Worlds in a Computer: Models of Reality and Reality of Models

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Feb 25, 2014
from 05:30 PM to 06:30 PM


Ken Edwards Building, Lecture Theatre 1

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0116 252 2320

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Professor Ruslan Davidchack 

Department of Mathematics

Lecture Summary

The invention of computers has changed all aspects of our lives, the way we communicate, entertain, retrieve information, and do business.  It also changed the way we do science by providing a bridge between the traditional experimental and theoretical branches of natural sciences.  Within computational modelling, we are creating virtual laboratories in which we can test our models and theories of the real world.  But perhaps more significantly, our ability to manipulate the virtual world far exceeds our experimental capabilities within the real world.  For example, the unrealisable dream of medieval alchemists of transforming one element into another is readily realised in the virtual laboratory and, in fact, is now extensively used in biomolecular simulations, especially in the computer assisted discovery of new drugs.  In my research, ‘alchemical transformations’ are used in the development of methods for the calculation of the solid-liquid interfacial free energy – a quantity of paramount scientific and technological importance which governs the processes of crystal nucleation and growth.

In addition to allowing us to evaluate and extend models of reality, computers allow us to compute properties of abstract mathematical models and visualise them, thus making them more ‘real’ and accessible to non-mathematicians.  This has been particularly evident in the study of complex dynamics of simple nonlinear systems, now known as the ‘chaos theory’.  Even though such complexity has been known by Poincare and other great mathematicians since the end of the 19th century, it is only after the use of computers in mathematical explorations became sufficiently common that the ubiquity of complex behaviour in simple nonlinear systems became widely recognised and studied, giving rise to such popularly known properties as the ‘butterfly effect’ and fractal structure.  We know that these and other properties of chaotic systems can be characterised by various regular coherent structures (equilibria, travelling waves, periodic and relative periodic orbits, etc), which are embedded within the complex irregular motion of chaotic systems.  With the help of powerful computers we can discover and explore such regular structures, thereby revealing great intrinsic beauty of abstract mathematical models.

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