Fluctuations & Broken Symmetries

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This grant supports theoretical research on condensed matter physics. Many systems are composed of basic elements with relatively simple interactions; yet their collective behavior can be quite complex and perplexing. Statistical physics utilizes powerful tools to describe how the myriad phases of matter emerge from the interactions of atoms. These methods may also shed light upon collective phenomena in biological and social contexts. This research aims at understanding the statistical basis of a diverse variety of phenomena in polymers, cell locomotion, visual processing, and wetting films.Fluctuations are an inherent component of the problems addressed in this research, necessitating the calculation of probability distributions and their time evolution. Adapting the methods of field theory, equations governing the variations of appropriate fields and order parameters in space and time are constructed on the basis of simple considerations such as symmetry and locality. The resulting collective behaviors are then analyzed by standard methods such as perturbation expansions and renormalization group. Numerical techniques, such as Monte Carlo simulations, are also an essential complement to analytical tools. Many problems of interest require creative use of these methods, and possible development of new tools.Specific questions asked in this research include: To what degree does the hydrophobicity of an amino acid sequence determine the structure of a folded protein; Are topological entanglements (such as knots) in polymers truly global entities, or forced to easily located configurations because of physical constraints; How does polymerization of actin propel a cell in a particular direction; What are the statistics of oriented segments common in natural images, and what are the implications for visual processing (artificial or biological); What are the forces that result from quantum fluctuations of the electromagnetic field between deformed (and possibly moving) plates; Are surface fluctuations responsible for the thinning of helium films as they become superfluid.The research will involve students and be closely linked to courses.%%%This grant supports theoretical research on condensed matter physics. Many systems are composed of basic elements with relatively simple interactions; yet their collective behavior can be quite complex and perplexing. Statistical physics utilizes powerful tools to describe how the myriad phases of matter emerge from the interactions of atoms. These methods may also shed light upon collective phenomena in biological and social contexts. This research aims at understanding the statistical basis of a diverse variety of phenomena in polymers, cell locomotion, visual processing, and wetting films. The research will involve students and be closely linked to courses.***