2,914 research outputs found
Subwavelength sound screening by coupling space-coiled Fabry-Perot resonators
We explore broadband and omnidirectional low frequency sound screening based
on locally resonant acoustic metamaterials. We show that the coupling of
different resonant modes supported by Fabry-Perot cavities can efficiently
generate asymmetric lineshapes in the transmission spectrum, leading to a
broadband sound opacity. The Fabry-Perot cavities are space-coiled in order to
shift the resonant modes under the diffraction edge, which guaranty the opacity
band for all incident angles. Indeed, the deep subwavelength feature of the
cavities leads to avoid diffraction that have been proved to be the main
limitation of omnidirectional capabilities of locally resonant perforated
plates. We experimentally reach an attenuation of few tens of dB at low
frequency, with a metamaterial thickness fifteen times smaller than the
wavelength (lambda / 15). The proposed design can be considered as a new
building block for acoustic metasurfaces having a high level of manipulation of
acoustic waves.Comment: 7 pages, 8 figure
On dual Schur domain decomposition method for linear first-order transient problems
This paper addresses some numerical and theoretical aspects of dual Schur
domain decomposition methods for linear first-order transient partial
differential equations. In this work, we consider the trapezoidal family of
schemes for integrating the ordinary differential equations (ODEs) for each
subdomain and present four different coupling methods, corresponding to
different algebraic constraints, for enforcing kinematic continuity on the
interface between the subdomains.
Method 1 (d-continuity) is based on the conventional approach using
continuity of the primary variable and we show that this method is unstable for
a lot of commonly used time integrators including the mid-point rule. To
alleviate this difficulty, we propose a new Method 2 (Modified d-continuity)
and prove its stability for coupling all time integrators in the trapezoidal
family (except the forward Euler). Method 3 (v-continuity) is based on
enforcing the continuity of the time derivative of the primary variable.
However, this constraint introduces a drift in the primary variable on the
interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte
stabilization to limit this drift and we derive bounds for the stabilization
parameter to ensure stability.
Our stability analysis is based on the ``energy'' method, and one of the main
contributions of this paper is the extension of the energy method (which was
previously introduced in the context of numerical methods for ODEs) to assess
the stability of numerical formulations for index-2 differential-algebraic
equations (DAEs).Comment: 22 Figures, 49 pages (double spacing using amsart
BDDC and FETI-DP under Minimalist Assumptions
The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary
simple abstract form. It is shown that their properties can be obtained from
only on a very small set of algebraic assumptions. The presentation is purely
algebraic and it does not use any particular definition of method components,
such as substructures and coarse degrees of freedom. It is then shown that
P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC
preconditioned operators are of the same algebraic form, and the standard
condition number bound carries over to arbitrary abstract operators of this
form. The equality of eigenvalues of BDDC and FETI-DP also holds in the
minimalist abstract setting. The abstract framework is explained on a standard
substructuring example.Comment: 11 pages, 1 figure, also available at
http://www-math.cudenver.edu/ccm/reports
Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets
We start by a review of the chronology of mathematical results on the
Dirichlet-to-Neumann map which paved the way towards the physics of
transformational acoustics. We then rederive the expression for the
(anisotropic) density and bulk modulus appearing in the pressure wave equation
written in the transformed coordinates. A spherical acoustic cloak consisting
of an alternation of homogeneous isotropic concentric layers is further
proposed based on the effective medium theory. This cloak is characterised by a
low reflection and good efficiency over a large bandwidth for both near and far
fields, which approximates the ideal cloak with a inhomogeneous and anisotropic
distribution of material parameters. The latter suffers from singular material
parameters on its inner surface. This singularity depends upon the sharpness of
corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak
becomes more and more singular when the number of vertices increases if it is
star shaped. We thus analyse the acoustic response of a non-singular spherical
cloak designed by blowing up a small ball instead of a point, as proposed in
[Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The
multilayered approximation of this cloak requires less extreme densities
(especially for the lowest bound). Finally, we investigate another type of
non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev.
Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion.
OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110)
Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic
optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices;
(160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility;
(230.3205) Invisibility cloak
Computational methods and software systems for dynamics and control of large space structures
Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers
Cloaking dielectric spherical objects by a shell of metallic nanoparticles
We show that dielectric spheres can be cloaked by a shell of amorphously
arranged metallic nanoparticles. The shell represents an artificial medium with
tunable effective properties that can be adjusted such that the scattered
signals of shell and sphere almost cancel each other. We provide an analytical
model for the cloak design and prove numerically that the cloak operates as
desired. We show that more than 70% of the scattered signal of the sphere can
be suppressed at the design wavelength. Advantages and disadvantages of such a
cloak when compared to other implementations are disclosed.Comment: 14 pages, 6 figure
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