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Unformatted text preview: Physics 127B – Homework Set 5: (due February 17) Problem 1: Superfluid He 4He 3 mixtures Problem 2.4 in Kardar, “Statistical Physics of Fields,” p. 33. Suggestion: For various formal manipulations, it can be convenient to write the terms containing c ( x ) as a complete square and shift variables. Problem 2: Thermal excitation of capillary waves Consider gas and liquid in equilibrium. The two phases are separated by an interface, which is microscopically nonflat. In this problem we study thermal excitation of the interface (capillary waves). Let h ( x,y ) denote the height (measured from appropriate reference). Consider first the situation in the presence of gravitation where the energy is given by E = integraldisplay dxdy ρ liquid − ρ gas 2 gh 2 ( x,y ) + integraldisplay dxdy σ radicalBigg 1 + parenleftbigg ∂h ∂x parenrightbigg 2 + parenleftbigg ∂h ∂y parenrightbigg 2 − 1 . (1) The first term is change in the gravitational energy due to the deformation...
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This note was uploaded on 03/07/2012 for the course PHYS 127b taught by Professor Olexeimotrunich during the Winter '11 term at Caltech.
 Winter '11
 OlexeiMotrunich
 Physics, Work

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