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N. B. Wilding

Publications and source records attributed to N. B. Wilding.

At least 19 recordsLinked to original sources
arXiv2021

dlmontepython: A Python library for automation and analysis of Monte Carlo molecular simulations

We present an open source Python 3 library aimed at practitioners of molecular simulation, especially Monte Carlo simulation. The aims of the library are to facilitate the generation of simulation data for a wide range of problems; and to support data analysis methods which enable one to make the most of previously generated data. The library contains a framework for automating the task of measuring target physical properties (e.g. density) over a range of thermodynamic parameters (e.g. temperature) calculated using a molecular simulation program, in particular the Monte Carlo program DL_MONTE. The library also supports analysis methods including block averaging, equilibration detection and histogram reweighting. Here we describe the library and provide examples to demonstrate its key functionality: we use the library to automatically calculate isotherms to a specified precision; and to calculate the surface tension and liquid-vapour coexistence properties of methane.

physics.comp-ph↗
arXiv2013

Monte Carlo methods for estimating depletion potentials in highly size-asymmetrical hard sphere mixtures

We investigate Monte Carlo simulation strategies for determining the effective ("depletion") potential between a pair of hard spheres immersed in a dense sea of much smaller hard spheres. Two routes to the depletion potential are considered. The first is based on estimates of the insertion probability of one big sphere in the presence of the other; we describe and compare three such methods. The second route exploits collective (cluster) updating to sample the depletion potential as a function of the separation of the big particles; we describe two such methods. For both routes we find that the sampling efficiency at high densities of small particles can be enhanced considerably by exploiting `geometrical shortcuts' that focus the computational effort on a subset of small particles. All the methods we describe are readily extendable to particles interacting via arbitrary potentials.

cond-mat.soft↗
arXiv2007

Continuous Capillary Condensation

We show that condensation in a capped capillary slit is a continuous interfacial critical phenomenon, related intimately to several other surface phase transitions. In three dimensions (3d), the adsorption and desorption branches correspond to the unbinding of the meniscus from the cap and opening, respectively and are equivalent to 2d-like complete-wetting transitions. For dispersion forces, the singularities on the two branches are distinct, owing to the different interplay of geometry and intermolecular forces. In 2d we establish precise connection, or covariance, with 2d critical-wetting and wedge-filling transitions, i.e. we establish that certain interfacial properties in very different geometries are identical. Our predictions of universal scaling and covariance in finite capillaries are supported by extensive Ising model simulation studies in 2d and 3d.

cond-mat.stat-mech↗
arXiv2003

A non-equilibrium Monte Carlo approach to potential refinement in inverse problems

The inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown (Phys. Rev. E63, 021111 (2001)) that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (`pseudo-species') $σ$ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution $\barρ(σ)$ measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution $μ(σ)$ which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of $μ(σ)$ for which $\barρ(σ)$ matches the available experimental data. The difficulty in doing so is that $μ(σ)$ is (in general) an unknown {\em functional} of $\barρ(σ)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $μ(σ)$ and $\barρ(σ)$ renders this process computationally problematic and laborious. Here we describe an efficient and robust {\em non-equilibrium} simulation scheme for finding the equilibrium form of $μ[\barρ(σ)]$. The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific log-normal distribution of particle sizes in a polydisperse fluid.

cond-mat.stat-mech↗
arXiv2003

Effects of weak surface fields on the density profiles and adsorption of a confined fluid near bulk criticality

The density profile and Gibbs adsorption of a near-critical fluid confined between two identical planar walls is studied by means of Monte Carlo simulation and by density functional theory for a Lennard-Jones fluid. By reducing the strength of wall-fluid interactions relative to fluid-fluid interactions we observe a crossover from behaviour characteristic of the normal surface universality class, strong critical adsorption, to behaviour characteristic of a 'neutral' wall. The crossover is reminiscent of that which occurs near the ordinary surface transition in Ising films subject to vanishing surface fields. For the 'neutral' wall the density profile, away from the walls, is almost constant throughout the slit capillary and gives rise to an adsorption that is constant along the critical isochore. The same 'neutral' wall yields a line of capillary coexistence that is almost identical to the bulk coexistence line. In the crossover regime we observe features in the density profile similar to those found in the magnetisation profile of the critical Ising film subject to weak surface fields, namely two smooth maxima, located away from the walls, which merge into a single maximum at midpoint as the strength of the wall-fluid interaction is reduced or as the distance between walls is decreased. We discuss similarities and differences between the surface critical behaviour of fluids and of Ising magnets.

cond-mat.stat-mech↗
arXiv2001

Liquid-gas phase behaviour of an argon-like fluid modelled by the hard-core two-Yukawa potential

We study a model for an argon-like fluid parameterised in terms of a hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behaviour of the model is obtained from the thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) of Hoye and Stell, the solution of which lends itself particularly well to a pair potential of this form. The predictions for the critical point and the coexistence curve are compared to new high resolution simulation data and to other liquid-state theories, including the hierarchical reference theory (HRT) of Parola and Reatto. Both SCOZA and HRT deliver results that are considerably more accurate than standard integral-equation approaches. Among the versions of SCOZA considered, the one yielding the best agreement with simulation successfully predicts the critical point parameters to within 1%.

cond-mat.stat-mech↗
arXiv2001

Computer simulation of fluid phase transitions

The task of accurately locating fluid phase boundaries by means of computer simulation is hampered by problems associated with sampling both coexisting phases in a single simulation run. We explain the physical background to these problems and describe how they can be tackled using a synthesis of biased Monte Carlo sampling and histogram extrapolation methods, married to a standard fluid simulation algorithm. It is demonstrated that the combined approach provides a powerful method for tracing fluid phase boundaries.

cond-mat.stat-mech↗
arXiv2000

Freezing by Monte Carlo Phase-Switch

We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the probabilities of gateway states (in each phase) which are such that a global switch (to the other phase) can be implemented. Equilibrium freezing-point parameters can be determined directly; statistical uncertainties prescribed transparently; and finite-size effects quantified systematically. The method is potentially quite general; we apply it to the freezing of hard spheres.

cond-mat.stat-mech↗
arXiv2000

Wetting of a symmetrical binary fluid mixture on a wall

We study the wetting behaviour of a symmetrical binary fluid below the demixing temperature at a non-selective attractive wall. Although it demixes in the bulk, a sufficiently thin liquid film remains mixed. On approaching liquid/vapour coexistence, however, the thickness of the liquid film increases and it may demix and then wet the substrate. We show that the wetting properties are determined by an interplay of the two length scales related to the density and the composition fluctuations. The problem is analysed within the framework of a generic two component Ginzburg-Landau functional (appropriate for systems with short-ranged interactions). This functional is minimized both numerically and analytically within a piecewise parabolic potential approximation. A number of novel surface transitions are found, including first order demixing and prewetting, continuous demixing, a tricritical point connecting the two regimes, or a critical end point beyond which the prewetting line separates a strongly and a weakly demixed film. Our results are supported by detailed Monte Carlo simulations of a symmetrical binary Lennard-Jones fluid at an attractive wall.

cond-mat.stat-mech↗
arXiv1999

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.

cond-mat.stat-mech↗
arXiv1999

Effects of Confinement on Critical Adsorption: Absence of Critical Depletion for Fluids in Slit Pores

The adsorption of a near-critical fluid confined in a slit pore is investigated by means of density functional theory and by Monte Carlo simulation for a Lennard-Jones fluid. Our work was stimulated by recent experiments for SF_6 adsorbed in a mesoporous glass which showed the striking phenomenon of critical depletion, i.e. the adsorption excess "Gamma" first increases but then decreases very rapidly to negative values as the bulk critical temperature T_c is approached from above along near-critical isochores. By contrast, our density functional and simulation results, for a range of strongly attractive wall-fluid potentials, show Gamma monotonically increasing and eventually saturating as the temperature is lowered towards T_c along both the critical (rho=rho_c) and sub-critical isochores (rho<ρ_c). Such behaviour results from the increasingly slow decay of the density profile away from the walls, into the middle of the slit, as T->T_c. For rho < rho_c we find that in the fluid the effective bulk field, which is negative and which favours desorption, is insufficient to dominate the effects of the surface fields which favour adsorption. We compare this situation with earlier results for the lattice gas model with a constant (negative) bulk field where critical depletion was found. Qualitatively different behaviour of the density profiles and adsorption is found in simulations for intermediate and weakly attractive wall-fluid potentials but in no case do we observe the critical depletion found in experiments. We conclude that the latter cannot be accounted for by a single pore model.

cond-mat.stat-mech↗
arXiv1999

Critical-point finite-size scaling in the microcanonical ensemble

We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.

cond-mat.stat-mech↗
arXiv1998

Recoil growth: an efficient simulation method for multi-polymer systems

We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler, which probes possible pathways ahead of the growing chain. By recoiling from traps and excessively dense regions, the growth process yields high success rates for both chain construction and acceptance. Extensive tests of the method using self-avoiding walks on a cubic lattice show that for long chains and at high densities it is considerably more efficient than Configurational Bias Monte Carlo, of which it may be considered a generalisation.

cond-mat.stat-mech↗
arXiv1998

A liquid state theory that remains successful in the critical region

A thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) is applied to a fluid of spherical particles with a pair potential given by a hard-core repulsion and a Yukawa attractive tail $w(r)=-\exp [-z(r-1)]/r$. This potential allows one to take advantage of the known analytical properties of the solution to the Ornstein-Zernike equation for the case in which the direct correlation function outside the repulsive core is given by a linear combination of two Yukawa tails and the radial distribution function $g(r)$ satisfies the exact core condition $g(r)=0$ for $r<1$. The predictions for the thermodynamics, the critical point, and the coexistence curve are compared here to other theories and to simulation results. In order to unambiguously assess the ability of the SCOZA to locate the critical point and the phase boundary of the system, a new set of simulations has also been performed. The method adopted combines Monte Carlo and finite-size scaling techniques and is especially adapted to deal with critical fluctuations and phase separation. It is found that the version of the SCOZA considered here provides very good overall thermodynamics and a remarkably accurate critical point and coexistence curve. For the interaction range considered here, given by $z=1.8$, the critical density and temperature predicted by the theory agree with the simulation results to about 0.6%.

cond-mat.stat-mech↗
arXiv1998

Liquid-vapour phase behaviour of a symmetrical binary fluid mixture

Using Monte-Carlo simulation and mean field calculations, we study the liquid-vapour phase diagram of a square well binary fluid mixture as a function of a parameter $δ$ measuring the relative strength of interactions between particles of dissimilar and similar species. The results reveal a rich variety of liquid-vapour coexistence behaviour as $δ$ is tuned. Specifically, we uncover critical end point behaviour, a triple point involving a vapour and two liquids of different density, and tricritical behaviour. For a certain range of $δ$, the mean field calculations also predict a `hidden' (metastable) liquid-vapour binodal.

cond-mat.stat-mech↗
arXiv1997

Effect of criticality on wetting layers: A Monte-Carlo simulation study

A solid substrate, when exposed to a vapour, can interact with it in such a way that sufficiently close to liquid-vapour coexistence a macroscopically thick liquid wetting layer is formed on the substrate surface. If such a wetting transition occurs for a binary fluid mixture in the vicinity of the critical end point of demixing transitions, critical fluctuations lead to additional long-ranged interactions (Casimir forces) within the wetting layer, changing its equilibrium thickness. We demonstrate this effect by Monte-Carlo simulations of wetting layers of a symmetrical Lennard-Jones binary fluid mixture near its critical end point. The results suggest that the effect should also be detectable in corresponding wetting experiments.

cond-mat.stat-mech↗
arXiv1997

Free energies of crystalline solids: a lattice-switch Monte Carlo method

We present a method for the direct evaluation of the difference between the free energies of two crystalline structures, of different symmetry. The method rests on a Monte Carlo procedure which allows one to sample along a path, through atomic-displacement-space, leading from one structure to the other by way of an intervening transformation that switches one set of lattice vectors for another. The configurations of both structures can thus be sampled within a single Monte Carlo process, and the difference between their free energies evaluated directly from the ratio of the measured probabilities of each. The method is used to determine the difference between the free energies of the fcc and hcp crystalline phases of a system of hard spheres.

cond-mat.stat-mech↗