4,372 research outputs found
Viscous effects in Rayleigh-Taylor instability
A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to Rayleigh‐Taylor instability. The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a light fluid (e.g., air) with negligible dynamic effect. The approximate picture may also be rigorously justified for the case of two fluids for which the differences in density and viscosity are small. The treatment of the interfacial waves may easily be extended to the case where one of the fluids has a small thickness; that is, the case in which one of the fluids is bounded by a free surface or by a rigid wall. The theory is used to give an explanation of the bioconvective patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than water, the conditions for Rayleigh‐Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh‐Taylor instability theory for a continuous medium with viscosity
Casimir Energies and Pressures for -function Potentials
The Casimir energies and pressures for a massless scalar field associated
with -function potentials in 1+1 and 3+1 dimensions are calculated. For
parallel plane surfaces, the results are finite, coincide with the pressures
associated with Dirichlet planes in the limit of strong coupling, and for weak
coupling do not possess a power-series expansion in 1+1 dimension. The relation
between Casimir energies and Casimir pressures is clarified,and the former are
shown to involve surface terms. The Casimir energy for a -function
spherical shell in 3+1 dimensions has an expression that reduces to the
familiar result for a Dirichlet shell in the strong-coupling limit. However,
the Casimir energy for finite coupling possesses a logarithmic divergence first
appearing in third order in the weak-coupling expansion, which seems
unremovable. The corresponding energies and pressures for a derivative of a
-function potential for the same spherical geometry generalizes the TM
contributions of electrodynamics. Cancellation of divergences can occur between
the TE (-function) and TM (derivative of -function) Casimir
energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX
Surface Divergences and Boundary Energies in the Casimir Effect
Although Casimir, or quantum vacuum, forces between distinct bodies, or
self-stresses of individual bodies, have been calculated by a variety of
different methods since 1948, they have always been plagued by divergences.
Some of these divergences are associated with the volume, and so may be more or
less unambiguously removed, while other divergences are associated with the
surface. The interpretation of these has been quite controversial. Particularly
mysterious is the contradiction between finite total self-energies and surface
divergences in the local energy density. In this paper we clarify the role of
surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0
Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light
We present a Green's dyadic formulation to calculate the Casimir energy for a
dielectric-diamagnetic cylinder with the speed of light differing on the inside
and outside. Although the result is in general divergent, special cases are
meaningful. It is pointed out how the self-stress on a purely dielectric
cylinder vanishes through second order in the deviation of the permittivity
from its vacuum value, in agreement with the result calculated from the sum of
van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
Fermionic Casimir effect for parallel plates in the presence of compact dimensions with applications to nanotubes
We evaluate the Casimir energy and force for a massive fermionic field in the
geometry of two parallel plates on background of Minkowski spacetime with an
arbitrary number of toroidally compactified spatial dimensions. The bag
boundary conditions are imposed on the plates and periodicity conditions with
arbitrary phases are considered along the compact dimensions. The Casimir
energy is decomposed into purely topological, single plate and interaction
parts. With independence of the lengths of the compact dimensions and the
phases in the periodicity conditions, the interaction part of the Casimir
energy is always negative. In order to obtain the resulting force, the
contributions from both sides of the plates must be taken into account. Then,
the forces coming from the topological parts of the vacuum energy cancel out
and only the interaction term contributes to the Casimir force. Applications of
the general formulae to Kaluza-Klein type models and carbon nanotubes are
given. In particular, we show that for finite length metallic nanotubes the
Casimir forces acting on the tube edges are always attractive, whereas for
semiconducting-type ones they are attractive for small lengths of the nanotube
and repulsive for large lengths.Comment: 20 pages, 3 figure
Neural Networks for Modeling and Control of Particle Accelerators
We describe some of the challenges of particle accelerator control, highlight
recent advances in neural network techniques, discuss some promising avenues
for incorporating neural networks into particle accelerator control systems,
and describe a neural network-based control system that is being developed for
resonance control of an RF electron gun at the Fermilab Accelerator Science and
Technology (FAST) facility, including initial experimental results from a
benchmark controller.Comment: 21 p
Deep Saturated Free Electron Laser Oscillators and Frozen Spikes
We analyze the behavior of Free Electron Laser (FEL) oscillators operating in
the deep saturated regime and point out the formation of sub-peaks of the
optical pulse. They are very stable configurations, having a width
corresponding to a coherence length. We speculate on the physical mechanisms
underlying their growth and attempt an identification with FEL mode locked
structures associated with Super Modes. Their impact on the intra-cavity
nonlinear harmonic generation is also discussed along with the possibility of
exploiting them as cavity out-coupler.Comment: 28 page
Comments on "Rayleigh–Taylor instability of thin viscous layers"
In a paper by Craik, (1) frequent references are made to our paper (2) which we believe are incorrect. It may also be pointed out that quite unusual circumstances would be required to provide a physical basis for Craik’s analysis; the experiments described in his paper are not appropriately explained by his analysis
Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
The vacuum expectation value of the fermionic current is evaluated for a
massive spinor field in spacetimes with an arbitrary number of toroidally
compactified spatial dimensions in presence of a constant gauge field. By using
the Abel-Plana type summation formula and the zeta function technique we
present the fermionic current in two different forms. Non-trivial topology of
the background spacetime leads to the Aharonov-Bohm effect on the fermionic
current induced by the gauge field. The current is a periodic function of the
magnetic flux with the period equal to the flux quantum. In the absence of the
gauge field it vanishes for special cases of untwisted and twisted fields.
Applications of the general formulae to Kaluz-Klein type models and to
cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic
flux the total fermionic current in carbon nanotubes vanishes, due to the
cancellation of contributions from two different sublattices of the graphene
hexagonal lattice.Comment: 18 pages, 5 figures, explicit regularization procedure adde
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