Using a combination of Kawashima- and Goodman-type energy estimates, we establish spectral stability of general small-amplitude relaxation shocks of symmetric dissipative systems. This extends previous results obtained by Plaza and Zumbrun [8] by singular perturbation techniques under an additional technical assumption, namely, that the background equation be noncharacteristic with respect to the shock.

In this paper we introduce a simulation algorithm based on fluid dynamic models to reproduce the behavior of traffic in a portion of the urban network in Rome. Numerical results, obtained comparing experimental data with numerical solutions, show the effectiveness of our approximation. (c) 2009 Elsevier Inc. All rights reserved.

This work reports on vehicular traffic modeling by methods of the discrete kinetic theory. The purpose is to detail a reference mathematical framework for some discrete velocity kinetic models recently introduced in the literature, which proved capable of reproducing interesting traffic phenomena without using experimental information as modeling assumptions. To this end, we firstly derive a general discrete velocity kinetic framework with binary nonlocal interactions. Then, resorting to some ideas of stochastic game theory, we outline specific modeling guidelines for vehicular traffic, and finally we discuss the derivation of the above-mentioned vehicular traffic models from these mathematical structures. © 2009.

Resorting to a multiphase modelling framework, tumours are described here as a mixture of tumour and host cells within a porous structure constituted by a remodelling extracellular matrix (ECM), which is wet by a physiological extracellular fluid. The model presented in this article focuses mainly on the description of mechanical interactions of the growing tumour with the host tissue, their influence on tumour growth, and the attachment/detachment mechanisms between cells and ECM. Starting from some recent experimental evidences, we propose to describe the interaction forces involving the extracellular matrix via some concepts coming from viscoplasticity. We then apply the model to the description of the growth of tumour cords and the formation of fibrosis. © 2008 Springer-Verlag.

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models. © EDP Sciences, 2009.

In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: on the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles. © 2009 Springer-Verlag.

In this work the phenomenon of contact inhibition of growth is studied by applying an individual based model and a continuum multiphase model to describe cell colony growth in vitro. The impact of different cell behavior in response to mechanical cues is investigated. The work aims at comparing the results from both models from the qualitative and, whenever possible, also the quantitative point of view. Crown Copyright © 2009.

Neural current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured in the outer space, gives rise to a highly ill-posed and ill-conditioned inverse problem. We use a joint sparsity constraint as a regularization term and we propose an efficient iterative thresholding algorithm to recover the current distribution. Some numerical tests are also displayed.

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured by sophisticated superconducting devices in a noninvasive way, gives rise to a highly ill-posed and ill-conditioned inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. In particular, we use a joint sparsity constraint as a regulariza- tion term and we propose an efficient iterative thresholding algorithm to reconstruct the current distribution. Some bidimensional experiments are presented in order to show the algorithm properties.

Direct numerical approximation of a continuous-time infinite horizon control problem, requires to recast the model as a discrete-time, finite-horizon control model. The quality of the optimization results can be heavily degraded if the discretization process does not take into account features of the original model to be preserved. Restricting their attention to optimal growh problems with a steady state, Mercenier and Michel in [1] and [2], studied the conditions to be imposed for ensuring that discrete first-order approximation models have the same steady states as the infinite-horizon continuous-times counterpart. Here we show that Mercenier and Michel scheme is a first order partitioned Runge-Kutta method applied to the state-costate differential system which arises from the Pontryagin maximum principle. The main consequence is that it is possible to consider high order schemes which generalize that algorithm by preserving the steady-growth invariance of the solutions with respect to the discretization process. Numerical examples show the efficiency and accuracy of the proposed methods when applied to the classical Ramsey growth model.

An improvement of a mathematical model of the galvanic iron corrosion, previously presented by one of the authors, is here proposed. The iron(III)-hydroxide formation is, now, considered in addition to the redox reaction. The PDE system, assembled on the basis of the fundamental holding electro-chemistry laws, is numerically solved by a locally refined FD method. For verification purpose we have assembled an experimental galvanic cell; in the present work, we report two tests cases, with acidic and neutral electrolitical solution, where the computed electric potential compares well with the measured experimental one.