Static and Dynamic Properties of Surfaces

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Theoretical research will be aimed at understanding the static and dynamic fluctuations of a variety of polymers, surfaces and networks. The many interesting and fundamental issues that can be probed are relevant to a diverse variety of subjects which can be broadly placed into the following categories: (1) Extended networks, such as polymers, membranes and gels, fluctuating in a higher dimensional space. The interplay between entropic elasticity, rigidity, and microscopic interactions leads to a number of unusual macroscopic phases. (2) Dynamic evolution of surfaces and paths far from equilibrium cannot be described by a Hamiltonian, and is instead probed by appealing to symmetries and conservation laws. Evolution equations relevant to roughening of crystal facets, moving lines, and flowing sandpiles are constructed and their dynamic steady states are explored. (3) Path integrals in random media are relevant to tunnelling of localized electrons, wave propagation in inhomogeneous media and pinning of vortex lines in superconductors. Numerical and analytical methods are developed for performing these path integrals. (4) Substrate roughness and its influence on adsorption and surface phase transitions is investigated. %%% The theoretical research to be conducted on this grant probes the behavior of extended objects such as surfaces and chains, including how these objects grow into various structures. The general treatment is then applied to such systems as polymers, membranes, interfaces and surfaces. The results have wide applicability in materials research and are also fundamental to modern condensed matter physics.