The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the nonstirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, U. For slow reaction, the front propagates with a speed proportional to U-1/4, conversely for fast reaction the front speed is proportional to U-3/4. In the geometrical optics limit, the front speed asymptotically behaves as U/ln U. (C) 2002 American Institute of Physics.

We derive an inversion formula for stationary Fokker-Plank equaion that can be usd for studying some inverse problems in dissipative dynamics

Magnetic resonance spectroscopy (MRS) has been shown to be a potentially important medical diagnostic tool. The success of MRS depends on the quantitative data analysis, i.e., the interpretation of the signal in terms of relevant physical parameters, such as frequencies, decay constants, and amplitudes. A variety of time-domain algorithms to extract parameters have been developed. On the one hand, there are so-called blackbox methods. Minimal user interaction and limited incorporation of prior knowledge are inherent to this type of method. On the other hand, interactive methods exist that are iterative, require user involvement, and allow inclusion of prior knowledge. We focus on blackbox methods. The computationally most intensive part of these blackbox methods is the computation of the singular value decomposition (SVD) of a Hankel matrix. Our goal is to reduce the needed computational time without affecting the accuracy of the parameters of interest. To this end, algorithms based on the Lanczos method are suitable because the main computation at each step, a matrix-vector product, can be efficiently performed by means of the fast Fourier transform exploiting the structure of the involved matrix. We compare the performance in terms of accuracy and efficiency of four algorithms: the classical SVD algorithm based on the QR decomposition, the Lanczos algorithm, the Lanczos algorithm with partial reorthogonalization, and the implicitly restarted Lanczos algorithm. Extensive simulation studies show that the latter two algorithms perform best. © 2002 Elsevier Science (USA).

In this paper we consider a collocation and a discrete collocation method for a Volterra integral equation with logarithmic perturbation kernel. We prove convergence and stability of these methods in a pair of Sobolev type spaces.

The problem of classifying multispectral image data is studied here. We propose a new Bayesian method for this. The method uses "a priori" spatial information modeled by means of a suitable Markov random field. The image data for each class are assumed to be i.i.d. following a multivariate Gaussian model with unknown mean and unknown diagonal covariance matrix. When the prior information is not used and the variances of the Gaussian model are equal, the method reduces to the standard K-means algorithm. All the parameters appearing in the posterior model are estimated simultaneously. The prior normalizing constant is approximated on the basis of the expectation of the energy function as obtained by means of Markov Chain Monte Carlo simulations. Some experimental results suggest calculating this expectation from a "standard" function by simple multiplication by the minimum value of the energy. A local solution to the problem of maximizing the posterior distribution is obtained by using the Iterated Conditional Modes algorithm. The implementation of this method is easy and the required computations are carried out quickly, The method was applied with success to classify simulated image data and real dynamic Magnetic Resonance Imaging data.

This paper is concerned with improving the performance of certain Markov chain algorithms for Monte Carlo simulation. We propose a new algorithm for simulating from multivariate Gaussian densities. This algorithm combines ideas from coupled Markov chain methods and from an existing algorithm based only on over-relaxation. The rate of convergence of the proposed and existing algorithms can be measured in terms of the square of the spectral radius of certain matrices. We present examples in which the proposed algorithm converges faster than the existing algorithm and the Gibbs sampler. We also derive an expression for the asymptotic variance of any linear combination of the variables simulated by the proposed algorithm. We outline how the proposed algorithm can be extended to non-Gaussian densities.

The long time behaviour of the solutions of the equation u(t) = Delta F(u) in exterior domains is studied.

A quadrature rule using Appell polynomials and generalizing both the Euler-MacLaurin quadrature formula and a similar quadrature rule, obtained in Bretti et al [15], which makes use of Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the extrema of the considered interval, is derived. An expression of the remainder term and a numerical example are also enclosed.

We study some numerical properties of a nonconvex variational problem which arises as the continuous limit of a discrete optimization method designed for the smoothing of images with preservation of discontinuities. The functional that has to be minimized fails to attain a minimum value. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. The oscillations of the gradient exhibit analogies with microstructures in ordered materials. The pattern of the oscillations is analysed numerically by using discrete parametrized measures.

Wavelet and Fourier regularization methods are effective for the nonparametric regression problem. We prove that the loss function evaluated for the regularization parameter chosen through GCV or Mallows criteria is asymptotically equivalent in probability to its minimum over the regularization parameter. © 2001 Elsevier Science B.V.

Mathematical modelling and numerical simulation of melting experiments of pure metals. The model adopted, recently proposed by Mansutti, Baldoni and Rajagopal (M3AS, 2001), has a multi-physics structure and includes the description of the mushy zone. For this reason it is suitable to focus the process of phase transition at the interface where laboratory experiments have pointed out the occurence of displacements within the solid phase, even in the case of pure materials. The laboratory experiments and related data and output are produced by the group lead by Roberto Montanari , DIM, Univ. Tor Vergata, Rome.

By coupling the wavelet transform with a particular nonlinear shrinking function, the Red-telescopic optimal wavelet estimation of the risk (TOWER) method is introduced for removing noise from signals. It is shown that the method yields convergence of the L2 risk to the actual solution with optimal rate. Moreover, the method is proved to be asymptotically efficient when the regularization parameter is selected by the generalized cross validation criterion (GCV) or the Mallows criterion. Numerical experiments based on synthetic data are provided to compare the performance of the Red-TOWER method with hard-thresholding, soft-thresholding, and neigh–coeff thresholding. Furthermore, the numerical tests are also performed when the TOWER method is applied to hard-thresholding, soft-thresholding, and neigh–coeff thresholding, for which the full convergence results are still open.

We deal with the numerical evaluation of the Hilbert transform on the real line by a Gauss type quadrature rule. The convergence and the stability of the method are investigated. The goodness of the numerical results for practical applications is examined.