3,716 research outputs found
Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves.
Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3–10 Hz, and for low-speed sedimentary soil (v(s): 300–500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency
Application of the Finite Element Method in a Quantitative Imaging technique
We present the Finite Element Method (FEM) for the numerical solution of the
multidimensional coefficient inverse problem (MCIP) in two dimensions. This
method is used for explicit reconstruction of the coefficient in the hyperbolic
equation using data resulted from a single measurement. To solve our MCIP we
use approximate globally convergent method and then apply FEM for the resulted
equation. Our numerical examples show quantitative reconstruction of the sound
speed in small tumor-like inclusions
High-frequency homogenization of zero frequency stop band photonic and phononic crystals
We present an accurate methodology for representing the physics of waves, for
periodic structures, through effective properties for a replacement bulk
medium: This is valid even for media with zero frequency stop-bands and where
high frequency phenomena dominate. Since the work of Lord Rayleigh in 1892, low
frequency (or quasi-static) behaviour has been neatly encapsulated in effective
anisotropic media. However such classical homogenization theories break down in
the high-frequency or stop band regime.
Higher frequency phenomena are of significant importance in photonics
(transverse magnetic waves propagating in infinite conducting parallel fibers),
phononics (anti-plane shear waves propagating in isotropic elastic materials
with inclusions), and platonics (flexural waves propagating in thin-elastic
plates with holes). Fortunately, the recently proposed high-frequency
homogenization (HFH) theory is only constrained by the knowledge of standing
waves in order to asymptotically reconstruct dispersion curves and associated
Floquet-Bloch eigenfields: It is capable of accurately representing
zero-frequency stop band structures. The homogenized equations are partial
differential equations with a dispersive anisotropic homogenized tensor that
characterizes the effective medium.
We apply HFH to metamaterials, exploiting the subtle features of Bloch
dispersion curves such as Dirac-like cones, as well as zero and negative group
velocity near stop bands in order to achieve exciting physical phenomena such
as cloaking, lensing and endoscope effects. These are simulated numerically
using finite elements and compared to predictions from HFH. An extension of HFH
to periodic supercells enabling complete reconstruction of dispersion curves
through an unfolding technique is also introduced
The regularized monotonicity method: detecting irregular indefinite inclusions
In inclusion detection in electrical impedance tomography, the support of
perturbations (inclusion) from a known background conductivity is typically
reconstructed from idealized continuum data modelled by a Neumann-to-Dirichlet
map. Only few reconstruction methods apply when detecting indefinite
inclusions, where the conductivity distribution has both more and less
conductive parts relative to the background conductivity; one such method is
the monotonicity method of Harrach, Seo, and Ullrich. We formulate the method
for irregular indefinite inclusions, meaning that we make no regularity
assumptions on the conductivity perturbations nor on the inclusion boundaries.
We show, provided that the perturbations are bounded away from zero, that the
outer support of the positive and negative parts of the inclusions can be
reconstructed independently. Moreover, we formulate a regularization scheme
that applies to a class of approximative measurement models, including the
Complete Electrode Model, hence making the method robust against modelling
error and noise. In particular, we demonstrate that for a convergent family of
approximative models there exists a sequence of regularization parameters such
that the outer shape of the inclusions is asymptotically exactly characterized.
Finally, a peeling-type reconstruction algorithm is presented and, for the
first time in literature, numerical examples of monotonicity reconstructions
for indefinite inclusions are presented.Comment: 28 pages, 7 figure
Detection of Buried Inhomogeneous Elliptic Cylinders by a Memetic Algorithm
The application of a global optimization procedure to the detection of buried inhomogeneities is studied in the present paper. The object inhomogeneities are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. An efficient recursive analytical procedure is used for the forward scattering computation. A functional is constructed in which the field is expressed in series solution of Mathieu functions. Starting by the input scattered data, the iterative minimization of the functional is performed by a new optimization method called memetic algorithm. (c) 2003 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works
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