23 research outputs found
Forest fire spreading: a nonlinear stochastic model continuous in space and time
Forest fire spreading is a complex phenomenon characterized by a stochastic
behavior. Nowadays, the enormous quantity of georeferenced data and the
availability of powerful techniques for their analysis can provide a very
careful picture of forest fires opening the way to more realistic models. We
propose a stochastic spreading model continuous in space and time that is able
to use such data in their full power. The state of the forest fire is described
by the subprobability densities of the green trees and of the trees on fire
that can be estimated thanks to data coming from satellites and earth
detectors. The fire dynamics is encoded into a density probability kernel which
can take into account wind conditions, land slope, spotting phenomena and so
on, bringing to a system of integro-differential equations for the probability
densities. Existence and uniqueness of the solutions is proved by using
Banach's fixed point theorem. The asymptotic behavior of the model is analyzed
as well. Stochastic models based on cellular automata can be considered as
particular cases of the present model from which they can be derived by space
and/or time discretization. Suggesting a particular structure for the kernel,
we obtain numerical simulations of the fire spreading under different
conditions. For example, in the case of a forest fire evolving towards a river,
the simulations show that the probability density of the trees on fire is
different from zero beyond the river due to the spotting phenomenon.
Firefighters interventions and weather changes can be easily introduced into
the model.Comment: 25 pages, 27 figure
A BGK type approximation for the collision operator of the transport equation for semiconductors
In the attempt of obtaining macroscopic models which describe the flow of electrons through a semiconductor crystal, many authors start from the Boltzmann transport equation, often using a generalized BGK type approximation for the collision operator. In this work, by means of this approximation, we shall show that it is possible to obtain a new drift-diffusion equation valid in the high electric field regime
Comparing kinetic and hydrodynamical models for electron transport in monolayer graphene
The aim of this work is to compare, in monolayer graphene, solutions of the
electron Boltzmann equation, obtained with a discontinuous Galerkin method, with those
of a hydrodynamical model based on the Maximum Entropy Principle
A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation
We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC
Nonlinear Models for Silicon Semiconductors
In this paper we present exact closures of the 8-moment and the 9-moment models for the charge transport in silicon semiconductors based on the maximum entropy principle. The validity of these models is assessed by numerical simulations of an n-n-n device. The results are compared with those obtained from the numerical solution of the Boltzmann Transport Equation both by Monte Carlo method and directly by a finite difference scheme
Dependence on Frequency of the Electromagnetic Field Distribution inside a Cylindrical CavityExcited through an Off-Axis Aperture
To explain the relevant changes in the electron cyclotron resonance ion source behaviour for small variations of the exciting radiation frequency, we determine the spatial distribution of the field within the cavity for every resonant mode
Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors
In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking—as macroscopic variables—suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two- or one-dimensional
Metodo dei momenti e principio di minima entropia
Dottorato di ricerca in matematica. 11 ciclo. Tutore A. M. Anile. Coordinatore G. RestucciaConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal
A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation
We present the first macroscopical model for charge transport in compound semiconductors to make use of analytic ellipsoidal approximations for the energy dispersion relationships in the neighbours of the lowest minima of the conduction bands. The model considers the main scattering mechanisms charges undergo in polar semiconductors, that is the acoustic, polar optical, intervalley non-polar optical phonon interactions and the ionized impurity scattering. Simulations are shown for the cases of bulk 4H and 6H-SiC