84,439 research outputs found
Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant
In this work we carry out a noncommutative analysis of several
Friedmann-Robert-Walker models, coupled to different types of perfect fluids
and in the presence of a cosmological constant. The classical field equations
are modified, by the introduction of a shift operator, in order to introduce
noncommutativity in these models. We notice that the noncommutative versions of
these models show several relevant differences with respect to the
correspondent commutative ones.Comment: 27 pages. 7 figures. JHEP style.arXiv admin note: substantial text
overlap with arXiv:1104.481
Modeling anisotropic diffusion using a departure from isotropy approach
There are a large number of finite volume solvers available for solution of isotropic diffusion equation. This article presents an approach of adapting these solvers to solve anisotropic diffusion equations. The formulation works by decomposing the diffusive flux into a component associated with isotropic diffusion and another component associated with departure from isotropic diffusion. This results in an isotropic diffusion equation with additional terms to account for the anisotropic effect. These additional terms are treated using a deferred correction approach and coupled via an iterative procedure. The presented approach is validated against various diffusion problems in anisotropic media with known analytical or numerical solutions. Although demonstrated for two-dimensional problems, extension of the present approach to three-dimensional problems is straight forward. Other than the finite volume method, this approach can be applied to any discretization method
A Grassmann integral equation
The present study introduces and investigates a new type of equation which is
called Grassmann integral equation in analogy to integral equations studied in
real analysis. A Grassmann integral equation is an equation which involves
Grassmann integrations and which is to be obeyed by an unknown function over a
(finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann
integral equations is explicitly studied for certain low-dimensional Grassmann
algebras. The choice of the equation under investigation is motivated by the
effective action formalism of (lattice) quantum field theory. In a very general
setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional
analogues of the generating functionals of the Green functions are worked out
explicitly by solving a coupled system of nonlinear matrix equations. Finally,
by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi},
{\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the
generators of the Grassmann algebra G_2n), between the finite-dimensional
analogues G_0 and G of the (``classical'') action and effective action
functionals, respectively, a special Grassmann integral equation is being
established and solved which also is equivalent to a coupled system of
nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann
integral equation exist for n=2 (and consequently, also for any even value of
n, specifically, for n=4) but not for n=3. If \lambda=1, the considered
Grassmann integral equation has always a solution which corresponds to a
Gaussian integral, but remarkably in the case n=4 a further solution is found
which corresponds to a non-Gaussian integral. The investigation sheds light on
the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the
reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54],
[61], [64], [139] added
A Novel Method for the Solution of the Schroedinger Eq. in the Presence of Exchange Terms
In the Hartree-Fock approximation the Pauli exclusion principle leads to a
Schroedinger Eq. of an integro-differential form. We describe a new spectral
noniterative method (S-IEM), previously developed for solving the
Lippman-Schwinger integral equation with local potentials, which has now been
extended so as to include the exchange nonlocality. We apply it to the
restricted case of electron-Hydrogen scattering in which the bound electron
remains in the ground state and the incident electron has zero angular
momentum, and we compare the acuracy and economy of the new method to three
other methods. One is a non-iterative solution (NIEM) of the integral equation
as described by Sams and Kouri in 1969. Another is an iterative method
introduced by Kim and Udagawa in 1990 for nuclear physics applications, which
makes an expansion of the solution into an especially favorable basis obtained
by a method of moments. The third one is based on the Singular Value
Decomposition of the exchange term followed by iterations over the remainder.
The S-IEM method turns out to be more accurate by many orders of magnitude than
any of the other three methods described above for the same number of mesh
points.Comment: 29 pages, 4 figures, submitted to Phys. Rev.
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