Convergence of the phase-field equations to the mullins-sekerka problem with kinetic undercooling

I prove that the solutions of the phase-field equations, on a subsequence, converge to a weak solution of the Mullins-Sekerka problem with kinetic undercooling. The method is based on energy estimates, a monotonicity formula, and the equipartition of the energy at each time. I also show that for almost all t, the limiting interface is (d – 1)-rectifiable with a square-integrable mean-curvature vector.Dedicated to Mort Gurtin on the occasion of his sixtieth birthday     

Kantowski-Sachs Cosmological Model in General Theory of Relativity

The field equations for perfect fluid coupled with massless scalar field are solved with two conditions p=ρ and R=AS ⁿ for Kantowski-Sachs space time in general theory of relativity. Various physical and geometrical properties of the model have also been discussed.     

Mathematical Modeling and Simulation of a Flexible Shaft-Flexible Link System With End Mass

In this study, the equation of motion of a single link flexible robotic arm with end mass, which is driven by a flexible shaft, is obtained by using Hamilton's principle. The physical system is considered as a continuous system. As a first step, the kinetic energy and the potential energy terms and the term for work done by the nonconservative forces are established. Applying Hamilton's principle the variations are calculated and the time integral is constructed. After a series of mathematical manipulations the coupled equations of motion of the physical system and the related boundary conditions are obtained. Numerical solutions of equations of motion are obtained and discussed for verification of the model used.     

Oxidative coupling as a biomimetic approach to the synthesis of scytonemin

The first total synthesis of the dimeric alkaloid pigment scytonemin is described. The key transformations in its synthesis from 3-indole acetic acid are a Heck carbocyclization and a Suzuki-Miyaura cross-coupling, orchestrated in a stereospecific tandem fashion, followed by a biosynthetically inspired oxidative dimerization. The tandem sequence generates a tetracyclic (E)-3-(arylidene)-3,4-dihydrocyclopenta[b]indol-2(1H)-one that is subsequently dimerized into the unique homodimeric core structure of scytonemin.     

Synthesis and Optical Characterization of Red-Emitting BaTa<Subscript>2</Subscript>O<Subscript>6</Subscript>:Eu<Superscript>3+</Superscript> Phosphors

Undoped and Eu³⁺ doped BaTa₂O₆ phosphors were synthesized via solid state reaction method and characterized by using XRD, SEM-EDS and photoluminescence (PL) analyses. The XRD results revealed that the crystal structure of BaTa₂O₆ allowed up to 10 mol% levels of Eu³⁺ ions due to the TTB characteristic network of adjacent octahedrals. SEM-EDS analyses confirmed the formation of BaTa₂O₆ structure and EuTaO₄ secondary phase. BaTa₂O_6:Eu³⁺ phosphors exhibited orange and red emissions at 592.2 nm and 615.7 nm in the visible region respectively. The Commission Internationale d’Eclairage (CIE) chromaticity coordinates of the BaTa₂O_6:Eu³⁺ phosphors that excited at λ _ex = 400 nm ranged from orangish-red to pinkish-red depending on increasing Eu³⁺ concentration.     

Trace element study of kidney stones from subjects belonging to stone belt region of India

Kidney stones obtained from six patients belonging to the stone belt region of India (Punjab) were analyzed for inorganic constituents using instrumental neutron activation analysis (INAA) and energy dispersive X-ray fluorescence (EDXRF) techniques. For INAA, samples were irradiated along with IAEA RM Soil 7 as reference standard in CIRUS reactor, BARC, Mumbai. Gamma activity of irradiated samples was measured using a 45% relative efficiency HPGe detector coupled to 8?k channel analyzer. EDXRF method was used for determination of concentration of Ca. The concentrations of ten elements namely Ca, Na, K, Mn, Co, Cr, Zn, Br, Sm and Cl, are reported and discussed.