Profile-unbiased thermostat

The original scheme utilized Gaussian isokinetic thermostats, whereas in Eqs. [217] we have replaced it with a Nose-Hoover thermostat. In this equation, the true local streaming velocity is given by iyy, + Usi(q,). In principle, there are no restrictions on u i, so the steady state velocity can be of any form hence, Evans and Morriss refer to Eqs. [217] as profile-unbiased thermostats (PUT). The PUT scheme requires only a reasonable prescription for determining the true local streaming velocity. 

It is then a straightforward task to construct the action of this operator on the phase space variables. Details can be found in Refs. 46 and 84. The algorithm is called a reversible profile-unbiased thermostat (RPUT). 

K. Bagchi, S. Balasubramanian, C. J. Mundy, and M. L. Klein,/. Chem. Phys., 105,11183 (1996). Profile Unbiased Thermostat with Dynamical Streaming Velocities. 

Clear evidence exists that beyond the linear regime the synthetic thermostat influences the results. The role of the heat removing mechanism becomes especially important at high shear rates where the assumption of the linear velocity profile (iyyi is incremented in the position equation of equations 27) of the SLLOD shear flow is unrealistic. To allow the formation of kink instabilities in the velocity profile (turbulent flow) the simple thermostating scheme of equations (27) mast be replaced by a profile unbiased thermostat which makes no assumption about the local streaming velocity. ... 

This can be done with just a single global scale factor, or a local factor which is different in every cell. For a known macroscopic flow profile, u, like in shear flow, the relative velocities v - u can be rescaled. This is known as a profile-unbiased thermostat however, it has been shown to have deficiencies in molecular dynamics simulations [41],... 

The LGV thermostat can be ruled out, even in its profile-unbiased version, whenever momentum transport is relevant, either in the form of hydrodynamic interactions or, for instance, due to a coupling between the shear and gradient directions. However, the LGV thermostat can be a powerful tool, as it stabilizes the particle trajectories very efficiently and allows the study of systems far from equilibrium. Excellent examples are investigations of polymer brushes at sufficiently large density, where situations far beyond linear response [137,139,141, 142,144,145,150] and nonstationary shear deformation [144,145,150] could be studied. 

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