Boedeker's effective theory: From Langevin dynamics to Dyson-Schwinger equations
Zahlten, Claus Hernandez, Andres Schmidt, Michael G.
2009-10-15
The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|{approx}g{sup 2}T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Boedeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: (
Satin, Seema
2015-01-01
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area...
Seema Satin
2015-09-28
We attempt to introduce an new approach towards study of certain interesting issues in classical gravity. This can be done for few confined, but interesting and meaningful physical situations, which can be modeled by a classical stochastic Einstein equation. The Einstein equation can be looked upon as an equation of motion, while introducing to it a classical stochastic source or classical fluctuations as driving source. This is analogous to the Langevin equation formalism, in Brownian motion studies. A justification for the validity of such an ansatz for classical gravity is given. The regime of validity of such an approach and the consequences and possible outcomes of this formulation are discussed. We also mention, further relevant directions and applications of the same,that act as motivation towards the new proposal. This field of study can be seen to emerge out of well established ideas and results in Brownian motion theory as well as the Stochastic Semiclassical Gravity (which is already an active area of research at present) and related issues in Thermodynamics . These two areas form the foundations for building up the theory. The applicability of the proposed theme can have a wider expanse than is mentioned here.
Complex Langevin Equations and Schwinger-Dyson Equations
Pehlevan, Cengiz
2007-01-01
Complex Langevin equations were proposed to study systems with complex valued path integral weights. A major problem in this proposal turned out to be the existence of possibly many stationary distributions of complex Langevin equations. We point out that these stationary distributions, as constructed by Salcedo \\cite{Salcedo93}, are also the solutions of the Schwinger-Dyson equations of the associated quantum field theory \\cite{Garcia96, Guralnik07}. In the latter references, the relation between the solution space of the Schwinger-Dyson equation and the phase space of the associated quantum field theory was studied. This suggests the use of complex Langevin equations in the study of phase spaces of quantum field theories.
The complex chemical Langevin equation
NASA Astrophysics Data System (ADS)
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2014-07-01
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.
Quantum Langevin equations for optomechanical systems
NASA Astrophysics Data System (ADS)
Barchielli, Alberto; Vacchini, Bassano
2015-08-01
We provide a fully quantum description of a mechanical oscillator in the presence of thermal environmental noise by means of a quantum Langevin formulation based on quantum stochastic calculus. The system dynamics is determined by symmetry requirements and equipartition at equilibrium, while the environment is described by quantum Bose fields in a suitable non-Fock representation which allows for the introduction of temperature. A generic spectral density of the environment can be described by introducing its state through a suitable P-representation. Including interaction of the mechanical oscillator with a cavity mode via radiation pressure we obtain a description of a simple optomechanical system in which, besides the Langevin equations for the system, one has the exact input-output relations for the quantum noises. The whole theory is valid at arbitrarily low temperature. This allows the exact calculation of the stationary value of the mean energy of the mechanical oscillator, as well as both homodyne and heterodyne spectra. The present analysis allows in particular to study possible cooling scenarios and to obtain the exact connection between observed spectra and fluctuation spectra of the position of the mechanical oscillator.
Generalized Langevin equations for dealing with nonadditive fluctuations
Grigolini, P.
1982-02-01
A suitable extension of the Mori memory-function formalism to the Hermitian case allows a ''multiplicative'' process to be described by a Langevin equation of non-Markoffian nature. This generalized Langevin equation is then shown to provide for the variable of interest the same autocorrelation function as the well-known theoretical approach developed by Kubo, the stochastic Liouville equation (SLE) theory. It is shown, furthermore, that the present approach does not disregard the influence of the variable of interest on the time evolution of its thermal bath. The stochastic process under study can also be described by a Fokker-Planck-like equation, which results in a Gaussian equilibrium distribution for the variable of interest. The main flaw of the SLE theory, that resulting in an uncorrect equilibrium distribution, is therefore completely eliminated.
Basharov, A. M.
2012-09-15
It is shown that the effective Hamiltonian representation, as it is formulated in author's papers, serves as a basis for distinguishing, in a broadband environment of an open quantum system, independent noise sources that determine, in terms of the stationary quantum Wiener and Poisson processes in the Markov approximation, the effective Hamiltonian and the equation for the evolution operator of the open system and its environment. General stochastic differential equations of generalized Langevin (non-Wiener) type for the evolution operator and the kinetic equation for the density matrix of an open system are obtained, which allow one to analyze the dynamics of a wide class of localized open systems in the Markov approximation. The main distinctive features of the dynamics of open quantum systems described in this way are the stabilization of excited states with respect to collective processes and an additional frequency shift of the spectrum of the open system. As an illustration of the general approach developed, the photon dynamics in a single-mode cavity without losses on the mirrors is considered, which contains identical intracavity atoms coupled to the external vacuum electromagnetic field. For some atomic densities, the photons of the cavity mode are 'locked' inside the cavity, thus exhibiting a new phenomenon of radiation trapping and non-Wiener dynamics.
The generalized Schrödinger–Langevin equation
Bargueño, Pedro; Miret-Artés, Salvador
2014-07-15
In this work, for a Brownian particle interacting with a heat bath, we derive a generalization of the so-called Schrödinger–Langevin or Kostin equation. This generalization is based on a nonlinear interaction model providing a state-dependent dissipation process exhibiting multiplicative noise. Two straightforward applications to the measurement process are then analyzed, continuous and weak measurements in terms of the quantum Bohmian trajectory formalism. Finally, it is also shown that the generalized uncertainty principle, which appears in some approaches to quantum gravity, can be expressed in terms of this generalized equation. -- Highlights: •We generalize the Kostin equation for arbitrary system–bath coupling. •This generalization is developed both in the Schrödinger and Bohmian formalisms. •We write the generalized Kostin equation for two measurement problems. •We reformulate the generalized uncertainty principle in terms of this equation.
Generalized Langevin equation with chaotic force
NASA Astrophysics Data System (ADS)
Shimizu, Toshihiro
1994-12-01
The generalized Langevin equation with chaotic force is investigated: ?(t) = - limit?0tdt??(t,t?)x(t?) + ƒ(t) , where ?(t,t?) = {?ƒ(t)ƒ(t?) ?}/{?x 2 ? }. The chaotic force ƒ( t) is defined by ƒ(t)= {(y n+1 - ?y? }/{?} for n? < t ? ( n + 1) ? ( n= 0,1,2,…), where yn+1 is a chaotic sequence: yn+1 = F( yn). The time evolution of x( t), which is generated by the chaotic force, is discussed. The approach of the distribution function of x to a stationary distribution is studied. It is shown that the distribution function satisfies the Fokker-Planck type equation with the memory effect in the small ? limit. The relation between the invariant density of F ( y) and the stationary distribution of x is discussed.
Langevin equation approach to reactor noise analysis: stochastic transport equation
Akcasu, A.Z. ); Stolle, A.M. )
1993-01-01
The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.
Langevin equation approach to reactor noise analysis: stochastic transport equation
Akcasu, A.Z.; Stolle, A.M. )
1991-01-01
This paper is concerned with an application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density, as well as in the detector outputs, in nuclear reactors. The Langevin equation in this case is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral density (PSD) of the NES is evaluated in nuclear engineering applications by adopting a generalization of the Shottky formula. In this paper, the authors extend calculations to include the space and velocity dependence of neutron density by starting from the stochastic transport equation and the stochastic detection rate equations within the detectors. In addition, they discuss the implementation of the Langevin equation approach at different levels of approximation and explicitly obtain the stochastic one-speed transport and one-group P{sub 1} equations by first integrating the transport equation over speed and then eliminating in the angular dependence by spherical harmonic expansion.
Simplified simulation of Boltzmann-Langevin equation
Ayik, S.; Randrup, J.
1994-06-01
We briefly recall the Boltzmann-Langevin model of nuclear dynamics. We then summarize recent progress in deriving approximate analytical expressions for the associated transport coefficients and describe a numerical method for simulating the stochastic evolution of the phase-space density.
Coherent state path integral and Langevin equations of interacting bosons
NASA Astrophysics Data System (ADS)
Mieck, B.
2001-05-01
Interacting excitons in a semiconductor coupled to a thermal reservoir are treated as bosons. We use a coherent state path integral formulation on the time contour and transform the quantum mechanical system of bosonic excitons to a classical Langevin equation with an inhomogenous random force which represents the influence of the thermal reservoir. However, this classical Langevin equation cannot take into account the different order of annihilation and creation operators or their correlations. This is achieved by an application of a Hubbard-Stratonovich transformation which introduces an auxiliary variable ?x( tp) related to the self-energy. In terms of this new field, an additional Langevin equation is derived which is similar to a saddle-point equation with a random force fx( t). This equation contains the mean value ?¯x(t) of the auxiliary fields ? x(t +), ? x(t -) as a fluctuating potential or self-energy in matrix-form on the time contour.
A path integral approach to the Langevin equation
Ashok K. Das; Sudhakar Panda; J. R. L. Santos
2015-01-07
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.
Numerical simulation of the Langevin equation for skewed turbulence
Ermak, D. L.; Nasstrom, J. S.
1994-12-01
In this paper the authors present a numerical method for the generalized Langevin equation of motion with skewed random forcing for the case of homogeneous, skewed turbulence. The authors begin by showing how the analytic solution to the Langevin equation for this case can be used to determine the relationship between the particle velocity moments and the properties of the skewed random force. They then present a numerical method that uses simple probability distribution functions to simulate the effect of the random force. The numerical solution is shown to be exact in the limit of infinitesimal time steps, and to be within acceptable error limits when practical time steps are used.
Quantum annealing and the Schrödinger-Langevin-Kostin equation
NASA Astrophysics Data System (ADS)
de Falco, Diego; Tamascelli, Dario
2009-01-01
We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schrödinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.
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.
An adaptive stepsize method for the chemical Langevin equation
NASA Astrophysics Data System (ADS)
Ilie, Silvana; Teslya, Alexandra
2012-05-01
Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.
The Schrödinger-Langevin equation with and without thermal fluctuations
Roland Katz; Pol Bernard Gossiaux
2015-05-26
The Schr\\"odinger-Langevin (SL) equation is considered as an effective open quantum system formalism suitable for phenomenological applications. We focus on two open issues relative to its solutions. We first show that the Madelung/polar transformation of the wavefunction leads to a nonzero friction for the excited states of the quantum subsystem. We then study analytically and numerically the SL equation ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states, quantum noises and their production are discussed and a detailed analysis is carried with two kinds of noise and potential.
Solving the generalized Langevin equation with the algebraically correlated noise
NASA Astrophysics Data System (ADS)
Srokowski, T.; P?oszajczak, M.
1998-04-01
We solve the Langevin equation with the memory kernel. The stochastic force possesses algebraic correlations, proportional to 1/t. The velocity autocorrelation function and related quantities characterizing transport properties are calculated with the assumption that the system is in thermal equilibrium. Stochastic trajectories are simulated numerically, using the kangaroo process as a noise generator. Results of this simulation resemble Lévy walks with divergent moments of the velocity distribution. We consider motion of a Brownian particle, both without any external potential and in the harmonic oscillator field, in particular the escape from a potential well. The results are compared with memory-free calculations for the Brownian particle.
Large Deviations for the Langevin Equation with Strong Damping
NASA Astrophysics Data System (ADS)
Cerrai, Sandra; Freidlin, Mark
2015-11-01
We study large deviations in the Langevin dynamics, with damping of order ? ^{-1} and noise of order 1, as ? downarrow 0. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then we use a weak convergence approach to large deviations and its equivalent formulation in terms of the Laplace principle, to determine the good action functional. Some applications of these results to the exit problem from a domain and to the wave front propagation for a suitable class of reaction diffusion equations are considered.
Weihua Mu; Xiaoqing Li; Zhongcan Ou-Yang
2010-09-19
The stochastic systems without detailed balance are common in various chemical reaction systems, such as metabolic network systems. In studies of these systems, the concept of potential landscape is useful. However, what are the sufficient and necessary conditions of the existence of the potential function is still an open problem. Use Hodge decomposition theorem in differential form theory, we focus on the general chemical Langevin equations, which reflect complex chemical reaction systems. We analysis the conditions for the existence of potential landscape of the systems. By mapping the stochastic differential equations to a Hamiltonian mechanical system, we obtain the Fokker-Planck equation of the chemical reaction systems. The obtained Fokker-Planck equation can be used in further studies of other steady properties of complex chemical reaction systems, such as their steady state entropies.
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…
Elimination of fast variables in chemical Langevin equations
NASA Astrophysics Data System (ADS)
Lan, Yueheng; Elston, Timothy C.; Papoian, Garegin A.
2008-12-01
Internal and external fluctuations are ubiquitous in cellular signaling processes. Because biochemical reactions often evolve on disparate time scales, mathematical perturbation techniques can be invoked to reduce the complexity of stochastic models. Previous work in this area has focused on direct treatment of the master equation. However, eliminating fast variables in the chemical Langevin equation is also an important problem. We show how to solve this problem by utilizing a partial equilibrium assumption. Our technique is applied to a simple birth-death-dimerization process and a more involved gene regulation network, demonstrating great computational efficiency. Excellent agreement is found with results computed from exact stochastic simulations. We compare our approach with existing reduction schemes and discuss avenues for future improvement.
On the environmental modes for the generalized Langevin equation
NASA Astrophysics Data System (ADS)
Kawai, Shinnosuke
2015-09-01
The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.
Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
Julian Schmidt; Alex Meistrenko; Hendrik van Hees; Carsten Greiner
2015-11-06
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.
From Langevin to generalized Langevin equations for the nonequilibrium Rouse model
NASA Astrophysics Data System (ADS)
Maes, Christian; Thomas, Simi R.
2013-02-01
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.
A new approach to solve the Boltzmann-Langevin equation for fermionic systems
J. Rizzo; Ph. Chomaz; M. Colonna
2008-02-04
We present a new method to introduce phase-space fluctuations in transport theories, corresponding to a full implementation of the Boltzmann-Langevin equation for fermionic systems. It is based on the procedure originally developed by Bauer et al. for transport codes employing the test particle method. In the new procedure, the Pauli principle is carefully checked, leading to a good reproduction of the correct fluctuations in the ``continuum limit'' ($h \\to 0$). Accurate tests are carried out in one and two dimensional idealized systems, and finally results for a full 3D application are shown. We stress the reliability of this method, which can be easily plugged into existing tranport codes using test particles, and its general applicability to systems characterized by instabilities, like for instance multifragmentation processes.
Complex Langevin method applied to the 2D S U (2 ) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Makino, Hiroki; Suzuki, Hiroshi; Takeda, Daisuke
2015-10-01
The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice S U (2 ) Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.
Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2015-11-01
The Schrödinger-Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger-Langevin equation yields the complex quantum Hamilton-Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.
Ayik, S. Joint Inst. for Heavy Ion Research, Oak Ridge, TN ); Ivanov, Y.B.; Russkikh, V.N.; Noerenberg, W. )
1993-01-01
A reduction of the relativistic Boltzmann-Langevin Equation (BLE), to a stochastic two-fluid model is presented, and transport coefficients associated with fluid dynamical variables are extracted. The approach is applied to investigate equilibration in a counter-streaming nuclear system.
Brett, Tobias Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
Dynamics of neutron-induced fission of 235U using four-dimensional Langevin equations
NASA Astrophysics Data System (ADS)
Pahlavani, M. R.; Mirfathi, S. M.
2015-08-01
Background: Langevin equations have been suggested as a key approach to the dynamical analysis of energy dissipation in excited nuclei, formed during heavy-ion fusion-fission reactions. Recently, a few researchers theoretically reported investigations of fission for light nuclei in a low excitation energy using the Langevin approach, without considering the contribution of pre- and post-scission particles and ? -ray emission. Purpose: We study the dynamical evolution of mass distribution of fission fragments, and neutron and ? -ray multiplicity for 236U as compound nuclei that are constructed after fusion of a neutron and 235U. Method: Energy dissipation of the compound nucleus through fission is calculated using the Langevin dynamical approach combined with a Monte Carlo method. Also the shape of the fissioning nucleus is restricted to "funny hills" parametrization. Results: Fission fragment mass distribution, neutron and ? -ray multiplicity, and the average kinetic energy of emitted neutrons and ? rays at a low excitation energy are calculated using a dynamical model, based on the four-dimensional Langevin equations. Conclusions: The theoretical results show reasonable agreement with experimental data and the proposed dynamical model can well explain the energy dissipation in low energy induced fission.
Phase space Langevin equation for spin relaxation in a dc magnetic field
NASA Astrophysics Data System (ADS)
Kalmykov, Yu. P.; Coffey, W. T.; Titov, S. V.
2009-10-01
A Langevin equation for the quantum Brownian motion of a spin of arbitrary size in a uniform external dc magnetic field is derived from the phase space master equation in the weak coupling and narrowing limits, for the quasiprobability distribution (Wigner) function of spin orientations in the configuration space of polar and azimuthal angles following methods long familiar in quantum optics. The closed system of differential-recurrence equations for the statistical moments describing magnetic relaxation of the spin is obtained as an example of applications of this equation.
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.
Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution
NASA Astrophysics Data System (ADS)
Kanazawa, Kiyoshi; Sano, Tomohiko G.; Sagawa, Takahiro; Hayakawa, Hisao
2015-09-01
We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601-090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.
Exact derivation of the Langevin and master equations for harmonic quantum Brownian motion
Edgardo T. Garcia Alvarez; Fabian H. Gaioli
1998-07-17
A many particle Hamiltonian, where the interaction term conserves the number of particles, is considered. A master equation for the populations of the different levels is derived in an exact way. It results in a local equation with time-dependent coefficients, which can be identified with the transition probabilities in the golden rule approximation. A reinterpretation of the model as a set of coupled harmonic oscillators enables one to obtain for one of them an exact local Langevin equation, with time-dependent coefficients.
A Langevin equation approach to electron transfer reactions in the diabatic basis
NASA Astrophysics Data System (ADS)
Song, XiaoGeng; Wang, Haobin; Van Voorhis, Troy
2008-10-01
A linear Langevin equation that governs the population dynamics of electron transfer reactions is derived. The noise in the Langevin equation is eliminated by treating the diabatic population fluctuations as the relevant variables, leaving only the memory kernel responsible for the population relaxation. Within the memory kernel, the diabatic coupling is treated perturbatively and a second order expansion is found to give a simple closed form expression for the kernel. The accuracy of the second order truncation is maximized by performing a fixed rotation of the diabatic electronic states that minimizes the first order free energy of the system and thus minimizes the effect of the perturbation on the thermodynamics. The resulting two-hop Langevin equation (THLE) is then validated by applying it to a simple spin-boson model, where exact results exist. Excellent agreement is found in a wide parameter range, even where the perturbation is moderately strong. Results obtained in the rotated electronic basis are found to be consistently more accurate than those from the unrotated basis. These benchmark calculations also allow us to demonstrate the advantage of treating the population fluctuations instead of the populations as the relevant variables, as only the former lead to reliable results at long time. Thus, the THLE appears to provide a viable alternative to established methods—such as Ehrenfest dynamics or surface hopping—for the treatment of nonadiabatic effects in electron transfer simulations.
Solving the Langevin equation with stochastic algebraically correlated noise
NASA Astrophysics Data System (ADS)
P?oszajczak, M.; Srokowski, T.
1997-05-01
The long time tail in the velocity and force autocorrelation function has been found recently in molecular dynamics simulations of peripheral collisions of ions. Simulation of those slowly decaying correlations in the stochastic transport theory requires the development of new methods of generating stochastic force of arbitrarily long correlation times. In this paper we propose a Markovian process, the multidimensional kangaroo process, which permits the description of various algebraically correlated stochastic processes.
NASA Astrophysics Data System (ADS)
Brett, Tobias; Galla, Tobias
2013-06-01
We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
NASA Astrophysics Data System (ADS)
Srokowski, T.
2001-09-01
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte Carlo method. Some results appear to be incompatible with requirements of the fluctuation-dissipation theorem because probability distributions change when the process is inserted into the equation. We demonstrate how one can construct a model of noise free of that difficulty. This form of the KP is especially suitable for physical applications.
Kwok, Sau Fa
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
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.
A reference trajectory approach to Langevin equations in gas phase collision dynamics
NASA Astrophysics Data System (ADS)
Schatz, George C.; Moser, Mark D.
1980-09-01
In this paper, a new approach to the development of Langevin-like equations for studying gas phase collisional energy tranfer and other dynamical problems is introduced based on the use of reference trajectories to describe memory effects and nonlinear interactions. In this development, the exact equations of motion are first expressed in terms of the deviations of the coordinates and momenta from some reference trajectory values and then linearized about those values. A partitioning between fast and slow variables is then assumed, and those members of the above mentioned linearized equations which refer to the fast variables are re-expressed as integral equations. A ''local Brownian-like'' approximation is then made in the memory kernel appearing in the integral equations to reduce them to algebraic equations, and upon substitution of these into the slow variable equations of motion, we obtain Langevin-like equations for the slow variables. In these equations the interaction between slow and fast variables appears as frictionlike and random forcelike terms, and in these terms, information about nonlinear interactions and correlated motions (including recurrences) is evaluated using the reference trajectory. In order to keep the deviations from the reference trajectory small during each collision, this trajectory is best chosen as the ensemble averaged trajectory, and we find that a good approximation to this for many problems is provided by a trajectory in which all initial vibrational energies are set equal to zero. Applications of this Langevin-like approach to several models of gas phase VT collisional energy transfer show that it is capable of quantitative predictions (errors typically<20%) of the first and second (classical) moments of the final translational distributions, provided that the initial translational energy is low enough to make the collision duration long compared with typical vibrational periods, and that the initial vibrational energy is low enough to make the deviations about the reference trajectory small. Often these restrictions are not particularly severe. For example, in a collinear Kr+CO2(000) model, the average energy transfer is accurate to 5% for initial translational energies as high as 10 eV, while for a collinear He+H2 model, energy transfers accurate to 30% or better are obtained with five quanta of initial vibrational excitation in the H2. In addition, accurate results are obtained even when the average energy transfer is of different sign than that of the reference, and in spite of the fact that the width of the translational distribution is a factor of 10 or more larger than its first moment. We also demonstrate that the Langevin equation works well when the average energy transfer becomes comparable to a quantum of vibrational energy (i.e., in the nonperturbative regime) provided that the necessary time scale separations for invoking the Langevin treatment exist.
Leung, Chun Sing; Harko, Tiberiu
2013-01-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the frictional force, and on the fluctuation-dissipation theorems. The vertical displacements, velocities and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The Power Spectral Distribution of the luminosity it is also obtained, and it is shown that it has non-standard values. The theoretical predictions of the model are compared with the observational data for the luminosity time variation of the BL Lac S5 0716+714 object.
NASA Astrophysics Data System (ADS)
Kazakevi?ius, R.; Ruseckas, J.
2015-11-01
Subdiffusive behavior of one-dimensional stochastic systems can be described by time-subordinated Langevin equations. The corresponding probability density satisfies the time-fractional Fokker-Planck equations. In the homogeneous systems the power spectral density of the signals generated by such Langevin equations has power-law dependency on the frequency with the exponent smaller than 1. In this paper we consider nonhomogeneous systems and show that in such systems the power spectral density can have power-law behavior with the exponent equal to or larger than 1 in a wide range of intermediate frequencies.
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.
NASA Astrophysics Data System (ADS)
Harko, Tiberiu; Leung, Chun Sing; Mocanu, Gabriela
2014-05-01
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects interacting with their external medium based on a generalized Langevin equation with colored noise and on the fluctuation-dissipation theorems. The former accounts for the general memory and retarded effects of the frictional force. The presence of the memory effects influences the response of the disk to external random interactions, and it modifies the dynamical behavior of the disk, as well as the energy dissipation processes. The generalized Langevin equation of the motion of the disk in the vertical direction is studied numerically, and the vertical displacements, velocities, and luminosities of the stochastically perturbed disks are explicitly obtained for both the Schwarzschild and the Kerr cases. The power spectral distribution of the disk luminosity is also obtained. As a possible astrophysical application of the formalism we investigate the possibility that the intra-day variability of the active galactic nuclei may be due to the stochastic disk instabilities. The perturbations due to colored/nontrivially correlated noise induce a complicated disk dynamics, which could explain some astrophysical observational features related to disk variability.
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.
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
Grima, Ramon; Thomas, Philipp; Straube, Arthur V
2011-08-28
The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?(-3?2) for reaction systems which do not obey detailed balance and at least accurate to order ?(-2) for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?(-1?2) and variance estimates accurate to order ?(-3?2). This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules. PMID:21895155
How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?
NASA Astrophysics Data System (ADS)
Grima, Ramon; Thomas, Philipp; Straube, Arthur V.
2011-08-01
The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order ?-3/2 for reaction systems which do not obey detailed balance and at least accurate to order ?-2 for systems obeying detailed balance, where ? is the characteristic size of the system. Hence, the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order ?-1/2 and variance estimates accurate to order ?-3/2. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.
Non-Gaussian statistics, classical field theory, and realizable Langevin models
Krommes, J.A.
1995-11-01
The direct-interaction approximation (DIA) to the fourth-order statistic Z {approximately}{l_angle}{lambda}{psi}{sup 2}){sup 2}{r_angle}, where {lambda} is a specified operator and {psi} is a random field, is discussed from several points of view distinct from that of Chen et al. [Phys. Fluids A 1, 1844 (1989)]. It is shown that the formula for Z{sub DIA} already appeared in the seminal work of Martin, Siggia, and Rose (Phys. Rev. A 8, 423 (1973)] on the functional approach to classical statistical dynamics. It does not follow from the original generalized Langevin equation (GLE) of Leith [J. Atmos. Sd. 28, 145 (1971)] and Kraichnan [J. Fluid Mech. 41, 189 (1970)] (frequently described as an amplitude representation for the DIA), in which the random forcing is realized by a particular superposition of products of random variables. The relationship of that GLE to renormalized field theories with non-Gaussian corrections (``spurious vertices``) is described. It is shown how to derive an improved representation, that realizes cumulants through O({psi}{sup 4}), by adding to the GLE a particular non-Gaussian correction. A Markovian approximation Z{sub DIA}{sup M} to Z{sub DIA} is derived. Both Z{sub DIA} and Z{sub DIA}{sup M} incorrectly predict a Gaussian kurtosis for the steady state of a solvable three-mode example.
NASA Astrophysics Data System (ADS)
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
2010-04-01
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1+m2 Wiener processes, whereas the standard approach uses 2m1+m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch.
Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations
NASA Astrophysics Data System (ADS)
Hasegawa, Yoshihiko
2015-04-01
We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.
NASA Astrophysics Data System (ADS)
Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho
2013-05-01
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom's degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model
NASA Astrophysics Data System (ADS)
Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan
2015-08-01
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.
Metastability in simple climate models Pathwise analysis of slowly driven Langevin equations
Berglund, N
2002-01-01
We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium, instead of adiabatically following the stationary distribution of the frozen system. This behaviour can be characterized by describing the location of typical paths, and bounding the probability of atypical paths. We illustrate this approach by giving a quantitative description of phenomena associated with bistability, for three famous examples of simple climate models: Stochastic resonance in an energy balance model describing Ice Ages; hysteresis in a box model for the Atlantic thermohaline circulation; and bifurcation delay in the case of the Lorenz model for Rayleigh-B'enard convection.
Metastability in simple climate models: Pathwise analysis of slowly driven Langevin equations
Nils Berglund; Barbara Gentz
2001-11-13
We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium, instead of adiabatically following the stationary distribution of the frozen system. This behaviour can be characterized by describing the location of typical paths, and bounding the probability of atypical paths. We illustrate this approach by giving a quantitative description of phenomena associated with bistability, for three famous examples of simple climate models: Stochastic resonance in an energy balance model describing Ice Ages; hysteresis in a box model for the Atlantic thermohaline circulation; and bifurcation delay in the case of the Lorenz model for Rayleigh-B'enard convection.
Kim, Min-Geun; Jang, Hong-Lae; Cho, Seonho
2013-05-01
An efficient adjoint design sensitivity analysis method is developed for reduced atomic systems. A reduced atomic system and the adjoint system are constructed in a locally confined region, utilizing generalized Langevin equation (GLE) for periodic lattice structures. Due to the translational symmetry of lattice structures, the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom’s degrees of freedom. For the problems of highly nonlinear design variables, the finite difference method is impractical for its inefficiency and inaccuracy. However, the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint GLE. Through numerical examples, the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity.
Yu, Hsiu-Yu; Eckmann, David M; Ayyaswamy, Portonovo S; Radhakrishnan, Ravi
2015-05-01
We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics. PMID:26066173
Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations.
Hasegawa, Yoshihiko
2015-04-01
We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises. PMID:25974567
NASA Astrophysics Data System (ADS)
Yu, Hsiu-Yu; Eckmann, David M.; Ayyaswamy, Portonovo S.; Radhakrishnan, Ravi
2015-05-01
We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan
2015-08-01
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases. PMID:26382386
Shimizu, Akira
Quantum Langevin equations for semiconductor light-emitting devices and the photon statistics at a low-injection level Hiroshi Fujisaki* and Akira Shimizu Institute of Physics, University of Tokyo, 3 noise correlations which are valid at a low-injection level and in real devices. Applying
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
Generalized Langevin equation for solids. I. Rigorous derivation and main properties
NASA Astrophysics Data System (ADS)
Kantorovich, L.
2008-09-01
We demonstrate explicitly that the derivation by Adelman and Doll (AD) [J. Chem. Phys. 64, 2375 (1976)] of the generalized Langevin equation (GLE) to describe dynamics of an extended solid system by considering its finite subsystem is inconsistent because it relies on performing statistical averages over the entire system when establishing properties of the random force. This results in the random force representing a nonstationary process opposite to one of the main assumptions made in AD that the random force corresponds to a stationary stochastic process. This invalidates the derivation of the Brownian (or Langevin) form of the GLE in AD. Here we present a different and more general approach in deriving the GLE. Our method generalizes that of AD in two main aspects: (i) the structure of the finite region can be arbitrary (e.g., anharmonic), and (ii) ways are indicated in which the method can be implemented exactly if the phonon Green’s function of the harmonic environment region surrounding the anharmonic region is known, which is, e.g., the case when the environment region represents a part of a periodic solid (the bulk or a surface). We also show that in general after the local perturbation has ceased, the system returns to thermodynamic equilibrium with the distribution function for region 1 being canonical with respect to an effective interaction between atoms, which includes instantaneous response of the surrounding region. Note that our method does not rely on the assumption made in AD that the stochastic force correlation function depends on the times difference only (i.e., the random force corresponds to a stationary random process). In fact, we demonstrate explicitly that generally this is not the case. Still, the correct GLE can be obtained, which satisfies exactly the fluctuation-dissipation theorem.
Hiroshi Fujisaki; Akira Shimizu
1998-04-22
From the microscopic quantum Langevin equations (QLEs) we derive the effective semiconductor QLEs and the associated noise correlations which are valid at a low-injection level and in real devices. Applying the semiconductor QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula for the Fano factor of photons which gives the photon-number statistics as a function of the pump statistics and several parameters of LEDs. Key ingredients are non-radiative processes, carrier-number dependence of the radiative and non-radiative lifetimes, and multimodeness of LEDs. The formula is applicable to the actual cases where the quantum efficiency $\\eta$ differs from the differential quantum efficiency $\\eta_{d}$, whereas previous theories implicitly assumed $\\eta = \\eta_{d}$. It is also applicable to the cases when photons in each mode of the cavity are emitted and/or detected inhomogeneously. When $\\eta_{d} light. This mechanism for generation of sub-Poissonian light is completely different from those of previous theories, which assumed sub-Poissonian statistics for the current injected into the active layers of LEDs. Our results agree with recent experiments. We also discuss frequency dependence of the photon statistics.
Growth-collapse and decay-surge evolutions, and geometric Langevin equations
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Klafter, Joseph
2006-07-01
We introduce and study an analytic model for physical systems exhibiting growth-collapse and decay-surge evolutionary patterns. We consider a generic system undergoing a smooth deterministic growth/decay evolution, which is occasionally interrupted by abrupt stochastic collapse/surge discontinuities. The deterministic evolution is governed by an arbitrary potential field. The discontinuities are multiplicative perturbations of random magnitudes, and their occurrences are state-dependent-governed by an arbitrary rate function. The combined deterministic-stochastic evolution of the system turns out to be governed by a geometric Langevin equation driven by a state-dependent noise. A statistical exploration of these growth-collapse and decay-surge systems is conducted, with a focus on two special classes of systems: scale-free systems and generalized power-law systems. For stationary scale-free systems we explicitly compute the distribution of the pre-discontinuity, post-discontinuity, and equilibrium levels. Generalized power-law systems are proved to display three possible qualitative types of behavior: (i) super-critical-in which the system eventually explodes/freezes; (ii) critical-in which the system's underlying dynamical structure is that of a geometric random walk; and, (iii) sub-critical-in which the system reaches statistical equilibrium.
Haas, Kevin R; Yang, Haw; Chu, Jhih-Wei
2013-09-28
The evaluation of the Fisher information matrix for the probability density of trajectories generated by the over-damped Langevin dynamics at equilibrium is presented. The framework we developed is general and applicable to any arbitrary potential of mean force where the parameter set is now the full space dependent function. Leveraging an innovative Hermitian form of the corresponding Fokker-Planck equation allows for an eigenbasis decomposition of the time propagation probability density. This formulation motivates the use of the square root of the equilibrium probability density as the basis for evaluating the Fisher information of trajectories with the essential advantage that the Fisher information matrix in the specified parameter space is constant. This outcome greatly eases the calculation of information content in the parameter space via a line integral. In the continuum limit, a simple analytical form can be derived to explicitly reveal the physical origin of the information content in equilibrium trajectories. This methodology also allows deduction of least informative dynamics models from known or available observables that are either dynamical or static in nature. The minimum information optimization of dynamics is performed for a set of different constraints to illustrate the generality of the proposed methodology. PMID:24089743
Takashi Uneyama; Tomoshige Miyaguchi; Takuma Akimoto
2015-08-30
The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.
Dynamics of protein-protein encounter: a Langevin equation approach with reaction patches
Jakob Schluttig; Denitsa Alamanova; Volkhard Helms; Ulrich S. Schwarz
2008-09-17
We study the formation of protein-protein encounter complexes with a Langevin equation approach that considers direct, steric and thermal forces. As three model systems with distinctly different properties we consider the pairs barnase:barstar, cytochrome c:cytochrome c peroxidase and p53:MDM2. In each case, proteins are modeled either as spherical particles, as dipolar spheres or as collection of several small beads with one dipole. Spherical reaction patches are placed on the model proteins according to the known experimental structures of the protein complexes. In the computer simulations, concentration is varied by changing box size. Encounter is defined as overlap of the reaction patches and the corresponding first passage times are recorded together with the number of unsuccessful contacts before encounter. We find that encounter frequency scales linearly with protein concentration, thus proving that our microscopic model results in a well-defined macroscopic encounter rate. The number of unsuccessful contacts before encounter decreases with increasing encounter rate and ranges from 20-9000. For all three models, encounter rates are obtained within one order of magnitude of the experimentally measured association rates. Electrostatic steering enhances association up to 50-fold. If diffusional encounter is dominant (p53:MDM2) or similarly important as electrostatic steering (barnase:barstar), then encounter rate decreases with decreasing patch radius. More detailed modeling of protein shapes decreases encounter rates by 5-95 percent. Our study shows how generic principles of protein-protein association are modulated by molecular features of the systems under consideration. Moreover it allows us to assess different coarse-graining strategies for the future modelling of the dynamics of large protein complexes.
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.
Nagata, Keitaro; Shimasaki, Shinji
2015-01-01
The complex Langevin method has been attracting much attention as a solution to the sign problem since the method was shown to work in finite density QCD in the deconfined phase by using the so-called gauge cooling procedure. Whether it works also in the confined phase with light quarks is still an open question, though. In order to shed light on this question, we apply the method to the chiral Random Matrix Theory, which describes the epsilon regime of finite density QCD. Earlier works reported that a naive implementation of the method fails to reproduce the known exact results and that the problem can be solved by choosing a suitable coordinate. In this work we stick to the naive implementation, and show that a generalized gauge cooling procedure can be used to avoid the problem.
Two critical issues in Langevin simulation of gas flows
Zhang, Jun; Fan, Jing
2014-12-09
A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.
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.
Ooi, C. H. Raymond; Sun, Qingqing; Zubairy, M. Suhail; Scully, Marlan O.
2007-01-01
: 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 ?Received 1 February 2007; published 6...
1/f noise from point process and time-subordinated Langevin equations
Ruseckas, J; Kaulakys, B
2015-01-01
Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise. After demonstrating the appearance of 1/f noise in the earlier proposed point process model, we generalize it starting from a stochastic differential equation which describes a Brownian-like motion in the internal (operational) time. We consider this equation together with an additional equation relating the internal time to the external (physical) time. We show that the relation between the internal time and the physical time that depends on the intensity of the signal can lead to 1/f noise in a wide interval of frequencies. The present model can be useful for the explanation of the appearance of 1/f noise in different systems.
NASA Astrophysics Data System (ADS)
Uneyama, Takashi; Miyaguchi, Tomoshige; Akimoto, Takuma
2015-09-01
The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long-time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to time-dependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.
NASA Astrophysics Data System (ADS)
Eslamizadeh, H.
2014-12-01
The dynamics of fission of excited nuclei has been studied by solving four-dimensional Langevin equations with dissipation generated through the chaos-weighted wall and window friction formula. The projection of the total spin of the compound nucleus to the symmetry axis, K, was considered as the fourth dimension in Langevin dynamical calculations. The average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy have been calculated in a wide range of fissile parameter for compound nuclei 162Yb, 172Yb, 215Fr, 224Th, 248Cf, 260Rf and results compared with the experimental data. Calculations were performed with a constant dissipation coefficient of K, ?K (MeV zs)-1/2, and with a non-constant dissipation coefficient. Comparison of the theoretical results for the average pre-scission neutron multiplicities, mean kinetic energy of fission fragments and the variances of the mass and kinetic energy with the experimental data showed that the results of four-dimensional Langevin equations with a non-constant dissipation coefficient are in better agreement with the experimental data. Furthermore, the difference between the results of two models for compound nuclei with low fissile parameter is low whereas, for heavy compound nuclei, is high.
Ooi, C. H. Raymond; Scully, Marlan O.; Sun, Qingqing; Zubairy, M. Suhail
2007-01-01
We present a largely analytical theory for two-photon correlations G((2)) between Stokes (s) and anti-Stokes (a) photon pairs from an extended medium (amplifier) composed of double-Lambda atoms in counterpropagating geometry. We generalize...
Lucarini, Valerio; Willeit, Matteo
2011-01-01
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies and show, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation...
Localised distributions and criteria for correctness in complex Langevin dynamics
Aarts, Gert; Giudice, Pietro; Seiler, Erhard
2013-10-15
Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the 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.
NASA Astrophysics Data System (ADS)
Kalmykov, Yu. P.; Coffey, W. T.; Waldron, J. T.
1996-08-01
The correlation time of the positional autocorrelation function is calculated exactly for one-dimensional translational Brownian motion of a particle in a 2-4 double-well potential in the noninertial limit. The calculations are carried out using the method of direct conversion (by averaging) of the Langevin equation for a nonlinear stochastic system to a set of differential-recurrence relations. These, in the present problem, reduce on taking the Laplace transform, to a three-term recurrence relation. Thus the correlation time Tc of the positional autocorrelation function may be formally expressed as a sum of products of infinite continued fractions which may be represented in series form as a sum of two term products of Whittaker's parabolic cylinder functions. The sum of this series may be expressed as an integral using the integral representation of the parabolic cylinder functions and subsequently the Taylor expansion of the error function, thus yielding the exact solution for Tc. This solution is in numerical agreement with that obtained by Perico et al. [J. Chem. Phys. 98, 564 (1993)] using the first passage time approach while previous asymptotic results obtained by solving the underlying Smoluchowski equation are recovered in the limit of high barrier heights. A simple empirical formula which provides a close approximation to the exact solution for all barrier heights is also given.
Inverse kinetic theory for quantum hydrodynamic equations
Massimo Tessarotto; Marco Ellero; Piero Nicolini
2006-06-10
We propose a solution for the inverse kinetic theory for quantum hydrodynamic equations associated to the non-relativistic Schr\\"{o}dinger equation. It is shown that an inverse kinetic equation of the form of the Vlasov equation can be non-uniquely determined under suitable mathematical prescriptions.
stanfordlogo Euclid's Elements as an Equational Theory
Bejerano, Gill
stanfordlogo Euclid's Elements as an Equational Theory Vaughan Pratt Stanford University 26 May, 2015 Vaughan Pratt (Stanford University) Euclid's Elements as an Equational Theory 26 May, 2015 1 / 49 and odd number of zeros, contradicting their equality. Vaughan Pratt (Stanford University) Euclid
Relativistic Langevin Dynamics in Expanding Media
Min He; Hendrik van Hees; Pol B. Gossiaux; Rainer J. Fries; Ralf Rapp
2013-05-27
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 pre-point (Ito) and post-point (H\\"anggi-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.
Prolongation theory. A new nonlinear Schroedinger equation
Roy, S.; Chowdhury, A.R.
1987-07-01
The authors discuss a new kind of nonlinear Schroedinger equation from the viewpoint of prolongation theory. It is shown that the equation possess a Lax pair with a 3 x 3 matrix structure. It is further demonstrated that by a multiple scale perturbation of Zakharov et al. it can be reduced to the usual KdV equation.
Boltzmann-Langevin transport model for heavy-ion collisions
Ayik, S. |
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.
Langevin's `Twin Paradox' paper revisited
J. H. Field
2015-08-04
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.
Langevin dynamics and decoherence of heavy quarks at high temperatures
NASA Astrophysics Data System (ADS)
Akamatsu, Yukinao
2015-10-01
A Langevin equation of heavy quarks in high-temperature quark-gluon plasma is derived. The dynamics of heavy quark color is coupled with the phase space dynamics and causes a macroscopic superposition state of heavy quark momentum. Decoherence of the superposition state allows one to use a classical description. The time scale of decoherence gives an appropriate discretization time scale ? t ˜?{M /CF? } for the classical Langevin equation, where M is heavy quark mass and ? is heavy quark momentum diffusion constant.
Is Schroedinger equation consistent with information theory?
R. P. Venkataraman
2000-07-03
It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann integrable density function that has real or imaginary zeros or singularities at end points of $[a,b] \\epsilon R$, a new variational formulation for quantum mechanics is proposed that yields a system of Euler-Lagrange equations that are non-linear. It is proved that the solutions of this system are unique, orthonormal and complete. One dimensional harmonic oscillator has been solved.
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].
Dynamical mean-field theory for correlated electrons by Dieter Vollhardt
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
Towards Collinear Evolution Equations in Electroweak Theory
M. Ciafaloni; P. Ciafaloni; D. Comelli
2001-11-09
We consider electroweak radiative corrections to hard inclusive processes at the TeV scale, and we investigate how collinear logarithms factorize in a spontaneously broken gauge theory, similarly to the DGLAP analysis in QCD. Due to the uncancelled double logs noticed previously, we find a factorization pattern which is qualitatively different from the analogous one in QCD. New types of splitting functions emerge which are needed to describe the initial beam charges and are infrared-sensitive, that is dependent on an infrared cutoff provided, ultimately, by the symmetry breaking scale. We derive such splitting functions at one-loop level in the example of SU(2) gauge theory, and we also discuss the structure functions' evolution equations, under the assumption that isospin breaking terms present in the Ward identities of the theory are sufficiently subleading at higher orders.
Collective Langevin Dynamics of Flexible Cytoskeletal Fibers
Francois Nedelec; Dietrich Foethke
2009-03-30
We develop a numerical method to simulate mechanical objects in a viscous medium at a scale where inertia is negligible. Fibers, spheres and other voluminous objects are represented with points. Different types of connections are used to link the points together and in this way create composite mechanical structures. The motion of such structures in a Brownian environment is described by a first-order multivariate Langevin equation. We propose a computationally efficient method to integrate the equation, and illustrate the applicability of the method to cytoskeletal modeling with several examples.
Wave Propagation Theory 2.1 The Wave Equation
2 Wave Propagation Theory 2.1 The Wave Equation The wave equation in an ideal fluid can be derived #12;66 2. Wave Propagation Theory quantities of the quiescent (time independent) medium are identified perturbations is much smaller than the speed of sound. 2.1.1 The Nonlinear Wave Equation Retaining higher
Unions of Equational Monadic Theories Piotr Ho man
Hoffman, Piotr
Unions of Equational Monadic Theories Piotr Ho#11;man Institute of Informatics, Warsaw University theories. We focus on monadic theories, i.e., theories over signa- tures with unary symbols only. This allows us to make use of the equiv- alence between monoid amalgams and unions of monadic theories. We
Data driven Langevin modeling of biomolecular dynamics
NASA Astrophysics Data System (ADS)
Schaudinnus, Norbert; Rzepiela, Andrzej J.; Hegger, Rainer; Stock, Gerhard
2013-05-01
Based on a given time series, the data-driven Langevin equation proposed by Hegger and Stock [J. Chem. Phys. 130, 034106 (2009), 10.1063/1.3058436] aims to construct a low-dimensional dynamical model of the system. Adopting various simple model problems of biomolecular dynamics, this work presents a systematic study of the theoretical virtues and limitations as well as of the practical applicability and performance of the method. As the method requires only local information, the input data need not to be Boltzmann weighted in order to warrant that the Langevin model yields correct Boltzmann-distributed results. Moreover, a delay embedding of the state vector allows for the treatment of memory effects. The robustness of the modeling with respect to wrongly chosen model parameters or low sampling is discussed, as well as the treatment of inertial effects. Given sufficiently sampled input data, the Langevin modeling is shown to successfully recover the correct statistics (such as the probability distribution) and the dynamics (such as the position autocorrelation function) of all considered problems.
Thermodynamic restrictions on the constitutive equations of electromagnetic theory
NASA Technical Reports Server (NTRS)
Coleman, B. D.; Dill, E. H.
1971-01-01
Thermodynamics second law restrictions on constitutive equations of electromagnetic theory for nonlinear materials with long-range gradually fading memory, considering dissipation principle consequences
Ramond Equations of Motion in Superstring Field Theory
Theodore Erler; Sebastian Konopka; Ivo Sachs
2015-06-18
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Morse Theory and Nonlinear Differential Equations Thomas Bartsch
Szulkin, Andrzej
Morse Theory and Nonlinear Differential Equations Thomas Bartsch Mathematisches Institut, Universit.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Morse inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Local theory 13 3.1 Morse lemma
The Boltzmann-Langevin approach: A simple quantum-mechanical derivation
NASA Astrophysics Data System (ADS)
Nagaev, K. E.
2015-11-01
We present a simple quantum-mechanical derivation of correlation function of Langevin sources in the semiclassical Boltzmann-Langevin equation. The specific case of electron-phonon scattering is considered. It is shown that the assumption of weak scattering leads to the Poisson nature of the scattering fluxes.
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
Fokker-Planck equation of Schramm-Loewner evolution
NASA Astrophysics Data System (ADS)
Najafi, M. N.
2015-08-01
In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE (? ,?c) . After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we obtain the long- and short-time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE (? ,?c) traces and show that it is related to the higher-order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented.
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...
Geodesic spaces: Euclid's five postulates as an equational theory,
Pratt, Vaughan
Geodesic spaces: Euclid's five postulates as an equational theory, starting with the second Vaughan of the 60th BirthdGeodesic spaces: Euclid's five postulates as an equational theory, starting and Applications A conference in honour of the 60th BirthdGeodesic spaces: Euclid's five postulates
Gap equation in scalar field theory at finite temperature
Krishnendu Mukherjee
1998-12-24
We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.
Dynamic correlation functions and Boltzmann-Langevin approach for driven one-dimensional lattice gas
von Oppen, Felix
Dynamic correlation functions and Boltzmann-Langevin approach for driven one-dimensional lattice Center and CeNS, Department of Physics, Ludwig-Maximilians-UniversitÃ¤t MÃ¼nchen, Theresienstrasse 37, D as Boltzmann-Langevin theory we are able to give a complete qualitative picture of the dynamics in the low
Applications of the theory of evolution equations to general relativity
Alan D. Rendall
2001-09-07
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are presented. After this recent applications of Fuchsian equations are described, with particular attention to work on the structure of singularities of solutions of the Einstein equations coupled to a massless scalar field. Next the relations between analytical and numerical studies of the Einstein equations are discussed. Finally an attempt is made to identify fruitful directions for future research within the analytic approach to the study of the Einstein equations.
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.
EVOLUTION EQUATIONS AND GEOMETRIC FUNCTION THEORY IN
Harris, Larry
of papers Ky Fan developed a geometric theory of holo- morphic functions of proper contractions on Hilbert Introduction In a series of papers Ky Fan [14][17] developed a geometric theory of holo- morphic functions
Universal Properties of the Langevin Diffusion Coefficients
Dimitrios Giataganas; Hesam Soltanpanahi
2014-03-21
We show that in generic isotropic holographic theories the longitudinal Langevin diffusion coefficient along the string motion is larger compared to that of the transverse direction. We argue that this is a universal relation and we derive the generic conditions in order to be satisfied. A way to violate the relation is to consider anisotropic gauge/gravity dualities. We give an explicit example of this violation where the noise along the transverse direction is larger than the noise occurring along the quark motion. Moreover, we derive the effective world-sheet temperature for any generic theory and then the conditions for negative excess noise. We argue that isotropic theories can not have negative excess noise and we additionally remark that these conditions are difficult to get satisfied, indicating positivity of the excess noise, even in a large class of anisotropic holographic theories.
Kim, Yong Jung
WHAT IS A KINETIC EQUATION ? WHY DO WE NEED A KINETIC THEORY ? WHEN DO WE USE KINETIC EQUATIONS A KINETIC THEORY ? WHEN DO WE USE KINETIC EQUATIONS ? HILBERT'S 6TH PRO Outline What is a kinetic equation ? Why do we need a kinetic theory ? When do we use kinetic equations ? Hilbert's 6th problem
Accurate Langevin approaches to simulate Markovian channel dynamics
NASA Astrophysics Data System (ADS)
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2015-12-01
The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu’s classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.
Accurate Langevin approaches to simulate Markovian channel dynamics.
Huang, Yandong; Rüdiger, Sten; Shuai, Jianwei
2015-12-01
The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed. PMID:26403205
THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES
The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...
Behavioral Momentum Theory: Equations and Applications
ERIC Educational Resources Information Center
Nevin, John A.; Shahan, Timothy A.
2011-01-01
Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those…
Item Response Theory Equating Using Bayesian Informative Priors.
ERIC Educational Resources Information Center
de la Torre, Jimmy; Patz, Richard J.
This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…
Kinetic equation and clipping - two limits of wave turbulence theory
E. Kartashova
2005-09-05
Different dynamics, described by kinetic equation and clipping method is shown as well as a role of approximate resonances in wave turbulence theory. Applications of clipping method are sketched for gravity-capillary and drift waves. Brief discussion of possible transition from continuous spectrum (= kinetic equation) to discrete spectrum (= clipping) is given at the end.
Computationally sound implementations of equational theories against passive adversaries I
International Association for Cryptologic Research (IACR)
Computationally sound implementations of equational theories against passive adversaries I Mathieu on the computational soundness of static equivalence, a standard tool in cryptographic pi calculi. We present a soundness criterion, which for many theories is not only su#cient but also necessary. Finally, to illustrate
Computationally sound implementations of equational theories against passive adversaries6
International Association for Cryptologic Research (IACR)
Computationally sound implementations of equational theories against passive adversaries6 Mathieu on the computational soundness of static equivalence, a standard tool in cryptographic pi calculi. We present a soundness criterion, which for many theories is not only sufficient but also necessary. Finally
Dyson-Schwinger equations in the theory of computation
Colleen Delaney; Matilde Marcolli
2015-01-24
Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of algorithms computing primitive and partial recursive functions and in the halting problem.
Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.; Evans, James W.
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.
Boltzmann equation in classical and quantum field theory
Jeon, Sangyong
2005-07-01
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given.
NASA Astrophysics Data System (ADS)
Fodor, Z.; Katz, S. D.; Sexty, D.; Török, C.
2015-11-01
We study lattice QCD at nonvanishing chemical potential using the complex Langevin equation. We compare the results with multiparameter reweighting both from ? =0 and phase-quenched ensembles. We find a good agreement for lattice spacings below ?0.15 fm . On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on Nt=4 , 6 and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
Combined Langevin dynamics/Monte-Carlo simulations of the non-equilibrium ferrofluid remagnetization
NASA Astrophysics Data System (ADS)
Berkov, D. V.; Gorn, N.; Stock, D.
2004-05-01
We present a powerful method for simulations of fast remagnetization processes in ferrofluids which combines the stochastic (Langevin) dynamics and Monte-Carlo method. Our Langevin equations for the description of ferrofluid dynamics include both the mechanical (translational and rotational particle motion) and magnetic (rotation of the magnetic moment with respect to the particle) degrees of freedom. As an application example we present new physical results concerning the dependence of the magnetization relaxation in ferrofluids after switching off the external field.
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.
Boltzmann-Langevin One-Body dynamics for fermionic systems
P. Napolitani; M. Colonna
2013-02-01
A full implementation of the Boltzmann-Langevin equation for fermionic systems is introduced in a transport model for dissipative collisions among heavy nuclei. Fluctuations are injected in phase space and not, like in more conventional approaches, as a projection on suitable subspaces. The advantage of this model is to be specifically adapted to describe processes characterised by instabilities, like the formation of fragments from a hot nuclear system, and by dissipation, like the transparency in nucleus-nucleus collisions.
Activity coefficients in aqueous salt solutions: 2, Hydration theory equations
Wolery, T.J.; Jackson, K.J.
1989-08-01
A new set of phenomenological equations for describing the activity coefficients of aqueous electrolytes has been derived, based on the hydration theory concept of Stokes and Robinson, but using the differentiate down'' approach in which an expression is first defined for the excess Gibbs energy. Separate equations are given for the activity of water and the activity coefficients of ionic solutes. The new equations incorporate an empirical but thermodynamically consistent scheme for using an average ion size parameter in the Debye-Hueckel part of the model. This permits the new equations to be applied to mixtures of aqueous electrolytes. The new equations, applied to the case of a pure aqueous electrolyte, do not reduce to the familiar Stokes-Robinson equation owing to a minor difference in how the Debye-Hueckel model is presumed to apply to formally hydrated solutes. As a first step in evaluating the usefulness of the equations, we have fit a two-parameter'' (ion size plus hydration number) model to data for a number of pure aqueous electrolytes. The quality of the fits is excellent in many cases, but there are indications that more satisfactory results would be obtained by fixing reasonable values for the ion sizes and compensating for the loss of a fitting parameter by including ion pairs in the models, by including virial coefficient terms in the equations, or both. 17 refs., 3 figs., 1 tab.
Translating Words into Equations: A Cognitive Load Theory Approach
ERIC Educational Resources Information Center
Pawley, Duncan; Ayres, Paul; Cooper, Martin; Sweller, John
2005-01-01
The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a…
Control theory based airfoil design using the Euler equations
NASA Technical Reports Server (NTRS)
Jameson, Antony; Reuther, James
1994-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.
Perturbation theory of a symmetric center within Liénard equations
NASA Astrophysics Data System (ADS)
Françoise, Jean-Pierre; Xiao, Dongmei
2015-09-01
In this article, we introduce the use of Lambert function to develop further the global perturbation theory of an integrable Liénard equation which displays a symmetric center. We prove a global Morse lemma for the first integral and deduce the existence of an associated Picard-Fuchs system. We revisit previous contributions to first-order perturbation theory with the help of these new analytic techniques and in particular, we check that the fundamental integrals are linearly independent. The Lambert function allows to find an expansion formula for these integrals. We also study the possibility to develop a higher-order perturbation theory. The algorithm of the successive derivatives works in general in the class of analytic functions on the domain D where the level sets of the first integral are ovals. We end the article with some results on the first integral of a symmetric Liénard equation deduced from the algorithm of successive derivatives.
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.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism
NASA Astrophysics Data System (ADS)
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436
Vaclav Zatloukal
2015-10-20
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory. Throughout, we use the mathematical formalism of geometric algebra and geometric calculus, which allows to perform completely coordinate-free manipulations.
Yang, Jianke
. The first one is the perturba- tion theory based on the inverse scattering transform IST 1,2 , which hasDirect 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
Black-Scholes equation from Gauge Theory of Arbitrage
Kirill Ilinski; Gleb Kalinin
1998-10-26
We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators reaction on it. The model accounts for both violation of the no-arbitrage constraint and non-Brownian price walks which resemble real financial data. The correction is nonlocal and transform the differential Black-Scholes equation to an integro-differential one.
Cosmological post-Newtonian equations from nonlinear perturbation theory
Noh, Hyerim; Hwang, Jai-chan E-mail: jchan@knu.ac.kr
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.
The Kelvin equation and self-consistent nucleation theory
Wilemski, G.
1995-07-15
Issues of self-consistency are reviewed for several unary equilibrium size distributions based on the capillarity approximation. Some apparent difficulties of interpretation are resolved. In terms of the kinetic approach to nucleation theory, the influence of self-consistency on the nucleation rate is shown to arise entirely from differences in the dimer evaporation rates for nearly all versions of classical theory. The nucleation rate behavior of the Kelvin model is explored. In this model, the Kelvin equation is used to prescribe all cluster evaporation rates. Nucleation rates predicted by the Kelvin model are quantitatively similar to those of the self-consistent classical (SCC) theory, but not to other simple versions of the classical theory. This behavior arises entirely from the relatively close coincidence of the SCC and Kelvin dimer evaporation rates. This means that, for the distribution-based versions of classical theory, the SCC model is the closest analogue of the Kelvin model. Because the Kelvin equation is fundamentally inadequate for very small clusters, the close relationship between the Kelvin and SCC formulations indicates that both are equally lacking in fundamental justification. The Kelvin model may, however, have some pragmatic utility, and a simple analytical rate expression is also derived for it to simplify the calculation of nucleation rates for this model. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
String, dilaton and divisor equation in Symplectic Field Theory
Oliver Fabert; Paolo Rossi
2011-04-30
Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an infinite number of symmetries of such systems . As in Gromov-Witten theory, the study of the topological meaning of gravitational descendants yields new differential equations for the SFT Hamiltonian, where the key point is to understand the dependence of the algebraic constructions on choices of auxiliary data like contact form, cylindrical almost complex structure, abstract perturbations, differential forms and coherent collections of sections used to define gravitational descendants.
Master equation based steady-state cluster perturbation theory
NASA Astrophysics Data System (ADS)
Nuss, Martin; Dorn, Gerhard; Dorda, Antonius; von der Linden, Wolfgang; Arrigoni, Enrico
2015-09-01
A simple and efficient approximation scheme to study electronic transport characteristics of strongly correlated nanodevices, molecular junctions, or heterostructures out of equilibrium is provided by steady-state cluster perturbation theory. In this work, we improve the starting point of this perturbative, nonequilibrium Green's function based method. Specifically, we employ an improved unperturbed (so-called reference) state ??S, constructed as the steady state of a quantum master equation within the Born-Markov approximation. This resulting hybrid method inherits beneficial aspects of both the quantum master equation as well as the nonequilibrium Green's function technique. We benchmark this scheme on two experimentally relevant systems in the single-electron transistor regime: an electron-electron interaction based quantum diode and a triple quantum dot ring junction, which both feature negative differential conductance. The results of this method improve significantly with respect to the plain quantum master equation treatment at modest additional computational cost.
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.
On a relativistic Fokker-Planck equation in kinetic theory
José Antonio Alcántara Félix; Simone Calogero
2011-05-13
A relativistic kinetic Fokker-Planck equation that has been recently proposed in the physical literature is studied. It is shown that, in contrast to other existing relativistic models, the one considered in this paper is invariant under Lorentz transformations in the absence of friction. A similar property (invariance by Galilean transformations in the absence of friction) is verified in the non-relativistic case. In the first part of the paper some fundamental mathematical properties of the relativistic Fokker-Planck equation are established. In particular, it is proved that the model is compatible with the finite propagation speed of particles in relativity. In the second part of the paper, two non-linear relativistic mean-field models are introduced. One is obtained by coupling the relativistic Fokker-Planck equation to the Maxwell equations of electrodynamics, and is therefore of interest in plasma physics. The other mean-field model couples the Fokker-Planck dynamics to a relativistic scalar theory of gravity (the Nordstr\\"om theory) and is therefore of interest in gravitational physics. In both cases the existence of steady states for all possible prescribed values of the mass is established. In the gravitational case this result is better than for the corresponding non-relativistic model, the Vlasov-Poisson-Fokker-Planck system, for which existence of steady states is known only for small mass.
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.
Inverse scattering theory of the heat equation for a perturbed one-soliton potential
Prinari, Barbara
Inverse scattering theory of the heat equation for a perturbed one-soliton potential M. Boiti and F The inverse scattering theory of the heat equation is developed for a special sub- class of potentials to the KPI equation, a new general approach to the inverse scattering theory was introduced, which was called
The lattice gluon propagator in numerical stochastic perturbation theory
The lattice gluon propagator in numerical stochastic perturbation theory E.-M. Ilgenfritz1, H. Torrero (Regensburg) Talk E.-M. Ilgenfritz (Berlin) Gluon propagator in NSPT Strong QCD at St. Goar 1 / 31 Langevin equation 3 Gluon propagator and NSPT Lattice gluon propagator Perturbative gluon propagator
Integrability of generalized (matrix) Ernst equations in string theory
G. A. Alekseev
2005-03-02
The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\\times 2d$-linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.
Justification of the complex Langevin method with the gauge cooling procedure
Nagata, Keitaro; Shimasaki, Shinji
2015-01-01
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus...
Maxwell's Equations, The Euler Index and Morse Theory
Carlos Valero
2013-11-04
We show show that the singularities of the Fresnel surface for Maxwell's equation on an anisotrpic material can be accounted from purely topological considerations. The importance of these singularities is that they explain the phenomenon of conical refraction predicted by Hamilton. We show how to de-singularise the Fresnel surface, which will allow us to use Morse theory to find lower bounds for the number of critical wave velocities inside the material under consideration. Finally, we propose a program to generalise the results obtained to the general case of hyperbolic differential operators on differentiable bundles.
Non-perturbative evolution equations for the tricritical theory
Flavio S. Nogueira
1996-12-23
The N component scalar tricritical theory is considered in a non-perturbative setting. We derive non-perturbative beta functions for the relevant couplings in $d\\leq 3$. The beta functions are obtained through the use of an exact evolution equation for the so called effective average action. In d=3 it is established the existence of an ultraviolet stable fixed point for N>4. This confirms earlier results obtained using the 1/N expansion where such a fixed point is believed to exist at least for $N\\gtrsim 1000$.
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.
Relative invariants, difference equations, and the Picard-Vessiot theory
Katsutoshi Amano
2006-12-21
This is a compilation of three separated studies. The main part (Part 3) deals with a unified Picard-Vessiot theory including Picard-Vessiot theories of differential and difference equations. Changes: [v1 -> v2] Corrected descriptions on "ZXi-linearly independece" in Part 2 (p11, p13, p16) [v2 -> v3] The proof of Proposition 3.5.7 (iii) in v2 is not completed. (Only the proof of Proposition 3.5.8 (ii) is influenced and a revised proof is given.) [v3 -> v4] Lemma 3.5.10 in the previous version is false (see Remark 3.5.10 in the presented version). The proof of Prop. 3.5.9 (ii) and the proof of Lemma 3.9.9 are influenced and revised proofs are given. There are several minor changes too. [v4 -> v5] Added some explanation before Contents, several minor changes. This shall be the final replacement.
Alexander Gorbatsievich; Ernst Schmutzer
2012-05-17
The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.
Part I Kinetic Theory Asymptotic solutions of the nonlinear Boltzmann equation
Luding, Stefan
Contents Part I Kinetic Theory Asymptotic solutions of the nonlinear Boltzmann equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Kinetic integrals in the kinetic theory of dissipative gases Thorsten P¨oschel, Nikolai Meerson . . . . . . . . . . . . . . . . . . . . . . . . 247 Kinetic theory for inertia flows of dilute
Wavelet theory for solution of the neutron diffusion equation
Cho, N.Z.; Park, C.J.
1996-11-01
The authors solve the neutron diffusion equation by a wavelet Galerkin scheme in this paper. Wavelet functions are generated by dilation and translation operation on a scaling function. The wavelet functions are localized in space and have a recursive property, so these properties may be utilized to solve a differential equation that has severe stiffness. The wavelet Galerkin method (WGM) represents the solution as a summation of Daubechies` scaling functions, which are also used as the weighting function. The Daubechies` scaling functions have the properties of orthogonality and high smoothness. Unlike the finite element method, the weighting function is the Daubechies` scaling function, and the unknowns determined are not the fluxes of the nodes but the coefficients of the scaling functions. The scaling functions are overlapping in the nodes and require special treatment at interfaces between nodes and at the boundaries. They tested the WGM with several diffusion theory problems in reactor physics. The solutions are very accurate with increasing Daubechies` order and dilation order. The boundary conditions are also satisfied very well. In particular, the WGM provides very accurate solutions for heterogeneous problems in which the flux distribution exhibits very steep gradients. They conclude that it is worthwhile investigating further the WGM for reactor physics problems and that numerical integration and acceleration of the matrix equation must be improved so as to reduce computing time.
Pictures and equations of motion in Lagrangian quantum field theory
Bozhidar Z. Iliev
2003-02-01
The Heisenberg, interaction, and Schr\\"odinger pictures of motion are considered in Lagrangian (canonical) quantum field theory. The equations of motion (for state vectors and field operators) are derived for arbitrary Lagrangians which are polynomial or convergent power series in field operators and their first derivatives. The general links between different time-dependent pictures of motion are derived. It is pointed that all of them admit covariant formulation, similar to the one of interaction picture. A new picture, called the momentum picture, is proposed. It is a 4-dimensional analogue of the Schr\\"odinger picture of quantum mechanics as in it the state vectors are spacetime-dependent, while the field operators are constant relative to the spacetime. The equations of motion in momentum picture are derived and partially discussed. In particular, the ones for the field operators turn to be of algebraic type. The general idea of covariant pictures of motion is presented. The equations of motion in these pictures are derived.
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.
Multiphoton-scattering theory and generalized master equations
NASA Astrophysics Data System (ADS)
Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio
2015-11-01
We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.
Multi-photon Scattering Theory and Generalized Master Equations
Tao Shi; Darrick E. Chang; J. Ignacio Cirac
2015-07-30
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in- and out- states. For the case of few incident photons in the waveguide, we also re-derive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the forth one, we show how a quantum emitter can generate entanglement of out-going photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.
Complex Langevin simulation of chiral symmetry restoration at finite baryonic density
NASA Astrophysics Data System (ADS)
Ilgenfritz, Ernst-Michael
1986-12-01
A recently proposed effective SU(3) spin model with chiral order parameter is studied by means of the complex Langevin equation. A first-order chiral symmetry restoring and deconfining transition is observed at sufficiently low temperature at finite baryonic density. Permanent address: Sektion Physik, Karl-Marx Universität, DDR-7010 Leipzig, German Democratic Republic.
Anisotropic Spheres with Barotropic Equation of State in Bimetric Theory of Relativity
Naveen Bijalwan
2011-07-13
Recently, Khadekar (2007) presented the solutions with uniform energy density for anisotropic spheres in bimetric theory. We present here a general analytic solution to the field equations in bimetric theory for anisotropic fluids for a general barotropic equation of state by representing equations in terms for effective radial pressure . We list and discuss some old and new solutions which fall in this category.
Minimum bases for equational theories of groups and rings: The work of Alfred Tarski
McNulty, George F.
Minimum bases for equational theories of groups and rings: The work of Alfred Tarski and Thomas Abstract Suppose that T is an equational theory of groups or of rings. If T is finitely axioma- tizable, then there is a least number Âµ so that T can be axiomatized by Âµ equations. This Âµ can depend on the operation symbols
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics
Cai, David
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics 2006; accepted 28 June 2006 Abstract Recently developed kinetic theory and related closures the moment equations of the kinetic theory are illustrated with numerical examples. It is further
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
Nuclear Density Functional Theory and the Equation of State
Yeunhwan Lim
2011-04-06
A nuclear density functional can be used to find the binding energy and shell structure of nuclei and the energy gap in superconducting nuclear matter. In this paper, we study the possible application of a nuclear density functional theory to nuclear astrophysics. From energy density functional theory, we can deduce the interaction between nucleons to find a rough estimate of the charge radius of the specific nuclei. Compared to the Finite-Range Thomas Fermi model, we include three-body forces, which might be important at densities several times that of nuclear matter density. We also add the momentum dependent interaction to take into account the effective mass of the nucleons. We study matter in the neutron star crust using the Wigner-Seitz cell method. By constructing the mass-radius relation of neutron stars and investigating lepton-rich nuclear matter in proto-neutron stars, we find that the density functional can be used to construct an equation of state of hot dense matter.
Complex Langevin simulation of quantum vortices in a Bose-Einstein condensate
Tomoya Hayata; Arata Yamamoto
2015-11-04
The ab-initio simulation of quantum vortices in a Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the nonrelativistic boson field theory at finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.
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
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.
Note on a well-known equation in cosmological perturbation theory which is in error
Hwang, Jai-chan; Park, Chan-Gyung; Noh, Hyerim
2010-08-15
We have a well-known equation in cosmological perturbation theory which appeared only by several simple algebraic errors made in many textbooks. There have been attempts to modify Newtonian equations aiming to reproduce that incorrect equation. We clarify why such attempts are wrong, present the correct equation to try in the modification, and explain its own limitation as well. We show that any form of density perturbation equation is possible by a suitable gauge condition.
Heavy quark master equations in the Lindblad form at high temperatures
Yukinao Akamatsu
2015-04-13
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 Schroedinger equations with stochastic potential.
Justification of the complex Langevin method with the gauge cooling procedure
Keitaro Nagata; Jun Nishimura; Shinji Shimasaki
2015-09-18
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooling was introduced and the full QCD simulation at finite density has been made possible in the high temperature (deconfined) phase or with heavy quarks. Here we provide a rigorous justification of the complex Langevin method including the gauge cooling procedure. We first show that the gauge cooling can be formulated as an extra term in the complex Langevin equation involving a gauge transformation parameter, which is chosen appropriately as a function of the configuration before cooling. The probability distribution of the complexified dynamical variables is modified by this extra term. However, this modification is shown not to affect the Fokker-Planck equation for the corresponding complex weight as far as observables are restricted to gauge invariant ones. Thus we demonstrate explicitly that the gauge cooling can be used as a viable technique to satisfy the convergence conditions for the complex Langevin method. We also discuss the "gauge cooling" in 0-dimensional systems such as vector models or matrix models.
Modern integral equation techniques for quantum reactive scattering theory
Auerbach, S.M.
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
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.
Theories and Algorithms for Several Nonlinear Matrix Equations
Ming, Ping-bing
symmetric nonlinear matrix equation (NME), nonsymmetric algebraic Riccati equation (NARE), and quadratic and algorithms about the nonsymmetric algebraic Riccati equation(NARE). Firstly, we study perturbation bound algorithm(SDA), for computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati
Kinetic-theory approach to Gluon Self-energy beyond Hard Thermal Loops
Zheng Xiaoping; Li Jiarong
2002-02-16
We compare the effective dynamics of soft fields, based on temperature field theory, with the mean field dynamics from non-Abelian kinetic theory. We derive the polarization tensor with the leading logarithmic factor $\\log({gT\\over\\mu})$ from the effective Boltzmann-Langevin equation given by Litim and Manuel. The tensor is identical with effective one-loop contributions within the hard thermal loop effective theory.
AN APPROXIMATION THEORY FOR STRONGLY STABILIZING SOLUTIONS TO THE OPERATOR LQ RICCATI EQUATION
Curtain, Ruth F.
. linear quadratic control problem, algebraic Riccati equation on Hilbert space, dissipative systems of algebraic Riccati equations. Many of the papers use an approach based on approximation results for C 0AN APPROXIMATION THEORY FOR STRONGLY STABILIZING SOLUTIONS TO THE OPERATOR LQ RICCATI EQUATION J
Solution to the nonlinear field equations of ten dimensional supersymmetric Yang-Mills theory
NASA Astrophysics Data System (ADS)
Mafra, Carlos R.; Schlotterer, Oliver
2015-09-01
In this paper, we present a formal solution to the nonlinear field equations of ten-dimensional super Yang-Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher-mass dimensions are defined and their equations of motion are spelled out.
Disabling equational theories in unification for cryptographic protocol analysis through tagging
Malladi, Sreekanth
2010-01-01
In this paper, we show a new tagging scheme for cryptographic protocol messages. Under this tagging, equational theories of operators such as exclusive-or, binary addition etc. are effectively disabled, when terms are unified. We believe that this result has a significant impact on protocol analysis and security, since unification is at the heart of symbolic protocol analysis. Hence, disabling equational theories in unification implies disabling them altogether in protocol analysis for most operators and theories.
Existence of a solution to an equation arising from the theory of Mean Field Games
NASA Astrophysics Data System (ADS)
Gangbo, Wilfrid; ?wi?ch, Andrzej
2015-12-01
We construct a small time strong solution to a nonlocal Hamilton-Jacobi equation (1.1) introduced in [48], the so-called master equation, originating from the theory of Mean Field Games. We discover a link between metric viscosity solutions to local Hamilton-Jacobi equations studied in [2,19,20] and solutions to (1.1). As a consequence we recover the existence of solutions to the First Order Mean Field Games equations (1.2), first proved in [48], and make a more rigorous connection between the master equation (1.1) and the Mean Field Games equations (1.2).
The Basic Theory 2.1 Weierstrass Equations
, . . . , a6 are constants. This more general form (we'll call it the gen- eralized Weierstrass equation somewhat more general equations of the form y2 + a1xy + a3y = x3 + a2x2 + a4x + a6, (2.1) where a1
Stellar convection theory. I - The anelastic modal equations
NASA Technical Reports Server (NTRS)
Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J.-P.
1976-01-01
Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed.
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
On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations
Michael K. -H. Kiessling; Carlo Lancellotti
2004-09-27
We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.
Study of a Model Equation in Detonation Theory
Faria, Luiz M.
Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 ...
Quantum theory of rotational isomerism and Hill equation
NASA Astrophysics Data System (ADS)
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.
2012-06-01
The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schrödinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schrödinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schrödinger equation spectrum the "right" points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schrödinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.
Quantum theory of rotational isomerism and Hill equation
Ugulava, A.; Toklikishvili, Z.; Chkhaidze, S.; Abramishvili, R.; Chotorlishvili, L.
2012-06-15
The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schroedinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schroedinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schroedinger equation spectrum the 'right' points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schroedinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.
NASA Astrophysics Data System (ADS)
Haddad, L. H.; Carr, Lincoln D.
2015-09-01
We present the theoretical and mathematical foundations of stability analysis for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination of s-wave scattering for bosons and lattice interaction places constraints on the mean-field description, and hence on vortex configurations in the Bloch-envelope function near the Dirac point. A full derivation of the relativistic linear stability equations (RLSE) is presented by two independent methods to ensure veracity of our results. Solutions of the RLSE are used to compute fluctuations and lifetimes of vortex solutions of the nonlinear Dirac equation, which include Anderson-Toulouse skyrmions with lifetime ? 4 s. Beyond vortex stabilities the RLSE provide insight into the character of collective superfluid excitations, which we find to encode several established theories of physics. In particular, the RLSE reduce to the Andreev equations, in the nonrelativistic and semiclassical limits, the Majorana equation, inside vortex cores, and the Dirac-Bogoliubov-de Gennes equations, when nearest-neighbor interactions are included. Furthermore, by tuning a mass gap, relative strengths of various spinor couplings, for the small and large quasiparticle momentum regimes, we obtain weak-strong Bardeen-Cooper-Schrieffer superconductivity, as well as fundamental wave equations such as Schrödinger, Dirac, Klein-Gordon, and Bogoliubov-de Gennes equations. Our results apply equally to a strongly spin-orbit coupled BEC in which the Laplacian contribution can be neglected.
Dynamic field theory and equations of motion in cosmology
Kopeikin, Sergei M.; Petrov, Alexander N.
2014-11-15
We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of 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.
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.
Quantum motion equation and Poincare translation invariance of noncommutative field theory
Zheng Ze Ma
2006-03-16
We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative $\\phi^{\\star4}$ scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity. Then we demonstrate the Poincar{\\' e} translation invariance for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity.
Alex Kaivarainen
2000-03-25
1. The state equation for real gas 2. New state equation for condensed matter 3.Vapor pressure 4. Surface tension 5. Mesoscopic theory of thermal conductivity 6. Mesoscopic theory of viscosity for liquids and solids 7. Brownian diffusion 8. Self-diffusion in liquids and solids 9. Mesoscopic approach to proton conductivity in water, ice and other systems, containing hydrogen bonds 10. Regulation of pH and shining of water by electromagnetic and acoustic fields
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|red-shift effect acts as a blue-shift instability when solving the wave equation backwards.
Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics
Yang, Jianke
Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics SchroÂ¨dinger equations, which govern the pulse propagation in birefringent nonlinear optical fibers in optical fibers has been studied over 30 years. The idea of using optical solitons as information bits
NASA Technical Reports Server (NTRS)
Pai, S. I.
1973-01-01
The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.
Z. Fodor; S. D. Katz; D. Sexty; C. Török
2015-10-27
We study lattice QCD at non-vanishing chemical potential using the complex Langevin equation. We compare the results with multi-parameter reweighting both from $\\mu=0$ and phase quenched ensembles. We find a good agreement for lattice spacings below $\\approx$0.15 fm. On coarser lattices the complex Langevin approach breaks down. Four flavors of staggered fermions are used on $N_t=4, 6$ and 8 lattices. For one ensemble we also use two flavors to investigate the effects of rooting.
Analytical approach for the Floquet theory of delay differential equations.
Simmendinger, C; Wunderlin, A; Pelster, A
1999-05-01
We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincaré-Lindstedt and the Shohat expansions, which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows us to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions. PMID:11969494
Effective equations and the inverse cascade theory for Kolmogorov flows
NASA Technical Reports Server (NTRS)
Weinan, E.; Shu, Chi-Wang
1992-01-01
We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.
NASA Astrophysics Data System (ADS)
Mücke, Tanja A.; Wächter, Matthias; Milan, Patrick; Peinke, Joachim
2015-11-01
Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power curve for different data samplings. We show, how to get reliable results from synthetic data and verify the applicability of the method for field measurements with ultra-sonic, cup and Lidar measurements. The independence of the fixed points on site specific turbulence effects is also confirmed with the numerical model. Furthermore, we demonstrate the potential of the Langevin approach to detect failures in the conversion process and thus show the potential of the Langevin approach for a condition monitoring system.
Spherically symmetric solutions of modified field equations in f(R) theories of gravity
Tuomas Multamaki; Iiro Vilja
2006-10-25
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In particular, we show that for a large class models, including e.g. the f(R)=R-\\mu^4/R model, the Schwarzschild-de Sitter metric is an exact solution of the field equations. The significance of these solutions is discussed in light of solar system constraints on $f(R)$ theories of gravity.
Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method
NASA Astrophysics Data System (ADS)
Fukushima, Kenji; Tanizaki, Yuya
2015-11-01
The Lefschetz-thimble method, i.e., integration along the steepest descent cycles, is a way to avoid the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave functions on a grid using a toy model and confirm their well-localized behavior.
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.
Application of integral equation theory to polyolefin liquids and blends
Curro, J.G.; Weinhold, J.D.
1997-11-01
The ability to model the packing of polymers in melts and blends is important in many polymer applications. One significant application is the development of new polymer blends. It would be exceedingly helpful to the materials chemist if molecular modeling could be employed to predict the thermodynamics and phase behavior of hypothetical polymer alloys before embarking on a time consuming and expensive synthesis program. The well known Flory-Huggins theory has been remarkably successful in describing many aspects of polymer mixing from a qualitative point of view. This theory is known, however, to suffer from several deficiencies which can be traceable to the fact that: (1) it is a lattice model requiring both monomer components to have the same volume; and (2) a mean field or random mixing approximation is made which effectively ignores chain connectivity. Because of these limitations the Flory-Huggins theory does not include packing effects and cannot be used to make quantitative molecular engineering calculations. Recently Curro and Schweizer developed a new approach for treating polymer liquids and mixtures which the authors call PRISM theory. This is an extension to polymers of the Reference Interaction Site Model (RISM Theory) developed by Chandler and Andersen to describe the statistical mechanics of small molecule liquids. The PRISM theory is a continuous space description of a polymer liquid, which includes chain connectivity and nonrandom mixing effects in a computationally tractable manner. The primary output from PRISM calculations is the average structure or packing of the amorphous liquid given by the radial distribution function denoted as g(r). This radial distribution function is employed to deduce thermodynamic or structural properties of interest. Here, the authors describe the theoretical approach and demonstrate its application to polyethylene, isotactic polypropylene, syndiotactic polypropylene, and polyisobutylene liquids and blends.
Langevin dynamics in inhomogeneous media: re-examining the Itô-Stratonovich dilemma.
Farago, Oded; Grønbech-Jensen, Niels
2014-01-01
The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral, known as the Itô-Stratonovich dilemma, is avoided since all interpretations converge to the same solution in the limit of small time steps. We use a newly developed method for Langevin simulations to measure the probability distribution of a particle diffusing in a flat potential. Our results reveal that both the Itô and Stratonovich interpretations converge very slowly to the uniform equilibrium distribution for vanishing time step sizes. Three other conventions exhibit significantly improved accuracy: (i) the "isothermal" (Hänggi) convention, (ii) the Stratonovich convention corrected by a drift term, and (iii) a newly proposed convention employing two different effective friction coefficients representing two different averages of the friction function during the time step. We argue that the most physically accurate dynamical description is provided by the third convention, in which the particle experiences a drift originating from the dissipation instead of the fluctuation term. This feature is directly related to the fact that the drift is a result of an inertial effect that cannot be well understood in the Brownian, overdamped limit of the Langevin equation. PMID:24580354
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.
Pure Gauge Configurations and Solutions to Fermionic Superstring Field Theories Equations of Motion
I. Ya. Aref'eva; R. V. Gorbachev; P. B. Medvedev
2009-03-15
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theories are discussed. To have a possibility to deal 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 parameterized by wedge states play an essential role. The matrix form of this parametrization for the 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 equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.
Kinetic Theory for Metallic Clusters II. Klimontovich Equation Approach
Bonitz, Michael
. The treatment of collective excitations in such an inhomogeneous plasma is described briefly. 1. Introduction a "simpler" field theory. All of non- equilibrium statistical mechanics is comprised of a solution of these fields. The difficult many-body problem is hidden in this final averaging process [4]. In quantum
Massless relativistic wave equations and quantum field theory
; models with nontrivial helicity. These constraints guarantee for example that one can embed the test reducibly on the test function space of the quantum field. The second one is a unitary and irreducible of nonscalar free quantum field theory on Minkowski space, one chooses as test function space H
Exact series model of Langevin transducers with internal losses.
Nishamol, P A; Ebenezer, D D
2014-03-01
An exact series method is presented to analyze classical Langevin transducers with arbitrary boundary conditions. The transducers consist of an axially polarized piezoelectric solid cylinder sandwiched between two elastic solid cylinders. All three cylinders are of the same diameter. The length to diameter ratio is arbitrary. Complex piezoelectric and elastic coefficients are used to model internal losses. Solutions to the exact linearized governing equations for each cylinder include four series. Each term in each series is an exact solution to the governing equations. Bessel and trigonometric functions that form complete and orthogonal sets in the radial and axial directions, respectively, are used in the series. Asymmetric transducers and boundary conditions are modeled by using axially symmetric and anti-symmetric sets of functions. All interface and boundary conditions are satisfied in a weighted-average sense. The computed input electrical admittance, displacement, and stress in transducers are presented in tables and figures, and are in very good agreement with those obtained using atila-a finite element package for the analysis of sonar transducers. For all the transducers considered in the analysis, the maximum difference between the first three resonance frequencies calculated using the present method and atila is less than 0.03%. PMID:24606259
Irreversible Langevin samplers and variance reduction: a large deviations approach
NASA Astrophysics Data System (ADS)
Rey-Bellet, Luc; Spiliopoulos, Konstantinos
2015-07-01
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists of constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e. they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose variance is not reduced reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.
Irreversible Langevin samplers and variance reduction: a large deviation approach
Luc Rey-Bellet; Kostantinos Spiliopoulos
2015-04-22
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov process one can then compute, approximately, expectations of observables with respect to the target distribution. Often the Markov processes used in practice are time-reversible (i.e., they satisfy detailed balance), but our main goal here is to assess and quantify how the addition of a non-reversible part to the process can be used to improve the sampling properties. We focus on the diffusion setting (overdamped Langevin equations) where the drift consists of a gradient vector field as well as another drift which breaks the reversibility of the process but is chosen to preserve the Gibbs measure. In this paper we use the large deviation rate function for the empirical measure as a tool to analyze the speed of convergence to the invariant measure. We show that the addition of an irreversible drift leads to a larger rate function and it strictly improves the speed of convergence of ergodic average for (generic smooth) observables. We also deduce from this result that the asymptotic variance decreases under the addition of the irreversible drift and we give an explicit characterization of the observables whose variance is not reduced reduced, in terms of a nonlinear Poisson equation. Our theoretical results are illustrated and supplemented by numerical simulations.
Theory of inert gas-condensing vapor thermoacoustics: transport equations.
Slaton, William V; Raspet, Richard; Hickey, Craig J; Hiller, Robert A
2002-10-01
The preceding paper [J. Acoust. Soc. Am. 112, 1414-1422 (2002)] derives the propagation equation for sound in an inert gas-condensing vapor mixture in a wet-walled pore with an imposed temperature gradient. In this paper the mass, enthalpy, heat, and work transport equations necessary to describe the steady-state operation of a wet-walled thermoacoustic refrigerator are derived and presented in a form suitable for numerical evaluation. The requirement that the refrigerator operate in the steady state imposes zero mass flux for each species through a cross section. This in turn leads to the evaluation of the mass flux of vapor in the system. The vapor transport and heat transport are shown to work in parallel to produce additional cooling power in the wet refrigerator. An idealized calculation of the coefficient of performance (COP) of a wet-walled thermoacoustic refrigerator is derived and evaluated for a refrigeration system. The results of this calculation indicate that the wet-walled system can improve the performance of thermoacoustic refrigerators. Several experimental and practical questions and problems that must be addressed before a practical device can be designed and tested are described. PMID:12398450
Consistency of Equations in the Second-Order Gauge-Invariant Cosmological Perturbation Theory
NASA Astrophysics Data System (ADS)
Nakamura, K.
2009-06-01
Along the general framework of the gauge-invariant perturbation theory developed in the papers [K.~Nakamura, Prog.~Theor.~Phys. 110 (2003), 723; Prog.~Theor.~Phys. 113 (2005), 481], we rederive the second-order Einstein equation on four-dimensional homogeneous isotropic background universe in a gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We also confirmed the consistency of all the equations of the second-order Einstein equation and the equations of motion for matter fields, which are derived in the paper [K.~Nakamura, arXiv:0804.3840]. This confirmation implies that all the derived equations of the second order are self-consistent and these equations are correct in this sense.
Gauge theories on noncommutative ?PN and Bogomol'nyi-Prasad-Sommerfield-like equations
NASA Astrophysics Data System (ADS)
Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi
2015-11-01
We give the Fock representation of a noncommutative ?PN and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ?PN. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Bogomol'nyi-Prasad-Sommerfield (BPS)-like equations on noncommutative ?P1 and ?P2 are derived from these actions. There are analogies between BPS-like equations on ?P1 and monopole equations on ?3 and BPS-like equations on ?P2 and instanton equations on ?8. We discuss solutions of these BPS-like equations.
Beyond complex Langevin equations I: two simple examples
Wosiek, Jacek
2015-01-01
By introducing a second complex variable, the integral relation between a complex density and the corresponding positive distribution is derived. Together with the positivity and normalizability conditions, this sum rule allows to construct explicitly equivalent pairs of distributions in simple cases discussed here. In particular the well known solution for a complex gaussian distribution is generalized to an arbitrary complex inverse dispersion parameter. This opens a possibility of positive representation of Feynman path integrals directly in the Minkowski time.
Complex Langevin dynamics in the SU(3) spin model at nonzero chemical potential revisited
Gert Aarts; Frank A. James
2012-01-25
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and assess in particular the justification of this approach, using analyticity at small mu^2 and the criteria for correctness developed recently. Finite-stepsize effects are discussed in some detail and a higher-order algorithm is employed to eliminate leading stepsize corrections. Our results strongly indicate that complex Langevin dynamics is reliable in this theory in both phases, including the critical region. This is in sharp contrast to the case of the XY model, where correct results were obtained in only part of the phase diagram.
Jin Shi Yin Dongsheng
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.
A theory of post-stall transients in axial compression systems. I - Development of equations
NASA Technical Reports Server (NTRS)
Moore, F. K.; Greitzer, E. M.
1985-01-01
An approximate theory is presented for post-stall transients in multistage axial compression systems. The theory leads to a set of three simultaneous nonlinear third-order partial differential equations for pressure rise, and average and disturbed values of flow coefficient, as functions of time and angle around the compressor. By a Galerkin procedure, angular dependence is averaged, and the equations become first order in time. These final equations are capable of describing the growth and possible decay of a rotating-stall cell during a compressor mass-flow transient. It is shown how rotating-stall-like and surgelike motions are coupled through these equations, and also how the instantaneous compressor pumping characteristic changes during the transient stall process.
Thermodynamics and structure of a two-dimensional electrolyte by integral equation theory
Aupic, Jana; Urbic, Tomaz
2014-05-14
Monte Carlo simulations and integral equation theory were used to predict the thermodynamics and structure of a two-dimensional Coulomb fluid. We checked the possibility that integral equations reproduce Kosterlitz-Thouless and vapor-liquid phase transitions of the electrolyte and critical points. Integral equation theory results were compared to Monte Carlo data and the correctness of selected closure relations was assessed. Among selected closures hypernetted-chain approximation results matched computer simulation data best, but these equations unfortunately break down at temperatures well above the Kosterlitz-Thouless transition. The Kovalenko-Hirata closure produces results even at very low temperatures and densities, but no sign of phase transition was detected.
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano; Mugnolo, Delio
2009-10-15
We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
Telleparallel Lagrange Geometry and a Unified Field Theory: Linearization of the Field Equations
M. I. Wanas; Nabil L. Youssef; A. M. Sid-Ahmed
2011-07-03
The present paper is a natural continuation of our previous paper: "Teleparallel Lagrange geometry and a unified field theory, Class. Quantum Grav., 27 (2010), 045005 (29pp)" \\cite{WNA}. In this paper, we apply a linearization scheme on the field equations obtained in \\cite{WNA}. Three important results under the linearization assumption are accomplished. First, the vertical fundamental geometric objects of the EAP-space loose their dependence on the positional argument $x$. Secondly, our linearized theory in the Cartan-type case coincides with the GFT in the first order of approximation. Finally, an approximate solution of the vertical field equations is obtained.
DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory
A. V. Kotikov; L. N. Lipatov
2001-12-28
We discuss DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the leading and next-to-leading approximations. Eigenvalues of the BFKL kernel in this model turn out to be analytic functions of the conformal spin. It allows us to find the residues of the anomalous dimensions of the twist-2 operators in the points j=1,0,-1, ... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. The holomorphic separability of the BFKL kernel and the integrability of the DGLAP dynamics in this model are also discussed.
Mücke, Tanja A; Milan, Patrick; Peinke, Joachim
2015-01-01
Based on the Langevin equation it has been proposed to obtain power curves for wind turbines from high frequency data of wind speed measurements u(t) and power output P (t). The two parts of the Langevin approach, power curve and drift field, give a comprehensive description of the conversion dynamic over the whole operating range of the wind turbine. The method deals with high frequent data instead of 10 min means. It is therefore possible to gain a reliable power curve already from a small amount of data per wind speed. Furthermore, the method is able to visualize multiple fixed points, which is e.g. characteristic for the transition from partial to full load or in case the conversion process deviates from the standard procedures. In order to gain a deeper knowledge it is essential that the method works not only for measured data but also for numerical wind turbine models and synthetic wind fields. Here, we characterize the dynamics of a detailed numerical wind turbine model and calculate the Langevin power...
On the consistent solution of the gap--equation for spontaneously broken $??^4$-theory
Herbert Nachbagauer
1994-10-07
We present a self--consistent solution of the finite temperature gap--equation for $\\lambda \\Phi^4$ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not only the so--called daisy and superdaisy graphs contribute to the resummed mass, but also resummed non--local diagrams are of the same order, thus altering the effective mass for small values of the latter.
Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form
NASA Astrophysics Data System (ADS)
Kim, Sunghan; Lee, Ki-Ahm
2015-08-01
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.
The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature
Bertolami, O.; Gomes, C. E-mail: claudio.gomes@fc.up.pt
2014-09-01
We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Approximating electronically excited states with equation-of-motion linear coupled-cluster theory
Byrd, Jason N; Perera, Ajith; Bartlett, Rodney J
2015-01-01
A new perturbative approach to canonical equation-of-motion coupled-cluster theory is presented using coupled-cluster perturbation theory. A second-order M{\\o}ller-Plesset partitioning of the Hamiltonian is used to obtain the well known equation-of-motion many-body perturbation theory (EOM-MBPT(2)) equations and two new equation-of-motion methods based on the linear coupled-cluster doubles (EOM-LCCD) and linear coupled-cluster singles and doubles (EOM-LCCSD) wavefunctions. This is achieved by performing a short-circuiting procedure on the MBPT(2) similarity transformed Hamiltonian. These new methods are benchmarked against very accurate theoretical and experimental spectra from 25 small organic molecules. It is found that the proposed methods have excellent agreement with canonical EOM-CCSD state for state orderings and relative excited state energies as well as acceptable quantitative agreement for absolute excitation energies compared with the best estimate theory and experimental spectra.
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…
Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions
NASA Astrophysics Data System (ADS)
Bikbaev, R. F.; Bobenko, A. I.; Its, A. R.
2014-02-01
Using the inverse scattering method, we study the XXZ Landau-Lifshitz equation well-known in the theory of ferromagnetism. We construct all elementary soliton-type excitations and study their interaction. We also obtain finite-gap solutions (in terms of theta functions) and select the real solutions among them.
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…
On the integro-di erential equation associated with di usive crack growth theory
Bath, University of
On the integro-di#11;erential equation associated with di#11;usive crack growth theory Y.A. Antipov, Seestrasse 92, Stuttgart 70174, Germany newline hjgao@mf.mpg.de Key words: di#11;usive crack, integro-di#11 that nucleation, propagation and linkage of interfacial cracks normal to the principal stress directions
Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory
ERIC Educational Resources Information Center
Brossman, Bradley Grant
2010-01-01
The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted.…
Perturbation theory for the diffusion equation by use of the moments of the generalized
Fantini, Sergio
with other numerical methods, such as the finite-element method3 (FEM) and the finite-difference method (FDMPerturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. II. Continuous-wave results Angelo Sassaroli Tufts University, Department
Hamiltonian Dyson-Schwinger and FRG Flow Equations of Yang-Mills Theory in Coulomb Gauge
Reinhardt, Hugo; Leder, Markus; Pawlowski, Jan M.; Weber, Axel
2011-05-23
A new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge is presented and solved for the static gluon and ghost propagators under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
NASA Astrophysics Data System (ADS)
Nakamura, K.
2007-01-01
Following the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid. 113 (2005), 481], we formulate second-order gauge invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe. We consider perturbations both in the universe dominated by a single perfect fluid and in that dominated by a single scalar field. We derive all the components of the Einstein equations in the case that the first-order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that second-order vector and tensor modes may be generated due to the mode-mode coupling of the linear-order scalar perturbations. We also briefly discuss the main progress of this work through comparison with previous works.
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
D. X. Horvath; S. Sotiriadis; G. Takacs
2015-10-06
We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to all methods available to treat integrable quantum quenches exactly. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provide a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
Initial states in integrable quantum field theory quenches from an integral equation hierarchy
Horvath, D X; Takacs, G
2015-01-01
We consider the problem of determining the initial state of integrable quantum field theory quenches in terms of the post-quench eigenstates. The corresponding overlaps are a fundamental input to all methods available to treat integrable quantum quenches exactly. We construct and examine an infinite integral equation hierarchy based on the form factor bootstrap, proposed earlier as a set of conditions determining the overlaps. Using quenches of the mass and interaction in Sinh-Gordon theory as a concrete example, we present theoretical arguments that the state has the squeezed coherent form expected for integrable quenches, and supporting an Ansatz for the solution of the hierarchy. Moreover we also develop an iterative method to solve numerically the lowest equation of the hierarchy. The iterative solution along with extensive numerical checks performed using the next equation of the hierarchy provide a strong numerical evidence that the proposed Ansatz gives a very good approximation for the solution.
Role of secondary instability theory and parabolized stability equations in transition modeling
NASA Technical Reports Server (NTRS)
El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.
1993-01-01
In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.
Transient intensity noise of semiconductor lasers; Experiments and comparison with theory
Czylwik, A., Eberle, W. )
1990-02-01
An experimental setup for the measurement of the non-stationary intensity fluctuations during the turn-on transient of semi-conductor lasers is presented. Measurements are carried out and compared with simulations, which are based on rate equations with Langevin fluctuation functions. Agreement between theory and measurements is found and is confirmed that the nonstationary intensity noise can be interpreted as timing jitter.
Equation of state for expanded fluid mercury: Variational theory with many-body interaction
NASA Astrophysics Data System (ADS)
Kitamura, Hikaru
2007-04-01
A variational associating fluid theory is proposed to describe equations of state for expanded fluid mercury. The theory is based on the soft-sphere variational theory, incorporating an ab initio diatomic potential and an attractive many-body potential; the latter is evaluated with quatnum chemical methods and expressed as a function of the local atomic coordination number and the nearest-neighbor distance. The resultant equation of state can reproduce the observed gas-liquid coexistence curve with good accuracy, without introducing phenomenological effective pair potentials. Various thermodynamic quantities such as pressure, isochoric thermal pressure coefficient, adiabatic sound velocity, and specific heat are calculated over a wide density-temperature range and compared with available experimental data.
Microscopic Theory of the Nuclear Equation of State and Neutron Star Structure
NASA Astrophysics Data System (ADS)
Baldo, Marcello; Burgio, Fiorella
The Bethe-Brueckner-Goldstone many-body theory of the Nuclear Equation of State is reviewed in some details. In the theory, one performs an expansion in terms of the Brueckner two-body scattering matrix and an ordering of the corresponding many-body diagrams according to the number of their hole-lines. Recent results are reported, both for symmetric and for pure neutron matter, based on realistic two-nucleon interactions. It is shown that there is strong evidence of convergence in the expansion. Once three-body forces are introduced, the phenomenological saturation point is reproduced and the theory is applied to the study of neutron star properties. One finds that in the interior of neutron stars the onset of hyperons strongly softens the Nuclear Equation of State. As a consequence, the maximum mass of neutron stars turns out to be at the lower limit of the present phenomenological observation.
On a derivation of the Boltzmann equation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Leiler, Gregor
The Boltzmann equation (BE) is a commonly used tool for the study of non-equilibrium many particle systems. It has been introduced in 1872 by Ludwig Boltzmann and has been widely generalized throughout the years. Today it is commonly used in physical applications, from the study of ordinary fluids to problems in particle Cosmology where Quantum Field Theoretical techniques are essential. Despite its numerous experimental successes, the conceptual basis of the BE is not entirely clear. For instance, it is well known that it is not a fundamental equation of physics like, say, the Heisenberg equation (HE). A natural question then arises whether it is possible to derive the BE from physical first principles, i.e. the Heisenberg equation in Quantum Field Theory. In this work we attempted to answer this question and succeeded in deriving the BE from the HE, thus further clarifying its conceptual status. In particular, the results we have obtained are as follows. Firstly, we establish the non-perturbative validity of what we call the "pre-Boltzmann equation". The crucial point here is that this latter equation is equivalent to the Heisenberg equation. Secondly, we proceed to consider various limits of the pre-Boltzmann equation, namly the "low density" and the "weak coupling" limits, to obtain two equations that can be considered as generalizations of the BE. These limits are always taken together with the "long time" limit, which allows us to interpret the BE as an appropriate long time limit of the HE. The generalization we obtain consists in additional "correction" terms to the usual Boltzmann collision factor, and can be associated to multiple particle scattering. Unlike the pre-Boltzmann equation, these latter results are only valid pertubatively. Finally, we briefly consider the possibility to extend these results beyond said limits and outline some important aspects in this case.
A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2015-10-01
This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.
Number-conserving master equation theory for a dilute Bose-Einstein condensate
Schelle, Alexej; Wellens, Thomas; Buchleitner, Andreas; Delande, Dominique
2011-01-15
We describe the transition of N weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and noncondensate thermalization, we derive a master equation for the condensate subsystem in the presence of the noncondensate environment under the inclusion of all two-body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakly interacting Bose-Einstein condensate is given by a Gibbs-Boltzmann thermal state of N noninteracting atoms.
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.
Hagedorn spectrum and equation of state of Yang-Mills theories
Michele Caselle; Alessandro Nada; Marco Panero
2015-09-23
We present a novel lattice calculation of the equation of state of SU(2) Yang-Mills theory in the confining phase. We show that a gas of massive, non-interacting glueballs describes remarkably well the results, provided that a bosonic closed-string model is used to derive an exponentially growing Hagedorn spectrum for the heavy glueball states with no free parameters. This effective model can be applied to SU(3) Yang-Mills theory and the theoretical prediction agrees nicely with the lattice results reported by Bors\\'anyi et al. in JHEP 07 (2012) 056.
Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory
NASA Astrophysics Data System (ADS)
Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio
2012-03-01
Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.
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.
Liao, David; Tlsty, Thea D
2014-08-01
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
NASA Astrophysics Data System (ADS)
Giraldi, Filippo
2015-09-01
The Schwinger-Keldysh nonequilibrium theory allows the description of various transport phenomena involving bosons (fermions) embedded in bosonic (fermionic) environments. The retarded Green's function obeys the Dyson equation and determines via its non-vanishing asymptotic behavior the dissipationless open dynamics. The appearance of this regime is conditioned by the existence of the solution of a general class of transcendental equations in complex domain that we study. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic, and special functions. The present analysis provides an analytical description of the thermal and temporal correlation function of two general observables of a quantum system in terms of the corresponding spectral function. Special integral properties of the spectral function guarantee non-vanishing asymptotic behavior of the correlation function.
NASA Astrophysics Data System (ADS)
Garnier, Josselin; Kalimeris, Konstantinos
2012-01-01
In this paper, a perturbation theory for the nonlinear Schrödinger equation with non-vanishing boundary conditions based on the inverse scattering transform is presented. It is applied to study the stability of the soliton propagation on a continuous-wave background. It is shown that the soliton is rather robust with respect to dispersive perturbations but it can be strongly affected by damping. In particular, it is shown that adiabatic approaches can underestimate the decay of the soliton energy.
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.
A Revisiting of the -Stability Theory of the Boltzmann Equation Near Global Maxwellians
NASA Astrophysics Data System (ADS)
Ha, Seung-Yeal; Xiao, Qinghua
2015-07-01
We study the -stability theory of the Boltzmann equation near a global Maxwellian. When an initial datum is a perturbation of a global Maxwellian, we show that the -distance between two classical solutions can be controlled by the initial data in a Lipschitz manner, which illustrates the Lipschitz continuity of the solution operator for the Boltzmann equation in -topology. Our local-in-time -stability results cover cutoff very soft potentials as well as non-cutoff hard and soft potentials. These cases were not treated in the previous work (Ha et al. in Arch Ration Mech Anal 197:657-688, 2010). Thus, our results together with the results in Ha et al. (2010) complete the -stability theory for the Boltzmann equation near a global Maxwellian. For this -stability estimate, we use the coercivity estimate of the linearized collision operator, the smallness of perturbation in a mixed Lebesgue norm, and Strichartz-type estimates of perturbation. We also show that for all classical solutions available in the literature, the Lipschitz constant can be chosen as independent of time to obtain the uniform -stability of the Boltzmann equation.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
George Chapline
2015-10-02
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations for this matrix wave function appear to be a promising starting point for resolving the unphysical features inherent in the general relativistic descriptions of gravitational collapse and the big bang.
NASA Astrophysics Data System (ADS)
Linscheid, A.; Sanna, A.; Essenberger, F.; Gross, E. K. U.
2015-07-01
We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory SpinSCDFT by extending the Hohenberg-Kohn theorem and constructing the noninteracting Kohn-Sham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham-Schlüter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.
Transport-level description of the sup 252 Cf-source method using the Langevin technique
Stolle, A.M.; Akcasu, A.Z. )
1991-01-01
The fluctuations in the neutron number density and detector outputs in a nuclear reactor can be analyzed conveniently by using the Langevin equation approach. This approach can be implemented at any level of approximation to describe the time evolution of the neutron population, from the most complete transport-level description to the very basic point reactor analysis of neutron number density fluctuations. In this summary, the complete space- and velocity-dependent transport-level formulation of the Langevin equation approach is applied to the analysis of the {sup 252}Cf-source-driven noise analysis (CSDNA) method, an experimental technique developed by J.T. Mihalczo at Oak Ridge National Laboratory, which makes use of noise analysis to determine the reactivity of subcritical media. From this analysis, a theoretical expression for the subcritical multiplication factor is obtained that can then be used to interpret the experimental data. Results at the transport level are in complete agreement with an independent derivation performed by Sutton and Doub, who used the probability density method to interpret the CSDNA experiment, but differed from other expressions that have appeared in the literature.
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation
NASA Astrophysics Data System (ADS)
Durán-Olivencia, Miguel A.; Lutsko, James F.
2015-09-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013), 10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.
Unification of classical nucleation theories via unified Itô-Stratonovich stochastic equation
Miguel A. Durán-Olivencia; James F. Lutsko
2015-08-29
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g. Zeldovich-Frenkel or Becker-D\\"oring-Tunitskii equations. Starting from a phenomenological stochastic differential equation a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J.F. Lutsko and M.A. Dur\\'an-Olivencia, J. Chem. Phys., 2013, 138, 244908] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios. In particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion or interface transfer.
Domenico Gazzillo; Achille Giacometti; Raffaele G. Della Valle; Elisabetta Venuti; Flavio Carsughi
1999-10-15
Integral equation of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of uncharged particles with polydispersity in size and energy parameters. Both hard spheres and Lennard-Jones interactions are considered. For polydisperse hard spheres, the scaling approximation is compared to theories utilized by small angle scattering experimentalists (decoupling approximation, local monodisperse approximation)and to the van der Waals one-fluid theory. The results are tested against predictions from analytical expressions, exact within the Percus-Yevick approximation. For polydisperse Lennard-Jones particles, the scaling approximation combined with a "modified hypernetted chain" integral equation, is tested against molecular dynamics data generated for the present work. Despite ist simplicity, the scaling approximation exhibits a satisfactory performance for both potentials and represents a considerable improvement over the above mentioned theories. Shortcomings of the proposed theory, its applicability to the analysis of experimental scattering data, and its possible extensions to different potentials are finally discussed.
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.
Géza, Makay
transport and in the traffic theory. Especially, the so-called quadratic integral equation of Chandrasekhar-integral equations encountered in nonlinear analysis. Also, the famous Chandrasekhar's integral equation
Stochastic quantization of real-time thermal field theory
Aguiar, T. C. de; Svaiter, N. F.; Menezes, G.
2010-10-15
We use the stochastic quantization method to obtain the free scalar propagator of a finite temperature field theory formulated in the Minkowski space-time. First, we use the Markovian stochastic quantization approach to present the two-point function of the theory. Second, we assume a Langevin equation with a memory kernel and a colored noise. The convergence of the Markovian and non-Markovian stochastic processes in the asymptotic limit of the fictitious time is obtained. Our formalism can be the starting point to discuss systems at finite temperature out of equilibrium.
Nakatsuji, Hiroshi Nakashima, Hiroyuki
2015-05-21
The Schrödinger equation (SE) and the antisymmetry principle constitute the governing principle of chemistry. A general method of solving the SE was presented before as the free complement (FC) theory, which gave highly accurate solutions for small atoms and molecules. We assume here to use the FC theory starting from the local valence bond wave function. When this theory is applied to larger molecules, antisymmetrizations of electronic wave functions become time-consuming and therefore, an additional breakthrough is necessary concerning the antisymmetry principle. Usually, in molecular calculations, we first construct the wave function to satisfy the antisymmetry rule, “electronic wave functions must be prescribed to be antisymmetric for all exchanges of electrons, otherwise bosonic interference may disturb the basis of the science.” Starting from determinantal wave functions is typical. Here, we give an antisymmetrization theory, called inter-exchange (iExg) theory, by dividing molecular antisymmetrizations to those within atoms and between atoms. For the electrons belonging to distant atoms in a molecule, only partial antisymmetrizations or even no antisymmetrizations are necessary, depending on the distance between the atoms. So, the above antisymmetry rule is not necessarily followed strictly to get the results of a desired accuracy. For this and other reasons, the necessary parts of the antisymmetrization operations become very small as molecules become larger, leading finally to the operation counts of lower orders of N, the number of electrons. This theory creates a natural antisymmetrization method that is useful for large molecules.
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.
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.
An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation
NASA Astrophysics Data System (ADS)
Pecina, P.
2016-01-01
We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.
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.
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)
Field theory and weak Euler-Lagrange equation for classical particle-field systems
NASA Astrophysics Data System (ADS)
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.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Davidson, Ronald C
2015-01-01
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 underly...
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Hong Qin; J. W. Burby; Ronald C. Davidson
2015-04-17
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.
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
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.
Quasi-particle re-summation and integral gap equation in thermal field theory
Andre LeClair
2005-05-03
A new approach to quantum field theory at finite temperature and density in arbitrary space-time dimension D is developed. We focus mainly on relativistic theories, but the approach applies to non-relativistic ones as well. In this quasi-particle re-summation, the free energy takes the free-field form but with the one-particle energy $\\omega (\\vec{k})$ replaced by $\\vep (\\vec{k})$, the latter satisfying a temperature-dependent integral equation with kernel related to a zero temperature form-factor of the trace of stress-energy tensor. For 2D integrable theories the approach reduces to the thermodynamic Bethe ansatz. For relativistic theories, a thermal c-function $C_{\\rm qs} (T)$ is defined for any $D$ based on the coefficient of the black body radiation formula. Thermodynamical constraints on it's flow are presented, showing that it can violate a ``c-theorem'' even in 2D. At a fixed point $C_{\\rm qs}$ is a function of thermal gap parameters which generalizes Roger's dilogarithm to higher dimensions. This points to a strategy for classifying rational theories based on ``polylogarithmic ladders'' in mathematics, and many examples are worked out. An argument suggests that the 3D Ising model has $C_{\\rm qs} = 7/8$. (In 3D a free fermion has $C_{\\rm qs} = 3/4$.) Other applications are discussed, including the free energy of anyons in 2D and 3D, phase transitions with a chemical potential, and the equation of state for cosmological dark energy.
Equation of state of detonation products based on statistical mechanical theory
NASA Astrophysics Data System (ADS)
Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng
2015-06-01
The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.
Equation of state of detonation products based on statistical mechanical theory
NASA Astrophysics Data System (ADS)
Zhao, Yanhong; Liu, Haifeng; Zhang, Gongmu; Song, Haifeng; Iapcm Team
2013-06-01
The equation of state (EOS) of gaseous detonation products is calculated using Ross's modification of hard-sphere variation theory and the improved one-fluid van der Waals mixture model. The condensed phase of carbon is a mixture of graphite, diamond, graphite-like liquid and diamond-like liquid. For a mixed system of detonation products, the free energy minimization principle is used to calculate the equilibrium compositions of detonation products by solving chemical equilibrium equations. Meanwhile, a chemical equilibrium code is developed base on the theory proposed in this article, and then it is used in the three typical calculations as follow: (i) Calculation for detonation parameters of explosive, the calculated values of detonation velocity, the detonation pressure and the detonation temperature are in good agreement with experimental ones. (ii) Calculation for isentropic unloading line of RDX explosive, whose starting points is the CJ point. Comparison with the results of JWL EOS it is found that the calculated value of gamma is monotonically decreasing using the presented theory in this paper, while double peaks phenomenon appears using JWL EOS.
B. M. Zupnik
1995-12-06
We consider the $SYM^1_6$ harmonic-superspace system of equations that contains superfield constraints and equations of motion for the simplest six-dimensional supersymmetric gauge theory. A special $A$-frame of the analytic basis is introduced where a kinematic equation for the harmonic connection $A^{\\s--}$ can be solved . A dynamical equation in this frame is equivalent to the zero-curvature equation corresponding to the covariant conservation of analyticity. Using a simple harmonic gauge condition for the gauge group $SU(2)$ we derive the superfield equations that produce the general $SYM^1_6$ solution . An analogous approach for the analysis of integrability conditions for the $SYM^2_4$-theory and $SYM$-supergravity-matter systems in harmonic superspace is discussed briefly.
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.
Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density
NASA Technical Reports Server (NTRS)
Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.
1988-01-01
The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.
Pure gauge configurations and tachyon solutions to string field theories equations of motion
NASA Astrophysics Data System (ADS)
Aref'eva, Irina Ya.; Gorbachev, Roman V.; Grigoryev, Dmitry A.; Khromov, Pavel N.; Maltsev, Maxim V.; Medvedev, Peter B.
2009-05-01
In construction of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motion one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.
Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion
I. Ya. Aref'eva; R. V. Gorbachev; D. A. Grigoryev; P. N. Khromov; M. V. Maltsev; P. B. Medvedev
2009-03-04
In constructions 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 motions 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 the 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.
Leonardo Chiatti
2009-01-23
A review is presented of the fundamental equations of point, perfect incompressible fluid and wave dynamics in the Fantappie-Arcidiacono theory of projective relativity, also known as De Sitter relativity. Compared to the original works, some deductions have been simplified and the physical meaning of the equations has been analyzed in greater depth.
Complex Langevin method: When can it be trusted?
Aarts, Gert; Seiler, Erhard; Stamatescu, Ion-Olimpiu
2010-03-01
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.
PHYSICAL REVIEW B 83, 134418 (2011) Langevin spin dynamics
2011-01-01
.134418 PACS number(s): 75.10.Hk, 75.40.Mg, 76.60.Es, 76.60.Jx I. INTRODUCTION Langevin dynamics is a subject to constraints limiting their application11,12 or contain mathematical inconsistencies.13,14 Some literature
A standard basis operator equation of motion impurity solver for dynamical mean field theory
NASA Astrophysics Data System (ADS)
Li, Hengyue; Tong, Ning-Hua
2015-12-01
We present an efficient impurity solver for the dynamical mean-field theory (DMFT). It is based on the separation of bath degrees of freedom into the low energy and the high energy parts. The former is solved exactly using exact diagonalization and the latter is treated approximately using Green's function equation of motion decoupling approximation. The two parts are combined coherently under the standard basis operator formalism. The impurity solver is applied to the Anderson impurity model and, combined with DMFT, to the one-band Hubbard model. Qualitative agreement is found with other well established methods. Some promising features and possible improvements of the present solver are discussed.
Poisson equation for the Mercedes diagram in string theory at genus one
Basu, Anirban
2015-01-01
The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three loop Feynman diagram contributes to the D^{12} R^4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one and two loop Feynman diagrams. We calculate its contribution to the D^{12} R^4 amplitude.
Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory
Subir K. Das; Sergei Egorov; Benjamin Trefz; Peter Virnau; Kurt Binder
2014-05-15
We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The inter-particle interactions in the system were 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 were made active using the Vicsek model for self-propelling particles. The resultant active system was 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.
Kinetic theory based wave-particle splitting scheme for Euler equations
NASA Astrophysics Data System (ADS)
Rao, S. V. R.; Deshpande, S. M.
1992-11-01
A new upwind wave-particle splitting scheme is developed, based on the connection between the kinetic theory of gased and Euler equations and using the concept of thermal velocity. The new upwind method is applied to the standard one-dimensional shock tube problem and to the problem of two-dimensional shock reflection from a flat plate. Results for the two-dimensional problem showed that the new scheme is much less dissipative than the kinetic flux vector splitting scheme of Deshpande (1986) and Mandal (1989).
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Chekhov, Leonid; Eynard, Bertrand; Ribault, Sylvain; Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5
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.
Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory
NASA Astrophysics Data System (ADS)
Hoferichter, Martin; Ruiz de Elvira, Jacobo; Kubis, Bastian; Meißner, Ulf-G.
2015-11-01
We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the ? (1232 ) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.
C. J. Fewster
1998-04-03
We consider 2-dimensional cylinder spacetimes whose metrics differ from the flat Minkowskian metric within a compact region. By choice of time orientation, these spacetimes may be regarded as either globally hyperbolic timelike cylinders or nonglobally hyperbolic spacelike cylinders. For generic metrics in our class, we classify all possible candidate quantum field algebras for massive Klein-Gordon theory which obey the F-locality condition introduced by Kay. This condition requires each point of spacetime to have an intrinsically globally hyperbolic neighbourhood, N, such that the commutator (in the candidate algebra) of fields smeared with test functions supported in N agrees with the value obtained in the usual construction of Klein-Gordon theory on N. By considering bisolutions to the Klein-Gordon equation, we prove that generic timelike cylinders admit a unique F-local algebra -- namely the algebra obtained by the usual construction -- and that generic spacelike cylinders do not admit any F-local algebras, and are therefore non F-quantum compatible. Refined versions of our results are obtained for subclasses of metrics invariant under a symmetry group. Thus F-local field theory on 2-dimensional cylinder spacetimes essentially coincides with the usual globally hyperbolic theory. In particular the result of the author and Higuchi that the Minkowskian spacelike cylinder admits infinitely many F-local algebras is now seen to represent an anomalous case.
A. H. M. Kierkels; J. J. L. Velázquez
2015-11-04
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schr\\"odinger equation. The solutions that we construct have finite mass, but infinite energy. In J. Stat. Phys. 159:668-712, self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
Advancing towards constitutive equations for the metal industry via the LEDS theory
NASA Astrophysics Data System (ADS)
Kuhlmann-Wilsdorf, Doris
2004-02-01
A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. They are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. While plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newton’s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.
Advancing towards constitutive equations for the metal industry via the LEDS theory
NASA Astrophysics Data System (ADS)
Kuhlmann-Wilsdorf, Doris
2004-02-01
A prime objective in the development of crystal dislocation theory has been, and at any rate should be, constitutive equations for practical use in the metal forming industry. Protracted controversies regarding workhardening theory have frustrated this goal for the past seven decades. The are fueled by the paradox that plastic deformation is a prime example for the second law of thermodynamics in converting mechanical work into heat with good efficiency, even while in seeming opposition to the second law it typically raises the internal energy of the deformed material. The low-energy dislocation structures (LEDS) theory resolves this difficulty by showing that, as always in inanimate nature, so also plastic deformation proceeds close to minimum free energy. Indeed recent evidence based on deformation band structures proves that plastic deformation typically proceeds very close to minimum energy among the accessible configurations. White plastic strain raises the flow stress, in ductile crystalline materials mostly through generating dislocation structures, but also through twins, kink bands, microcracks and others, Newton’s third law, i.e., force equilibrium, is always stringently obeyed. Therefore, deformation dislocation structures are in thermal equilibrium as long as the stress that generated them remains in place. Based on this concept of free energy minimization, the LEDS theory has long since explained, at least semiquantitatively, all significant aspects of metal strength and deformation, as well as the effects of heat treatments. The LEDS theory is the special case, namely, as pertaining to dislocation structures, of the more general low-energy structures (LEDS) theory that governs all types of deformation independent of the deformation mechanism, and that operates in all types of materials, including plastics.
On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory
John M. Cornwall
1997-10-15
Recently several workers have attempted determinations of the so-called magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap equation, using a free massive propagator as input. Self-consistency is attained only on-shell, because the usual Feynman-graph construction is gauge-dependent off-shell. We examine two previous studies of the pinch technique proper self-energy, which is gauge-invariant at all momenta, using a free propagator as input, and show that it leads to inconsistent and unphysical result. In one case the residue of the pole has the wrong sign (necessarily implying the presence of a tachyonic pole); in the second case the residue is positive, but two orders of magnitude larger than the input residue, which shows that the residue is on the verge of becoming ghostlike. This happens because of the infrared instability of d=3 gauge theory. A possible alternative one-loop determination via the effective action also fails. The lesson is that gap equations must be considered at least at two-loop level.
Effective field theory during inflation: Reduced density matrix and its quantum master equation
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-07-01
We study the power spectrum of super-Hubble fluctuations of an inflatonlike scalar field, the "system," coupled to another scalar field, the "environment" during de Sitter inflation. We obtain the reduced density matrix for the inflaton fluctuations by integrating out the environmental degrees of freedom. These are considered to be massless and conformally coupled to gravity as a proxy to describe degrees of freedom that remain sub-Hubble all throughout inflation. The time evolution of the density matrix is described by a quantum master equation, which describes the decay of the vacuum state, the production of particles and correlated pairs and quantum entanglement between super and sub-Hubble degrees of freedom. The quantum master equation provides a nonperturbative resummation of secular terms from self-energy (loop) corrections to the inflaton fluctuations. In the case studied here these are Sudakov-type double logarithms which result in the decay of the power spectrum of inflaton fluctuations upon horizon crossing with a concomitant violation of scale invariance. The reduced density matrix and its quantum master equation furnish a powerful nonperturbative framework to study the effective field theory of long wavelength fluctuations by tracing short wavelength degrees of freedom.
Integrable structure of conformal field theory; 2, q-operator and DDV equation
Bazhanov, V V; Zamolodchikov, A B
1996-01-01
This paper is a direct continuation of \\BLZ\\ where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators {\\bf Q}_{\\pm}(\\lambda) which act in highest weight Virasoro module and commute for different values of the parameter \\lambda. These operators appear to be the CFT analogs of the Q - matrix of Baxter\\ \\Baxn , in particular they satisfy famous Baxter's {\\bf T}-{\\bf Q} equation. We also show that under natural assumptions about analytic properties of the operators {\\bf Q}(\\lambda) as the functions of \\lambda the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) \\dVega\\ for the eigenvalues of the {\\bf Q}-operators. We then use the DDV equation to obtain the asymptotic expansions of the {\\bf Q} - operators at large \\lambda; it is remarkable that unlike the expansions of the {\\bf T} operators of \\ \\BLZ, the asymptotic series for {\\bf Q}(\\lambda) contains the "dual" nonlocal Integrals of Motion along wit...
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
V. Bazhanov; S. Lukyanov; A. Zamolodchikov
1996-04-17
This paper is a direct continuation of\\ \\BLZ\\ where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\\bf Q}_{\\pm}(\\lambda)$ which act in highest weight Virasoro module and commute for different values of the parameter $\\lambda$. These operators appear to be the CFT analogs of the $Q$ - matrix of Baxter\\ \\Baxn, in particular they satisfy famous Baxter's ${\\bf T}-{\\bf Q}$ equation. We also show that under natural assumptions about analytic properties of the operators ${\\bf Q}(\\lambda)$ as the functions of $\\lambda$ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV)\\ \\dVega\\ for the eigenvalues of the ${\\bf Q}$-operators. We then use the DDV equation to obtain the asymptotic expansions of the ${\\bf Q}$ - operators at large $\\lambda$; it is remarkable that unlike the expansions of the ${\\bf T}$ operators of \\ \\BLZ, the asymptotic series for ${\\bf Q}(\\lambda)$ contains the ``dual'' nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the ${\\bf Q}$ - operators and the stationary transport properties in boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in quantum Hall system.
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
NASA Astrophysics Data System (ADS)
Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Zamolodchikov, Alexander B.
This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q+/-(? ) which act in the highest weight Virasoro module and commute for different values of the parameter ?. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of ? the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large ? it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(?) contains the ``dual'' nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system.
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.
Stochastic modification of the Schrödinger-Newton equation
NASA Astrophysics Data System (ADS)
Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.
2015-07-01
The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.
Stochastic modification of the Schrodinger-Newton equation
Sayantani Bera; Ravi Mohan; Tejinder P. Singh
2015-08-01
The Schr\\"odinger-Newton [SN] equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation by itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schr\\"odinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Di\\'osi - Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is however linear at the level of the approximation we use to prove decoherence, hence the no-signalling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.
Padé Approximants for the Equation of State for Relativistic Hydrodynamics by Kinetic Theory
NASA Astrophysics Data System (ADS)
Tsai, Shang-Hsi; Yang, Jaw-Yen
2015-07-01
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell-Boltzmann statistics and the semiclassical Fermi-Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
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.
Theoretical understanding of the problem with a singular drift term in the complex Langevin method
Nishimura, Jun
2015-01-01
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur in general when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
New insights into the problem with a singular drift term in the complex Langevin method
Jun Nishimura; Shinji Shimasaki
2015-09-02
The complex Langevin method aims at performing path integral with a complex action numerically based on complexification of the original real dynamical variables. One of the poorly understood issues concerns occasional failure in the presence of logarithmic singularities in the action, which appear, for instance, from the fermion determinant in finite density QCD. We point out that the failure should be attributed to the breakdown of the relation between the complex weight that satisfies the Fokker-Planck equation and the probability distribution associated with the stochastic process. In fact, this problem can occur in general when the stochastic process involves a singular drift term. We show, however, in a simple example that there exists a parameter region in which the method works although the standard reweighting method is hardly applicable.
Elementary solutions of coupled model equations in the kinetic theory of gases
NASA Technical Reports Server (NTRS)
Kriese, J. T.; Siewert, C. E.; Chang, T. S.
1974-01-01
The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.
Tu, Fei-Quan; Chen, Yi-Xin E-mail: yxchen@zimp.zju.edu.cn
2013-05-01
It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Ho?ava-Lifshitz(HL) theory.
Pelinovsky, D. E.; Stefanov, A.
2008-11-15
Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, H{phi}=(-{delta}+V){phi}=-({phi}{sub n+1}+{phi}{sub n-1}-2{phi}{sub n})+V{sub n}{phi}{sub n}. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sub {sigma}{sup 2}}{yields}{sub l-{sigma}{sup 2}}} < or approx. t{sup -3/2} for any fixed {sigma}>(5/2) and any t>0, where P{sub a.c.}(H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e{sup itH}P{sub a.c.}(H) parallel {sub l{sup 1}{yields}{sub l{sup {infinity}}}} < or approx. t{sup -1/3}, which are sharp for the discrete Schroedinger operators even for V=0.
Mixing of equations of state for xenon-deuterium using density functional theory
Magyar, Rudolph J.; Mattsson, Thomas R.
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.
Boozer, Allen H.
2015-03-15
The plasma current in ITER cannot be allowed to transfer from thermal to relativistic electron carriers. The potential for damage is too great. Before the final design is chosen for the mitigation system to prevent such a transfer, it is important that the parameters that control the physics be understood. Equations that determine these parameters and their characteristic values are derived. The mitigation benefits of the injection of impurities with the highest possible atomic number Z and the slowing plasma cooling during halo current mitigation to ?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.
Virial equation of state of water based on Wertheim's association theory.
Kim, Hye Min; Schultz, Andrew J; Kofke, David A
2012-12-01
Wertheim's multidensity formalism for pairwise additive molecular interaction is extended to handle nonadditive contributions and is applied to formulate an equation of state (WEOS) for the Gaussian-charge polarizable model (GCPM) of water, with cluster integrals appearing in the theory calculated via the Mayer sampling Monte Carlo method. At both sub- and supercritical temperatures, the equation of state of GCPM water obtained from WEOS converges well to Monte Carlo simulation data, and performs significantly better than the conventional virial treatment (VEOS). The critical temperature for GCPM water using a fourth-order WEOS is given to within 1.3% of the established value, compared to a 17% error shown by fifth-order VEOS; as seen in previous applications, the critical density obtained from both VEOS and WEOS significantly underestimates the true critical density for GCPM water. Examination of the magnitudes of the computed cluster diagrams at the critical density finds that negligible contributions are made by clusters in which a water molecule has both of its hydrogens involved in association interactions. PMID:23148680
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)
Kiani, M.; Alavianmehr, M. M.; Otoofat, M.; Mohsenipour, A. A.; Ghatee, A.
2015-11-01
In this work, we identify a simple method for predicting transport properties of fluids over wide ranges of temperatures and pressure. In this respect, the capability of several equations of state (EOS) and second virial coefficient correlations to predict transport properties of fluids including carbon dioxide, methane and argon using modified Enskog theory (MET) is investigated. The transport properties in question are viscosity and thermal conductivity. The results indicate that the SRK EOS employed in the modified Enskog theory outperforms other equations of state. The average absolute deviation was found to be 12.2 and 18.5% for, respectively, the calculated thermal conductivity and viscosity using the MET.
NASA Astrophysics Data System (ADS)
Lathiotakis, Nektarios N.; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I.
2014-09-01
We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.
Hybrid two-chain simulation and integral equation theory : application to polyethylene liquids.
Huimin Li, David T. Wu; Curro, John G.; McCoy, John Dwane
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.
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.
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Ross, John
2002-12-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.
A kinetic-theory approach to turbulent chemically reacting flows
NASA Technical Reports Server (NTRS)
Chung, P. M.
1976-01-01
The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.
C. W. Gardiner; P. Zoller
1996-11-25
A Quantum Kinetic Master Equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the Quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.
A Kinetic Theory Approach to Quantum Gravity
B. L. Hu
2002-04-22
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).
ERIC Educational Resources Information Center
van den Putte, Bas; Hoogstraten, Johan
1997-01-01
Problems found in the application of structural equation modeling to the theory of reasoned action are explored, and an alternative model specification is proposed that improves the fit of the data while leaving intact the structural part of the model being tested. Problems and the proposed alternative are illustrated. (SLD)
Straube, Arthur V.
Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme
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…
Híjar, Humberto
2015-02-01
We study the Brownian motion of a particle bound by a harmonic potential and immersed in a fluid with a uniform shear flow. We describe this problem first in terms of a linear Fokker-Planck equation which is solved to obtain the probability distribution function for finding the particle in a volume element of its associated phase space. We find the explicit form of this distribution in the stationary limit and use this result to show that both the equipartition law and the equation of state of the trapped particle are modified from their equilibrium form by terms increasing as the square of the imposed shear rate. Subsequently, we propose an alternative description of this problem in terms of a generalized Langevin equation that takes into account the effects of hydrodynamic correlations and sound propagation on the dynamics of the trapped particle. We show that these effects produce significant changes, manifested as long-time tails and resonant peaks, in the equilibrium and nonequilibrium correlation functions for the velocity of the Brownian particle. We implement numerical simulations based on molecular dynamics and multiparticle collision dynamics, and observe a very good quantitative agreement between the predictions of the model and the numerical results, thus suggesting that this kind of numerical simulations could be used as complement of current experimental techniques. PMID:25768490
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.
Langevin dynamics of proteins at constant pH
NASA Astrophysics Data System (ADS)
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 pKa 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.
ERIC Educational Resources Information Center
Ryan, Joseph; Brockmann, Frank
2009-01-01
Equating is an essential tool in educational assessment due the critical role it plays in several key areas: establishing validity across forms and years; fairness; test security; and, increasingly, continuity in programs that release items or require ongoing development. Although the practice of equating is rooted in long standing practices that…
Interpretation of non-Markovian stochastic Schroedinger equations as a hidden-variable theory
Gambetta, Jay; Wiseman, H.M.
2003-12-01
Do diffusive non-Markovian stochastic Schroedinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function z(t) appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value z(t) even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system 'conditioned' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.
NASA Astrophysics Data System (ADS)
Sohrab, S. H.
1998-03-01
An invariant statistical theory of fields from cosmic to tachyonic scales is presented. The invariant wavefunction is defined as the first perturbation of action S_? = ?_??_?, the product of density and velocity potential. The invariant Schrödinger equation is derived, and invariant forms of Planck constant, de Broglie matter wave hypothesis, and Heisenberg uncertainty relation are presented. The field of tachyon-dynamics is identified as the physical space that is the stochastic ether of Dirac, or the "hidden thermostat" of de Broglie, and is assumed to be compressible in harmony with compressible ether of Planck. Compressibility of physical space is suggested to account for Fitzgerald-Lorentz contraction, thus providing an explanation of relativistic effects in harmony with the physical perceptions of Poincaré and Lorentz. Following the definition of Planck constant h = m_??_?c = 6.626x10-34 J-s, the definition of Boltzmann constant is introduced as k = m_??_?c = 1.381x10-23 J/K, where m_?, ?_?,?_?, and c are the photon mass, wavelength, frequency, and velocity. Parallel to the de Broglie relation ?_? = h/p_? for matter waves, the relation ?_? = k/p_? is introduced to give the frequency of matter waves. Therefore, the mass of the photon is predicted as m_? = (hk/c^3)^1/2 = 1.84278x10-41 kg.
Droegemeier, Kelvin K.
1 Theory of Thunderstorm Dynamics Houze sections 7.4, 8.3, 8.5, Refer back to equations in Section Thunderstorms" by Klemp handout. A. Equations of Motion Boussinesq approximated equations (neglecting friction in thunderstorms, look at the vertical component of vorticity ^k = r ^ ^ ^ ^( ) ( ) ( )k V k Bk k V
Kelly, Aaron; Markland, Thomas E.; Brackbill, Nora
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
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
Giacometti, Achille; Gögelein, Christoph; Lado, Fred; Sciortino, Francesco; Ferrari, Silvano
2014-03-07
Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function.
NASA Technical Reports Server (NTRS)
Cheng, H. K.; Wong, Eric Y.; Dogra, V. K.
1991-01-01
Grad's thirteen-moment equations are applied to the flow behind a bow shock under the formalism of a thin shock layer. Comparison of this version of the theory with Direct Simulation Monte Carlo calculations of flows about a flat plate at finite attack angle has lent support to the approach as a useful extension of the continuum model for studying translational nonequilibrium in the shock layer. This paper reassesses the physical basis and limitations of the development with additional calculations and comparisons. The streamline correlation principle, which allows transformation of the 13-moment based system to one based on the Navier-Stokes equations, is extended to a three-dimensional formulation. The development yields a strip theory for planar lifting surfaces at finite incidences. Examples reveal that the lift-to-drag ratio is little influenced by planform geometry and varies with altitudes according to a 'bridging function' determined by correlated two-dimensional calculations.
M5-branes in the ABJM theory and the Nahm equation
NASA Astrophysics Data System (ADS)
Nosaka, Tomoki; Terashima, Seiji
2012-12-01
We explicitly construct two classes of the BPS solutions in the Aharony-Bergman-Jafferis-Maldacena action—the funnel type solutions and the ’t Hooft-Polyakov type solutions—and study their physical properties as the M2-M5 bound state. Furthermore, we give a one-to-one correspondence between the solutions of the BPS equation and the ones of an extended Nahm equation which includes the Nahm equation. This enables us to construct infinitely many conserved quantities from the Lax form of the Nahm equation.
2D/1D approximations to the 3D neutron transport equation. I: Theory
Kelley, B. W.; Larsen, E. W.
2013-07-01
A new class of '2D/1D' approximations is proposed for the 3D linear Boltzmann equation. These approximate equations preserve the exact transport physics in the radial directions x and y and diffusion physics in the axial direction z. Thus, the 2D/1D equations are more accurate approximations of the 3D Boltzmann equation than the conventional 3D diffusion equation. The 2D/1D equations can be systematically discretized, to yield accurate simulation methods for 3D reactor core problems. The resulting solutions will be more accurate than 3D diffusion solutions, and less expensive to generate than standard 3D transport solutions. In this paper, we (i) show that the simplest 2D/1D equation has certain desirable properties, (ii) systematically discretize this equation, and (iii) derive a stable iteration scheme for solving the discrete system of equations. In a companion paper [1], we give numerical results that confirm the theoretical predictions of accuracy and iterative stability. (authors)
Du Kai Qiu, Jinniao Tang Shanjian
2012-04-15
This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.
Nagy, A.
2011-09-15
A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).
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…
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.
General fractional multiparameter white noise theory and stochastic partial differential equations
Hu, Yaozhong; Oksendal, B.; Zhang, T. S.
2004-01-01
derivativex(l)...partial derivativex(d)), and D subset of R-d is a given bounded smooth domain. We also solve the linear stochastic heat equation (partial derivativeU/partial derivativet)(t, x) = 1/2 DeltaU(t, x) + W-H (t, x). For each equation we give...
A Generalized Equation of Motion for the Linear Response. I ---General Theory---
NASA Astrophysics Data System (ADS)
Saeki, M.
1982-05-01
A time-convolutionless expression for the quantal equation of motion for the linear response of a system in contact with a heat bath to an external, time-varying driving field is derived from the quantal Liouville equation of motion for the total system. This is done by renormalizing the memory effect by the method of Shibata, Takahashi and Hashitsume. It has a form convenient for the perturbational expansion. It is shown that this equation coincides with the time-convolution equation of Argyres and Kelley in their Markoffian approximation in the narrowing limit and in the lowest Born approximation for the system-bath interaction. This equation is expanded up to fourth order in powers of the system-bath interaction.
NASA Astrophysics Data System (ADS)
Chen, Gui-Qiang; Glimm, James
2012-02-01
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in {mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the ? th -order fractional derivatives of the velocity for some ? > 0 in the space variables in L 2, which is independent of the viscosity ? > 0. Then it is shown that this key observation yields the L 2-equicontinuity in the time variable and the uniform bound in L q , for some q > 2, of the velocity independent of ? > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations in {mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of ? > 0, that is in the high Reynolds number limit.
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)
Hahn, Y.K.
2014-12-15
The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model. - Highlights: • First extension of HF to scattering states, with proper asymptotic conditions. • Orbital equations with asymptotic sources and integrable orbital solutions. • Construction of self-averaged potentials, and orbital energy fixing. • Channel coupling and configuration mixing, involving the new orbitals. • Critical evaluation of the continuum HF and its improvements.
A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory
Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.
2010-12-14
A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work, with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Juettner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.
A generalized equation of motion for gravity theories with non-minimal kinetic scalar couplings
Saugata Chatterjee
2014-12-08
A general form for the equation of motion for higher-curvature gravity is obtained. The interesting feature of the analysis is that it can handle Lagrangians which contain non-minimal kinetic scalar couplings. Certain subtle features, which are absent for the Einstein-Hilbert term, arise in higher-curvature gravity. These are identified and an algorithmic prescription is presented for the evaluation of the generalized equation of motion.
Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
NASA Astrophysics Data System (ADS)
Kumar, N.; Vijay Kumar, K.
2009-04-01
It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.
Rosinberg, M L; Munakata, T; Tarjus, G
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups. PMID:25974446
NASA Astrophysics Data System (ADS)
Rosinberg, M. L.; Munakata, T.; Tarjus, G.
2015-04-01
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small stochastic systems governed by an underdamped Langevin equation and driven out of equilibrium by a time-delayed continuous feedback control. In their normal operating regime, these systems settle in a nonequilibrium steady state in which work is permanently extracted from the surrounding heat bath. By using the Fokker-Planck representation of the dynamics, we derive a set of second-law-like inequalities that provide bounds to the rate of extracted work. These inequalities involve additional contributions characterizing the reduction of entropy production due to the continuous measurement process. We also show that the non-Markovian nature of the dynamics requires a modification of the basic relation linking dissipation to the breaking of time-reversal symmetry at the level of trajectories. The modified relation includes a contribution arising from the acausal character of the reverse process. This, in turn, leads to another second-law-like inequality. We illustrate the general formalism with a detailed analytical and numerical study of a harmonic oscillator driven by a linear feedback, which describes actual experimental setups.
Iyer, Ramakrishnan; Mukhopadhyay, Ayan
2010-04-15
The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.
Unexpected Applications of Hill's Differential Equations in Quantum Field Theory and Cosmology
NASA Astrophysics Data System (ADS)
Mostepanenko, V. M.
The effect of the exponential pair creation from vacuum by the external field periodic in time is discussed. Two prospective applications of this physical effect in quantum field theory and in inflationary cosmology are considered. Being a nontrivial example of a parametric resonance, the effect of exponential pair creation may serve as an illustration of the effectiveness of mathematics in physical theory.
Pierce, Allan D
2008-01-01
A connection between Maxwell's equations, Newton's laws, and the special theory of relativity is established with a derivation that begins with Newton's verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and Maxwell's equations for free space emerge with the assumption that the tensor and its dual must both satisfy first order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton's third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that bo...
NASA Astrophysics Data System (ADS)
Sjostrom, Travis; Crockett, Scott
2015-09-01
The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 -15 g/cm 3 and with temperatures from 0.5 to 100 eV, including the ? -quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.
Equations of motion and conservation laws in a theory of stably stratified turbulence
NASA Astrophysics Data System (ADS)
L'vov, Victor S.; Rudenko, Oleksii
2008-12-01
This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.
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.
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…
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.
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.
R. E. Brodskii; Yu P. Virchenko
2008-08-10
The cascade kinetic fragmentation process of solids is investigated when the condition probability density of splinter formation do not depends on time and has the property $P(\\rho, r, t) = P(\\rho/r)$. It is obtained the evolution equation for the probability distribution density in terms of its Mellin transformation. In the particular case $P(\\rho/r) = C (\\rho/r)^\\alpha$, the limit solution of this equation at $t \\to \\infty$ is found. It differs essentially from the Kolmogorov law.
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.
Tanimura, Shogo )
1992-12-01
R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs.
Clausius-Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice
NASA Astrophysics Data System (ADS)
Koutsoyiannis, Demetris
2012-03-01
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 assumption unnecessary and excessive, but it is also contradictory to entropy maximization. There is an additional erroneous assumption for the derivation of the Clausius-Clapeyron equation, related to the equality of chemical potentials of the two phases, which does not affect the final result but puts into question the logical coherence of the equation's derivation. Removing these assumptions and using a pure entropy maximization framework we obtain a simple closed solution which is both theoretically consistent and accurate. Our discussion and derivation are relevant to students and specialists in statistical thermophysics and in geophysical sciences, and our results are ready for practical application in physics as well as in such disciplines as hydrology, meteorology and climatology.
Huš, Matej; Urbic, Tomaz; Munaò, Gianmarco
2014-10-28
Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.
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.
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/cm(3)) 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 2-6g/cm(3). The minimum density for the metallization of argon is found to be about 5.8 g/cm(3), 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. PMID:25768617
Bavarian, Niloofar; Flay, Brian R.; Ketcham, Patricia L.; Smit, Ellen; Kodama, Cathy; Martin, Melissa; Saltz, Robert F.
2014-01-01
Objective To test a theory-driven model of health behavior to predict the illicit use of prescription stimulants (IUPS) among college students. Participants A probability sample of 554 students from one university located in California (response rate = 90.52%). Methods Students completed a paper-based survey developed with guidance from the Theory of Triadic Influence. We first assessed normality of measures and checked for multicollinearity. A single structural equation model of frequency of IUPS in college was then tested using constructs from the theory’s three streams of influence (i.e., intrapersonal, social situation/context, and sociocultural environment) and four levels of causation (i.e., ultimate causes, distal influences, proximal predictors, and immediate precursors). Results Approximately 18% of students reported engaging in IUPS during college, with frequency of use ranging from never to 40 or more times per academic term. The model tested had strong fit and the majority of paths specified within and across streams were significant at the p<.01 level. Additionally, 46% of the variance in IUPS frequency was explained by the tested model. Conclusions Results suggest the utility of the TTI as an integrative model of health behavior, specifically in predicting IUPS, and provide insight on the need for multifaceted prevention and intervention efforts. PMID:24647369
Pernal, Katarzyna; Baerends, Evert Jan
2006-01-01
Starting from the variational equations for the natural occupation numbers and the recently proposed eigenequations for the natural spin-orbitals, we derive coupled-perturbed density-matrix equations that furnish a linear response of the one-electron reduced density matrix to a static perturbation when the total energy is a functional of the one-electron reduced density matrix. Cases when some occupation numbers achieve exactly 0 or 1 or when the total number of the particles in a system is not preserved are taken into consideration. The scheme is applied to computing static polarizabilities from two simple density-matrix functionals. The behavior of the functionals is erratic and they provide only little or no improvement over the coupled-perturbed Hartree-Fock results. PMID:16409019
General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations
Doktorov, Alexander B.; Kipriyanov, Alexey A.
2014-05-14
General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of “effective” particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.
Quantum Kinetic Theory III: Simulation of the Quantum Boltzmann Master Equation
D. Jaksch; C. W. Gardiner; P. Zoller
1997-01-10
We present results of simulations of a em quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equations derived in previous work. We consider two cases of trapping potentials: a 3D square well potential with periodic boundary conditions, and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.
Coupled Gap Equations for the Screening Masses in Hot SU(N) Gauge Theory
A. Patkos; P. Petreczky; Zs. Szep
1998-02-13
Coupled 1-loop gap equations are studied numerically for non-Abelian electric and magnetic screening in various versions of the three-dimensional effective gauge models. Corrections due to higher dimensional and non-local operators are assessed quantitatively. Comparison with numerical Monte-Carlo investigations suggests that quantitative understanding beyond the qualitative features can be achieved only by going beyond the present treatment.
F. Sammarruca; L. Coraggio; J. W. Holt; N. Itaco; R. Machleidt; L. E. Marcucci
2015-04-18
We calculate the nuclear and neutron matter equations of state from microscopic nuclear forces at different orders in chiral effective field theory and with varying momentum-space cutoff scales. We focus attention on how the order-by-order convergence depends on the choice of resolution scale and the implications for theoretical uncertainty estimates on the isospin asymmetry energy. Specifically we study the equations of state using consistent NLO and N2LO (next-to-next-to-leading order) chiral potentials where the low-energy constants cD and cE associated with contact vertices in the N2LO chiral three-nucleon force are fitted to reproduce the binding energies of 3H and 3He as well as the beta-decay lifetime of 3H. At these low orders in the chiral expansion there is little sign of convergence, while an exploratory study employing the N3LO two-nucleon force together with the N2LO three-nucleon force give first indications for (slow) convergence with low-cutoff potentials and poor convergence with higher-cutoff potentials. The consistent NLO and N2LO potentials described in the present work provide the basis for estimating theoretical uncertainties associated with the order-by-order convergence of nuclear many-body calculations in chiral effective field theory.
Quantitative test of general theories of the intrinsic laser linewidth
NASA Astrophysics Data System (ADS)
Cerjan, Alexander; Pick, Adi; Chong, Y. D.; Johnson, Steven G.; Douglas Stone, A.
2015-11-01
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and thus includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations ($\\alpha$ factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.
Quantitative test of general theories of the intrinsic laser linewidth.
Cerjan, Alexander; Pick, Adi; Chong, Y D; Johnson, Steven G; Douglas Stone, A
2015-11-01
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (? factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations. PMID:26561103
Forster, Otto
______________________O._Forster:_Analytic_Number_Theory_______________________ 10). The theta series is defined for real x > 0 by X 2 `(x) := e-ssn x`(x) for allx > 0, x i.e. X 2 1 X 2 e-ssn x= ___p_ e-ssn =x
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly
Capolupo, Antonio; Illuminati, Fabrizio
2013-01-01
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.
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
NASA Astrophysics Data System (ADS)
Xing, Xiusan
2010-12-01
In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type's Langevin equation in 6 N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6 N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6 N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.
NASA Astrophysics Data System (ADS)
Planková, Barbora; Hrubý, Jan; Vinš, Václav
2013-04-01
In this work, we used the density gradient theory (DGT) combined with the cubic equation of state (EoS) by Peng and Robinson (PR) and the perturbed chain (PC) modification of the SAFT EoS developed by Gross and Sadowski [1]. The PR EoS is based on very simplified physical foundations, it has significant limitations in the accuracy of the predicted thermodynamic properties. On the other hand, the PC-SAFT EoS combines different intermolecular forces, e.g., hydrogen bonding, covalent bonding, Coulombic forces which makes it more accurate in predicting of the physical variables. We continued in our previous works [2,3] by solving the boundary value problem which arose by mathematical solution of the DGT formulation and including the boundary conditions. Achieving the numerical solution was rather tricky; this study describes some of the crucial developments that helped us to overcome the partial problems. The most troublesome were computations for low temperatures where we achieved great improvements compared to [3]. We applied the GT for the n-alkanes: nheptane, n-octane, n-nonane, and n-decane because of the availability of the experimental data. Comparing them with our numerical results, we observed great differences between the theories; the best results gave the combination of the GT and the PC-SAFT. However, a certain temperature drift was observed that is not satisfactorily explained by the present theories.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Third order wave equation in Duffin-Kemmer-Petiau theory: Massive case
NASA Astrophysics Data System (ADS)
Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.
2015-11-01
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [1] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q -commutator (q is a primitive cubic root of unity) and a new set of matrices ?? instead of the original matrices ?? of the DKP algebra are introduced. It is shown that in terms of these ?? matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z ?q , where z is some complex deformation parameter entering into the definition of the ? -matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ? (x ;z ) is performed and it is shown that the solution is singular in the z ?q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.
Time-optimal path planning in dynamic flows using level set equations: theory and schemes
NASA Astrophysics Data System (ADS)
Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.
2014-10-01
We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.
Time-optimal path planning in dynamic flows using level set equations: theory and schemes
NASA Astrophysics Data System (ADS)
Lolla, Tapovan; Lermusiaux, Pierre F. J.; Ueckermann, Mattheus P.; Haley, Patrick J.
2014-09-01
We develop an accurate partial differential equation-based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong, and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned even in the presence of complex flows in domains with obstacles. Finally, we present and support through illustrations several remarks that describe specific features of our methodology.
Blending Brownian motion and heat equation
Cristiani, Emiliano
2015-01-01
In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom.
Diffusion of Single layer Clusters: Langevin Analysis and Monte Carlo Simulations^*
NASA Astrophysics Data System (ADS)
Khare, S. V.
1996-03-01
In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius R, the cluster diffusion constant Dc is found to vary as R-1 and R-2 in studies by Wen et al. ( J. M. Wen, S. -L. Chang, J. W. Burnett, J. W. Evans and P. A. Thiel, Phys. Rev. Lett. 73), 2591 (1994). and Morgenstern et al. (K. Morgenstern, G. Rosenfeld, B. Poelsema, and G. Comsa, Phys. Rev. Lett. 74), 2058 (1995)., repectively. From an analytical continuum description of the cluster's step-like boundary, we find a single Langevin equation for the motion of the cluster boundary. From this we determine the cluster diffusion constant and the fluctuations of the shape around an assumed equilibrium circular shape. In three limiting cases this leads to the scaling of the diffusion constant with the radius as Dc ~ R^-? and the scaling of a shape fluctuations correlation function with the elapsed time as t^1/(1+? ). These three cases correspond to the three microscopic surface mass-transport mechanisms of straight steps, namely: evaporation condensation (EC) giving ?=1, terrace diffusion (TD) implying ?=2 and periphery diffusion (PD) yielding ? = 3. We thereby provide a unified treatment of the dynamics of steps and of clusters ( S. V. Khare, N. C. Bartelt, and T. L. Einstein, Phys. Rev. Lett. 75), 2148 (1995); in preparation.. To check how well the continuum results apply to real systems with finite lattice constants, we perform Monte Carlo simulations of simple lattice gas models for these three cases. We also relate the the experimentally measured diffusion coefficients of the clusters to atomic diffusion parameters. ^* This work was done in collaboration with N. C. Bartelt and T. L. Einstein and was supported in part by NSF DMR-MRG 91-03031.
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
Perturbation theories of a discrete, integrable nonlinear Schr{umlt o}dinger equation
Cai, D.; Bishop, A.R.; Gro/nbech-Jensen, N.
1996-04-01
We rederive the discrete inverse-scattering transform (IST) perturbation results for the time evolution of the parameters of a discrete nonlinear Schr{umlt o}dinger soliton from certain mathematical identities that can be viewed as conserved quantities in the discrete, integrable nonlinear Schr{umlt o}dinger equation in (1+1) dimension. This method significantly simplifies the derivation of the IST perturbation results. We also present a specific example for which the adiabatic IST perturbation results and the collective coordinate method results exactly coincide. This is achieved by establishing a correct Lagrangian formalism for soliton parameters via transforming dynamical variables that obey a deformed Poisson structure to ones that possess a canonical Poisson structure. {copyright} {ital 1996 The American Physical Society.}
Scattering theory for the radial H?1/2-critical wave equation with a cubic convolution
NASA Astrophysics Data System (ADS)
Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang
2015-12-01
In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ?t2 u - ?u = ± (| x | - 3 *| u | 2) u in dimensions d ? 4. We prove that if the radial solution u with life-span I obeys (u, ut) ? Lt? (I ; H?x 1 / 2 (Rd) × H?x - 1 / 2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.
Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications
NASA Technical Reports Server (NTRS)
Rai, M. M.
1986-01-01
A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.
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
NASA Astrophysics Data System (ADS)
Fu, Xilin; Zheng, Shasha
2014-09-01
In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow's dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.
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.
Thermodynamic of fluids from a general equation of state: The molecular discrete perturbation theory
NASA Astrophysics Data System (ADS)
Gámez, Francisco
2014-06-01
An extensive generalisation of the discrete perturbation theory for molecular multipolar non-spherical fluids is presented. An analytical expression for the Helmholtz free energy for an equivalent discrete potential is given as a function of density, temperature, and intermolecular parameters with implicit shape and multipolar dependence. By varying the intermolecular parameters through their geometrical and multipolar dependence, a set of molecular fluids are considered and their vapor-liquid phase diagrams are tested against available simulation data. Concretely, multipolar and non-polar Kihara and chainlike fluids are tested and it is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the Monte Carlo data for the selected molecular potentials, except near the critical region.
The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems.
Vardeman, Charles F; Stocker, Kelsey M; Gezelter, J Daniel
2011-04-12
We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the "Langevin Hull", can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015
The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems
Vardeman, Charles F.; Stocker, Kelsey M.; Gezelter, J. Daniel
2011-01-01
We have developed a new isobaric-isothermal (NPT) algorithm which applies an external pressure to the facets comprising the convex hull surrounding the system. A Langevin thermostat is also applied to the facets to mimic contact with an external heat bath. This new method, the “Langevin Hull”, can handle heterogeneous mixtures of materials with different compressibilities. These systems are problematic for traditional affine transform methods. The Langevin Hull does not suffer from the edge effects of boundary potential methods, and allows realistic treatment of both external pressure and thermal conductivity due to the presence of an implicit solvent. We apply this method to several different systems including bare metal nanoparticles, nanoparticles in an explicit solvent, as well as clusters of liquid water. The predicted mechanical properties of these systems are in good agreement with experimental data and previous simulation work. PMID:21547015
Schieber, Jay D.
in large-amplitude oscillatory shear (LAOS): Application to theoretical nonlinear models J. Rheol. 56, 1 (2012) Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers J of the material in the frequency-domain. Therefore, methods of analysis require conversion of the data
Song, XiaoGeng, Ph. D. Massachusetts Institute of Technology
2009-01-01
In this dissertation, we discuss two methods developed during my PhD study to simulate electron transfer systems. The first method, the semi-classical approximation, is derived from the stationary phase approximation to ...
NASA Astrophysics Data System (ADS)
Xaplanteris, C. L.; Filippaki, E. D.; Xaplanteris, L. C.; Xaplanteris
2013-04-01
Among the theoretical and experimental situations of interest in plasma physics are the waves that rise into the plasma and are strongly affected from the plasma parameters. Therefore, the development of strong relations between unperturbed and perturbed quantities is proved to exist both experimentally and theoretically. In the present paper, the mathematical solution ended in a relation between drift and perturbed velocities, which presupposes the perturbed velocity value to be very small in comparison with the drift velocity. However, the experiment has shown that the presupposition of the small value of the perturbations is not satisfied in many laboratory instances; as a result the use of the perturbation theory is limited. To surpass this difficulty, the big perturbed quantity was divided into small and equal parts, and by using the equation between unperturbed and perturbed velocities as a repeating relation, the perturbed theory may be extended and generalized beyond the small disturbances. In addition, calculations with a little change in the initial conditions were carried out, to determine when the plasma obtains chaotic behavior.
NASA Astrophysics Data System (ADS)
Ohzeki, Masayuki; Ichiki, Akihisa
2015-09-01
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs- Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition- probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.
Lattice model theory of the equation of state covering the gas, liquid, and solid phases
NASA Technical Reports Server (NTRS)
Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.
1975-01-01
The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.
NASA Astrophysics Data System (ADS)
Ray, Deb Shankar
1990-01-01
A new quantum statistical formulation of a damped classically driven Morse oscillator is presented. The theory is based on the realization of the Morse oscillator in terms of generators of an SU(2) Lie algebra, which allows us to construct the spin coherent states for the Morse oscillator. The c-number equivalents of the master equation in the form of the Fokker-Planck and Langevin equations have been derived and solved in the mean field limit to demonstrate the existence of multiple steady states and the associated molecular bistability. The nonstationary solution derived under adiabatic elimination of relevant variable and secular approximation is also presented. Some spectral characteristics such as shift and linewidth due to phase fluctuations have been calculated.
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
Spectral Decomposition of a Fokker-Planck Equation at Criticality
NASA Astrophysics Data System (ADS)
Bologna, M.; Beig, M. T.; Svenkeson, A.; Grigolini, P.; West, B. J.
2015-07-01
The mean field for a complex network consisting of a large but finite number of random two-state elements, , has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to . In the limiting case , the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When , the inverse power law is truncated by an exponential decay with rate , the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker-Planck equation and its equivalent Schrödinger equation representation.
Theory 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
NASA Astrophysics Data System (ADS)
Hollingshead, Kyle B.; Truskett, Thomas M.
2015-04-01
We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair-interaction forms comprising a hard core and a combination of two shoulders and/or wells. Since model pair potentials like these are of interest for discretized or coarse-grained representations of effective interactions in complex fluids (e.g., for computationally intensive inverse optimization problems), we focus here on assessing how accurately their properties can be predicted by analytical or simple numerical closures including Percus-Yevick, hypernetted-chain, and reference hypernetted-chain closures and first-order mean spherical and modified first-order mean spherical approximations. To make quantitative comparisons between the predicted and simulated radial distribution functions, we introduce a cumulative structural error metric. For equilibrium fluid state points of these models, we find that the reference hypernetted-chain closure is the most accurate of the tested approximations as characterized by this metric or related thermodynamic quantities.
Palmer, David S; Mišin, Maksim; Fedorov, Maxim V; Llinas, Antonio
2015-09-01
We report a method to predict physicochemical properties of druglike molecules using a classical statistical mechanics based solvent model combined with machine learning. The RISM-MOL-INF method introduced here provides an accurate technique to characterize solvation and desolvation processes based on solute-solvent correlation functions computed by the 1D reference interaction site model of the integral equation theory of molecular liquids. These functions can be obtained in a matter of minutes for most small organic and druglike molecules using existing software (RISM-MOL) (Sergiievskyi, V. P.; Hackbusch, W.; Fedorov, M. V. J. Comput. Chem. 2011, 32, 1982-1992). Predictions of caco-2 cell permeability and hydration free energy obtained using the RISM-MOL-INF method are shown to be more accurate than the state-of-the-art tools for benchmark data sets. Due to the importance of solvation and desolvation effects in biological systems, it is anticipated that the RISM-MOL-INF approach will find many applications in biophysical and biomedical property prediction. PMID:26212723
A study of Kramers' turnover theory in the presence of exponential memory friction
NASA Astrophysics Data System (ADS)
Ianconescu, Reuven; Pollak, Eli
2015-09-01
Originally, the challenge of solving Kramers' turnover theory was limited to Ohmic friction, or equivalently, motion of the escaping particle governed by a Langevin equation. Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)] (MM) presented a solution valid for Ohmic friction. The turnover theory was derived more generally and for memory friction by Pollak, Grabert, and Hänggi [J. Chem. Phys. 91, 4073 (1989)] (PGH). Mel'nikov proceeded to also provide finite barrier corrections to his theory [Phys. Rev. E 48, 3271 (1993)]. Finite barrier corrections were derived only recently within the framework of PGH theory [E. Pollak and R. Ianconescu, J. Chem. Phys. 140, 154108 (2014)]. A comprehensive comparison between MM and PGH theories including finite barrier corrections and using Ohmic friction showed that the two methods gave quantitatively similar results and were in quantitative agreement with numerical simulation data. In the present paper, we extend the study of the turnover theories to exponential memory friction. By comparing with numerical simulation, we find that PGH theory is rather accurate, even in the strong friction long memory time limit, while MM theory fails. However, inclusion of finite barrier corrections to PGH theory leads to failure in this limit. The long memory time invalidates the fundamental assumption that consecutive traversals of the well are independent of each other. Why PGH theory without finite barrier corrections remains accurate is a puzzle.
2015-01-01
Reduced Langevin recombination has been observed in organic solar cells (OSCs) for many years, but its origin is still unclear. A recent work by Burke et al. (Adv. Energy Mater.2015, 5, 1500123-1) was inspired by this reduced Langevin recombination, and they proposed an equilibrium model of charge-transfer (CT) states that correlates the open-circuit voltage of OSCs with experimentally available device parameters. In this work, we extend Burke et al.’s CT model further and for the first time directly correlate the reduced Langevin recombination with the energetic and dynamic behavior of the CT state. Recombination through CT states leads in a straightforward manner to a decrease in the Langevin reduction factor with increasing temperature, without explicit consideration of the temperature dependence of the mobility. To verify the correlation between the CT states and reduced Langevin recombination, we incorporated this CT model and the reduced Langevin model into drift-diffusion simulations of a bilayer OSC. The simulations not only successfully reproduced realistic current–voltage (J–V) characteristics of the bilayer OSC, but also demonstrate that the two models consistently lead to same value of the apparent Langevin reduction factor. PMID:26640611
Jia Ying; Bao Jingdong
2007-03-15
The anisotropy of the fission fragment angular distribution defined at the saddle point and the neutron multiplicities emitted prior to scission for fissioning nuclei {sup 224}Th, {sup 229}Np, {sup 248}Cf, and {sup 254}Fm are calculated simultaneously by using a set of realistic coupled two-dimensional Langevin equations, where the (c,h,{alpha}=0) nuclear parametrization is employed. In comparison with the one-dimensional stochastic model without neck variation, our two-dimensional model produces results that are in better agreement with the experimental data, and the one-dimensional model is available only for low excitation energies. Indeed, to determine the temperature of the nucleus at the saddle point, we investigate the neutron emission during nucleus oscillation around the saddle point for different friction mechanisms. It is shown that the neutrons emitted during the saddle oscillation cause the temperature of a fissioning nuclear system at the saddle point to decrease and influence the fission fragment angular distribution.
NASA Astrophysics Data System (ADS)
Yedlin, Matthew; Virieux, Jean
2010-05-01
As data collection in both seismic data acquisition and radar continues to improve, more emphasis is being placed on data pre-processing and inversion, in particular frequency domain waveform inversion in seismology [1], and, for example, time-domain waveform inversion in crosshole radar measurements [2]. Complementary to these methods are the sensitivity kernel techniques established initially in seismology [3, 4]. However, these methods have also been employed in crosshole radar tomography [5]. The sensitivity kernel technique has most recently been applied to the analysis of diffraction of waves in shallow water [6]. Central to the sensitivity kernel techniques is the use of an appropriate Green's function in either two or three dimensions and a background model is assumed for the calculation of the Green's function. In some situations, the constant velocity Green's function is used [5] but in other situations a smooth background model is used in a ray-type approximation. In the case of the smooth background model, computation of a ray-tracing type Green's function is problematic since at the source point the rays convergence, creating a singularity in the computation of the Jacobian used in the amplitude calculation. In fact the source is an axial caustic in two dimensions and a point caustic in three dimensions [7]. To obviate this problem, we will create a uniform asymptotic ansatz [8], explaining in detail how it is obtained in two dimensions. We will then show how to extend the results to three dimensions. In both cases, the Green's function will be obtained in the frequency domain for the acoustic equation with smoothly varying density and bulk modulus. The application of the new Green's function technique will provide more flexibility in the computation of sensitivities, both in seismological and radar applications. References [1] R. G. Pratt. 1999, Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics 64(3), pp. 888-901. [2] J. R. Ernst, A. G. Green, H. Maurer and K. Holliger. 2007, Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data. Geophysics 72, pp. J53. [3] H. Marquering, F. Dahlen and G. Nolet. 1999, Three-dimensional sensitivity kernels for finite-frequency traveltimes: The banana-doughnut paradox. Geophysical Journal International 137(3), pp. 805-815. [4] J. Tromp, C. Tape and Q. Liu. 2005, Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophysical Journal International 160(1), pp. 195-216. [5] M. L. Buursink, T. C. Johnson, P. S. Routh and M. D. Knoll. 2008, Crosshole radar velocity tomography with finite-frequency fresnel volume sensitivities. Geophysical Journal International 172(1), pp. 1-17. [6] I. Iturbe, P. Roux, J. Virieux and B. Nicolas. 2009, Travel-time sensitivity kernels versus diffraction patterns obtained through double beam-forming in shallow water. J. Acoust. Soc. Am. 126(2), pp. 713-720. [7] E. Zauderer. 1971, Uniform asymptotic solutios of the reduced wave equation. Journal of Mathematical Analysis and Application 30, pp. 157-171. [8] M. J. Yedlin. 1987, Uniform asymptotic solution for the Green's function for the two-dimensional acoustic equation. J. Acoust. Soc. Am. 81(2) pp. 238-243.
Banik, Sarmistha; Hempel, Matthias; Bandyopadhyay, Debades
2014-10-01
We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of ?s. We have developed two variants of hyperonic EoS tables: in the np?? case the repulsive hyperon-hyperon interaction mediated by the strange ? meson is taken into account, and in the np? case it is not. The EoS tables for the two cases encompass a wide range of densities (10{sup –12} to ?1 fm{sup –3}), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of ? hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, ?-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M {sub ?} maximum mass neutron star for the np?? case, whereas that for the np? case is 1.95 M {sub ?}. The np?? EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M {sub ?} neutron stars.
NASA Astrophysics Data System (ADS)
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I.
2015-08-01
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Epifanovsky, Evgeny; Klein, Kerstin; Stopkowicz, Stella; Gauss, Jürgen; Krylov, Anna I
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results. PMID:26277122
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.
Design of Experiment for Measurement of Langevin Function
NASA Astrophysics Data System (ADS)
Tu?ek, P.; Tu?ková, M.; Fišerová, E.; Tu?ek, J.; Kubá?ek, L.
2012-01-01
The presented study focuses on a confrontation of the theory of regression models and theory of experiment with the real situation of determining properties of magnetic (nano)materials. Their magnetic properties can be deduced by measuring their magnetization, being the fundamental magnetic quantity of an arbitrary (nano)material. The results of the magnetization measurements determine the unknown parameters of a known nonlinear function that characterizes the (nano)material under investigation. Knowledge of the values of the uknkown parameters enables to decide whether the (nano)material is suitable or not for a particular application. Thus, in this work, we present a possible approach how to estimate the unknown parameters of the nonlinear function by the regression models, taking into account a relevant linearization criterion. Then, we suggest an appropriate design for the measurement to get better estimators of the parameters.
Shehadeh, Zuhair F.; Scott, Jeremy S.; Malik, F. Bary
2011-10-27
The elastic scattering cross sections for {pi}{sup +} by {sup 40}Ca have been analyzed, for the first time, using the Klein-Gordon (KG) equation that incorporates the Coulomb interaction between the charged pions and targets explicitly for the incident energies of 163.3 and 180 MeV. The nuclear part of the potentials is determined using an inverse scattering theory as a guide. Our results are then compared to those where the Coulomb potential has not been explicitly included in the KG equation but its effect is studied by modifying the incident kinetic energy following the prescription of Stricker. Our calculations that include the Coulomb potential in the KG equation reproduce the results using the Stricker prescription for {pi}{sup +}. The Stricker method is then used to calculate {pi}{sup -} scattering. In all cases, the data have been well accounted for.
Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation
Stinson, Jake L.; Kathmann, Shawn M.; Ford, Ian J.
2014-11-17
We investigate some unusual behaviour observed while performing molecular dynamics simulations with the DL_POLY_4.03 code. Under the standard Langevin thermostat, atoms appear to be thermalised to different temperatures, depending on their mass and on the total number of particles in the system. We find that an imposed constraint whereby no thermal noise acts on the centre of mass of the system is the cause of the unexpected behaviour. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. The effect of the constraint can be considerable for small systems with disparate masses. By removing the constraint the Langevin thermostat may be restored to its intended behaviour and this has been implemented as an option in DL_POLY_4.05. SMK was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.
Robust and efficient configurational molecular sampling via Langevin Dynamics
Leimkuhler, Benedict
2013-01-01
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 (th...
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
Howieson, William B
2008-01-01
In 1996, Professor Robert J House published a reformulated Path-Goal Theory of Work Unit Leadership, based on his earlier 1971 and 1974 theories. Path-goal leadership attempts to explain the impact that leader behaviour ...
GÃ©za, Makay
://www.math.u-szeged.hu/ejqtde/ Nonradial solutions for semilinear SchrÃ¶dinger equations with sign-changing potential Dingyang Lv and Xuxin. In this paper, we investigate the existence of infinite nonradial solutions for the SchrÃ¶dinger equations - u many nonradial solutions. The method of proof relies on critical point theorem. Keywords: SchrÃ¶dinger
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
Yi-An Ma; Hong Qian
2015-11-04
We carry out mathematical analyses, {\\em \\`{a} la} Helmholtz's and Boltzmann's 1884 studies of monocyclic Newtonian dynamics, for the Lotka-Volterra (LV) equation exhibiting predator-prey oscillations. In doing so a novel "thermodynamic theory" of ecology is introduced. An important feature, absent in the classical mechanics, of ecological systems is a natural stochastic population dynamic formulation of which the deterministic equation (e.g., the LV equation studied) is the infinite population limit. Invariant density for the stochastic dynamics plays a central role in the deterministic LV dynamics. We show how the conservation law along a single trajectory extends to incorporate both variations in a model parameter $\\alpha$ and in initial conditions: Helmholtz's theorem establishes a broadly valid conservation law in a class of ecological dynamics. We analyze the relationships among mean ecological activeness $\\theta$, quantities characterizing dynamic ranges of populations $\\mathcal{A}$ and $\\alpha$, and the ecological force $F_{\\alpha}$. The analyses identify an entire orbit as a stationary ecology, and establish the notion of "equation of ecological states". Studies of the stochastic dynamics with finite populations show the LV equation as the robust, fast cyclic underlying behavior. The mathematical narrative provides a novel way of capturing long-term dynamical behaviors with an emergent {\\em conservative ecology}.
Choi, Eunsong; Yethiraj, Arun
2015-07-23
We study the conformational properties of polymers in room temperature ionic liquids using theory and simulations of a coarse-grained model. Atomistic simulations have shown that single poly(ethylene oxide) (PEO) molecules in the ionic liquid 1-butyl 3-methyl imidazolium tetrafluoroborate ([BMIM][BF4]) are expanded at room temperature (i.e., the radius of gyration, Rg), scales with molecular weight, Mw, as Rg ? Mw(0.9), instead of the expected self-avoiding walk behavior. The simulations were restricted to fairly short chains, however, which might not be in the true scaling regime. In this work, we investigate a coarse-grained model for the behavior of PEO in [BMIM][BF4]. We use existing force fields for PEO and [BMIM][BF4] and Lorentz–Berthelot mixing rules for the cross interactions. The coarse-grained model predicts that PEO collapses in the ionic liquid. We also present an integral equation theory for the structure of the ionic liquid and the conformation properties of the polymer. The theory is in excellent agreement with the simulation results. We conclude that the properties of polymers in ionic liquids are unusually sensitive to the details of the intermolecular interactions. The integral equation theory is sufficiently accurate to be a useful guide to computational work. PMID:25310685
Beklaryan, Leva A
2011-03-31
A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.
Jadrich, Ryan; Schweizer, Kenneth S
2013-08-01
Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions. PMID:23927265
NASA Astrophysics Data System (ADS)
Jadrich, Ryan; Schweizer, Kenneth S.
2013-08-01
Building on the equation-of-state theory of Paper I, we construct a new thermodynamically consistent integral equation theory for the equilibrium pair structure of 3-dimensional monodisperse hard spheres applicable up to the jamming transition. The approach is built on a two Yukawa generalized mean spherical approximation closure for the direct correlation function (DCF) beyond contact that reproduces the exact contact value of the pair correlation function and isothermal compressibility. The detailed construction of the DCF is guided by the desire to capture its distinctive features as jamming is approached. Comparison of the theory with jamming limit simulations reveals good agreement for many, but not all, of the key features of the pair correlation function. The theory is more accurate in Fourier space where predictions for the structure factor and DCF are accurate over a wide range of wavevectors from significantly below the first cage peak to very high wavevectors. New features of the equilibrium pair structure are predicted for packing fractions below jamming but well above crystallization. For example, the oscillatory DCF decays very slowly at large wavevectors for high packing fractions as a consequence of the unusual structure of the radial distribution function at small separations. The structural theory is used as input to the nonlinear Langevin equation theory of activated dynamics, and calculations of the alpha relaxation time based on single particle hopping are compared to recent colloid experiments and simulations at very high volume fractions.
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
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.
Hiroaki Kohyama
2015-07-29
We study the regularization dependence on the quenched Schwinger-Dyson equations in general gauge by applying the two types of regularizations, the four and three dimensional momentum cutoffs. The obtained results indicate that the solutions are not drastically affected by the choice of two different cutoff prescriptions. We then think that both the regularizations can nicely be adopted in the analyses for the Schwinger-Dyson equations.
Doktorov, A. B.
2014-09-14
In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.
Non-Gaussian statistics, classical eld theory, and realizable Langevin models John A. Krommes
. INTRODUCTION The importance and utility of statistical closure ap- proximations applied to the nonlinear consider the possibility of deriving ZDIA by routes alter- native to the one based on the RCM. First, I
Kinematic matrix theory and universalities in self-propellers and active swimmers
Amir Nourhani; Paul E. Lammert; Ali Borhan; Vincent H. Crespi
2014-09-10
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.
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.
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…
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward. PMID:26323089
Charles R. Tolle; Mark Pengitore
2009-08-01
This paper explores the overlaps between the Control 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.
Mingtian Xu; Frank Stefani; Gunter Gerbeth
2007-04-20
The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed into an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting fluid and to its boundary. This integral equation approach is first employed to simulate kinematic dynamos excited by Beltrami-like flows in a finite cylinder. The impact of externally added layers around the cylinder on the onset of dynamo actions is investigated. Then it is applied to simulate dynamo experiments within cylindrical geometry including the von Karman sodium (VKS) experiment and the Riga dynamo experiment. A modified version of this approach is utilized to investigate magnetic induction effects under the influence of externally applied magnetic fields which is also important to measure the proximity of a given dynamo facility to the self-excitation threshold.
Pei Wang
2007-05-09
We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric tensor on reduced dimensions is negligible it becomes a pure antisymmetric tensor.
Moore, John Barratt
(t)a(t Â t) + /l'(t)o(t,z)k(T )l(t Â 7) + k'(t)@ '('r,t)ll(7)l(7 Â t), (3) where 0( c,c) is the transition with nonmixed boundary conditions, is desciibed for the case when the kernel of the integral equation is known
Non-linear Langevin model for the early-stage dynamics of electrospinning jets
Lauricella, Marco; Pisignano, Dario; Succi, Sauro
2015-01-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
Nonlinear Langevin model for the early-stage dynamics of electrospinning jets
NASA Astrophysics Data System (ADS)
Lauricella, Marco; Pontrelli, Giuseppe; Pisignano, Dario; Succi, Sauro
2015-09-01
We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle. Numerical simulations show that the elongation of the jet filament close to the injection point is significantly affected by the non-linear drag exerted by the surrounding air. These result provide useful insights for the optimal design of current and future electrospinning experiments.
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 ...
Stolle, A.M.
1991-01-01
The expressions for the power spectral density of the noise equivalent sources have been calculated explicitly for the (a) stochastic transport equation, (b) the one-speed transport equaton, (c) the one-speed P{sub 1} equations, (d) the one-speed diffusion equation and (e) the point kinetic equation. The stochastic nature of Fick's law in (d) has been emphasized. The Langevin technique has been applied at various levels of approximation to the interpretation of the Californium-252 Source-Driven Noise Analysis (CSDNA) experiment for determining the reactivity in subcritical media. The origin of the controversy surrounding this method has been explained. The foundations of the CSDNA method as a viable experimental technique to infer subcriticality from a measured ratio of power spectral densities of the outputs of two neutron detectors and a third external source detector has been examined by solving the one-speed stochastic diffusion equation for a point external Californium-252 source and two detectors in an infinite medium. The expression relating reactivity to the measured ratio of PSDs was found to depend implicitly on k itself. Through a numerical analysis fo this expression, the authors have demonstrated that for a colinear detector-source-detector configuration for neutron detectors far from the source, the expression for the subcritical multiplication factor becomes essentially insensitive to k, hence, demonstrating some possibility for the viability of this technique. However, under more realistic experimental conditions, i.e., for finite systems in which diffusion theroy is not applicable, the measurement of the subcritical multiplication factor from a single measured ratio of PSDs, without extensive transport calculations, remains doubtful.
Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling
NASA Astrophysics Data System (ADS)
Wu, Xiongwu; Hodoscek, Milan; Brooks, Bernard R.
2012-07-01
This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.
Introduction Basics of gravity theory
Visser, Matt
Introduction Basics of gravity theory Actions and Field Equations Phenomenology Discussion;Introduction Basics of gravity theory Actions and Field Equations Phenomenology Discussion and Conclusions Einstein completes the General Theory of Relativity (GR). The theory explains Mercury's precession. 1919
Podgornik, Rudolf
, tubulin. In most cases biology controls elastic properties by controlled polymerization March 1998 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
ERIC Educational Resources Information Center
Mayhew, Matthew J.; Hubbard, Steven M.; Finelli, Cynthia J.; Harding, Trevor S.; Carpenter, Donald D.
2009-01-01
The purpose of this paper is to validate the use of a modified Theory of Planned Behavior (TPB) for predicting undergraduate student cheating. Specifically, we administered a survey assessing how the TPB relates to cheating along with a measure of moral reasoning (DIT- 2) to 527 undergraduate students across three institutions; and analyzed the…
Evans, J W; Li, M; Bartelt, M C
2002-12-05
Extensive information on the distribution of islands formed during submonolayer deposition is provided by the joint probability distribution (JPD) for island sizes, s, and capture zone areas, A. A key ingredient determining the form of the JPD is the impact of each nucleation event on existing capture zone areas. Combining a realistic characterization of such spatial aspects of nucleation with a factorization ansatz for the JPD, we provide a concise rate equation formulation for the variation with island size of both the capture zone area and the island density.
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.
Electromagnetic Theory 1 /56 Electromagnetic Theory
Bicknell, Geoff
Electromagnetic Theory 1 /56 Electromagnetic Theory Summary: · Maxwell's equations · EM Potentials · Equations of motion of particles in electromagnetic fields · Green's functions · Lienard-Weichert potentials · Spectral distribution of electromagnetic energy from an arbitrarily moving charge #12;Electromagnetic
NASA Astrophysics Data System (ADS)
Bankovi?, A.; Dujko, S.; White, R. D.; Buckman, S. J.; Petrovi?, Z. Lj.
2012-07-01
A multi term theory for solving Boltzmann's equation is briefly reviewed and used to test various concepts and approximate expressions for the determination of the positron transport properties in neutral molecular gases in crossed electric and magnetic fields. Among many important approximations which have found their way into contemporary positron studies, the following are particularly discussed: (1) is the approximation of using the cross sections for the electron scattering to describe the positron behavior satisfactory, (2) how accurate is two term approximation for solving Boltzmann's equation in the context of positron studies, and (3) what is the domain of applicability of Langevin elementary transport theory and Tonks' theorem for positrons in electric and magnetic fields. We highlight the limitations, range of applicability and inadequacies of such assumptions for positrons in H2 and N2. It is pointed out that there is no real alternative to the accurate multi term theory and/or Monte Carlo simulations if high precision is required. It is demonstrated that if the demands for accuracy associated with some of these approximations are relaxed, results may not be even qualitatively correct.
Ye Jingxin; Zhao Bin; Zheng Jian
2011-03-15
Under hypernetted chain (HNC) approximation, effective ion pair interaction potentials for the warm dense matter are extracted by using available radial distribution functions (RDFs). The effective ion pair potentials extracted from first-principles simulation results are found containing the short-ranged attraction (SRA) component for both warm dense helium and beryllium plasmas. The SRA potentials can be well represented by Gaussian functions in both cases and then the extracted effective ion potentials are well fitted. As an application, the well fitted potentials are used to describe ion-ion interactions in classical molecular dynamics simulations. The yield RDFs are in excellent agreement with those computed by HNC equations and first-principles simulations, respectively.
Hironobu Sasaki; Akito Suzuki
2011-01-01
An inverse scattering problem for a quantized scalar field ${\\bm \\phi}$ obeying a linear Klein-Gordon equation $(\\square + m^2 + V) {\\bm \\phi} = J \\mbox{in $\\mathbb{R} \\times \\mathbb{R}^3$}$ is considered, where $V$ is a repulsive external potential and $J$ an external source $J$. We prove that the scattering operator $\\mathscr{S}= \\mathscr{S}(V,J)$ associated with ${\\bm \\phi}$ uniquely determines $V$. Assuming that $J$ is of the form $J(t,x)=j(t)\\rho(x)$, $(t,x) \\in \\mathbb{R} \\times \\mathbb{R}^3$, we represent $\\rho$ (resp. $j$) in terms of $j$ (resp. $\\rho$) and $\\mathscr{S}$.
Aboulhamid, El Mostapha
units and an interconnection network. I. INTRODUCTION Hardware/Software (HW/SW) co-synthesis [7] refers Modules RTL Software Yes No Architecture Architecture Processor compilationsynthesis No Yes PerformancePerformance Analysis for Hardware/Software Co-synthesis 1 Imed E. Bennour, Michel Langevin and El M
NASA Astrophysics Data System (ADS)
Myeong, Jeon-Ok; Crawley, Frank E.
The theory of reasoned action (Ajzen & Fishbein, 1980; Fishbein & Ajzen, 1975) was used to predict and understand Korean high school students' track choice for college entrance. First-year high school students (N = 665) from four representative regions of Korea participated in the study. The survey instruments were questionnaires developed according to the guidelines of the TRA. The target behavior of interest in this study was Korean students' choice of the science track when they completed the track application forms during the first year of high school. Predictors included TRA model and external variables. Multiple regression and the structural equation modeling with LISREL (Jöreskog & Sörbom, 1986) were used to analyze the data. The TRA was found to be applicable for understanding and predicting track choice, with minor modifications. Subjective norm was found to exert a direct influence on personal beliefs and the target behavior.
Victor F. Los; Nicholas V. Los
2015-06-29
An exact time-dependent solution for the wave function $\\psi(r,t)$ of a particle moving in the presence of an asymmetric rectangular well/barrier potential varying in one dimension is obtained by applying a novel for this problem approach using multiple scattering theory (MST) for the calculation of the space-time propagator. This approach, based on the localized at the potential jumps effective potentials responsible for transmission through and reflection from the considered rectangular potential, enables considering these processes from a particle (rather than a wave) point of view. The solution describes these quantum phenomena as a function of time and is related to the fundamental issues (such as measuring time) of quantum mechanics. It is presented in terms of integrals of elementary functions and is a sum of the forward- and backward-moving components of the wave packet. The relative contribution of these components and their interference as well as of the potential asymmetry to the probability density $|\\psi(x,t)|^2$ and particle dwell time is considered and numerically visualized for narrow and broad energy (momentum) distributions of the initial Gaussian wave packet. The obtained solution is also related to the kinetic theory of nanostructures due to the fact that the considered potential can model the spin-dependent potential profile of the magnetic multilayers used in spintronics devices.
Distributed-order diffusion equations and multifractality: Models and solutions
NASA Astrophysics Data System (ADS)
Sandev, Trifce; Chechkin, Aleksei V.; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M.; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Distributed-order diffusion equations and multifractality: Models and solutions.
Sandev, Trifce; Chechkin, Aleksei V; Korabel, Nickolay; Kantz, Holger; Sokolov, Igor M; Metzler, Ralf
2015-10-01
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided. PMID:26565178
Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA.
de Los Santos, F; Al Hammal, Omar; Muñoz, Miguel A
2008-03-01
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 nonzero values of the stiffness parameter. Not surprisingly, we also find that, for heterogeneous DNA, within this model the largest bubbles in the premelting 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. PMID:18517446
A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II
Uchida, Waka; Kimura, Yoshiro; Wakabayashi, Masamitsu; Hatakeyama, Makoto; Ogata, Koji; Nakamura, Shinichiro; Yokojima, Satoshi
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.
A study of QM/Langevin-MD simulation for oxygen-evolving center of photosystem II
NASA Astrophysics Data System (ADS)
Uchida, Waka; Kimura, Yoshiro; Hatakeyama, Makoto; Wakabayashi, Masamitsu; Yokojima, Satoshi; Ogata, Koji; Nakamura, Shinichiro
2013-12-01
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 Mn4O5Ca 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 Mn4O5Ca 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.
SuperADAM: Upgraded polarized neutron reflectometer at the Institut Laue-Langevin
NASA Astrophysics Data System (ADS)
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 × 104 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 3He 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.
Langevin model for real-time Brownian dynamics of interacting nanodefects in irradiated metals
Dudarev, S. L.; Arakawa, K.; Mori, H.; Yao, Z.; Jenkins, M. L.; Derlet, P. M.
2010-06-01
In situ real-time electron microscope observations of metals irradiated with ultrahigh-energy electrons or energetic ions show that the dynamics of microstructural evolution in these materials is strongly influenced by long-range elastic interactions between mobile nanoscale radiation defects. Treating long-range interactions is also necessary for modeling microstructures formed in ex situ high-dose-rate ion-beam irradiation experiments, and for interpolating the ion-beam irradiation data to the low-dose-rate limit characterizing the neutron irradiation environments of fission or fusion power plants. We show that simulations, performed using an algorithm where nanoscale radiation defects are treated as interacting Langevin particles, are able to match and explain the real-time dynamics of nanodefects observed in in situ electron microscope experiments.
On Application Of Langevin Dynamics In Logarithmic Potential To Model Ion Channel Gate Activity.
Wawrzkiewicz-Ja?owiecka, Agata; Borys, Przemys?aw; Grzywna, Zbigniew J
2015-12-01
We model the activity of an ion channel gate by Langevin dynamics in a logarithmic potential. This approach enables one to describe the power-law dwell-time distributions of the considered system, and the long-term correlations between the durations of the subsequent channel states, or fractal scaling of statistical characteristics of the gate's movement with time. Activity of an ion channel gate is described as an overdamped motion of the reaction coordinate in a confining logarithmic potential, which ensures great flexibility of the model. Depending on the chosen parameters, it allows one to reproduce many types of gate dynamics within the family of non-Markovian, anomalous conformational diffusion processes. In this study we apply the constructed model to largeconductance voltage and Ca2+-activated potassium channels (BKCa). The interpretation of model assumptions and parameters is provided in terms of this biological system. Our results show good agreement with the experimental data. PMID:26317442
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
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; Philippa, Bronson; White, Ronald D.
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.
Curro, John G.; Frischknecht, Amalie Lucile
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).
NASA Astrophysics Data System (ADS)
Su, Ninghu; Nelson, Paul N.; Connor, Sarah
2015-10-01
We present a distributed-order fractional diffusion-wave equation (dofDWE) to describe radial groundwater flow to or from a well, and three sets of solutions of the dofDWE for flow from a well for aquifer tests: one for pumping tests, and two for slug tests. The dofDWE is featured by two temporal orders of fractional derivatives, ?1 and ?2, which characterise small and large pores, respectively. By fitting the approximate solutions of the dofDWE to data from slug tests in the field, we determined the effective saturated hydraulic conductivity, Ke, transmissivity, Tf, and the order of fractional derivatives, ?2 in one test and ?2 and ?1 in the second test. We found that the patterns of groundwater flow from a well during the slug tests at this site belong to the class of sub-diffusion with ?2 < 1 and ?1 < 1 using both the short-time and large-time solutions. We introduce the concept of the critical time to link Ke as a function of ?2 and ?1. The importance of the orders of fractional derivatives is obvious in the approximate solutions: for short time slug tests only the parameter ?2 for flow in large pores is present while for long time slug tests the parameters ?2 and ?1 are present indicating both large and small pores are functioning.
G. B. Alaverdyan
2009-07-23
The equation of state of neutron star matter is examined in terms of the relativistic mean-field theory, including a scalar-isovector $\\delta$-meson effective field. The constants of the theory are determined numerically so that the empirically known characteristics of symmetric nuclear matter are reproduced at the saturation density. The thermodynamic characteristics of both asymmetric nucleonic matter and $\\beta$-equilibrium hadron-electron $npe$-plasmas are studied. Assuming that the transition to strange quark matter is an ordinary first-order phase transition described by Maxwell's rule, a detailed study is made of the variations in the parameters of the phase transition owing to the presence of a $\\delta$-meson field. The quark phase is described using an improved version of the bag model, in which interactions between quarks are accounted for in a one-gluon exchange approximation. The characteristics of the phase transition are determined for various values of the bag parameter within the range $B\\in[60,120]$ $MeV/fm^{3}$ and it is shown that including a $\\delta$-meson field leads to a reduction in the phase transition pressure $P_{0}$ and in the concentrations $n_{N}$ and $n_{Q}$ at the phase transition point.
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.
Wosiek, Jacek
2015-01-01
Recently found positive representation for an arbitrary complex, gaussian weight is used to construct a statistical formulation of gaussian path integrals directly in the Minkowski time. The positivity of Minkowski weights is achieved by doubling the number of real variables. The continuum limit of the new representation exists only if some of the additional couplings tend to infinity and are tuned in a specific way. The construction is then successfully applied to three quantum mechanical examples including a particle in a constant magnetic field -- a simplest prototype of a Wilson line. Further generalizations are shortly discussed and an intriguing interpretation of new variables is alluded to.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Microscopic Theory of Activated Penetrant Diffusion in Liquids and Glasses
NASA Astrophysics Data System (ADS)
Zhang, Rui; Schweizer, Kenneth
2015-03-01
We formulate a force-level, self-consistent, nonlinear Langevin equation theory for the long-time diffusivity of a penetrant in molecular and polymeric supercooled liquids and glasses. The theory predicts that for a wide range of penetrant to matrix molecular unit size ratios (R), activated hopping is the dominant transport mechanism. The penetrant diffusivity (D) and jump distance exhibit different R-dependences in three dynamic regimes: R<0.5, 0.5
Non-equilibrium theory of arrested spinodal decomposition
NASA Astrophysics Data System (ADS)
Olais-Govea, José Manuel; López-Flores, Leticia; Medina-Noyola, Magdaleno
2015-11-01
The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ram?ez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.
Non-equilibrium theory of arrested spinodal decomposition.
Olais-Govea, José Manuel; López-Flores, Leticia; Medina-Noyola, Magdaleno
2015-11-01
The non-equilibrium self-consistent generalized Langevin equation theory of irreversible relaxation [P. E. Ram?ez-González and M. Medina-Noyola, Phys. Rev. E 82, 061503 (2010); 82, 061504 (2010)] is applied to the description of the non-equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermodynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass transition and from above by the spinodal dynamic arrest line, we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the formation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system. PMID:26547174
Non-equilibrium Theory of Arrested Spinodal Decomposition
José Manuel Olais-Govea; Leticia López-Flores; Magdaleno Medina-Noyola
2015-10-20
The Non-equilibrium Self-consistent Generalized Langevin Equation theory of irreversible relax- ation [Phys. Rev. E (2010) 82, 061503; ibid. 061504] is applied to the description of the non- equilibrium processes involved in the spinodal decomposition of suddenly and deeply quenched simple liquids. For model liquids with hard-sphere plus attractive (Yukawa or square well) pair potential, the theory predicts that the spinodal curve, besides being the threshold of the thermo- dynamic stability of homogeneous states, is also the borderline between the regions of ergodic and non-ergodic homogeneous states. It also predicts that the high-density liquid-glass transition line, whose high-temperature limit corresponds to the well-known hard-sphere glass transition, at lower temperature intersects the spinodal curve and continues inside the spinodal region as a glass-glass transition line. Within the region bounded from below by this low-temperature glass-glass tran- sition and from above by the spinodal dynamic arrest line we can recognize two distinct domains with qualitatively different temperature dependence of various physical properties. We interpret these two domains as corresponding to full gas-liquid phase separation conditions and to the for- mation of physical gels by arrested spinodal decomposition. The resulting theoretical scenario is consistent with the corresponding experimental observations in a specific colloidal model system.
Exponential differential equations Some applications and motivation
Pillay, Anand
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
Meini, Beatrice
of algebraic Riccati equations and a description of both the classical and the more advanced algorithms for their solution. Algebraic Riccati equations are a class of matrix equations which model a variety of different and techniques for dealing with algebraic Riccati equations. The literature on this topic includes some books
Wu, Wei; Wang, Jin
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.
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
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…
Bravaya, Ksenia B.; Zuev, Dmitry; Epifanovsky, Evgeny; Krylov, Anna I.
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.
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
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
Partial differential equations M VANNINATHAN
Giri, Ranjit K.
Partial differential equations M VANNINATHAN TIFR Centre for Applicable Mathematics, Post Bag 6503 that the Indian contributions to the theory of partial differential equations in general, and that of elliptic into seven subsections which present various aspects of partial differ- ential equation (PDE) highlighting
Heavy dense QCD and nuclear matter from an effective lattice theory
Langelage, Jens; Philipsen, Owe
2014-01-01
A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, \\kappa, whose action is correct to \\kappa^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute va...
Sutherland, Scott
Partial Differential Operators, Vol. 1-4, Springer, 1983-85. 5) F. John, Partial Differential Equations, and parabolic equations. 4) De Giorgi-Nash-Moser Theory. 5) General techniques for nonlinear equations: calculus
Stochastic delay differential equations for genetic regulatory networks
NASA Astrophysics Data System (ADS)
Tian, Tianhai; Burrage, Kevin; Burrage, Pamela M.; Carletti, Margherita
2007-08-01
Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical master equation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of intrinsic noise on the system dynamics where there are delays.