SLLOD dynamics

It is interesting to analyze Eqs. [129] further to point out interesting features of SLLOD dynamics. 

However, it is clear that for a general tensor Vu, trajectory analysis based on the SLLOD dynamics in Eqs. [129] will yield incorrect results. Equation [132] has an extra term in the force, which is equivalent to saying that the momenta in Eqs. [129] are not peculiar with respect to a general flow (indeed, Eqs. [129] yield peculiar velocities for the case of planar Couette flow), and therefore the flow profile produced will not be q Vu as expected. Equations [129] also lead to problems when one is considering definitions of pressure... 

SLLOD Dynamics for Planar Couette Flow in the Canonical Ensemble... 

We thus conclude the section on the numerical implementation of SLLOD dynamics for two very important and useful ensembles. However, our work is not yet complete. The use of periodic boundary conditions in the presence of a shear field must be reconsidered. This is explained in detail in the next section. Furthermore, one could imagine a situation in which SLLOD dynamics is executed in conjunction with constraint algorithms for the internal degrees of freedom and electrostatic interactions. An immediate application of this extension would be the simulation of polar fluids (e.g., water) under shear. This extension has been performed, and the integrator is discussed in detail in Ref. 42. 

We have thus far discussed the basic foundations of nonequilibrium molecular dynamics, its methodology, and the details of numerically integrating the equations of motion for SLLOD dynamics. The next section presents applications of these methods. 

In the preceding sections, we have presented simulation methodologies to study systems away from equilibrium. In particular, we have concentrated on the problem of shear flow in bulk systems. In the present section, we illustrate the effectiveness of the SLLOD dynamics coupled with the robustness of the extended system approach to initiate and sustain a shear flow in a fluid in the absence of moving boundary conditions. 

Also, note that in Eq. [202] we have introduced a variable, I, which although inconsequential to the dynamics of the variables representing the fluid (i.e., p, q) is essential to obtain a conserved energy for SLLOD dynamics with time-independent boundary conditions. The conserved energy for the dynamics in Eqs. [202] is given by... 

For SLLOD dynamics coupled to a Nose-Hoover thermostat, the metric determinant is given by The first and third terms in Eq. [229] become Nfe f feqPr /Q with Opposite signs and thus cancel. We are left with the expression... 

It has turned out to be impossible thus far to derive simple NEMD algorithms with (mechanical) external fields analogous to the equilibrium case to determine self-diffusion or heat flow coefficients superimposed on the SLLOD dynamics of the system. ... 

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