Fluctuating electromagnetic interactions of solids terminated by nonplanar surfaces

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Abstract
Based on the known solutions for van der Waals forces and heat flow caused by fluctuating electromagnetic fields in a plane-parallel gap between two half-spaces, here we present related solutions for bodies terminated by surfaces with various curvatures, as derived by conformal mapping. The expressions were obtained for the force and heat flow between two solids, the boundaries of which are represented by two hyperbolic surfaces, a hyperbolic surface and plane, two parallel cylindrical surfaces, and also by surfaces, the traces of which are formed by a kinked curve and plane. A comparison with other results obtained by previous studies is done.