Continued fraction representation for slow neutron scattering

1969 ◽  
Vol 47 (2) ◽  
pp. 199-208 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Scattering Theory ◽  
Continued Fraction ◽  
Ad Hoc ◽  
Coherent Scattering ◽  
Liquid Argon ◽  
Slow Neutron ◽  
Velocity Autocorrelation Function ◽  
Velocity Autocorrelation ◽  
Long Time

Mori's continued fraction representation for calculating autocorrelation functions of dynamical variables is applied to the problem of slow neutron scattering by simple classical liquids. In particular, the first few "long-time" approximations are evaluated for the velocity autocorrelation function and for the incoherent and coherent scattering functions. In this way, many of the standard results of slow neutron scattering theory are obtained without having to make any of the ad hoc assumptions which usually enter the derivation of these results. In addition, the continued fraction representation provides a natural method of extending these results to higher order. Numerical calculations are made for liquid argon and compared with available experimental data and with Rahman's machine computations.

Continued fraction representation for slow neutron scattering. II

1970 ◽  
Vol 48 (5) ◽  
pp. 616-629 ◽  
Author(s):  
V. F. Sears
Keyword(s):  
Neutron Scattering ◽  
Cross Sections ◽  
Continued Fraction ◽  
Linear Response Theory ◽  
Liquid Argon ◽  
Slow Neutron ◽  
New Approach ◽  
Time Approximation ◽  
Long Time ◽  
Scattering Cross Sections

The calculation of slow neutron scattering cross sections for simple classical liquids by means of Mori's continued fraction representation was discussed in a previous article on the basis of the long-time approximation. In the present work it is shown that by going beyond the long-time approximation one can eliminate certain difficulties that arose in the previous work. This new approach yields results equivalent to those found by Kadanoff and Martin, and others, from linear response theory. Numerical calculations are made for liquid argon and compared with available experimental data.

scholarly journals New Possibilities Provided by the Analysis of the Molecular Velocity Autocorrelation Function in Liquids

2018 ◽  
Vol 63 (4) ◽  
pp. 317 ◽  
Author(s):  
N. P. Malomuzh ◽  
K. S. Shakun ◽  
A. A. Kuznetsova
Keyword(s):  
Autocorrelation Function ◽  
Liquid Argon ◽  
Velocity Autocorrelation Function ◽  
Molecular Velocity ◽  
Self Diffusion ◽  
Viscosity Coefficients ◽  
Velocity Autocorrelation ◽  
Kinetic Coefficients ◽  
Temperature Dependences ◽  
Long Time

Long-time tails of the molecular velocity autocorrelation function (VACF) in liquid argon at temperatures higher and lower than the spinodal temperature have been analyzed. By considering the time dependence of the VACF, the self-diffusion and shear viscosity coefficients, and the Maxwell relaxation time are determined, as well as their changes when crossing the spinodal. It is shown that the characteristic changes in the temperature dependences of the indicated kinetic coefficients allow the spinodal position to be determined with a high accuracy. A possibility toapply the proposed method to other low-molecular liquids is considered. As an example, nitrogen and oxygen are used, for which the averaged potential of intermolecular interaction has the Lennard-Jones form.

scholarly journals Velocity autocorrelation function and self-diffusion coefficient in large molecular dynamics models of liquid argon and water

2021 ◽  
Vol 13 (2) ◽  
pp. 149-156
Author(s):  
Yuri I. Naberukhin ◽  
◽  
Alexey V. Anikeenko ◽  
Vladimir P. Voloshin ◽  
◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Diffusion Coefficient ◽  
Autocorrelation Function ◽  
Liquid Argon ◽  
Time Interval ◽  
Velocity Autocorrelation Function ◽  
Self Diffusion ◽  
Velocity Autocorrelation ◽  
The Difference ◽  
Self Diffusion Coefficient

Autocorrelation function of the particle velocity Z(t) is calculated using the molecular dynamics method in the models of liquid argon and water. The large size of the models (more than a hundred thousand particles) allowed us to trace these functions up to 50 picoseconds in argon and up to 10 picoseconds in water, and to achieve a calculation accuracy sufficient for analytical analysis of their shape. The difference in the determination of the self-diffusion coefficient using Einstein's law and the integral of Z(t) (Green-Kubo integral) is analyzed and it is shown to be 3% at best when t is of the order of several picoseconds. The asymptote of the function Z(t) in argon is close to the power law αt–3/2 predicted by hydrodynamics, but with an amplitude that depends on the time interval under consideration. In water, the asymptote of Z(t) has nothing in common with that in argon: it has α < 0 and the exponent is close to -5/2, and not to -3/2.

Velocity autocorrelation function of simple dense fluids from neutron scattering experiments

1989 ◽  
Vol 39 (5) ◽  
pp. 2731-2733 ◽  
Author(s):  
Wouter Montfrooij ◽  
Ignatz de Schepper
Keyword(s):  
Neutron Scattering ◽  
Autocorrelation Function ◽  
Velocity Autocorrelation Function ◽  
Dense Fluids ◽  
Velocity Autocorrelation
Sign in / Sign up

Export Citation Format

Share Document