Past Seminars

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Untangling polymer systems: Structure prediction in polymer networks with quenched disorder
Dr Abigail Klopper
Max Planck Institute for the Physics of Complex Systems
Start time: 11:00 am
Date: Wednesday 13 December 2006
Location: Room 213, Dept. of Mathematics and Statistics, The University of Melbourne

Highly concentrated liquids comprising long polymeric chains can undergo processes of cross-linking and entanglement, giving rise to intriguing macroscopic properties. The key ingredient is connective quenched disorder, which freezes the topology of the liquid in the form of a polymer network. The translational invariance in the system is spontaneously broken and the phase space is divided into disjoint ergodic regions. Such behaviour is well-known from a large class of systems exhibiting the so-called glassy phase, characterised by randomness and slow dynamics. This opens the door to an extensive analytic formalism for structure prediction in cross-linked polymer systems. By constructing a theoretical framework which makes use of simulation data, one can draw from these techniques without resorting to microscopic detail and otherwise unphysical assumptions. In the study presented, the spin-glass replica formalism is applied to data from molecular dynamics simulations of ideal non-interacting cross-linked polymer systems in order to describe neutron scattering measurements in interacting systems.

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From series expansions to exact solutions
Dr Iwan Jensen
MASCOS, The University of Melbourne
Start time: 3:15 pm
Date: Monday 27 November 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

Recently we have been able to find numerically the exact solutions for a number of lattice polygon models. In all cases we start by calculating an exact series expansion for the problem at hand and we then proceed to find the exact solution. In the simplest cases this is done via an educated guess of the form of the solution leaving only some polynomials to be determined. In more complicated cases we find solutions in the form of high order linear ODEs. In one particular instance we are able to find a closed form solution to a problem involving a 4th order ODE. In this talk I will briefly outline why we study these problems, how we calculate the series and find the exact solutions and discuss what we have learned. This is joint work (in part) with Tony Guttmann and Christoph Richard.

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Multifractal Analysis : the wavelet leaders contribution
Patrice Abry
CNRS, Laboratoire de Physique, Ecole Normale Supérieure de Lyon
Start time: 3:15 pm
Date: Friday 24 November 2006
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton.

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, in order to yield the entire and correct spectrum of Hölder singularities. The properties of this new multifractal formalism and of the alternative weak scaling exponent multifractal formalism are investigated. Examples based on known synthetic multifractal processes illustrate its numerical implementation and abilities. The benefits of the use of wavelet leaders is also illustrated on actual empirical data coming from hydrodynamics turbulence experiments. (Joint work with S. Jaffard, Dept. of Mathematics, Université Paris XII, Creteil France)

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Some hidden Markov models I have known
Professor Terry Speed
University of California, Berkeley and Walter & Eliza Hall Institute of Medical Research, Melbourne
Start time: 3:15 pm
Date: Friday 17 November 2006
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton.

Hidden Markov models emerged in the late 1960s in the literature of probability and statistics. They were introduced into genetics in the mid-1980s, and shortly after that into biomolecular sequence analysis, now part of what is known as bioinformatics. Their range of applications in that field is now very wide. In this talk I'll describe some examples, including a few with which I have been associated.

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Self-avoiding walk enumeration via the lace expansion
Dr Nathan Clisby
MASCOS, The University of Melbourne
Start time: 3:15 pm
Date: Friday 20 October 2006
Location: Theatre 2, Ground Floor, 111 Barry Street, Carlton.

We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion. Combined with another algorithmic improvement which we call the two step method, we have been able to significantly extend the series for the simple cubic lattice from 26 to 30 terms, and dramatically extend series for hypercubic lattices with dimensions greater than three.

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