Spatiotemporal pattern formation in a diffusive predator-prey system: an analytical approach

In this paper, we propose and analyse a mathematical model to study the mathematical aspect of reaction diffusion pattern formation mechanism in a predator-prey system. An attempt is made to provide an analytical explanation for understanding plankton patchiness in a minimal model of aquatic ecosystem consisting of phytoplankton, zooplankton, fish and nutrient. The reaction diffusion model system exhibits spatiotemporal chaos causing plankton patchiness in marine system. Our analytical findings, supported by the results of numerical experiments, suggest that an unstable diffusive system can be made stable by increasing diffusivity constant to a sufficiently large value. It is also observed that the solution of the system converges to its equilibrium faster in the case of two-dimensional diffusion in comparison to the one-dimensional diffusion. The ideas contained in the present paper may provide a better understanding of the pattern formation in marine ecosystem.     

An e.p.r. study of tetradentate Schiff base copper complexes with an N–(CH2)n–N,n = 3–6 backbone

Cu^II complexes of Schiff-base ligands with a general formulation o-HOC₆H₄CH=N–(CH₂) _n –N=CHC₆H₄OH-o, where n = 3–6 have been prepared and their e.p.r. spectra investigated in order to determine the effect of the flexible methylene backbone length on the structure. The room temperature and 77 K e.p.r. spectra of the compounds, n = 3 and 4, are typical of the axially symmetric ground state with g > g . When n = 5, on the other hand, the complex gives an isotropic spectrum at room temperature. For n = 6, g appears to be greater than g . The g _iso value increases gradually from n = 3 to n = 6 indicating deviation from planarity. Simulation of the 77 K spectrum for n = 6 shows the presence of two distinct Cu²⁺ sites of equal probability. The Q-band spectrum of this compound exhibits a narrowed g signal indicative of exchange coupling. The spectrum is a consequence of intermolecular electron exchange giving a pseudo d² _z state.     

MHD slow motion past a sphere

The slow motion of an incompressible, viscous electrically conducting fluid, in the presence of a uniform aligned magnetic field, past a sphere is studied. Solutions obtained by Chester, using Stokes’ approximations, and by Blerkom and Ludford, using Ossen’ approximations, are reviewed. Expressions for stream functions are obtained for MHD Stokes’ flow and Oseen’ flow respectively.     

Equilibrium studies on binary and ternary Cu(II) complexes containing ethylenediaminediacetic acid and a series of O?-O?, N-O? and N-N donor ligands

The formation constants for ternary metal complexes (MLA) where L = ethylenediaminediacetic acid (EDDA), M = Cu(II) and A = glycine, alanine, leucine, serine, threonine, methionine, proline, phenylalanine, tryptophan, histidine, aspartic acid, ethylenediamine, histamine, 2,2′-bipyridyl, 1,10-phenanthroline, imidazole, oxalic acid, malonic acid, pyrocatechol and nitropyrocatechol have been investigated by pH-metric method at 35°C andμ = 0.2 M (KNO₃). With respect to the donor atoms on ligand A, the stabilities of the ternary complexes increase in the order O⁻-O⁻ < N-O⁻≈N-N. The stabilities of the various ternary complexes decrease with the increasing number of carboxylate groups on the ligand in the order ethylenediamine (EN) < ethylenediamine monoacetic acid (EDMA) < EDDA. Various factors influencing the formation and stabilities of ternary complexes are discussed.     

Evaluation of photoelastic constants from first-order Raman intensities of MgF2

A formalism to connect first-order Raman intensities of MgF₂ and its photoelastic constants is developed by developing a method of writing internal coordinates in terms of displacement gradientsu _ij which are not symmetric. It is found that for crystals containing only one line inA ₁ species, the ratiosP ₁₃/P ₃₃ and (P ₁₁ +P ₁₂)/P ₃₁ can be directly evaluated from the intensities, without having to derive the intensity formulae; while (P ₁₁ +P ₁₂)/P ₁₃ is independent of the intensities as well as the refractive index of the crystal. It is a function of only the dimensional parameters. In this crystal, since the speciesB _1g andB _2g also contain only one line each, the ratio (P ₁₁ −P ₁₂)/P ₆₆ can also be directly obtained from the intensities.     

Theoretical study of nematic to smectic transition in cylindrical porous media

Experimental observations show that the nematic–isotropic (N–I) transition temperature (T_NI) and nematic to smectic transition temperature (T_NA) for liquid crystal (LC) embedded in solid porous materials is lower compared to that of the bulk LC. To explain this, various theoretical studies have been proposed. We propose to use the mean field approach considering cylindrical pores. We have earlier modified the Maier–Saupe (M–S) mean field theory to include the disordering effects of porosity as a disordering surface potential. A molecule near the surface is assumed to feel the mean field potential (M–S type) and also the surface induced potential. Our earlier calculations of extension of M–S theory on the variation of T_NI with pore diameter agree with experimental data. In the present article, we propose the extension of McMillan theory to include the disordering effects of porosity as a disordering surface potential. Our calculations on the variation of TNA with different pore diameters agree qualitatively with experimental data.     

Synthesis,characterization, and catalytic oxidation of styrene,cyclohexene, allylbenzene,and cis-cyclooctene by recyclable polymer-grafted Schiff base complexes of vanadium(IV)

Schiff base-functionalized chloromethylated polystyrenes, PS-[Ae-Eol] (I), PS-[Hy-Eda] (II) and PS-[HyP-Eda] (III), were synthesized by reacting 2-(2-aminoethoxy)ethanol (Ae-Eol), N-(2-hydroxyethyl)ethylenediamine (Hy-Eda), and N-(2-hydroxpropyl)ethylenediamine (HyP-Eda) with oxidized chloromethylated polystyrene. Oxidized chloromethylated polystyrene (PS-CHO) was prepared by oxidation of chloromethylated polystyrene (PS) with sodium bicarbonate in DMSO. By reacting DMSO solution of [VO(acac)₂] with polymer-anchored Schiff base ligands I, II, and III, vanadium(IV) complexes PS-[V^IVO(Ae-Eol)] (1), PS-[V^IVO(Hy-Eda)] (2), and PS-[V^IVO(HyP-Eda)] (3) were prepared. Structure and bonding of I, II, and III as well as corresponding vanadium complexes 1, 2, and 3 were confirmed by FT-IR, UV–vis spectroscopy, SEM, EDX, AAS, TGA, EPR, etc. Polymer-anchored vanadium(IV) complexes 1, 2, and 3 show, efficient catalysis toward oxidation of styrene, cyclohexene, allylbenzene, and cis-cyclooctene in the presence of hydrogen peroxide. Optimized reaction conditions for the oxidation of these alkenes was achieved by changing various reaction parameters (like amount of catalyst, amount of oxidizing agent, volume of solvent, etc.). Polymer-grafted 1, 2, and 3 can be reused multiple times without depletion of their activity.