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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

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.

3

Configurational Temperature and Monte Carlo Simulations

Brańka A. C., Pieprzyk S.

Computational Methods in Science and Technology

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2010

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Vol. 16, No. 2

119-125

EN

Two configurational temperature expressions are investigated from the point of view of their utility as a diagnostic tool for Monte Carlo (MC) simulations. The MC calculations were performed for systems of spherically symmetric particles in the bulk and in a channel. Different density and system size conditions are considered. It is shown that the configurational temperature based on the ratio of two averages of the force functions can serve as a suitable method for calculating the temperature for the MC simulation. This configurational temperature can signal the presence of random number correlations and can serve as a cross-check formula in MC studies of strongly confined systems.

4

Elastic properties of inverse power fluids

Brańka A. C., Heyes M.

Computational Methods in Science and Technology

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2004

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Vol. 10, nr 2

127-136

EN

We investigated the consequences of variable potential softness on elastic properties, using the repulsive inverse power potential. With this potential the softness can be changed continuously from very soft to extremely steep or hard. An explicit formula for the equation of state is derived and discussed. It is shown how this formula can be exploited to determine the infinite frequency elastic properties of the inverse power fluid. Explicit formulae for the elastic constants, the high-frequency elastic moduli, the longitudinal- and transverse-wave ve1ocities and Poisson's ratio are obtained. Their behaviour in the steeply repulsive limit is discussed. It is demonstrated that the softness directly determines the Poisson's ratio, and it is shown that in order to decrease the value of the Poisson's ratio a harder potential interaction must be applied.

5

On algorithms for Brownian dynamics computer simulations

Brańka A. C.

Computational Methods in Science and Technology

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1998

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Vol. 4

35-42

EN

Several Brownian Dynamics numerical schemes for treating stochastic differential equations at the position Langevin level are analyzed from the point of view of their algorithmic efficiency. The algorithms are tested using model colloidal fluid of particles interacting via the Yukawa potential. Limitations in the conventional Brownian Dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical and static quantities can be achieved with an algorithm based on the stochastic expansion and second-order stochastic Runge-Kutta algorithms. Mutual merits of the second-order algorithms are discussed.