The density profile for the Klein-Kramers equation near an absorbing wall

We derive asymptotic series for the expansion coefficients of a function in terms of the Pagani functions, which occur in the boundary layer solutions of the Klein-Kramers equation. The results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall, with an accuracy of about 2%. We also obtain information about the analytic behavior of the density profile: this profile increases near the wall with the square root of the distance to the wall. Finally, the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing-wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz. This is used to obtain a better variational estimate for the density at the wall.     

Nonlocal gravity-induced density profiles in gases near the critical point

The gravitational field induces density gradients in gases near the critical point. These density gradients are usually evaluated with the assumption that the relationship between the local density and local chemical potential is the same as for a macroscopic system in thermodynamic equilibrium. Very close to the critical point the assumption of local equilibrium ceases to be valid. In this paper we obtain the actual density profiles including nonlocal effects. For this purpose we extend the theory of van der Waals and of Fisk and Widom for the interfacial density profile below the critical temperature to the one-phase region above the critical temperature. The nonlocal effects in the density profiles are found to be significant in temperature intervals that are accessible with currently available experimental techniques for temperature control.     

Competitive trapping effects in a set of partially absorbing traps

This note contains a formalism for calculating properties of random walks in the presence of a set of partially absorbing traps. The properties that are considered are the probability of trapping at a specific point and the survival probability as a function of step number. The results are expressed in terms of determinants, but approximations to these can be found.     

High-contrast organic light emitting diodes with a partially absorbing anode

To be legible in high-ambient light conditions, organic light-emitting-diode displays should be optically designed to have a minimal reflectance without significantly affecting their overall efficiency. We demonstrate the use of an anode consisting of a partially absorbing metal layer and a multilayer distributed Bragg reflector to simultaneously absorb rather than reflect incoming light and to take advantage of a weak microcavity effect in the diode to improve light outcoupling.     

Non-stationary radiative-conductive heat transfer in a layer with partially absorbing boundaries

Here we consider one-dimensional heating of a layer of gray semitransparent medium by an outer source of radiation and convection. The sample boundaries reflect, absorb (radiate), and transmit radiation. It is shown that heating dynamics and character of temperature fields depend significantly on optic parameters of the boundaries. The work was financially supported by the President of the Russian Federation (MK-601.2008.8) and Russian Foundation for Basic Research (Grant No. 08-08-00527-a).     

Fluctuation-magnification of non-equilibrium membranes near a wall

Membranes in thermal equilibrium are well known to exhibit Brownian motion type shape fluctuations. Membranes containing active force centers -- such as chemically active membrane proteins -- suffer additional non-equilibrium shape fluctuations due to the activity of these force centers. We demonstrate, using scaling arguments, that non-equilibrium shape fluctuations are in general greatly amplified by the presence of a nearby wall or membrane due to the absence of a fluctuation-dissipation theorem. For adhesive membranes, this fluctuation magnification effect may facilitate the establishment of bonding. For non-adhesive membranes, fluctuation magnification produces a long-range repulsive pressure which can exceed the well known Helfrich repulsion due to purely thermal fluctuations. Received: 1 September 1997 / Accepted: 3 December 1997     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

Acoustic pulse propagation near a right-angle wall

Experimental measurements were conducted around a right-angle wall to investigate the effect of this obstacle on sound propagation outdoors. Using small explosions as the source of the acoustic waves allowed reflected and diffracted arrivals to be discerned and investigated in detail. The measurements confirm that diffraction acts as a low-pass filter on acoustic waveforms in agreement with simple diffraction theory, reducing the peak pressure and broadening the waveform shape received by a sensor in the shadow zone. In addition, sensors mounted directly on the wall registered pressure doubling for nongrazing angles of incidence in line-of-sight conditions. A fast two-dimensional finite difference time domain (FDTD) model was developed and provided additional insight into the propagation around the wall. Calculated waveforms show good agreement with the measured waveforms.     

Optimized staircase profiles for diffractive optical devices made from absorbing materials

We report on the optimization of staircase grating profiles for the case of absorbing grating materials. Using a simple numerical algorithm, we determined the grating parameters, maximizing the first-order diffraction efficiency for different numbers of staircase steps. The results show that there is a significant difference between the staircase profiles for nonnegligible and negligible absorption. The obtained solutions are of importance for diffractive optics in the soft-x-ray and extreme-ultraviolet ranges.     

Optical levitation of absorbing particles with a nominally Gaussian laser beam

We use a Gaussian laser beam to study the levitation of absorbing Mie particles. Several metal oxide particles are stably levitated, and their movement over time is recorded. Our studies show that the position of each particle is highly dependent on the other particles' locations. The observations are explained by the phenomenon of thermal creep. The increased local pressure that is due to a temperature gradient along the particle's surface induces levitation. The particles rest close to minima in the intensity distribution near the optical axis. An experiment is suggested that can be used to locate these minima in a laser beam.     

Sound generation in a flow near a compliant wall

The generation of sound near an infinite compliant wall is studied, with account taken of a uniform mean flow. Stable and unstable configurations are looked at. It is shown that a possible influence of the wall on the sound generation occurs only via a modification of the turbulence if hydrodynamic non-linearities are responsible for the levelling-off of the instabilities. Then no fundamentally more efficient sound sources are found. An increase of the radiated sound may be possible because of the mirror sources and because of their possibly reduced compactness.     

Dynamics of a cavitation bubble near a solid wall

The cavitation bubble dynamics, the variation of pressure and velocity fields of the surrounding liquid in the process of the bubble axisymmetric compression near a planar solid wall are considered. It is assumed that the liquid is at rest at the initial moment of time, and the bubble has a spheroidal shape. The liquid is assumed inviscid and incompressible, its motion being potential. The bubble surface deformation and the liquid velocity on the surface are computed by the Euler scheme using the boundary element method until the moment of the collision of some parts of the bubble surface with one another. The influence of the distance of the bubble from the wall and its initial nonsphericity on the liquid pressure and velocity fields, the bubble shape, and the pressure inside the bubble at the end of the time interval under consideration are studied. The maximum pressure in liquid is shown to realize at the bottom of the cumulative jet arising at the bubble collapse with direction to the wall. In the upper part of this jet, the velocity and pressure are practically constant, and the pressure in the jet is approximately equal to the pressure in the bubble.     

Stochastic elastohydrodynamics of a microcantilever oscillating near a wall

We consider the thermally driven motion of a microcantilever in a fluid environment near a wall, a configuration characteristic of the atomic force microscope. A theoretical model is presented which accounts for hydrodynamic interactions between the cantilever and wall over a wide range of frequencies and which exploits the fluctuation-dissipation theorem to capture the Brownian dynamics of the coupled fluid-cantilever system. Model predictions are tested against experimental thermal spectra for a cantilever in air and water. The model shows how, in a liquid environment, the effects of non-delta-correlated Brownian forcing appear in the power spectrum, particularly at low frequencies. The model also predicts accurately changes in the spectrum in liquid arising through hydrodynamic wall effects, which we show are strongly mediated by the angle at which the cantilever is tilted relative to the wall.     

Stability of a charged drop near a conductor wall

The effect of conductor boundaries on the deformation and stability of a charged drop is presented. The motivation for such a study is the occurrence of a charged conductor drop near a conductor wall in experiments (Millikan-like set-up in studies on Rayleigh break-up) and applications (such as electrospraying, ink-jet printing and ion mass spectroscopy). In the present work, analytical (linear stability analysis (LSA)) and numerical methods (boundary element method (BEM)) are used to understand the instability. Two kinds of boundaries are studied: a spherical, conducting, grounded enclosure (similar to a spherical capacitor) and a planar conducting wall. The LSA of a charged drop placed at the center of a spherical cavity shows that the Rayleigh critical charge (corresponding to the most unstable l = 2 Legendre mode) is reduced as the non-dimensional distance ?d = (b - a)/a decreases, where a and b are the radii of the drop and spherical cavity, respectively. The critical charge is independent of the assumptions of constant charge or constant potential conditions. The trans-critical bifurcation diagram, constructed using BEM, shows that the prolate shapes are subcritically unstable over a much wider range of charge as [Formula: see text] decreases. The study is then extended to the stability of a charged conductor drop near a flat conductor wall. Analytical theory for this case is difficult and the stability as well as the bifurcation diagram are constructed using BEM. Moreover, the induced charges in the conductor wall lead to attraction of the drop to the wall, thereby making it difficult to conduct a systematic analysis. The drop is therefore assumed to be held at its position by an external force such as the electric field. The case when the applied field is much smaller than the field due to inherent charge on the drop ((a(3)ρg)/(3ε(0)Ψ(2)) ? 1 is considered. The wall breaks the fore-aft symmetry in the problem, and equilibrium, predominantly prolate shapes corresponding to the legendre mode, l = 2 , are observed. The deformation increases with increasing charge on the drop. The breakup of the prolate equilibrium shapes is independent of the legendre modes of the initial perturbations. The prolate perturbations are subcritically unstable. Since the equilibrium prolate shapes cannot continuously exchange instability with equilibrium oblate shapes, an imperfect transcritical bifurcation is observed. A variety of highly deformed equilibrium oblate shapes are predicted by the BEM calculations.     

Vacuum polarization near a black hole creating particles

The renormalized expectation value of the energy-momentum tensor associated with scalar massless particles created by a Schwarzschild black hole is calculated by performing a numerical computation.     

Asymmetry in colloidal diffusion near a rigid wall

The three-dimensional motion of single colloidal particles close to a plane wall is measured by optical microscopy. In accordance with classical theoretical predictions, we find an asymmetric motion of the particles in the directions parallel and perpendicular to the wall. We also find that, close to the wall, the distribution functions of perpendicular steps are asymmetric, being shorter toward the wall and longer away from it.     

Langevin dynamics of an interface near a wall

We study dynamical contact angles and precursor films using Langevin dynamics for SOS type models, near a wall which favors spreading. We first solve exactly the Gaussian model and discuss various asymptotic regimes. This is only appropriate to partial wetting. We then consider more general models. Using local equilibrium and scaling arguments, we derive the shape of the dynamical profile and the speed of the precursor film which exists when the spreading coefficient is strictly positive. Long-range potentials lead to a layered structure of the precursor film. We also consider the case of a meniscus in a capillary.