Interdisciplinary Applied Mathematics

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TABLE 16.2. Summary of the commonly employed thermostats.


Thermostat


Key concept


Suit ability/ Application


Berendsen


First-order-kinetics-based weak coupling


Easy implementation and computationally inexpensive.


Nose—Hoover


Extended


Lagrangian


Most rigorous implementation of the NVT ensemble.


Andersen


Stochastic


collision


Suitable for thermal coupling of atomistic and continuum domains; also for DPD.

Density Profiles


To investigate nanoflows in channels and pores, where the fluid density is inhomogeneous (see Chapters 10 and 11), it is useful to compute the spatial distribution of fluid density, e.g., density profile along the radial direction of a nanopore. This is usually performed using the “binning method” (Allen and Tildesley, 1994). In this scheme the relevant spatial domain (i.e., the domain where the density distribution of the species needs to be computed) is partitioned into a number of cells, which are identified as the “bins.” The number of atoms in each bin is computed from the knowledge of the positions of the atoms. In order to obtain a better statistical analysis of the number density in a bin, we add the number of atoms in the bin for a number of steps and then divide the total number of atoms in the bin by the number of steps and the volume of the bin. Thus, the number density, ci, of the *th bin, averaged over s steps, is given by


Ci = /VOLj)s,


where ni is the total number of atoms in the *th bin during each step and VOLi is the volume of the *th bin.

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