2,030 research outputs found
Local well posedness for a linear coagulation equation
In this paper we derive some a priori estimates for a class of linear
coagulation equations with particle fluxes towards large size particles. The
derived estimates allow us to prove local well posedness for the considered
equations. Some regularizing effects exhibited by the equations in the particle
distributions for large particle sizes are discussed in detail.Comment: 71 page
Self-Similarity for Ballistic Aggregation Equation
We consider ballistic aggregation equation for gases in which each particle
is iden- ti?ed either by its mass and impulsion or by its sole impulsion. For
the constant aggregation rate we prove existence of self-similar solutions as
well as convergence to the self-similarity for generic solutions. For some
classes of mass and/or impulsion dependent rates we are also able to estimate
the large time decay of some moments of generic solutions or to build some new
classes of self-similar solutions
Asymptotics of self-similar solutions to coagulation equations with product kernel
We consider mass-conserving self-similar solutions for Smoluchowski's
coagulation equation with kernel with
. It is known that such self-similar solutions
satisfy that is bounded above and below as . In
this paper we describe in detail via formal asymptotics the qualitative
behavior of a suitably rescaled function in the limit . It turns out that as . As becomes larger
develops peaks of height that are separated by large regions
where is small. Finally, converges to zero exponentially fast as . Our analysis is based on different approximations of a nonlocal
operator, that reduces the original equation in certain regimes to a system of
ODE
Magnetoswitching of current oscillations in diluted magnetic semiconductor nanostructures
Strongly nonlinear transport through Diluted Magnetic Semiconductor
multiquantum wells occurs due to the interplay between confinement, Coulomb and
exchange interaction. Nonlinear effects include the appearance of spin
polarized stationary states and self-sustained current oscillations as possible
stable states of the nanostructure, depending on its configuration and control
parameters such as voltage bias and level splitting due to an external magnetic
field. Oscillatory regions grow in size with well number and level splitting. A
systematic analysis of the charge and spin response to voltage and magnetic
field switching of II-VI Diluted Magnetic Semiconductor multiquantum wells is
carried out. The description of stationary and time-periodic spin polarized
states, the transitions between them and the responses to voltage or magnetic
field switching have great importance due to the potential implementation of
spintronic devices based on these nanostructures.Comment: 14 pages, 4 figures, Revtex, to appear in PR
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