Travel Time Tomography

We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

An example of a non-linear evolution equation showing ‘chaos-enhancement’

It is shown that for a non-linear evolution equation—a caricature of Boltzmann's equation—a family of H-theorems exists.     

Analysis of 3-chlorotyrosine as a specific marker of protein oxidation: the use of N(O,S)-ethoxycarbonyltrifluoroethyl ester derivatives and gas chromatography/mass spectrometry

N(O,S)-ethoxycarbonyltrifluoroethyl amino acid esters are formed by the reaction of amino acids with ethylchloroformate plus trifluoroethanol plus pyridine. The use of these derivatives for a rapid and sensitive determination of 3-chlorotyrosine, a highly specific marker of myeloperoxidase-catalyzed protein oxidation, by using standard gas chromatography/electron impact mass spectrometry, is discussed.     

Heterogeneous freezing on pyroelectric poly(vinylidene fluoride-co-trifluoroethylene) thin films

Active deicing of technical surfaces, such as for wind turbines and heat exchangers, currently requires the usage of heat or chemicals. Passive coating strategies that postpone the freezing of covering water would be beneficial in order to save costs and energy. One hypothesis is that pyroelectric active materials can achieve this because of the surface charges generated on these materials when they are subject to a temperature change. High-quality poly(vinylidene fluoride-co-trifluoroethylene) (P(VDF-TrFE)) thin films with a high crystallinity, prefererd edge-on orientation, low surface roughness, and comprised of the β-analogous ferroelectric phase were deposited by spin-coating. Freezing experiments with a cooling rate of 1 K min⁻¹ were made on P(VDF-TrFE) coatings in order to separate the effect of different parameters such as the poling direction, film thickness, used solvent, deposition process, underlying substrate, and annealing temperature on the achievable supercooling. The topography and the underlying substrate significantly changed the distribution of freezing temperatures of water droplets in contact with these thin films. In contrast, no significant effect of the thickness, morphology, or pyroelectric effect of the as-prepared domain-state on the freezing temperatures was found.     

Effect of post-metallization annealing on the ferroelectric properties of sol-gel derived PZT thin films

A series of monolithic Pt-PZT-Pt capacitors was prepared based on sol-gel derived PZT 53/47 films fired to 700 C. After deposition of top Pt electrodes, the capacitors were subjected to post-metallization annealing (PMA) temperatures of 100 C to 700 C. Dielectric and ferroelectric (FE) characterizations were performed. Increasing the PMA temperature produced lower values of spontaneous and remanent polarizations, dielectric constant and leakage currents. The observations are correlated with a proposed FE capacitor model.