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# NP - Limitations of simulations in the microcanonical...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Limitations of simulations in the microcanonical ensemble T Nk 2 3 m 2 p B i i 2 i = r In a classical mechanical system free from an external force the total energy E is conserved => simulations are performed at a constant (E,V,N) condition => this correspond to the microcanonical ensemble in statistical mechanics. Problems: 1. Experiments are usually performed at constant temperature and pressure. Simulation results for the microcanonical ensemble is difficult to relate to experiments. 2. It is difficult to perform simulation at specific T and P. Int i 1 i i i i 2 i F r m p V 3 1 P r r r + = = We can try to control T and P at the first stage of the simulation by scaling the velocity and the size of the unit cell . But A. It is difficult to predict them a priory , before the simulation; B. P and T can keep changing during the simulation. 3. Difficult to relate to theory. Statistical mechanics for microcanonical ensemble is less studied.

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Early attempts of constant T simulations . 1. The constraint methods = = i i i i i i p ζ F dt p d m p dt r d r r r r r A. K.E. = const by velocity scaling (not only during a preliminary simulation stage, but during the main part of the simulation). Velocities of all particles are rescaled to keep kinetic energy constant. This
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NP - Limitations of simulations in the microcanonical...

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