88 research outputs found
The transition between Neumann and Dirichlet boundary conditions in isotropic elastic plates
The official published version can be obtained from the link below - Copyright @ 2010 by SAGE PublicationsThe transition from Neumann (traction-free) to Dirichlet (fixed-face) boundary conditions is investigated in respect of wave propagation in a linear isotropic elastic layer. Attention is focused on the implications of such a transition on the dispersion curve branches within the long-wave region. The formation of low-frequency band gap that is expected to exist in layers with Dirichlet boundary condition is shown to be caused by different mechanisms in anti-symmetric and symmetric cases. Certain implications to short-wave propagation in the layer are also investigated. The study includes both a numerical investigation and a multi-parameter asymptotic analysis.The work of the first author was supported by an INTAS grant, YSF/06-10000014-5790
Resonant Magnetic Vortices
By using the complex angular momentum method, we provide a semiclassical
analysis of electron scattering by a magnetic vortex of Aharonov-Bohm-type.
Regge poles of the -matrix are associated with surface waves orbiting around
the vortex and supported by a magnetic field discontinuity. Rapid variations of
sharp characteristic shapes can be observed on scattering cross sections. They
correspond to quasibound states which are Breit-Wigner-type resonances
associated with surface waves and which can be considered as quantum analogues
of acoustic whispering-gallery modes. Such a resonant magnetic vortex could
provide a new kind of artificial atom while the semiclassical approach
developed here could be profitably extended in various areas of the physics of
vortices.Comment: 6 pages, 7 figure
Kirchhoff's Loop Law and the maximum entropy production principle
In contrast to the standard derivation of Kirchhoff's loop law, which invokes
electric potential, we show, for the linear planar electric network in a
stationary state at the fixed temperature,that loop law can be derived from the
maximum entropy production principle. This means that the currents in network
branches are distributed in such a way as to achieve the state of maximum
entropy production.Comment: revtex4, 5 pages, 2 figure
Wave scattering from self-affine surfaces
Electromagnetic wave scattering from a perfectly reflecting self-affine
surface is considered. Within the framework of the Kirchhoff approximation, we
show that the scattering cross section can be exactly written as a function of
the scattering angle via a centered symmetric Levy distribution for general
roughness amplitude, Hurst exponent and wavelength of the incident wave. The
amplitude of the specular peak, its width and its position are discussed as
well as the power law decrease (with scattering angle) of the scattering cross
section.Comment: RevTeX, 4 pages including 2 figures. Submitted Phys. Rev. Let
On the Propagation of Slip Fronts at Frictional Interfaces
The dynamic initiation of sliding at planar interfaces between deformable and
rigid solids is studied with particular focus on the speed of the slip front.
Recent experimental results showed a close relation between this speed and the
local ratio of shear to normal stress measured before slip occurs (static
stress ratio). Using a two-dimensional finite element model, we demonstrate,
however, that fronts propagating in different directions do not have the same
dynamics under similar stress conditions. A lack of correlation is also
observed between accelerating and decelerating slip fronts. These effects
cannot be entirely associated with static local stresses but call for a dynamic
description. Considering a dynamic stress ratio (measured in front of the slip
tip) instead of a static one reduces the above-mentioned inconsistencies.
However, the effects of the direction and acceleration are still present. To
overcome this we propose an energetic criterion that uniquely associates,
independently on the direction of propagation and its acceleration, the slip
front velocity with the relative rise of the energy density at the slip tip.Comment: 15 pages, 6 figure
The Basics of Water Waves Theory for Analogue Gravity
This chapter gives an introduction to the connection between the physics of
water waves and analogue gravity. Only a basic knowledge of fluid mechanics is
assumed as a prerequisite.Comment: 36 pages. Lecture Notes for the IX SIGRAV School on "Analogue
Gravity", Como (Italy), May 201
Control of Rayleigh-Taylor instability by vertical vibration in large aspect ratio containers
We consider a horizontal heavy fluid layer supported by a light, immiscible one in a wide (as compared to depth) container, which is vertically vibrated intending to counterbalance the Rayleigh-Taylor instability of the flat, rigid-body vibrating state. In the simplest case when the density and viscosity of the lighter fluid are small compared to their counterparts in the heavier fluid, we apply a long wave, weakly nonlinear analysis that yields a generalized Cahn-Hilliard equation for the evolution of the fluid interface. This equation shows that the stabilizing effect of vibration is like that of surface tension, and is used to analyze the linear stability of the flat state, the local bifurcation at the instability threshold and some global existence and stability properties concerning the steady states without dry spots. The analysis is extended to two cases of practical interest. Namely, (a) the viscosity of one of the fluids is much smaller than that of the other one, and (b) the densities and viscosities of both fluids are quite close to each other
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