# Project Details

### Description

TECHNICAL SUMMARY: This award supports theoretical research and education in a variety of subfields of statistical mechanics. This work is jointly supported by the Division of Materials Research and the Division of Mathematical Sciences. The central theme of the effort is a better understanding of the properties of macroscopic systems originating in the collective behavior of their microscopic constituents. The methods used range from exact mathematical analysis to computer simulations. These approaches bridge the gap between rigorous results and applications. Research topics employed by PI and collaborators are varied. Using mesoscopic free energy functionals allows investigation of periodic states, wetting in mixtures and droplet formation in supersaturated vapor. An ongoing effort continues on fluctuations and large deviations in nonequilibrium stationary states and partial currents. This includes cases where the hydrodynamic scaling is inadequate. Significant advance continue in fundamental studies such as establishing Fourier's law of heat conduction in open systems with anharmonic interactions. In quantum statistical physics, the study of subsystems of large quantum systems leads to understanding of when these systems have density matrices given by canonical Gibbs measures. In some cases, such as the study of ionization of model quantum systems in time periodic fields, there are applications to laser induced transitions in atoms and molecules. Beyond physics, researchers also apply statistical mechanical methods to the mathematical study of epidemics taking into account correlations as well as saturation effects on networks. Extension of these techniques to models of population dynamics and ecology involves derivation of reaction-diffusion equations via scaling limits and these are planned investigations. The research activities are highly interdisciplinary, bringing together physicists, mathematicians, chemists and those working in theoretical areas of the biological and social sciences. The expected applications are in material science, complex fluids and in biological systems. The project also includes the organization of two conferences every year in which both core subjects and new developments in statistical mechanics are discussed in a collegial atmosphere. Graduate students, postdocs and minority scientists are involved and present talks on their work and interact with established researchers in the field. The conferences also serve as an opportunity for professional networking and can lead to new collaborations. NONTECHNICAL SUMMARY: This award supports theoretical research and education in a variety of subfields of statistical mechanics. This work is jointly supported by the Division of Materials Research and the Division of Mathematical Sciences. The central theme of the effort is a better understanding of the properties of material systems originating in the collective behavior of their elementary atomic constituents. The methods used range from exact mathematical analysis to computer simulations. These approaches bridge the gap between rigorous results and applications. Topics range from classical physics to quantum physics and highly formal to applications of technological relevance and even dynamics of disease propagation. The research activities are highly interdisciplinary, bringing together physicists, mathematicians, chemists and those working in theoretical areas of the biological and social sciences. The expected applications are in material science, complex fluids and in biological systems. The project also includes the organization of two conferences every year in which both core subjects and new developments in statistical mechanics are discussed in a collegial atmosphere. Graduate students, postdocs and minority scientists are involved and present talks on their work and interact with established researchers in the field. The conferences also serve as an opportunity for professional networking and can lead to new collaborations.

Status | Finished |
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Effective start/end date | 9/15/08 → 9/30/14 |

### Funding

- National Science Foundation (NSF)