2,920 research outputs found
Transient Anomaly Imaging in Visco-Elastic Media Obeying a Frequency Power-Law
In this work, we consider the problem of reconstructing a small anomaly in a
viscoelastic medium from wave-field measurements. We choose Szabo's model to
describe the viscoelastic properties of the medium. Expressing the ideal
elastic field without any viscous effect in terms of the measured field in a
viscous medium, we generalize the imaging procedures, such as time reversal,
Kirchhoff Imaging and Back propagation, for an ideal medium to detect an
anomaly in a visco-elastic medium from wave-field measurements
Asymptotic Expansion for Harmonic Functions in the Half-Space with a Pressurized Cavity
In this paper, we address a simplified version of a problem arising from
volcanology. Specifically, as reduced form of the boundary value problem for
the Lam\'e system, we consider a Neumann problem for harmonic functions in the
half-space with a cavity . Zero normal derivative is assumed at the boundary
of the half-space; differently, at , the normal derivative of the
function is required to be given by an external datum , corresponding to a
pressure term exerted on the medium at . Under the assumption that
the (pressurized) cavity is small with respect to the distance from the
boundary of the half-space, we establish an asymptotic formula for the solution
of the problem. Main ingredients are integral equation formulations of the
harmonic solution of the Neumann problem and a spectral analysis of the
integral operators involved in the problem. In the special case of a datum
which describes a constant pressure at , we recover a simplified
representation based on a polarization tensor
Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy
This paper concerns a fast, one-step iterative technique of imaging extended
perfectly conducting cracks with Dirichlet boundary condition. In order to
reconstruct the shape of cracks from scattered field data measured at the
boundary, we introduce a topological derivative-based electromagnetic imaging
function operated at several nonzero frequencies. The properties of the imaging
function are carefully analyzed for the configurations of both symmetric and
non-symmetric incident field directions. This analysis explains why the
application of incident fields with symmetric direction operated at multiple
frequencies guarantees a successful reconstruction. Various numerical
simulations with noise-corrupted data are conducted to assess the performance,
effectiveness, robustness, and limitations of the proposed technique.Comment: 17 pages, 27 figure
Multi-frequency based location search algorithm of small electromagnetic inhomogeneities embedded in two-layered medium
In this paper, we consider a problem for finding the locations of
electromagnetic inhomogeneities completely embedded in homogeneous two layered
medium. For this purpose, we present a filter function operated at several
frequencies and design an algorithm for finding the locations of such
inhomogeneities. It is based on the fact that the collected Multi-Static
Response (MSR) matrix can be modeled via a rigorous asymptotic expansion
formula of the scattering amplitude due to the presence of such
inhomogeneities. In order to show the effectiveness, we compare the proposed
algorithm with traditional MUltiple SIgnal Classification (MUSIC) algorithm and
Kirchhoff migration. Various numerical results demonstrate that the proposed
algorithm is robust with respect to random noise and yields more accurate
location than the MUSIC algorithm and Kirchhoff migration.Comment: 21 pages, 25 figure
A biomimetic basis for auditory processing and the perception of natural sounds
Biomimicry is a powerful science that aims to take advantage of nature's
remarkable ability to devise innovative solutions to challenging problems. In
the setting of hearing, mimicking how humans hear is the foremost strategy in
designing effective artificial hearing approaches. In this work, we explore the
mathematical foundations for the exchange of design inspiration and features
between biological hearing systems, artificial sound-filtering devices, and
signal processing algorithms. Our starting point is a concise asymptotic
analysis of subwavelength acoustic metamaterials. We are able to fine tune this
structure to mimic the biomechanical properties of the cochlea, at the same
scale. We then turn our attention to developing a biomimetic signal processing
algorithm. We use the response of the cochlea-like structure as an initial
filtering layer and then add additional biomimetic processing stages, designed
to mimic the human auditory system's ability to recognise the global properties
of natural sounds
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability
We are concerned with the problem of determining the damping boundary
coefficient appearing in a dissipative wave equation from a single boundary
measurement. We prove that the uniqueness holds at the origin provided that the
initial condition is appropriately chosen. We show that the choice of the
initial condition leading to uniqueness is related to a fine version of unique
continuation property for elliptic operators. We also establish a Lipschitz
directional stability estimate at the origin, which is obtained by a
linearization process
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