14,890 research outputs found
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Cloaking and anamorphism for light and mass diffusion
We first review classical results on cloaking and mirage effects for
electromagnetic waves. We then show that transformation optics allows the
masking of objects or produces mirages in diffusive regimes. In order to
achieve this, we consider the equation for diffusive photon density in
transformed coordinates, which is valid for diffusive light in scattering
media. More precisely, generalizing transformations for star domains introduced
in [Diatta and Guenneau, J. Opt. 13, 024012, 2011] for matter waves, we
numerically demonstrate that infinite conducting objects of different shapes
scatter diffusive light in exactly the same way. We also propose a design of
external light-diffusion cloak with spatially varying sign-shifting parameters
that hides a finite size scatterer outside the cloak. We next analyse
non-physical parameter in the transformed Fick's equation derived in [Guenneau
and Puvirajesinghe, R. Soc. Interface 10, 20130106, 2013], and propose to use a
non-linear transform that overcomes this problem. We finally investigate other
form invariant transformed diffusion-like equations in the time domain, and
touch upon conformal mappings and non-Euclidean cloaking applied to diffusion
processes.Comment: 42 pages, Latex, 14 figures. V2: Major changes : some formulas
corrected, some extra cases added, overall length extended from 21 pages (V1)
to 42 pages (present version V2). The last version will appear at Journal of
Optic
Asymptotic wave-splitting in anisotropic linear acoustics
Linear acoustic wave-splitting is an often used tool in describing sound-wave
propagation through earth's subsurface. Earth's subsurface is in general
anisotropic due to the presence of water-filled porous rocks. Due to the
complexity and the implicitness of the wave-splitting solutions in anisotropic
media, wave-splitting in seismic experiments is often modeled as isotropic.
With the present paper, we have derived a simple wave-splitting procedure for
an instantaneously reacting anisotropic media that includes spatial variation
in depth, yielding both a traditional (approximate) and a `true amplitude'
wave-field decomposition. One of the main advantages of the method presented
here is that it gives an explicit asymptotic representation of the linear
acoustic-admittance operator to all orders of smoothness for the smooth,
positive definite anisotropic material parameters considered here. Once the
admittance operator is known we obtain an explicit asymptotic wave-splitting
solution.Comment: 20 page
Multiple scattering theory for polycrystalline materials with strong grain anisotropy: theoretical fundamentals and applications
This work is a natural extension of the authors previous work, Multiple
scattering theory for heterogeneous elastic continua with strong property
fluctuation, theoretical fundamentals and applications, which established the
foundation for developing multiple scattering model for strongly scattering
heterogeneous elastic continua. In this work, the corresponding multiple
scattering theory for polycrystalline materials with randomly oriented
anisotropic crystallites is developed. As applications in ultrasonic
nondestructive evaluation, we calculated the dispersion and attenuation
coefficient of one of the most important polycrystalline materials in
aeronautics engineering, high temperature titanium alloys. The effects of grain
symmetry, grain size, and alloying elements on the dispersion and attenuation
behaviors are examined. Key information is obtained which has significant
implications for quantitatively evaluating the average grain size, monitoring
the phase transition, and even estimating gradual change in chemical
composition of titanium components in gas turbine engines. For applications in
seismology, the velocities and Q-factors for both hexagonal and cubic
polycrystalline iron models for the Earth uppermost inner core are obtained in
the whole frequency range. This work provides a universal, quantitative model
for characterization of a large variety of polycrystalline materials. It also
can be extended to incorporate more complicated microstructures, including
ellipsoidal grains with or without textures, and even multiphase
polycrystalline materials. The new model demonstrates great potential of
applications in ultrasonic nondestructive evaluation and inspection of
aerospace and aeronautic structures. It also provides a theoretical framework
for quantitative seismic data explanation and inversion for the material
composition and structural formations of the Earth inner core.Comment: 37 pages, 16 figure
Absorption and Scattering 2D Volcano Images from Numerically Calculated Space-weighting functions
Acknowledgments Yosuke Aoki and an anonymous reviewer greatly improved the quality of the paper. All calculations were made with Mathematica-10TM. Discussions with Marie Calvet, Danilo Galluzzo, Mario La Rocca, Salvatore De Lorenzo, Jessie Mayor and Ludovic Margerin are gratefully acknowledged. The authors are supported by MEDSUV European project and by Spanish Project Ephestos, CGL2011-29499-C02-01 and NOWAVES, TEC2015-68752. The TIDES EU travel Cost action provided travel money to support cooperation between Luca De Siena and the other authors.Peer reviewedPostprin
Full correction of scattering effects by using the radiative transfer theory for improved quantitative analysis of absorbing species in suspensions
Sample-to-sample photon path length variations that arise due to multiple scattering can be removed by decoupling absorption and scattering effects by using the radiative transfer theory, with a suitable set of measurements. For samples where particles both scatter and absorb light, the extracted bulk absorption spectrum is not completely free from nonlinear particle effects, since it is related to the absorption cross-section of particles that changes nonlinearly with particle size and shape. For the quantitative analysis of absorbing-only (i.e., nonscattering) species present in a matrix that contains a particulate species that absorbs and scatters light, a method to eliminate particle effects completely is proposed here, which utilizes the particle size information contained in the bulk scattering coefficient extracted by using the Mie theory to carry out an additional correction step to remove particle effects from bulk absorption spectra. This should result in spectra that are equivalent to spectra collected with only the liquid species in the mixture. Such an approach has the potential to significantly reduce the number of calibration samples as well as improve calibration performance. The proposed method was tested with both simulated and experimental data from a four-component model system
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