1,497 research outputs found
Backpropagation Imaging in Nonlinear Harmonic Holography in the Presence of Measurement and Medium Noises
In this paper, the detection of a small reflector in a randomly heterogenous
medium using second-harmonic generation is investigated. The medium is
illuminated by a time-harmonic plane wave at frequency omega. It is assumed
that the reflector has a non-zero second-order nonlinear susceptibility, and
thus emits a wave at frequency two omega in addition to the fundamental
frequency linear scattering. It is shown how the fundamental frequency signal
and the second-harmonic signal propagate in the medium. A statistical study of
the images obtained by migrating the boundary data is performed. It is proved
that the second-harmonic image is more stable with respect to medium noise than
the one obtained with the fundamental signal. Moreover, the signal-to-noise
ratio for the second-harmonic image does not depend neither on the second-order
susceptibility tensor nor on the volume of the particle.Comment: 36 pages, 18 figure
A mathematical and numerical framework for ultrasonically-induced Lorentz force electrical impedance tomography
We provide a mathematical analysis and a numerical framework for Lorentz
force electrical conductivity imaging. Ultrasonic vibration of a tissue in the
presence of a static magnetic field induces an electrical current by the
Lorentz force. This current can be detected by electrodes placed around the
tissue; it is proportional to the velocity of the ultrasonic pulse, but depends
nonlinearly on the conductivity distribution. The imaging problem is to
reconstruct the conductivity distribution from measurements of the induced
current. To solve this nonlinear inverse problem, we first make use of a
virtual potential to relate explicitly the current measurements to the
conductivity distribution and the velocity of the ultrasonic pulse. Then, by
applying a Wiener filter to the measured data, we reduce the problem to imaging
the conductivity from an internal electric current density. We first introduce
an optimal control method for solving such a problem. A new direct
reconstruction scheme involving a partial differential equation is then
proposed based on viscosity-type regularization to a transport equation
satisfied by the current density field. We prove that solving such an equation
yields the true conductivity distribution as the regularization parameter
approaches zero. We also test both schemes numerically in the presence of
measurement noise, quantify their stability and resolution, and compare their
performance
A Note On Computing Set Overlap Classes
Let be a finite set of elements and a family of subsets of Two sets and of
overlap if and Two sets
are in the same overlap class if there is a series of
sets of in which each overlaps. In this note, we focus
on efficiently identifying all overlap classes in
time. We thus revisit the clever algorithm of Dahlhaus of which we give a clear
presentation and that we simplify to make it practical and implementable in its
real worst case complexity. An useful variant of Dahlhaus's approach is also
explained
Subquadratic-time algorithm for the diameter and all eccentricities on median graphs
On sparse graphs, Roditty and Williams [2013] proved that no
-time algorithm achieves an approximation factor smaller
than for the diameter problem unless SETH fails. In this article,
we solve an open question formulated in the literature: can we use the
structural properties of median graphs to break this global quadratic barrier?
We propose the first combinatiorial algorithm computing exactly all
eccentricities of a median graph in truly subquadratic time. Median graphs
constitute the family of graphs which is the most studied in metric graph
theory because their structure represents many other discrete and geometric
concepts, such as CAT(0) cube complexes. Our result generalizes a recent one,
stating that there is a linear-time algorithm for all eccentricities in median
graphs with bounded dimension , i.e. the dimension of the largest induced
hypercube. This prerequisite on is not necessarily anymore to determine all
eccentricities in subquadratic time. The execution time of our algorithm is
.
We provide also some satellite outcomes related to this general result. In
particular, restricted to simplex graphs, this algorithm enumerates all
eccentricities with a quasilinear running time. Moreover, an algorithm is
proposed to compute exactly all reach centralities in time
.Comment: 43 pages, extended abstract in STACS 202
Entrepreneurial Spawning and Firm Characteristics
We analyze the implications of entrepreneurial spawning for a variety of firm characteristics such as size, focus, profitability, and innovativeness. We examine the dynamics of spawning over time. Our model accounts for much of the empirical evidence relating to the relation between spawning and firm characteristics. Firms that have higher patent quality spawn more, as do firms that have higher knowhow. Older firms spawn less, they are more diversified and less profitable. Spawning frequency, focus, and profitability are positively related where spawning is driven by the value of organizational fit; they are negatively related with firm size
Modal expansion for plasmonic resonators in the time domain
We study the electromagnetic field scattered by a metallic nanoparticle with
dispersive material parameters placed in a homogeneous medium in a low
frequency regime. We use asymptotic analysis and spectral theory to diagonalise
a singular integral operator, which allows us to write the field inside and
outside the particle in the form of a complete and orthogonal modal expansion.
We find the eigenvalues of the volume operator to be associated, via a
non-linear relation, to the resonant frequencies of the problem. We prove that
all resonances lie in a bounded region near the origin. Finally we use complex
analysis to compute the Fourier transform of the scattered field and obtain its
modal expansion in the time domain
Etude de la solidification rapide d'une lamelle métallique en contact imparfait avec un substrat céramique
International audienceCe travail s'intéresse au problÚme de solidification de matériaux bicouche en régime transitoire, dont les propriétés thermophysiques dépendent de la température. Le modÚle numérique utilisé est basé sur une approche enthalpique pour résoudre le problÚme de changement de phase dans chacun des matériaux en présence. Les résultats sont présentés pour plusieurs paramÚtres tel que l'épaisseur de la lamelle, la résistance thermique de contact, la nature des matériaux et leurs températures à l'impact
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