NP 4 - The extended system method for constant temperature...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei The extended system method for constant temperature IV i i 1 i i i x s m s F x m = s s Q sgkT x m s s Q 2 i 2 i i + = All derivatives here are derivatives by real time. Hoover [Phys. Rev. A 31 , 1695 (1985)] proposed to use a new variable ζ = d(ln s)/dt which gives and leads to an alternative formulation for the equations of motion (Nosé-Hoover thermostat): i i i i i x m F x m ζ = = ζ i 2 i i gkT x m Q A negative feedback is apparent in this formulation: Equations for x i describe the motion of a body with frictional force. The time development of the friction coefficient ζ is driven by the imbalance between the kinetic energy and and its average value (g/2)kT. If the kinetic energy is larger than (g/2)kT, then d ζ /dt’>0, ζ increases and becomes positive. The equation for x i with positive ζ describes a system with frictional force. The velocities and kinetic energy decrease. If the kinetic energy is lower than (g/2)kT, then d
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This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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NP 4 - The extended system method for constant temperature...

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