181 research outputs found
Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition
In the selective withdrawal experiment fluid is withdrawn through a tube with
its tip suspended a distance S above a two-fluid interface. At sufficiently low
withdrawal rates, Q, the interface forms a steady state hump and only the upper
fluid is withdrawn. When Q is increased (or S decreased), the interface
undergoes a transition so that the lower fluid is entrained with the upper one,
forming a thin steady-state spout. Near this transition the hump curvature
becomes very large and displays power-law scaling behavior. This scaling allows
for steady-state hump profiles at different flow rates and tube heights to be
scaled onto a single similarity profile. I show that the scaling behavior is
independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl
Thermostatistics of overdamped motion of interacting particles
We show through a nonlinear Fokker-Planck formalism, and confirm by molecular
dynamics simulations, that the overdamped motion of interacting particles at
T=0, where T is the temperature of a thermal bath connected to the system, can
be directly associated with Tsallis thermostatistics. For sufficiently high
values of T, the distribution of particles becomes Gaussian, so that the
classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures
of the thermal bath, the system displays a mixed behavior that follows a novel
type of thermostatistics, where the entropy is given by a linear combination of
Tsallis and Boltzmann-Gibbs entropies.Comment: 4 pages, 2 figure
Logarithmic diffusion and porous media equations: a unified description
In this work we present the logarithmic diffusion equation as a limit case
when the index that characterizes a nonlinear Fokker-Planck equation, in its
diffusive term, goes to zero. A linear drift and a source term are considered
in this equation. Its solution has a lorentzian form, consequently this
equation characterizes a super diffusion like a L\'evy kind. In addition is
obtained an equation that unifies the porous media and the logarithmic
diffusion equations, including a generalized diffusion equation in fractal
dimension. This unification is performed in the nonextensive thermostatistics
context and increases the possibilities about the description of anomalous
diffusive processes.Comment: 5 pages. To appear in Phys. Rev.
Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
A general type of nonlinear Fokker-Planck equation is derived directly from a
master equation, by introducing generalized transition rates. The H-theorem is
demonstrated for systems that follow those classes of nonlinear Fokker-Planck
equations, in the presence of an external potential. For that, a relation
involving terms of Fokker-Planck equations and general entropic forms is
proposed. It is shown that, at equilibrium, this relation is equivalent to the
maximum-entropy principle. Families of Fokker-Planck equations may be related
to a single type of entropy, and so, the correspondence between well-known
entropic forms and their associated Fokker-Planck equations is explored. It is
shown that the Boltzmann-Gibbs entropy, apart from its connection with the
standard -- linear Fokker-Planck equation -- may be also related to a family of
nonlinear Fokker-Planck equations.Comment: 19 pages, no figure
Fluid Flows of Mixed Regimes in Porous Media
In porous media, there are three known regimes of fluid flows, namely,
pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are
usually treated separately in literature. To study complex flows when all three
regimes may be present in different portions of a same domain, we use a single
equation of motion to unify them. Several scenarios and models are then
considered for slightly compressible fluids. A nonlinear parabolic equation for
the pressure is derived, which is degenerate when the pressure gradient is
either small or large. We estimate the pressure and its gradient for all time
in terms of initial and boundary data. We also obtain their particular bounds
for large time which depend on the asymptotic behavior of the boundary data but
not on the initial one. Moreover, the continuous dependence of the solutions on
initial and boundary data, and the structural stability for the equation are
established.Comment: 33 page
Absence of squirt singularities for the multi-phase Muskat problem
In this paper we study the evolution of multiple fluids with different
constant densities in porous media. This physical scenario is known as the
Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that
the fluids do not develop squirt singularities.Comment: 16 page
Nonlinear porous medium flow with fractional potential pressure
We study a porous medium equation, with nonlocal diffusion effects given by
an inverse fractional Laplacian operator. We pose the problem in n-dimensional
space for all t>0 with bounded and compactly supported initial data, and prove
existence of a weak and bounded solution that propagates with finite speed, a
property that is nor shared by other fractional diffusion models.Comment: 32 pages, Late
Matter-wave interferometry in a double well on an atom chip
Matter-wave interference experiments enable us to study matter at its most
basic, quantum level and form the basis of high-precision sensors for
applications such as inertial and gravitational field sensing. Success in both
of these pursuits requires the development of atom-optical elements that can
manipulate matter waves at the same time as preserving their coherence and
phase. Here, we present an integrated interferometer based on a simple,
coherent matter-wave beam splitter constructed on an atom chip. Through the use
of radio-frequency-induced adiabatic double-well potentials, we demonstrate the
splitting of Bose-Einstein condensates into two clouds separated by distances
ranging from 3 to 80 microns, enabling access to both tunnelling and isolated
regimes. Moreover, by analysing the interference patterns formed by combining
two clouds of ultracold atoms originating from a single condensate, we measure
the deterministic phase evolution throughout the splitting process. We show
that we can control the relative phase between the two fully separated samples
and that our beam splitter is phase-preserving
Radio-frequency dressed state potentials for neutral atoms
Potentials for atoms can be created by external fields acting on properties
like magnetic moment, charge, polarizability, or by oscillating fields which
couple internal states. The most prominent realization of the latter is the
optical dipole potential formed by coupling ground and electronically excited
states of an atom with light. Here we present an experimental investigation of
the remarkable properties of potentials derived from radio-frequency (RF)
coupling between electronic ground states. The coupling is magnetic and the
vector character allows to design state dependent potential landscapes. On atom
chips this enables robust coherent atom manipulation on much smaller spatial
scales than possible with static fields alone. We find no additional heating or
collisional loss up to densities approaching atoms / cm compared
to static magnetic traps. We demonstrate the creation of Bose-Einstein
condensates in RF potentials and investigate the difference in the interference
between two independently created and two coherently split condensates in
identical traps. All together this makes RF dressing a powerful new tool for
micro manipulation of atomic and molecular systems
A maximum principle for the Muskat problem for fluids with different densities
We consider the fluid interface problem given by two incompressible fluids
with different densities evolving by Darcy's law. This scenario is known as the
Muskat problem for fluids with the same viscosities, being in two dimensions
mathematically analogous to the two-phase Hele-Shaw cell. We prove in the
stable case (the denser fluid is below) a maximum principle for the
norm of the free boundary.Comment: 16 page
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