Search

One of the simplest deterministic mathematical model for the spread of an epidemic disease is the so-called SI system made of two Ordinary Differential Equations. It exhibits simple dynamics: a bifurcation parameter \(\mathscr {T}_0\) yielding persistence of the disease when \(\mathscr {T}_0 > 1\), else extinction occurs. A natural question is whether this gentle dynamic can be disturbed by spatial diffusion. It is straightforward to check it is not feasible for linear/nonlinear diffusions. When cross diffusion is introduced for suitable choices of the parameter data set this persistent state of the ODE model system becomes linearly unstable for the resulting initial and no-flux boundary value problem. On the other hand “natural” weak solutions can be defined for this initial and no-flux boundary value problem and proved to exist provided nonlinear and cross diffusivities satisfy some constraints. These constraints are not fully met for the parameter data set yielding instability. A remaining open question is: to which solutions does this apply? Periodic behaviors are observed for a suitable range of cross diffusivities.

In this paper we present a noncooperative game theoretical model for the well known problem of experimental design. A virtual player decides the design variables of an experiment and all the players solve a Nash equilibrium problem by optimizing suitable payoff functions. We consider the case where the design variables are the coordinates of n points in a region of the plane and we look for the optimal configuration of the points under some constraints. Arising from a concrete situation, concerning the ARGO-YBJ experiments, the goal is to find the optimal configuration of the detector, consisting of a single layer of resistive plate counters. Theoretical and computational results are presented for this location problem.

chapitre 7; Level set methods have recently gained much popularity to capture discontinuities, including their possible propagation. In this contribution we present a finite element approach for solving the governing equations of level set methods. After a review of the governing equations, the initialisation of the level sets, the discretisation on a finite domain and the stabilisation of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions.

In this work a mathematical model for mono dimensional, two-phase, bubbly flow, is presented. The mathematical model consists of the motion equations (i.e. mass, momentum and energy balance equation) for each phase, obtained applying a suitable phase-average procedure. Such motion equations determine the evolution of the homogenized hydrodynamic variables and contain both the inter phase interaction terms and the dispersive terms too. The latter terms are usually calculated by means of closure relations or even neglected. In this work, introducing a suitable description for the local perturbation induced by the bubbles on the liquid phase motion, the inter phase momentum exchange terms are analytically calculated. Numerical simulations are performed in order to simulate an experimental case of water hammer. The agreement is good, although further work is needed on both dissipative and mass exchange terms.

Interface boundary conditions are the key ingredient to design efficient domain decomposition methods. However, convergence cannot be obtained for any method in a number of iterations less than the number of subdomains minus one in the case of a one-way splitting. This optimal convergence can be obtained with generalized Robin type boundary conditions associated with an operator equal to the Schur complement of the outer domain. Since the Schur complement is too expensive to compute exactly, a new approach based on the computation of the exact Schur complement for a small patch around each interface node is presented for the two-Lagrange multiplier FETI method.

Unsteady turbulent transonic flows over oscillating airfoils are investigated by using a novel third-order accurate scheme on block-structured meshes. Two turbulence models ( algebraic and two-transport equation models) are studied in order to generate flow fields in agreement with experimental data. Numerical results are presented for 2-D problems related to helicopter rotors in forward flight, including shock-stall phenomena. The advantages of using a high-order accurate method and a suitable turbulence model for this kind of applications are demonstrated.

Publisher Summary Air quality models (AQMs) play a fundamental role in forecasting air pollution phenomena and are an important tool in the development of control strategies for reducing the damaging effects of heavy concentrations of pollutants. The space and time scales for an effective simulation of air pollution problems on urban, regional, or global domains, and the wide range of chemical–physical phenomena included in AQMs require very powerful computational resources. Therefore, the development of efficient parallel software for AQMs is an active research field. The choice of the numerical solution method for the problem is driven by several considerations. The most widely used computational approach for the solution to the problem is based on splitting techniques. Two basic splitting approaches can be identified—that is, physical and dimensional splitting. The vertical turbulent diffusion and chemical kinetics are usually coupled because they have similar time scales, especially for highly turbulent wind fields. In a parallel distributed-memory environment, the dimensional splitting does not seem to be very effective, in terms of efficiency and scalability.