3,020 research outputs found
Anisotropic particles near surfaces: Self-propulsion and friction
We theoretically study the phenomenon of self-propulsion through Casimir
forces in thermal non-equilibrium. Using fluctuational electrodynamics, we
derive a formula for the self-propulsion force for an arbitrary small object in
two scenarios, i) for the object being isolated, and ii) for the object being
close to a planar surface. In the latter case, the self-propulsion force (i.e.,
the force parallel to the surface) increases with decreasing distance, i.e., it
couples to the near-field. We numerically calculate the lateral force acting on
a hot spheroid near a surface and show that it can be as large as the
gravitational force, thus being potentially measurable in fly-by experiments.
We close by linking our results to well-known relations of linear response
theory in fluctuational electrodynamics: Looking at the friction of the
anisotropic object for constant velocity, we identify a correction term that is
additional to the typically used approach.Comment: 13 pages, 8 figures (v2: References updated
Limit experiments of GARCH
GARCH is one of the most prominent nonlinear time series models, both widely
applied and thoroughly studied. Recently, it has been shown that the COGARCH
model (which was introduced a few years ago by Kl\"{u}ppelberg, Lindner and
Maller) and Nelson's diffusion limit are the only functional continuous-time
limits of GARCH in distribution. In contrast to Nelson's diffusion limit,
COGARCH reproduces most of the stylized facts of financial time series. Since
it has been proven that Nelson's diffusion is not asymptotically equivalent to
GARCH in deficiency, in the present paper, we investigate the relation between
GARCH and COGARCH in Le Cam's framework of statistical equivalence. We show
that GARCH converges generically to COGARCH, even in deficiency, provided that
the volatility processes are observed. Hence, from a theoretical point of view,
COGARCH can indeed be considered as a continuous-time equivalent to GARCH.
Otherwise, when the observations are incomplete, GARCH still has a limiting
experiment, which we call MCOGARCH, which is not equivalent, but nevertheless
quite similar, to COGARCH. In the COGARCH model, the jump times can be more
random than for the MCOGARCH, a fact practitioners may see as an advantage of
COGARCH.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ328 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Heat radiation and transfer for point particles in arbitrary geometries
We study heat radiation and heat transfer for pointlike particles in a system
of other objects. Starting from exact many-body expressions found from
scattering theory and fluctuational electrodynamics, we find that transfer and
radiation for point particles are given in terms of the Green's function of the
system in the absence of the point particles. These general expressions contain
no approximation for the surrounding objects. As an application, we compute the
heat transfer between two point particles in the presence of a sphere of
arbitrary size and show that the transfer is enhanced by several orders of
magnitude through the presence of the sphere, depending on the materials.
Furthermore, we compute the heat emission of a point particle in front of a
planar mirror. Finally, we show that a particle placed inside a spherical
mirror cavity does not radiate energy.Comment: 14 pages, 9 figures (v2: Sec. IIIE was added; explanation of Eq. (29)
was added; sentence in Acknowledgments was added; Ref. [69] was added; minor
changes in text
Effective fluid transport properties of deformable rocks
Modern reservoir monitoring technologies often make use of diffusion waves in order to estimate the hydraulic conductivity and diffusivity of reservoir rocks. However, most theoretical descriptions for these effective uid transport properties assume that the host rock is elastically rigid. Inhomogeneous poroelastic continua described by Biot's equations of dynamic or quasi-static poroelasticity provide an adequate framework to study the dependence of uid transport properties on the elastic properties of the host rock. Analysis of diffusion wave elds in randomly inhomogeneous poroelastic structures provides new insight into how uctuations of the compressible constituents of the rock affect the effective diffusivity. Using the method of statistical smoothing we derive an effective wave number of the coherent diffusion wave eld. This wave number yields expressions for the effective conductivity and diffusivity of a deformable and inhomogeneous porous medium. These uid transport properties are frequency-dependent. Comparison of the hydraulic conductivity derived here with that estimated from unsteady ow through porous media based on Darcy's law shows that they are identical in the limits of low and high frequencies
Oscillating Modes of Driven Colloids in Overdamped Systems
Microscopic particles suspended in liquids are the prime example of an
overdamped system because viscous forces dominate over inertial effects. Apart
from their use as model systems, they receive considerable attention as
sensitive probes from which forces on molecular scales can be inferred. The
interpretation of such experiments rests on the assumption, that, even if the
particles are driven, the liquid remains in equilibrium, and all modes are
overdamped. Here, we experimentally demonstrate that this is no longer valid
when a particle is forced through a viscoelastic fluid. Even at small driving
velocities where Stokes law remains valid, we observe particle oscillations
with periods up to several tens of seconds. We attribute these to
non-equilibrium fluctuations of the fluid, which are excited by the particle's
motion. The observed oscillatory dynamics is in quantitative agreement with an
overdamped Langevin equation with negative friction-memory term and which is
equivalent to the motion of a stochastically driven underdamped oscillator.
This fundamentally new oscillatory mode will largely expand the variety of
model systems but has also considerable implications on how molecular forces
are determined by colloidal probe particles under natural viscoelastic
conditions.Comment: Accepted with Nat. Comm. (originally submitted version, complying
with Nature policies). 10 pages, 8 figure
Cross-over frequencies of seismic attenuation in fractured porous rocks
We analyze compressional wave attenuation in fluid saturated porous material with porous inclusions having different compressibilities and very different spatial scales in comparison with the background. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interface between inclusion and background. For the representative element containing two layers (one of them representing inclusion), we show that overall wave attenuation is governed by the superposition of two coupled fluid-diffusion processes. Associated with two characteristic spatial scales, we compute two cross-over frequencies that separate three different frequency regimes. At low frequencies inverse quality factor scales with the first power of frequency ?, while at high frequencies the attenuation is proportional to ?12. In the intermediate range of frequencies inverse quality factor scales with ?12. These characteristic frequency regimes can be observed in all theoretical models of wave-induced attenuation, but complete physical explanation is still missing. The potential application of this model is in estimation of the background permeability as well as inclusion scale (thickness) by identifying these frequencies from attenuation measurements
Simulating Self-gravitating Hydrodynamic Flows
An efficient algorithm for solving Poisson's equation in two and three
spatial dimensions is discussed. The algorithm, which is described in detail,
is based on the integral form of Poisson's equation and utilizes spherical
coordinates and an expansion into spherical harmonics. The solver can be
applied to and works well for all problems for which the use of spherical
coordinates is appropriate. We also briefly discuss the implementation of the
algorithm into hydrodynamic codes which are based on a conservative
finite--difference scheme.Comment: 15 pages, compressed uu-encoded postscript file (232kB), to appear in
Computer Physics Communications, special issue Computational Hydrodynamics in
Astrophysic
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