1,721,025 research outputs found
Kinetic calculations for chemical reactions and inelastic transitions in a gas mixture
No full textA kinetic model for a gas mixture consisting of three species of structureless particles and one species of two-level atoms is considered. Elastic scattering and chemical reactions are taken into account, along with (de-) excitation processes triggered by inelastic collisions and interactions with photons. Two different strategies are proposed in order to obtain approximate solutions from the kinetic model. The former resorts to the derivation of a closed set of macroscopic equations in a proper asymptotic limit (moment-equation approach); the latter applies a suitable discretization of the extended kinetic equations (semi-continuous approach). Numerical solutions to spatially homogeneous test cases are provided and compared
The evaporation–condensation problem for a binary mixture of rarefied gases
Full text linkHalf space problems of evaporation and condensation for a binary mixture of inert gases are investigated when the dynamics is governed by a system of Navier–Stokes equations, obtained as hydrodynamic limit of a BGK-type description with dominant elastic collisions. Typical methods of qualitative theory of dynamical systems are used to investigate the one-dimensional stationary problem and to classify the solutions both in subsonic and supersonic cases. Numerical results for a mixture of noble gases are presented; the shock wave structure, representing transition between a subsonic and a supersonic steady flow in thermodynamic equilibrium, and the occurrence of under- and overshoots are discussed
Glioma invasion and its interplay with nervous tissue and therapy: A multiscale model
Full text linkA multiscale mathematical model for glioma cell migration and proliferation is proposed, taking into account a possible therapeutic approach. Starting with the description of processes occurring at the subcellular level, the equation for the mesoscopic level is formulated and a macroscopic model is derived, via parabolic limit and Hilbert expansions in the moment equations. After the model set up and the study of the well-posedness of this macroscopic setting, we investigate the role of the fibers in the tumor dynamics. In particular, we focus on the fiber density function, with the aim of comparing some common choices present in the literature and understanding which differences arise in the description of the actual fiber density and orientation. Finally, some numerical simulations, based on real data, highlight the role of each modelled process in the evolution of the solution of the macroscopic equation
Approximate solutions to the problem of stationary shear flow of smooth granular materials
No full textThe inelastic Boltzmann equation is used in order to study stationary shear flows in a rarefield granular gas of hard spheres. We resort to a Gaussian moment approximation in order to calculate the pressure tensor in three dimensions. The method is discussed along with previously introduced techniques: asymptotic expansion in the near elastic limit, and pseudo-Maxwellian approximation. Numerical results and approximate analytic formulas for the pressure tensor are presented and briefly commented on. A comparison with the pseudo-Maxwellian solution is discussed in detail
On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies
No full textMathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions
On the shock thickness for a binary gas mixture
Full text linkWe discuss the structure of the shock wave solution for a system of Navier–Stokes equations, obtained as hydrodynamic limit of a BGK description of the dynamics of monoatomic gases at kinetic level. We investigate first the thickness of the transition region of the shock profile for a monoatomic gas, for varying Mach number and different physical options for the viscosity coefficient. The analysis is then extended to a binary gas mixture. Some numerical results for noble gases are presented and discussed
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