Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [T.S. Chow, J.J. Hermans, Physica 65, 156 (1973)] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point. We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.     

The autocorrelation function of a pseudointegrable system

The autocorrelation function of a pseudointegrable system is considered. The system consists of “billiards” on plane surface formed out of three squares arranged in an “L” shape. This system has the important property of being constructed from copies of an integrable subsystem, the single square. The motion can be decomposed into a continuous and a discrete part, the unpredictability in the system being associated with the latter. A discrete autocorrelation function is calculated, and its decay properties investigated. Structure found in this autocorrelation function is associated with the continued fraction expansion of the ratio of velocity components. For repeating continued fractions, such as the golden mean, the autocorrelation function exhibits a selfsimilar structure. For the general case of a randomly chosen velocity ratio, we derive the time dependence of the number of occurences of “large” autocorrelation values, which differs from the behavior in integrable and chaotic systems.     

The velocity autocorrelation function of a finite model system

We investigate in detail the dependence of the velocity autocorrelation function of a one-dimensional system of hard, point particles with a simple velocity distribution function (all particles have velocities ±c) on the size of the system. In the thermodynamic limit, when both the number of particlesN and the length of the boxL approach infinity andN/L , the velocity autocorrelation function(t) is given simply by c² exp(–2ct@#@). For a finite system, the function _N(t) is periodic with period 2L/c. We also show that for more general velocity distribution functions (particles can have velocities ±c_i,i = 1,...), _N(t) is an almost periodic function oft. These examples illustrate the role of the thermodynamic limit in nonequilibrium phenomena: We must keept fixed while letting the size of the system become infinite to obtain an auto-correlation function, such as(t), which decays for all times and can be integrated to obtain transport coefficients. For any finite system, our _N (t) will be very close to(t) as long ast is small compared to the effective size of the system, which is 2L/c for the first model.Supported in part by the AFOSR under Contract No. F44620-71-C-0013.     

The exact velocity autocorrelation function of a model system

The velocity autocorrelation function of a particle in a model system with realistic diffusion is calculated exactly and compared with the corresponding result in the one-dimensional case. The method employed yields the result of Lebowitz and Sykes in one dimension in a very simple manner.Research Supported by NSF Grant No. R019881001.     

Spectrum of the velocity autocorrelation function of a molecule in a liquid

The theory of the autocorrelation function _V(t) of the velocity of an isolated molecule is formulated, taking into account the contributions of longitudinal and transverse modes of motion. The spectral density function of _V(t) accordingly, turns out to be expressed in terms of two independent susceptibilities, one of the relaxation type and the other of the wave type. The simple dispersion model constructed on the basis of the theory developed in the article agrees very precisely with the data of a computer experiment for liquid argon over the entire range of variation of.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 27–32, August, 1978.     

Momentum autocorrelation function of a classical oscillator chain with alternating masses

A classical harmonic oscillator chain with alternating masses is studied using the recurrence relations method. The momentum autocorrelation function changes from combination of cosines to Bessel functions when the number of oscillators increases from finite to infinite bringing about irreversibility. Optic and acoustic branches of the momentum autocorrelation function are expanded in terms of even-order Bessel functions and are shown to be finite and well behaved. Irreversibility and ergodicity are discussed.     

Analytical expressions for momentum autocorrelation function of a classic diatomic chain

We use recurrence relations method to study a classical harmonic diatomic chain. The momentum autocorrelation function results from contributions of acoustic and optical branches. By use of convolution theorem, analytical expressions for the acoustic and optical branches are derived as even-order Bessel function expansions. The expansion coefficients are given in terms of integrals of real and complex elliptic functions for the acoustic and optical branches, respectively. Double convolution results respectively in integrals of trigonometric and hyperbolic functions for expansion coefficients of acoustic and optical branches.     

A comparison of methods to compute the "effective duration" of the autocorrelation function and an alternative proposal

The "effective duration" of the autocorrelation function (ACF), τ(e), is an important factor in architectural and musical acoustics. For a general application, an accurate evaluation of τ(e) is relevant. This paper is focused to the methods for the extraction of τ(e) values from the ACF. Various methods have been proposed in literature for the extraction of the τ(e) from a given signal, but these methods are not unambiguously defined or may not work properly in case of particular signals. Therefore, the general use of these methods may sometimes give rise to questionable results. In the present work, the methods existing in literature for extracting τ(e) are analyzed, their advantages and drawbacks are summarized, and finally an alternative method is proposed. The proposed algorithm is compared to those found in previous literature, applying them on the same sound signals (classic literature references and other ones publicly available on the Internet). It is shown that the results obtained with the proposed method are consistent with the results of the previous literature; moreover the proposed method may overcome some of the limitations of the existing methods.     

Does the velocity autocorrelation function oscillate in a hard-sphere crystal?

An approximate kinetic theory is used to compute the velocity autocorrelation function (VACF) in a hard-sphere crystal. In general the theory predicts that the VACF is oscillatory in time. However, in practice, near coexistence the oscillations will be difficult if not impossible to observe because by the time the oscillations occur the VACF has decayed almost to zero. At higher densities the theory predicts that the oscillations are probably just barely observable. In all cases the time integral of the VACF is zero.     

Complex singularities of the fluid velocity autocorrelation function

There are intensive debates regarding the nature of supercritical fluids: if their evolution from liquid-like to gas-like behavior is a continuous multistage process or there is a sharp well-defined crossover. Velocity auto-correlation function Z is the established detector of evolution of fluid particles dynamics. Usually, complex singularities of correlation functions give more information. For this reason, we investigate Z in complex plane of frequencies using numerical analytic continuation. We have found that naive picture with few isolated poles fails describing Z(ω) of one-component Lennard-Jones (LJ) fluid. Instead, we see the singularity manifold forming branch cuts extending approximately parallel to the real frequency axis. That suggests LJ velocity autocorrelation function is a multivalued function of complex frequency. The branch cuts are separated from the real axis by the well-defined “gap” whose width corresponds to an important time scale of a fluid characterizing crossover of system dynamics from kinetic to hydrodynamic regime. Our working hypothesis is that the branch cut origin is related to competition between one-particle dynamics and hydrodynamics. The observed analytic structure of Z is very stable under changes in the temperature; it survives at temperatures two orders of magnitude higher than the critical one.     

The long time behavior of the velocity autocorrelation function in a plasma

The utilization of the Landau-Placzek method results in a velocity autocorrelation function for a one component plasma having oscillatory behavior (at the plasma frequency) in addition to the t^?(d/2) (d = dimension) behavior previously found in neutral gas systems.     

Short time behavior of the velocity autocorrelation function

A systematic method for evaluating velocity correlation functions of a hard sphere fluid for short times is presented The complete contributions ～ t and t² are obtained, formally valid for all densities.     

Clipped time autocorrelation function of intensity fluctuations for a non gaussian field

Numerical results for the single and double clipped autocorrelation functions of intensity fluctuations of squared intensity of gaussian-exponential field are reported and compared with the unclipped ones.     

The non-exponential behavior of the velocity autocorrelation function

The contribution to the velocity autocorrelation function from ring events is studied for low densities and t?2t₀ using a kinetic model. Agreement with computer experiments for $\text{V}\text{V}{}_0\text{= 18}$ is found to be good.     

一种基于自相关函数的幂律检测器

针对水下高斯噪声中非高斯瞬态信号的检测问题,在研究Nuttall提出的power-law(幂律)检测器的基础上,为了提高其检测性能,依据信号和噪声的自相关函数的差异,提出了基于自相关函数的power-law检测器,并对其参数的最佳选取及检测性能进行了仿真研究。仿真结果表明,基于自相关函数的检测器较基于DFT的power-law检测器性能有所提高,有一定的可行性。