Diagrammatic valence bond studies on hemocyanin

The Diagrammatic Valence Bond studies on the active sites of hemocyanin, consisting of two Cu(I) ions and an oxygen molecule, are performed to find out the stable geometrical pattern and electronic structure. Different parameters used in this theoretical approach are taken from existing literature on high T-c superconductors. Attempts have been made to find out the differences in electronic structure of [Cu2O2](+2) and [Cu2O2N4](+2) as it is observed that coordination of nitrogen ligand do affect electronic structure i.e. spin excitation gaps and charge and spin density distribution. A comparison of our results with earlier theoretical results are also presented.

Boson Inverse Operators and a New Family of Two-photon Annihilation Operators

We introduce the inverse of the Hermitian operator (acircacirc†) and express the Boson inverse operators acirc-1 and acirc†-1 in terms of the operators acirc, acirc† and (acircacirc†)-1. We show that these Boson inverse operators may be realized by Susskind-Glogower phase operators. In this way, we find a new two-photon annihilation operator and denote it as acirc2(acircacirc†)-1. We show that the eigenstates of this operator have interesting non-classical properties. We find that the eigenstates of the operators (acircacirc†)-1 acirc2, acirc(acircacirc†)-1 acirc and acirc2(acircacirc†)-1 have many similar properties and thus they constitute a family of two-photon annihilation operators.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

Production of Dirac particles due to riccion coupling

It has been noted that at high energy the Ricci scalar is manifested in two different ways, as a matter field as well as a geometrical field (which is its usual nature even at low energy). Here, using the material aspect of the Ricci scalar, its interaction with Dirac spinors is considered in four-dimensional curved spacetime. We find that a large number of fermion-antifermion pairs can be produced by the exponential expansion of the early universe.

Optical phase conjugation by two-wave mixing in iron-doped lithium niobate

A novel technique to generate forward phase conjugate wave by two-wave mixing (TWM) in photorefractive iron-doped lithium niobate crystal has been demonstrated. An optical beam from a positive transparency was forward phase conjugated by TWM technique. The experimental scheme was then extended to a specific interferometric application.

Synthesis and characterization of photo-crosslinkable main-chain liquid-crystalline polymers containing bis(benzylidene)cycloalkanone units

A series of new photo-crosslinkable main-chain liquid-crystalline polymers containing bis(benzylidene)cycloalkanone units have been studied. These units in the polymers function as mesogens as well as photoactive centres. Polyesters with three different bis(4-hydroxybenzylidene)cycloalkanones corresponding to three cycloalkanones, namely cyclopentanone, cyclohexanone and cycloheptanone, have been prepared. Three dicarboxylic acids with ether linkages, which were derived from oligoethylene oxides, namely triethylene glycol, tetraethylene glycol and pentaethylene glycol, have been used as spacers in these polymers. Polymerization was carried out by both solution and interfacial polycondensation; the latter method gave high-molecular-weight polymers. Structural characterizations were done by ultra-violet, infra-red and H-1 nuclear magnetic resonance spectroscopy. Liquid-crystalline properties were studied by differential scanning calorimetry and polarized-light optical microscopy. These polymers show a nematic mesophase. Liquid-crystalline transition temperatures were correlated with polymer structure. The decrease in transition temperature with increase in cycloalkanone ring size was explained in terms of the change in geometrical anisotropy of bis(benzylidene)cycloalkanone units. MNDO (modified neglect of differential overlap) calculations were performed on the model compounds, bis(4-acetyloxybenzylidene)cycloalkanone to elucidate the geometrical variation of the mesogenic units with cycloalkanone ring size. Studies of photolysis reveal the two kinds of photoreactions that proceed in these polymer systems, namely photoisomerization and photo-crosslinking. The former reaction disrupts the parallel stacking of the chromophores and is reflected as an increase in the ultra-violet spectral intensity. The favourability of these two reactions depends on the mobility of the polymer chains. When the photolysis was done below T-g, photo-crosslinking dominates over photoisomerization. Above T-g, photoisomerization is followed by photo-crosslinking. The photosensitivity of the polymers decreases with increase in size of the cycloalkanone ring.

Lasing in active, sub-mean-free path-sized systems with dense, random, weak scatterers

We report enhanced emission and gain narrowing in Rhodamine 590 perchlorate dye in an aqueous suspension of polystyrene microspheres. A systematic experimental study of the threshold condition for and the gain narrowing of the stimulated emission over a wide range of dye concentrations and scatterer number densities showed several interesting features, even though the transport mean free path far exceeded the system size. The conventional diffusive-reactive approximation to radiative transfer in an inhomogeneously illuminated random amplifying medium, which is valid for a transport mean-free path much smaller than the system size, is clearly inapplicable here. We propose a new probabilistic approach for the present case of dense, random, weak scatterers involving the otherwise rare and ignorable sub-mean-free-path scatterings, now made effective by the high gain in the medium, which is consistent: with experimentally observed features. (C) 1997 Optical Society of America.

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique. (C) 2011 Optical Society of America

Effect of Melt Convection on The Optimum Thermal Design Of Heat Sinks With Phase Change Material

In this paper, the role of melt convection on the performance of heat sinks with phase change material (PCM) is investigated numerically. The heat sink consists of aluminum plate fins embedded in PCM, and is subjected to heat flux supplied from the bottom. A single-domain enthalpy-based CFD model is developed, which is capable of simulating the phase change process and the associated melt convection. The CFD model is coupled with a genetic algorithm for carrying out the optimization. Two cases are considered, namely, one without melt convection (i.e., conduction heat transfer analysis), and the other with convection. It is found that the geometrical optimizations of heat sinks are different for the two cases, indicating the importance of melt convection in the design of heat sinks with PCMs. In the case of conduction analysis, the optimum width of half fin (i.e., sum of half pitch and half fin thickness) is a constant, which is in good agreement with results reported in the literature. On the other hand, if melt convection is considered, the optimum half fin width depends on the effective thermal diffusivity due to conduction and convection. With melt convection, the optimized design results in a significant improvement of operational time.

Simulation and modelling of orbital debris environment by equivalent breakups

It is well known that the increasing space activities pose a serious threat to future missions. This is mainly due to the presence of spent stages, rockets spacecraft and fragments which can lead to collisions. The calculation of the collision probability of future space vehicles with the orbital debris is necessary for estimating the risk. There is lack of adequately catalogued and openly available detailed information on the explosion characteristics of trackable and untrackable debris data. Such a situation compels one to develop suitable mathematical modelling of the explosion and the resultant debris environment. Based on a study of the available information regarding the fragmentation, subsequent evolution and observation, it turns out to be possible to develop such a mathematical model connecting the dynamical features of the fragmentation with the geometrical/orbital characteristics of the debris and representing the environment through the idea of equivalent breakup. (C) 1997 COSPAR.

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

Halogen Bonding in 2,5-Dichloro-1,4-benzoquinone: Insights from Experimental and Theoretical Charge Density Analysis

Experimental charge density distribution in 2, 5-dichloro-1, 4-benzoquinone has been carried out using high resolution X-ray diffraction data at 90 K to quantitatively evaluate the nature of C-Cl center dot center dot center dot O=C halogen bond in molecular crystals. Additionally, the halogen bond is studied from geometrical point of view and the same has been visualized using Hirshfeld surface analysis. The obtained results from experimental charge density analysis are compared with periodic quantum calculations using B3LYP 6-31G(d,p) level of theory. The topological values at bond critical point, three-dimensional static deformation density features and electrostatic potential isosurfaces unequivocally establish the attractive nature of C-Cl center dot center dot center dot O=C halogen bond in crystalline lattice.

Non-interferometric methods of phase estimation for application in optical tomography

We describe here two non-interferometric methods for the estimation of the phase of transmitted wavefronts through refracting objects. The phase of the wavefronts obtained is used to reconstruct either the refractive index distribution of the objects or their contours. Refraction corrected reconstructions are obtained by the application of an iterative loop incorporating digital ray tracing for forward propagation and a modified filtered back projection (FBP) for reconstruction. The FBP is modified to take into account non-straight path propagation of light through the object. When the iteration stagnates, the difference between the projection data and an estimate of it obtained by ray tracing through the final reconstruction is reconstructed using a diffraction tomography algorithm. The reconstruction so obtained, viewed as a correction term, is added to the estimate of the object from the loop to obtain an improved final refractive index reconstruction.

Post-seizure EEG fractal dimension of first ECT predicts antidepressant response at two weeks

Background: Duration of seizure by itself is an insufficient criterion for a therapeutically adequate seizure in ECT. Therefore, measures of seizure EEG other than its duration need to be explored as indices of seizure adequacy and predictors of treatment response. We measured the EEG seizure using a geometrical method-fractal dimension (FD) and examined if this measure predicted remission. Methods: Data from an efficacy study on melancholic depressives (n = 40) is used for the present exploration. They received thrice or once weekly ECTs, each schedule at two energy levels - high or low energy level. FD was computed for early-, mid- and post-seizure phases of the ictal EEG. Average of the two channels was used for analysis. Results: Two-thirds of the patients (n = 25) were remitted at the end of 2 weeks. As expected, a significantly higher proportion of patients receiving thrice weekly ECT remitted than in patients receiving once weekly ECT. Smaller post-seizure FD at first ECT is the only variable which predicted remission status after six ECTs. within the once weekly ECT group too, smaller post-seizure FD was associated with remission status. Conclusions: Post-seizure FD is proposed as a novel measure of seizure adequacy and predictor of treatment response. Clinical implications: Seizure measures at first ECT may guide selection of ECT schedule to optimize ECT. Limitations: The study examined short term antidepressant effects only. The results may not be generalized to medication-resistant depressives. (C) 1999 Elsevier Science B.V. All rights reserved.