Search results for "Approx"
showing 10 items of 922 documents
Indicators of Errors for Approximate Solutions of Differential Equations
2014
Error indicators play an important role in mesh-adaptive numerical algorithms, which currently dominate in mathematical and numerical modeling of various models in physics, chemistry, biology, economics, and other sciences. Their goal is to present a comparative measure of errors related to different parts of the computational domain, which could suggest a reasonable way of improving the finite dimensional space used to compute the approximate solution. An “ideal” error indicator must possess several properties: efficiency, computability, and universality. In other words, it must correctly reproduce the distribution of errors, be indeed computable, and be applicable to a wide set of approxi…
Coherent potential approximation for diffusion and wave propagation in topologically disordered systems
2013
Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent-potential approximation (CPA) suited for describing ($i$) the diffusive (hopping) motion of classical particles in a random environment and ($ii$) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown …
Effect of reactant spatial distribution in theA+B→0reaction kinetics in one dimension with Coulomb interaction
1996
The effect of nonequilibrium charge screening in the kinetics of the one-dimensional, diffusion-controlled $A+B\ensuremath{\rightarrow}0$ reaction between charged reactants in solids and liquids is studied. The incorrectness of the static, Debye-H\"uckel theory is shown. Our microscopic formalism is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the nonuniform spatial distribution of similar and dissimilar reactants treated in terms of the relevant joint correlation functions. Special attention is paid to the pattern formation due to a reaction-induced non-Poissonian fluctuation sp…
Filter performance parameters for vectorial high-aperture wave fields.
2008
Performance parameters have been presented that can be used to compare the focusing performance of different optical systems, including the effect of pupil filters. These were originally given for the paraxial case and recently extended to the high-aperture scalar regime. We generalize these parameters to the full vectorial case for an aplanatic optical system illuminated by a plane-polarized wave. The behavior of different optical systems is compared.
RPA in wavefunction representation
1992
The RPA is formulated in subspaces of coordinate-like and momentum-like I ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.
Neutrinoless double beta decays of 106Cd revisited
2011
Abstract Neutrinoless double beta ( 0 ν 2 β ) decays of 106 Cd are studied for the transitions to the ground state, 0 gs + , and 0 + excited states in 106 Pd by using realistic many-body wave functions calculated in the framework of the quasiparticle random-phase approximation and its extensions. Effective, G-matrix-based nuclear forces are used in large single-particle model spaces. Both the β + β + and β + EC channels of the 0 ν 2 β decay are discussed and half-lives are computed. Particular attention is devoted to the study of the detectability of the resonant neutrinoless double electron capture ( R 0 ν ECEC ) process in 106 Cd. The calculations of the present article constitute the thu…
Comment on "Highly nonlinear, sign-varying shift of hydrogen spectral lines in dense plasmas".
2004
The shift of hydrogen and hydrogenlike spectral lines in dense plasmas, calculated with the full computer simulation method, in nonquenching, classical path, dipole approximation for plasma-emitter interaction, is equal to zero. In the paper commented on, Escarguel et al., Phys. Rev. E 62, 2667 (2000) the electron concentrations ${N}_{e}$ and the corresponding temperature values T are shown to have been determined incorrectly.
The eikonal model of reactions involving exotic nuclei; Roy Glauber's legacy in today's nuclear physics
2020
In this contribution, the eikonal approximation developed by Roy Glauber to describe high-energy quantum collisions is presented. This approximation has been-and still is-extensively used to analyse reaction measurements performed to study the structure of nuclei far from stability. This presentation focuses more particularly on the application of the eikonal approximation to the study of halo nuclei in modern nuclear physics. To emphasise Roy Glauber's legacy in today's nuclear physics, recent extensions of this model are reviewed.
Phenomenological applications of rational approximants
2016
We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function [Formula: see text] is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract [Formula: see text] from the semileptonic [Formula: see text] decays. Finally, the [Formula: see text] vector form factor in the TL region is explored using QAs.
A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole
1997
We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenv…