By Philip Phillips
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Evidently j (x + 12 ) = f (x, t − t)q+ (x) − f (x + 1, t − t)q− (x + 1). (a) Express the change of f during a timestep, f (x, t) − f (x, t − t) in terms of the currents j (x − 12 ) and j (x + 12 ) for any q(x)’s that have q− + q0 + q+ = 1. (b) Find a relationship between f (x), f (x + 1) and the q’s such that j (x + 12 ) = 0. (c) When the system reaches equilibrium, f (x) becomes independent of time. This can only happen if j (x + 12 ) = constant for all x. In the Metropolis process, this constant is zero.
In order for the molecule to be in equilibrium with ice, its free energy in the ice must increase by this amount. For this purpose we may estimate that the free energy is of order T , so that the needed shift in temperature T required to provide the needed increase in temperature is given roughly by T vw . (a) Find vw in nm3 given its mass density and molecular weight. 001◦ , what is the largest volume per solute particle V that it can detect? One of the most important macroscopic properties in a structured fluid is almost trivial to measure.
This temperature rises as the molecules get larger, but only to a limited extent: it rises from roughly 200–400◦ K. The liquid density is also roughly constant; the atoms stay roughly at the separation that minimizes their interaction potential. This potential is virtually independent of temperature. Thus, it remains roughly true that the interaction energy per atom is roughly T . Accordingly, the energy scale of the viscosity should not be greatly altered as the molecules become larger. The timescale for a distortion to relax is also not greatly altered.