Diffuse Scattering and Diffuse Optical Tomography on Graphs

We formulate and analyze difference equations on graphs analogous to time- independent diffusion equations arising in the study of diffuse scattering in con- tinuous media and consider the associated inverse problem, which we call discrete diffuse optical tomography. For the forward problem we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous (background problem) using Born series, providing necessary conditions for convergence and demonstrating the process through numerous examples. In addition, we outline a method for finding Green’s functions for Cayley graphs for both abelian and non-abelian groups. Finally, we conclude our discussion of the forward problem by considering the effects of sparsity on our method and results, outlining the simplifications that can be made provided that the scatterers are weak and well-separated. For the inverse problem, we present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving estimates characterizing the domain of convergence, approximation errors, and stability of our approach. We also present a modification which allows additional information on the structure of the potential to be incorporated, facilitating recovery for a broader class of problems.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138547/1/jhoskin_1.pd

The modeling of diffuse boundaries in the 2-D digital waveguide mesh

The digital waveguide mesh can be used to simulate the propagation of sound waves in an acoustic system. The accurate simulation of the acoustic characteristics of boundaries within such a system is an important part of the model. One significant property of an acoustic boundary is its diffusivity. Previous approaches to simulating diffuse boundaries in a digital waveguide mesh are effective but exhibit limitations and have not been analyzed in detail. An improved technique is presented here that simulates diffusion at boundaries and offers a high degree of control and consistency. This technique works by rotating wavefronts as they pass through a special diffusing layer adjacent to the boundary. The waves are rotated randomly according to a chosen probability function and the model is lossless. This diffusion model is analyzed in detail, and its diffusivity is quantified in the form of frequency dependent diffusion coefficients. The approach used to measuring boundary diffusion is described here in detail for the 2-D digital waveguide mesh and can readily be extended for the 3-D case

High-pressure study of X-ray diffuse scattering in ferroelectric perovskites

We present a high-pressure x-ray diffuse scattering study of the ABO$_3$ ferroelectric perovskites BaTiO_3 and KNbO_3. The well-known diffuse lines are observed in all the phases studied. In KNbO_3, we show that the lines are present up to 21.8 GPa, with constant width and a slightly decreasing intensity. At variance, the intensity of the diffuse lines observed in the cubic phase of BaTiO_3 linearly decreases to zero at $\sim 11$ GPa. These results are discussed with respect to x-ray absorption measurements, which leads to the conclusion that the diffuse lines are only observed when the B atom is off the center of the oxygen tetrahedron. The role of such disorder on the ferroelectric instability of perovskites is discussed.Comment: 4 pages, Accepted in PR

Recovery of surface orientation from diffuse polarization

When unpolarized light is reflected from a smooth dielectric surface, it becomes partially polarized. This is due to the orientation of dipoles induced in the reflecting medium and applies to both specular and diffuse reflection. This paper is concerned with exploiting polarization by surface reflection, using images of smooth dielectric objects, to recover surface normals and, hence, height. This paper presents the underlying physics of polarization by reflection, starting with the Fresnel equations. These equations are used to interpret images taken with a linear polarizer and digital camera, revealing the shape of the objects. Experimental results are presented that illustrate that the technique is accurate near object limbs, as the theory predicts, with less precise, but still useful, results elsewhere. A detailed analysis of the accuracy of the technique for a variety of materials is presented. A method for estimating refractive indices using a laser and linear polarizer is also given

Anomalous pressure dependence of the atomic displacements in the relaxor ferroelectric PbMg1/3_{1/3}Ta2/3_{2/3}O3_3

The crystal structure of the PbMg$_{1/3}$Ta$_{2/3}$O$_3$ (PMT) relaxor ferroelectric was studied under hydrostatic pressure up to $\sim 7$ GPa by means of powder neutron diffraction. We find a drastic pressure-induced decrease of the lead displacement from the inversion centre which correlates with an increase by $\sim$ 50 % of the anisotropy of the oxygen temperature factor. The vibrations of the Mg/Ta are, in contrast, rather pressure insensitive. We attribute these changes being responsible for the previously reported pressure-induced suppression of the anomalous dielectric permittivity and diffuse scattering in relaxor ferroelectrics

The June 2012 transit of Venus. Framework for interpretation of observations

Ground based observers have on 5/6th June 2012 the last opportunity of the century to watch the passage of Venus across the solar disk from Earth. Venus transits have traditionally provided unique insight into the Venus atmosphere through the refraction halo that appears at the planet outer terminator near ingress/egress. Much more recently, Venus transits have attracted renewed interest because the technique of transits is being successfully applied to the characterization of extrasolar planet atmospheres. The current work investigates theoretically the interaction of sunlight and the Venus atmosphere through the full range of transit phases, as observed from Earth and from a remote distance. Our model predictions quantify the relevant atmospheric phenomena, thereby assisting the observers of the event in the interpretation of measurements and the extrapolation to the exoplanet case. Our approach relies on the numerical integration of the radiative transfer equation, and includes refraction, multiple scattering, atmospheric extinction and solar limb darkening, as well as an up to date description of the Venus atmosphere. We produce synthetic images of the planet terminator during ingress/egress that demonstrate the evolving shape, brightness and chromaticity of the halo. Guidelines are offered for the investigation of the planet upper haze from vertically-unresolved photometric measurements. In this respect, the comparison with measurements from the 2004 transit appears encouraging. We also show integrated lightcurves of the Venus/Sun system at various phases during transit and calculate the respective Venus-Sun integrated transmission spectra. The comparison of the model predictions to those for a Venus-like planet free of haze and clouds (and therefore a closer terrestrial analogue) complements the discussion and sets the conclusions into a broader perspective.Comment: 14 pages; 14 figures; Submitted on 02/06/2012; A&A, accepted for publication on 30/08/201

Reconciliation of CDM abundance and μ→eγ\mu\to e\gamma in a radiative seesaw model

We reexamine relic abundance of a singlet fermion as a CDM candidate, which contributes to the neutrino mass generation through radiative seesaw mechanism. We search solutions for Yukawa couplings and the mass spectrum of relevant fields to explain neutrino oscillation data. For such solutions, we show that an abundance of a lightest singlet fermion can be consistent with WMAP data without conflicting with both bounds of $\mu\to e\gamma$ and $\tau\to \mu\gamma$. This reconciliation does not need any modification of the original radiative seesaw model other than by specifying flavor structure of Yukawa couplings and taking account of coannihilation effects.Comment: 16 pages, 2 figures, accepted version for publication