Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria

We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a Boltzmann type kinetic equation containing a full nonlinear electron-electron collision term as well as linear terms representing collisions with reservoir particles having a specified Maxwellian distribution. We show that when the constant in front of the nonlinear collision kernel, thought of as a scaling parameter, is sufficiently strong, then the $L^1$ distance between $f$ and a certain time dependent Maxwellian stays small uniformly in $t$. Moreover, the mean and variance of this time dependent Maxwellian satisfy a coupled set of nonlinear ODE's that constitute the ``hydrodynamical'' equations for this kinetic system. This remain true even when these ODE's have non-unique equilibria, thus proving the existence of multiple stabe stationary solutions for the full kinetic model. Our approach relies on scale independent estimates for the kinetic equation, and entropy production estimates. The novel aspects of this approach may be useful in other problems concerning the relation between the kinetic and hydrodynamic scales globably in time.Comment: 30 pages, in TeX, to appear in Archive for Rational Mechanics and Analysis: author's email addresses: [email protected], [email protected], [email protected], [email protected], [email protected]

Propagation of Chaos for a Thermostated Kinetic Model

We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model.Comment: This version adds affiliation and grant information; otherwise it is unchange

A persistente migração rural-urbana.

O êxodo rural perde ímpeto no Brasil todo, mas ainda é expressivo, exceto no Centro-Oeste, por causa da pujança de sua agricultura e do pequeno tamanho de sua população rural. Em 2007, as regiões conservaram, com alguma perda, suas populações rurais de 2000, exceto o Centro-Oeste, cuja população rural aumentou. Não obstante o intenso êxodo rural do pós-década de 60, o pessoal ocupado no meio rural cresceu de 1940 a 1985. Logo, parte da população urbana, nesse período, empregou-se no meio rural. Nos períodos subsequentes a 1985, a ocupação rural decresceu intensamente, e as duas séries (população rural e ocupação) passaram a ter tendências semelhantes, de queda. O corpo do trabalho procura explicar as razões que explicam esse comportamento. O êxodo rural acelera a urbanização. Mas, o crescimento de nossas cidades é cada vez menos influenciado pelo êxodo rural. Pelas estimativas feitas do êxodo rural em relação ao crescimento da população urbana, no período de 1991 a 2000, 33,1% do crescimento da população urbana foi contribuição do êxodo rural. Já no período de 2000 a 2007, é verdade que se trata de um período mais curto, a contribuição do êxodo rural caiu para 19,2%. Muito mais forte que qualquer programa específico para segurar as famílias no campo, de um lado é expandir a demanda de alimentos via exportações e via mercado interno de alimentos, e de outro é dar condições à agricultura de responder à demanda. É essa a lição que o período de 2000 a 2007 encerra, no qual houve forte expansão da agricultura e no qual se manteve a população rural do início do período, sem sermos, pelo menos, capazes de segurar o excedente de nascimentos em relação às mortes.Na publicação: Eliseu Alves

Stability for Rayleigh-Benard convective solutions of the Boltzmann equation

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 2-dimensional convective stationary solution, which is close for small Knudsen number to the convective stationary solution of the Oberbeck-Boussinesq equations, near above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh number above and close to the bifurcation point and for small Knudsen number

Radiation from collision-dominated relativistic pair fireballs

It is generally accepted that gamma-ray bursts (GRBs) are initiated by a relativistic pair fireball, converting its internal energy into kinetic energy of a relativistically moving plasmoid and subsequently into radiation. Here, we investigate the early stages of this evolution, after the pair fireball has become optically thin to gamma-gamma pair production. We show that for a short period of time, ~ 0.1 - a few seconds after the initial explosion, the pair plasmoid evolution might be dominated by collisional processes prior to the formation of a collisionless shock. We simulate these processes during the early pair plasmoid evolution and calculate the expected radiative signatures. We show that the radiation from the collision-dominated pair plasmoid phase results in a short (~ a few ms) flash of thermal soft X-ray emission, followed by a transition phase of < 1 s during which the fireball turns Thomson thin, but its radiation remains dominated by thermal Comptonization, peaking at around E_pk ~ 100 MeV - a few GeV. While the very early thermal emission could be associated with the quasi-thermal radiation signatures found in the very early phases of several bright BATSE GRBs, the predicted subsequent flash of high-energy emission should be easily detectable with the GLAST satellite.Comment: AASTeX, 25 pages, including 7 figures. Accepted for publication in Ap

Groundwater seepage landscapes from distant and local sources in experiments and on Mars

© 2014 Author(s). Valleys with theater-shaped heads can form due to the seepage of groundwater and as a result of knickpoint (waterfall) erosion generated by overland flow. This ambiguity in the mechanism of formation hampers the interpretation of such valleys on Mars, particularly since there is limited knowledge of material properties. Moreover, the hydrological implications of a groundwater or surface water origin are important for our understanding of the evolution of surface features on Mars, and a quantification of valley morphologies at the landscape scale may provide diagnostic insights on the formative hydrological conditions. However, flow patterns and the resulting landscapes produced by different sources of groundwater are poorly understood. We aim to improve the understanding of the formation of entire valley landscapes through seepage processes from different groundwater sources that will provide a framework of landscape metrics for the interpretation of such systems. We study groundwater seepage from a distant source of groundwater and from infiltration of local precipitation in a series of sandbox experiments and combine our results with previous experiments and observations of the Martian surface. Key results are that groundwater flow piracy acts on valleys fed by a distant groundwater source and results in a sparsely dissected landscape of many small and a few large valleys. In contrast, valleys fed by a local groundwater source, i.e., nearby infiltration, result in a densely dissected landscape. In addition, valleys fed by a distant groundwater source grow towards that source, while valleys with a local source grow in a broad range of directions and have a strong tendency to bifurcate, particularly on flatter surfaces. We consider these results with respect to two Martian cases: Louros Valles shows properties of seepage by a local source of groundwater and Nirgal Vallis shows evidence of a distant source, which we interpret as groundwater flow from Tharsis

Penalised maximum likelihood estimation in multi-state models for interval-censored data

Continuous-time multi-state Markov models can be used to describe transitions over time across health states. Given longitudinal interval-censored data on transitions between states, statistical inference on changing health is possible by specifying models for transition hazards. Parametric time-dependent hazards can be restrictive, and nonparametric hazard specifications using splines are presented as an alternative. The smoothing of the splines is controlled by using penalised maximum likelihood estimation. With multiple time-dependent hazards in a multi-state model, there are multiple penalty parameters and selecting the optimal amount of smoothing is a challenge. A grid search to estimate the penalty parameters is computational intensive especially when combined with methods to deal with interval-censored transition times. A new and efficient method is proposed to estimate multi-state models with splines where the estimation of the penalty parameters is automatic. A simulation study is undertaken to validate the method and to illustrate the effect of interval censoring. The feasibility of the method is illustrated with two applications

Light-cone averages in a swiss-cheese universe

We analyze a toy swiss-cheese cosmological model to study the averaging problem. In our model, the cheese is the EdS model and the holes are constructed from a LTB solution. We study the propagation of photons in the swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the the expansion scalar is unaffected by the inhomogeneities. This is because of spherical symmetry. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the concordance model. Although the sole source in the swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w_0 and w_a follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.Comment: 20 pages, 14 figures; replaced to fit the version accepted for publication in Phys. Rev.

Êxodo e sua contribuição à urbanização de 1950 a 2010.

Este artigo trata da contribuição do êxodo rural na urbanização brasileira, de 1950 a 2010, e discute também o efeito da concentração da produção e as políticas de transferência de renda na agricultura familiar, nesse êxodo. Conclui-se que a contribuição do êxodo rural foi expressiva de 1960 a 1980. Em seguida, perdeu ímpeto e, de 2000 a 2010, foi responsável por apenas 3,5% de toda a urbanização. Uma das principais causas do êxodo rural é a concentração de produção, 9,7% do total dos estabelecimentos contribuiu com 86,4% do valor bruto da produção. E 70,7% de todos os estabelecimentos foram responsáveis por apenas 3,4% daquele valor. Estima-se que 11 milhões de pessoas vivam nessa situação de penúria.Na publicação: Eliseu Alves