Homogeneous nucleation under shear in a two-dimensional Ising model: Cluster growth, coalescence, and breakup

Allen, Rosalind J.; Valeriani, Chantal; Tănase‐Nicola, Sorin; Wolde, Pieter Rein ten; Frenkel, Daan

doi:10.1063/1.2981052

Cited by 69 publications

(103 citation statements)

References 58 publications

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“…For now, we confine ourselves to an equilibrium system without any external shear; nonequilibrium nucleation in an Ising model with an external shearing field will be considered in future work. 27 The two-dimensional Ising model consists of an L ϫ L square lattice of spins with nearest neighbor interactions and periodic boundary conditions. Its Hamiltonian 28…”

Section: Homogeneous Nucleation In a Two-dimensional Ising Modelmentioning

confidence: 99%

Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

Valeriani

Allen

Morelli

et al. 2007

The Journal of Chemical Physics

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141

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We present a method for computing stationary distributions for activated processes in equilibrium and nonequilibrium systems using forward flux sampling. In this method, the stationary distributions are obtained directly from the rate constant calculations for the forward and backward reactions; there is no need to perform separate calculations for the stationary distribution and the rate constant. We apply the method to the nonequilibrium rare event problem proposed by Maier and Stein, to nucleation in a 2-dimensional Ising system, and to the flipping of a genetic switch.

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Section: Homogeneous Nucleation In a Two-dimensional Ising Modelmentioning

confidence: 99%

Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

Valeriani

Allen

Morelli

et al. 2007

The Journal of Chemical Physics

Self Cite

110

141

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“…The nucleation mechanism in Ising systems is sensitive to the update rule; 23) it would be interesting to repeat this study for an update rule in which transport processes are accurately modelled, such as Kawasaki dynamics. 24) We apply shear to the system using a modification of the algorithm proposed by Cirillo et al 8), 25) After every MC cycle, we make N s × L attempts to shear the system. In each attempt, we choose a row at random and, with probability P s , move all rows above this one to the right by one lattice site.…”

Section: )-7)mentioning

confidence: 99%

Nucleation in a Sheared Ising Model: Effects of External Field

Allen

Valeriani

Tănase‐Nicola

2008

Prog. Theor. Phys. Suppl.

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Simulations using the Forward Flux Sampling method have shown a nonmonotonic dependence of the homogeneous nucleation rate on the shear rate for a sheared two dimensional Ising model [R. J. Allen et al, arXiv:cond-mat/0805.3029]. For quasi-equilibrium systems (i.e. in the absence of shear), Classical Nucleation Theory (CNT) predicts the dependence of the critical cluster size and the nucleation rate on the external magnetic field. We investigate the behaviour of the sheared Ising model as a function of the external field. At low external field strength, the same nonmonotonic behaviour holds and the peak in the nucleation rate is remarkably insensitive to the field strength. This suggests that the same external field-dependence holds for the enhancement of nucleation by shear at low shear rates and the suppression of shear at high shear rates. At high field strength, the nucleation behaviour is qualitatively different. We also analyse the size and shape of the largest cluster in the transition state configurations, as a function of the external field. In the sheared system, the transition state cluster becomes larger and more elongated as the field strength decreases. We compare our results for the sheared system to the predictions of the CNT for the quasiequilibrium case, and find that the CNT cannot easily be used to describe nucleation in the system under shear.Nucleation in driven systems is a widespread and important phenomenon that remains poorly understood. For "quasi-equilibrium" systems, in the absence of external driving, Classical Nucleation Theory (CNT) predicts the dependence of the nucleation rate and the critical cluster size on the degree of supersaturation and the interfacial tension of the growing cluster, for moderate values of the supersaturation. No such simple theoretical description is available for nucleation in driven systems. In this paper, we consider nucleation in a system under shear. In experimental sheared systems, nucleation is likely to be affected by a wide range of factors including transport of particles to the growing cluster, changes in cluster shape, shear-induced ordering of the cluster, polydispersity and shear-induced cluster breakup. Intuition suggests that nucleation will be suppressed for high enough shear rates. At low shear rates, some simulations and experiments have observed suppression of nucleation, 1)-3) while others have suggested that nucleation may be enhanced by the shear. 4)-7)In a recent paper, we studied nucleation in a sheared two-dimensional Ising model, for a fixed value of the external magnetic field. 8) Although this is a highly simplified model system, it nevertheless shows a nonmonotonic dependence of the nucleation rate as a function of the shear rate. The nucleation rate increases, apparently linearly, with the shear rate for weak shear, achieves a peak for shear ratė γ max , and decreases nonlinearly as the shear rate is further increased. These results were obtained using the Forward Flux Sampling rare event simulation method. 9)-11) typeset us...

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“…We should further mention that not all rare event problems in molecular dynamics are related to sampling the underlying Gibbs-Boltzmann statistics, e.g., nucleation events under shear [15] or genuine nonequilibrium systems without a stationary probability distribution [16].…”

Section: Introductionmentioning

confidence: 99%

Characterization of Rare Events in Molecular Dynamics

Hartmann

Banisch

Sarich

et al. 2013

Entropy

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A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.

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Homogeneous nucleation under shear in a two-dimensional Ising model: Cluster growth, coalescence, and breakup

Cited by 69 publications

References 58 publications

Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

Computing stationary distributions in equilibrium and nonequilibrium systems with forward flux sampling

Nucleation in a Sheared Ising Model: Effects of External Field

Characterization of Rare Events in Molecular Dynamics

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