Local identities involving Jacobi elliptic functions

We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities. Second, we obtain a generalization to cyclic identities in which successive terms have a multiplicative phase factor exp(2iπ/s), wheres is any integer. Third, we systematize the local identities by deriving four local ‘master identities’ analogous to the master identities for the cyclic sums discussed by us previously. Fourth, we point out that many of the local identities can be thought of as exact discretizations of standard non-linear differential equations satisfied by the Jacobi elliptic functions. Finally, we obtain explicit answers for a number of definite integrals and simpler forms for several indefinite integrals involving Jacobi elliptic functions.     

Studies on the characterisation of l-proline thiourea monohydrate nonlinear optical single crystal

l-Proline thiourea monohydrate nonlinear optical single crystal of size 65 × 15 mm² was grown by slow evaporation technique at room temperature. The grown crystal was characterised by single crystal XRD, absorption spectrum, FTIR, EDAX, Vicker’s microhardness test, DSC, dielectric and photoconductivity studies. Second harmonic generation efficiency of the grown crystal makes it a higher order second harmonic material with good conversion efficiency. The reported crystal is an efficient nonlinear optical material with good optical transparency, thermal, mechanical strength and dielectric property.     

Hybrid density functional theory/molecular mechanics calculations of two-photon absorption of dimethylamino nitro stilbene in solution

The dimethylamino nitro stilbene (DANS) molecule is studied for exploring solvent effects on two-photon absorption using the quantum mechanical/molecular mechanical (QM/MM) response theory approach, where the quantum part is represented by density functional theory. We have explored the role of geometrical change of the chromophore in solution, the importance of taking a dynamical average over the sampled structures and the role of a granular representation of the polarization and electrostatic interactions with the classically described medium. The line shape function was simulated by the QM/MM technique thereby allowing for non-empirical prediction of the absolute two-photon cross section. We report a maximum in the TPA cross section for a medium of intermediate solvent polarity (i.e. in chloroform) and provide the grounds for an explanation of this effect which recently has been experimentally observed for a series of charge transfer species in solvents of different polarity. The calculations of absorption energies reproduce well the positive solvatochromic behavior of DANS and are in good agreement with experimental spectra available for the chloroform and DMSO solvents. In line with recent development of the QM/MM response technique for color modeling, we find this methodology to offer a versatile tool to predict and analyze two-photon absorption phenomena taking place within a medium.     

Sub wavelength multiple focal spot generation of high NA objective lens using diffractive optical element

In this article, based on the vector diffraction theory, the effect of specially designed phase modulating optical element by means of an incident tightly focused azimuthally polarized Bessel Gaussian beam in the focal region of high NA lens is investigated numerically. It is observed, that a specially designed diffractive optical modulation element (DOE) can generate multiple focal spot segment of transversely polarized in the focal region by controlling the angles of DOE. Such kind of sub wavelength transversely polarized focal spots segment may find wide applications in multiple optical traps and optical manipulation technology.     

Numerical simulation of the target system of an ADSS

The study of thermal–hydraulic issues related to target module of an accelerator driven sub-critical nuclear reactor system (ADSS) play a crucial role in its design. For this, one needs to analyze laminar/turbulent flow and heat transfer characteristics of lead bismuth eutectic (LBE), target cum coolant liquid, at low Prandtl number in the target system of an ADSS. In this work, equations governing conservation of mass, momentum and energy together with equations for kinetic energy and its dissipation rate are solved numerically using streamline upwind Petrov-Galerkin (SUPG)-finite element (FE) method in a two-dimensional axisymmetric ADSS target system. The transfer of kinetic energy and its dissipation rate are modeled using standard k ? ε equations with the wall function approach. The complex target module comprises a 180° turn-around flow along a straight flow guide and a window interfacing the proton beam interaction with LBE. The principal purpose of the analysis is to trace the flow structure in the domain and the temperature distribution on the window. Increasing flow rate to turbulent regime is seen to minimize the number of re-circulation or stagnation zones that may lead to the development of hot spots in the flow domain.     

Synthesis and Functional Characterization of Antibiofilm Exopolysaccharide Produced by Enterococcus faecium MC13 Isolated from the Gut of Fish

The synthesis and functional characterization of an antibiofilm exopolysaccharide (EPS) from a probiotic Enterococcus faecium MC13 were investigated. The temperature of 35 °C, pH of 6.5, and salinity of 1–2 % were found to be optimum for EPS production. The sucrose (30 g?l^?1) and yeast extract (20 g?l^?1) acted as suitable carbon and nitrogen sources, respectively, which strongly influenced EPS production with yield of 11.33 and 11.91 g?l^?1. Based on the thin layer chromatography, EPS of E. faecium MC13 was found to be a heteropolysaccharide, composed of galactose and glucose sugar units with a molecular mass of 2.0?×?10⁵?Da. Fourier transform infrared spectrum analysis of the EPS revealed many predominant functional groups including hydroxyl, carboxyl, and amide groups. EPS exhibited better emulsifying and flocculating activities which is relatively similar to those of commercial polysaccharides. In vitro antioxidant inspect of EPS showed lesser antioxidant activity than that of the control ascorbic acid. Thermal behavior of EPS was different from the other EPS produced by other lactic acid bacteria. In vitro antibiofilm assay of EPS exhibited significant biofilm inhibition, especially with Listeria monocytogenes. To the best of our knowledge, this is the first report on EPS of E. faecium with strong emulsifying and flocculating activities.     

Insulin immobilized PCL‐cellulose acetate micro‐nanostructured fibrous scaffolds for tendon tissue engineering

Use of growth factors as biochemical molecules to elicit cellular differentiation is a common strategy in tissue engineering. However, limitations associated with growth factors, such as short half‐life, high effective physiological doses, and high costs, have prompted the search for growth factor alternatives, such as growth factor mimics and other proteins. This work explores the use of insulin protein as a biochemical factor to aid in tendon healing and differentiation of cells on a biomimetic electrospun micro‐nanostructured scaffold. Dose response studies were conducted using human mesenchymal stem cells (MSCs) in basal media supplemented with varied insulin concentrations. A dose of 100‐ng/mL insulin showed increased expression of tendon markers. Synthetic‐natural blends of various ratios of polycaprolactone (PCL) and cellulose acetate (CA) were used to fabricate micro‐nanofibers to balance physicochemical properties of the scaffolds in terms of mechanical strength, hydrophilicity, and insulin delivery. A 75:25 ratio of PCL:CA was found to be optimal in promoting cellular attachment and insulin immobilization. Insulin immobilized fiber matrices also showed increased expression of tendon phenotypic markers by MSCs similar to findings with insulin supplemented media, indicating preservation of insulin bioactivity. Insulin functionalized scaffolds may have potential applications in tendon healing and regeneration.     

Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a random real and a random complex state. Our results are relevant to the entanglement properties of eigenvectors of the orthogonal and unitary ensembles of random matrix theory and quantum chaotic systems. They also provide a rare exactly solvable case for the distribution of the minimum of a set of N strongly correlated random variables for all values of N (and not just for large N).     

Numerical simulation of thermal hydraulics in an ADSS model

Accelerator Driven Sub-critical nuclear reactor Systems (ADSS) are envisaged to enhance neutronics of reactors as well as safety physics. The spallation target module is the most innovative and key component for an ADSS. A conjugate heat transfer analysis is accomplished to mimic the physical operating condition of an ADSS in a more realistic way. The conduction equation of the beam window is solved in conjunction with the energy equation using the paradigm of domain decomposition parallelization method and the temperature distribution along the beam window is found. Finally, the thermal and mechanical stresses along the radial direction on the beam window is determined using temperature and pressure values. The stress values are found to increase with increasing Reynolds number (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)