Correlation functions, in simulations

Correlation functions, in simulations, 380 Correlation consistent basis sets, 162 COSMIC force field, 40 Coulomb correlation, 99... 

Thus, while the experimental situation has matured significantly with consistent results for pair and self correlation functions, in the area of simulations fully atomistic MD-calculations on long-enough chains are needed in order to resolve the existing discrepancies between different simulation approaches and experiment. 

Fig. 4.1 a Typical time evolution of a given correlation function in a glass-forming system for different temperatures (T >T2>...>T ), b Molecular dynamics simulation results [105] for the time decay of different correlation functions in polyisoprene at 363 K normalized dynamic structure factor at the first static structure factor maximum solid thick line)y intermediate incoherent scattering function of the hydrogens solid thin line), dipole-dipole correlation function dashed line) and second order orientational correlation function of three different C-H bonds measurable by NMR dashed-dotted lines)... 

D.F. Coker and S. Bonella, Linearized path integral methods for quantum time correlation functions, in Computer simulations in condensed matter From materials to chemical biology, eds. M. Ferrario and G. Ciccotti and K. Binder, Lecture Notes in Physics 703, (Springer-Verlag, Berlin), p. 553, 2006. 

Figures 7.2 and 7.3 show the relevant correlation functions. In three dimensions at the dimensionless time pvot = 10 the steady-state is already nearly achieved (the deviation from the unity is seen only at r < lOro). Since the correlation length at large t is finite, microscopic defect segregation takes place for d = 3. Quite contrary, for low (J < 2) dimensions the correlation functions are no longer stationary. Similarly to the recombination decay kinetics treated in [14], the accumulation kinetics demonstrates also an infinite increase in time of the correlation length (defined by a coordinate where X (r, f) 1 or F(r, t)

A complication arising from the extension of the theory to flexible macromolecules is that in general, the intermolecular and intramolecular radial distribution functions depend on each other.In modeling the bulk of a one-phase polymer melt, however, the situation resolves itself because the excluded volume effect is insignificant under these conditions the polymer chains assume unperturbed dimensions (see also the section on Monte Carlo simulations by Corradini, as described originally in Ref. 99). One may therefore calculate the structure of the unperturbed single chain and employ the result as input to the PRISM theory to calculate the intermolecular correlation functions in the melt. 

Fluid microstructure may be characterized in terms of molecular distribution functions. The local number of molecules of type a at a distance between r and r-l-dr from a molecule of type P is Pa T 9afi(r)dr where Pa/j(r) is the spatial pair correlation function. In principle, flr (r) may be determined experimentally by scattering experiments however, results to date are limited to either pure fluids of small molecules or binary mixtures of monatomic species, and no mixture studies have been conducted near a CP. The molecular distribution functions may also be obtained, for molecules interacting by idealized potentials, from molecular simulations and from integral equation theories. 

Figure 12. Orientational dynamics of the discotic system GBDII (N = 500) at several temperatures across the isotropic-nematic transition along the isobar at pressure P — 25. (a) Time evolution of the single-particle second-rank orientational time correlation function in a log-log plot. Temperature decreases from left to right, (b) Time dependence the OKE signal at short-to-intermediate times in a log-log plot. Temperature decreases from top to bottom on the left side of the plot T = 2.991,2.693,2.646, and 2.594. The dashed lines are the simulation data and the continuous lines are the linear fits to the data, showing the power law decay regimes at temperatures. (Reproduced from Ref. 115.)...

So far we have employed the exponential model for the memory kernel appearing in the GLE for the density correlation functions. In [60] the model based on the mode-coupling theory described in Sec. 5.2.4is applied to the calculation of the longitudinal current spectra of the same diatomic liquid as discussed here. It is found that the essential features of the results remained the same as far as the collective dynamics is concerned. It is also demonstrated that the results are in fair agreement with those determined from the molecular dynamics simulation. 

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