10,375 research outputs found
A rapidly converging domain decomposition method for the Helmholtz equation
A new domain decomposition method is introduced for the heterogeneous 2-D and
3-D Helmholtz equations. Transmission conditions based on the perfectly matched
layer (PML) are derived that avoid artificial reflections and match incoming
and outgoing waves at the subdomain interfaces. We focus on a subdivision of
the rectangular domain into many thin subdomains along one of the axes, in
combination with a certain ordering for solving the subdomain problems and a
GMRES outer iteration. When combined with multifrontal methods, the solver has
near-linear cost in examples, due to very small iteration numbers that are
essentially independent of problem size and number of subdomains. It is to our
knowledge only the second method with this property next to the moving PML
sweeping method.Comment: 16 pages, 3 figures, 6 tables - v2 accepted for publication in the
Journal of Computational Physic
Diffuse-Charge Dynamics in Electrochemical Systems
The response of a model micro-electrochemical system to a time-dependent
applied voltage is analyzed. The article begins with a fresh historical review
including electrochemistry, colloidal science, and microfluidics. The model
problem consists of a symmetric binary electrolyte between parallel-plate,
blocking electrodes which suddenly apply a voltage. Compact Stern layers on the
electrodes are also taken into account. The Nernst-Planck-Poisson equations are
first linearized and solved by Laplace transforms for small voltages, and
numerical solutions are obtained for large voltages. The ``weakly nonlinear''
limit of thin double layers is then analyzed by matched asymptotic expansions
in the small parameter , where is the
screening length and the electrode separation. At leading order, the system
initially behaves like an RC circuit with a response time of
(not ), where is the ionic diffusivity, but nonlinearity
violates this common picture and introduce multiple time scales. The charging
process slows down, and neutral-salt adsorption by the diffuse part of the
double layer couples to bulk diffusion at the time scale, . In the
``strongly nonlinear'' regime (controlled by a dimensionless parameter
resembling the Dukhin number), this effect produces bulk concentration
gradients, and, at very large voltages, transient space charge. The article
concludes with an overview of more general situations involving surface
conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference
Dynamics of the Innermost Accretion Flows Around Compact Objects: Magnetosphere-Disc Interface, Global Oscillations and Instabilities
We study global non-axisymmetric oscillation modes and instabilities in
magnetosphere- disc systems, as expected in neutron star X-ray binaries and
possibly also in accreting black hole systems. Our two-dimensional
magnetosphere-disc model consists of a Keplerian disc in contact with an
uniformly rotating magnetosphere with low plasma density. Two types of global
overstable modes exist in such systems, the interface modes and the disc
inertial-acoustic modes. We examine various physical effects and parameters
that influence the properties of these oscillation modes, particularly their
growth rates, including the magnetosphere field configuration, the velocity and
density contrasts across the magnetosphere-disc interface, the rotation profile
(with Newtonian or General Relativistic potential), the sound speed and
magnetic field of the disc. The interface modes are driven unstable by
Rayleigh-Taylor and Kelvin-Helmholtz in- stabilities, but can be stabilized by
the toroidal field (through magnetic tension) and disc differential rotation
(through finite vorticity). General relativity increases their growth rates by
modifying the disc vorticity outside the magnetosphere boundary. The interface
modes may also be affected by wave absorption associated with corotation
resonance in the disc. In the presence of a magnetosphere, the
inertial-acoustic modes are effectively trapped at the innermost region of the
relativistic disc just outside the interface. They are driven unstable by wave
absorption at the corotation resonance, but can be stabilized by modest disc
magnetic fields. The overstable oscillation modes studied in this paper have
characteristic properties that make them possible candidates for the
quasi-periodic oscillations observed in X-ray binaries.Comment: 18 pages, 9 figures, MNRAS accepte
Induced-Charge Electro-Osmosis
We describe the general phenomenon of `induced-charge electro-osmosis' (ICEO)
-- the nonlinear electro-osmotic slip that occurs when an applied field acts on
the ionic charge it {\sl induces} around a polarizable surface. Motivated by a
simple physical picture, we calculate ICEO flows around conducting cylinders in
steady (DC), oscillatory (AC), and suddenly-applied electric fields. This
picture, and these systems, represent perhaps the clearest example of nonlinear
electrokinetic phenomena. We complement and verify this physically-motivated
approach using a matched asymptotic expansion to the electrokinetic equations
in the thin double-layer and low potential limits. ICEO slip velocities vary
like , where is the field strength and is a
geometric length scale, and are set up on a time scale , where is the screening length and is the ionic diffusion
constant. We propose and analyze ICEO microfluidic pumps and mixers that
operate without moving parts under low applied potentials. Similar flows around
metallic colloids with fixed total charge have been described in the Russian
literature (largely unnoticed in the West). ICEO flows around conductors with
fixed potential, on the other hand, have no colloidal analog and offer further
possibilities for microfluidic applications.Comment: 36 pages, 8 figures, to appear in J. Fluid Mec
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