Dr D A Lavis Emeritus Senior Lecturer Department of Mathematics Room K4U25, King's
Building |
Since my formal retirement my main area of interest has moved towards the foundations of statistical mechanics and thermodynamics. In particular I am interested in exploring the nature of irreversibility and equilibrium. In a number of papers on statistical mechanics I have argued that, in order to reconcile the Boltzmann and Gibbs approaches to statistical mechanics, it is necessary to abandon the binary property of being or not being in equilibrium in favour of a continuous property which I call 'commonness'. Related to this I contend that rather than a preoccupation with 'local' increase in entropy a more fruitful approach is to consider the global picture where thermodynamic-like behaviour is associated with entropy mostly fluctuating to values close to its maximum with infrequent larger fluctuations to lower values. In thermodynamics I have investigated and published papers on the problem of equilibrium processes and the contentious question of negative temperatures. I am currently, in collaboration with Roman Frigg, writing a book on the fundamentals of thermodynamics.
In the past series expansion methods have been used with one expansion parameter and numerical coefficients to obtain critical properties at one point in phase space. The object of my research with B. W. Southern of the University of Manitoba is to provide the beginning of a general methodology for using series to explore the whole of the phase space. We are using the finite-lattice method to develop series where the coefficients are polynomial functions of the Boltzmann factors for a number of other couplings. We are currently investigating a modified three-state Potts model on a triangular lattice with a chiral term around each triangle. This chiral term is of particular interest as it forms the basis for the development of lattice models with directional bonding. These have been used to simulate water-like behaviour.
A list of my papers with downloads is given here.
In 1999 I wrote, in collaboration with the late Professor G. M. Bell, two books on the Statistical Mechanics of Lattice Systems. I have now completed a successor to these books. Details of all three are given here.
I am no longer teaching any courses but here are copies of my notes for:
Non-Linear Dynamics and Control Theory
Go to my Departmental Webpage