68 research outputs found
Gradient Clogging in Depth Filtration
We investigate clogging in depth filtration, in which a dirty fluid is
``cleaned'' by the trapping of dirt particles within the pore space during flow
through a porous medium. This leads to a gradient percolation process which
exhibits a power law distribution for the density of trapped particles at
downstream distance x from the input. To achieve a non-pathological clogging
(percolation) threshold, the system length L should scale no faster than a
power of ln w, where w is the width. Non-trivial behavior for the permeability
arises only in this extreme anisotropic geometry.Comment: 4 pages, 3 figures, RevTe
Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction
Experiments on the motion of a particle on an inclined rough plane have
yielded some surprising results. For example, it was found that the frictional
force acting on the ball is viscous, {\it i.e.} proportional to the velocity
rather than the expected square of the velocity. It was also found that, for a
given inclination of the plane, the velocity of the ball scales as a power of
its radius. We present here a one dimensional stochastic model based on the
microscopic equations of motion of the ball, which exhibits the same behaviour
as the experiments. This model yields a mechanism for the origins of the
viscous friction force and the scaling of the velocity with the radius. It also
reproduces other aspects of the phase diagram of the motion which we will
discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil
Comparison between three-dimensional linear and nonlinear tsunami generation models
The modeling of tsunami generation is an essential phase in understanding
tsunamis. For tsunamis generated by underwater earthquakes, it involves the
modeling of the sea bottom motion as well as the resulting motion of the water
above it. A comparison between various models for three-dimensional water
motion, ranging from linear theory to fully nonlinear theory, is performed. It
is found that for most events the linear theory is sufficient. However, in some
cases, more sophisticated theories are needed. Moreover, it is shown that the
passive approach in which the seafloor deformation is simply translated to the
ocean surface is not always equivalent to the active approach in which the
bottom motion is taken into account, even if the deformation is supposed to be
instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid
Dynamics. Several references have been adde
Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D
In this note we propose a new set of coordinates to study the hyperbolic or
non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on
these coordinates, we study the existence of bounded and continuous
hyperbolically radial standing waves, as well as hyperbolically radial
self-similar solutions. Many of the arguments can easily be adapted to more
general nonlinearities.Comment: 19 pages, 1 Figure, to appear in Nonlinearit
Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves
We prove unique continuation properties for solutions of the evolution
Schr\"odinger equation with time dependent potentials. As an application of our
method we also obtain results concerning the possible concentration profiles of
blow up solutions and the possible profiles of the traveling waves solutions of
semi-linear Schr\"odinger equations.Comment: 23 page
Non-Spinning Black Holes in Alternative Theories of Gravity
We study two large classes of alternative theories, modifying the action
through algebraic, quadratic curvature invariants coupled to scalar fields. We
find one class that admits solutions that solve the vacuum Einstein equations
and another that does not. In the latter, we find a deformation to the
Schwarzschild metric that solves the modified field equations in the small
coupling approximation. We calculate the event horizon shift, the innermost
stable circular orbit shift, and corrections to gravitational waves, mapping
them to the parametrized post-Einsteinian framework.Comment: 7 pages, submitted to PR
Global Attractors for an Extensible Thermoelastic Beam System
This work is focused on the dissipative system describing the dynamics of an
extensible thermoelastic beam, where the dissipation is entirely contributed by
the second equation ruling the evolution of the temperature. Under natural
boundary conditions, we prove the existence of bounded absorbing sets. When
both the external body force and the heat source are time-independent, the
related semigroup of solutions is shown to possess the global attractor of
optimal regularity for all values of the external axial load. The same result
holds true when the rotational inertia is taken into consideration. In both
cases, the solutions on the attractor are strong solutions.Comment: 21 pages, no figur
Nearly inviscid Faraday waves
Many powerful techniques from Hamiltonian mechanics are available for the study of ideal hydrodynamics. This article explores some of the consequences of including small viscosity in a study of surface gravity-capillary waves excited by the vertical vibration of a container. It is shown that in this system, as in others, the addition of small viscosity provides a singular perturbation of the ideal fluid system, and that as a result its effects are nontrivial. The relevance of existing studies of ideal fluid problems is discussed from this point of view
Estimates of asymptotic degrees of freedom for solutions to the Navier-Stokes equations
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