Compressed lattice sums arising from the Poisson equation Dedicated to Professor
نویسندگان
چکیده
1 Lawrence Berkeley National Laboratory, Berkeley, CA 94720. Research supported in part by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. 2 Laureate Professor and Director, Centre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Research supported in part by the Australian Research Council.
منابع مشابه
Computer Discovery and Analysis of Large Poisson Polynomials
In two earlier studies of lattice sums arising from the Poisson equation of mathematical physics, it was established that the lattice sum 1/π· ∑ m,n odd cos(mπx) cos(nπy)/(m2+n2) = logA, where A is an algebraic number, and explicit minimal polynomials associated with A were computed for a few specific rational arguments x and y. Based on these results, one of us (Kimberley) conjectured a number...
متن کاملLattice Sums for the Helmholtz Equation
A survey of different representations for lattice sums for the Helmholtz equation is given. These sums arise naturally when dealing with wave scattering by periodic structures. One of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension dΛ. Lattice sums are related to, and can be calculated from, the quasi-periodic Gree...
متن کاملMultiresolution Representation of Operators with Boundary Conditions on Simple Domains
We develop a multiresolution representation of a class of integral operators satisfying boundary conditions on simple domains in order to construct fast algorithms for their application. We also elucidate some delicate theoretical issues related to the construction of periodic Green’s functions for Poisson’s equation. By applying the method of images to the non-standard form of the free space o...
متن کاملCompressed Liquid Densities for Binary Mixtures at Temperatures from 280- 440K at Pressures up to 200 MPa
A method for predicting liquid densities of binary mixtures from heat of vaporization and liquid densityat boiling point temperature (ΔHvap and n b ρ ) as scaling constants, is presented. B2(T) follows a promisingcorresponding-states principle. Calculation of α(T) and b(T), the two other temperature-dependentconstants of the equation of state, are made possible by scaling. As a result ΔHvap and...
متن کاملDistributive lattices with strong endomorphism kernel property as direct sums
Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of ...
متن کامل