5,818 research outputs found
General solution of overdamped Josephson junction equation in the case of phase-lock
The first order nonlinear ODE d phi(t)/d t + sin phi(t)=B+A cos(omega t),
(A,B,omega are real constants) is investigated. Its general solution is derived
in the case of the choice of parameters ensuring the phase-lock mode. It is
represented in terms of Floquet solution of double confluent Heun equation.Comment: 28 page
A new approach to the homogenization of heterogeneous media for neutron diffusion calculations
Mathematical formulation for homogenization of heterogeneous media for neutron diffusion transport theor
Proof of Razumov-Stroganov conjecture for some infinite families of link patterns
We prove the Razumov--Stroganov conjecture relating ground state of the O(1)
loop model and counting of Fully Packed Loops in the case of certain types of
link patterns. The main focus is on link patterns with three series of nested
arches, for which we use as key ingredient of the proof a generalization of the
Mac Mahon formula for the number of plane partitions which includes three
series of parameters
Parallel tridiagonal equation solvers
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases
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