A formalism for modelling the dynamics of genetic algorithms using methods from statistical physics, originally due to Pr¨ugel-Bennett and Shapiro, is extended to ranking selection, a form of selection commonly used in the genetic algorithm community. The extension allows a reduction in the number of macroscopic variables required to model the mean behaviour of the genetic algorithm. This reduction allows a more qualitative understanding of the dynamics to be developed without sacrificing quantitative accuracy. The work is extended beyond modelling the dynamics of the genetic algorithm. A caricature of an optimisation problem with many local minima is considered — the basin with a barrier problem. The first passage time — the time required to escape the local minima to the global minimum — is calculated and insights gained as to how the genetic algorithm is searching the landscape. The interaction of the various genetic algorithm operators and how these interactions give rise to optimal parameters values is studied.

published_or_final_version / Physics / Master / Master of Philosophy

For systems that are in equilibrium, fluctuations can be understood through interactions with external heat reservoirs. For this reason these fluctuations are known as thermal noise, and they usually become vanishingly small in the thermodynamic limit. However, many systems comprising interacting constituents studied by physicists in recent years are both far from equilibrium, and sufficiently small so that they must be considered finite. The finite number of constituents gives rise to an inherent demographic noise in the system, a source of fluctuations that is always present in the stochastic dynamics. This thesis investigates the role of stochastic fluctuations in the macroscopically observable dynamical behaviour of non-equilibrium, finite systems. To facilitate such a study, we construct microscopic models using an individual based modelling approach, allowing the explicit form of the demographic noise to be identified. In many physical systems and theoretical models, absorbing states are a defining feature. Once a system enters one, it cannot leave. We study the dynamics of a system with two symmetric absorbing states, finding that the amplitude of the multiplicative noise can induce a transition between two universal modes of domain coarsening as the system evolves to one of the absorbing states. In biological and ecological systems, cycles are a ubiquitously observed phenomenon, but are di cult to predict analytically from stochastic models. We examine a potential mechanism for cycling behaviour due to the flow of probability currents, induced by the athermal nature of the demographic noise, in a single patch population comprising two competing species. We find that such a current by itself cannot generate macroscopic cycles, but when combined with deterministic dynamics which constrain the system to a closed circular manifold, gives rise to global quasicycles in the population densities. Finally, we examine a spatially extended system comprising many such patch populations, exploring the emergence of synchronisation between the different cycles. By a stability analysis of the global synchronised state, we probe the relationship between the synchronicity of the metapopulation and the magnitude of the coupling between patches due to species migration. In all cases, we conclude that the nature of the demographic noise can play a pivotal role in the macroscopically observed dynamical behaviour of the system.

Thesis (Ph.D.)--University of the Witwatersrand, Science Faculty (Physics), 2000. / Percolation phenomena are studied in a series of composites, each with a cellular structure (small conductor particles embedded on the surfaces of large insulator particles). The DC and AC conductivities, l/f noise and magnetic properties (in some series) are measured in the systems consisting of Graphite, Graphite-Boron Nitride, Carbon Black, Niobium Carbide, Nickel and Magnetite (Fe304) as the conducting components with Talc-wax (Talc powder coated with 4% wax by volume) being the common insulating component. Compressed discs of 26mm diameter and about 3mm thickness (with various conductor volume fractions covering both the insulating and conducting region) were made from the respective powders at a pressure of 380MPa and all measurements were taken in the axial (pressure) direction. The conductivity (σm) and dielectric constant (εm) of percolation systems obey the equations: σm = σc( ɸ - ɸc)t for ɸ >ɸc; σm = σi( ɸc - ɸ-s and εm = εi( ɸc - ɸ-s' for ɸ < ɸc; outside of the crossover region given by ɸc± (δdc ~=(σi/σc)1/(t+s). Here ɸc is the critical volume fraction of the conductor (with conductivity σ = σc) and cri is the conductivity of the insulator, t and s are the conductivity exponents in the conducting and insulating regions respectively and S’ is the dielectric exponent. The values of s and t are obtained by fitting the DC conductivity results to the combined Percolation or the two exponent phenomenological equations. Both universal and non-universal values of the sand t exponents were obtained. The dielectric exponent S’, obtained from the low frequency AC measurements, is found to be frequency-dependent. The real part of the dielectric constant of the systems, has been studied as a function of the volume fraction (ɸ) of the conducting component. In systems where it is measurable beyond the DC percolation threshold, the dielectric constant has a peak at ɸ > ɸ, which differs from key predictions of the original Percolation Theory. This behaviour of the dielectric constant can be qualitatively modeled by the phenomenological two exponent equation given in Chapter two of this thesis. Even better fits to the data are obtained when the same equation is used in conjunction with ideas from Balberg's extensions to the Random Void model (Balberg 1998a and 1998b). At high frequency and closer to the percolation threshold, the AC conductivity and dielectric constant follow the power laws: σm( ɸ,שּׂ) ~ שּׂX and εm( ɸ,שּׂ) ~ שּׂ-Y respectively. In some of the systems studied, the x and y exponents do not sum up to unity as expected from the relation x + y = 1. Furthermore, the exponent q obtained from שּׂ x σm( ɸ,O)q in all but the Graphite-containing systems is greater than 1, which agrees with the inter-cluster model prediction (q = (s + t)/t). The Niobium Carbide system is the first to give an experimental q exponent greater than the value calculated from the measured DC s and t exponents. l/f or flicker noise (Sv) on the conducting side (ɸ > ɸc) of some of the systems has been measured, which gives the exponents k and w from the well-established relationships Sv/V2 = D(ɸ - ɸc)-k and Sv/V2 = KRw. V is the DC voltage across the sample with resistance R while D and K are constants. A change in the value of the exponent k and w has been observed with k taking the values kl ~ 0.92 - 5.30 close to ɸc and k2 ~ 2.55 - 3.65 further into the conducting region. Values of WI range from 0.36 -1.1 and W2 ~ 1.2 - 1.4. These values of ware generally well within the limits of the noise exponents proposed by Balberg (1998a and 1998b) for the Random Void model. The t exponents calculated from k2 and W2 (using t = k/w) are self-consistent with the t values from DC conductivity measurements. Magnetic measurements in two of the systems (Fe304 and Nickel) show unexpected behaviour of the coercive field and remnant magnetisation plotted as a function of magnetic volume fraction. Fitting the permeability results to the two exponent phenomenological equation gives t values much smaller than the corresponding DC conductivity exponents. A substantial amount of data was obtained and analysed as part of this thesis. Experimental results, mostly in the form of exponents obtained from the various scaling laws of Percolation Theory, are presented in tabular form throughout the relevant chapters. The results have been tested against various models and compare with previous studies. While there is some agreement with previous work, there are some serious discrepancies between the present work and some aspects of the standard or original Percolation Theory, for example the dielectric constant behaviour with conductor volume fraction close to but above ɸc. New results have also emerged from the present work. This includes the change in the noise exponent k with (ɸ - ɸc), the variation of the dielectric exponent s' with frequency and some DC scaling results from the Fe304 system. The present work has dealt with some intriguing aspects of Percolation Theory in real continuum composites and hopefully opened avenues for further theoretical and experimental research. / AC 2016

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves [101]-106). Also available in electronic version.

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Thesis (Ph.D.)--Tufts University, 2005. / Adviser: Peggy Cebe. Submitted to the Dept. of Physics. Includes bibliographical references. Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (M. Phil.)--University of Hong Kong, 2008. / Also available in print.

Thesis (M. S.)--Aerospace Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Dr. Dimitri Mavris; Committee Member: Dean Ward; Committee Member: Dr. Daniel Schrage; Committee Member: Dr. Danielle Soban; Committee Member: Dr. Sriram Rallabhandi; Committee Member: Mathias Emeneth.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 103-111).