1,730,109 research outputs found
Evaluation of possible correlation between dental occlusion and posture by a force platform exam
No full textDerivation of the Linear Landau Equation and Linear Boltzmann Equation from the Lorentz Model with Magnetic Field
No full textWe consider a test particle moving in a random distribution of obstacles in the plane, under the action of a uniform magnetic field, orthogonal to the plane. We show that, in a weak coupling limit, the particle distribution behaves according to the linear Landau equation with a magnetic transport term. Moreover, we show that, in a low density regime, when each obstacle generates an inverse power law potential, the particle distribution behaves according to the linear Boltzmann equation with a magnetic transport term. We provide an explicit control of the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. We compare these results with those ones obtained for a system of hard disks in Bobylev et al. (Phys Rev Lett 75:2, 1995), which show instead that the memory effects are not negligible in the Boltzmann-Grad limit
Diffusive Limit for the Random Lorentz Gas
No full textWe review some recent results concerning the derivation of the diffusion equation and the validation of Fick’s law for the microscopic model given by the random Lorentz Gas. These results are achieved by using a linear kinetic equation as an intermediate level of description between our original mechanical system and the diffusion equation. The diffusion coefficient is given by the Green-Kubo formula associated to the generator of the stochastic process dictated by the linear Landau equation and the linear Boltzmann equation respectively, according to the weak coupling regime and low density regime we are considering
On the theory of Lorentz gases with long range interactions
No full textWe construct and study the stochastic force field generated by a Poisson distribu- tion of sources at finite density, x1, x2, · · · in R3 each of them yielding a long range potential QiΦ(x − xi) with possibly different charges Qi ∈ R. The potential Φ is assumed to behave typically as |x|−s for large |x|, with s > 1/2. We will denote the resulting random field as “generalized Holtsmark field”. We then consider the dynamics of one tagged particle in such random force fields, in several scaling limits where the mean free path is much larger than the average distance between the scatterers. We estimate the diffusive time scale and identify conditions for the vanishing of correlations. These results are used to obtain appropriate kinetic descriptions in terms of a linear Boltzmann or Landau evolution equation depending on the specific choices of the interaction potential
Kinetic Description of a Rayleigh Gas with Annihilation
No full textIn this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to this model the possibility of annihilation (ideal Rayleigh gas with annihilation), requiring that each obstacle is either annihilating or elastic, which determines whether the tagged particle is elastically reflected or removed from the system. We provide a rigorous derivation of a linear Boltzmann equation with annihilation from this particle model in the Boltzmann–Grad limit. Moreover, we give explicit estimates for the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. The estimates show that the system can be approximated by the Boltzmann equation on an algebraically long time scale in the scaling parameter
Nota a los Medios de Comunicación sobre las II Jornadas Andalucistas de Formación Municipal en Almería
No full textNota a los Medios de Comunicación sobre las II Jornadas Andalucistas de Formación Municipal en Almería con fecha del 30 de noviembre de 199
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