Electrokinetic Transport Properties of Ionic Systems |
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Principal InvestigatorJonathan Ennis-KingResearch School of Chemistry Co-InvestigatorDenis EvansResearch School of Chemistry Projectsx05 - VPP |
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This project is concerned with methods for simulating transport properties in fluids. The eventual aim of the project is to establish the connection between non-equilibrium molecular dynamics simulations (NEMD), in which all the molecules in the fluid are simulated explicitly, and non-equilibrium Brownian Dynamics simulations, in which only the particles of interest (e.g. the ions or the heavy solute particles) are simulated. | ||||||||||
What are the results to date and the future of the work?During 1998, a vectorizable Brownian Dynamics code was developed for simple fluids. This Brownian Dynamics code was then used to examine the properties of the recently derived expressions for configurational temperature in equilibrium systems. It was demonstrated that the average configurational temperature of an equilibrium system converges as 1/N to the input temperature for a system of N particles. Simulations were then conducted to examine the response of the configurational temperature of the system to changes in the input temperature. It was demonstrated that the response is very fast for short-range potentials (in agreement with the results of some recent Monte Carlo simulations), but quite slow for long-range potentials. In the latter case the configurational temperature may thus prove useful in investigating metastability. This phenomena was further studied by analysing the equilibrium time-correlation functions for various quantities. This study established that for all potentials used the configurational temperature had a much faster relaxation time than other quantities such as the pressure and internal energy, and gave some insight into the mechanism for this fast relaxation. The next part of the project is to perform NEMD simulations of a single solute particle in a solvent under shear, and development of the code for this is to be completed in early 1999. The most appropriate machine to use is the SGI Power Challenge, since the forces between particles are short-range, and so a cell code (which does not vectorize well) is appropriate. Mattieu McPhie of the Department of Applied Physics at RMIT has recently obtained a result for the generalized Langevin equation in a non-equilibrium system, via the theory of projection operators. Using this theory one should be able to construct an algorithm for a generalised Brownian Dynamics (GBD) simulation of a non-equilibrium system, in which the required memory functions and random force are obtained from an analysis of the full NEMD simulations. |
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Appendix A - |
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Thus our aim is to perform NEMD simulations of a single heavy solvent particle in a solvent of light particles, extract the required memory functions etc, and then perform the equivalent GBD simulation for a single particle. This should prove to be a stringent test of the theoretical result. By increasing the mass of the solute particle relative to that of the solvent particles, it should be possible to approach the Brownian limit, and thus test the widely used heuristic algorithms currently employed for non-equilibrium Brownian Dynamics. What computational techniques are used?The vectorization of the Brownian Dynamics code was made possible using recently developed random number generators, some rewriting of the inner loop for force calculations, and a 'binning' method for computing pair correlation functions. For the largest systems studied (2048 particles) the vectorization was 98.4%. This approach was best for systems with fairly long-range forces, for which the code on a scalar machine would run as^{ }O(N^{2}) for N particles. |
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- Appendix A |
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