MSI Weekly Bulletin - Week starting Monday 3 April, 2006

Abstract: The promise that quantum mechanics can explain all chemistry has not been fully realised due to the rapid increase in computational cost with molecular size. As a consequence, great effort has been directed towards developing highly efficient algorithms that can be applied to chemically interesting systems. Many of these algorithms rely on projecting the electron density onto a smaller auxiliary basis set. The development of such bases and the associated projection methods has attracted a lot of attention, however, little is understood about the analytic behaviour of the expansion coefficients and in particular about their decay behaviour. We investigate how the expansion coefficients decay with respect to distance from the target charge density, and show how this decay behaviour is heavily dependent on the dimensionality of the auxiliary basis.

TALK 1: In the subatomic world, things don't always behave in the same way that our intuition would lead us to believe. Quantum Mechanics, the study of subatomic phenomena has revolutionised physics since its inception in the 1920's. In this talk, I will discuss some famous experiments which provided the inspiration for the Quantum Mechanics revolution, and give an introduction to the mathematical theory used to describe the subatomic world. TALK 2: The Smoluchowski equation is a partial differential equation that describes many processes in physics, chemistry and biology. In this talk I will present a finite element approximation to the Smoluchowski equation, and compare this to stochastic simulation results.

This talk will cover Protein structure, a brief review on secondary structure prediction and compare simple and realistic hidden Markov models.

Quantization involves replacing some algebra of observables by a non-commutative deformed algebra. From the point of view of noncommutative geometry, such deformed algebras should be thought of as noncommutative manifolds. They are often given in terms of generators and relations. In my talk I will review several simple examples of noncommutative spaces and their properties.