Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Elastic waves propagation in 1D fractional non-local continuum
2008
Aim of this paper is the study of waves propagation in a fractional, non-local 1D elastic continuum. The non-local effects are modeled introducing long-range central body interactions applied to the centroids of the infinitesimal volume elements of the continuum. These non-local interactions are proportional to a proper attenuation function and to the relative displacements between non-adjacent elements. It is shown that, assuming a power-law attenuation function, the governing equation of the elastic waves in the unbounded domain, is ruled by a Marchaud-type fractional differential equation. Wave propagation in bounded domain instead involves only the integral part of the Marchaud fraction…
Ansatz independent solution of a soliton in a strong dispersion-management system
2001
We introduce a theoretical approach to the study of propagation in systems with periodic strongmanagement dispersion. Our approach does not assume any ansatz about the form of the solution nor does it make use of any average procedure. We find an explicit solution for the pulse evolution in the fast dynamics regime ~distances smaller than the dispersion period!. We also establish the equation of motion governing the slow dynamics of an arbitrary pulse and prove that the pulse evolution is nonlinear and Hamiltonian. We solve this equation and find that a nonlinear solitonlike solution occurs self-consistently in the form of an asymptotic stationary eigenfunction of the Hamiltonian.
A Look at Some Remarkable Mathematical Techniques
1996
The nonlinear equations that we have encountered in the previous chapters can be solved by using mathematical techniques such as the powerful inverse scattering transform (IST) (Gardner et al. 1967) and the remarkable Hirota method (Hirota 1971). Specifically, in addition to the one-soliton solutions, explicit multisoliton solutions representing the interaction of any number of solitons can be constructed. Moreover, in several cases a precise prediction, closely related to experiments, can be made by the IST of the nonlinear response of the physical system, that is, of the number of solitons that can emerge from a finite initial disturbance (Zakharov, 1980. Ablowitz and Segur 1981; Calogero…
Stationary semiconductor equations
1996
The behaviour of a semiconductor device is usually modelled by three coupled nonlinear partial differential equations of elliptic type. Such a system for the transport of mobile charge carriers was first introduced by Van Roosbroeck [Van Roosbroeck] in 1950. Nowadays there are many models which differ in their choice of unknowns, scales, various types of nonlinearities etc. (see, e.g., [Brezzi], [Groger], [Markowich], [Markowich, Ringhofer, Schmeiser], [Mock, 1972], [Polak, den Heijer, Schilders, Markowich], [Pospisek], [Pospisek, Segeth, Silhan], [Selberherr], [Sze], [Zlamal, 1986]).
Large data scattering for NLKG on waveguide ℝd × 𝕋
2020
We consider the pure-power defocusing nonlinear Klein–Gordon equation, in the [Formula: see text]-subcritical case, posed on the product space [Formula: see text], where [Formula: see text] is the one-dimensional flat torus. In this framework, we prove that scattering holds for any initial data belonging to the energy space [Formula: see text] for [Formula: see text]. The strategy consists in proving a suitable profile decomposition theorem on the whole manifold to pursue a concentration-compactness and rigidity method along with the proofs of (global in time) Strichartz estimates.
Study of the $\bar K N$ system and coupled channels in a finite volume
2013
We investigate the $\bar KN$ and coupled channels system in a finite volume and study the properties of the $\Lambda(1405)$ resonance. We calculate the energy levels in a finite volume and solve the inverse problem of determining the resonance position in the infinite volume. We devise the best strategy of analysis to obtain the two poles of the $\Lambda(1405)$ in the infinite volume case, with sufficient precision to distinguish them.
A model study of Hartree-Fock and Linear Response in coordinate space
1979
A fast procedure for spherical Hartree-Fock is obtained by coordinate space representation and a modification of gradient iteration. Along similar lines, the corresponding Linear Response equations are derived and solved, in order to achieve a fully consistent treatment. The Linear Response equations are applied to a change in particle numbers, i.e. to the description of isotopic differences. In a model study we look for their physical and numerical properties, i.e. linearity of the response, numerical stability and consistency requirements for the Hartree-Fock basis.
A two-center-oscillator-basis as an alternative set for heavy ion processes
1977
The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higher oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy surface are comparable with the results of more elaborate models.
Geometric efficiency for a circular detector and a linear source of arbitrary orientation and position
2010
A new axisymmetric radiation vector potential which is singular along its entire axis of symmetry is derived for a spherically symmetric point radiation source. This potential and a previously given non-singular point source potential are integrated to give radiation vector potentials for a straight linear source of constant strength. Analytical solutions are given for the geometric efficiency G of a line source and a circular disk detector when the line source is parallel to the detector axis. The analytical solution is also given for the case where the line source is parallel to the disk surface, such that the source axis and the detector axis intersect. All other cases are given as simpl…
Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
2008
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic system. We have carried out a preliminary analysis of the mathematical structure of that system, in particular focusing on the equations governing the evolution for the deviation of a conformal metric from a flat fiducial one. The choice of a Dirac's gauge for the spatial coordinates guarantees the mathematical characterization of that system as a (strongly) hyperbolic system of conservation laws. In the presence of boundaries, this characterization also depen…