On a phase-change problem arising from inductive heating

In this paper we study a phase-change problem arising from induction heating. The mathematical model consists of time-harmonic Maxwell’s system in a quasi-stationary field coupled with nonlinear heat conduction. The enthalpy form is used to characterize the phase-change in the material. It is shown that the problem has a global solution. Moreover, it is shown that the solution is unique and regular in one-space dimension even with an unbounded resistivity. This work is supported in part by a NSF grant: DMS-0102261     

Scaling properties of image textures: A detrending fluctuation analysis approach

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study roughness features of images. Unidimensional sequences at different image orientations are extracted and their average scaling exponent is estimated. In this form, the existence of anisotropies can be detected when considerable variations in the scaling exponent at different image orientation are observed. Different images from grass to solar granulation are analyzed and the underlying physics of such results is briefly commented.     

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.     

Skew Models II

If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.      

Nitric oxide concentration measurements in atmospheric pressure flames using electronic-resonance-enhanced coherent anti-Stokes Raman scattering

We report the application of electronic-resonance-enhanced coherent anti-Stokes Raman scattering (ERE-CARS) for measurements of nitric oxide concentration ([NO]) in three different atmospheric pressure flames. Visible pump (532 nm) and Stokes (591 nm) beams are used to probe the Q-branch of the Raman transition. A significant resonance enhancement is obtained by tuning an ultraviolet probe beam (236 nm) into resonance with specific rotational transitions in the (v’=0, v”=1) vibrational band of the A²Σ⁺–X²Π electronic system of NO. ERE-CARS spectra are recorded at various heights within a hydrogen-air flame producing relatively low concentrations of NO over a Hencken burner. Good agreement is obtained between NO ERE-CARS measurements and the results of flame computations using UNICORN, a two-dimensional flame code. Excellent agreement between measured and calculated NO spectra is also obtained when using a modified version of the Sandia CARSFT code for heavily sooting acetylene-air flames (φ=0.8 to φ=1.6) on the same Hencken burner. Finally, NO concentration profiles are measured using ERE-CARS in a laminar, counter-flow, non-premixed hydrogen-air flame. Spectral scans are recorded by probing the Q₁ (9.5), Q₁ (13.5) and Q₁ (17.5) Raman transitions. The measured shape of the [NO] profile is in good agreement with that predicted using the OPPDIF code, even without correcting for collisional effects. These comparisons between [NO] measurements and predictions establish the utility of ERE-CARS for detection of NO in flames with large temperature and concentration gradients as well as in sooting environments. PACS 07.88.+y; 42.62.Fi; 42.65.Dr     

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

Mesopore size dependence of the ionic diffusivity in alumina based composite lithium ionic conductors

Ordered-mesoporous Al₂O₃ was synthesized by a sol–gel method using neutral copolymer surfactants as structure-directing agents. The pore size was controlled over the 3–15 nm range by the use of various surfactants. Composites composed of the synthesized mesoporous Al₂O₃ and a lithium ion conductor (LiI) were prepared. The maximum dc electrical conductivity, 2.6 × 10^− 4 S cm^− 1 at 298 K, was observed for 50 LiI·50 Al₂O₃ composite with 4.2 nm average mesopore size, which was considerably higher than the previously reported LiI-alumina composites. A systematic dependence of conductivity upon pore size was observed, in which conductivity increased with decreasing pore size, except for samples with a pore size of 2.8 nm. The lithium ion diffusion coefficient determined by the ⁷Li pulsed field gradient nuclear magnetic resonance (PFG-NMR) showed excellent agreement with the measured conductivity calculated by the Nernst-Einstein equation. On the other hand, lithium migration activation energies obtained by quasielastic neutron scattering (QENS) and ⁷Li NMR spin-lattice relaxation time (T₁) were considerably smaller than those obtained from electrical conductivity and PFG-NMR. This could be explained by the ion migration mechanism in heterogeneous composites and a possible enhancement of conductivity in mesoscopically confined spaces.     

Mixed conducting perovskite-like ceramics on the base of lanthanum gallate

Ceramic perovskite solid solutions (La_0.9Sr_0.1)[(Ga_1−xM_x)_0.8Mg_0.2]O_3−y, 0 ≤ x ≤ 0.5, M = Fe, Ni, Cr (systems I–III) and brownmillerite solid solutions (La_0.2Sr_1.8)[Ga(Fe_1−xMg_x)]O_5−z, 0 ≤ x ≤ 0.5, (system IV) have been prepared. The samples have been studied by X-ray diffraction and electron microscopy methods, dielectric spectroscopy and permeability measurements. The correlation between the composition, unit cell parameter changes, electrical transport and oxygen permeation properties has been revealed. Introduction of transition metals (Fe, Ni, or Cr), substituting for gallium, ensures the enhancement of the electronic constituent of the conductivity in the perovskite systems I–III. Stabilization of the transition metal high valence states 4+ or 5+ has been suggested for compositions I and III. This leads to a unit cell volume contraction and provides a decrease in the concentration of oxygen vacancies. The oxygen permeability reaches its maximum values in compositions I–III with x ∼ 0.3. On the contrary, increasing concentration of the doping element with lower valence state (magnesium), substituting for iron, determines the expansion of the brownmillerite unit cell volume and provides an increase of the oxygen vacancy concentration, which in turn, favors the enhancement of oxygen permeability of composition IV.