80,811 research outputs found
Instantons in non-Cartesian coordinates
The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi
are generalized to curvilinear coordinates. The idea is that a gauge
transformation can notably simplify the expressions obtained after the change
of variables. The gauge transform generates a compensating addition to the
gauge potential of pseudoparticles. Singularities of the compensating field are
irrelevant for physics but may affect gauge dependent quantities.Comment: 10 pages, LaTeX, talk given at Quarks-2000 (Pushkin, Russia) and
E.S.Fradkin (Moscow, Russia) conference
Applications of an exponential finite difference technique
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods
Particle correlation from uncorrelated non Born-Oppenheimer SCF wavefunctions
We analyse a nonadiabatic self-consistent field method by means of an
exactly-solvable model. The method is based on nuclear and electronic orbitals
that are functions of the cartesian coordinates in the laboratory-fixed frame.
The kinetic energy of the center of mass is subtracted from the molecular
Hamiltonian operator in the variational process. The results for the simple
model are remarkably accurate and show that the integration over the redundant
cartesian coordinates leads to couplings among the internal ones
Transonic airfoil design using Cartesian coordinates
A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight
From angle-action to Cartesian coordinates: A key transformation for molecular dynamics
The transformation from angle-action variables to Cartesian coordinates is a
crucial step of the (semi) classical description of bimolecular collisions and
photo-fragmentations. The basic reason is that dynamical conditions
corresponding to experiments are ideally generated in angle-action variables
whereas the classical equations of motion are ideally solved in Cartesian
coordinates by standard numerical approaches. To our knowledge, the previous
transformation is available in the literature only for triatomic systems. The
goal of the present work is to derive it for polyatomic ones.Comment: 10 pages, 11 figures, submitted to J. Chem. Phy
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