The use of a mathematical model is proposed in order to denoise X-ray two-dimensional patterns. The method relies on a generalized diffusion equation whose diffusion constant depends on the image gradients. The numerical solution of the diffusion equation provides an efficient reduction of pattern noise as witnessed by the computed peak of signal-to-noise ratio. The use of experimental data with different inherent levels of noise allows us to show the success of the method even in the case, experimentally relevant, when patterns are blurred by Poissonian noise.

In this paper we revisit the problem of performing a QZ step with a so-called "perfect shift", which is an "exact" eigenvalue of a given regular pencil lambda B-A in unreduced Hessenberg-Triangular form. In exact arithmetic, the QZ step moves that eigenvalue to the bottom of the pencil, while the rest of the pencil is maintained in Hessenberg-Triangular form, which then yields a deflation of the given eigenvalue. But in finite-precision the QZ step gets "blurred" and precludes the deflation of the given eigenvalue.

Front propagation in two-dimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. For the steady flow, a simplified model allows for an analytical prediction of the front speed v(f) dependence on the stirring intensity U, which is in good agreement with numerical estimates. In particular, at large U, the behavior v(f)similar toU/log(U) is predicted. By adding small scales to the velocity field we found that their main effect is to renormalize the flow intensity.

Internal waves describe the (linear) response of an incompressible sta- bly stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes' laws, and it is expected to be singular if the slope has the same inclination as the group velocity.

The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler--MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given. © 2001, Heldermann Verlag. All rights reserved.

The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a QR sweep and part of a QL sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method.

Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete agent-based simulations in continuous space allow for accurate treatment of advection and number fluctuations, but can be computationally expensive for even modest organism densities. In this report, we propose an algorithm to overcome some of these challenges. We first provide a thorough validation of the algorithm in one and two dimensions without flow.

In this paper, we study the retrieval of water vapor profiles from simulated FORUM measurements. We show that the bias towards the a-priori introduced by the Optimal Estimation technique can be reduced by using larger errors for the a-priori. Reducing the strength of the a-priori may, however, cause unphysical oscillations in the resulting profiles because of the ill-conditioning of the retrieval problem. An a-posteriori regularization technique, the Iterative Variable Strength method, is thus applied to reduce the amplitude of the oscillations.

The exit-time statistics of experimental turbulent data is analyzed. By looking at the exit-time moments (inverse structure functions) it is possible to have a direct measurement of scaling properties of the laminar statistics. It turns out that the inverse structure functions show a much more extended intermediate dissipative range than the structure functions, leading to the first clear evidence of the existence of such a range of scales. [S1063-651X(99)51012-X].