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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online