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We investigate five different problems in the field of the statistical mechanics of neural networks. The first three problems involve attractor neural networks that optimise particular cost functions for storage of static memories as attractors of the neural dynamics. We study the effects of replica symmetry breaking (RSB) and attempt to find algorithms that will produce the optimal network if error-free storage is impossible. For the Gardner-Derrida network we show that full RSB is necessary for an exact solution everywhere above saturation. We also show that, no matter what the cost function that is optimised, if the distribution of stabilities has a gap then the Parisi replica ansatz that has been made is unstable. For the noise-optimal network we find a continuous transition to replica symmetry breaking at the AT line, in line with previous studies of RSB for different networks. The change to RSBl improves the agreement between "experimental" and theoretical calculations of the local stability distribution ρ(λ) significantly. The effect on observables is smaller. We show that if the network is presented with a training set which has been generated from a set of prototypes by some noisy rule, but neither the noise level nor the prototypes are known, then the perceptron algorithm is the best initial choice to produce a network that will generalise well. If additional information is available more sophisticated algorithms will be faster and give a smaller generalisation error. The remaining problems deal with attractor neural networks with separable interaction matrices which can be used (under parallel dynamics) to store sequences of patterns without the need for time delays. We look at the effects of correlations on a singlesequence network, and numerically investigate the storage capacity of a network storing an extensive number of patterns in such sequences. When correlations are implemented along with a term in the interaction matrix designed to suppress some of the effects of those correlations, the competition between the two produces a rich range of behaviour. Contrary to expectations, increasing the correlations and the operating temperature proves capable of improving the sequenceprocessing behaviour of the network. Finally, we demonstrate that a network storing a large number of sequences of patterns using a Hebb-like rule can store approximately twice as many patterns as the network trained with the Hebb rule to store individual patterns.

The statistical mechanics of the interfacial region is studied using the Monte Carlo and molecular dynamics simulation techniques. The penetrable-sphere model of the liquid/vapour interface is simulated using the Monte Carlo method. The pressure equation of state is calculated in the one-phase region and compared to analytic virial expansions of the system. Density profiles of the gas/liquid surface in the two-phase region are calculated and are compared to profiles solved in the mean-field approximation. The effect of the profile near a hard wall is investigated and as a consequence the theory is modified to account for a hard wall. The theory agrees well with the computer result. This is a simple model for adsorption of a gas at a solid surface. A model for methane adsorbed on graphite is proposed. A number of simplifying assumptions are made. The surface is assumed to be perfectly smooth and rigid, and quantum effects are neglected. An effective site-site pair potential for the methane-graphite interaction is adjusted to fit the rotational barriers at OK. The isosteric enthalpy at zero coverage is predicted in the range OK to 200K, by averaging the configurational energy during a molecular dynamics simulation of one methane molecule. The surface second virial coefficients are calculated in the range 225K to 300K and agree with the experimental measurements. The effective pairwise potential predicts the height of the monolayer above the surface and the vibrational frequency against the surface. The translational and rotational behaviour of a single methane molecule are examined. Solid √3 x √3 epitaxial methane is studied at a constant coverage of θ = 0.87 by molecular dynamics simulation. The specific heat and configurational energy are monitored. A slow phase transition occurs between OK and 30K and a sharp transition is observed at 90K. Calculation of the centre-centre distribution functions and order parameters indicates the first transition is due to a slow rotational phase change. At 90K some molecules evaporate from the surface and the remaining bound molecules relax into a 2-d liquid. Between 10K and 25K the adsorbed methane floats across the surface and the question remains open whether this phenomenon is an artifact of the model system or does occur in nature. The dynamical behaviour of adsorbed methane is compared to incoherent inelastic neutron scattering. The principal peaks in the self part of the incoherent structure factor S_s (0,_ω) should correspond to the peaks in the Fourier transforms of the velocity and angular velocity auto-correlation functions. The peaks calculated from the Fourier transform of the auto-correlation functions agree with all the assignments in the experiments. The reorientational motion in the monolayer is monitored and the reorientational auto-correlation functions characterize the slow phase transition from UK to 30K. Three methane molecules are scattered on top of the θ = 0.87 monolayer at 30K. Reorientational correlation functions are compared for the single adsorbed molecule, the monolayer and a few particles in the bilayer. Rotation is less hindered in the monolayer than for a single adsorbed molecule and least hindered in the second layer. Adsorbed methane is studied at coverages of θ < 0.87 over a wide range of temperature in order to unravel various conflicting solid and liquid phases predicted by experiment. By careful monitoring of the structure via changes in the specific heat, the distribution functions and order parameters a liquid/gas coexistence is not observed in the region 56K to 75K. This result is confirmed by calculating the self diffusion coefficients over two isotherms at 65K and 95K. The diffusion coefficients decrease with increasing coverage over both isotherms. If liquid and gas coexist the diffusion coefficient should not change with increasing coverage. The statistical mechanical expression for the spreading pressure of an adsorbed fluid is derived and reported over a wide range of temperature and coverage. Experimental techniques are not as yet sufficiently highly developed to measure this quantity directly. An expression for the coherent neutron scattering structure factor for a model of liquid benzene adsorbed on graphite is derived. This expression is a function of the 2-dimensional centre-centre distribution function and we solve the Ornstein-Zernike equation in the Percus-Yevick approximation to obtain the 2-d distribution functions for hard discs. Agreement with present experimental results is reasonable, but a more highly orientated substrate needs to be used in experiment before a more exact comparison can be made.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 136-143).

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 123-135).

Thesis (Ph.D.)--Australian National University, 2005.

Thesis (Ph. D.)--University of Oregon, 2002. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 223-225). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Chicago, Dept. of Philosophy. / Includes bibliographical references. Also available on the Internet.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Qu, Jianmin; Committee Member: Kohl,Paul A.; Committee Member: Liu, Meilin; Committee Member: McDowell, David L.; Committee Member: Zhu, Ting.