Fiammetta Conforto

Steady detonation waves via the Boltzmann equation for a reacting mixture

Based on the Boltzmann equation, the detonation problem is dealt with on a mesoscopic level. The model is based on the assumption that ahead of a shock an explosive gas mixture is in meta stable equilibrium. Starting from the Von Neumann point the chemical reaction, initiated by the pressure jump, proceeds until the chemical equilibrium is reached. Numerical solutions of the derived macroscopic equations as well as the corresponding Hugoniot diagrams which reveal the physical relevance of the mathematical model are provided.

Wave features and group analysis for an axi-symmetric model of a dusty gas

Abstract The governing equations of a dusty gas with cylindrical or spherical symmetry are considered. Using the commuting properties of the invariance groups of the system, we are able to characterize appropriate “canonical” variables allowing to reduce the equations to autonomous form. In this way, we characterize particular exact solutions and the propagation of weak discontinuities is considered in such non-constant states.

On shock solutions to balance equations for slow and fast chemical reaction

This paper deals with shock propagation features in a gas mixture undergoing reversible bimolecular reactions, governed by suitable closures at Euler level of Boltzmann-type equations. Slow and fast chemical processes are considered. At macroscopic level, the slow case is described by a set of balance laws, whereas the fast one yields a set of conservation equations. Within the framework of hierarchies of hyperbolic systems, it is possible to prove that the system governing fast reactions is an equilibrium subsystem of the one describing slow reactions, and then to show how the solutions of the slow system converge to those of the fast system, in case of steady shock problems as well as of Riemann problems.

About reaction–diffusion systems involving the Holling-type II and the Beddington–DeAngelis functional responses for predator–prey models

We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching predators, and show that its solutions converge when a small parameter tends to 0 towards the solutions of a reaction–cross diffusion system of predator–prey type involving a Holling-type II or Beddington–DeAngelis functional response. We also provide a study of the Turing instability domain of the obtained equations and (in the case of the Beddington–DeAngelis functional response) compare it to the same instability domain when the cross diffusion is replaced by a standard diffusion.

Sub-shock Formation in Reacting Gas Mixtures

The shock-wave structure problem is investigated for a gas mixture of four species, undergoing a reversible bimolecular reaction, modelled by a 10 moment Grad closure of reactive Boltzmann equations. The presence of jump discontinuities within the shock structure solution is discussed, the supersonic regime is characterized, and the critical values of Mach number allowing the formation of sub-shocks in the field variables of one or more components of the mixture are pointed out.

An extended thermodynamic description of mass diffusion in elastic solids

We present here a non-conventional model for a themoelastic body, based on the Extended Irreversible Thermodynamics, of physical processes in which mass diffusion occurs.Then we linearize the field equations around a constant state in order to obtain the dispersion relation pointing out the interaction between diffusive field and thermal field.

Weakly non-linear high frequency waves for a first order quasi-linear system involving source-like terms

Making use of the method of asymptotic expansion of multiple scales, a study of weakly non-linear, high frequency waves, through “homogeneous” media characterized by dissipative or dispersive hyperbolic systems of partial differential equations, is proposed.Within the present theoretical framework, asymptotic waves in a heat-conducting fluid are considered.