Global thermostat

In the confined fluid problem, in the absence of time-dependent shearing boundary conditions, we needed a massive thermostating scheme to stabilize the shear flow. In this scheme, each degree of freedom represented in Eqs. [202] is attached to a separate thermostat, to make the p,- of every particle truly peculiar with respect to the flow profile. The use of one global thermostat for... 

By water we were born, and by its disappearance we shall perish. Eor water maintains one of the most powerful control mechanisms we know. The Earth seen from space is a blue planet scattered with cloud. The cloudy whiteness of the Earth s face is as vital as its aquatic blue. Cloud cover and ice layers are effective regulators in the short term, but the Earth s main thermostat resides in the relation between carbon dioxide and global surface temperature. 

The latter condition is commonly known as microscopic reversibility or local detailed balance. This property is equivalent to time reversal invariance in deterministic (e.g., thermostatted) dynamics. Although it can be relaxed by requiring just global (rather than detailed) balance, it is physically natural to think of equilibrium as a local property. Microscopic reversibility, a common assumption in nonequilibrium statistical mechanics, is the crucial ingredient in the present derivation. 

Figure 3.2 Radial runs of various disk variables according to the simple steady-state toy disk model described in the main text for three different global accretion rates. The central star is Sun-like. We have assumed a gray opacity of k = 1 in regions where Tm < 1500K. In regions where Tm > 1500 K we switched to k = 0.01 to mimic the effect of dust evaporation. Since dust evaporation reduces the mid-plane temperature there will be a region where dust is only partly evaporated to keep Tm at 1500K. Dust evaporation acts as a thermostat here.

In a KMC method, it is typically assumed that various possible state-to-state transitions from a given state are well modelled by the Arrenhius law and then molecular dynamics is used to calculate the prefactor A and energy difference AE in order to understand the timescales and relative probabilities of different rare events. A Markov state model can be developed to help understand the global dynamics and simplify the model as a whole. For references on many interesting approaches to this important topic, the reader is referred to [36,42,137,149,391]. Andersen Thermostat. Of particular interest is the simple and useful Andersen thermostat [11]. This method works by selecting atoms at random and randomly perturbing their momenta in a way consistent with prescribed thermodynamic conditions. It has been rigorously proven to sample the canonical distribution [114],... 

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],... 

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