Search results for "Mathematical analysis"
showing 10 items of 2409 documents
NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
2011
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previ…
Exact analytic expressions for electromagnetic propagation in a finite one-dimensional periodic multilayer
2004
Translation Matrix Formalism has been used to find an exact analytic solution for light propagation in a finite one-dimensional (1-D) periodic stratified structure. This modal approach allows to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. As an example it is also shown how to extend this result to gratings featuring defects.
Computation of Amplitudes in the Discretized Approach to String Field Theory
1988
An approach to Witten string field theory based on the discretization of the world sheet is adopted. We use it to calculate tree amplitudes with the formulation of the theory based on string functionals. The results are evaluated numerically and turn out to be very accurate, giving, for a string approximated by 600 points, values within 0.02% of the prediction of the dual model. The method opens a way to calculate amplitudes in string field theory using nonflat backgrounds as well as compactified dimensions.
Intermittent-Type Chaos in Nonsinusoidal Driven Oscillators
2000
The intermittent-type chaos occurring in rf- and dc- nonsinusoidal driven oscillators is investigated analytically and numerically. The attention is focused on a general class of oscillators in which the total potential VRP(,r) is the Remoissenet-Peyrard potential which has constant amplitude and is 2π-periodic in , and whose shape can be varied as a function of parameter r ( |r| < 1). A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behaviour predicted by the theore…
A Unified Disk Scattering Model and Its Angle-of-Departure and Time-of-Arrival Statistics
2013
This paper proposes a novel probability density function (PDF) for the distribution of local scatterers inside a disk centered on the mobile station (MS). The new scattering model is introduced as the unified disk scattering model (UDSM), as it unifies a variety of typical circularly symmetric scattering models into one simple model. By adjusting a designated shape factor controlling the distribution of the scatterers, both the uniform circular and uniform ring scattering models can be obtained as special cases. Furthermore, the original Gaussian and uniform hollow-disk scattering models can be approximated with a high level of accuracy. In addition to these established scattering models, a…
Multivalued solutions for the output intensity of a semilinear photorefractive oscillator and stability analysis
2007
The analysis of pump-ratio dependences of the output intensity for a semilinear photorefractive coherent oscillator reveals two domains of multivalued solutions for sufficiently large coupling strength ensured by the crystal. We show that even in a strictly degenerate case the nonzero output intensity can be reached in a broad range of pump ratios r from 10−6 to infinity, including the interval where both pump intensities coincide or are very close to each other. This does not contradict the existence of the known gap in the oscillation threshold near the equal intensities of two pump waves: in this particular region the oscillation is not self-starting. The output intensities for frequency…
On the lower bound on the exchange-correlation energy in two dimensions
2010
We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. Fil: Räsänen, Esa. Universi…
ON FRACTIONAL RELAXATION
2003
Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leffler functions. The associated frequency dependent susceptibilities are related to symmetrically broadened Cole-Cole susceptibilities occurring as Johari Goldstein β-relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.
Hyperbolic character of the angular moment equations of radiative transfer and numerical methods
2000
We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods), to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in any kind of regime, from diffusion to free-streaming, is demonstrat…
Amplitude- and truncated partial-wave analyses combined: A single-channel method for extracting photoproduction multipoles directly from measured data
2020
Amplitude- and truncated partial-wave analyses are combined into a single-channel method for extracting multipoles directly from measured data. In practice, we have created a two-step procedure which is fit to the same database: in the first step we perform an energy-independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy-independent, truncated partial-wave analysis is done. The method is tested on the world collection of data for $\ensuremath{\eta}$ photoproduction, and the obtained fit results are very good. The sensitivity to different p…