeng [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, University of Science and Technology of China, Hefei 230026 (China); Wang Shikun [College of Mathematics and Information Science, Henan University, Kaifeng 475004 (China); KLMM, AMSS, Chinese Academy of Sciences, Beijing 100080 (China); Wu Ke [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); KLMM, AMSS, Chinese Academy of Sciences, Beijing 100080 (China); Zhao Weizhong [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing 100048 (China)
2010-09-15
We investigate the superprincipal bundle and its associated superbundle. The super(nonlinear)connection on the superfiber bundle is constructed. Then by means of the connection theory, we establish the fermionic covariant prolongation structure theory of the supernonlinear evolution equation. In this geometry theory, the fermionic covariant fundamental equations determining the prolongation structure are presented. As an example, the supernonlinear Schroedinger equation is analyzed in the framework of this fermionic covariant prolongation structure theory. We obtain its Lax pairs and Baecklund transformation.
The DeWitt Equation in Quantum Field Theory
Parikshit Dutta; Krzysztof A. Meissner; Hermann Nicolai
2013-03-14
We take a new look at the DeWitt equation, a defining equation for the effective action functional in quantum field theory. We present a formal solution to this equation, and discuss the equation in various contexts, and in particular for models where it can be made completely well defined, such as the Wess-Zumino model in two dimensions.
Theory of relativistic Brownian motion: the (1+1)-dimensional case.
Dunkel, Jörn; Hänggi, Peter
2005-01-01
We construct a theory for the (1+1)-dimensional Brownian motion in a viscous medium, which is (i) consistent with Einstein's theory of special relativity and (ii) reduces to the standard Brownian motion in the Newtonian limit case. In the first part of this work the classical Langevin equations of motion, governing the nonrelativistic dynamics of a free Brownian particle in the presence of a heat bath (white noise), are generalized in the framework of special relativity. Subsequently, the corresponding relativistic Langevin equations are discussed in the context of the generalized Ito (prepoint discretization rule) versus the Stratonovich (midpoint discretization rule) dilemma: It is found that the relativistic Langevin equation in the Hänggi-Klimontovich interpretation (with the postpoint discretization rule) is the only one that yields agreement with the relativistic Maxwell distribution. Numerical results for the relativistic Langevin equation of a free Brownian particle are presented. PMID:15697675
The Langevin Approach: a simple stochastic method for complex phenomena
Reinke, Nico; Medjroubi, Wided; Lind, Pedro G; Wächter, Matthias; Peinke, Joachim
2015-01-01
We describe a simple stochastic method, so-called Langevin approach, which enables one to extract evolution equations of stochastic variables from a set of measurements. Our method is parameter-free and it is based on the nonlinear Langevin equation. Moreover, it can be applied not only to processes in time, but also to processes in scale, given that the data available shows ergodicity. This chapter introduces the mathematical foundations of the Langevin approach and describes how to implement it numerically. A specific application of the method is presented, namely to a turbulent velocity field measured in the laboratory, retrieving the corresponding energy cascade and comparing with the results from a computational simulation of that experiment. In addition, we describe a physical interpretation bridging between processes in time and in scale. Finally, we describe extensions of the method for time series reconstruction and applications to other fields such as finance, medicine, geophysics and renewable ener...
On Theories Explaining the Success of the Gravity Equation
Simon J. Evenett; Wolfgang Keller
2001-01-01
We examine whether two important theories of trade, the Heckscher-Ohlin theory and the Increasing Returns theory, can account for the empirical success of the so-called gravity equation. Since versions of both theories can predict this equation, we tackle the model identification problem by conditioning bilateral trade relations on factor endowment differences and on the share of intra-industry trade. Only for
THEORY FOR THE KOLMOGOROV OPERATORS OF STOCHASTIC GENERALIZED BURGERS EQUATIONS
RÃ¶ckner, Michael
L1 ÂTHEORY FOR THE KOLMOGOROV OPERATORS OF STOCHASTIC GENERALIZED BURGERS EQUATIONS MICHAEL R variables which e.g. are associated to stochastic generalized Burgers equations. Their L1Âtheory) on (0, 1), and F : H1 0 X is a measurable vector field satisfying certain conditions specified below
Number Theory Integer points on cubic Thue equations
Number Theory Integer points on cubic Thue equations C.L. Stewart 1 Department of Pure Mathematics 1 for which the Thue equation F(x, y) = m has (log m)6/7 solutions in integers x and y for infinitely many integers m. R´esum´e Points entiers sur les ´equations cubiques de Thue. Nous d´emontrons qu
On the Statistical Theory of Nonequilibrium Processes
V. B. Magalinskij; Ja. P. Terletskij
1960-01-01
A general method is worked out on the basis of principles of Gibbs' statistical mechanics which allows to find stationary probabilities and transition probabilities for physical quantities provided either the behaviour of their mean values or the general form of corresponding equations of motion (Langevin equations) is known.The proposed method is free from ordinary restrictions of the theory of fluctuations
New nonlinear evolution equations from surface theory
Metin Gürses; Yavuz Nutku
1981-01-01
We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso–Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results
Takano's Theory of Quantum Painleve Equations
Yuichi Ueno
2008-04-10
Recently, a quantum version of Painleve equations from the point of view of their symmetries was proposed by H. Nagoya. These quantum Painleve equations can be written as Hamiltonian systems with a (noncommutative) polynomial Hamiltonian. We give a characterization of the quantum Painleve equations by certain holomorphic properties. Namely, we introduce canonical transformations such that the Painleve Hamiltonian system is again transformed into a polynomial Hamiltonian system, and we show that the Hamiltonian can be uniquely characterized through this holomorphic property.
On Pokrovskii's anisotropic gap equations in superconductivity theory
NASA Astrophysics Data System (ADS)
Yang, Yisong
2003-11-01
An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.
Existence Theory for the Isentropic Euler Equations
GUI-QIANG Chen; PHILIPPE G. LEFLOCH
2003-01-01
We establish an existence theorem for entropy solutions to the Euler equations modeling isentropic compressible fluids. We\\u000a develop a new approach for constructing mathematical entropies for the Euler equations, which are singular near the vacuum.\\u000a In particular, we identify the optimal assumption required on the singular behavior on the pressure law at the vacuum in order to validate the two-term
Morse Theory and Nonlinear Differential Equations Thomas Bartsch
Szulkin, Andrzej
Morse Theory and Nonlinear Differential Equations Thomas Bartsch Mathematisches Institut, Universit differential equations -¨q = Vq(q, t), q RN . However, since we consider the more general and more difficult is the study of exis- tence of periodic solutions for the second order Newtonian systems of ordinary
Wave Propagation Theory 2.1 The Wave Equation
perturbations is much smaller than the speed of sound. 2.1.1 The Nonlinear Wave Equation Retaining higher2 Wave Propagation Theory 2.1 The Wave Equation The wave equation in an ideal fluid can be derived.3) and for convenience we define the quantity c2 p S , (2.4) where c will turn out to be the speed of sound in an ideal
Poisson vertex algebras in the theory of Hamiltonian equations
Aliaa Barakat; Alberto De Sole; Victor G. Kac
2009-01-01
. We lay down the foundations of the theory of Poisson vertex algebras aimed at its applications to integrability of Hamiltonian\\u000a partial differential equations. Such an equation is called integrable if it can be included in an infinite hierarchy of compatible\\u000a Hamiltonian equations, which admit an infinite sequence of linearly independent integrals of motion in involution. The construction\\u000a of a hierarchy
METHOD OF INTEGRAL EQUATIONS IN STATISTICAL THEORY OF LIQUIDS
N T Kovalenko; I Z Fisher
1973-01-01
CONTENTS1. Introduction 592 a) Problem of the Theory of the Liquid State 592 b) The Method of Integral Equations 593 2. The Percus-Yevick Equation 594 a) Functional Definition of the Direct Correlation Function 594 b) The Percus Approximation 595 c) Analytic Solution of the Percus-Yevick Equation for a System of Hard Spheres 597 3. Results of Numerical Calculations by the
Statistical mechanical theory of the nonlinear steady state
Hiroshi Furukawa
1974-01-01
By making use of perturbation techniques, we develop a theory of the non-linear steady state. We find that the linear term of a mechanical equation such as the Langevin equation is not responsible for the nonlinear terms of its expectation values at the nonequilibrium state arbitrarily far from the thermal equilibrium. The nonlinear steady state is formulated in the two
NASA Astrophysics Data System (ADS)
Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.; Evans, James W.
2014-07-01
Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P ˜(R-Rc)?, where passing is sterically blocked for R ?Rc, with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.
Wang, Chi-Jen [Ames Laboratory; Ackerman, David M. [Ames Laboratory; Slowing, Igor I. [Ames Laboratory; Evans, James W. [Ames Laboratory
2014-07-14
Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P?(R?Rc)?, where passing is sterically blocked for R?Rc, with ? below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotational degrees of freedom for elongated molecules.
M. V. Borunov; P. N. Nadtochy; G. D. Adeev
2008-01-01
A multi-dimensional stochastic approach based on three-dimensional Langevin equations is applied for calculation of the first four moments of the kinetic-energy distribution of fission fragments in a wide range of Coulomb parameter 700Z2\\/A1\\/31700. A modified one-body mechanism of nuclear dissipation with reduction factor ks=0.25 and different scission criteria widely used in modern fission theory are applied: zero-neck-radius RN=0 and finite-neck-radius
Oppenheimer-Volkoff Equation in Relativistic MOND Theory
Xing-hua Jin; Xin-zhou Li
2006-06-23
In this paper, we discuss the internal and external metric of the semi-realistic stars in relativistic MOND theory. We show the Oppenheimer-Volkoff equation in relativistic MOND theory and get the metric and pressure inside the stars to order of post-Newtonian corrections. We study the features of motion around the static, spherically symmetric stars by Hamilton-Jacobi mothod, and find there are only some small corrections in relativistic MOND theory.
The Boltzmann Equation in Classical and Quantum Field Theory
Sangyong Jeon
2005-07-18
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.
Theory of freezing: The inhomogeneous Ornstein-Zernike equation
McCoy, J.D.; Haymet, A.D.J.
1989-01-01
The authors present a new freezing theory based on the inhomogeneous Ornstein-Zernike equation. The new theory is nonperturbative, in the sense that crystal and liquid are treated at the same level of approximation. This is in contrast to the popular density functional theory of freezing, which uses the liquid as a reference state for perturbation theory. Due to the the demanding nature of the numerical method, preliminary calculations are presented for a model problem-which, in the strictest sense, is unphysical-namely, the freezing of hard disks in two dimensions. They also explore a generalized Percus-Yevick closure appropriate for the crystal.
On Approximate Asymptotic Solution of Integral Equations of Collision Theory
Vagner Jikia; Jemal Mebonia
2014-02-19
It is well known that multi-particle integral equations of collision theory, in general, are not compact. At the same time it has been shown that the motion of three and four particles is described with consistent integral equations. In particular, by using identical transformations of the kernel of the Lipman-Schwinger equation for certain classes of potentials Faddeev obtained Fredholm type integral equations for three-particle problems $[1]$. The motion of for bodies is described by equations of Yakubovsky and Alt-Grassberger-Sandhas-Khelashvili $[2.3]$, which are obtained as a result of two subsequent transpormations of the kernel of Lipman-Schwinger equation. in the case of $N>4$ the compactness of multi-particle equations has not been proven yet. In turn out that for sufficiently high energies the $N$-particle $\\left( {N \\ge 3} \\right)$ dynamic equations have correct asymptotic solutions satisfying unitary condition $[4]$. In present paper by using the Heitler formalism we obtain the results briefly summarized in Ref. [4]. In particular, on the bases of Heitler's equation [5] a unitary asymptotic solution of the system of $N$-particle scattering integral equations is found, which represents a generalization to any number of particles of the result of Ref. $[6]$ obtained for three particles.
Einstein equations and MOND theory from Debye entropic gravity
Sheykhi, A. [Center for Excellence in Astronomy and Astrophysics (CEAA-RIAAM) Maragha, P.O. Box 55134-441 (Iran, Islamic Republic of); Sarab, K. Rezazadeh, E-mail: sheykhi@uk.ac.ir, E-mail: kazem.rezazadeh.sarab@gmail.com [Department of Physics, Shahid Bahonar University, P.O. Box 76175, Kerman (Iran, Islamic Republic of)
2012-10-01
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.
Combined Field Integral Equation Based Theory of Characteristic Mode
Qi I. Dai; Qin S. Liu; Hui Gan; Weng Cho Chew
2015-03-04
Conventional electric field integral equation based theory is susceptible to the spurious internal resonance problem when the characteristic modes of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field integral equation based theory to remove the difficulty of internal resonances in characteristic mode analysis. The electric and magnetic field integral operators are shown to share a common set of non-trivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to characteristic mode analysis which involves electrically large closed surfaces.
Semigroup theory and numerical approximation for equations in linear viscoelasticity
NASA Technical Reports Server (NTRS)
Fabiano, R. H.; Ito, K.
1990-01-01
A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.
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.
Duality, Mechanical Wave Theory, New Quantum Operators and Nonlinear Equations in Quantum Theory
Yi-Fang Chang
2010-08-17
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various mechanical equations, and may be derive some new results. It is called the mechanical wave theory. From this we derive new operators which represent more physical quantities. Further, we propose some nonlinear equations and their solutions, which may be probably applied to quantum theory.
Cosmological post-Newtonian equations from nonlinear perturbation theory
Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Hwang, Jai-chan, E-mail: hr@kasi.re.kr, E-mail: jchan@knu.ac.kr [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of)
2013-08-01
We derive the basic equations of the cosmological first-order post-Newtonian approximation from the recently formulated fully nonlinear and exact cosmological perturbation theory in Einstein's gravity. Apparently the latter, being exact, should include the former, and here we use this fact as a new derivation of the former. The complete sets of equations in both approaches are presented without fixing the temporal gauge conditions so that we can use the gauge choice as an advantage. Comparisons between the two approaches are made. Both are potentially important in handling relativistic aspects of nonlinear processes occurring in cosmological structure formation. We consider an ideal fluid and include the cosmological constant.
Tutorial on Optimization Theory and Difference and Differential Equations
NSDL National Science Digital Library
This online tutorial is intended for college students taking an early course in mathematical optimization or linear differential equations. Although it is written by a professor of economics, little economic theory is presented. This keeps the material centered on the mathematical aspects of optimization and differential equations, which have a wide range of scientific applications. The text is very well organized and is accompanied by illustrative figures. No prerequisites to the tutorial are listed; however, a fairly strong background in undergraduate calculus would probably be useful.
Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
Zhi-Qiang Guo; Ivan Schmidt
2012-08-03
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the massive term for the fermion.
Converting Classical Theories to Quantum Theories by Solutions of Hamilton-Jacobi Equation
Guo, Zhi-Qiang
2012-01-01
By employing special solutions of Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some non-trivial results are obtained for gauge field and fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce a massive term for fermion.
Converting classical theories to quantum theories by solutions of the Hamilton-Jacobi equation
NASA Astrophysics Data System (ADS)
Guo, Zhi-Qiang; Schmidt, Iván
2012-08-01
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained for a gauge field and a fermion field. For a topologically massive gauge theory, we can obtain a first order Lagrangian with mass term. For the fermion field, in order to make our approach feasible, we supplement the conventional Lagrangian with a surface term. This surface term can also produce the mass term for the fermion.
On the WDVV Equation and M-Theory
J. M. Isidro
1998-05-25
A wide class of Seiberg-Witten models constructed by M-theory techniques and described by non-hyperelliptic Riemann surfaces are shown to possess an associative algebra of holomorphic differentials. This is a first step towards proving that also these models satisfy the Witten-Dijkgraaf-Verlinde-Verlinde equation. In this way, similar results known for simpler Seiberg-Witten models (described by hyperelliptic Riemann surfaces and constructed without recourse to M-theory) are extended to certain non-hyperelliptic cases constructed in M-theory. Our analysis reveals a connection between the algebra of holomorphic differentials on the Riemann surface and the configuration of M-theory branes of the corresponding Seiberg-Witten model.
Fluid moment hierarchy equations derived from quantum kinetic theory
F. Haas; M. Marklund; G. Brodin; J. Zamanian
2009-10-27
A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.
The noise spectra comparison of cavity and population inversion Langevin forces in class-A lasers
NASA Astrophysics Data System (ADS)
Soleimani, A.; Jahanpanah, J.
2014-12-01
We have investigated the single role of cavity Langevin force on the noise spectra of class-A and -B lasers for the first time in 2012. The present aim is to consider the simultaneous effect of cavity and population inversion Langevin forces on the noise spectra of class-A lasers. The Maxwell-Bloch equations of motion are thus solved in the presence of both Langevin forces. The solutions give the fluctuations that are imposed to the cavity electric field and atomic population inversion by the Langevin forces. The noise fluxes of stimulated and spontaneous emission radiations are then calculated by using the notion of correlation function. It is demonstrated that the noise fluxes generated by the cavity Langevin force can be comparable or even larger than those produced by the population inversion Langevin force in some rates of laser pumping. The results are ultimately confirmed by illustrating the flux conservation so that the noise flux entered into laser by pumping is equal to those superimposed on the spontaneous and stimulated emission radiations.
On Complex Langevin Dynamics and the Evaluation of Observables
Amel Durakovic; Emil Cortes Andre; Anders Tranberg
2014-08-15
In stochastic quantisation, quantum mechanical expectation values are computed as averages over the time history of a stochastic process described by a Langevin equation. Complex stochastic quantisation, though theoretically not rigorously established, extends this idea to cases where the action is complex-valued by complexifying the basic degrees of freedom, all observables and allowing the stochastic process to probe the complexified configuration space. We review the method for a previously studied one-dimensional toy model, the U(1) one link model. We confirm that complex Langevin dynamics only works for a certain range of parameters, misestimating observables otherwise. A curious effect is observed where all moments of the basic stochastic variable are misestimated, although these misestimated moments may be used to construct, by a Taylor series, other observables that are reproduced correctly. This suggests a subtle but not completely resolved relationship between the original complex integration measure and the higher-dimensional probability distribution in the complexified configuration space, generated by the complex Langevin process.
Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing
NASA Astrophysics Data System (ADS)
Joubaud, R.; Pavliotis, G. A.; Stoltz, G.
2015-01-01
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez in (J Math Biol, 56(6):765-792 2008). In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level—a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.
Equation of state for polymer liquid crystals: theory and experiment
H. H. Strey; V. A. Parsegian; R. Podgornik
1998-07-22
The first part of this paper develops a theory for the free energy of lyotropic polymer nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic phase. By evaluating the partition function, considering only harmonic fluctuations, we derive an expression for the free energy of the system. We find that the configurational entropic part of the free energy enhances the effective repulsive interactions between the chains. This configurational contribution goes as the fourth root of the direct interactions. Enhancement originates from the coupling between bending fluctuations and the compressibility of the nematic array normal to the average director. In the second part of the paper we use osmotic stress to measure the equation of state for DNA liquid crystals in 0.1M to 1M NaCl solutions. These measurements cover 5 orders of magnitude in DNA osmotic pressure. At high osmotic pressures the equation of state, dominated by exponentially decaying hydration repulsion, is independent of the ionic strength. At lower pressures the equation of state is dominated by fluctuation enhanced electrostatic double layer repulsion. The measured equation of state for DNA fits well with our theory for all salt concentrations. We are able to extract the strength of the direct electrostatic double layer repulsion. This is a new and alternative way of measuring effective charge densities along semiflexible polyelectrolytes.
Supersymmetric electroweak baryogenesis, nonequilibrium field theory and quantum Boltzmann equations
Antonio Riotto
1997-12-03
The closed time-path (CTP) formalism is a powerful Green's function formulation to describe nonequilibrium phenomena in field theory and it leads to a complete nonequilibrium quantum kinetic theory. In this paper we make use of the CTP formalism to write down a set of quantum Boltzmann equations describing the local number density asymmetries of the particles involved in supersymmetric electroweak baryogenesis. These diffusion equations automatically and self-consistently incorporate the CP-violating sources which fuel baryogenesis when transport properties allow the CP-violating charges to diffuse in front of the bubble wall separating the broken from the unbroken phase at the electroweak phase transition. This is a significant improvement with respect to recent approaches where the CP-violating sources are inserted by hand into the diffusion equations. Furthermore, the CP-violating sources and the particle number changing interactions manifest ``memory'' effects which are typical of the quantum transp ort theory and are not present in the classical approach. The slowdown of the relaxation processes may keep the system out of equilibrium for longer times and therefore enhance the final baryon asymmetry. We also stress that the classical approximation is not adequate to describe the quantum interference nature of CP-violation and that a quantum approach should be adopted to compute the sources since they are most easily built up by the transmission of low momentum particles.
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.
Renormalization Group Equation for Weakly Power Counting Renormalizable Theories
D. Bettinelli; D. Binosi; A. Quadri
2014-07-15
We study the renormalization group flow in weak power counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent amplitudes order by order in the loop expansion. Using as a toolbox the well-known SU(2) non linear sigma model, we prove that for such theories a renormalization group equation holds that does not violate the WPC condition: that is, the sliding of the scale $\\mu$ for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by the WPC itself. We explore in some detail the consequences of this result; in particular, we prove that it holds in the framework of a recently introduced beyond the Standard Model scenario in which one considers non-linear St\\"uckelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.
On Some Nonlinear Integral Equation in the (Super)String Theory
D. V. Prokhorenko
2006-11-25
In this work some nonlinear integral equation is studied. This equation has arisen in the (super)string field theory and cosmology. In this work it is proved that some boundary problem for this equation has a solution.
Yang, Jianke
Direct perturbation theory for solitons of the derivative nonlinear SchroÂ¨dinger equation 2002 A direct perturbation theory for solitons of the derivative nonlinear SchroÂ¨dinger DNLS equation-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained
Th. Klupsch
1969-01-01
Based on equations, symmetry and boundary conditions of quantum statistical correlation functions of renormalized spin wave excitations in a HEISENBERG ferromagnet including dipolar coupling, the parallel pumping effect under special considering the nonlinear three magnon interaction is discussed. An asymptotic approximation procedure enables us to interpret the fundamental equations in terms of the LANGEVIN theory of BROWNian motion and to
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.
Equation solving program for aerodynamic lifting surface theory
NASA Technical Reports Server (NTRS)
Medan, R. T.; Lemmer, O. J.
1974-01-01
A description of and user's manual are presented for one of a group of FORTRAN programs which, together, can be used for the analysis and design of wings in steady, subsonic flow according to a kernel function method lifting surface theory. This particular program is the one which solves the sets of simultaneous, linear, algebraic equations arising from the thin wing analysis. This program has the capability of striking out rows and columns of the aerodynamic influence matrix and rows of the associated boundary condition vectors (right hand sides). This capability significantly enhances the effectiveness of the kernel function method of lifting surface theory because studies of the convergence of solutions with the number of control points can be done with the calculation of only a single influence matrix.
Classical irregular block, = 2 pure gauge theory and Mathieu equation
NASA Astrophysics Data System (ADS)
Pi?tek, Marcin; Pietrykowski, Artur R.
2014-12-01
Combining the semiclassical/Nekrasov-Shatashvili limit of the AGT conjecture and the Bethe/gauge correspondence results in a triple correspondence which identifies classical conformal blocks with twisted superpotentials and then with Yang-Yang functions. In this paper the triple correspondence is studied in the simplest, yet not completely understood case of pure SU(2) super-Yang-Mills gauge theory. A missing element of that correspondence is identified with the classical irregular block. Explicit tests provide a convincing evidence that such a function exists. In particular, it has been shown that the classical irregular block can be recovered from classical blocks on the torus and sphere in suitably defined decoupling limits of classical external conformal weights. These limits are "classical analogues" of known decoupling limits for corresponding quantum blocks. An exact correspondence between the classical irregular block and the SU(2) gauge theory twisted superpotential has been obtained as a result of another consistency check. The latter determines the spectrum of the 2-particle periodic Toda (sin-Gordon) Hamiltonian in accord with the Bethe/gauge correspondence. An analogue of this statement is found entirely within 2 d CFT. Namely, considering the classical limit of the null vector decoupling equation for the degenerate irregular block a celebrated Mathieu's equation is obtained with an eigenvalue determined by the classical irregular block. As it has been checked this result reproduces a well known weak coupling expansion of Mathieu's eigenvalue. Finally, yet another new formulae for Mathieu's eigenvalue relating the latter to a solution of certain Bethe-like equation are found.
A Second-Order Stochastic Leap-Frog Algorithm for Langevin Simulation
Qiang, J; Qiang, Ji; Habib, Salman
2000-01-01
Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
Theory of Partial Differential Equations (155010) Exercises WC #1 (Week 46) 2011.11.18
Al Hanbali, Ahmad
Theory of Partial Differential Equations (155010) Exercises WC #1 (Week 46) 2011.11.18 01. Consider partial differential equation yux + xuy + (y2 - x2 )u = y2 - x2 . (4) (a) Apply the transformation satisfies equation (4). 03. Consider the first order partial differential equation ux + exuy = 1. (5) (a
Dynamical Theories Brownian Motion
Nelson, Edward
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. Albert Einstein. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3. The period before Einstein phenomenon. I will review the theories put forward to account for it by Einstein, Smoluchowski, Langevin
The Interface Between Theory and Data in Structural Equation Models
Grace, James B.; Bollen, Kenneth A.
2006-01-01
Structural equation modeling (SEM) holds the promise of providing natural scientists the capacity to evaluate complex multivariate hypotheses about ecological systems. Building on its predecessors, path analysis and factor analysis, SEM allows for the incorporation of both observed and unobserved (latent) variables into theoretically based probabilistic models. In this paper we discuss the interface between theory and data in SEM and the use of an additional variable type, the composite, for representing general concepts. In simple terms, composite variables specify the influences of collections of other variables and can be helpful in modeling general relationships of the sort commonly of interest to ecologists. While long recognized as a potentially important element of SEM, composite variables have received very limited use, in part because of a lack of theoretical consideration, but also because of difficulties that arise in parameter estimation when using conventional solution procedures. In this paper we present a framework for discussing composites and demonstrate how the use of partially reduced form models can help to overcome some of the parameter estimation and evaluation problems associated with models containing composites. Diagnostic procedures for evaluating the most appropriate and effective use of composites are illustrated with an example from the ecological literature. It is argued that an ability to incorporate composite variables into structural equation models may be particularly valuable in the study of natural systems, where concepts are frequently multifaceted and the influences of suites of variables are often of interest.
Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
NASA Astrophysics Data System (ADS)
Greensite, Jeff
2014-12-01
Effective Polyakov line models, derived from SU(3) gauge-matter systems at finite chemical potential, have a sign problem. In this article I solve two such models, derived from SU(3) gauge-Higgs and heavy quark theories by the relative weights method, over a range of chemical potentials where the sign problem is severe. Two values of the gauge-Higgs coupling are considered, corresponding to a heavier and a lighter scalar particle. Each model is solved via the complex Langevin method, following the approach of Aarts and James, and also by a mean field technique. It is shown that where the results of mean field and complex Langevin agree, they agree almost perfectly. Where the results of the two methods diverge, it is found that the complex Langevin evolution has a branch cut crossing problem, associated with a logarithm in the action, that was pointed out by Møllgaard and Splittorff.
Carl Svard; Mattias Nyberg
The FDI approach to model-based diagnosis is considered. We present a method for residual generation that combines integral and derivative causality, and also uti- lizes equation system solvers and theory of differential-algebraic equation systems. To achieve this, a framework for computation of variables from sets of dependent differential and\\/or algebraic equations is introduced. The proposed method is ap- plied to
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 Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion. PMID:20364950
Study on the multifrequency Langevin ultrasonic transducer
Shuyu Lin
1995-01-01
Langevin ultrasonic transducers are widely used in high-power ultrasonics and underwater sound. In ultrasonic cleaning, a matching metal horn rather than a metal cylinder is used as the radiator in order to enhance the radiating surface and improve the acoustic matching between the transducer and the processed medium. To raise the effect of ultrasonic cleaning, the standing wave in the
A. V. Latyshev; A. D. Kurilov
2014-07-28
We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Based homogeneous Riemann boundary value problem with a coefficient equal to the ratio of the boundary values dispersion function, develops the theory of the half-space orthogonality of generalized singular eigenfunctions corresponding characteristic equations, which leads separation of variables. And in this two boundary value problems of the kinetic theory (diffusion light component of a binary gas and Kramers problem about isothermal slip) shows the application of the theory orthogonality eigenfunctions for analytical solutions these tasks.
Heavy quark master equations in the Lindblad form at high temperatures
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao
2015-03-01
We derive the quantum master equations for heavy quark systems in a high-temperature quark-gluon plasma in the Lindblad form. The master equations are derived in the influence functional formalism for open quantum systems in perturbation theory. These master equations have a wide range of applications, such as decoherence of a heavy quarkonium and Langevin dynamics of a heavy quark in the quark-gluon plasma. We also show the equivalence between the quarkonium master equations in the recoilless limit and the Schrödinger equations with stochastic potential.
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.
Ordinary differential equations, transport theory and Sobolev spaces
R. J. DiPerna; P. L. Lions
1989-01-01
Summary We obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions.
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.
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
Fouxon, Itzhak; Oz, Yaron [Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978 (Israel)
2008-12-31
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.
Multiscale Dynamics of Macromolecules Using Normal Mode Langevin
Izaguirre, J. A.; Sweet, C. R.; Pande, V. S.
2014-01-01
Proteins and other macromolecules have coupled dynamics over multiple time scales (from femtosecond to millisecond and beyond) that make resolving molecular dynamics challenging. We present an approach based on periodically decomposing the dynamics of a macromolecule into slow and fast modes based on a scalable coarse-grained normal mode analysis. A Langevin equation is used to propagate the slowest degrees of freedom while minimizing the nearly instantaneous degrees of freedom. We present numerical results showing that time steps of up to 1000 fs can be used, with real speedups of up to 200 times over plain molecular dynamics. We present results of successfully folding the Fip35 mutant of WW domain. PMID:19908376
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 dynamics for the transport of flexible biological macromolecules in confined geometries
NASA Astrophysics Data System (ADS)
Peters, Michael H.
2011-01-01
The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an ?-helix protein through a carbon nanotube is simulated.
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
An inverse kinetic theory for the incompressible Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Ellero, M.; Tessarotto, M.
2005-09-01
An inverse kinetic theory applying specifically to incompressible Newtonian fluids which permits us to avoid the N2 algorithmic complexity of the Poisson equation for the fluid pressure is presented. The theory is based on the construction of a suitable kinetic equation in phase space, which permits us to determine exactly the fluid equations by means of the velocity moments of the kinetic distribution function. It is found that the fluid pressure can also be determined as a moment of the distribution function without solving the Poisson equation, as is usually required in direct solution methods for the incompressible fluid equations. Finally, the dynamical system, underlying the incompressible Navier-Stokes equations and advancing in time the fluid fields, has been also identified and proven to produce an unique set of fluid equations.
Heavy Flavor in Medium Momentum Evolution: Langevin vs Boltzmann
Santosh K. Das; Francesco Scardina; Salvatore Plumari; Vincenzo Greco
2014-09-19
The propagation of heavy quarks in the quark-gluon plasma (QGP) has been often treated within the framework of the Langevin equation (LV), i.e. assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass $m_D$. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked ($m_D\\cong T $) or the mass to temperature ratio is quite large ($M_{HQ}/T \\gtrsim 8-10$) there are significant differences in the evolution of the $p-$spectra and consequently on nuclear modification factor $R_{AA}(p_T)$. However for charm quark we find that very similar $R_{AA}(p_T)$ between the LV and BM can be obtained, but with a modified diffusion coefficient by about $\\sim 15-50\\%$ depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by a single heavy quarks we see that at temperatures $T\\gtrsim \\, 250\\,\\rm MeV$ the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultra-relativistic heavy-ion collisions. Finally, we have shown the possible impact of this study on $R_{AA}(p_T)$ and $v_2(p_T)$ for a realistic simulation of relativistic HIC. For larger $m_D$ the elliptic flow can be about $50\\%$ larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of $R_{AA}(p_T)$ and $v_2(p_T)$.
NASA Astrophysics Data System (ADS)
Chandler, David; McCoy, John D.; Singer, Sherwin J.
1986-11-01
With the density functional theory outlined in paper I, we address and formally solve the nonlinear inversion problem associated with identifying the entropy density functional for systems with bonding constraints. With this development, we derive a nonlinear integral equation for the average site density fields of a polyatomic system. When external potential fields are set to zero, the integral equation represents a mean field theory for symmetry breaking and thus phase transformations of polyatomic systems. In the united atom limit where the intramolecular interaction sites become coincident, the mean field theory becomes identical to that developed for simple atomic systems by Ramakrishnan, Yussouff, and others. When the external potential fields are particle producing fields (in the sense introduced long ago by Percus), the integral equation represents a theory for the solvation of a simple spherical solute by a polyatomic solvent. In the united atom limit for the solvent, the theory reduces to the hypernetted chain (HNC) integral equation. This reduction is not found with the so-called ``extended'' RISM equation; indeed, the extended RISM equation—the theory in which the HNC closure of simple systems is inserted directly into the Chandler-Andersen (i.e., RISM or SSOZ) equation—behaves poorly in the united atom limit. The integral equation derived herein with the density functional approach however suggests a rational closure of the RISM equation which does pass over to the HNC theory in the united atom limit. The new integral equation for pair correlation functions arising from this suggested closure is presented and discussed.
Cm-theory of damped wave equations with stabilisation
NASA Astrophysics Data System (ADS)
Hirosawa, Fumihiko; Wirth, Jens
2008-07-01
The aim of this note is to extend the energy decay estimates from [J. Wirth, Wave equations with time-dependent-dissipation. I: Non-effective dissipation, J. Differential Equations 222 (2006) 487-514] to a broader class of time-dependent dissipation including very fast oscillations. This is achieved using stabilisation conditions on the coefficient in the spirit of [F. Hirosawa, On the asymptotic behavior of the energy for wave equations with time-depending coefficients, Math. Ann. 339 (4) (2007) 819-839].
The Witten equation, mirror symmetry and quantum singularity theory
Huijun Fan; Tyler J. Jarvis; Yongbin Ruan
2012-07-26
For any non-degenerate, quasi-homogeneous hypersurface singularity, we describe a family of moduli spaces, a virtual cycle, and a corresponding cohomological field theory associated to the singularity. This theory is analogous to Gromov-Witten theory and generalizes the theory of r-spin curves, which corresponds to the simple singularity A_{r-1}. We also resolve two outstanding conjectures of Witten. The first conjecture is that ADE-singularities are self-dual; and the second conjecture is that the total potential functions of ADE-singularities satisfy corresponding ADE-integrable hierarchies. Other cases of integrable hierarchies are also discussed.
Asymptotics of Few-body Equations of Collision Theory
Vagner Jikia; Jemal Mebonia
2014-11-03
A correct high-energy asymptotic form of Faddeev type few-body integral equations is found. Iterative series corresponding to these asymptotic relations converge with a certain accuracy to a finite sum, which satisfies the corresponding condition of unitarity.
Shock wave equation of state and finite strain theory
Raymond Jeanloz
1989-01-01
The linear shock-velocity (Us), particle-velocity (up) relation, which is known to be exceptionally successful in describing a wide variety of Hugoniot equation of state measurements, is shown to be virtually indistinguishable from the Birch-Murnaghan (third-order Eulerian finite strain) equation of state. For typical values of zero-pressure parameters, specially for the pressure derivative of the adiabatic bulk modulus K0S~=3 to 6,
Denicol, G. S. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Koide, T. [Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany); Rischke, D. H. [Institute fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Str. 1, D-60438 Frankfurt am Main (Germany)
2010-10-15
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.
Quantum theory of rotational isomerism and Hill equation
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R. [I. Javakhishvili Tbilisi State University, 3, I. Chavchavadze Avenue, 0179 Tbilisi (Georgia); Chotorlishvili, L. [Institut fuer Physik, Martin-Luther Universitat Halle-Wittenberg, Heinrich-Damerow-Str. 4, 06120 Halle (Germany)
2012-06-15
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.
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.
611: Electromagnetic Theory II Special relativity; Lorentz covariance of Maxwell equations
Pope, Christopher
611: Electromagnetic Theory II CONTENTS Â· Special relativity; Lorentz covariance of Maxwell equations Â· Scalar and vector potentials, and gauge invariance Â· Relativistic motion of charged particles Â· Action principle for electromagnetism; energy-momentum tensor Â· Electromagnetic waves; waveguides
611: Electromagnetic Theory II . Special relativity; Lorentz covariance of Maxwell equations
Pope, Christopher
611: Electromagnetic Theory II CONTENTS . Special relativity; Lorentz covariance of Maxwell equations . Scalar and vector potentials, and gauge invariance . Relativistic motion of charged particles . Action principle for electromagnetism; energyÂmomentum tensor . Electromagnetic waves; waveguides
611: Electromagnetic Theory II Special relativity; Lorentz covariance of Maxwell equations
Pope, Christopher
611: Electromagnetic Theory II CONTENTS #15; Special relativity; Lorentz covariance of Maxwell equations #15; Scalar and vector potentials, and gauge invariance #15; Relativistic motion of charged particles #15; Action principle for electromagnetism; energy-momentum tensor #15; Electromagnetic waves
Dynamic field theory and equations of motion in cosmology
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-01
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein's equations in the form of the Friedmann-Lemaître-Robertson-Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast ?? / ? ? 1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits ?? / ? ? 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.
The application of the integral equation theory to study the hydrophobic interaction
Mohori?, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara
2014-01-01
The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891
Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.
NASA Astrophysics Data System (ADS)
Auerbach, Scott Michael
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is discussed. We find no feasible expansion which has a fixed and small memory requirement, and is guaranteed to converge. We have found, however, that exploiting the time dependent picture of the ABC-DVR Green's function leads to a stable and efficient algorithm. The new method, which uses Newton interpolation polynomials to compute the time dependent wavefunction, gives a vastly improved version of the power series Green's function. We show that this approach is capable of obtaining converged reaction probabilities with very straightforward accuracy control. We use the ABC-DVR-Newton method to compute cross sections and rate constants for the initial state selected D + H_2(v = 1,j) to DH + H reaction. We obtain converged cross sections using no more than 4 Mbytes of core memory, and in as little CPU time as 10 minutes on a small workstation. With these cross sections, we calculate exact thermal rate constants for comparison with experiment. For the first time, quantitative agreement with experiment is obtained for the rotationally averaged rate constant k_{v=1}(T = 310 K) = 1.9 times 10^{-13} cm^3 sec^ {-1} molecule^{-1 }. The J-shifting approximation using accurate J = 0 reaction probabilities is tested against the exact results. It reliably predicts k_{v=1 }(T) for temperatures up to 700 K, but individual (v = 1, j)-selected rate constants are in error by as much as 41%.
Birkhoff Normal Forms and KAM Theory for Gumowski-Mira Equation
Kulenovi?, M. R. S.; Nurkanovi?, Z.; Pilav, E.
2014-01-01
By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1 = (2axn)/(1 + xn2) ? xn?1, n = 0,1,…, where x?1, x0 ? (??, ?), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions. PMID:24558333
Soliton perturbation theory for phi-four model and nonlinear Klein-Gordon equations
NASA Astrophysics Data System (ADS)
Sassaman, Ryan; Biswas, Anjan
2009-08-01
This paper obtains the adiabatic variation of the soliton velocity, in presence of perturbation terms, of the phi-four model and the nonlinear Klein-Gordon equations. There are three types of models of the nonlinear Klein-Gordon equation, with power law nonlinearity, that are studied in this paper. The soliton perturbation theory is utilized to carry out this investigation.
Kinetic theory and Lax equations for shock clustering and Burgers turbulence
Menon, Govind
Kinetic theory and Lax equations for shock clustering and Burgers turbulence Govind Menon1 and Ravi remarkable exact solutions for Burgers equation (f(u) = u2 /2) suggesting the complete integrability of Burgers turbulence. MSC classification: 60J75, 35R60, 35L67, 82C99 1 Introduction We consider the scalar
A scalar potential formulation and translation theory for the time-harmonic Maxwell equations
Nail A. Gumerov; Ramani Duraiswami
2007-01-01
We develop a computational method based on the Debye scalar potential representation, which efficiently reduces the solution of Maxwell’s equations to the solution of two scalar Helmholtz equations. One of the key contributions of this paper is a theory for the translation of Maxwell solutions using such a representation, since the scalar potential form is not invariant with respect to
Percus-Yevick integral equation theory for athermal hard-sphere chains
Yee C. Chiew
1991-01-01
Equations for three intermolecular correlation functions for athermal hardsphere chain fluids are derived in the context of the Percus-Yevick (PY) integral equation theory. The approach employed here is based on a particle-particle description of chain molecules developed in part I of this series. Specifically, we obtained equations for the site-site total correlation function h??(r), the single index average total correlation
On a local theory of asymptotic integration for nonlinear ordinary differential equations
Octavian G. Mustafa; Ravi P. Agarwal
2009-01-01
By revisiting an asymptotic integration theory of nonlinear ordinary differential equations due to J.K. Hale and N. Onuchic [Contributions Differential Equations 2 (1963), 61--75], we improve and generalize several recent results in the literature. As an application, we study the existence of bounded positive solutions to a large class of semi-linear elliptic partial differential equations via the subsolution-supersolution approach.
Geometric phases in the asymptotic theory of coupled wave equations
Littlejohn, R.G.; Flynn, W.G. (Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, California (USA))
1991-10-15
Traditional approaches to the asymptotic behavior of coupled wave equations have difficulties in the formulation of a consistent version of the Bohr-Sommerfeld quantization conditions. These difficulties can be circumvented by using the Weyl calculus to diagonalize the matrix of wave operators. In analyzing the diagonalized wave equations, geometric phases enter in an important way, especially in the development of Bohr-Sommerfeld quantization rules. It turns out that a version of Berry's phase is incorporated into the symplectic structure in the ray phase space, influencing the classical Hamiltonian orbits, the construction of solutions to the Hamiltonian-Jacobi equation, and the computation of action integrals. Noncanonical coordinates in the ray phase space are useful in carrying out these calculations and in making the construction of eigenvalues and wave functions manifestly gauge invariant.
Stochastic quantization in field theory with a fundamental mass
Petriashvili, G.G.
1986-08-01
Stochastic quantization of fermions is developed in the framework of quantum field theory with non-Euclidean momentum space. Analogs of the Langevin and Fokker-Planck equations taking into account the new geometrical properties of the momentum space are obtained by using Grassmann variables to describe the non-Euclidean Fermi fields. It is shown that the stochastic method and the second-quantization method are equivalent in path-integral terms.
NASA Astrophysics Data System (ADS)
Zhang, Yan-Lai; Sun, Mao
2010-08-01
In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical simulation. The theory is based on the averaged model (which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings' degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments); the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low (the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
Itzhak Fouxon; Yaron Oz
2008-09-28
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the non-relativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.
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.
Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzmann equation
Freericks, Jim
Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzmann equation J. K for steady state nonequilibrium dynamical mean-field theory in a real-time formalism along the Keldysh a number of technical complications. In this chapter, we describe the steady-state limit, where we start
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
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
Plotnitsky, Arkady
2015-01-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be 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 for the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall, however, also consider Heisenberg's derivation of quantum mechanics, which inspired Dirac. I argue that Heisenberg's and Dirac's work alike was guided by their adherence to and confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by G. M. D' Ariano and his coworkers on the principles of quantum information theory, which extends quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equation from these principles alone...
Covariant hamiltonian formalism for field theory: Hamilton-Jacobi equation on the space G
Carlo Rovelli
2002-07-26
Hamiltonian mechanics of field theory can be formulated in a generally covariant and background independent manner over a finite dimensional extended configuration space. The physical symplectic structure of the theory can then be defined over a space G of three-dimensional surfaces without boundary, in the extended configuration space. These surfaces provide a preferred over-coordinatization of phase space. I consider the covariant form of the Hamilton-Jacobi equation on G, and a canonical function S on G which is a preferred solution of the Hamilton-Jacobi equation. The application of this formalism to general relativity is equivalent to the ADM formalism, but fully covariant. In the quantum domain, it yields directly the Ashtekar-Wheeler-DeWitt equation. Finally, I apply this formalism to discuss the partial observables of a covariant field theory and the role of the spin networks --basic objects in quantum gravity-- in the classical theory.
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.
Closed equations of the two-point functions for tensorial group field theory
NASA Astrophysics Data System (ADS)
Ousmane Samary, Dine
2014-09-01
In this paper, we provide the closed equations that satisfy two-point correlation functions of rank 3 and 4 tensorial group field theory. The formulation of the current problem extends the method used by Grosse and Wulkenhaar (2009 arXiv:0909.1389) to the tensor case. Ward-Takahashi identities and Schwinger-Dyson equations are combined to establish a nonlinear integral equation for the two-point functions. In the three-dimensional case, the solution of this equation is given perturbatively at the second order of the coupling constant.
Pseudo-Poles in the Theory of Emden's Equation
Hille, Einar
1972-01-01
It is known that Emden's equation y? = x1-mym has movable singularities where the solution becomes infinite for one-sided approach. If m = (p + 2)/p, p positive integer, the singularities look like poles of order p. In this note expansions in terms of powers and logarithms are obtained from which the nonpolar nature of these “pseudo-poles” becomes evident. Various extensions are considered. Convergence proofs are deferred to a more detailed publication. PMID:16591989
Equation-of-motion coupled cluster perturbation theory revisited
Eriksen, Janus J., E-mail: janusje@chem.au.dk; Jørgensen, Poul; Olsen, Jeppe [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark)] [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C (Denmark); Gauss, Jürgen [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)] [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Modified equations in the theory of induced gravity. Solution to the cosmological constant problem
Farkhat Zaripov
2014-10-10
This research is an extension of the author's article \\cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of gravity and string theory. This work is devoted to the formation of self-consistent equations of the theory of induced gravity \\cite{zar}, \\cite{zari} in the presence of matter in the form of a perfect fluid that interacts with scalar fields. The study is done to solve these equations for the case of the cosmological model. In this model time-evolving gravitational and cosmological "constants" take place which are determined by the square of scalar fields. The values of which can be matched with the observational data. The equations that describe the theory have solutions that can both match with the solutions of the standard theory of gravity as well as it can differ from it. This is due to the fact that the fundamental "constants" of the theory, such as gravitational and cosmological, can evolve over time and also depend of the coordinates. Thus, in a rather general case the theory describes the two systems (stages): Einstein and "evolving" or "restructuring" (the name suggested by the author). This process is similar to the phenomenon of phase transition, where the different phases (Einstein gravity system, but with different constants) transit into each other.
Ompong, David; Singh, Jai
2015-04-27
We derived new expressions for the diffusion length of singlet and triplet excitons by using the Föster and Dexter transfer mechanisms, respectively, and have found that the diffusion lengths of singlet and triplet excitons are comparable. By using the Langevin recombination theory, we derived the rate of recombination of dissociated free charges into their excitonic states. We found that in some organic polymers the probabilities of recombination of free charge carriers back into the singlet and triplet states are approximately 65.6 and 34.4?%, respectively, indicating that Langevin-type recombination into triplet excitons in organic semiconductors is less likely. This implies that the creation of triplet excitons may be advantageous in organic solar cells, because this may lead to dissociated free charge carriers that can be collected at their respective electrodes, which should result in better conversion efficiency. PMID:25735545
Edinburgh Research Explorer The complex chemical Langevin equation
Millar, Andrew J.
is retained by the author(s) and / or other copyright owners and it is a condition of accessing of combining both the sensing and processing of biochemical signals to generate autonomous programmed output
Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties
NASA Astrophysics Data System (ADS)
Fodor, Étienne; Grebenkov, Denis S.; Visco, Paolo; van Wijland, Frédéric
2015-03-01
We review equilibrium properties for the dynamics of a single particle evolving in a visco-elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time-reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed.
Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory
Aupic, Jana; Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si [Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ašker?eva 5, SI-1000 Ljubljana (Slovenia)] [Faculty of Chemistry and Chemical Technology, University of Ljubljana, Ašker?eva 5, SI-1000 Ljubljana (Slovenia)
2014-05-14
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.
Jin Shi [Department of Mathematical Sciences, Tsinghua University, Beijing 100084 (China); Department of Mathematics, University of Wisconsin, Madison, WI 53706 (United States)], E-mail: jin@math.wisc.edu; Yin Dongsheng [Department of Mathematical Sciences and the Center for Advanced Study, Tsinghua University, Beijing 100084 (China)], E-mail: dyin@math.tsinghua.edu.cn
2008-06-01
We construct a class of numerical schemes for the Liouville equation of geometric optics coupled with the Geometric Theory of Diffractions to simulate the high frequency linear waves with a discontinuous index of refraction. In this work [S. Jin, X. Wen, A Hamiltonian-preserving scheme for the Liouville equation of geometric optics with partial transmissions and reflections, SIAM J. Numer. Anal. 44 (2006) 1801-1828], a Hamiltonian-preserving scheme for the Liouville equation was constructed to capture partial transmissions and reflections at the interfaces. This scheme is extended by incorporating diffraction terms derived from Geometric Theory of Diffraction into the numerical flux in order to capture diffraction at the interface. We give such a scheme for curved interfaces. This scheme is proved to be positive under a suitable time step constraint. Numerical experiments show that it can capture diffraction phenomena without fully resolving the wave length of the original wave equation.
Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.
Das, Shankar P; Yoshimori, Akira
2013-10-01
Exact equations of motion for the microscopically defined collective density ?(x,t) and the momentum density ?(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations. PMID:24229277
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano [Bernstein Center for Computational Neuroscience, Hansastrasse 9A, D-79104 Freiburg (Germany); Mugnolo, Delio [Institut fuer Analysis, Universitaet Ulm, Helmholtzstrasse 18, D-89081 Ulm (Germany)
2009-10-15
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.
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
Darryl D. Holm; Jerrold E. Marsden; Tudor S. Ratiu
1998-01-01
We study Euler–Poincaré systems (i.e., the Lagrangian analogue of Lie–Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincaré equations for a parameter dependent Lagrangian by using a variational principle of Lagrange d'Alembert type. Then we derive an abstract Kelvin–Noether theorem for these equations. We also explore their relation with the theory of
NASA Astrophysics Data System (ADS)
Grössing, Gerhard
2002-04-01
The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.
Percus-Yevick integral-equation theory for athermal hard-sphere chains
Yee C. Chiew
1990-01-01
A theoretical method for the modelling of athermal freely jointed tangent hard-sphere chain fluids, of fixed length r, is developed based on a ‘particle-particle’ description of the chain system. This approach is based on the Percus-Yevick (PY) theory in the context of the particle-particle Ornstein-Zernike integral equation subject to some imposed connectivity constraints. Analytical expressions for the compressibility equations of
On differential equation on four-point correlation function in the Conformal Toda Field Theory
V. A. Fateev; A. V. Litvinov
2005-05-13
The properties of completely degenerate fields in the Conformal Toda Field Theory are studied. It is shown that a generic four-point correlation function that contains only one such field does not satisfy ordinary differential equation in contrast to the Liouville Field Theory. Some additional assumptions for other fields are required. Under these assumptions we write such a differential equation and solve it explicitly. We use the fusion properties of the operator algebra to derive a special set of three-point correlation function. The result agrees with the semiclassical calculations.
Constructing a class of solutions for the Hamilton-Jacobi equation in field theory
Bruno, Danilo [Dipartimento di Matematica, Universita di Genova, Via Dodecaneso, 35-16146 Genova (Italy)
2007-11-15
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet bundles and multisymplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions.
Constructing a class of solutions for the Hamilton-Jacobi equation in field theory
Danilo Bruno
2007-09-12
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions.
On a local theory of asymptotic integration for nonlinear ordinary differential equations
Octavian G. Mustafa; Ravi P. Agarwal
2009-01-01
By revisiting an asymptotic integration theory of nonlinear ordinary\\u000adifferential equations due to J.K. Hale and N. Onuchic [Contributions\\u000aDifferential Equations 2 (1963), 61--75], we improve and generalize several\\u000arecent results in the literature. As an application, we study the existence of\\u000abounded positive solutions to a large class of semi-linear elliptic partial\\u000adifferential equations via the subsolution-supersolution approach.
Polynomial elimination theory and non-linear stability analysis for the Euler equations
NASA Technical Reports Server (NTRS)
Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.
1986-01-01
Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.
CKN theory of singularities of weak solutions of the Navier-Stokes equations
Giovanni Gallavotti
2005-03-16
The lectures are devoted to a complete exposition of the theory of singularities of the Navier Stokes equations solution studied by Leray, in a simple geometrical setting in which the fluid is enclosed in a container $\\O$ with periodic boundary conditions and side size $L$. The theory is due to the work of Scheffer, Caffarelli, Kohn, Nirenberg and is called here CKN-theory as it is inspired by the work of the last three authors which considerably improved the earlier estimates of Scheffer.
Higher order asymptotics for the Hirota equation via Deift-Zhou higher order theory
NASA Astrophysics Data System (ADS)
Huang, Lin; Xu, Jian; Fan, En-gui
2015-01-01
In this paper, the Deift-Zhou higher order asymptotic theory is used to further establish the full asymptotic expansion for the solution of the Hirota equation to all order, as t ? ?. The method is rigorous and does not rely on an a priori ansatz for the form of the solution.
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…
Using the gravity equation to differentiate among alternative theories of trade
Robert C. Feenstra; James R. Markusen; Andrew K. Rose
2001-01-01
The simple gravity equation explains a great deal about the data on bilateral trade flows and is consistent with several theoretical models of trade. We argue that alternative theories nevertheless predict subtle differences in key parameter values, depending on whether goods are homogeneous or differentiated and whether or not there are barriers to entry. Our empirical work for differentiated goods
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…
NASA Astrophysics Data System (ADS)
Borunov, M. V.; Nadtochy, P. N.; Adeev, G. D.
2008-02-01
A multi-dimensional stochastic approach based on three-dimensional Langevin equations is applied for calculation of the first four moments of the kinetic-energy distribution of fission fragments in a wide range of Coulomb parameter 700
Comment on the consistency of truncated nonlinear integral equation based theories of freezing
Cerjan, C.; Bagchi, B.; Rice, S.A.
1985-09-01
We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim--Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions.
Game theory to characterize solutions of a discrete-time Hamilton-Jacobi equation
NASA Astrophysics Data System (ADS)
Toledo, Porfirio
2013-12-01
We study the behavior of solutions of a discrete-time Hamilton-Jacobi equation in a minimax framework of game theory. The solutions of this problem represent the optimal payoff of a zero-sum game of two players, where the number of moves between the players converges to infinity. A real number, called the critical value, plays a central role in this work; this number is the asymptotic average action of optimal trajectories. The aim of this paper is to show the existence and characterization of solutions of a Hamilton-Jacobi equation for this kind of games.
Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory
F. Haas; J. Zamanian; M. Marklund; G. Brodin
2009-12-23
The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.
Number-conserving master equation theory for a dilute Bose-Einstein condensate
Schelle, Alexej [Physikalisches Institut der Albert-Ludwigs Universitaet Freiburg, Hermann-Herder Str. 3, D-79104 Freiburg (Germany); Laboratoire Kastler-Brossel, Universite Pierre et Marie Curie-Paris 6, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France); Wellens, Thomas; Buchleitner, Andreas [Physikalisches Institut der Albert-Ludwigs Universitaet Freiburg, Hermann-Herder Str. 3, D-79104 Freiburg (Germany); Delande, Dominique [Laboratoire Kastler-Brossel, Universite Pierre et Marie Curie-Paris 6, ENS, CNRS, 4 Place Jussieu, F-75005 Paris (France)
2011-01-15
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.
N=1 Super Yang-Mills Theory in Ito Calculus
Naohito Nakazawa
2006-08-23
The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM_4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an '' almost Wess-Zumino gauge ''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM_10, the IIB matirx model is studied in this context.
Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories
Wulf Boettger; Henning Wissowski; Hans A. Kastrup
1995-01-25
The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and $\\phi^4$ theories. For simplicity we use the Hamilton--Jacobi equation of DeDonder and Weyl. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations between Hamilton--Jacobi wave fronts and the corresponding families of extremals embedded therein. B\\"acklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.
From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
Pasquale Calabrese; Marton Kormos; Pierre Le Doussal
2014-05-11
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.
Prescission neutron multiplicity and fission probability from Langevin dynamics of nuclear fission
NASA Astrophysics Data System (ADS)
Chaudhuri, Gargi; Pal, Santanu
2002-05-01
A theoretical model of one-body nuclear friction, which was developed earlier, namely, the chaos-weighted wall formula, is applied to a dynamical description of compound nuclear decay in the framework of the Langevin equation coupled with statistical evaporation of light particles and photons. We have used both the usual wall formula friction and its chaos-weighted version in the Langevin equation to calculate the fission probability and prescission neutron multiplicity for the compound nuclei 178W, 188Pt, 200Pb, 213Fr, 224Th, and 251Es. We have also obtained the contributions of the presaddle and postsaddle neutrons to the total prescission multiplicity. A detailed analysis of our results leads us to conclude that the chaos-weighted wall formula friction can adequately describe the fission dynamics in the presaddle region. This friction, however, turns out to be too weak to describe the postsaddle dynamics properly. This points to the need for a suitable explanation for the enhanced neutron emission in the postsaddle stage of nuclear fission.
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.
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.
Stochastic Gravity: Theory and Applications
B. L. Hu; E. Verdaguer
2008-02-05
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole
Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation
NASA Astrophysics Data System (ADS)
Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng
2014-05-01
Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.
Cosmological models with viscous fluid and time- dependent equation of state in Wesson’s theory
G. S. Khadekar; G. R. Avachar
2007-01-01
Assuming the time-dependent equation of state p=?(t)?, five dimensional cosmological models with viscous fluid for an open universe (k=?1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys.\\u000a 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this
Five-dimensional cosmological model with a time-dependent equation of state in Wesson's theory
G. S. Khadekar; G. R. Avachar
2007-01-01
Exact solution for a homogeneous cosmological model in 5D space-time-mass gravity theory proposed by Wesson (Astron. Astrophys. 119:145, 1983) is obtained by assuming the time-dependent equation of state. The behavior of the solution is discussed for the two cases k<0 and k=0. It is found that the observed constancy of the rest mass of an isolated particle in the present
Cosmological models with viscous fluid and time- dependent equation of state in Wesson's theory
G. S. Khadekar; G. R. Avachar
2007-01-01
Assuming the time-dependent equation of state p=lambda(t)rho, five dimensional cosmological models with viscous fluid for an open universe (k=-1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys. 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this
Closed String Field Theory: Quantum Action and the BV Master Equation
Barton Zwiebach
1992-01-01
The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra $L_\\\\infty$, and the higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation.
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
Skontorp, A.; Wang, S.S. [Univ. of Houston, TX (United States). Dept. of Mechanical Engineering; Shibuya, Y. [Akita Univ., (Japan). Dept. of Mechanical Engineering
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.
Stochastic quantization of the Chern-Simons theory
Cugliandolo, L.F. (Universita di Roma, Rome (Italy)); Rossini, G.L.; Schaposnik, F.A. (Universidad Nacional de La Plata (Argentina))
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.
Diffusion in the special theory of relativity
Joachim Herrmann
2009-03-04
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on Lorentzian manifolds with an indefinite metric. 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 J\\"{u}ttner distribution. Besides a non-stationary analytical solution is derived for the example of force-free relativistic diffusion.
Heavy-flavor in-medium momentum evolution: Langevin versus Boltzmann approach
NASA Astrophysics Data System (ADS)
Das, Santosh K.; Scardina, Francesco; Plumari, Salvatore; Greco, Vincenzo
2014-10-01
The propagation of heavy quarks in the quark-gluon plasma was often treated within the framework of the Langevin equation (LV), i.e., assuming the momentum transfer is small or the scatterings are sufficiently forward peaked, small screening mass mD. We address a direct comparison between the Langevin dynamics and the Boltzmann collisional integral (BM) when a bulk medium is in equilibrium at fixed temperature. We show that unless the cross section is quite forward peaked (mD?T) or the mass to temperature ratio is quite large (MHQ/T? 8-10) there are significant differences in the evolution of the p spectra and consequently on the nuclear modification factor RAA(pT). However, for charm quark we find that very similar RAA(pT) between the LV and BM can be obtained, but with a modified diffusion coefficient of about ˜15%-50% depending on the angular dependence of the cross section which regulates the momentum transfer. Studying also the momentum spread suffered by the single heavy quarks we see that at temperatures T ?250MeV the dynamics of the scatterings is far from being of Brownian type for charm quarks. In the case of bottom quarks we essentially find no differences in the time evolution of the momentum spectra between the LV and the BM dynamics independently of the angular dependence of the cross section, at least in the range of temperature relevant for ultrarelativistic heavy-ion collisions (HICs). Finally, we have shown the possible impact of this study on RAA(pT) and v2(pT) for a realistic simulation of relativistic HICs. For larger mD the elliptic flow can be about 50% larger for the Boltzmann dynamics with respect to the Langevin. This is helpful for a simultaneous reproduction of RAA(pT) and v2(pT).
The solids-flux theory--confirmation and extension by using partial differential equations.
Diehl, Stefan
2008-12-01
The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts. PMID:18926553
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.
Aminova, Asya V [Kazan State University, Kazan (Russian Federation); Aminov, Nail' A-M [Kazan State Technological University, Kazan (Russian Federation)
2010-06-29
In the framework of the projective geometric theory of systems of differential equations, which is being developed by the authors, conditions which ensure that a family of graphs of solutions of a system of m second-order ordinary differential equations y-vector-ddot=f-vector(t,y-vector,y-vector-dot) with m unknown functions y{sup 1}(t),...,y{sup m}(t) can be straightened (that is, transformed into a family of straight lines) by means of a local diffeomorphism of the variables of the system which takes it to the form z-vector''=0 (straightens the system) are investigated. It is shown that the system to be straightened must be cubic with respect to the derivatives of the unknown functions. Necessary and sufficient conditions for straightening the system are found, which have the form of differential equations for the coefficients of the system or are stated in terms of symmetries of the system. For m=1 the system consists of a single equation y-ddot=f-vector(t,y,y-dot), and the tests obtained reduce to the conditions for straightening this equations which were derived by Lie in 1883. Bibliography: 34 titles.
Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of ??4 field theory
NASA Astrophysics Data System (ADS)
Cooper, Fred; Mihaila, Bogdan; Dawson, John F.
2004-11-01
In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) ?4 field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field ?, once the effective action is obtained by integrating over the ? fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson (SD) equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent SD equations valid to order 1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green’s functions with the related sunset approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.
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.
An anisotropic constitutive equation for the stress tensor of blood based on mixture theory
Massoudi, Mehrdad; Antaki, J.F.
2008-09-12
Based on ideas proposed by Massoudi and Rajagopal (M-R), we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells (RBCs) suspended in plasma, where the plasma behaves as a linearly viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.
Exceptional thermodynamics: the equation of state of G2 gauge theory
NASA Astrophysics Data System (ADS)
Bruno, Mattia; Caselle, Michele; Panero, Marco; Pellegrini, Roberto
2015-03-01
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G2 gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU( N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU( N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
Exceptional thermodynamics: The equation of state of G(2) gauge theory
Mattia Bruno; Michele Caselle; Marco Panero; Roberto Pellegrini
2015-03-12
We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G(2) gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.
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)]. 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. PMID:25019714
Takeshi Matsumoto; Michio Otsuki; Ooshida Takeshi; Susumu Goto; Akio Nakahara
2014-06-30
For a shell model of the fully developed turbulence and the incompressible Navier-Stokes equations in the Fourier space, when a Gaussian white noise is artificially added to the equation of each mode, an expression of the mean linear response function in terms of the velocity correlation functions is derived by applying the method developed for nonequilibrium Langevin systems [Harada and Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. We verify numerically for the shell model case that the derived expression of the response function, as the noise tends to zero, converges to the response function of the noiseless shell model.
Gravitational Field Equations and Theory of Dark Matter and Dark Energy
Tian Ma; Shouhong Wang
2012-07-11
The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential $\\varphi$ are derived using the Einstein-Hilbert functional, and the scalar potential $\\varphi$ is a natural outcome of the divergence-free constraint of the variational elements. Gravitation is now described by the Riemannian metric $g_{ij}$, the scalar potential $\\varphi$ and their interactions, unified by the new gravitational field equations. Associated with the scalar potential $\\varphi$ is the scalar potential energy density $\\frac{c^4}{8\\pi G} \\Phi=\\frac{c^4}{8\\pi G} g^{ij}D_iD_j \\varphi$, which represents a new type of energy caused by the non-uniform distribution of matter in the universe. The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: $\\int_M \\Phi dM=0$. The sum of this new potential energy density $\\frac{c^4}{8\\pi G} \\Phi$ and the coupling energy between the energy-momentum tensor $T_{ij}$ and the scalar potential field $\\varphi$ gives rise to a new unified theory for dark matter and dark energy: The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies. In addition, the scalar curvature of space-time obeys $R=\\frac{8\\pi G}{c^4} T + \\Phi$. Furthermore, the new field equations resolve a few difficulties encountered by the classical Einstein field equations.
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: 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)
Gauge cooling in complex Langevin for QCD with heavy quarks
Erhard Seiler; Dénes Sexty; Ion-Olimpiu Stamatescu
2012-11-20
We employ a new method, "gauge cooling", to stabilize complex Langevin simulations of QCD with heavy quarks. The results are checked against results obtained with reweigthing; we find agreement within the estimated errors. The method allows us to go to previously unaccessible high densities.
Two-dimensional Langevin approach to nuclear fission
N. Carjan; T. Wada; Y. Abe
1992-01-01
The bidimensional Langevin for the symmetric fission of 213At were solved without approximations using computer generated stochastic forces. Two dissipation mechanisms have been studied: a typical weak one (hydrodynamical viscosity) and a typical strong one (energy transferred to nucleonic motions from their changing self consistent potential). Calculated transient times (2.10-20 sec or less) are comparable with those extracted from measurements
Energy and equations of motion in a tentative theory of gravity with a privileged reference frame
Mayeul Arminjon
2007-09-04
Based on a tentative interpretation of gravity as a pressure force, a scalar theory of gravity was previously investigated. It assumes gravitational contraction (dilation) of space (time) standards. In the static case, the same Newton law as in special relativity was expressed in terms of these distorted local standards, and was found to imply geodesic motion. Here, the formulation of motion is reexamined in the most general situation. A consistent Newton law can still be defined, which accounts for the time variation of the space metric, but it is not compatible with geodesic motion for a time-dependent field. The energy of a test particle is defined: it is constant in the static case. Starting from 'dust', a balance equation is then derived for the energy of matter. If the Newton law is assumed, the field equation of the theory allows to rewrite this as a true conservation equation, including the gravitational energy. The latter contains a Newtonian term, plus the square of the relative rate of the local velocity of gravitation waves (or that of light), the velocity being expressed in terms of absolute standards.
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.
A scattering theory for the wave equation on Kerr black hole exteriors
Mihalis Dafermos; Igor Rodnianski; Yakov Shlapentokh-Rothman
2014-12-29
We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|past horizon and past null infinity to radiation fields on the future horizon and future null infinity is a bounded operator. The latter allows us to give a time-domain theory of superradiant reflection. The boundedness of the scattering matrix shows in particular that the maximal amplification of solutions associated to ingoing finite-energy wave packets on past null infinity is bounded. On the frequency side, this corresponds to the novel statement that the suitably normalised reflection and transmission coefficients are uniformly bounded independently of the frequency parameters. We further complement this with a demonstration that superradiant reflection indeed amplifies the energy radiated to future null infinity of suitable wave-packets as above. The results make essential use of a refinement of our recent proof [M. Dafermos, I. Rodnianski and Y. Shlapentokh-Rothman, Decay for solutions of the wave equation on Kerr exterior spacetimes III: the full subextremal case |a|energy is assumed finite. We show in contrast that the analogous scattering maps cannot be defined for the class of finite non-degenerate energy solutions. This is due to the fact that the celebrated horizon red-shift effect acts as a blue-shift instability when solving the wave equation backwards.
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.
Equation of State of a Relativistic Theory from a Moving Frame
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Pepe, Michele
2014-07-01
We propose a new strategy for determining the equation of state of a relativistic thermal quantum field theory by considering it in a moving reference system. In this frame, an observer can measure the entropy density of the system directly from its average total momentum. In the Euclidean path integral formalism, this amounts to computing the expectation value of the off-diagonal components T0k of the energy-momentum tensor in the presence of shifted boundary conditions. The entropy is, thus, easily measured from the expectation value of a local observable computed at the target temperature T only. At large T, the temperature itself is the only scale which drives the systematic errors, and the lattice spacing can be tuned to perform a reliable continuum limit extrapolation while keeping finite-size effects under control. We test this strategy for the four-dimensional SU(3) Yang-Mills theory. We present precise results for the entropy density and its step-scaling function in the temperature range 0.9Tc-20Tc. At each temperature, we consider four lattice spacings in order to extrapolate the results to the continuum limit. As a by-product, we also determine the ultraviolet finite renormalization constant of T0k by imposing suitable Ward identities. These findings establish this strategy as a solid, simple, and efficient method for an accurate determination of the equation of state of a relativistic thermal field theory over several orders of magnitude in T.
K. P. SOLDATOS; C. Sophocleous
2001-01-01
This paper provides a step forwards the construction and documentation of the frequency equations and the characteristic functions of a general three-degrees-of-freedom theory that describes the plane motion of shear deformable elastic beams. The governing equations of this shear deformable beam theory (G3DOFBT) involve a general shape function of the transverse beam co-ordinate parameter, the a posteriori choice of which
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.
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 ? determines the relative weight of linear versus nonlinear terms in the population number n ? N entering the loss term. By varying ? from 0 to 1 the equilibrium distribution changes from maximum growth to almost extinction. The former is a Gaussian centered at n = N, the latter is a power law peaked at n = 1. A bimodal distribution is observed in the transition region. When N grows and tends to ?, keeping the value of ? fixed, the distribution tends to a Gaussian centered at n = N whose limit is a delta function corresponding to the stable equilibrium of the mean field equation. The choice of the master equation in this family depends on the equilibrium distribution for finite values of N. The presence of an absorbing state for n = 0 does not change this picture since the extinction mean time grows exponentially fast with N. As a consequence for ? close to zero extinction is not observed, whereas when ? approaches 1 the relaxation to a power law is observed before extinction occurs. We extend this approach to a well known model of synaptic plasticity, the so called BCM theory in the case of a single neuron with one or two synapses.
Incompressible Navier-Stokes Equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell Theories
Chao Niu; Yu Tian; Xiao-Ning Wu; Yi Ling
2012-04-26
The dual fluid description for a general cutoff surface at radius r=r_c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter \\epsilon, the coupled Einstein-Maxwell equations are solved up to O(\\epsilon^2). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density \\eta/s is independent of both the cutoff r_c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio \\eta/s is independent of the cutoff r_c but dependent on the charge density of the black brane.
Einstein-Cartan Theory of Gravitation: Kinematical Parameters and Maxwell Equations
NASA Astrophysics Data System (ADS)
Katkar, L. N.
2015-03-01
In the space-time manifold of Einstein-Cartan Theory (ECT) of gravitation, the expressions for the time-like kinematical parameters are derived and the propagation equation for expansion is obtained.It has been observed that when the spin tensor is u-orthogonal the spin of the gravitating matter has no influence on the propagation equation of expansion while it has influence when it is not u-orthogonal. The usual formula for the curl of gradient of a scalar function is not zero in ECT. So is the case with the divergence of the curl of a vector.Their expressions on the space-time manifold of ECT are derived. A new derivative operator d ? is introduced to develop the calculus on space-time manifold of ECT. It is obtained by taking the covariant derivative of an associated tensor of a form with respect to an asymmetric connections. We have used this differential operator to obtain the form of the Maxwell's equations in the ECT of gravitation. Cartan's equations of structure are also derived through the new derivative operator. It has been shown that unlike the consequences of exterior derivative in Einstein space-time, the repetition of d ? on a form of any degree is not zero.
Straube, Arthur V.
Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction
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.
Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
R. Giachetti; V. Grecchi
2009-05-13
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.
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.
Yang Lei; Devi, Murali; Jang, Seogjoo [Department of Chemistry and Biochemistry, Queens College of the City University of New York, 65-30 Kissena Boulevard, Flushing, New York 11367 (United States)
2012-07-14
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.
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.
A theory of tension fluctuations due to muscle cross-bridges.
Thomas, N; Thornhill, R A
1995-03-22
We present an analytical theory for the spectrum of tension fluctuations due to muscle cross-bridges. The theory is based upon the Langevin theory of brownian motion, and is illustrated using a simplified three-state model for the cross-bridge cycle, which is intended to model cross-bridges in fibrillar insect flight muscle. Langevin white-noise sources, representing fluctuations in the net transition rates for each step in the cycle, are introduced into the rate equations, and their strengths are adjusted to give the correct mean-square fluctuations in the occupation probabilities. The Langevin theory shows that the noise is closely related to the elastic properties of cross-bridges, and it also shows in detail how each step in the cross-bridge cycle contributes differently to the noise spectrum. We find that the total noise increases with filament displacement. For small filament displacements, the noise is dominated by the power stroke and by dissociation at the end of the cycle. These contributions increase in the region of stretch activation, whilst at larger displacements, where the cross-bridge becomes locked in the strong-binding state, the noise is much larger and is dominated by attachment and detachment at the beginning of the cycle. The cross-bridge properties in this regime are strongly affected by free inorganic phosphate. Finally, we show how the noise spectrum is modified by the inclusion of a series compliance representing a practical force transducer. PMID:7740044
Hamilton-Jacobi Equation for Brans-Dicke Theory and Its Long-wavelength Solution
Jiro Soda; Hideki Ishihara; Osamu Iguchi
1995-09-06
Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a long-wavelength approximation. We examine the non-linear evolution of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust fluid, it turns out that the inhomogeneities of space-time grow. In the case of cosmological constant, the inhomogeneities decay, which is consistent with the cosmic no hair conjecture. The inhomogeneities of the density perturbation and the gravitational constant behave similarly with that of space-time.
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Chekhov, Leonid [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom)] [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom); Eynard, Bertrand [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France)] [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Ribault, Sylvain [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France) [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5 (France)
2013-02-15
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
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.
Analysis of High-Pressure Equation of State for Solids Based on the Lattice Potential Theory
NASA Astrophysics Data System (ADS)
Liu, Quan; Niu, Zhong-Ming
2012-12-01
A two-parameter high-pressure equation of state (EOS) is derived on the basis of the lattice potential theory using the concept of a short-range force constant as introduced by Born and Huang. The application of the EOS to some solids is presented and compared with the Birch-Murnaghan (BM) third-order EOS, the BM fourth-order EOS, and the Vinet EOS. A comparison of the results provides a crucial test for the EOSs used in this article.
Didactic derivation of the special theory of relativity from the Klein-Gordon equation
NASA Astrophysics Data System (ADS)
Arod?, H.
2014-09-01
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are ‘discovered’ as symmetry transformations of the Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound |{\\bf v}| is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition (‘addition’) of velocities.
Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory
NASA Astrophysics Data System (ADS)
Das, Subir K.; Egorov, Sergei A.; Trefz, Benjamin; Virnau, Peter; Binder, Kurt
2014-05-01
We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The interparticle interactions in the system are taken from the Asakura-Oosawa model for colloid-polymer mixtures for which the phase diagram is known. In the current model version, the colloid particles are made active using the Vicsek model for self-propelling particles. The resultant active system is studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model-based activity facilitates phase separation, thus, broadening the coexistence region.
A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2009-01-01
This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.
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.
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.
Precise determination of critical exponents and equation of state by field theory methods
NASA Astrophysics Data System (ADS)
Zinn-Justin, J. Z.
2001-04-01
Renormalization group, and in particular its quantum field theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized ?34 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N-vector model (Le Guillou and Zinn-Justin, Phys. Rev. Lett. 39 (1977) 95; Phys. Rev. B 21 (1980) 3976; Guida and Zinn-Justin, J. Phys. A 31 (1998) 8103; cond-mat/9803240) and of the equation of state of the 3D Ising model (Guida and Zinn-Justin, Nucl. Phys. B 489 [FS] (1997) 626, hep-th/9610223). These results are among the most precise available probing field theory in a non-perturbative regime. Precise calculations first require enough terms of the perturbative expansion. However perturbation series are known to be divergent. The divergence has been characterized by relating it to instanton contributions. The information about large-order behaviour of perturbation series has then allowed to develop efficient “summation” techniques, based on Borel transformation and conformal mapping (Le Guillou and Zinn-Justin (Eds.), Large Order Behaviour of Perturbation Theory, Current Physics, vol. 7, North-Holland, Amsterdam, 1990). We first discuss exponents and describe our recent results (Guida and Zinn-Justin, 1998). Compared to exponents, the determination of the scaling equation of state of the 3D Ising model involves a few additional (non-trivial) technical steps, like the use of the parametric representation, and the order dependent mapping method. From the knowledge of the equation of state a number of ratio of critical amplitudes can also be derived. Finally we emphasize that few physical quantities which are predicted by renormalization group to be universal have been determined precisely, and much work remains to be done. Considering the steady increase in the available computer resources, many new calculations will become feasible. In addition to the infinite volume quantities, finite size universal quantities would also be of interest, to provide a more direct contact with numerical simulations. Let us also mention dynamical observables, a largely unexplored territory.
Yethiraj, A.; Schweizer, K.S. (Departments of Materials Science and Engineering and Chemistry, University of Illinois, Urbana, Illinois 61801 (United States))
1993-06-01
The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and Curro [J. Chem. Phys. [bold 91], 5059 (1989); Chem. Phys. [bold 149], 105 (1990)] (in which the critical temperature is proportional to the square root of the degree of polymerization), the molecular closures predict a linear dependence of the critical temperature on the degree of polymerization, in agreement with classical mean field theory. Detailed numerical calculations using the reference molecular mean spherical approximation (R-MMSA) and the reference molecular Percus--Yevick (R-MPY) closures are presented for the intermolecular structure and effective chi parameter in symmetric blends of semiflexible chains. For the symmetric blend, the R-MMSA closure is almost an integral equation realization of mean field theory, consistent with the analytical results presented in the previous paper. With the R-MPY closure, at low densities, the effective chi parameter is significantly renormalized down from its mean field value and displays a strong composition dependence. As the density is increased, both the renormalization of the effective chi parameter and its composition dependence become weaker. These trends are consistent with recent computer simulations. The influence of chain aspect ratio and the precise choice of intermolecular potentials on blend thermodynamics and phase separation are also explored. With the exception of the composition dependence of the effective chi parameter in the R-MPY theory, the analytical thread calculations are shown to be in qualitative, and sometimes quantitative, agreement with all the numerical results for symmetric blends.
Ning Wu; Dahua Zhang
2005-01-01
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the Schwarzschild solution. In gauge theory of
Stochastic theory of an optical vortex in nonlinear media
NASA Astrophysics Data System (ADS)
Kuratsuji, Hiroshi
2013-07-01
A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.
Novoderezhkin, Vladimir; van Grondelle, Rienk
2013-09-26
We model the spectra (absorption and circular dichroism) and excitation dynamics in the B800 ring of the LH2 antenna complex from Rs. molischianum using different theoretical approaches, i.e., Förster theory, standard and modified versions of the Redfield theory, and the more versatile nonperturbative approach based on hierarchically coupled equations for the reduced density operator. We demonstrate that, although excitations in the B800 ring are localized due to disorder, thermal effects, and phonons, there are still sizable excitonic effects producing shift, narrowing, and asymmetry of the spectra. Moreover, the excitation dynamics reveals the presence of long-lived (up to 1 ps) non-oscillatory coherences between the exciton states maintained due to nonsecular population-to-coherence transfers. The sub-ps decay of the coherences is followed by slow motion of the excitation around the ring, producing equilibration of the site populations with a time constant of about 3-4 ps, which is slower than the B800 ? B850 transfer. The exact solution obtained with the hierarchical equations is compared with other approaches, thus illustrating limitations of the Förster and Redfield pictures. PMID:23531197
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.
On the derivation of the Wheeler-Dewitt equation in the heterotic superstring theory
Pollack, M.D. (L.D. Landau Inst. for Theoretical Physics, Academy of Sciences of the USSR, Ulitsa Kosygina 2, Moscow 117940 (USSR))
1992-07-10
It has been shown by Pollock that the Wheeler-DeWitt equation for the wave function of the Universe [psi] cannot be derived for the D-dimensional, heterotic superstring theory, when higher-derivative terms [alpha][prime][ital R][sup 2] are included in the effective Lagrangian [ital L], because they occur as the Euler-number density [ital R][sup 2][sub E]. This means that [ital L] cannot be written in the standard Hamiltonian form, and hence that macroscopic quantum mechanics does not exist at this level of approximation. It was further conjectured that the solution to this difficulty is to take into account the effect of the terms [alpha][prime][sup 3][ital R][sup 4], an expression for which has been obtained by Gross and Witten, and by Freeman et al. In this paper, this conjecture is proved, but it is pointed out that the theory must first be reduced to a lower dimensionality [ital D] [lt] D. When this is done, the reduced term [ital R][sup 2] is no longer proportional to [ital R][sup 2][sub E], because of additional contributions arising from the dimensional reduction of [ital R][sup 4]. The Wheeler-DeWitt equation can now be derived in the form of a Schrodinger equation, in particular when [ital D] = 4 (and [ital R][sup 2][sub E] is a total divergence which can be discarded), and quantum mechanics can be set up in the usual way. In the light of these results, it is argued that the non-locality of quantum mechanics is related to the cosmological horizon problem.
Equations of state of freely jointed hard-sphere chain fluids: Theory
Stell, G.; Lin, C. [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States)] [Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400 (United States); Kalyuzhnyi, Y.V. [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv (Ukraine)] [Institute for Condensed Matter Physics, Svientsitskoho 1, 290011 Lviv (Ukraine)
1999-03-01
Using the analytical solution of a multidensity integral equation solved in our previous papers [J. Chem. Phys. {bold 108}, 6513, 6525 (1998)], we derive two compressibility and two virial equations of state (EOS) for freely jointed hard-sphere chain fluids on the basis of the approximations defined by the polymer Percus{endash}Yevick (PPY) closure and of the PPY ideal-chain closure for the integral equations. We also extend a version of first-order thermodynamic perturbation theory to polymers, using a dimer fluid as the reference system, to treat mixtures of heteronuclear chain fluids and polymer solutions; the structural information of the dimer fluid is obtained from the PPY ideal-chain approximation in the complete-association limit. The attractive forces between monomers of chain molecules are treated using simple perturbation theory. We find that the compressibility EOS derived on the basis of the PPY approximation subject to the chain-connectivity condition reduces to the compressibility EOS based upon the PPY ideal-chain approximation in the complete-association limit, which is also equivalent to the EOS derived by Chiew [Mol. Phys. {bold 70}, 129 (1990)] and to the EOS derived by Kalyuzhnyi and Cummings [J. Chem. Phys. {bold 105}, 2011 (1996)]. On the other hand, the virial EOS derived on the basis of the PPY ideal-chain approximation coincides with Attard{close_quote}s virial EOS [J. Chem. Phys. {bold 102}, 5411 (1995)] only in the zero-density limit. The advantages in numerical implementation of the EOS presented in this work are also discussed, but a full quantitative assessment of our results and a detailed numerical comparison among them are made in a companion paper, as is comparison with available simulation results. {copyright} {ital 1999 American Institute of Physics.}
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.
LE DERNIER THEOR`EME DE FERMAT PHILIPPE LANGEVIN
Faccanoni, Gloria
`ere modification : octobre 2004. 2. Prologue Au milieu du xviie si`ecle, le toulousain Pierre de Fermat consigneLE DERNIER THÂ´EOR`EME DE FERMAT PHILIPPE LANGEVIN RÂ´esumÂ´e. Pour les Â« f^etes de la science Â» de- plines scientifiques, l'Â´etude des nombres, sur les sentiers du dernier thÂ´eor`eme de Fermat. Le texte
Perturbation theory for Maxwell's equations with shifting material boundaries Steven G. Johnson, M 20 June 2002 Perturbation theory permits the analytic study of small changes on known solutions perturbation-theory tech- niques, however, have difficulties when applied to Maxwell's equations for small
Tu, Fei-Quan
2013-01-01
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, we also obtain the corresponding dynamic equations by using the idea of emergence of space in the $f(R)$ theory and deformed Ho\\v{r}ava-Lifshitz (HL) theory.
Tu, Fei-Quan; Chen, Yi-Xin, E-mail: fqtuzju@foxmail.com, E-mail: yxchen@zimp.zju.edu.cn [Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, 310027 (China)
2013-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Ho?ava-Lifshitz(HL) theory.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
NASA Technical Reports Server (NTRS)
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
Didactic derivation of the special theory of relativity from Klein-Gordon equation
Arod?, H
2014-01-01
We present a didactic derivation of the special theory of relativity in which Lorentz transformations are `discovered' as symmetry transformations of Klein-Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity $\\textbf{v}$ of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound $|\\textbf{v}|
On the question of current conservation for the Two-Body Dirac equations of constraint theory
Matthias Lienert
2015-03-09
The Two-Body Dirac 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 Two-Body Dirac 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.
NASA Astrophysics Data System (ADS)
Boozer, Allen H.
2015-03-01
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 ?40 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.
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.
Actinide electronic structure based on the Dirac equation and density functional theory
NASA Astrophysics Data System (ADS)
Wills, John M.; Mattsson, Ann E.
2013-03-01
Density functional theory (DFT) provides a formally predictive basis for predicting the structural properties of actinides. Although available approximations to the exchange/correlation functional provide accurate predictions for many materials, they fail qualitatively and sometimes quantitatively when applied to actinides. Major contributors to this deficiency are an inadequate treatment of confinement physics and an incomplete treatment of relativity in the underlying equations. The development of a functional correctly incorporating confinement physics with a proper treatment of relativity would provide definitive, internally consistent predictions of actinide properties. To enable the development of such a functional and quantify the predictions of currently available functionals, we have developed an efficient first-principles electronic structure method based on the Dirac equation. Results are compared with current methods, and the implications for relativistic density functionals discussed. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Mixing of equations of state for xenon-deuterium using density functional theory
Magyar, Rudolph J.; Mattsson, Thomas R. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)
2013-03-15
We report on a theoretical study of equation of state (EOS) properties of fluid and dense plasma mixtures of xenon and deuterium to explore and illustrate the basic physics of the mixing of a light element with a heavy element. Accurate EOS models are crucial to achieve high-fidelity hydrodynamics simulations of many high-energy-density phenomena, for example inertial confinement fusion and strong shock waves. While the EOS is often tabulated for separate species, the equation of state for arbitrary mixtures is generally not available, requiring properties of the mixture to be approximated by combining physical properties of the pure systems. Density functional theory (DFT) at elevated-temperature is used to assess the thermodynamics of the xenon-deuterium mixture at different mass ratios. The DFT simulations are unbiased as to elemental species and therefore provide comparable accuracy when describing total energies, pressures, and other physical properties of mixtures as they do for pure systems. The study focuses on addressing the accuracy of different mixing rules in the temperature range 1000-40 000 K for pressures between 100 and 600 GPa (1-6 Mbar), thus, including the challenging warm dense matter regime of the phase diagram. We find that a mix rule taking into account pressure equilibration between the two species performs very well over the investigated range.
Covariant field equations of the M-theory five-brane
P. S. Howe; E. Sezgin; P. C. West
1997-01-01
The component form of the equations of motion for the 5-brane in eleven dimensions is derived from the superspace equations. These equations are fully covariant in six dimensions. It is shown that double-dimensional reduction of the bosonic equations gives the equations of motion for a 4-brane in ten dimensions governed by the Born-Infeld action.
Elements for a Theory of Financial Risks
NASA Astrophysics Data System (ADS)
Bouchaud, J.-Ph.
1999-02-01
Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditional theories based on Gaussian statistics), and their practical implementation Here we describe three interrelated aspects of this program: we first give a brief survey of the peculiar statistical properties of the empirical price fluctuations. We then review how an option pricing theory consistent with these statistical features can be constructed, and compared with real market price for options. We finally argue that a true ‘microscopic’ theory of price fluctuations (rather than a statistical model) would be most valuable for risk assessment. A simple Langevin-like equation is proposed, as a possible step in this direction.
Elements for a theory of Finacial Risk
NASA Astrophysics Data System (ADS)
Bouchaud, Jean-Philippe
2000-03-01
Estimating and controlling large risks has become one of the main concern of financial institutions. This requires the development of adequate statistical models and theoretical tools (which go beyond the traditionnal theories based on Gaussian statistics), and their practical implementation. Here we describe three interrelated aspects of this program: we first give a brief survey of the peculiar statistical properties of the empirical price fluctuations. We then review how an option pricing theory consistent with these statistical features can be constructed, and compared with real market prices for options. We finally argue that a true `microscopic' theory of price fluctuations (rather than a statistical model) would be most valuable for risk assessment. A simple Langevin-like equation is proposed, as a possible step in this direction.
Chang, J.; Sandler, S.I. [Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States)] [Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 (United States)
1995-08-22
We have extended the Wertheim integral equation theory to mixtures of hard spheres with two attraction sites in order to model homonuclear hard-sphere chain fluids, and then solved these equations with the polymer-Percus--Yevick closure and the ideal chain approximation to obtain the average intermolecular and overall radial distribution functions. We obtain explicit expressions for the contact values of these distribution functions and a set of one-dimensional integral equations from which the distribution functions can be calculated without iteration or numerical Fourier transformation. We compare the resulting predictions for the distribution functions with Monte Carlo simulation results we report here for five selected binary mixtures. It is found that the accuracy of the prediction of the structure is the best for dimer mixtures and declines with increasing chain length and chain-length asymmetry. For the equation of state, we have extended the dimer version of the thermodynamic perturbation theory to the hard-sphere chain mixture by introducing the dimer mixture as an intermediate reference system. The Helmholtz free energy of chain fluids is then expressed in terms of the free energy of the hard-sphere mixture and the contact values of the correlation functions of monomer and dimer mixtures. We compared with the simulation results, the resulting equation of state is found to be the most accurate among existing theories with a relative average error of 1.79% for 4-mer/8-mer mixtures, which is the worst case studied in this work. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
A cold energy mixture theory for the equation of state in solid and porous metal mixtures
NASA Astrophysics Data System (ADS)
Zhang, X. F.; Qiao, L.; Shi, A. S.; Zhang, J.; Guan, Z. W.
2011-07-01
Porous or solid multi-component mixtures are ubiquitous in nature and extensively used as industrial materials such as multifunctional energetic structural materials (MESMs), metallic and ceramic powder for shock consolidation, and porous armor materials. In order to analyze the dynamic behavior of a particular solid or porous metal mixture in any given situation, a model is developed to calculate the Hugoniot data for solid or porous mixtures using only static thermodynamic properties of the components. The model applies the cold energy mixture theory to calculate the isotherm of the components to avoid temperature effects on the mixtures. The isobaric contribution from the thermodynamic equation of state is used to describe the porous material Hugoniot. Dynamic shock responses of solid or porous powder mixtures compacted by shock waves have been analyzed based on the mixture theory and Hugoniot for porous materials. The model is tested on both single-component porous materials such as aluminum 2024, copper, and iron; and on multi-component mixtures such as W/Cu, Fe/Ni, and Al/Ni. The theoretical calculations agree well with the corresponding experimental and simulation results. The present model produces satisfactory correlation with the experimentally obtained Hugoniot data for solid porous materials over a wide pressure range.
Hybrid two-chain simulation and integral equation theory : application to polyethylene liquids.
Huimin Li, David T. Wu (Colorado School of Mines Golden, CO.); Curro, John G.; McCoy, John Dwane (New Mexico Institute of Mining & Technology Socorro, NM.)
2006-02-01
We present results from a hybrid simulation and integral equation approach to the calculation of polymer melt properties. The simulation consists of explicit Monte Carlo (MC) sampling of two polymer molecules, where the effect of the surrounding chains is accounted for by an HNC solvation potential. The solvation potential is determined from the Polymer Reference Interaction Site Model (PRISM) as a functional of the pair correlation function from simulation. This hybrid two-chain MC-PRISM approach was carried out on liquids of polyethylene chains of 24 and 66 CH{sub 2} units. The results are compared with MD simulation and self-consistent PRISM-PY theory under the same conditions, revealing that the two-chain calculation is close to MD, and able to overcome the defects of the PRISM-PY closure and predict more accurate structures of the liquid at both short and long range. The direct correlation function, for instance, has a tail at longer range which is consistent with MD simulation and avoids the short-range assumptions in PRISM-PY theory. As a result, the self-consistent two-chain MC-PRISM calculation predicts an isothermal compressibility closer to the MD results.
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.
NASA Astrophysics Data System (ADS)
Planková, Barbora; Hrubý, Jan; Vinš, Václav
2013-05-01
We combined the density gradient theory (DGT) with the PC-SAFT and Peng-Robinson equations of state to model the homogeneous droplet nucleation and compared it to the classical nucleation theory (CNT) and experimental data. We also consider the effect of capillary waves on the surface tension. DGT predicts nucleation rates smaller than the CNT and slightly improves the temperature-dependent deviation of the predicted and experimental nucleation rates.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Nakatsuji, Hiroshi; Nakashima, Hiroyuki
2015-02-01
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 HTQ 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.
Langevin dynamics of proteins at constant pH.
Walczak, Aleksandra M; Antosiewicz, Jan M
2002-11-01
An application of the Langevin dynamics algorithm for simulation of protein conformational equilibria at constant pH is presented. The algorithm is used to compute average protonation of titratable groups in ovomucoid third domain, as functions of pH, resulting in data, basically equivalent to the pH dependencies of chemical shifts obtained from multidimensional nuclear magnetic resonance (NMR) spectroscopy, for the protein titratable residues. The pK(a) values obtained from the simulation are in reasonable agreement with experimental data. Possible improvements of this methodology, using achievements from other fields of mesoscopic biomolecular simulations, are also discussed. PMID:12513527
ERIC Educational Resources Information Center
Huggins, Anne Corinne
2012-01-01
Population invariance in equating exists when the relationship between two scales is the same for two or more subpopulations of examinees and hence the function used to equate the scales is not dependent on subpopulations. A lack of equating invariance (i.e., equating dependence) leads to a situation whereby examinees having the same score on one…
NASA Astrophysics Data System (ADS)
Wu, Rengmao; Zhang, Yaqin; Benítez, Pablo; Miñano, Juan C.
2014-12-01
The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L2 Monge-Kantorovich (LMK) theory, and introduce an efficient approach for finding the optimal mapping of the LMK problem. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.
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.
Podgornik, Rudolf
Equation of state for polymer liquid crystals: Theory and experiment H. H. Strey,* V. A. Parsegian nematic liquid crystals. We use a continuum model with macroscopic elastic moduli for a polymer nematic-chain and side-chain polymer liquid crystals are most often thermotropic, because of their flexible backbones
Sobolevskii, A N [M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
1999-10-31
It is proved that the one-dimensional Hamilton-Jacobi equation with a periodic non-homogeneous term admits a family of generalized solutions, each of which can be represented as the sum of a linear and a periodic function; a condition for the uniqueness of such a solution is given in terms of Aubry-Mather theory.
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…
NASA Astrophysics Data System (ADS)
Singh, R. C.
2009-07-01
The effects of quadrupole moments on the phase behaviour of isotropic-nematic transition are studied by using density functional theory for a system of molecules which interact via the Gay-Berne pair potential. The pair correlation functions of isotropic phase, which enter in the theory as input information, are found from the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to six have been considered. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures and quadrupole moments. The results have been compared with the available computer simulation results.
NASA Astrophysics Data System (ADS)
Belmonte-Beitia, Juan; Calvo, Gabriel F.; Pérez-García, Víctor M.
2014-09-01
Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics. Here we obtain a small number of effective equations describing the dynamics of single-front and localized solutions of Fisher-Kolmogorov type equations. These solutions are parametrized by means of a minimal set of time-dependent quantities for which ordinary differential equations ruling their dynamics are found. A comparison of the finite dimensional equations and the dynamics of the full partial differential equation is made showing a very good quantitative agreement with the dynamics of the partial differential equation. We also discuss some implications of our findings for the understanding of the growth progression of certain types of primary brain tumors and discuss possible extensions of our results to related equations arising in different modeling scenarios.
J. Kohano; Alfredo Caro; Michael W. Finnis
2005-01-01
We present a method for simulating clusters or molecules subjected to an external pressure, which is exerted by a pressure-transmitting medium. It is based on the canonical Langevin thermostat, but extended in such a way that the Brownian forces are allowed to operate only from the region exterior to the cluster. We show that the frictional force of the Langevin
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
Gambetta, Jay; Wiseman, H.M. [Centre for Quantum Dynamics, School of Science, Griffith University, Brisbane 4111 (Australia)
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.
NASA Astrophysics Data System (ADS)
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E.
2015-03-01
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.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-01
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. PMID:25747064
On the theory of convolution equations of the third kind, II
NASA Astrophysics Data System (ADS)
von Wolfersdorf, Lothar; Janno, Jaan
2008-06-01
Existence results of Part I of the paper are generalized to two types of autoconvolution equations of the third kind having free terms with nonzero values at x=0 like the well-known Bernstein-Doetsch equation for the Jacobian theta zero functions. Also uniqueness results for the linear convolution equations in Part I of the paper are extended to more general function spaces. Further, a special class of integro-differential equations with autoconvolution integral and two classes of the linear singular Abel-Volterra equations are dealt with.
Giacometti, Achille, E-mail: achille.giacometti@unive.it [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia (Italy)] [Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123 Venezia (Italy); Gögelein, Christoph, E-mail: christoph.goegelein@ds.mpg.de [Max-Planck-Institute for Dynamics and Self-Organization, Göttingen (Germany)] [Max-Planck-Institute for Dynamics and Self-Organization, Göttingen (Germany); Lado, Fred, E-mail: lado@ncsu.edu [Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 (United States)] [Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202 (United States); Sciortino, Francesco [Dipartimento di Fisica and CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma (Italy)] [Dipartimento di Fisica and CNR-SOFT, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma (Italy); Ferrari, Silvano, E-mail: silvano.ferrari@tuwien.ac.at [Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wiedner Hauptstraße 8-10/136, A-1040 Wien (Austria)] [Institut für Theoretische Physik and Center for Computational Materials Science, Technische Universität Wien, Wiedner Hauptstraße 8-10/136, A-1040 Wien (Austria); Pastore, Giorgio, E-mail: pastore@ts.infn.it [Dipartimento di Fisica dell’ Università di Trieste and CNR-IOM, Strada Costiera 11, 34151 Trieste (Italy)] [Dipartimento di Fisica dell’ Università di Trieste and CNR-IOM, Strada Costiera 11, 34151 Trieste (Italy)
2014-03-07
Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.
Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano; Pastore, Giorgio
2014-03-01
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
Langevin dynamics simulations of biomolecules on graphics processors
Zhmurov, A; Kholodov, Y; Barsegov, V
2010-01-01
Due to the very long timescales involved (us-s), theoretical modeling of fundamental biological processes including folding, misfolding, and mechanical unraveling of biomolecules, under physiologically relevant conditions, is challenging even for distributed computing systems. Graphics Processing Units (GPUs) are emerging as an alternative programming platform to the more traditional CPUs as they provide high raw computational power that can be utilized in a wide range of scientific applications. Using a coarse-grained Self Organized Polymer (SOP) model, we have developed and tested the GPU-based implementation of Langevin simulations for proteins (SOP-GPU program). Simultaneous calculation of forces for all particles is implemented using either the particle based or the interacting pair based parallelization, which leads to a ~30-fold acceleration compared to an optimized CPU version of the program. We assess the computational performance of an end-to-end application of the SOP-GPU program, where all steps o...
Five-dimensional cosmological model with a time-dependent equation of state in Wesson’s theory
G. S. Khadekar; G. R. Avachar
2007-01-01
Exact solution for a homogeneous cosmological model in 5D space-time-mass gravity theory proposed by Wesson (Astron. Astrophys.\\u000a 119:145, 1983) is obtained by assuming the time-dependent equation of state. The behavior of the solution is discussed for the two cases\\u000a kk=0. It is found that the observed constancy of the rest mass of an isolated particle in the present era may
Du Kai, E-mail: kdu@fudan.edu.cn; Qiu, Jinniao, E-mail: 071018032@fudan.edu.cn; Tang Shanjian, E-mail: sjtang@fudan.edu.cn [Fudan University, Department of Finance and Control Sciences, School of Mathematical Sciences, and Laboratory of Mathematics for Nonlinear Sciences (China)
2012-04-15
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.
METHODS OF ALGEBRAIC GEOMETRY IN THE THEORY OF NON-LINEAR EQUATIONS
I M Krichever
1977-01-01
CONTENTSIntroduction § 1. The Akhiezer function and the Zakharov-Shabat equations § 2. Commutative rings of differential operators § 3. The two-dimensional Schrödinger operator and the algebras associated with it § 4. The problem of multi-dimensional -algebraic operators Appendix 1. The Hamiltonian formalism in equations of Lax and Novikov types Appendix 2. Elliptic and rational solutions of the K-dV equations and
Effective Field Theory out of Equilibrium: Brownian quantum fields
Boyanovsky, D
2015-01-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field --the system-- interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the \\emph{influence action} from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At $T=0$ we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At $T\
Critical dynamics in systems controlled by fractional kinetic equations
NASA Astrophysics Data System (ADS)
Batalov, Lev; Batalova, Anastasia
2013-02-01
The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0
NASA Astrophysics Data System (ADS)
Hahn, Y. K.
2014-12-01
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.
Xiusan Xing
2010-01-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental\\u000a equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity\\u000a type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It
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.
On the theory of nonlinear response in a nonideal plasma
NASA Astrophysics Data System (ADS)
Pavlov, G. A.
2008-06-01
A theory of nonlinear response is developed for studying nonlinear phenomena and nonlinear transport processes in nonideal Coulomb systems. Temporal plasma echo and transformation of waves in a nonideal Coulomb system are studied on the basis of the theory of nonlinear response to mechanical perturbations. General constraints imposed on nonlinear response functions are considered, and the model for determining quadratic response functions is formulated. The conditions for the emergence of temporal plasma echo and wave transformation are determined. It is shown that these nonlinear effects in a nonideal plasma can be initiated by ultrashort field pulses. A theory of transport is developed for determining the Burnett transport properties of a nonideal multielement plasma. A procedure is proposed for comparing the phenomenological conservation equations for a charged continuous medium and equations of motion for the operators of corresponding dynamic variables. The Mori algorithm is used for deriving the equations of motion for operators of dynamic variables in the form of generalized Langevin equations. The linearized Burnett approximation is considered in detail. The properties of the matrices of coefficients of higher-order derivatives in the system of conservation equations in the linearized Burnett approximation, which are important for hydrodynamic applications, are discussed. Various versions of the theory of nonlinear response are 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…
Second Order perturbation Theory: A covariant approach involving a barotropic equation of state
Bob Osano
2015-04-07
We first revisit the motivations for developing techniques to study Second-Order effects, before presenting the formalism. We study second-order tensor perturbations about FLRW with dust on the one hand, and with a general barotropic equation of state on the other. Solutions to the wave equations are presented.
L. Joukovskaya
2007-08-04
We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges.
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.
Ising field theory: Quadratic difference equations for the n-point Green's functions on the lattice
Barry McCoy; Jacques Perk; Tai Wu
1981-01-01
For the two-dimensional Ising model at arbitrary temperature, we present a system of quadratic difference equations involving the correlations of n order variables and that of n-2 order and 2 disorder variables. With suitable boundary conditions these equations specify the correlations.
Walter Bergweiler; Alexandre Eremenko
2010-01-25
The equation in the title describes the number of bright images of a point source under lensing by an elliptic object with isothermal density. We prove that this equation has at most 6 solutions. Any number of solutions from 1 to 6 can actually occur.
On the numerical solution of a hypersingular integral equation in scattering theory
Rainer Kress
1995-01-01
We describe a fully discrete method for the numerical solution of the hypersingular integral equation arising from the combined double- and single-layer approach for the solution of the exterior Neumann problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Hölder space setting with pointwise estimates and prove an exponential convergence rate for analytic
Cooper, Fred; Mihaila, Bogdan; Dawson, John F. [National Science Foundation, Division of Physics, Arlington, Virginia 22230 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States) and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Department of Physics, University of New Hampshire, Durham, New Hampshire 03824 (United States)
2004-11-15
In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O(N) {phi}{sup 4} field theory. The auxiliary field formulation allows a simple interpretation of the large-N expansion as a loop expansion of the generating functional in the auxiliary field {chi}, once the effective action is obtained by integrating over the {phi} fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson (SD) equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent SD equations valid to order 1/N, in both 2+1 and 3+1 dimensions. We compare the results for the real and imaginary parts of the renormalized Green's functions with the related sunset approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.
Simone Farinelli
2014-07-21
We prove that Jormakka's classical solution of the Yang-Mills equations for the Minkowskian $\\mathbf{R}^{1,3}$ can be quantized to field maps satisfying Wightman's axioms of Constructive Quantum Field Theory and that the spectrum of the corresponding Hamilton operator is positive and bounded away from zero except for the case of the vacuum state which has vanishing energy level. By continuity this implies the existence of a mass gap for any four dimensional quantum Yang-Mills theory on the Minkoswki space, provided this theory exists. The positive mass gap result holds true at second quantization level as well, two of eights Wightman's axioms don't. The (virtual) particles corresponding to all solution fields are fermionic ghosts.
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)
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.
Mass, Energy, Space And Time Systemic Theory--MEST--photoelectric conversion equation
NASA Astrophysics Data System (ADS)
Cao, Dayong
2010-03-01
Things have their physical system of the mass, energy, space and time of themselves-MEST. The time is from the frequency of wave, the space is from the amplitude of wave. In the system, the mass-energy is center and the space-time is around. In the general relativity, there is the equation: ma=mg . So get the equation: mar=mv^2=mgr. We use the data of the planets into this equation, and find it is right. (see the figure 1 and table 2) But the kinetic energy's equation is: Ek=mv^2/2mgr. How do explain it? Because the other kinetic energy's equations: Ek=?mc^2 like the wave's energy equation: E'=m'c^2. And things have both of the matter and the wave. So the equation belong to the wave. So the ?m can be see like the increased mass of wave of the things. The matter's kinetic energy equal the wave's energy: mv^2/2=?mc^2=?m'c^2. And them give the things the repulsion force together. So the repulsion energy equation is: Er=mv^2=mv^2/2+?m'c^2=mar. The repulsion energy of the planets equal it's potential energy: Er=Ep=GMm/r=mgr. In photoelectron conversion, Not only there is a relationship between the wave and the kinetic energy of the photoelectron, but also there is a relationship between the wave and the mass of the photoelectron. So get the photoelectric conversion equation: m ev^2/2=?m'c^2-E= h?-E, and ?m e= h/c ?-m e. The mass of the photoelectron is bigger than the electron's mass.
On a system of equations arising in viscoelasticity theory of fractional type
Teodor M. Atanackovic; Stevan Pilipovic; Dusan Zorica
2012-05-24
We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in the constitutive equation instead the constitutive equation itself. Both, a rod and a body are assumed to have finite mass. The motion of a body is assumed to be translatory. Existence and uniqueness for the corresponding initial-boundary value problem is proved within the spaces of functions and distributions.
General representations of the equations of the linear theory of mixtures of elastic media
NASA Astrophysics Data System (ADS)
Rushchitskii, Ia. Ia.
1980-08-01
As in a classical theory, knowledge of the general representations of the solutions of the theory of mixtures provides not only information on the general structure of the solutions, but also simplifies the solution of some classes of boundary value problems. In the present paper, general representations of the solutions of the linear theory of a mixture of two elastic media are obtained from an analysis of Papkovich-Neuber, Galerkin, Boussinesq, Love, and Lame representations.
Jeffrey H Bergstrand
1989-01-01
A general equilibrium model of world trade with two differentiated-product industries and two factors is developed to illustrate how the gravity equation, including exporter and importer populations, as well as incomes, \\
Callan-Symanzik and renormalization group equation in theories with spontaneously broken symmetry
Elisabeth Kraus
1997-03-31
Callan-Symanzik and renormalization group equation are discussed for the $U(1)$-axial model and it is shown that the symmetric model is not the asymptotic version of the spontaneously broken one due to mass logarithms in the $\\beta$-functions. The Callan-Symanzik equation of the standard model is seen to have the same form as the one of the simple model.
Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals
Michael Ricker; Rolf Schilling
2004-01-01
We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation. The one-particle orientational distribution function rho(1) (Omega) has a nontrivial dependence on the orientation Omega , in contrast to a liquid, and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids.
A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory
NASA Astrophysics Data System (ADS)
Chacón-Acosta, Guillermo; Dagdug, Leonardo; Morales-Técotl, Hugo A.
2010-12-01
A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work [1], with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Jüttner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.
Masahiro Iwano
1977-01-01
Summary This paper studies the two boundary value problems (A) and (B) as applications of Nagumo-Hukuhara theory on the boundary value problems for the second order nonlinear ordinary differential\\u000a equations.
Quantum Langevin model for exoergic ion-molecule reactions and inelastic processes
Gao Bo [Department of Physics and Astronomy, Mailstop 111, University of Toledo, Toledo, Ohio 43606 (United States)
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.
Closed string field theory: Quantum action and the Batalin-Vilkovisky master equation
Barton Zwiebach
1993-01-01
The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L? encoding the gauge symmetry of the classical theory. The higher genus
Tian Hao
2014-09-05
Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in literature: The inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept, we obtain the tap density equations and they can be reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environment temperature are grouped into one parameter that weighs the pace of packing process. The current results, in conjunction with our previous findings, may imply that both dry(granular)and wet(colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).
Wu Shuangqing [College of Physical Science and Technology, Central China Normal University, Wuhan, Hubei 430079 (China)
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.
Shuang-Qing Wu
2009-09-01
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 can not 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 Stackel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.
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.
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…
Langevin dynamics simulations of biomolecules on graphics processors
A. Zhmurov; R. I. Dima; Y. Kholodov; V. Barsegov
2010-03-04
Due to the very long timescales involved (us-s), theoretical modeling of fundamental biological processes including folding, misfolding, and mechanical unraveling of biomolecules, under physiologically relevant conditions, is challenging even for distributed computing systems. Graphics Processing Units (GPUs) are emerging as an alternative programming platform to the more traditional CPUs as they provide high raw computational power that can be utilized in a wide range of scientific applications. Using a coarse-grained Self Organized Polymer (SOP) model, we have developed and tested the GPU-based implementation of Langevin simulations for proteins (SOP-GPU program). Simultaneous calculation of forces for all particles is implemented using either the particle based or the interacting pair based parallelization, which leads to a ~30-fold acceleration compared to an optimized CPU version of the program. We assess the computational performance of an end-to-end application of the SOP-GPU program, where all steps of the algorithm are running on the GPU, by profiling the associated simulation time and memory usage for a number of small proteins, long protein fibers, and large-size protein assemblies. The SOP-GPU package can now be used in the theoretical exploration of the mechanical properties of large-size protein systems to generate the force-extension and force-indentation profiles under the experimental conditions of force application, and to relate the results of single-molecule experiments in vitro and in silico.
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.
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.
Agung Trisetyarso
2014-11-23
We present the recent works \\cite{trisetyarso2011} on the application of Darboux transformation on one-dimensional Dirac equation related to the field of Quantum Information and Computation (QIC). The representation of physical system in one-dimensional equation and its transformation due to the Bagrov, Baldiotti, Gitman, and Shamshutdinova (BBGS)-Darboux transformation showing the possibility admitting the concept of relativity and the trade-off of concurrent condition of quantum and classical physics play into the area of QIC. The applications in cavity quantum electrodynamics and on the proposal of quantum transistor are presented.
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.
Huš, Matej; Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si [Department of Chemistry and Chemical Technology, University of Ljubljana, Chair of Physical Chemistry, Ve?na pot 113, SI-1000 Ljubljana (Slovenia); Munaò, Gianmarco [Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Viale F. Stagno d'Alcontres 31, 98166 Messina (Italy)
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.
NASA Astrophysics Data System (ADS)
Quan, W. L.; Chen, Q. F.; Fu, Z. J.; Sun, X. W.; Zheng, J.; Gu, Y. J.
2015-02-01
A consistent theoretical model that can be applied in a wide range of densities and temperatures is necessary for understanding the variation of a material's properties during compression and heating. Taking argon as an example, we show that the combination of self-consistent fluid variational theory and linear response theory is a promising route for studying warm dense matter. Following this route, the compositions, equations of state, and transport properties of argon plasma are calculated in a wide range of densities (0.001 -20 g /c m3) and temperatures (5 -100 kK ) . The obtained equations of state and electrical conductivities are found in good agreement with available experimental data. The plasma phase transition of argon is observed at temperatures below 30 kK and density about 2 -6 g /c m3 . The minimum density for the metallization of argon is found to be about 5.8 g /c m3 , occurring at 30 -40 kK . The effects of many-particle correlations and dynamic screening on the electrical conductivity are also discussed through the effective potentials.
Quantum Stress Tensor Fluctuations and Raychaudhuri's Equation
NASA Astrophysics Data System (ADS)
Borgman, J.; Ford, L. H.
2006-02-01
The quantum fluctuations of the stress tensor of matter fields lead to fluctuations of the spacetime geometry. One way in which these fluctuations might manifest themselves is through expansion fluctuations of the rays from a distant object viewed through the fluctuating spacetime. We discuss this issue by using the Raychaudhuri equation as a Langevin equation. Some explicit results for the case of a thermal bath are presented.
NASA Astrophysics Data System (ADS)
Slyusarchuk, Vasilii E.
2010-10-01
Conditions for the existence of solutions to the nonlinear functional-differential equation \\displaystyle \\frac{d^mx(t)}{dt^m}+(Fx)(t)=h(t), \\qquad t\\in\\ R, in the space of functions bounded on the axes are obtained by using local linear approximation to the operator F. Bibliography: 21 items.
Slyusarchuk, Vasilii E [Ukranian State Academy of Water Economy (Ukraine)
2010-10-06
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.
Zhou, Y.; Stell, G.
1988-12-01
Integral equations that yield the charge and density profiles are derived for a Donnan system, in which an ionic solution is separated into two regions by a semipermeable membrane (SPM) or a spherical semipermeable vesicle (SPV). These equations are obtained from the Ornstein--Zernike (OZ) equation. We show how quantitative results can be obtained from either the mean spherical approximation (MSA) closure or the hypernetted-chain (HNC) closure for profiles. Use is made of bulk-correlation input obtained by means of the Debye--Hueckel approximation, the MSA approximation, or the HNC approximation. The resulting approximations will be referred as MSA/DH, HNC/DH, MSA/MSA, etc. The system on which we focus contains three charged hard-sphere species: cation, anion, and a large ion (a protein or polymer ion) separated by a plane SPM, through which the large ion cannot pass, and to one side of which all large ions are confined, or a spherical SPV, outside of which the large ions are confined. Analytical expressions for the bulk density ratio between the two sides of a plane membrane as well as the membrane potential in various approximations are obtained. Results obtained from these expresssions are compared with the results obtained by equating electrochemical potentials. A new contact-value theorem is provided for the plane SPM system. Analytical solutions for the charge profile and the potential profile in the MSA/DH approximation are obtained. It turns out that results obtained in the HNC/DH approximation are exactly the same as those obtained by using 1D nonlinear Poisson--Boltzmann equations if the repulsive cores of the macroions are neglected.
Theory of SNAP devices: basic equations and comparison with the experiment.
Sumetsky, M
2012-09-24
A SNAP (Surface Nanoscale Axial Photonics) device consists of an optical fiber with introduced nanoscale effective radius variation, which is coupled to transverse input/output waveguides. The input waveguides excite whispering gallery modes circulating near the fiber surface and slowly propagating along the fiber axis. In this paper, the theory of SNAP devices is developed and applied to the analysis of transmission amplitudes of simplest SNAP models exhibiting a variety of asymmetric Fano resonances and also to the experimental characterization of a SNAP bottle microresonator and to a chain of 10 coupled microresonators. Excellent agreement between the theory and the experiment is demonstrated. PMID:23037403
The influence of compressibility on the equations of the rapid distortion theory of turbulence
NASA Astrophysics Data System (ADS)
Boyd, C.
1982-02-01
Batchelor's theory of the effect of rapid distortion on turbulence level in incompressible flow, is extended in order to account for compressibility. The theory was applied to the flow through a wind tunnel contraction cone. Compressibility has only a small effect on the change of turbulence intensity, but it favorably affects the reduction of the percentage of total turbulence. The contraction ratio needed in order to achieve a given reduction in the level of turbulence, or in the level of nonuniformity, decreases as the outlet Mach number increases.
Geodesic Deviation Equation in GR equivalent theory of $f(T)$ gravity
F. Darabi; M. Mousavi; K. Atazadeh
2014-12-31
In this work, we show that it is possible to study the GR equivalent notion of geodesic deviation in $f(T)$ gravity, in spite of the fact that in teleparallel gravity there is no notion of geodesics, and the torsion is responsible for the appearance of gravitational interaction. In this regard, we obtain the GR equivalent of $f(T)$ gravity whose equations are in the modified gravity form such as $f(R)$ gravity. Then, we obtain the GDE within the context of this modified gravity. In this way, the obtained geodesic deviation equation will correspond to the $f(T)$ gravity. Eventually, we extend the calculations to obtain the modification of Matting relation.
General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations
Doktorov, Alexander B.; Kipriyanov, Alexey A. [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090 (Russian Federation)] [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk State University, Novosibirsk 630090 (Russian Federation)
2014-05-14
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.
On a Solution of Field Equations in Einstein's Unified Field Theory, II
N. N. Ghosh
1957-01-01
This paper contains some observations regarding a type of non-static solution of Einstein's field equations in ``strong'' form. Denoting the coordinates by x_k, x_m, x_n, x_l a static field gmu{nu} with components involving the coordinate x_k is made non-static by changing x_k into x_k + ?x_l where ? is a constant. For the spherically symmetric case we find that such
The Geometry of the Master Equation and Topological Quantum Field Theory
M. Alexandrov; A. Schwarz; O. Zaboronsky; M. Kontsevich
1997-01-01
In Batalin-Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some
The fractional stochastic heat equation on the circle: Time regularity and potential theory
Eulalia Nualart; Frederi Viens
2009-01-01
We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S1. We obtain sharp results on the Hölder continuity in time of the paths of the solution u={u(t,x)}t?R+,x?S1. We then establish upper and lower bounds on hitting probabilities of u, in terms of the Hausdorff measure and Newtonian
Interpretation of quantum Hall effect from angular momentum theory and Dirac equation.
NASA Astrophysics Data System (ADS)
Shrivastava, Keshav
2007-03-01
It is found that when suitable modifications to the g values are made, the effective charge of a particle is determined by eeff =(1/2)ge, which enters in the Dirac equation to yield the fractional charges. The calculated values of the fractional charges agree with the data on fractional charge deduced from the quantum Hall effect. Therefore, the Dirac equation can accommodate not only particles of charges 0 and ± 1 but also fractional charges such as 1/3 and 2/3. This means that spin and charge get coupled. There are two g values for two signs of the spin. Hence 4 eigen values emerge, two for positive spin and two for negative spin. Therefore a 4x4 matrix has to be added to the eigen value E in the Dirac equation. This matrix has interesting anticommuting properties. K. N. Shrivastava, Phys. Lett. A 113,435-6(1986);115, 459(1986)(E). K. N. Shrivastava, Phys. Lett. A 326, 469-472(2004) K. N. Shrivastava, Mod. Phys. Lett. B 13, 1087-1090(1999); 14, 1009-1013(2000).
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
Vladimir V. Bazhanov; Sergei L. Lukyanov; Alexander B. Zamolodchikov
1996-01-01
This paper is a direct continuation of [1] where we begun the study of the integrablestructures in Conformal Field Theory. We show here how to construct the operatorsQ \\\\Sigma () which act in highest weight Virasoro module and commute for different values ofthe parameter . These operators appear to be the CFT analogs of the Q - matrix ofBaxter [2],
Photons and Gravitons in Perturbation Theory: Derivation of Maxwell's and Einstein's Equations
Steven Weinberg
1965-01-01
The S matrix for photon and graviton processes is studied in perturbation theory, under the restriction that the only creation and annihilation operators for massless particles of spin j allowed in the interaction are those for the physical states with helicity +\\/-j. The most general covariant fields that can be constructed from such operators cannot represent real photon and graviton
Generalized Langevin model for molecular dynamics of an activated reaction in solution
NASA Astrophysics Data System (ADS)
Benjamin, I.; Lee, Lloyd L.; Li, Y. S.; Liu, Antonio; Wilson, Kent R.
1991-04-01
The molecular dynamics (MD) by which an A+BC?AB+C atom exchange reaction takes place in rare gas solvent are modeled using the generalized Langevin equation (GLE) and are compared in terms of energy flow to the results of full deterministic MD. A simple single atom model is used for the force-force correlation function and the corresponding fluctuation-response derived memory kernel. We model both the generation from an equilibrium ensemble of the specific fluctuation by which the reactants climb the barrier to the transition state and the dissipation of the fluctuation as the reagents descend the barrier to equilibrated products. This model of the generation and decay of the fluctuation by which an activated process emerges from and returns to equilibrium is an extension beyond the usual use of the GLE to model the dynamics of equilibrium systems, barrier recrossings in the vicinity of a barrier top (Grote-Hynes), or the decay of nonequilibrium systems toward equilibrium. An analysis of reagent translational motion for this reaction in terms of the GLE shows that there are several identifiable epochs in the time history of this reaction: (1) a ± 10 fs time period (the recrossing epoch) immediately before and after the transition state at t = 0 during which the reaction coordinate dynamics are dominated by the random forces; (2) periods of ± (10-60) fs (intrinsic potential epochs) during which the mutual forces among the reagents dominate; (3) periods of ± (60-300) fs (generative-dissipative epochs) in which the generative-dissipative forces dominate; and (4) initial and final periods < -300 and > 300 fs (equilibrium epochs) during which the generative-dissipative and random forces are in balance. This example calculation illustrates that in favorable cases a simple GLE approach can be useful in modeling and understanding both the reactant and product time histories of the MD of activated solution reactions.
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.
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
Theory of warm ionized gases: Equation of state and kinetic Schottky anomaly
NASA Astrophysics Data System (ADS)
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.
Microscopic theory of warm ionized gases: equation of state and kinetic Schottky anomaly
NASA Astrophysics Data System (ADS)
Capolupo, A.; Giampaolo, S. M.; Illuminati, F.
2013-06-01
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 analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed.
The local theory for viscous Hamilton–Jacobi equations in Lebesgue spaces
Matania Ben-Artzi; Philippe Souplet; Fred B. Weissler
2002-01-01
We consider viscous Hamilton–Jacobi equations of the form (VHJ)ut??u=a|?u|p,x?RN,t>0,u(x,0)=u0(x),x?RN, where a?R, a?0 and p?1. We provide an extensive investigation of the local Cauchy problem for (VHJ) for irregular initial data u0, namely for u0 in Lebesgue spaces Lq=Lq(RN), 1?q
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong [PPPL; Burby, Joshua W [PPPL; Davidson, Ronald C [PPPL
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.
General planetary theory in elliptic variables. I - Expansion of the equations
L. Duriez
1977-01-01
A program aimed at some improvements in Le Verrier theory, with the object of constructing highly precise ephemerides over an extended time span, is detailed. Analytic expressions containing up to high orders (with respect to masses) of long-period and very-long-period terms are arrived at, and their interrelations are explored. Expansions of some terms and algorithms of the expansions are worked
Integrable Structure of Conformal Field Theory II.Q-operator and DDV equation
Vladimir V. Bazhanov; Sergei L. Lukyanov; Alexander B. Zamolodchikov
1997-01-01
: This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory.\\u000a We show here how to construct the operators ${\\\\bf Q}_{\\\\pm}(\\\\lambda)$ which act in the highest weight Virasoro module and commute\\u000a for different values of the parameter ?. These operators appear to be the CFT analogs of the Q -
Mahdi Abbasi; Nadereh Golshan Ebrahimi; Mahdi Nadali; Masood Khabazian Esfahani
Molecular stress function theory with new strain energy function is used to analyze transient extensional viscosity data of\\u000a seven low-density polyethylene (LDPE) melts with various molecular structures as published by Stadler et al. (Rheol Acta 48:479–490,\\u000a 2009) Pivokonsky et al. (J Non Newton Fluid Mech 135:58–67, 2006) and Wagner et al. (J Rheol 47(3):779–793, 2003). The new strain energy function
NASA Astrophysics Data System (ADS)
Lin, Yuan; Wei, X.; Qian, J.; Sze, K. Y.; Shenoy, V. B.
2014-01-01
A Langevin dynamics based formulation is proposed to describe the shape fluctuations of biopolymer filaments. We derive a set of stochastic partial differential equations (SPDEs) to describe the temporal evolution of the shape of semiflexible filaments and show that the solutions of these equations reduce to predictions from classical modal analysis. A finite element formulation to solve these SPDEs is also developed where, besides entropy, the finite deformation of the filaments has been taken into account. The validity of the proposed finite element-Langevin dynamics (FEM-LD) approach is verified by comparing the simulation results with a variety of theoretical predictions. The method is then applied to study the mechanical behavior of randomly cross-linked F-actin networks. We find that as deformation progresses, the response of such networks undergoes transitions from being entropy dominated to being governed by filament bending and then, eventually, to being dictated by filament stretching. The levels of macroscopic stress at which these transitions take place were found to be around 1% and 10%, respectively, of the initial bulk modulus of the network, in agreement with recent experimental observations.
NASA Astrophysics Data System (ADS)
Buceta, R. C.; Hansmann, D.; von Haeften, B.
2014-12-01
We present several approaches for deriving the coarse-grained continuous Langevin equation (or Edwards-Wilkinson equation) from a random deposition with surface relaxation (RDSR) model. First we introduce a novel procedure to divide the first transition moment into the three fundamental processes involved: deposition, diffusion and volume conservation. We show how the diffusion process is related to the antisymmetric contribution and the volume conservation process is related to the symmetric contribution, which renormalizes to zero in the coarse-grained limit. In another approach, we find the coefficients of the continuous Langevin equation, by regularizing the discrete Langevin equation. Finally, in a third approach, we derive these coefficients from the set of test functions supported by the stationary probability density function (SPDF) of the discrete model. The applicability of the approaches used to other discrete random deposition models with instantaneous relaxation to a neighboring site is discussed.
Edwards-Wilkinson equation from lattice transition rules
NASA Astrophysics Data System (ADS)
Vvedensky, Dimitri D.
2003-02-01
Continuum equations of motion for the height fluctuations of lattice growth models are derived from their transition rules by regularizing and coarse-graining the associated discrete Langevin equations. For models with random deposition followed by instantaneous relaxation to a neighboring site based on identifying the local height minimum, our methodology yields the Edwards-Wilkinson equation. The application of this procedure to other growth models is discussed.
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
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˜)=A˜X˜2+B˜X˜+C˜. To use the mentioned EP method, at first the 1-cut solution of FFQE as a real root is obtained and then unknown manipulated unsymmetrical spreads are allocated to the core point. To this purpose we find ? and ? as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826
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 ? and ? as optimum values which construct the best spreads. Finally to illustrate easy application and rich behavior of EP method, several examples are given. PMID:25009826
The Quasi-Maxwellian Equations of General Relativity: Applications to Perturbation Theory
NASA Astrophysics Data System (ADS)
Novello, M.; Bittencourt, E.; Salim, J. M.
2014-12-01
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is presented. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lemaître-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge-independent quantities. We shall see that in the QM-scheme, we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz that deals with perturbation in the standard framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting of particular choices of the perturbed variables as a combination of gauge-dependent quantities.
The Quasi-Maxwellian Equations of General Relativity: Applications to the Perturbation Theory
M. Novello; E. Bittencourt; J. M. Salim
2013-02-28
A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lema\\^itre-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.
The role of the l1-norm in quantum information theory and two types of the Yang-Baxter equation
NASA Astrophysics Data System (ADS)
Niu, Kai; Xue, Kang; Zhao, Qing; Ge, Mo-Lin
2011-07-01
The role of the l1-norm in the Yang-Baxter system has been studied through Wigner's D-functions, where l1-norm means ?i|Ci| for |?rang = ?iCi|?irang with |?irang being the orthonormal basis. It is shown that the existing two types of braiding matrices, which can be viewed as particular solutions of the Yang-Baxter equation (YBE) with different spectral parameters can be unified in the 2D YBE. We prove that the maximum of the l1-norm is connected with the maximally entangled states and topological quantum field theory with two-component anyons, while the minimum leads to the deformed permutation related to the familiar integrable models.
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.
Effect of rotation symmetry to abelian Chern-Simons field theory and anyon equation on a sphere
Park, N W; Soh, D S; Rim, Chaiho
1994-01-01
We analyze the Chern-Simons field theory coupled to non-relativistic matter field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invariance restricts the Hilbert space to the one with a definite number of charges and dictates Dirac quantization condition to the Chern-Simons coefficient, whereas SO(2) invariance does not. The corresponding Schr\\"odinger equation for many anyons (and for multispecies) on the sphere are presented with appropriate boundary condition. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translation and modular symmetry on a torus is also expounded.
Langevin equations and computed correlation functions for a rotating and translating asymmetric top
M. W. Evans; G. J. Evans
1986-01-01
The three-dimensional diffusion in condensed material of a rotating and translating asymmetric-top molecule is considered with use of three frames of reference: the laboratory frame (x,y,z), a rotating frame (1,2,3)', and a moving frame (1,2,3). The frame (1,2,3)' has the same origin as (x,y,z), but rotates with an angular velocity omega, the molecular angular velocity. The frame (1,2,3) is defined
NASA Astrophysics Data System (ADS)
Kim, Changho; Karniadakis, George Em
2015-03-01
We study confined Brownian motion by investigating the memory function of a -dimensional hypercube (), which is subject to a harmonic potential and suspended in an ideal gas confined by two parallel walls. For elastic walls and under the infinite-mass limit, we obtain analytic expressions for the force autocorrelation function and the memory function. The transverse-direction memory function possesses a nonnegative tail decaying like , from which anomalous diffusion is expected for . For , the position-dependent friction coefficient becomes larger than the unconfined case and the increment is inversely proportional to the square of the distance from the wall. We also perform molecular dynamics simulations with thermal walls and/or a finite-mass hypercube. We observe faster decay due to the thermal wall ( for and for under the fully thermalizing wall) and convergence behaviors of the finite-mass memory function, which are different from the unconfined case.
Yu. A. Kashlev; N. M. Sadykov
1997-01-01
The kinetic theory of motion for fast particles in a crystal is elaborated, based on the Bogoliubov chain of equations. A\\u000a local kinetic equation is derived for the one-particle distribution function in conditions of particle interaction with thermal\\u000a lattice oscillations and valence electrons. A characteristic of the particle subsystem in the de-channeling problem—the diffusion\\u000a function B(??) in the space of
NASA Astrophysics Data System (ADS)
Carrier, Pierre; Tang, Jok M.; Saad, Yousef; Freericks, James K.
Inhomogeneous dynamical mean-field theory has been employed to solve many interesting strongly interacting problems from transport in multilayered devices to the properties of ultracold atoms in a trap. The main computational step, especially for large systems, is the problem of calculating the inverse of a large sparse matrix to solve Dyson's equation and determine the local Green's function at each lattice site from the corresponding local self-energy. We present a new e_cient algorithm, the Lanczos-based low-rank algorithm, for the calculation of the inverse of a large sparse matrix which yields this local (imaginary time) Green's function. The Lanczos-based low-rank algorithm is based on a domain decomposition viewpoint, but avoids explicit calculation of Schur complements and relies instead on low-rank matrix approximations derived from the Lanczos algorithm, for solving the Dyson equation. We report at least a 25-fold improvement of performance compared to explicit decomposition (such as sparse LU) of the matrix inverse. We also report that scaling relative to matrix sizes, of the low-rank correction method on the one hand and domain decomposition methods on the other, are comparable.
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.
Sean Fleming
2014-04-22
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 $n$-$\\bar{n}$ 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 counterterm 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.
Slavchov, Radomir I
2014-04-28
If the molecules of a given solvent possess significant quadrupolar moment, the macroscopic Maxwell equations must involve the contribution of the density of the quadrupolar moment to the electric displacement field. This modifies the Poisson-Boltzmann equation and all consequences from it. In this work, the structure of the diffuse atmosphere around an ion dissolved in quadrupolarizable medium is analyzed by solving the quadrupolar variant of the Coulomb-Ampere's law of electrostatics. The results are compared to the classical Debye-Hückel theory. The quadrupolar version of the Debye-Hückel potential of a point charge is finite even in r = 0. The ion-quadrupole interaction yields a significant expansion of the diffuse atmosphere of the ion and, thus, it decreases the Debye-Hückel energy. In addition, since the dielectric permittivity of the electrolyte solutions depends strongly on concentration, the Born energy of the dissolved ions alters with concentration, which has a considerable contribution to the activity coefficient ?± known as the self-salting-out effect. The quadrupolarizability of the medium damps strongly the self-salting-out of the electrolyte, and thus it affects additionally ?±. Comparison with experimental data for ?± for various electrolytes allows for the estimation of the quadrupolar length of water: LQ ? 2 Å, in good agreement with previous assessments. The effect of quadrupolarizability is especially important in non-aqueous solutions. Data for the activity of NaBr in methanol is used to determine the quadrupolarizability of methanol with good accuracy. PMID:24784290
The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory
NASA Astrophysics Data System (ADS)
Lewin, Mathieu; Sabin, Julien
2015-02-01
We show local and global well-posedness results for the Hartree equation where ? is a bounded self-adjoint operator on , ? ? ( x) = ?( x, x) and w is a smooth short-range interaction potential. The initial datum ?(0) is assumed to be a perturbation of a translation-invariant state ? f = f(-?) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state ?( t), counted relatively to the stationary state ? f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-?). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.
NASA Astrophysics Data System (ADS)
Babin, A. V.
1985-02-01
The steady-state equation Au_0=f, the parabolic Cauchy problem u_1'(t)=Au_1(t), u_1(0)=f, and the hyperbolic problem u_2''(t)=Au_2(t), u_2(0)=f, u_2'(0)=0, are considered, where A is a matrix-valued positive selfadjoint second-order partial differential operator with analytic coefficients, and f is an analytic function. Methods in the theory of weighted approximation of functions by polynomials on the line are used to construct polynomial representations of solutions of these problems of the form u_i=\\lim_{n\\to\\infty}P_n^i(A)f, where the polynomials P_n^i(\\lambda), i=0,\\,1,\\,2, are constructed in explicit form. Estimates of the rate of convergence are given. With the help of these estimates and Bernstein's inverse theorems in approximation theory, theorems are obtained on the smoothness and analyticity of solutions of degenerate systems whose coefficients are trigonometric polynomials.Bibliography: 9 titles.
The Non-Perturbative Analytical Equation of State for SU(3) Gauge Theory
V. Gogokhia; M. Vasúth
2014-04-17
The effective potential approach for composite operators is generalized to non-zero temperature in order to derive the non-perturbative analytical equation of state for pure SU(3) Yang-Mills fields valid in the whole temperature range. Adjusting our parametrization of the gluon plasma pressure to the lattice pressure at high temperature for SU(3) Yang-Mills case, we have reproduced well our analytical curves and numbers not only for the pressure but for all other independent thermodynamic quantities as well in the whole temperature range $[0, \\infty)$. We explicitly show that the pressure is a continuous function of the temperature across a phase transition at $T_c = 266.5 \\MeV$. The entropy and energy densities have finite jump discontinuities at $T_c$ with latent heat $\\epsilon_{LH}= 1.414$. This is a firm evidence of the first-order phase transition in SU(3) pure gluon plasma. The heat capacity has a $\\delta$-type singularity (an essential discontinuity) at $T_c$, so that the velocity of sound squared becomes zero at this point. All the independent thermodynamic quantities are exponentially suppressed below $T_c$ and rather slowly approach their respective Stefan-Boltzmann limits at high temperatures. Those thermodynamic quantities which are the ratios of their independent counterparts such as conformity, conformality and the velocity of sound squared approach their Stefan-Boltzmann limit at high temperatures rather rapidly and demonstrate the non-trivial dependence on the temperature below $T_c$. We predict the existence of the three massive and the two massless excitations, all of non-perturbative dynamical origin. One of the massive excitations has an effective mass $1.17 \\GeV$ and the two others have the same effective mass $0.585 \\GeV$, but are propagating in different ways.
Alexander G. Kyriakos
2004-07-09
In the present paper it is shown that the Yang-Mills equation can be represented as the equation of the non-linear electromagnetic waves superposition. The research of the topological characteristics of this representation allows us to discuss a number of the important questions of the quantum chromodynamics.
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
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
Interpretation of surface diffusion data with Langevin simulations: a quantitative assessment
NASA Astrophysics Data System (ADS)
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.
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
Ross, Joseph
Physics 489 Solid State Superconductivity notes Nov. 20, 2014 1. London equation, London penetration depth: The London theory was obtained by making simple assumptions about the behavior through it. The brothers Fritz and Heinz London noted that setting the parenthetical expression to zero
NASA Astrophysics Data System (ADS)
Nadtochy, P. N.; Ryabov, E. G.; Adeev, G. D.
2015-04-01
A four-dimensional dynamical model based on Langevin equations was applied to calculate a wide set of experimental observables for heavy fissioning compound nuclei. Three collective shape coordinates plus the tilting coordinate were considered dynamically from the ground state deformation to the scission into fission fragments. A modified one-body mechanism for nuclear dissipation with a reduction coefficient ks of the contribution from a ‘wall’ formula was used for shapes parameters. Different possibilities of deformation-dependent dissipation coefficient for the tilting coordinate ({{? }K}) were investigated. Presented results demonstrate that the influence of the ks and ?K parameters on the calculated quantities can be selectively probed. The nuclear viscosity with respect to the nuclear shape parameters influences the \\lt {{n}pre}\\gt , the fission fragment mass–energy distribution parameters, and the angular distribution of fission fragments. At the same time the viscosity coefficient ?K affects the angular distribution of fission fragments only. The independence of anisotropy on the fission fragment mass is found at both Langevin calculations performed with deformation-dependent and constant ?K coefficients.
Kawamura, Hiroyuki [Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX (United Kingdom); Tanaka, Kazuhiro [Department of Physics, Juntendo University, Inba-gun, Chiba 270-1695 (Japan)
2010-06-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.
Alexander D. Dymnikov
2012-11-19
During the last century the tensor theory of the gravitational field was developed. We propose and develop the novel, pure mathematical, matrix theory of the field in n-dimensional metric space. The definition of the mathematical field matrix and the equations of motion of the mathematical point are given. The interpretation of the nature of the mathematical field and the mathematical points can be different and depends on our knowledge of the nature. It is shown that the equations of motion are different for symmetric and antisymmetric field matrices. In the matrix field theory the equations of the field are rigorously derived. This theory reveals that in the 4-dimensional metric space the field matrix is the electromagnetic-gravitational field matrix, where the antisymmetric part is the matrix of electromagnetic field and the symmetric part is the gravitational field matrix. The partial cases of this matrix are electric-gravitational, magnetic-gravitational and gravitational field matrices. It is shown that the elements of all obtained matrices are the Christoffel symbols of the first and the second order or their derivatives.
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
Constant pressure and temperature discrete-time Langevin molecular dynamics
Niels Grønbech-Jensen; Oded Farago
2014-11-13
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 build 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 & Dunweg, 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.
Wu, Rengmao; Zhang, Yaqin; Sulman, Mohamed M; Zheng, Zhenrong; Benítez, Pablo; Miñano, Juan C
2014-06-30
The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L(2)-Kantorovich (LMK) theory. An efficient approach is proposed to find the optimal mapping of the LMK problem. The characteristics of the new approach are introduced and the limitations of the LMK theory in illumination design are presented. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design. PMID:24977868
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 mm?s(-1), and 5.6%, respectively. PMID:24985842
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.
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.
Wang, Xiao; Weinberg, Seth H; Hao, Yan; Sobie, Eric A; Smith, Gregory D
2015-03-01
Population density approaches to modeling local control of Ca(2+)-induced Ca(2+) release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca(2+) signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca(2+) release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca(2+) concentration ([Ca(2+)]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker-Planck equation, yielding an extremely compact and efficient local/global whole cell model that reproduces and helps interpret recent experiments that investigate Ca(2+) homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca(2+)] promotes elevated network sarcoplasmic reticulum (SR) [Ca(2+)] via SR Ca(2+)-ATPase-mediated Ca(2+) uptake. However, elevated myoplasmic [Ca(2+)] may also activate RyRs and promote stochastic SR Ca(2+) release, which can in turn decrease SR [Ca(2+)]. Increasing myoplasmic [Ca(2+)] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca(2+)] depending on whether myoplasmic [Ca(2+)] is low or high. In the later case, spontaneous release decreases SR [Ca(2+)] in a manner that maintains robust Ca(2+) sparks. PMID:25485896
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
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.
Alexander G. Kyriakos
2005-03-09
In previous paper we have shown that there is a special kind of nonlinear electrodynamics - Curvilinear Wave Electrodynamics (CWED), whose equations are mathematically equivalent to the equations of quantum electrodynamics. The purpose of the present paper is to show that in framework of CWED the known solutions of the nonlinear electromagnetic equations can be considered as the approximate solutions of the nonlinear equation of CWED. Another purpose of this paper is to show, that these solutions allow the description of electron-like particle of CWED as point of non-point particles, depending on mathematical approach.
High nonlinearities in Langevin transducer: a comprehensive model.
Guyomar, D; Ducharne, B; Sebald, G
2011-12-01
The design and simulation of power transducers are difficult since piezoelectric, dielectric and elastic properties of ferroelectric materials differ from linear behavior when driven at large levels. This paper is devoted to modeling of a resonant power transducer at a high level of dynamic mechanical stress. The power transducer is subjected to a sine electrical field E of varying frequency which was considered as the excitation of the transducer. The mechanical equation of the piezoelectric element is written using electrostriction. The dielectric part is written as a nonlinear function of an equivalent electric field including stress influence (scaling relationship between electric field and mechanical stress). Using various simulations, we show then that typical resonance nonlinearities are obtained, such as jump phenomenon of transducer speed amplitude and phase, resonance peak that become asymmetric, and diminution of mechanical quality factor. As a consequence, we state that those typical nonlinearities are only due to dielectric nonlinearities, in good correlation with typical ferroelectric behavior. Moreover, this demonstrates the usefulness of scaling relationships in ferroelectrics, which explain static depoling under stress and butterfly strain hysteresis loop. The same scaling law gives here several nonlinearities for resonant transducers as well. PMID:21724220
Robust and efficient configurational molecular sampling via Langevin dynamics.
Leimkuhler, Benedict; Matthews, Charles
2013-05-01
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian motions in some combination. The Baker-Campbell-Hausdorff expansion is used to study sampling accuracy following recent work by the authors, which allows determination of the stepsize-dependent bias in configurational averaging. For harmonic oscillators, configurational averaging is exact for certain schemes, which may result in improved performance in the modelling of biomolecules where bond stretches play a prominent role. For general systems, an optimal method can be identified that has very low bias compared to alternatives. In simulations of the alanine dipeptide reported here (both solvated and unsolvated), higher accuracy is obtained without loss of computational efficiency, while allowing large timestep, and with no impairment of the conformational exploration rate (the effective diffusion rate observed in simulation). The optimal scheme is a uniformly better performing algorithm for molecular sampling, with overall efficiency improvements of 25% or more in practical timestep size achievable in vacuum, and with reductions in the error of configurational averages of a factor of ten or more attainable in solvated simulations at large timestep. PMID:23656109
NASA Astrophysics Data System (ADS)
Ellis, George F. R.
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
Microscopic theories of the structure and glassy dynamics of ultra-dense hard sphere fluids
NASA Astrophysics Data System (ADS)
Jadrich, Ryan; Schweizer, Kenneth
2013-03-01
We construct a new thermodynamically self-consistent integral equation theory (IET) for the equilibrium metastable fluid structure of monodisperse hard spheres that incorporates key features of the jamming transition. A two Yukawa generalized mean spherical IET closure for the direct correlation function tail is employed to model the distinctive short and long range contributions for highly compressed fluids. The exact behavior of the contact value of the radial distribution function (RDF) and isothermal compressibility are enforced, as well as an approximate theory for the RDF contact derivative. Comparison of the theoretical results for the real and Fourier space structure with nonequilibrium jammed simulations reveals many similarities, but also differences as expected. The new structural theory is used as input into the nonlinear Langevin equation (NLE) theory of activated single particle dynamics to study the alpha relaxation time, and good agreement with recent experiments and simulations is found. We demonstrate it is crucial to accurately describe the very high wave vector Fourier space to reliably extract the dynamical predictions of NLE theory, and structural precursors of jamming play an important role in determining entropic barriers.
The lattice gluon propagator in stochastic perturbation theory
E. -M. Ilgenfritz; H. Perlt; A. Schiller
2007-10-02
We calculate loop contributions up to four loops to the Landau gauge gluon propagator in numerical stochastic perturbation theory. For different lattice volumes we carefully extrapolate the Euler time step to zero for the Langevin dynamics derived from the Wilson action. The one-loop result for the gluon propagator is compared to the infinite volume limit of standard lattice perturbation theory.
Non-Gaussian statistics, classical eld theory, and realizable Langevin models John A. Krommes
Navier{Stokes turbulence vanish in the DIA; this led them to argue for the necessity of closures based that of the canon- ical three-dimensional (3D) homogeneous, isotropic, in- compressible Navier{Stokes problem
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.
NSDL National Science Digital Library
2010-01-01
This activity will help the students understand that science theories change in the face of new evidence, but those changes can be slow in coming. Students will observe how scientific theories change over time, Be introduced to the sophistication of the geocentric model and the time it took to change the theory underpinning the heliocentric model, Compare the heliocentric model to the geocentric model.
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
Derivation of Cahn-Hilliard equations from Ginzburg-Landau models
L. Bertini; C. Landim; S. Olla
1997-01-01
The generalized Cahn-Hilliard equation is obtained as the hydrodynamic limit from a stochastic Ginzburg-Landau model. The\\u000a associated large-deviation principle is also proved. In the one-dimensional case, we prove a related result about the scaling\\u000a limit of conservative Langevin dynamics of an SOS surface.
Doktorov, A. B. [Voevodsky Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia and Physics Department Novosibirsk State University, Novosibirsk 630090 (Russian Federation)
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.
Uma, B.; Eckmann, D.M.; Ayyaswamy, P.S.; Radhakrishnan, R.
2012-01-01
A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature. PMID:22865935
L. Duriez; A. Vienne
1991-01-01
A new method to construct an analytical theory of motion of Saturn's satellites is presented. It is an extension of the methods already used by Duriez (1979) and Laskar (1984) to construct a general planetary theory, using the same formalism to deal with the multiple resonances occurring in the saturnian system. The present goal is to obtain accurate representations of
ERIC Educational Resources Information Center
Teo, Timothy; Tan, Lynde
2012-01-01
This study applies the theory of planned behavior (TPB), a theory that is commonly used in commercial settings, to the educational context to explain pre-service teachers' technology acceptance. It is also interested in examining its validity when used for this purpose. It has found evidence that the TPB is a valid model to explain pre-service…
L. I. Petrova
2005-12-21
In the paper it is shown that, even without a knowledge of the concrete form of the equations of mathematical physics and field theories, with the help of skew-symmetric differential forms one can see specific features of the equations of mathematical physics, the relation between mathematical physics and field theory, to understand the mechanism of evolutionary processes that develop in material media and lead to emergency of physical structures forming physical fields. This discloses a physical meaning of such concepts like "conservation laws", "postulates" and "causality" and gives answers to many principal questions of mathematical physics and general field theory. In present paper, beside the exterior forms, the skew-symmetric differential forms, whose basis (in contrast to the exterior forms) are deforming manifolds, are used. Mathematical apparatus of such differential forms(which were named evolutionary ones) includes nontraditional elements like nonidentical relations and degenerate transformations and this enables one to describe discrete transitions, quantum steps, evolutionary processes, and generation of various structures.
Charles R. Tolle; Mark Pengitore
2009-08-01
This paper explores the overlaps between the Control community’s work on System Identification (SysID) and the Physics, Mathematics, Chaos, and Complexity communities’ work on phase-space reconstruction via time-delay embedding. There are numerous overlaps between the goals of each community. Nevertheless, the Controls community can gain new insight as well as some new very powerful tools for SysID from the latest developments within the Physics, Mathematics, Chaos, and Complexity communities. These insights are gained via the work on phase-space reconstruction of non-linear dynamics. New methods for discovering non-linear differential based equations that evolved from embedding operations can shed new light on hybrid-systems theory, Nyquest-Shannon’s Theories, and network based control theory. This paper strives to guide the Controls community towards a closer inspection of the tools and additional insights being developed within the Physics, Mathematics, Chaos, and Complexity communities for discovery of system dynamics, the first step in control system development. The paper introduces the concepts of phase-space reconstruction via time-delay embedding (made famous byWhitney, Takens, and Sauer’s Thoreoms), intergrate-and-fire embedding, and non-linear differential equation discovery based on Perona’s method.
Estimation of in situ hydraulic conductivity function from nonlinear filtering theory
Gabriel G. Katul; Ole Wendroth; Marc B. Parlange; Carlos E. Puente; Marcos V. Folegatti; Donald R. Nielsen
1993-01-01
A method based on an optimal nonlinear filtering technique is proposed and tested for the determination of the hydraulic conductivity function from a field drainage experiment. Simplifications to Richard's equation lead to a Langevin type differential equation to describe the redistribution of stored water as a function of drainage flux excited by a random initial condition and state forcing. The
NASA Astrophysics Data System (ADS)
Lisin, E. A.; Lisina, I. I.; Vaulina, O. S.; Petrov, O. F.
2015-03-01
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.
First results of the (n,?) EXILL campaigns at the Institut Laue Langevin using EXOGAM and FATIMA
NASA Astrophysics Data System (ADS)
Jolie, J.; Régis, J.-M.; Wilmsen, D.; Ahmed, S.; Pfeiffer, M.; Saed-Samii, N.; Warr, N.; Blanc, A.; Jentschel, M.; Köster, U.; Mutti, P.; Soldner, T.; Simpson, G.; de France, G.; Urban, W.; Bruce, A. M.; Roberts, O. J.; Fraile, L. M.; Paziy, V.; Ignatov, A.; Ilieva, S.; Kröll, Th; Scheck, M.; Thürauf, M.; Ivanova, D.; Kisyov, S.; Lalkovski, S.; Podolyak, Zs; Regan, P. H.; Korten, W.; Habs, D.; Thirolf, P. G.; Ur, C. A.
2014-09-01
At the PF1B cold neutron beam line at the Institut Laue Langevin the EXILL array consisting of EXOGAM, GASP and LOHENGRIN detectors was used to perform (n,?) measurements under very high coincidence rates. About ten different reactions were then measured in autumn 2012. In spring 2013 the EXOGAM array was combined with 16 LaBr3(Ce) scintillators in the FATIMA@EXILL campaign for the measurement of lifetimes using the generalised centroid difference method. We report on the properties of both set-ups and present first results on Pt isotopes from both campaigns.
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
A. H. M. Kierkels; J. J. L. Velázquez
2014-10-08
We study the mathematical properties of a kinetic equation which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schr\\"odinger equation. In particular, we give a precise definition of weak solutions and prove global existence of solutions for all initial data with finite mass. We also prove that any nontrivial initial datum yields the instantaneous onset of a condensate, i.e. a Dirac mass at the origin for any positive time. Furthermore we show that the only stationary solutions with finite total measure are Dirac masses at the origin. We finally construct solutions with finite energy, which is transferred to infinity in a self-similar manner.
NASA Astrophysics Data System (ADS)
Kierkels, A. H. M.; Velázquez, J. J. L.
2015-01-01
We study the mathematical properties of a kinetic equation, derived in Escobedo and Velázquez (arXiv:1305.5746v1 [math-ph]), which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schrödinger equation. In particular, we give a precise definition of weak solutions and prove global existence of solutions for all initial data with finite mass. We also prove that any nontrivial initial datum yields the instantaneous onset of a condensate, by which we mean that for any nontrivial solution the mass of the origin is strictly positive for any positive time. Furthermore we show that the only stationary solutions with finite total measure are Dirac masses at the origin. We finally construct solutions with finite energy, where the energy is transferred to infinity in a self-similar manner.
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.
K. Iida; K. Oyamatsu; B. Abu-Ibrahim; A. Kohama
2011-07-05
We calculate the proton-nucleus total reaction cross sections at different energies of incident protons within the optical limit approximation of the Glauber theory. The isospin effect has been taken into account. The nucleon distribution is obtained in the framework of macroscopic nuclear models in a way depending on the equation of state of uniform nuclear matter near the saturation density. We find that at an energy of order 40 MeV, the reaction cross section calculated for neutron- rich isotopes significantly increases as the parameter L characterizing the density dependence of the symmetry energy increases, while at energies of order 300 and 800 MeV, it is almost independent of L. This is a feature of the optical limit Glauber theory in which an exponential dependence of the reaction cross section on the neutron skin thickness remains when the total proton-neutron cross section is small enough.
Theoretical and Numerical Studies of the Shell Equations of Bauer, Reiss and Keller, Part I nonlinear twoÂpoint boundary value problem suggested by Bauer et al. (1970). This problem describes compressive load. In the sequel we refer to â?? as the load. The above BVP was at first treated by Bauer, Reiss
H. Kleinert
2012-10-09
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal L\\'evy walks rather than Gaussian random walks with perturbations.
Nishimura, Takuma; Hosaka, Hiroshi; Morita, Takeshi
2012-01-01
The Smooth Impact Drive Mechanism (SIDM) is a linear piezoelectric actuator that has seen practically applied to camera lens modules. Although previous SIDM actuators are easily miniaturized and enable accurate positioning, these actuators cannot actuate at high speed and cannot provide powerful driving because they are driven at an off-resonant frequency using a soft-type PZT. In the present study, we propose a resonant-type SIDM using a bolt-clamped Langevin transducer (BLT) with a hard-type PZT. The resonant-type SIDM overcomes the above-mentioned problems and high-power operation becomes possible with a very simple structure. As a result, we confirmed the operation of resonant-type SIDM by designing a bolt-clamped Langevin transducer. The properties of no-load maximum speed was 0.28m/s at driving voltages of 80V(p-p) for 44.9kHz and 48V(p-p) for 22.45kHz with a pre-load of 3.1N. PMID:21784499
Thermal equilibrium properties of surface hopping with an implicit Langevin bath
NASA Astrophysics Data System (ADS)
Sherman, M. C.; Corcelli, S. A.
2015-01-01
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.
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. PMID:25591341
Ooi, C. H. Raymond [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse, D-85748, Garching (Germany); Applied Physics and Materials Science Group, Eng. Quad., Princeton University, New Jersey 08544 (United States); Institute for Quantum Studies and Department of Physics, Texas A and M University, Texas 77843-4242 (United States); Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701 (Korea, Republic of); Department of Physics, Korea University, Anam-dong, Seongbuk-gu, Seoul, 136-713 (Korea, Republic of); Scully, Marlan O. [Max-Planck-Institut fuer Quantenoptik, Hans-Kopfermann-Strasse, D-85748, Garching (Germany); Applied Physics and Materials Science Group, Eng. Quad., Princeton University, New Jersey 08544 (United States); Institute for Quantum Studies and Department of Physics, Texas A and M University, Texas 77843-4242 (United States)
2007-10-15
We study several aspects of two-photon correlation of an optically driven extended medium (amplifier) with parametric down-conversion (PDC) scheme and three-level cascade scheme. The correlation for the PDC scheme is modeled by coupled parametric equations with constant self-coupling and cross coupling coefficients. This provides simple physical insights to how the correlation profile depends on the sign and magnitude of the coefficients in the presence of propagation group delay between signal and idler photons. The results with constant coefficients are related to the results of the driven three-level cascade scheme obtained from quantum Langevin-Maxwell's equations. The correlation transforms from bunching to antibunching as the pump field increases. Cauchy-Schwartz inequality is violated for all time delay in the case of off-resonant pump, showing nonclassical correlation. We verify that the correlation obtained without noise operators is qualitatively correct regardless of the optical density, especially for large detuning. We also discuss the interesting physics behind antibunching and oscillations found in the reverse correlation.
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.
Feng, Xiaobing
2011-01-01
The vanishing moment method was introduced by the authors in [37] as a reliable methodology for computing viscosity solutions of fully nonlinear second order partial differential equations (PDEs), in particular, using Galerkin-type numerical methods such as finite element methods, spectral methods, and discontinuous Galerkin methods, a task which has not been practicable in the past. The crux of the vanishing moment method is the simple idea of approximating a fully nonlinear second order PDE by a family (parametrized by a small parameter $\\vepsi$) of quasilinear higher order (in particular, fourth order) PDEs. The primary objectives of this book are to present a detailed convergent analysis for the method in the radial symmetric case and to carry out a comprehensive finite element numerical analysis for the vanishing moment equations (i.e., the regularized fourth order PDEs). Abstract methodological and convergence analysis frameworks of conforming finite element methods and mixed finite element methods are ...
V. K. Chandrasekar; M. Senthilvelan; M. Lakshmanan
2006-01-01
In this letter, we introduce a new generalized linearizing transformation (GLT) for second-order nonlinear ordinary differential equations (SNODEs). The well-known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to
Jean-Michel Caillol
2004-01-01
We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard–Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger–Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field,
Yuki IKEYA; H. Kuramae; H. Morimoto; Hidetoshi SAKAMOTO; Tsutao KATAYAMA; Eiji NAKAMACHI
2010-01-01
In this study, we try to reveal the relationship between the plastic deformation and the microscopic crystallographic misorientation evolution by using our multi-scale finite element (FE) code by using a crystallographic misorientation theory. We employed two-scale structure, such as a microscopic polycrystal structure and a macroscopic elastic plastic continuum. Our analysis code predicts the deformation behavior of polycrystal metal in
Pieper
1989-01-01
This is the third volume of a series of reports containing the proceedings of the Focused Research Program on ''Spectral Theory and Boundary Value Problems,'' which was held at Argonne National Laboratory during the period 1986-1987. The program was organized by the Mathematics and Computer Science (MCS) Division as part of its activities in applied analysis. The objective of the
H. G. Kaper; Man Kam Kwong; A. Zettl
1988-01-01
This is the second volume of a series of reports containing the proceedings of the Focused Research Program on ''Spectral Theory and Boundary Value Problems,'' which was held at Argonne National Laboratory during the period 1986-1987. The program was organized by the Mathematics and Computer Science (MCS) Division as part of its activities in applied analysis. The objective of the
Existence Theorems for Some Quadratic Integral Equations
Józef Bana?; Millenia Lecko; Wagdy Gomaa El-Sayed
1998-01-01
Using the theory of measures of noncompactness, we prove a few existence theorems for some quadratic integral equations. The class of quadratic integral equations considered below contains as a special case numerous integral equations encountered in the theories of radiative transfer and neutron transport, and in the kinetic theory of gases. In particular, the well-known Chandrasekhar integral equation also belongs
Dahms, Rainer N
2015-05-01
The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. The new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces. PMID:25596368
Fluctuations destroying long-range order in SU(2) Yang-Mills theory
Koma, Tohru [Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171-8588 (Japan)
2010-08-01
We study lattice SU(2) Yang-Mills theory with dimension d{>=}4. The model can be expressed as a (d-1)-dimensional O(4) nonlinear {sigma} model in a d-dimensional heat bath. As is well known, the nonlinear {sigma} model alone shows a phase transition. If the quark confinement is a consequence of the absence of a phase transition for the Yang-Mills theory, then the fluctuations of the heat bath must destroy the long-range order of the nonlinear {sigma} model. In order to clarify whether this is true, we replace the fluctuations of the heat bath with Gaussian random variables, and obtain a Langevin equation which yields the effective action of the nonlinear {sigma} model by analyzing the Fokker-Planck equation. It turns out that the fluctuations indeed destroy the long-range order of the nonlinear {sigma} model within a mean-field approximation estimating a critical point, whereas for the corresponding U(1) gauge theory, the phase transition to the massless phase remains against the fluctuations.
Cheol-Ho Yun; Takaaki Ishii; Kentaro Nakamura; Sadayuki Ueha; Koji Akashi
2001-01-01
A hybrid transducer type ultrasonic linear motor using the 1st longitudinal and the 2nd bending vibration modes of a bolt-clamped Langevin type transducer has been proposed and studied for accomplishing high mechanical output. The longitudinal vibration generates the mechanical driving force and the bending vibration controls the frictional force. To obtain large vibration amplitude and large mechanical output, a method
Burgers' Equation Burgers' equation
Gardner, Carl
Burgers' Equation Burgers' equation ut + uux = uxx is the simplest PDE that models the more complicated Navier-Stokes equa- tions (viscous fluid dynamics, boundary layers, etc.). The inviscid Burgers of ideal gas dynamics (shock and rarefaction waves). The inviscid Burgers' equation ut + uux = 0
Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter
2003-03-01
In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545-548; Fluct. Noise Lett. 1, L181 (2001)]. PMID:12689134
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.
Wu Shuangqing
2009-01-01
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
Frederic Boyer; Mathieu Porez; Alban Leroyer
2010-01-01
In this article, we describe a dynamic model of the three-dimensional eel swimming. This model is analytical and suited to\\u000a the online control of eel-like robots. The proposed solution is based on the Large Amplitude Elongated Body Theory of Lighthill\\u000a and a framework recently presented in Boyer et al. (IEEE Trans. Robot. 22:763–775, 2006) for the dynamic modeling of hyper-redundant
Heller, Barbara
Math 512 Â Partial Differential Equations Course Description from Bulletin: Basic model equations function, and eigenfunction expansions; elementary theory of partial differential equations; Sobolev spaces; linear elliptic equations; energy methods; semigroup methods; applications to partial differential
Manson, Anthony C; Coalson, Rob D
2012-10-11
Langevin dynamics is used to compute the time evolution of the nonequilibrium motion of the atomic coordinates of a protein in response to ligand dissociation. The protein potential energy surface (PES) is approximated by a harmonic basin about the minimum of the unliganded state. Upon ligand dissociation, the protein undergoes relaxation from the bound to the unbound state. A coarse graining scheme based on rotation translation blocks (RTB) is applied to the relaxation of the two domain iron transport protein, ferric binding protein. This scheme provides a natural and efficient way to freeze out the small amplitude, high frequency motions within each rigid fragment, thereby allowing for the number of dynamical degrees of freedom to be reduced. The results obtained from all flexible atom (constraint free) dynamics are compared to those obtained using RTB-Langevin dynamics. To assess the impact of the assumed rigid fragment clustering on the temporal relaxation dynamics of the protein molecule, three distinct rigid block decompositions were generated and their responses compared. Each of the decompositions was a variant of the one-block-per-residue grouping, with their force and friction matrices being derived from their fully flexible counterpart. Monitoring the time evolution of the distance separating a selected pair of amino acids, the response curves of the blocked decompositions were similar in shape to each other and to the control system in which all atomic degrees of freedom are fully independent. The similar shape of the blocked responses showed that the variations in grouping had only a minor impact on the kinematics. Compared with the all atom responses, however, the blocked responses were faster as a result of the instantaneous transmission of force throughout each rigid block. This occurred because rigid blocking does not permit any intrablock deformation that could store or divert energy. It was found, however, that this accelerated response could be successfully corrected by scaling each eigenvalue in the appropriate propagation matrix by the least-squares fitted slope of the blocked vs nonblocked eigenvalue spectra. The RTB responses for each test system were dominated by small eigenvalue overdamped Langevin modes. The large eigenvalue members of each response dissipated within the first 5 ps, after which the long time response was dominated by a modest set of low energy, overdamped normal modes, that were characterized by highly cooperative, functionally relevant displacements. The response assuming that the system is in the overdamped limit was compared to the full phase space Langevin dynamics results. The responses after the first 5 ps were nearly identical, confirming that the inertial components were significant only in the initial stages of the relaxation. Since the propagator matrix in the overdamped formulation is real-symmetric and does not require the inertial component in the propagator, the computation time and memory footprint was reduced by 1 order of magnitude. PMID:22924611
A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II
Uchida, Waka; Kimura, Yoshiro; Wakabayashi, Masamitsu [Department of Biomolecular Engineering, Tokyo Institute of Technology, Nagatsuta, Midori-ku, Yokohama 226-8503 (Japan); Hatakeyama, Makoto; Ogata, Koji; Nakamura, Shinichiro [RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan); Yokojima, Satoshi [Tokyo University of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo 192-0392, Japan and RIKEN Research Cluster for Innovation, Nakamura Laboratory, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
2013-12-10
We have performed three QM/Langevin-MD simulations for oxygen-evolving complex (OEC) and surrounding residues, which are different configurations of the oxidation numbers on Mn atoms in the Mn{sub 4}O{sub 5}Ca cluster. By analyzing these trajectories, we have observed sensitivity of the change to the configuration of Mn oxidation state on O atoms of carboxyl on three amino acids, Glu354, Ala344, and Glu333. The distances from Mn to O atoms in residues contacting with the Mn{sub 4}O{sub 5}Ca cluster were analyzed for the three trajectories. We found the good correlation of the distances among the simulations. However, the distances with Glu354, Ala344, and Glu333 have not shown the correlation. These residues can be sensitive index of the changes of Mn oxidation numbers.
Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review
Paquet, Eric; Viktor, Herna L.
2015-01-01
Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods. PMID:25785262
Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA
Francisco de los Santos; Omar Al Hammal; Miguel Angel Munoz
2008-04-07
A simple Langevin approach is used to study stationary properties of the Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered in an easy way. Results are shown for the denaturation transition in homogeneous samples, for which some implications, so far overlooked, of an analogy with equilibrium wetting transitions are highlighted. This analogy implies that the order-parameter, asymptotically, exhibits a second order transition even if it may be very abrupt for non-zero values of the stiffness parameter. Not surprisingly, we also find that for heterogeneous DNA, within this model the largest bubbles in the pre-melting stage appear in adenine-thymine rich regions, while we suggest the possibility of some sort of not strictly local effects owing to the merging of bubbles.
Langevin dynamics simulation of 3D colloidal crystal vacancies and phase transitions.
Laghaei, Rozita; Asher, Sanford A; Coalson, Rob D
2013-05-01
We study the mechanism of vacancy migration and phase transitions of 3D crystalline colloidal arrays (CCA) using Langevin dynamics simulations. We calculate the self-diffusion coefficient of the colloid particles and the diffusion constant for vacancies as a function of temperature and DLVO potential parameters. We investigate the phase behavior of several systems with different interaction potential parameters using Voronoi analysis. Voronoi polyhedra tessellation, which is a useful method for characterizing the nearest neighbor environment around each atom, provides an efficient and effective way to identify phase transitions as well as geometrical changes in crystals. Using Voronoi analysis, we show that several neighboring particles are involved in the vacancy migration process that causes the vacancy to diffuse. PMID:23477620
Advantage of suppressed non-Langevin recombination in low mobility organic solar cells
Stolterfoht, Martin; Armin, Ardalan; Pandey, Ajay K.; Burn, Paul L.; Meredith, Paul; Pivrikas, Almantas, E-mail: almantas.pivrikas@uq.edu.au [Centre for Organic Photonics and Electronics (COPE), School of Chemistry and Molecular Biosciences and School of Mathematics and Physics, The University of Queensland, Brisbane 4072 (Australia); Philippa, Bronson; White, Ronald D. [School of Engineering and Physical Sciences, James Cook University, Townsville 4811 (Australia)
2014-07-07
Photovoltaic performance in relation to charge transport is studied in efficient (7.6%) organic solar cells (PTB7:PC{sub 71}BM). Both electron and hole mobilities are experimentally measured in efficient solar cells using the resistance dependent photovoltage technique, while the inapplicability of classical techniques, such as space charge limited current and photogenerated charge extraction by linearly increasing voltage is discussed. Limits in the short-circuit current originate from optical losses, while charge transport is shown not to be a limiting process. Efficient charge extraction without recombination can be achieved with a mobility of charge carriers much lower than previously expected. The presence of dispersive transport with strongly distributed mobilities in high efficiency solar cells is demonstrated. Reduced non-Langevin recombination is shown to be beneficial for solar cells with imbalanced, low, and dispersive electron and hole mobilities.
NONE
1998-11-01
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.
NASA Astrophysics Data System (ADS)
Crawford, T. Daniel; Sekino, Hideo
The modified equation-of-motion coupled cluster approach of Sekino and Bartlett is extended to computations of the mixed electric-dipole/magnetic-dipole polarizability tensor associated with optical rotation in chiral systems. The approach - referred to here as a linearized equation-of-motion coupled cluster (EOM-CCL) method - is a compromise between the standard EOM method and its linear response counterpart, which avoids the evaluation of computationally expensive terms that are quadratic in the field-perturbed wave functions, but still yields properties that are size-extensive/intensive. Benchmark computations on five representative chiral molecules, including (P)-hydrogen peroxide, (S)-methyloxirane, (S)-2-chloropropionitrile, (R)-epichlorohydrin, and (1S,4S)-norbornenone, demonstrate typically small deviations between the EOM-CCL results and those from coupled cluster linear response theory, and no variation in the signs of the predicted rotations. In addition, the EOM-CCL approach is found to reduce the overall computing time for multi-wavelength-specific rotation computations by up to 34%.
Curro, John G.; Frischknecht, Amalie Lucile (University of New Mexico in Albuquerque, NM.)
2005-01-01
Polymer reference interaction site model (PRISM) calculations and molecular dynamics (MD) simulations were carried out on poly(ethylene oxide) liquids using a force field of Smith, Jaffe, and Yoon. The intermolecular pair correlation functions and radius of gyration from theory were in very good agreement with MD simulations when the partial charges were turned off. When the charges were turned on, considerably more structure was seen in the intermolecular correlations obtained from MD simulation. Moreover, the radius of gyration increased by 38% due to electrostatic repulsions along the chain backbone. Because the partial charges greatly affect the structure, significant differences were seen between the PRISM calculations (without charges) and the wide angle neutron scattering measurements of Annis and coworkers for the total structure factor, and the hydrogen/hydrogen intermolecular correlation function. This is in contrast to previous PRISM calculations on poly (dimethyl siloxane).
Neutral Equations of Mixed Type
Lamb, Charles
2012-12-31
In this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. ...
Gallas, Jason
Pedro G. Lind,1,2 Alejandro Mora,3 Jason A. C. Gallas,1,4 and Maria Haase3 1 Institute for Computational Physics, Universität Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany 2 Centro de Física Teórica Höchsleistungsrechnen, Universität Stuttgart, Nobelstr. 19, D-70569 Stuttgart, Germany 4 Instituto de Física
Gutowitz, H.A.
1988-11-18
This is the second of two lectures. In the first lecture the map from a cellular automaton to a sequence of analytical approximations called the local structure theory was described. In this lecture the inverse map from approximation to the class of cellular automata approximated is constructed. The key matter is formatting the local structure theory equations in terms of block probability estimates weighted by coefficients. The inverse mapping relies on this format. Each possible assignment of values to the coefficients defines a class of automata with related statistical properties. It is suggested that these coefficients serve to smoothly parameterize the space of cellular automata. By varying the values of the parameters a cellular automaton network may be designed so that it has a specified invariant measure. If an invariant measure is considered a ''memory'' of the network, then this variation of parameters to specify the invariant measure must be considered ''learning.'' It is important to note that in this view learning is not the storage of patterns in a network, but rather the tailoring of the dynamics of a network. 7 figs.
NASA Astrophysics Data System (ADS)
Amos, Michael D.; Jackson, George
1992-03-01
The bonded hard-sphere (BHS) approach originally developed for diatomic and triatomic molecules is generalized to hard-sphere polyatomic models which are formed by bonding together their constituent hard spheres. The thermodynamic properties of the polyatomic fluid are obtained from the known properties of a corresponding multicomponent mixture of different sized hard spheres with bonding sites. In the limit of complete bonding, hard-sphere polyatomic molecules are formed. As well as the general expressions for polyatomic molecules and their mixtures, the equation of state of hard-sphere chain molecules, which are simple models of homologous series such as the alkanes, perfluoroalkanes, etc., is presented. More specifically, the chain molecules are formed from two different types of hard spheres 1 and 2. Spheres of type 1 make up the backbone of the chain and, in this case, would represent the carbon atoms; spheres of type 2 represent the substituents, i.e., the hydrogen or fluorine atoms. Although the BHS theory is only strictly valid for molecules of tangent spheres, the theory can also be applied to fused hard-sphere (FHS) molecules with overlapping spheres. The latter are more realistic models of actual molecules. In the spirit of the semiempirical scaled particle theories (SPT), the properties of the FHS molecule can be related to those of an equivalent BHS molecule of tangent spheres with the same parameter of nonsphericity, ?. When dealing with large polyatomic molecules, ? does not need to be calculated numerically as is the case with the usual SPT approach. As an approximation one may use the analytical values of ? for the diatomic segments making up the molecule. This simple approach turns out to be quite successful. The BHS equation of state has been compared with ``exact'' computer simulation data for homonuclear and heteronuclear FHS systems of diatomics, linear and nonlinear triatomics, and tetrahedral pentatomics, as well as mixtures of FHS molecules. Good agreement is found for all of these systems. In general, the BHS approach is more rigorous and easier to extend to larger polyatomic molecules and their mixtures than SPT.
Nonsymmetric Gravitational Theory
J. W. Moffat
1994-11-10
A new version of nonsymmetric gravitational theory is presented. The field equations are expanded about the Minkowski metric, giving in lowest order the linear Einstein field equations and massive Proca field equations for the antisymmetric field $g_{[\\mu\
Equations For Rotary Transformers
NASA Technical Reports Server (NTRS)
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Wu, Wei [Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States); Wang, Jin, E-mail: jin.wang.1@stonybrook.edu [Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794 (United States); State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun (China)
2014-09-14
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
NASA Astrophysics Data System (ADS)
Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter
2003-03-01
In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545 548; Fluct. Noise Lett. 1, L181 (2001)].
Exponential differential equations Some applications and motivation
Kirby, Jonathan
Exponential differential equations The theory Some applications and motivation Exponential Differential Equations of Semiabelian Varieties Jonathan Kirby University of Oxford and University of Illinois at Chicago Differential Fields meeting Leeds, 9th June 2007 Jonathan Kirby Exponential Differential Equations
Differential Equations Textbook
NSDL National Science Digital Library
William F. Trench
2014-04-04
This is a free textbook which covers material for an introductory course on differential equations with some partial differential equations material, though it assumes knowledge of matrix theory. It includes a section on computing Fourier series of polynomials. It also includes a link to the freely available student solutions manual.
MATH 411 SPRING 2001 Ordinary Differential Equations
Alekseenko, Alexander
MATH 411 SPRING 2001 Ordinary Differential Equations Schedule # 749025 TR 01:00-02:15 316 Boucke will be an introduction to ordinary differential equations. During the classes basic concepts of theory theory and implementations of ordinary differential equations. Text. Ray Redhefer Differential equations
Excitability in a stochastic differential equation model for calcium puffs
NASA Astrophysics Data System (ADS)
Rüdiger, S.
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
Langevin dynamics simulations of a two-dimensional colloidal crystal under confinement and shear
NASA Astrophysics Data System (ADS)
Wilms, D.; Virnau, P.; Sengupta, S.; Binder, K.
2012-06-01
Langevin dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal (with implicit solvent) confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing an incommensurability between the periodicity of the confined crystal and the walls, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible anymore. Instead, similar structures like in the case without mismatch result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.
Modelling Protein-induced Membrane Deformation using Monte Carlo and Langevin Dynamics Simulations
NASA Astrophysics Data System (ADS)
Radhakrishnan, R.; Agrawal, N.; Ramakrishnan, N.; Kumar, P. B. Sunil; Liu, J.
2010-11-01
In eukaryotic cells, internalization of extracellular cargo via the cellular process of endocytosis is orchestrated by a variety of proteins, many of which are implicated in membrane deformation/bending. We model the energetics of deformations membranes by using the Helfrich Hamiltonian using two different formalisms: (i) Cartesian or Monge Gauge using Langevin dynamics; (ii) Curvilinear coordinate system using Monte Carlo (MC). Monge gauge approach which has been extensively studied is limited to small deformations of the membrane and cannot describe extreme deformations. Curvilinear coordinate approach can handle large deformation limits as well as finite-temperature membrane fluctuations; here we employ an unstructured triangular mesh to compute the local curvature tensor, and we evolve the membrane surface using a MC method. In our application, we compare the two approaches (i and ii above) to study how the spatial assembly of curvature inducing proteins leads to vesicle budding from a planar membrane. We also quantify how the curvature field of the membrane impacts the spatial segregation of proteins.
Critical fluctuations and anomalous transport in soft Yukawa-Langevin systems
S. Ratynskaia; G. Regnoli; K. Rypdal; B. Klumov; G. Morfill
2009-07-06
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. It has been suggested that these anomalies derive from particular non-equilibrium physics, but our model does not contain such physics: 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 $\\tau^{1/2}$ approaches the mean inter-grain distance $\\Delta$. Others are development of humps in the distributions on multiples of $\\Delta$, anomalous Hurst exponents, and transitions from leptokurtic towards Gaussian displacement distributions on time scales $\\tau>\\tau_{\\Delta}$. 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.
A travelling wave rotary motor driven by three pairs of Langevin transducers.
Iula, Antonio; Bollino, Giulio
2012-01-01
In this work, numerical simulations and experimental measurements carried out on a high-power ultrasonic motor are presented. The proposed motor is composed of an annular shaped stator and two cone-shaped rotors. The rotors are pressed into contact with the edges of the inner surface of the stator by means of a pre-stress system. A traveling rotating wave is generated in the stator by three pairs of Langevin transducers suitably shifted both in space and time. Each transducer is designed to excite radial nonaxisymmetric modes in the ring. The motor has been effectively clamped to the housing by using two flanges passing through the middle plane of 2 transducers. Finite element analysis was employed to evaluate two different configurations of the motor, both using 6 driving transducers, and to analyze the effect of the flange on the design and on the performance of the transducer. Experimental measurements carried out on a manufactured prototype show that the proposed motor exhibits greatly improved performance in terms of output torque and mechanical power compared with similar previous prototypes which use fewer driving transducers and a different clamping system. The motor weighed 0.67 kg, and had a working frequency of 23.6 kHz, maximum rotational speed of 116 rpm, and static torque of 0.94 Nm. PMID:22293742
Langevin Dynamics simulations of a 2-dimensional colloidal crystal under confinement and shear
D. Wilms; P. Virnau; S. Sengupta; K. Binder
2012-03-16
Langevin Dynamics simulations are used to study the effect of shear on a two-dimensional colloidal crystal confined by structured parallel walls. When walls are sheared very slowly, only two or three crystalline layers next to the walls move along with them, while the inner layers of the crystal are only slightly tilted. At higher shear velocities, this inner part of the crystal breaks into several pieces with different orientations. The velocity profile across the slit is reminiscent of shear-banding in flowing soft materials, where liquid and solid regions coexist; the difference, however, is that in the latter case the solid regions are glassy while here they are crystalline. At even higher shear velocities, the effect of the shearing becomes smaller again. Also the effective temperature near the walls (deduced from the velocity distributions of the particles) decreases again when the wall velocity gets very large. When the walls are placed closer together, thereby introducing a misfit, a structure containing a soliton staircase arises in simulations without shear. Introducing shear increases the disorder in these systems until no solitons are visible any more. Instead, similar structures like in the case without misfit result. At high shear rates, configurations where the incommensurability of the crystalline structure is compensated by the creation of holes become relevant.
SuperADAM: upgraded polarized neutron reflectometer at the Institut Laue-Langevin.
Devishvili, A; Zhernenkov, K; Dennison, A J C; Toperverg, B P; Wolff, M; Hjörvarsson, B; Zabel, H
2013-02-01
A new neutron reflectometer SuperADAM has recently been built and commissioned at the Institut Laue-Langevin, Grenoble, France. It replaces the previous neutron reflectometer ADAM. The new instrument uses a solid state polarizer/wavelength filter providing a highly polarized (up to 98.6%) monochromatic neutron flux of 8 × 10(4) n?cm(-2)?s(-1) with monochromatization ???? = 0.7% and angular divergence ?? = 0.2 mrad. The instrument includes both single and position sensitive detectors. The position sensitive detector allows simultaneous measurement of specular reflection and off-specular scattering. Polarization analysis for both specular reflection and off-specular scattering is achieved using either mirror analyzers or a (3)He spin filter cell. High efficiency detectors, low background, and high flux provides a dynamic range of up to seven decades in reflectivity. Detailed specifications and the instrument capabilities are illustrated with examples of recently collected data in the fields of thin film magnetism and thin polymer films. PMID:23464256
NASA Astrophysics Data System (ADS)
Vinš, Václav; Planková, Barbora; Hrubý, Jan
2013-05-01
In this study, the Cahn-Hilliard density gradient theory (GT) is used for predicting the surface tension of various binary mixtures at relatively wide temperature ranges and for testing the application of the GT for predictions of homogeneous nucleation. The GT was combined with two physically based equations of state (EoS), namely the perturbed-chain (PC) statistical associating fluid theory (SAFT) and its modification for polar substances the perturbed-chain polar (PCP) SAFT. The GT applied to the planar phase interface was employed to predict the interfacial tension for various quadrupolar (CO2 and benzene) and dipolar (difluoromethane, i.e., R32; pentafluoroethane, i.e., R125; and 1,1,1,2-tetrafluoroethane, i.e., R134a) substances and for five binary mixtures including polar components ( n-decane + CO2, benzene + CO2, R32 + R125, R32 + R134a, R134a + R125). The PCP-SAFT EoS combined with the GT provides more accurate results for both the quadrupolar and dipolar substances than the original PC-SAFT EoS. Besides the planar phase interface, the GT was also applied to the spherical phase interface simulating a critical cluster occurring in homogeneous nucleation of droplets. Carbon dioxide was considered, because it has a relatively high quadrupole moment and because of its relevance to natural gas processing. Application of the PCP-SAFT EoS provides a significant improvement compared to the PC-SAFT EoS, and it is clearly superior to the classical cubic Peng-Robinson EoS, which is still used for modeling droplet nucleation.
Sassaroli, Angelo; Martelli, Fabrizio; Fantini, Sergio
2010-07-01
We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4-10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Deltamu(a)
Modelling by Differential Equations
ERIC Educational Resources Information Center
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Computation of rare transitions in the barotropic quasi-geostrophic equations
NASA Astrophysics Data System (ADS)
Laurie, Jason; Bouchet, Freddy
2015-01-01
We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherwise. We adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.
Bravaya, Ksenia B.; Zuev, Dmitry; Epifanovsky, Evgeny; Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)
2013-03-28
Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H{sup -}, and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, {theta}. Standard basis sets that are optimized for not-complex-scaled calculations ({theta} = 0) are not sufficiently flexible to describe the {theta}-dependence of the wave functions even when heavily augmented by additional sets.
Explicit equations for infiltration
NASA Astrophysics Data System (ADS)
Swamee, Prabhata K.; Rathie, Pushpa N.; Ozelim, Luan Carlos de S. M.
2012-03-01
SummaryUnderstanding infiltration processes is one of the fundamental points in the theory of drainage and irrigation engineering. The infiltration phenomenon has two limiting behaviors given by the two-parameter Green-Ampt and Talsma-Parlange equations. Both equations are unified to form a general three-parameter formula. The third parameter interpolates between these two limiting cases. This investigation attempts to find an explicit form of the generalized equation. The explicit equation is accurate, simple and easy to use in practical situations.
Optimization of one-way wave equations.
Lee, M.W.; Suh, S.Y.
1985-01-01
The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors
Liouville equation and schottky problem
Marco Matone; G. Galilei
1995-01-01
An Ansatz for the Poincaré metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a nonchiral analogous of the higher genus relationships (KP equation) arising within the framework of Schottky's problem solution. This approach connects uniformization (Fuchsian groups) and moduli space theories with KP hierarchy. Besides its mathematical interest, the Ansatz
Many-particle Brownian and Langevin Dynamics Simulations with the Brownmove package
2011-01-01
Background Brownian Dynamics (BD) is a coarse-grained implicit-solvent simulation method that is routinely used to investigate binary protein association dynamics, but due to its efficiency in handling large simulation volumes and particle numbers it is well suited to also describe many-protein scenarios as they often occur in biological cells. Results Here we introduce our "brownmove" simulation package which was designed to handle many-particle problems with varying particle numbers and allows for a very flexible definition of rigid and flexible protein and polymer models. Both a Brownian and a Langevin dynamics (LD) propagation scheme can be used and hydrodynamic interactions are treated efficiently with our recently introduced TEA-HI ansatz [Geyer, Winter, JCP 130 (2009) 114905]. With simulations of constrained polymers and flexible models of spherical proteins we demonstrate that it is crucial to include hydrodynamics when multi-bead models are used in BD or LD simulations. Only then both the translational and the rotational diffusion coefficients and the timescales of the internal dynamics can be reproduced correctly. In the third example project we show how constant density boundary conditions [Geyer et al, JCP 120 (2004) 4573] can be used to set up a non-equilibrium simulation of diffusional transport across an array of fixed obstacles. Finally, we demonstrate how the agglomeration dynamics of multiple particles with attractive patches can be analysed conveniently with the help of a dynamic interaction network. Conclusions Combining BD and LD propagation, fast hydrodynamics, a flexible protein model, and interfaces for "open" simulation settings, our freely available "brownmove" simulation package constitutes a new platform for coarse-grained many-particle simulations of biologically relevant diffusion and transport processes. PMID:21596002
NSDL National Science Digital Library
Michael Kimmel
2007-12-12
This lesson includes a theory-evaluation activity. A set of five scenarios (theories for how diverse life came into existence on Earth) is divided evenly throughout the class, so each student is asked to evaluate one theory. Students then come together in groups of five, so that all theories are represented in each group, where they are compared and evaluated. Each group reports to the entire class for further discussion and clarifications.
Mirigian, Stephen [University of Illinois, Urbana-Champaign] [University of Illinois, Urbana-Champaign; Schweizer, Kenneth [University of Illinois] [University of Illinois
2014-01-01
Building on the elastically collective nonlinear Langevin equation theory developed for hard spheres in Paper I, we propose and implement a quasi-universal theory for the alpha relaxation of thermal liquids based on mapping them to an effective hard sphere fluid via the dimensionless compressibility. The result is a zero adjustable parameter theory that can quantitatively address in a unified manner the alpha relaxation time over 14 or more decades. The theory has no singularities above zero Kelvin, and relaxation in the equilibrium low temperature limit is predicted to be of a roughly Arrhenius form. The two-barrier (local cage and long range collective elastic) description results in a rich dynamic behavior including apparent Arrhenius, narrow crossover, and deeply supercooled regimes, and multiple characteristic or crossover times and temperatures of clear physical meaning. Application of the theory to nonpolar molecules, alcohols, rare gases, and liquids metals is carried out. Overall, the agreement with experiment is quite good for the temperature dependence of the alpha time, plateau shear modulus, and Boson-like peak frequency for van der Waals liquids, though less so for hydrogen-bonding molecules. The theory predicts multiple growing length scales upon cooling, which reflect distinct aspects of the coupled local hopping and cooperative elastic physics. Calculations of the growth with cooling of an activation volume, which is strongly correlated with a measure of dynamic cooperativity, agree quantitatively with experiment. Comparisons with elastic, entropy crisis, dynamic facilitation, and other approaches are performed, and a fundamental basis for empirically extracted crossover temperatures is established. The present work sets the stage for addressing distinctive glassy phenomena in polymer melts, and diverse liquids under strong confinement.