Scanning paraxial optical tomography

We present a solution to this problem in the form of a fast algorithm with computational complexity that scales as N log N , where N is the number of spatial measurements of the scattered field.     

Averaging of nonlinearity-managed pulses

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.     

Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10(8) source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly scattering medium containing absorbing inhomogeneities.     

Deflagrations and detonations in thermonuclear supernovae

We study a type Ia supernova explosion using three-dimensional numerical simulations based on reactive fluid dynamics. We consider a delayed-detonation model that assumes a deflagration-to-detonation transition. In contrast with the pure deflagration model, the delayed-detonation model releases enough energy to account for a healthy explosion, and does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between simulations and observations, and makes a delayed detonation the mostly likely mechanism for type Ia supernovae.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Coherent backscattering spectroscopy

Coherent backscattering (CBS) of light in random media has been previously investigated by use of coherent light sources. Here we report a novel method of CBS measurement that combines low spatial coherence, broadband illumination, and spectrally resolved detection. We show that low spatial coherence illumination leads to an anomalously broad CBS peak and a dramatic speckle reduction; the latter is further facilitated by low temporal coherence detection. Thus CBS can be observed in biological tissue and other media that previously were beyond the reach of conventional CBS measurements. We also demonstrate, for the first time to our knowledge, spectroscopic analysis of CBS. CBS spectroscopy may find important applications in probing random media such as biological tissue in which depth-selective measurements are crucial.     

Molecular structure design and synthetic approaches to the heterometallic alkoxide complexes (soft chemistry approach to inorganic materials by the eyes of a crystallographer)

General principles of formation and stability of the heterometallic alkoxides existing due to Lewis Acid-Base interaction, isomorphous substitution and heterometallic metal-metal bonds are discussed. The molecular structure design approach based on the choice of a proper molecular structure type and completing it with the ligands, providing both the necessary number of donor atoms and the sterical protection of the metaloxygen core, is presented. Its applications in prediction of the composition and structure of single source precursors of inorganic materials are demonstrated for such classes of compounds as oxoalkoxides, alkoxide beta-diketonates, alkoxide carboxylates, derivatives of functional alcohols, metallatranes and metallasiloxanes.     

Enantioselective ligand exchange in modern separation techniques

As a follow-up to a series of review articles on enantioselective ligand exchange chromatography, the present contribution critically evaluates achievements in this area of active and successful research which have been reported in the scientific literature since 1992. Also discussed is enantioselective ligand exchange in electromigration techniques which have developed especially fruitfully during the last decade.