Statistical Mechanics and Phase Transitions

University Of Maryland, College Park, College Park MD

Investigators

Abstract

Michael Fisher of the University of Maryland is cofunded by a grant from the Theoretical and Computational Chemistry Program and the Materials Theory Program to continue his basic theoretical research in statistical mechanics and the study of states of matter, phase transitions between these states, and related critical phenomena. Specific problems to be studied include: 1) the origin and nature of crossover critical behavior observed experimentally in certain electrolytes that undergo a phase separation; 2) the role of symmetry in continuum fluids and the linear scaling fields that govern near-critical thermodynamics; 3) the refinement of finite-size scaling techniques for discriminating between universality classes in Monte Carlo simulations; 4) the exact analysis of multi-species ionic spherical models and of a novel compressible cell gas; 5) the study of universal relations between interfacial tension near a critical endpoint and special free energy functional that accommodate non-classical critical exponents; 6) the use of this free energy functional approach to compute universal critical adsorption and density profiles in the critical neighborhood; 7) the analysis of the forces exerted by molecular motors using a recently developed theory; and 8) the development of the mathematics needed for the treatment of molecular motor models that employs biased, linear, periodic random walks with waiting time distributions including branching and death processes. Fisher's theoretical research will further the understanding of electrolyte solutions under various physical conditions. Electrolyte solutions are important in many industrial and biological processes. A novel extension of this research is the probing of how molecular motors move along linear tracks within cells to perform functions vital to the life of the organism.