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