4,204 research outputs found
Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions
We study the high-energy asymptotics of the steady velocity distributions for
model systems of granular media in various regimes. The main results obtained
are integral estimates of solutions of the hard-sphere Boltzmann equations,
which imply that the velocity distribution functions behave in a certain
sense as for large. The values of , which we call
{\em the orders of tails}, range from to , depending on the model of
external forcing. The method we use is based on the moment inequalities and
careful estimating of constants in the integral form of the Povzner-type
inequalities.Comment: 22 page
Optimality in self-organized molecular sorting
We introduce a simple physical picture to explain the process of molecular
sorting, whereby specific proteins are concentrated and distilled into
submicrometric lipid vesicles in eukaryotic cells. To this purpose, we
formulate a model based on the coupling of spontaneous molecular aggregation
with vesicle nucleation. Its implications are studied by means of a
phenomenological theory describing the diffusion of molecules towards multiple
sorting centers that grow due to molecule absorption and are extracted when
they reach a sufficiently large size. The predictions of the theory are
compared with numerical simulations of a lattice-gas realization of the model
and with experimental observations. The efficiency of the distillation process
is found to be optimal for intermediate aggregation rates, where the density of
sorted molecules is minimal and the process obeys simple scaling laws.
Quantitative measures of endocytic sorting performed in primary endothelial
cells are compatible with the hypothesis that these optimal conditions are
realized in living cells
1D-Disordered Conductor with Loops Immersed in a Magnetic Field
We investigate the conductance of a 1-D disordered conducting loop with two
contacts, immersed in a magnetic flux. We show the appearance in this model of
the Al'tshuler-Aronov-Spivak behaviour. We also investigate the case of a chain
of loops distributed with finite density: in this case we show that the
interference effects due to the presence of the loops can lead to the
delocalization of the wave function.Comment: 8 pages; LaTeX; IFUM 463/FT; to appear in Phys. Lett.
Teaching Students to Become Responsible Citizens
While in school, it is a wonderful time to begin to teach upcoming professionals about giving back to the communities they live or work within. These young adults can inspire the next generation of students to do the same. Participating in service learning allows students to see the impact of their hard efforts on the communities they serve. Witnessing the specific needs or purposes that need to be addressed by the community should inspire the students to get involved in order to make a difference. Teaching should focus on enabling students to enter the workplace, including opportunities for personal development
Octonic Electrodynamics
In this paper we present eight-component values "octons", generating
associative noncommutative algebra. It is shown that the electromagnetic field
in a vacuum can be described by a generalized octonic equation, which leads
both to the wave equations for potentials and fields and to the system of
Maxwell's equations. The octonic algebra allows one to perform compact combined
calculations simultaneously with scalars, vectors, pseudoscalars and
pseudovectors. Examples of such calculations are demonstrated by deriving the
relations for energy, momentum and Lorentz invariants of the electromagnetic
field. The generalized octonic equation for electromagnetic field in a matter
is formulated.Comment: 12 pages, 1 figur
Linear Theory of Electron-Plasma Waves at Arbitrary Collisionality
The dynamics of electron-plasma waves are described at arbitrary
collisionality by considering the full Coulomb collision operator. The
description is based on a Hermite-Laguerre decomposition of the velocity
dependence of the electron distribution function. The damping rate, frequency,
and eigenmode spectrum of electron-plasma waves are found as functions of the
collision frequency and wavelength. A comparison is made between the
collisionless Landau damping limit, the Lenard-Bernstein and Dougherty
collision operators, and the electron-ion collision operator, finding large
deviations in the damping rates and eigenmode spectra. A purely damped entropy
mode, characteristic of a plasma where pitch-angle scattering effects are
dominant with respect to collisionless effects, is shown to emerge numerically,
and its dispersion relation is analytically derived. It is shown that such a
mode is absent when simplified collision operators are used, and that
like-particle collisions strongly influence the damping rate of the entropy
mode.Comment: 23 pages, 10 figures, accepted for publication on Journal of Plasma
Physic
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