Green-Kubo formalism

It is straightforward to show that this behavior also holds for fc-mers which perform elementary jumps of lenght equal to one lattice constant in one dimension. From the Green-Kubo formalism, the chemical diffusion coefficient is D(Q) = Dj(Q)Th(Q), where... 

A more sophisticated version of basically this same idea is associated with the Green-Kubo formalism in which the relevant transport coefficient is seen as an average of the appropriate velocity autocorrelation function. In particular, the diffusion coefficient may be evaluated as... 

Another theme often explored with model alkanes is the relative merits of equilibrium MD (EMD) and non-equilibrium MD (NEMD) as methods for obtaining transport coefficients. Dysthe et al. explored some aspects of the methodology used to obtain transport coefficients by MD. They applied the Green-Kubo formalism to flexible multicentre models fi om linear and branched... 

Transport properties, such as diffusion coefficients, shear viscosity, fhermal or electrical conductivity, can be determined from the time evolution of the autocorrelation function of a particular microscopic flux in a system in equilibrium based on the Green-Kubo formalism [217, 218] or the Einstein equations [219], Autocorrelation functions give an insight into the dynamics of a fluid and their Fourier transforms can be related to experimental spectra. The general Green-Kubo expression for an arbitrary transport coefficient y is given by ... 

The gas diffusion coefficient D may be extracted from a simulation in various ways. In a Molecular Dynamics simulation, if the hydrodynamk limit is reached (Le., the simulation time is long enough), D may be calculated either from the evolution of the penetrants instantaneous velocities by means of the Green-Kubo formalism or, alternatively, with the aid of the Einstein relation from their spatial positions. For TSA, there is only the Hnstein-route, via the mean-square displacement =< r(t) — r(0) > which is plotted against time, best in a log-log plot. The portion of the curve that represents oc t is used to fit a least-squares line, the slope of which (in a vs t plot) or the ptmtion of which (in a log [Pg.211]

Let us first consider nonequilibrium properties of dense fluids. Linear response theory relates transport coefficients to the decay of position and velocity correlations among the particles in an equilibrium fluid. For example, the shear viscosity ti can be expressed in Green-Kubo formalism as a time integral of a particular correlation function ... 

Fig. 11. Shear viscosity for the [C2-mim][Q] ionic Hquid at different temperatures. Sohd symbols are results obtained by the rigid model, while open symbols are the values from the flexible model, using the Green-Kubo formalism in the NVE simulations. Crosses represent experimental (Earle Seddon, 2002). The hnes are just a guide to the eyes.

Andreu, J.S. Vega, L.F. (2010). On the Transport properties of [emimjCl through the Green Kubo formalism. Submitted. 

T. Ihle and D. M. Kroll, Stochastic rotation dynamics. I. Formalism, Galilean invariance, and Green—Kubo relations, Phys. Rev. E 67, 066705 (2003). 

The formally exact general result for T in (4b) can be applied to compute the thermodynamic transverse stress, (7(y) = Oxy /V. Equation (4b) leads to an exact non-linear Green-Kubo relation ... 

Dfle, T. and KroU, D.M., Stochastic Rotation Dynamics I Formalism, Gahlean invariance, and Green-Kubo relations, Phys. Rev. E, 67 (6), 066705, 2003. 

For the largest system (NS2), the computation of viscosity can be performed by using the Green-Kubo (GK) formalism [108] which is based on the calculation of the stress tensor auto-correlation function, given by ... 

As stated in the introduction, molecular simulations can be used as complementary tools to characterize ionic liquids from a modelling approach. The transport coefficients can be calculated through the corresponding Green-Kubo relations (Allen Tildesley, 1987 Frenkel Smit, 2002). Within this formalism, the self-diffusion coefficient (D) of each ion is calculated from its velocity autocorrelation function (vacf) through the following expression ... 

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