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1

A Nosé-Hoover Thermostat Adapted to a Slab Geometry

Maćkowiak S., Pieprzyk S., Brańka A. C., Heyes D. M.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 3

211--218

EN

A Nosé-Hoover (NH) type thermostat is considered for Molecular Dynamics (MD) simulations of confined systems. This is based on a generalised velocity of the same generic form as the NH thermostat of Allen and Schmid, [Mol. Sim. 33, 21 (2007)]. An unthermostatted confined region is sandwiched between two walls which are thermostatted. No external shearing is imposed. Non-equilibrium Molecular Dynamics (NEMD) simulations were carried out of the time evolution of the wall and confined region temperature after a jump in temperature of the walls. Relaxation of the confined region temperature to the target value was found to be typically slower than that of the wall. An analysis of the system parameter dependence of the lag time, , and departures from what would be expected from Fourier’s law suggest that a boundary transmission heat flux bottleneck is a significant factor in the time delay. This delayed thermal equilibration would therefore become an important factor when a time-dependent (e.g., oscillatory) temperature or shearing of the walls is implemented using NEMD. Adjustments between the response time of the wall thermostat should be made compatible with that of the rest of the system, to minimise its effects on the observed behaviour.

2

Statistical Fluctuations along the Lennard-Jones Melting Curve

Patra R., Heyes D. M.

Computational Methods in Science and Technology

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2016

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Vol. 22, No. 1

5--17

EN

Statistical fluctuations and correlations between thermodynamic properties along the fluid side of the melting line of the Lennard-Jones (LJ) are determined using Molecular Dynamics (MD) computer simulation. Linear regression, the Pearson coefficient and other statistical measures are calculated. The cross correlation between the configurational part of the pressure and potential energy, and the repulsive and attractive parts of the potential energy are focussed on. Regression plots show that at constant temperature and constant total energy the Weeks-Chandler-Andersen (WCA) decomposition of the Lennard-Jones repulsive and attractive potential energy components show a qualitative change along the melting line. At low temperature the two components are correlated, while they are anticorrelated in the high temperature limit. There is an intermediate temperature range in which the two potential energy components are effectively uncorrelated. The various fluctuation trends along the melting line were found to be weakly dependent on the force field used to generate the distribution of states, namely, the LJ potential, inverse power potential with exponent 12, and the repulsive term in the WCA decomposition of the LJ potential.

3

The Lennard-Jones Fluid in the Liquid-Vapour Critical Region

Heyes D. M.

Computational Methods in Science and Technology

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2015

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Vol. 21, No. 4

169--179

EN

The equation of state of the Lennard-Jones (LJ) fluid in the liquid-vapour (LV) critical region is investigated by Molecular Dynamics simulation (MD). The calculated pressure (P) and chemical potential (μ) are, within the simulation statistics, flat at the critical temperature between LJ reduced densities of ca. 0:26 to 0:34. The critical temperature, Tc, determined for an isotherm where (∂P/∂)T = 0 and (∂μ/∂ρ)T = 0, is shown to decrease with increasing system size and pure LJ potential interaction range, rc, using a tapering function going to zero beyond rc. The value of Tc obtained by extrapolating the system size and rc to ∞ is 1:316 ± 0:001, which is statistically within the uncertainties of previous literature values. The percolation threshold separation, rp, along the critical isotherm decreases monotonically with increasing density, ρ, and is for intermediate densities lower than that of the nearest equivalent hard-sphere system. The lines of constant percolation distance on the density-temperature projection of the phase diagram reveal a difference in qualitative behaviour, indicative of underlying structural differences on either side of the critical envelope. The mean square force in the critical region near to Tc is linear in ρ. Probability distributions of the nearest neighbour distance, absolute particle force and potential energy per molecule are presented.

4

Method of Planes Normal Pressure for Slit Geometries in Molecular Dynamics Simulations

Maćkowiak S., Heyes D. M., Dini D., Brańka A. C.

Computational Methods in Science and Technology

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2013

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Vol. 19, No. 3

167--173

EN

The resolution and convergence properties of the Method of Planes (MOP) local pressure tensor method is analyzed for a slit geometry in which a system of interacting particles is placed between movable walls composed of atoms. Boundarydriven Molecular Dynamics (BMD) simulations were performed for different situations in which solid or fluid phases are formed between crystalline or amorphous walls. It is shown that for these inhomogeneous, steady state structures the total force exerted by a wall atoms on the inside particles is consistent with the normal pressure component obtained from the MOP method if a sufficiently small integration time step is applied. The work demonstrates that the numerical errors associated with computing the MOP pressure can be non-negligible and should be a consideration when determining the BMD algorithm parameters.