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.     

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.     

Robust Algorithms for the Stable Set Problem

The stable set problem is to find in a simple graph a maximum subset of pairwise non-adjacent vertices. The problem is known to be NP-hard in general and can be solved in polynomial time on some special classes, like cographs or claw-free graphs. Usually, efficient algorithms assume membership of a given graph in a special class. Robust algorithms apply to any graph G and either solve the problem for G or find in it special forbidden configurations. In the present paper we describe several efficient robust algorithms, extending some known results.     

Critical Independent Sets and König–Egerváry Graphs

A set S of vertices is independent or stable in a graph G, and we write S ∈ Ind (G), if no two vertices from S are adjacent, and α(G) is the cardinality of an independent set of maximum size, while core(G) denotes the intersection of all maximum independent sets. G is called a König–Egerváry graph if its order equals α(G) + μ(G), where μ(G) denotes the size of a maximum matching. The number def (G) = | V(G) | ?2μ(G) is the deficiency of G. The number \({d(G)=\max\{\left\vert S\right\vert -\left\vert N(S)\right\vert :S\in\mathrm{Ind}(G)\}}\) is the critical difference of G. An independent set A is critical if \({\left\vert A\right\vert -\left\vert N(A)\right\vert =d(G)}\) , where N(S) is the neighborhood of S, and α _c (G) denotes the maximum size of a critical independent set. Larson (Eur J Comb 32:294–300, 2011) demonstrated that G is a König–Egerváry graph if and only if there exists a maximum independent set that is also critical, i.e., α _c (G) = α(G). In this paper we prove that: (i) \({d(G)=\left \vert \mathrm{core}(G) \right \vert -\left \vert N (\mathrm{core}(G))\right\vert =\alpha(G)-\mu(G)=def \left(G\right)}\) holds for every König–Egerváry graph G; (ii) G is König–Egerváry graph if and only if each maximum independent set of G is critical.     

Parallel MRI at microtesla fields

Parallel imaging techniques have been widely used in high-field magnetic resonance imaging (MRI). Multiple receiver coils have been shown to improve image quality and allow accelerated image acquisition. Magnetic resonance imaging at ultra-low fields (ULF MRI) is a new imaging approach that uses SQUID (superconducting quantum interference device) sensors to measure the spatially encoded precession of pre-polarized nuclear spin populations at microtesla-range measurement fields. In this work, parallel imaging at microtesla fields is systematically studied for the first time. A seven-channel SQUID system, designed for both ULF MRI and magnetoencephalography (MEG), is used to acquire 3D images of a human hand, as well as 2D images of a large water phantom. The imaging is performed at 46 mu T measurement field with pre-polarization at 40 mT. It is shown how the use of seven channels increases imaging field of view and improves signal-to-noise ratio for the hand images. A simple procedure for approximate correction of concomitant gradient artifacts is described. Noise propagation is analyzed experimentally, and the main source of correlated noise is identified. Accelerated imaging based on one-dimensional undersampling and 1D SENSE (sensitivity encoding) image reconstruction is studied in the case of the 2D phantom. Actual threefold imaging acceleration in comparison to single-average fully encoded Fourier imaging is demonstrated. These results show that parallel imaging methods are efficient in ULF MRI, and that imaging performance of SQUID-based instruments improves substantially as the number of channels is increased.     

Structural, spectral, electric-field-induced second harmonic, and theoretical study of Ni(II), Cu(II), Zn(II), and VO(II) complexes with [N2O2] unsymmetrical schiff bases of S-methylisothiosemicarbazide derivatives

New unsymmetrical [N2O2] tetradentate Schiff base complexes of Ni(II), Cu(II), Zn(II), and VO(II) were synthesized by template condensation of the tetradentate precursor 1-phenylbutane-1,3-dione mono-S-methylisothiosemicarbazone with o-hydroxybenzaldehyde or its 5-phenylazo derivative. They were characterized by elemental analysis, IR, UV-vis, electron spin resonance, and NMR spectroscopy, mass spectrometry, and magnetic measurements. The crystal structures of five of them have been determined by X-ray diffraction using, in some cases, synchrotron radiation. These compounds are characterized by a large thermal stability; their decomposition temperatures range from 240 up to 310 degrees C. Complexes with the phenylazo substituent were found to possess a large second-order nonlinear optical (NLO) response, as determined both by measurements of solution-phase direct current electric-field-induced second harmonic generation and by theoretical time-dependent density functional theory (TDDFT) calculations. The molecular hyperpolarizability was found to decrease in the order Zn(II) > Cu(II) > Ni(II) approximately VO(II). The active role of the metal in determining the NLO properties of the complexes was shown through an analysis of their UV-vis spectra, which revealed the presence of metal-to-ligand (in closed-shell complexes) and ligand-to-metal (in open-shell complexes) charge-transfer bands together with intra-ligand charge-transfer transitions. Assignment of the bands was based on the analysis of the TDDFT computed spectra.