Research in our group focusses on solving theoretical and
computational problems related to the molecular scale transport of
matter and energy. By constructing new methods we characterize,
understand, and control the dynamical processes of complex systems
evolving far from thermodynamic equilibrium.
Statistical dynamics of mixing liquids
Natural phenomena mix matter, energy or both.
The mixing of liquids is particular important; it is responsible for
the molecular structure and function of biological cells, the
production and processing of everyday products, and the yield of
chemical reactions. For liquids that are sufficiently alike,
thermodynamics makes predictions about whether the liquids will mix.
However, the entropy associated with the interdiffusion of liquids is
difficult to estimate, say, from molecular simulations, especially if
the liquids are dissimilar or the mixing requires heat transfer. We
have developed theory and computational strategies that enable the
direct calculation of statistical entropy changes from the underlying
molecular dynamics involved in mixing two liquids. These entropy
changes are related to dynamical randomness and, yet, are consistent
with the thermodynamic entropy of mixing.
Fluctuating and disordered rate processes
Kinetics provides predictions about how fast a
particular process will happen - its rate. For example, predicting the
rate of making and breaking hydrogen bonds in liquid water can give
insight into the role of this process in the function of biomolecules.
Many such processes present a theoretical challenge to kinetics because
of the intrinsic fluctuations in the rate caused by the surrounding
environment; the interaction between two water molecules sensitively
depends on the proximity, geometry, and behavior of the water molecules
surrounding them. We are designing a general theoretical framework that
applies to this broad class of rate processes, including water. This
framework is being implemented as a computational algorithm to analyze
the results of both computer simulations and laboratory