178 research outputs found

    Exact steady state solution of the Boltzmann equation: A driven 1-D inelastic Maxwell gas

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    The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of the distribution function f(c)f(c). In this paper we have inverted the Fourier transform to express f(c)f(c) in the form of an infinite series of exponentially decaying terms. The dominant high energy tail is exponential, f(c)A0exp(ac)f(c)\simeq A_0\exp(-a|c|), where a2/1α2a\equiv 2/\sqrt{1-\alpha^2} and the amplitude A0A_0 is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit (α0\alpha\to 0) and in the quasi-elastic limit (α1\alpha\to 1). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high energy tail exists for velocities cc01/q|c-c_0|\sim 1/\sqrt{q} around a crossover velocity c0lnq1/qc_0\simeq \ln q^{-1}/\sqrt{q}, where q(1α)/21q\equiv (1-\alpha)/2\ll 1. In this crossover region the distribution function is extremely small, lnf(c0)q1lnq\ln f(c_0)\simeq q^{-1}\ln q.Comment: 11 pages, 4 figures; a table and a few references added; to be published in PR

    Quantificação do carbono das substâncias húmicas em diferentes sistemas de uso do solo e épocas de avaliação.

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    A quantificação do carbono nas diferentes frações da matéria orgânica do solo (MOS) torna-se necessária devido ao interesse de se conhecer o potencial de captura e armazenamento do carbono nos diferentes sistemas de uso do solo. O objetivo deste trabalho foi quantificar o carbono das substâncias húmicas em diferentes sistemas de uso do solo e épocas de avaliação e correlacioná-lo com algumas propriedades químicas e físicas do solo. Os sistemas selecionados foram: preparo convencional (PC-milho/feijão), plantio direto (PD-berinjela/milho), consórcio maracujá/Desmodium sp, cultivo com figo e sistema agroflorestal. As amostras de solo foram coletadas em duas profundidades (0-5 e 5-10 cm) e épocas (17/11/2005–verão e 23/6/2006-inverno). Foi determinado o carbono orgânico total (COT) e realizado o fracionamento químico da MOS, quantificando-se o carbono da fração humina (C-HUM), fração ácido húmico (C-FAH) e fração ácido fúlvico (C-FAF). O C-HUM constituiu a maior parte do COT, havendo correlação significativa com o COT em todos os sistemas avaliados e estações. Analisando o C-FAH foi possível identificar alterações no solo relacionadas aos sistemas de uso, na profundidade de 0-5 cm e no verão, destacando-se o PD com os maiores teores. Com o C-FAF ocorreu este mesmo comportamento, mas na profundidade de 5-10 cm e no inverno, destacando-se o PC com maiores valores. Foram verificadas correlações significativas entre Valor S, Valor T e DMP em todos os sistemas, com exceção da área de PC. O PD aumenta os teores de C-FAH, nas duas profundidades e nas duas estações, quando comparado ao PC do solo

    Gravitational Lensing at Millimeter Wavelengths

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    With today's millimeter and submillimeter instruments observers use gravitational lensing mostly as a tool to boost the sensitivity when observing distant objects. This is evident through the dominance of gravitationally lensed objects among those detected in CO rotational lines at z>1. It is also evident in the use of lensing magnification by galaxy clusters in order to reach faint submm/mm continuum sources. There are, however, a few cases where millimeter lines have been directly involved in understanding lensing configurations. Future mm/submm instruments, such as the ALMA interferometer, will have both the sensitivity and the angular resolution to allow detailed observations of gravitational lenses. The almost constant sensitivity to dust emission over the redshift range z=1-10 means that the likelihood for strong lensing of dust continuum sources is much higher than for optically selected sources. A large number of new strong lenses are therefore likely to be discovered with ALMA, allowing a direct assessment of cosmological parameters through lens statistics. Combined with an angular resolution <0.1", ALMA will also be efficient for probing the gravitational potential of galaxy clusters, where we will be able to study both the sources and the lenses themselves, free of obscuration and extinction corrections, derive rotation curves for the lenses, their orientation and, thus, greatly constrain lens models.Comment: 69 pages, Review on quasar lensing. Part of a LNP Topical Volume on "Dark matter and gravitational lensing", eds. F. Courbin, D. Minniti. To be published by Springer-Verlag 2002. Paper with full resolution figures can be found at ftp://oden.oso.chalmers.se/pub/tommy/mmviews.ps.g

    An energy-stable time-integrator for phase-field models

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    We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework

    Granular fluid thermostatted by a bath of elastic hard spheres

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    The homogeneous steady state of a fluid of inelastic hard spheres immersed in a bath of elastic hard spheres kept at equilibrium is analyzed by means of the first Sonine approximation to the (spatially homogeneous) Enskog--Boltzmann equation. The temperature of the granular fluid relative to the bath temperature and the kurtosis of the granular distribution function are obtained as functions of the coefficient of restitution, the mass ratio, and a dimensionless parameter β\beta measuring the cooling rate relative to the friction constant. Comparison with recent results obtained from an iterative numerical solution of the Enskog--Boltzmann equation [Biben et al., Physica A 310, 308 (202)] shows an excellent agreement. Several limiting cases are also considered. In particular, when the granular particles are much heavier than the bath particles (but have a comparable size and number density), it is shown that the bath acts as a white noise external driving. In the general case, the Sonine approximation predicts the lack of a steady state if the control parameter β\beta is larger than a certain critical value βc\beta_c that depends on the coefficient of restitution and the mass ratio. However, this phenomenon appears outside the expected domain of applicability of the approximation.Comment: 16 pages, 7 figures; minor changes; to be published in Phys. Rev.
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