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NON-EQUILIBRIUM FLUCTUATIONS IN MU-SPACE

JOURNAL OF STATISTICAL PHYSICS 1981年第1期25卷 153-180页

作者： ERNST, MH COHEN, EGD ROCKEFELLER UNIV NEW YORKNY 10021

The properties of fluctuations inμ space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations inμ space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.

关键词： Fluctuations hierarchy equations master equation master hierarchy nonequilibrium statistical mechanics pair correlation function time correlation functions

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MODE-COUPLING FROM LINEAR AND NON-LINEAR KINETIC-EQUATIONS

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JOURNAL OF STATISTICAL PHYSICS 1983年第2期33卷 261-286页

作者： DUFTY, JW RODRIGUEZ, RF NBS DIV THERMOPHYSWASHINGTONDC 20234

The calculation of mode coupling contributions to equilibrium time correlation functions from the nonlinear Boltzmann equation is reconsidered. It is suggested that the use of a nonlinear kinetic equation is not appropriate in this context, but instead such calculations should be reinterpreted in terms of the Klimontovich equation for the microscopic phase space density. For hard spheres the Klimontovich equation is formally similar to the nonlinear Boltzmann equation, and this similarity is exploited to explain the successful calculation of mode coupling effects from the latter. The relationship of the Klimontovich formulation to the linear ring approximation is also established.

关键词： hard spheres Kinetic equation Klimontovich equation mode coupling nonlinear dynamics time correlation functions

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SYMMETRICAL LINEAR COLLISION OPERATORS IN KINETIC-THEORY

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JOURNAL OF STATISTICAL PHYSICS 1987年第5-6期46卷 949-969页

作者： COHEN, EGD DESCHEPPER, IM The Rockefeller University New York

We consider a class of equilibrium time correlation functions, in fluids, between local physical quantities. We investigate whether the symmetry these correlation functions display with respect to these quantities on theN-particle level also exists on the one-particle (kinetic) level. In this context we derive a new symmetric kinetic operator for a dense, hard sphere fluid.

关键词： Boltzmann equation decay Enskog equation hard spheres kinetic theory symmetric collision operator time correlation functions

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TAIL SHORTENING BY DISCRETE HYDRODYNAMICS

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JOURNAL OF STATISTICAL PHYSICS 1982年第2期27卷 389-405页

作者： KIEFER, J VISSCHER, PB Department of Physics and Astronomy The University of Alabama University Alabama

A discrete formulation of hydrodynamics was recently introduced, whose most important feature is that it is exactly renormalizable. Previous numerical work has found that it provides a more efficient and rapidly convergent method for calculating transport coefficients than the usual Green-Kubo method. The latter's convergence difficulties are due to the well-known “long-time tail” of the time correlation function which must be integrated over time. The purpose of the present paper is to present additional evidence that these difficulties are really absent in the discrete equation of motion approach. The “memory” terms in the equation of motion are calculated accurately, and shown to decay much more rapidly with time than the equilibrium time correlat

关键词： long-time tails Molecular dynamics time correlation functions transport coefficients viscosity

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Frequency-dependent fluidity and conductivity of an ionic liquid

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PHYSICAL CHEMISTRY CHEMICAL PHYSICS 2009年第28期11卷 5930-5934页

作者： Santic, Ana Wrobel, Wojciech Mutke, Monika Banhatti, Radha D. Funke, Klaus Univ Munster Inst Phys Chem D-48149 Munster Germany Univ Munster Sonderforsch Bereich 458 D-48149 Munster Germany Rudjer Boskovic Inst NMR Ctr Zagreb Croatia Warsaw Univ Technol Fac Phys Warsaw Poland Univ Munster NRW Int Grad Sch Chem D-48149 Munster Germany

The frequency- and temperature-dependent shear fluidity, f(nu, T), of the ionic liquid [BMIm]BF4 is presented and compared with its ionic conductivity, sigma(nu,T). [BMIm]BF4 is short for 1-butyl-3-methyl-imidazolium tetrafluoroborate. Its DC fluidity, f(DC)(T), and DC conductivity, sigma(DC)(T), are non-Arrhenius and superimpose in an Arrhenius-type representation if the respective inverse temperature axes are made to differ by a small amount, Delta = (1/T-circle times - 1/T) > 0. The observed superposition suggests that f(nu, T) should display a frequency dependence similar to sigma(nu, T-circle times). We have therefore measured f(nu, T) of [BMIm]BF4 over five decades of frequency at different temperatures. The spectra thus obtained corroborate our expectations. We model our experimental results in terms of the MIGRATION concept and arrive at the conclusion that f(nu, T) and sigma(nu, T-circle times) are Fourier transforms of quite similar time correlation functions.

关键词： Ionic liquids direct current Fluidity time correlation functions time DEPENDENCE conductivity Frequency dependence Fourier Transform

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Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

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Physical Review E 2012年第5期85卷 051124-051124页

作者： A. Dechant E. Lutz D. A. Kessler E. Barkai Department of Physics University of Augsburg 86135 Augsburg Germany Dahlem Center for Complex Quantum Physics FU Berlin 14195 Berlin Germany Department of Physics Bar Ilan University Ramat-Gan 52900 Israel

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

关键词： Logarithmic time correlation functions Brownian motion correlation function Destruction particles

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THE DISORDERED SOLID-PHASES OF POTASSIUM CYANIDE

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JOURNAL OF PHYSICS C-SOLID STATE PHYSICS 1983年第17期16卷 3217-3232页

作者： MCDONALD, IR BOUNDS, DG KLEIN, ML NATL RES COUNCIL CANADA DIV CHEMOTTAWA K1A 0R6ONTARIOCANADA

Molecular dynamics calculations have been carried out for the orientationally disordered phases of solid potassium cyanide. It has been found that the properties of the simulated crystal are very sensitive to the assumed charge distribution of the cyanide ion and that there is a strong correlation between the static and dynamic consequences of assumptions about the form of the interionic potential. Results are reported for the orientational distribution of the cyanide ions and for time correlation functions relevant to polarised Raman and inelastic neutron scattering experiments. The anomalous dispersion characteristic of transverse acoustic phonons in phase I is shown to be reproducible, but no single model has been found that will account for all the existing experimental data.

关键词： time correlation functions Potassium Cyanide Solid phases Acoustic phonon Experimental data CHARGE DISTRIBUTION Molecular Dynamics cyanides

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Ion solvation dynamics in supercritical water

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CHEMICAL PHYSICS LETTERS 1998年第1-3期290卷 223-228页

作者： Biswas, R Bagchi, B Indian Inst Sci Solid State & Struct Chem Unit Bangalore 560012 Karnataka India Indian Inst Sci Jawaharlal Nehru Ctr Adv Sci Res Bangalore 560012 Karnataka India

A theoretical study of ionic solvation dynamics in supercritical water is presented. The short-time decay of the calculated equilibrium solvation energy time correlation function (S-E(t)) is found to be in good agreement with the recent computer simulation results, The simulated long-time decay is, however, somewhat slower than that which is predicted by the present theory. Two plausible molecular explanations for the slow long-time decay of S-E(t) are offered. (C) 1998. Published by Elsevier Science B.V. All rights reserved.

关键词： time correlation functions dynamics Theoretical Study solvation supercritical water

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Forward-backward semiclassical simulation of dynamical processes in liquids

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JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2004年第3期3卷 391-417页

作者： Makri, N Nakayama, A Wright, NJ Univ Illinois Dept Chem Urbana IL 61801 USA

Forward-backward semiclassical dynamics (FBSD) provides a practical methodology for including quantum mechanical effects in classical trajectory simulations of polyatomic systems. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. Quantization through a discretized path integral representation of the Boltzmann operator ensures a proper treatment of zero point energy effects and of imaginary components in finite-temperature correlation functions, and extension to systems obeying Bose statistics is possible. Accelerated convergence is achieved via Monte Carlo or molecular dynamics sampling techniques and through the construction of improved imaginary time propagators. The accuracy of the methodology is demonstrated on several model systems, including models of Bose and Fermi particles. Applications to liquid argon, neon and para-hydrogen are presented.

关键词： simulation semiclassical propagation time correlation functions quantum mechanical effects liquids

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Vibrational Transition Frequency Fluctuation of the NO Stretching Mode of Sodium Nitroprusside in Aqueous Solutions

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CHEMISTRY LETTERS 2012年第4期41卷 366-368页

作者： Tayama, Jumpei Ohta, Kaoru Tominaga, Keisuke Kobe Univ Mol Photosci Res Ctr Nada Ku Kobe Hyogo 6578501 Japan JST PRESTO Kawaguchi Saitama 3320012 Japan

Frequency fluctuation of the NO stretching mode of the sodium nitroprusside, [Fe(CN)(5)NO](2-), in H2O and D2O was studied by three-pulse infrared photon echo spectroscopy. It is found that the time-correlation function of the frequency fluctuation of this mode is characterized by time constants similar to those of the triply degenerate T-1u mode of the CN stretching of [Fe(CN)(6)](4-), showing that the vibrational frequency fluctuation is not dominated by the time-dependent anisotropic solute-solvent interaction.

关键词： Sodium Nitroprusside Nitroprusside aqueous solutions Stretch NOBELIUM time correlation functions cyanogen Vibrational transition frequency fluctuations

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