38 research outputs found
Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D
We prove global existence for a nonlinear Smoluchowski equation (a nonlinear
Fokker-Planck equation) coupled with Navier-Stokes equations in two dimensions.
The proof uses a deteriorating regularity estimate and the tensorial structure
of the main nonlinear terms
Wave decay on convex co-compact hyperbolic manifolds
For convex co-compact hyperbolic quotients X=\Gamma\backslash\hh^{n+1}, we
analyze the long-time asymptotic of the solution of the wave equation
with smooth compactly supported initial data . We show that, if
the Hausdorff dimension of the limit set is less than , then
u(t) = C_\delta(f) e^{(\delta-\ndemi)t} / \Gamma(\delta-n/2+1) +
e^{(\delta-\ndemi)t} R(t) where and
||R(t)||=\mc{O}(t^{-\infty}). We explain, in terms of conformal theory of the
conformal infinity of , the special cases \delta\in n/2-\nn where the
leading asymptotic term vanishes. In a second part, we show for all \eps>0
the existence of an infinite number of resonances (and thus zeros of Selberg
zeta function) in the strip \{-n\delta-\eps<\Re(\la)<\delta\}. As a byproduct
we obtain a lower bound on the remainder for generic initial data .Comment: 18 page
Global generalized solutions for Maxwell-alpha and Euler-alpha equations
We study initial-boundary value problems for the Lagrangian averaged alpha
models for the equations of motion for the corotational Maxwell and inviscid
fluids in 2D and 3D. We show existence of (global in time) dissipative
solutions to these problems. We also discuss the idea of dissipative solution
in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit
Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial
dimensions with spatial diffusion of the polymeric stresses
Surfactant effect in heteroepitaxial growth. The Pb - Co/Cu(111) case
A MonteCarlo simulations study has been performed in order to study the
effect of Pb as surfactant on the initial growth stage of Co/Cu(111). The main
characteristics of Co growing over Cu(111) face, i.e. the decorated double
layer steps, the multiple layer islands and the pools of vacancies, disappear
with the pre-evaporation of a Pb monolayer. Through MC simulations, a full
picture of these complex processes is obtained. Co quickly diffuses through the
Pb monolayer exchanging place with Cu atoms at the substrate. The exchange
process diffusion inhibits the formation of pure Co islands, reducing the
surface stress and then the formation of multilayer islands and the pools of
vacancies. On the other hand, the random exchange also suppress the nucleation
preferential sites generated by Co atoms at Cu steps, responsible of the step
decoration.Comment: 4 pages, latex, 2 figures embedded in the tex
Distribution of resonances for open quantum maps
We analyze simple models of classical chaotic open systems and of their
quantizations (open quantum maps on the torus). Our models are similar to
models recently studied in atomic and mesoscopic physics. They provide a
numerical confirmation of the fractal Weyl law for the density of quantum
resonances of such systems. The exponent in that law is related to the
dimension of the classical repeller (or trapped set) of the system. In a
simplified model, a rigorous argument gives the full resonance spectrum, which
satisfies the fractal Weyl law. For this model, we can also compute a quantity
characterizing the fluctuations of conductance through the system, namely the
shot noise power: the value we obtain is close to the prediction of random
matrix theory.Comment: 60 pages, no figures (numerical results are shown in other
references