Devonport, Craig (2020) Thermalisation and memory in crystal nucleation. PhD thesis, University of Warwick.

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Abstract

In this thesis, we examine two assumptions made in classical nucleation theory. Those being, the cluster size n is a slow degree of freedom and all other degrees of freedom thermalise on more rapid timescales, and that the dynamics of that slow degree of freedom are well described by a Markovian random walk on the resulting free energy landscape. We examine the quasi-equilibrium assumption using a substantial set of Lennard-Jones simulations and plotting the velocity distribution of the particles for each n sampled over the course of a seeded nucleation trajectory. Comparing these distributions we find that all degrees of freedom other than n are in thermal equilibrium, provided these are sampled from both trajectories which include growing and shrinking clusters. The consequences of this for calculations of the nucleation rate via variants of seed methods are discussed.

To examine the Markovian assumption we take a maximum likelihood approach to score trajectories against reference stochastic process based on two memory models, one with a linear memory function and one with a reciprocal length function. Applying these models to molecular dynamics seeding style trajectories we find that the trajectories are best described by allowing for steps in n greater than 1 and either a short non zero memory (length 1 to 3) with a linear memory function or simply a non zero memory (length 1 to 10) with the reciprocal memory function.

In the final chapter we explore the feasibility of using neural network models to predict the committor for nucleation via magnetisation reversal in the 2D Ising model. These predictions are calculated from from collective variables as well as from the current grid state of the simulation and perform better than a polynomial regression fitted using two collective variables, the size of largest cluster n and the total number of spin up site in the grid N↑.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Nucleation
Official Date:	December 2020
Dates:	Date Event December 2020 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Department of Physics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Quigley, D. (David)
Format of File:	pdf
Extent:	xvi, 140 leaves : colour illustrations
Language:	eng

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