Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Growth and characterization of some novel crystals for nonlinear optical applications

The advent of high intensity lasers coupled with the recent advances in crystal technology has led to rapid progress in the field of nonlinear optics. This article traces the history of materials development that has taken place over the past forty odd years and dwells on the current status in this important area. The materials aspect is discussed under three classes viz. inorganic, organic and semiorganic crystals. In the end, some of the crystal growth work that has been carried out in author's laboratory is presented.

Hydrogen-bond-directed self-assembly of D-(+)-dibenzoyltartaric acid and 4-aminopyridine: optical nonlinearities and stoichiometry-dependent novel structural features

Attempts to prepare hydrogen-bond-directed nonlinear optical materials from a 1:1 molar mixture Of D-(+)-dibenzoyltartaric acid (DBT, I) and 4-aminopyridine (4-AP, II) resulted in two salts of different stoichiometry. One of them crystallizes in an unusual 1.5:1 (acid:base) monohydrate salt form III while the other one crystallizes as 1:1 (acid:base) salt IV. Crystal structures of both of the salts were determined from single-crystal X-ray diffraction data. The salt III crystallizes in a monoclinic space group C2 with a = 30.339(l), b = 7.881(2), c = 14.355(1) angstrom, beta = 97.48(1)degrees, V = 3403.1(9) angstrom3, Z = 4, R(w) = 0.058, R(w)= 0.058. The salt IV also crystallizes in a monoclinic space group P2(1) with a = 7.500(1), b = 14.968(2), c = 10.370(1) angstrom, beta = 102.67(1)degrees, V = 1135.9(2) angstrom3, Z = 2, R = 0.043, R(w) = 0.043. Interestingly, two DBT molecules with distinctly different conformation are present in the same crystal lattice of salt III. Extensive hydrogen-bonding interactions are found in both of the salts, and both of them show SHG intensity 1.4-1.6 times that of urea.

Optical absorption and photoluminescence studies of Nd3 doped alkali boro germanate glasses

Optical absorption and photoluminescence studies have been carried out at room temperature in 25 R2O-25 GeO2-49.5 B2O3-0.5 Nd2O3 glass systems, (Composition in mol%, R= Li, Na, K and Rb). Judd Ofelt Intensity parameters and other parameters like Racah (E-1, E-2 and E-3), Slater-Condon-Shortley (F-2, F-4 and F-6) Spin-Orbit Coupling (xi(4f)) and Configuration Interaction (alpha,beta and gamma) for Nd3+ ion in the glass system are calculated. The variation of the 02 parameters are interpreted in terms of the covalency of the RE ion in the glass matrix. Further the hypersensitive transition I-4(9/2) -> (4)G(5/2), (2)G(7/2) is analyzed with respect to the intensity ratio I-L/I-S and is found to be dependent on the type of alkali in the glass matrix. The Photoluminescence studies do not show any appreciable shift in the peak emission wavelength of the F-4(3/2) to I-4(11/2) transition with the change in alkali type. (C) 2010 Elsevier B.V. All rights reserved.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a time-varying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme [Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Physical characterization of the organic nonlinear optical crystal � 3-methoxy 4-hydroxy benzaldehyde

We highlight our recent experimental work on an efficient molecular nonlinear optical crystal, 3-methoxy 4-hydroxy benzaldehyde (MHBA). Optical quality single crystals of MHBA were grown from mixtures of solvents and from melt. The overall absorption and transparency window were improved by growing them in a mixture of chloroform and acetone. The grown crystals were characterized for their optical transmission, mechanical hardness and laser damage. We have observed a strong correlation between mechanical properties and laser induced damage.

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Linear optical properties of BaNaB9O15, BaLiB9O15 and SrLiB9O15 glasses

Transparent BaNaB9O15 (BNBO), BaLiB9O15 (BLBO) and SrLiB9O15 (SLBO) glasses were fabricated via the conventional melt-quenching technique. X-ray diffraction (XRD) and Differential thermal analysis (DTA) studies carried out on the as-quenched glasses confirmed their amorphous and glassy nature, respectively. The optical properties for these as-quenched glasses were investigated. The refractive index, optical band gap. Urbach energy and Fermi energy were determined. The average electronic polarizability calculated from the refractive index expression. (C) 2011 Elsevier B.V. All rights reserved.

Soft-chemical synthesis of new non-linear optical materials, K0.5M0.5Ti0.5OPO4(M = Nb, Ta),related to KTiOPO4

Soft-chemical oxidation of KTiOPO4-like KM(0.5)(V)Ti(0.5)(III)OPO(4) (M = Nb, Ta) using chlorine in CHCl3 is accompanied by partial deintercalation of potassium, yielding K(0.5)MV(0.5)Ti(0.5)(IV)OPO(4) compounds which are new non-linear optical materials that exhibit efficient second-harmonic generation of 1064 nm radiation, as does KTiOPO4.

Solvothermal synthesis of Hg1-xCdxTe nanostructures-Their structural and optical properties

This article describes a facile, low-cost, solution-phase approach to the large-scale preparation of Hg1-xCdxTe nanostructures of different shapes such as nanorods, quantum dots, hexagonal cubes of different sizes and different compositions at a growth temperature of 180 degrees C using an air stable Te source by solvothermal technique. The XRD spectrum shows that the crystals are cubic in their basic structure and reveals the variation in lattice constant as a function of composition. The size and morphology of the products were examined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The formation of irregular shaped particles and few nano-rods in the present synthesis is attributed to the cetyl trimethylammonium bromide (CTAB). The room temperature FTIR absorption and PL studies for a compositon of x = 0.8 gives a band gap of 1.1 eV and a broad emission in NIR region (0.5-0.9 eV) with all bands attributed to surface defects.

Lanthanide Sulfate Frameworks: Synthesis, Structure, and Optical Properties

Layered lanthanide sulfate compounds with three different structures have been prepared and characterized. The compounds C10H10N2] La(SO4)(2)]center dot 2H(2)O (I), C10H10N2] La(SO4)(2)(H2O)(2)](2) (Ha), C10H10N2]Pr(SO4)(2)(H2O)(2)](2) (IIb), C10H10N2]Nd-2(SO4)(4)(H2O)(2)](2) (IIIa), C10H10N2]Sm-2(SO4)(4)(H2O)(2)](2) (IIIb), and C10H10N2]Eu-2(SO4)(4)(H2O)(2)] 2 (IIIC) have anionic lanthanide sulfate layers separated by protonated bipyridine molecules. The layers are formed by the connectivity between the lanthanide polyhedra and sulfate tetrahedra. The formation of a two-dimensional La-O-La layer (la), Pr-O-Pr chains (IIb), and a tetramer cluster (IIIa) is noteworthy. The compounds exhibit honeycomb (I), square (IIa, IIb), and honeycomb (IIIa-IIIc) net arrangements, when the connectivity between the lanthanide ions is considered. Optical studies indicate the observation of characteristic metal-centered emission at room temperature. The Nd compound (IIIa) exhibits a two-photon upconversion behavior.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions

Bloch-Nordsieck thermometers: One-loop exponentiation in finite temperature QED

We study the scattering of hard external particles in a heat bath in a real-time formalism for finite temperature QED. We investigate the distribution of the 4-momentum difference of initial and final hard particles in a fully covariant manner when the scale of the process, Q, is much larger than the temperature, T. Our computations are valid for all T subject to this constraint. We exponentiate the leading infra-red term at one-loop order through a resummation of soft (thermal) photon emissions and absorptions. For T > 0, we find that tensor structures arise which are not present at T = 0. These carry thermal signatures. As a result, external particles can serve as thermometers introduced into the heat bath. We investigate the phase space origin of log (Q/M) and log (Q/T) terms.

Design of logical topologies for wavelength-routed optical networks

his paper studies the problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology, The physical topology consists of the nodes and fiber links in the network, On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics, The set of lightpaths along with the nodes constitutes the logical topology, For a given network physical topology and traffic pattern (relative traffic distribution among the source-destination pairs), our objective is to design the logical topology and the routing algorithm on that topology so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology), We will see that ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays, On the other hand, in all our examples, imposing it results in a minimal increase in congestion, While the number of wavelengths required to imbed the resulting logical topology on the physical all optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small, We formulate the combined logical topology design and routing problem described above (ignoring the constraint on the number of available wavelengths) as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network, Since this programming problem is computationally intractable for larger networks, we split it into two subproblems: logical topology design, which is computationally hard and will probably require heuristic algorithms, and routing, which can be solved by a linear program, We then compare the performance of several heuristic topology design algorithms (that do take wavelength assignment constraints into account) against that of randomly generated topologies, as well as lower bounds derived in the paper.