3,560 research outputs found
Wetting on Nanorough Surfaces
We present in this Letter a free-energy approach to the dynamics of a fluid
near a nanostructured surface. The model accounts both for the static phase
equilibrium in the vicinity of the surface (wetting angles, Cassie-Wenzel
transition) and the dynamical properties like liquid slippage at the boundary.
This method bridges the gap between phenomenological phase-field approaches and
more macroscopic lattice-Boltzmann models
Numerical aspects of nonlinear Schrodinger equations in the presence of caustics
The aim of this text is to develop on the asymptotics of some 1-D nonlinear
Schrodinger equations from both the theoretical and the numerical perspectives,
when a caustic is formed. We review rigorous results in the field and give some
heuristics in cases where justification is still needed. The scattering
operator theory is recalled. Numerical experiments are carried out on the focus
point singularity for which several results have been proven rigorously.
Furthermore, the scattering operator is numerically studied. Finally,
experiments on the cusp caustic are displayed, and similarities with the focus
point are discussed.Comment: 20 pages. To appear in Math. Mod. Meth. Appl. Sc
Exponential decay for the damped wave equation in unbounded domains
We study the decay of the semigroup generated by the damped wave equation in
an unbounded domain. We first prove under the natural geometric control
condition the exponential decay of the semigroup. Then we prove under a weaker
condition the logarithmic decay of the solutions (assuming that the initial
data are smoother). As corollaries, we obtain several extensions of previous
results of stabilisation and control
Blow-Up of Test Fields Near Cauchy Horizons
The behaviour of test fields near a compact Cauchy horizon is investigated.
It is shown that solutions of nonlinear wave equations on Taub spacetime with
generic initial data cannot be continued smoothly to both extensions of the
spacetime through the Cauchy horizon. This is proved using an energy method.
Similar results are obtained for the spacetimes of Moncrief containing a
compact Cauchy horizon and for more general matter models.Comment: 10 pages, Plain TeX, MPA-AR-92-
Geometric optics and instability for semi-classical Schrodinger equations
We prove some instability phenomena for semi-classical (linear or) nonlinear
Schrodinger equations. For some perturbations of the data, we show that for
very small times, we can neglect the Laplacian, and the mechanism is the same
as for the corresponding ordinary differential equation. Our approach allows
smaller perturbations of the data, where the instability occurs for times such
that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde
Inelastic X-ray scattering from valence electrons near absorption edges of FeTe and TiSe
We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to
low energy particle-hole excited states of metallic FeTe and semi-metallic
TiSe for photon incident energy tuned near the absorption edge of
Fe and Ti respectively. We show that the cross section amplitudes are well
described within a renormalization group theory where the effect of the core
electrons is captured by effective dielectric functions expressed in terms of
the the atomic scattering parameters of Fe and Ti. This method can be
used to extract the dynamical structure factor from experimental RIXS spectra
in metallic systems.Comment: 6 pages, 4 figure
Diffusion in pores and its dependence on boundary conditions
We study the influence of the boundary conditions at the solid liquid
interface on diffusion in a confined fluid. Using an hydrodynamic approach, we
compute numerical estimates for the diffusion of a particle confined between
two planes. Partial slip is shown to significantly influence the diffusion
coefficient near a wall. Analytical expressions are derived in the low and high
confinement limits, and are in good agreement with numerical results. These
calculations indicate that diffusion of tagged particles could be used as a
sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in
Liquids, Polymers, Biophysics and Chemical Dynamics
Effective temperatures of a heated Brownian particle
We investigate various possible definitions of an effective temperature for a
particularly simple nonequilibrium stationary system, namely a heated Brownian
particle suspended in a fluid. The effective temperature based on the
fluctuation dissipation ratio depends on the time scale under consideration, so
that a simple Langevin description of the heated particle is impossible. The
short and long time limits of this effective temperature are shown to be
consistent with the temperatures estimated from the kinetic energy and Einstein
relation, respectively. The fluctuation theorem provides still another
definition of the temperature, which is shown to coincide with the short time
value of the fluctuation dissipation ratio
Resonant X-ray diffraction studies on the charge ordering in magnetite
Here we show that the low temperature phase of magnetite is associated with
an effective, although fractional, ordering of the charge. Evidence and a
quantitative evaluation of the atomic charges are achieved by using resonant
x-ray diffraction (RXD) experiments whose results are further analyzed with the
help of ab initio calculations of the scattering factors involved. By
confirming the results obtained from X-ray crystallography we have shown that
RXD is able to probe quantitatively the electronic structure in very complex
oxides, whose importance covers a wide domain of applications.Comment: 4 pages 4 figures, accepted for publication in PR
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