15,277 research outputs found
Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors
International audienceA mathematical study of the focusing properties of acoustic fields obtained by a time-reversal process is presented. The case of time-harmonic waves propagating in a nondissipative medium containing sound-soft obstacles is considered. In this context, the so-called D.O.R.T. method (decomposition of the time-reversal operator in French) was recently proposed to achieve selective focusing by computing the eigenelements of the time-reversal operator. The present paper describes a justification of this technique in the framework of the far field model, i.e., for an ideal time-reversal mirror able to reverse the far field of a scattered wave. Both cases of closed and open mirrors, that is, surrounding completely or partially the scatterers, are dealt with. Selective focusing properties are established by an asymptotic analysis for small and distant obstacles
Fluid-loaded metasurfaces
We consider wave propagation along fluid-loaded structures which take the
form of an elastic plate augmented by an array of resonators forming a
metasurface, that is, a surface structured with sub-wavelength resonators. Such
surfaces have had considerable recent success for the control of wave
propagation in electromagnetism and acoustics, by combining the vision of
sub-wavelength wave manipulation, with the design, fabrication and size
advantages associated with surface excitation. We explore one aspect of recent
interest in this field: graded metasurfaces, but within the context of
fluid-loaded structures.
Graded metasurfaces allow for selective spatial frequency separation and are
often referred to as exhibiting rainbow trapping. Experiments, and theory, have
been developed for acoustic, electromagnetic, and even elastic, rainbow devices
but this has not been approached for fluid-loaded structures that support
surface waves coupled with the acoustic field in a bulk fluid. This surface
wave, coupled with the fluid, can be used to create an additional effect by
designing a metasurface to mode convert from surface to bulk waves. We
demonstrate that sub-wavelength control is possible and that one can create
both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic
plate model.Comment: 13 pages, 10 figure
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
We develop the shape derivative analysis of solutions to the problem of
scattering of time-harmonic electromagnetic waves by a bounded penetrable
obstacle. Since boundary integral equations are a classical tool to solve
electromagnetic scattering problems, we study the shape differentiability
properties of the standard electromagnetic boundary integral operators. The
latter are typically bounded on the space of tangential vector fields of mixed
regularity TH\sp{-1/2}(\Div_{\Gamma},\Gamma). Using Helmholtz decomposition,
we can base their analysis on the study of pseudo-differential integral
operators in standard Sobolev spaces, but we then have to study the G\^ateaux
differentiability of surface differential operators. We prove that the
electromagnetic boundary integral operators are infinitely differentiable
without loss of regularity. We also give a characterization of the first shape
derivative of the solution of the dielectric scattering problem as a solution
of a new electromagnetic scattering problem.Comment: arXiv admin note: substantial text overlap with arXiv:1002.154
Nonlinear pre-stress for cloaking from antiplane elastic waves
A theory is presented showing that cloaking of objects from antiplane elastic
waves can be achieved by elastic pre-stress of a neo-Hookean nonlinear elastic
material. This approach would appear to eliminate the requirement of
metamaterials with inhomogeneous anisotropic shear moduli and density. Waves in
the pre-stressed medium are bent around the cloaked region by inducing
inhomogeneous stress fields via pre-stress. The equation governing antiplane
waves in the pre-stressed medium is equivalent to the antiplane equation in an
unstressed medium with inhomogeneous and anisotropic shear modulus and
isotropic scalar mass density. Note however that these properties are induced
naturally by the pre-stress. Since the magnitude of pre-stress can be altered
at will, this enables objects of varying size and shape to be cloaked by
placing them inside the fluid-filled deformed cavity region.Comment: 21 pages, 4 figure
On-surface radiation condition for multiple scattering of waves
The formulation of the on-surface radiation condition (OSRC) is extended to
handle wave scattering problems in the presence of multiple obstacles. The new
multiple-OSRC simultaneously accounts for the outgoing behavior of the wave
fields, as well as, the multiple wave reflections between the obstacles. Like
boundary integral equations (BIE), this method leads to a reduction in
dimensionality (from volume to surface) of the discretization region. However,
as opposed to BIE, the proposed technique leads to boundary integral equations
with smooth kernels. Hence, these Fredholm integral equations can be handled
accurately and robustly with standard numerical approaches without the need to
remove singularities. Moreover, under weak scattering conditions, this approach
renders a convergent iterative method which bypasses the need to solve single
scattering problems at each iteration.
Inherited from the original OSRC, the proposed multiple-OSRC is generally a
crude approximate method. If accuracy is not satisfactory, this approach may
serve as a good initial guess or as an inexpensive pre-conditioner for Krylov
iterative solutions of BIE
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