Numerical Implementation of SLLOD Dynamics

The distribution of Eq. [137] is canonical in laboratory momentum and positions for a general strain rate tensor Vu this is the expected form for a system subject to an external field. Equation [137] is the first distribution function to be derived for SLLOD-type dynamics and has provided impetus for studies concerning the nature of the distribution function in the nonequilibrium steady state. 

---

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. 

---