Supersymmetry, PT-symmetry and spectral bifurcation

We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by real units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces complex parametric shifts.     

Structural and photoluminescence studies on europium-doped lithium tetraborate(Eu:Li_2B_4O_7) single crystal grown by microtube Czochralski(μT-Cz) technique

Rare earth europium(Eu(3+))-doped lithium tetraborate(Eu:Li_2B_4O_7) crystal is grown from its stoichiometric melt by microtube Czochralski pulling technique(μT-Cz) for the first time. The grown crystals are subjected to powder x-ray diffraction(PXRD) analysis which reveals the tetragonal crystal structure of the crystals. UV–vis–NIR spectral analysis is carried out to study the optical characteristics of the grown crystals. The crystal is transparent in the entire visible region, and the lower cutoff is observed to be at 304 nm. The existence of BO_3 and BO_4 bonding structure and the molecular associations are analyzed by Fourier transform infrared(FTIR) spectroscopy. The results of excitation and emission-photoluminescence spectra of europium ion incorporated in lithium tetraborate(LTB) single crystal reveal that the observations of peaks at 258,297, and 318 nm in the excitation spectra and peaks at 579, 591, 597, 613, and 651 nm are observed in the emission spectra.The chromaticity coordinates are calculated from the emission spectra, and the emission intensity of the grown crystal is characterized through a CIE 1931(Commission International d'Eclairage) color chromaticity diagram.     

Dynamics of electronic motion in hydrogen atom under parallel strong oscillating magnetic field and intense laser fields

The mechanism of ionization of an H atom interacting with intense laser electric fields is altered when a strong, oscillating magnetic field is applied along a direction parallel to the laser field. In this first study, these two strongly nonperturbative situations have been combined together and the corresponding time‐dependent (TD) Schrödinger equation has been numerically solved without using any basis set. The electric field arising out of the magnetic field and the magnetic field arising out of the laser electric field are found to be negligibly small, thereby not affecting the results. There are two main, apparently counter‐intuitive results from this study of parallel fields of the same frequency but different field strengths: (1) In presence of an oscillating magnetic field, the ionization rate due to the laser field diminishes, and (2) increasing the laser intensity, keeping the magnetic field strength the same, makes the electron density ionize with a lesser rate, in contrast to the situation with intense lasers in the absence of a strong TD magnetic field. © 2015 Wiley Periodicals, Inc.     

Unraveling siRNA unzipping kinetics with graphene

Using all atom molecular dynamics simulations, we report spontaneous unzipping and strong binding of small interfering RNA (siRNA) on graphene. Our dispersion corrected density functional theory based calculations suggest that nucleosides of RNA have stronger attractive interactions with graphene as compared to DNA residues. These stronger interactions force the double stranded siRNA to spontaneously unzip and bind to the graphene surface. Unzipping always nucleates at one end of the siRNA and propagates to the other end after few base-pairs get unzipped. While both the ends get unzipped, the middle part remains in double stranded form because of torsional constraint. Unzipping probability distributions fitted to single exponential function give unzipping time (τ) of the order of few nanoseconds which decrease exponentially with temperature. From the temperature variation of unzipping time we estimate the energy barrier to unzipping.     

The Non-Collinearity Graph of the O+(8,2) Quadric Is Uniquely Geometrisable

The graph of the titlehas the points of the O⁺(8,2) polar space as itsvertices, two such vertices being adjacent iff the correspondingpoints are non-collinear in the polar space. We prove that, uptoisomorphism, there is a unique partial geometry pg(8,7,4)whose point graph is this graph. This is the partial geometryof Cohen, Haemers and Van Lint and De Clerck, Dye and Thas. Ouruniqueness proof shows that this geometry has a subgeometry isomorphicto the affine plane of order three, and the geometry is canonicallydescribeable in terms of this affine plane.     

Chern-Simons terms in string theories

The origin of Chern-Simons terms in string theories is clarified in a fermionic formulation of the closed bosonic strings. A connection is established between the induced Chern-Simons terms in 2+1 dimensional field theories and the ones appearing in the field strength tensor of the antisymmetric tensor field in string theories.     

Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph

The present study is concerned with the quantitative imaging of buoyancy-driven convection in a fluid medium that is confined in a horizontal differentially heated rectangular cavity. The horizontal surfaces of the cavity provide a temperature difference, for initiating convection in the fluid. The vertical side walls are thermally insulated. Three imaging techniques, namely laser interferometry, schlieren, and shadowgraph have been utilized. Experiments have been conducted in a cavity of length 447 mm and 32 mm vertical height. The cavity is square in cross-section, and the imaging direction is parallel to its longer side. Convection in air and water have been investigated. Temperature differences in the range of 5–50 K for air and 3–10 K for water have been employed in the experiments. Quantities of interest are the temperature profiles in unsteadiness in the thermal field. At lower temperature differences across the fluid region, temperatures as recorded by interferometry and schlieren are in good agreement with each other. Further, they match the numerical predictions, as well as correlations available in the literature. Imaging based on shadowgraph is not as satisfactory at lower temperature differences. At larger cavity temperature differences, the shadowgraph images become clear enough for quantitative analysis, but the flow becomes time-dependent. The three techniques reveal similar trends in terms of the spatial distribution of temperature gradients and the time scales of unsteadiness. The schlieren and shadowgraph are more suitable for high gradients and interferometry is suitable for low gradients and all these three techniques are not flow visualization tools alone but are appropriate for quantitative imaging of thermal field.     

A new perspective on single and multi-variate differential equations

We elaborate upon a new method of solving linear differential equations, of arbitrary order, which is applicable to a wide class of single and multi-variate equations. Our procedure separates the operator part of the equation under study in to a part containing a function of the Euler operator and constants, and another one retaining the rest. The solution of the equation is then obtained from the monomials (or the monomial symmetric functions, for the multi-variate case), which are the eigenfunctions of the Euler operator. Novel exponential forms of the solutions of the differential equations enable one to analyze the underlying symmetries of the equations and explore the algebraic structures of the solution spaces in a straightforward manner. The procedure allows one to derive various properties of the orthogonal polynomials and functions in a unified manner. After showing how the generating functions and Rodriguez formulae emerge naturally in this method, we briefly outline the generalization of the present approach to the multi-variate case.     

Photo-induced decolorization of dimethylmethylene blue with selenious acid: a novel method to examine selective monomer-dimer distribution of the dye in micelle

In this report, selenious acid (H2SeO3) has been exploited to study the decolorization of a cationic dye, dimethylmethylene blue (DMMB) with UV-light. Micelles have effectively been employed as organized media to promote the rate of decolorization of the dye molecules. Micellar catalysis has been explained as a consequence of electrostatic, hydrophobic and charge transfer interactions. It has also been shown that strong charge transfer and electrostatic interaction lead to an appreciable enhancement of the reaction rate in micelle, whereas, weak hydrophobic interaction is of marginal importance. Existence of monomer-dimer equilibrium for the dye molecules under certain selective environments has been identified spectrophotometrically. Then the shift of dimer-monomer equilibrium of the dye has been successfully studied in aqueous and micellar environments exploiting photodecolorization process for the dye in solution. 'Salting-in' and 'salting-out' agents were introduced into the reaction mixture to examine the viability of the dye decolorization process for dye contaminated water samples.