Search results for "Applied Mathematic"

2014

Codebook is an effective image representation method. By clustering in local image descriptors, a codebook is shown to be a distinctive image feature and widely applied in object classification. In almost all existing works on codebooks, the building of the visual vocabulary follows a basic routine, that is, extracting local image descriptors and clustering with a user-designated number of clusters. The problem with this routine lies in that building a codebook for each single dataset is not efficient. In order to deal with this problem, we investigate the influence of vocabulary sizes on classification performance and vocabulary universality with the kNN classifier. Experimental results in…

An adaptive method for Volterra–Fredholm integral equations on the half line

2009

AbstractIn this paper we develop a direct quadrature method for solving Volterra–Fredholm integral equations on an unbounded spatial domain. These problems, when related to some important physical and biological phenomena, are characterized by kernels that present variable peaks along space. The method we propose is adaptive in the sense that the number of spatial nodes of the quadrature formula varies with the position of the peaks. The convergence of the method is studied and its performances are illustrated by means of a few significative examples. The parallel algorithm which implements the method and its performances are described.

Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

2013

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present a discussion of the observed blow-up scenarios.

A posteriori error estimates for Webster's equation in wave propagation

2015

We consider a generalised Webster’s equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster’s equation in generalised form has been rigorously derived in a previous article starting from the wave equation, and it approximates cross-sectional averages of the propagating wave. Here, the approximation error is estimated by an a posteriori technique. peerReviewed

Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion

2012

In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through a weakly nonlinear analysis, we are able to predict the shape and the amplitude of the pattern. For the amplitude, in the supercritical and in the subcritical case, we derive the cubic and the quintic Stuart–Landau equation respectively. When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a travelin…

Wave propagation in anisotropic turbulent superfluids

2013

In this work, a hydrodynamical model of Superfluid Turbulence previously formulated is applied to study how the presence of a non-isotropic turbulent vortex tangle modifies the propagation of waves. Two cases are considered: wave front parallel and orthogonal to the heat flux. Using a perturbation method, the first-order corrections due to the presence of the vortex tangle to the speeds and to the amplitudes of the first and second sound are determined. It is seen that the presence of the quantized vortices couples first and second sound, and the attenuation of second sound is proportional to the line density L if the wave propagates orthogonal to the heat flux, while it is proportional to …

Pseudodifferential operators of Beurling type and the wave front set

2008

AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.

Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

2013

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…

Well-posedness of Prandtl equations with non-compatible data

2013

In this paper we shall be concerned with Prandtl's equations with incompatible data, i.e. with initial data that, in general, do not fulfil the boundary conditions imposed on the solution. Under the hypothesis of analyticity in the streamwise variable, we shall prove that Prandtl's equations, on the half-plane or on the half-space, are well posed for a short time.

Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring

2013

We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional precondi…