Condenser capacity and hyperbolic perimeter

On the Capacity of a Condenser

Capacity of a condenser whose plates are circular arcs

We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear plate condenser found by Simonenko and Chekulaeva in 1972 and sheds light on the problem of finding an asymptotic formula for the capacity of condenser whose p...

Vertical perimeter versus horizontal perimeter

Given k ∈ N, the k’th discrete Heisenberg group, denoted H Z , is the group generated by the elements a1, b1, . . . , ak, bk, c, subject to the commutator relations [a1, b1] = . . . = [ak, bk] = c, while all the other pairs of elements from this generating set are required to commute, i.e., for every distinct i, j ∈ {1, . . . , k} we have [ai, aj ] = [bi, bj ] = [ai, bj ] = [ai, c] = [bi, c] = ...

Condenser-Based Instant Reflectometry

We present a technique for rapid capture of high quality bidirectional reflection distribution functions(BRDFs) of surface points. Our method represents the BRDF at each point by a generalized microfacet model with tabulated normal distribution function (NDF) and assumes that the BRDF is symmetrical. A compact and light-weight reflectometry apparatus is developed for capturing reflectance data ...

Measurement of water holding capacity using a condenser-chamber TEWL instrument