6,822 research outputs found
Scaling Solutions of Inelastic Boltzmann Equations with Over-populated High Energy Tails
This paper deals with solutions of the nonlinear Boltzmann equation for
spatially uniform freely cooling inelastic Maxwell models for large times and
for large velocities, and the nonuniform convergence to these limits. We
demonstrate how the velocity distribution approaches in the scaling limit to a
similarity solution with a power law tail for general classes of initial
conditions and derive a transcendental equation from which the exponents in the
tails can be calculated. Moreover on the basis of the available analytic and
numerical results for inelastic hard spheres and inelastic Maxwell models we
formulate a conjecture on the approach of the velocity distribution function to
a scaling form.Comment: 15 pages, 4 figures. Accepted in J. Statistical Physic
Extension of Haff's cooling law in granular flows
The total energy E(t) in a fluid of inelastic particles is dissipated through
inelastic collisions. When such systems are prepared in a homogeneous initial
state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ -
2\epsilon \tau] (known as Haff's law), where \tau is the average number of
collisions suffered by a particle within time t, and \epsilon=1-\alpha^2
measures the degree of inelasticity, with \alpha the coefficient of normal
restitution. This decay law is extended for large times to E(t) \aprox
\tau^{-d/2} in d-dimensions, far into the nonlinear clustering regime. The
theoretical predictions are quantitatively confirmed by computer simulations,
and holds for small to moderate inelasticities with 0.6< \alpha< 1.Comment: 7 pages, 4 PostScript figures. To be published in Europhysics Letter
Asymptotic solutions of the nonlinear Boltzmann equation for dissipative systems
Analytic solutions of the nonlinear Boltzmann equation in
-dimensions are studied for a new class of dissipative models, called
inelastic repulsive scatterers, interacting through pseudo-power law
repulsions, characterized by a strength parameter , and embedding
inelastic hard spheres () and inelastic Maxwell models (). The
systems are either freely cooling without energy input or driven by
thermostats, e.g. white noise, and approach stable nonequilibrium steady
states, or marginally stable homogeneous cooling states, where the data,
plotted versus , collapse on a scaling or
similarity solution , where is the r.m.s. velocity. The
dissipative interactions generate overpopulated high energy tails, described
generically by stretched Gaussians, with , where with in free cooling, and with when driven by white noise. Power law tails, , are
only found in marginal cases, where the exponent is the root of a
transcendental equation. The stability threshold depend on the type of
thermostat, and is for the case of free cooling located at . Moreover we
analyze an inelastic BGK-type kinetic equation with an energy dependent
collision frequency coupled to a thermostat, that captures all qualitative
properties of the velocity distribution function in Maxwell models, as
predicted by the full nonlinear Boltzmann equation, but fails for harder
interactions with .Comment: Submitted to: "Granular Gas Dynamics", T. Poeschel, N. Brilliantov
(eds.), Lecture Notes in Physics, Vol. LNP 624, Springer-Verlag,
Berlin-Heidelberg-New York, 200
Towards a Landau-Ginzburg-type Theory for Granular Fluids
In this paper we show how, under certain restrictions, the hydrodynamic
equations for the freely evolving granular fluid fit within the framework of
the time dependent Landau-Ginzburg (LG) models for critical and unstable fluids
(e.g. spinodal decomposition). The granular fluid, which is usually modeled as
a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the
spontaneous formation of vortices and of high density clusters. We suppress the
clustering instability by imposing constraints on the system sizes, in order to
illustrate how LG-equations can be derived for the order parameter, being the
rate of deformation or shear rate tensor, which controls the formation of
vortex patterns. From the shape of the energy functional we obtain the
stationary patterns in the flow field. Quantitative predictions of this theory
for the stationary states agree well with molecular dynamics simulations of a
fluid of inelastic hard disks.Comment: 19 pages, LaTeX, 8 figure
On the Modeling of Droplet Evaporation on Superhydrophobic Surfaces
When a drop of water is placed on a rough surface, there are two possible
extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets
trapped underneath the droplet and the one characterized by the homogeneous
wetting of the surface, called the Wenzel (W) state. A way to investigate the
transition between these two states is by means of evaporation experiments, in
which the droplet starts in a CB state and, as its volume decreases, penetrates
the surface's grooves, reaching a W state. Here we present a theoretical model
based on the global interfacial energies for CB and W states that allows us to
predict the thermodynamic wetting state of the droplet for a given volume and
surface texture. We first analyze the influence of the surface geometric
parameters on the droplet's final wetting state with constant volume, and show
that it depends strongly on the surface texture. We then vary the volume of the
droplet keeping fixed the geometric surface parameters to mimic evaporation and
show that the drop experiences a transition from the CB to the W state when its
volume reduces, as observed in experiments. To investigate the dependency of
the wetting state on the initial state of the droplet, we implement a cellular
Potts model in three dimensions. Simulations show a very good agreement with
theory when the initial state is W, but it disagrees when the droplet is
initialized in a CB state, in accordance with previous observations which show
that the CB state is metastable in many cases. Both simulations and theoretical
model can be modified to study other types of surface.Comment: 23 pages, 7 figure
Characterization of a rare analphoid supernumerary marker chromosome in mosaic
Abstract publicado em: Chromosome Research. 2015;23(Suppl 1):67-8. doi:10.1007/s10577-015-9476-6Analphoid supernumerary marker chromosomes (SMCs) are a rare subclass of SMCs C-band-negative
and devoid of alpha-satellite DNA. These marker chromosomes cannot be identified unambiguously by conventional banding techniques alone being necessary to apply molecular cytogenetic methods in favour of a detailed characterization. In this work we report an analphoid SMC involving the terminal long arm of chromosome 7, in 9 years-old boy with several dysmorphic features and severe development delay.
Cytogenetic analysis revealed a mosaic karyotype with the presence of an extra SMC, de novo, in 20 %
of lymphocytes and 73 % of fibroblast cells. FISH analysis with alpha-satellite probes for all chromosomes, whole chromosome painting probe for chromosome 7, and D7S427 and TelVysion 7q probes, allowed
establishing the origin of the SMC as an analphoidmarker resulting of an invdup rearrangement of 7q36-qter region. Affimetrix CytoScan HD microarray analysis, redefined the SMC to arr[hg19] 7q35(143696249-159119707)×2~3, which correspond to a gain of 15.42 Mb and encloses 67 OMIM genes, 16 of which are associated to disease. This result, combined with detailed clinical description, will provide an important means for better genotype-phenotype correlation and a more suitable genetic counselling to the patient and his parents, despite the additional difficulty resulting from being a mosaic (expression varies in different tissues). Analphoid SMCs derived from chromosome 7 are very rare, with only three cases reported so far. With this case we hope contribute to a better understanding of this type of chromosome rearrangements which are difficult for genetic counselling
Information and Multi-Period Optimal Income Taxation with Government Commitment
The optimal income taxation problem has been extensively studied in one- period models. When consumers work for many periods, this paper analyzes what information, if any, that the government learns about abilities in one period can be used in later periods to attain more redistribution than in a one- period world. liken the government must commit itself to future tax schedules, the gains cane from relaxing self-selection constraints by intertemporal nonstationarity. The effect of nonstationarity is analogous to that of randomization in one-period models. In a model with two ability classes it is shown that the key use of information is that only a single lifetime self-selection constraint for each type of consumer must be imposed. Sane necessary and sufficient conditions for randomization or nonstationarity are given. The planner can make additional use of the information when individual and social rates of time discounting differ. In this case, the limiting tax schedule is a nondistorting one if the government has a lower discount rate than individuals.
- …