62,407 research outputs found
A Parallel Method for Population Balance Equations Based on the Method of Characteristics
In this paper, we present a parallel scheme to solve the population balance
equations based on the method of characteristics and the finite element
discretization. The application of the method of characteristics transform the
higher dimensional population balance equation into a series of lower
dimensional convection-diffusion-reaction equations which can be solved in a
parallel way.Some numerical results are presented to show the accuracy and
efficiency.Comment: 10 pages, 0 figur
Analytical result on the supercurrent through a superconductor/quantum-dot/superconductor junction
We present an analytical result for the supercurrent across a
superconductor/quantum-dot/superconductor junction. By converting the current
integration into a special contour integral, we can express the current as a
sum of the residues of poles. These poles are real and give a natural
definition of the Andreev bound states. We also use the exact result to explain
some features of the supercurrent transport behavior.Comment: 8 pages, 2 figure
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