Soluções analíticas da equação de Duffin-Kemmer-Petiau

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

STRUCTURE OF THE ELECTROMAGNETIC FIELD ALLOWING EXACT SOLUTION OF THE SCHRODINGER EQUATION IN SUPERPOSITION WITH AN AHARONOV-BOHM FIELD

A charged particle is considered in a complex external electromagnetic field. The field is a superposition of an Aharonov-Bohm field and some additional field. Here we describe all additional fields known up to the present time that allow exact solution of the Schrodinger equation in a complex field.

Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Two-wave-mixing induced self-focusing in an active photorefractive oscillator

We derive a nonlinear wave equation for a signal beam which is coupled to a pump beam by two-wave-mixing in a photorefractive crystal. This equation describes self-focusing of the signal beam. We compare two-wave-mixing induced spatial self-focusing of single-pass experiments in a diffusion-type photorefractive crystal and of a photorefractive oscillator using the same crystal. We observe that the nonlinear refractive index change in the oscillator is decreased while increasing resonator losses.

Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed.

The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Quantitative comparison between simulations of seismic wave propagation in heterogeneous poro-elastic media and equivalent visco-elastic solids for marine-type environments

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes an important seismic attenuation mechanism in porous rocks. As a consequence, centimetre-scale perturbations of the rock physical properties should be taken into account for seismic modelling whenever detailed and accurate responses of specific target structures are desired, which is, however, computationally prohibitive. A convenient way to circumvent this problem is to use an upscaling procedure to replace each of the heterogeneous porous media composing the geological model by corresponding equivalent visco-elastic solids and to solve the visco-elastic equations of motion for the inferred equivalent model. While the overall qualitative validity of this procedure is well established, there are as of yet no quantitative analyses regarding the equivalence of the seismograms resulting from the original poro-elastic and the corresponding upscaled visco-elastic models. To address this issue, we compare poro-elastic and visco-elastic solutions for a range of marine-type models of increasing complexity. We found that despite the identical dispersion and attenuation behaviour of the heterogeneous poro-elastic and the equivalent visco-elastic media, the seismograms may differ substantially due to diverging boundary conditions, where there exist additional options for the poro-elastic case. In particular, we observe that at the fluid/porous-solid interface, the poro- and visco-elastic seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an important result which has potentially far-reaching implications for wave-equation-based algorithms in exploration geophysics involving fluid/porous-solid interfaces, such as, for example, wavefield decomposition.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

BREAKING WAVES IN AN IDEAL QUARK GLUON PLASMA

We study the propagation of perturbations in the energy density in a quark gluon plasma. Expanding the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations we obtain a nonlinear differential equation called the breaking wave equation. We solve it numerically and follow the time-evolution of initially localized pulses. We find that, quite unexpectedly, these pulses live for a very long time (compared to the reaction time-scales) before breaking. In practice, they mimick the Korteweg-de Vries solitons. Their existence may have some observable consequences.

Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations

For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary condition in L-2(Omega). For a dissipative nonlinearity f satisfying a suitable growth restrictions these equations define on the phase space H-0(1)(Omega) x L-2(Omega) semigroups {T-eta(t) : t >= 0} which have global attractors A(eta) eta >= 0. We show that the family {A(eta)}(eta >= 0), behaves upper and lower semi-continuously as the parameter eta tends to 0(+).

The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein-Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin-1/2 field. © 1988 American Institute of Physics.