Velocity inversion: A case study in infinite-dimensional optimization

The goal of seismic velocity inversion is the estimation of seismic wave velocities inside the earth by attempting to predict, in a least-error sense, seismic waveforms measured at its surface. We present velocity inversion as a case study in the various infinite-dimensional pathologies which may afflict practically important problems of distributed parameter identification, treated as optimization problems in function spaces. These features differentiate various problem formulations far beyond the degree one would expect for finite- (small-) dimensional problems. We illustrate this differentiation by comparing the characteristics of three different least-squares formulations of velocity inversion.     

Determination of the size and composition of multicomponent ethanol/water droplets by cavity-enhanced Raman scattering

Cavity-enhanced Raman scattering is used to determine the size and composition of multicomponent ethanol/water droplets in the concentration range 7.5–19% ethanol by volume. Under the experimental conditions presented here, the integrated CERS signal from ethanol shows an exponential increase with increase in ethanol concentration when compared with the integrated intensity of the water band. The calibration is shown to be invariant with particle size over the droplet radius range 20–35 μm. In addition to providing a method for determining particle size and composition, initial studies show that the evaporation dynamics of these multicomponent droplets can be probed by CERS.     

Control of strong-laser-field coupling to electrons in solid targets with wavelength-scale spheres

Irradiation of a planar solid by an intense laser pulse leads to fast electron acceleration and hard x-ray production. We have investigated whether this high field production of fast electrons can be controlled by introducing dielectric spheres of well-defined size on the target surface. We find that the presence of spheres with a diameter slightly larger than half the laser wavelength leads to Mie enhancements of the laser field which, accompanied by multipass stochastic heating of the electrons, leads to significantly enhanced hard x-ray yield and temperature.     

Dynamic acceleration effects in explosions of laser-irradiated heteronuclear clusters

Intense, femtosecond irradiation of atomic and molecular clusters can initiate Coulomb explosions, generating particle energies sufficient to drive nuclear fusion. Last and Jortner have proposed, based on particle dynamics simulations, that heteronuclear clusters with a mixture of heavy and light ions will not explode by the simple, equilibrium Coulomb model but that dynamic effects can lead to a boosting of energy of the lighter ejected ions [Phys. Rev. Lett. 87, 033401 (2001)]. We present experimental confirmation of this theoretically predicted ion energy enhancement in methane clusters.     

Visual spatial memory is enhanced in female rats (but inhibited in males) by dietary soy phytoestrogens

Background  

In learning and memory tasks, requiring visual spatial memory (VSM), males exhibit superior performance to females (a difference attributed to the hormonal influence of estrogen). This study examined the influence of phytoestrogens (estrogen-like plant compounds) on VSM, utilizing radial arm-maze methods to examine varying aspects of memory. Additionally, brain phytoestrogen, calbindin (CALB), and cyclooxygenase-2 (COX-2) levels were determined.     

An Infeasible Point Method for Minimizing the Lennard-Jones Potential

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.     

Bidirectional and unidirectional PCET in a molecular model of a cobalt-based oxygen-evolving catalyst

The oxidation of water to molecular oxygen is a kinetically demanding reaction that requires efficient coupling of proton and electron transfer. The key proton-coupled electron transfer (PCET) event in water oxidation mediated by a cobalt-phosphate-based heterogeneous catalyst is the one-electron, one-proton conversion of Co(III)-OH to Co(IV)-O. We now isolate the kinetics of this PCET step in a molecular Co(4)O(4) cubane model compound. Detailed electrochemical, stopped-flow, and NMR studies of the Co(III)-OH to Co(IV)-O reaction reveal distinct mechanisms for the unidirectional PCET self-exchange reaction and the corresponding bidirectional PCET. A stepwise mechanism, with rate-limiting electron transfer is observed for the bidirectional PCET at an electrode surface and in solution, whereas a concerted proton-electron transfer displaying a moderate KIE (4.3 ± 0.2), is observed for the unidirectional self-exchange reaction.     

Impedance profile inversion via the first transport equation

The subject of this paper is the inverse reflection problem for a stratified elastic half-space. That is, a linear elastic medium, whose elastic properties depend only on depth from a planar free surface, is stimulated at t = 0 by a plane wave impulsive source. The motion of a typical surface element is recorded for 0 ? t ? 2T. It is shown that this surface trace determines the acoustic impedance of the medium as a function of travel time, to (travel-time) depth T. Moreover, we give a precise characterization of those functions which may appear as surface traces, and show uniqueness, existence, and continuous dependence of the logarithm of the impedance as a function of the surface trace in the Sobolev H¹ topology.     

Inverse boundary value problems and a theorem of Gel'fand and Levitan

This report concerns two so-called inverse problems of mathematical physics. These are: (i) the problem of determining a second-order differential operator (in a normal form) on the half-axis from its spectral function; and, (ii) the problem of determining a hyperbolic boundary value problem of a special form in a (non-characteristic) half-plane from its response on the boundary to a unit impulse at some reference time t = 0 (boundary value of the Riemann function). We solve problem (ii) by a natural approach, and then indicate how the solution of problem (i) follows from the solution of problem (ii). Our solution of problem (ii) is constructive, and we obtain stability of the solution under perturbation of the data, in a well-defined sense. For problem (i), we obtain the well-known result of Gel'fand and Levitan, in the sharp formulation given by Levitan and Gasymov ([6]).