Analytic solution of nonlinear singularly perturbed initial value problems through iteration

This paper is concerned with singularly perturbed initial value problems for systems of ordinary differential equations. Here our emphasis will be on nonlinear phenomena and properties, particularly those with physical relevance. Since very few nonlinear systems can be solved explicitly, one must typically rely on a numerical scheme to accurately approximate the solution. However, numerical schemes do not always give accurate results, and we discuss the class of stiff differential equations, which present a more serious challenge to numerical analysts. In this paper, we derive in closed from, analytic solution of stiff nonlinear initial value problems, through iteration. The obtained sequence of iterates is based on the use of Lagrange multipliers. Moreover, the illustrative examples shows the efficiency of the method.     

Nuclease activity via self-activation and anticancer activity of a mononuclear copper(II) complex: novel role of the tertiary butyl group in the ligand frame

The copper complex [Cu((t)BuPhimp)(Cl)] (1) derived from tridentate ligand (t)BuPhimpH having N(2)O donors was synthesized, and its molecular structure was determined. A phenoxyl radical complex was generated in solution at room temperature using Ce(IV). The nuclease and anticancer activities of 1 were investigated. The roles of the tert-butyl group and singlet oxygen in the DNA cleavage activity were also discussed.     

Explicit all-atom modeling of realistically sized ligand-capped nanocrystals

We present a study of an explicit all-atom representation of nanocrystals of experimentally relevant sizes (up to 6 nm), "capped" with alkyl chain ligands, in vacuum. We employ all-atom molecular dynamics simulation methods in concert with a well-tested intermolecular potential model, MM3 (molecular mechanics 3), for the studies presented here. These studies include determining the preferred conformation of an isolated single nanocrystal (NC), pairs of isolated NCs, and (presaging studies of superlattice arrays) unit cells of NC superlattices. We observe that very small NCs (3 nm) behave differently in a superlattice as compared to larger NCs (6 nm and above) due to the conformations adopted by the capping ligands on the NC surface. Short ligands adopt a uniform distribution of orientational preferences, including some that lie against the face of the nanocrystal. In contrast, longer ligands prefer to interdigitate. We also study the effect of changing ligand length and ligand coverage on the NCs on the preferred ligand configurations. Since explicit all-atom modeling constrains the maximum system size that can be studied, we discuss issues related to coarse-graining the representation of the ligands, including a comparison of two commonly used coarse-grained models. We find that care has to be exercised in the choice of coarse-grained model. The data provided by these realistically sized ligand-capped NCs, determined using explicit all-atom models, should serve as a reference standard for future models of coarse-graining ligands using united atom models, especially for self-assembly processes.     

Viability of Noether Symmetry of F(R) Theory of Gravity

Recently, we have explored vices and virtues of $R^{\frac{3}{2}}$ term in the action which has in-built Noether symmetry and anticipated that a linear term might improve the situation (Sarkar et al., arXiv:1201.2987 [astro-ph.CO], 2012). In the absence of a conserved current it is extremely difficult to obtain an analytical solution of the said fourth order theory of gravity in the presence of a linear term. Here, we therefore enlarge the configuration space by including a scalar field in addition and also taking some of the anisotropic models (in the absence of a scalar field) into account. We observe that Noether symmetry remains obscure and it does not even reproduce the one that already exists in the literature (Sanyal, Gen. Relativ. Gravit., 37:407, 2005). However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar field (Sanyal, Phys. Lett. B, 624:81, 2005; Mod. Phys. Lett. A, 25:2667, 2010), which simplifies the field equations considerably. Here, we briefly expatiate the non-Noether conserved current and show that indeed the situation is modified.     

Concentration-dependent luminescence of Tb ions in high calcium aluminosilicate glasses

This study deals with the results on the concentration-dependent fluorescence properties of Tb³⁺-doped calcium aluminosilicate (CAS) glasses of composition (100−x)(58SiO₂–23CaO–5Al₂O₃–4MgO–10NaF in mol%)-x Tb₂O₃ (x=0, 0.25, 0.5, 1, 2, 4, 8, 16, 24, 32, 40 in wt%). The FTIR reflectance spectra suggested the role of dopant ions as network modifiers in the glass network. The fluorescence spectra of low Tb³⁺-doped glasses have revealed prominent blue and green emissions from ⁵D₃ and ⁵D₄ excited levels to ⁷F_j ground state multiplet, respectively. The glass with 2 wt% of Tb₂O₃ has exhibited maximum intensity of blue emission from ⁵D₃ level, while green emission from ⁵D₄ level has increased linearly up to 24 wt% and showed reduction in the rate of increase for higher Tb₂O₃ concentrations. The concentration quenching of blue emission (⁵D₃→⁷F_j) is attributed mainly to the resonant energy transfer (RET) assisted cross-relaxation (CR) among the excited and nearest neighbour unexcited Tb³⁺ ions in the glass matrix. The decline in rate of increase of green emission (⁵D₄→⁷F_j) at higher concentrations has been explained due to a possible occurrence of cooperative energy transfers leading to 4f⁸→4f⁷5d transition interactions. The blue and green emission decay kinetics have been recorded to compute the excited level (⁵D₃ and ⁵D₄) lifetimes, which confirmed the Tb³⁺ concentration quenching of the blue emission in these glasses.     

Non-minimally coupled dark fluid in Schwarzschild spacetime

If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid–gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in the presence of non-minimal coupling with a fluid, and find out the energy–density and pressure of the fluid. In the present case the perfect fluid is part of the solution of the modified Einstein equation. We also solve the modified Einstein equation, using the flat spacetime metric and show that in the presence of non-minimal coupling one can accommodate a perfect fluid of uniform energy–density and pressure in the flat spacetime. In both the cases the fluid pressure turns out to be negative. Except these non-trivial solutions it must be noted that the vacuum solutions also remain as trivial valid solutions of the modified Einstein equation in the presence of non-minimal coupling.     

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space–times that are seeded by galactic dark matter. To this end, we identify a class of space–times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space–time is seen to be the Bertrand space–time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two-fluid models, we show that our galactic space–times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.     

Performance study of unglazed cylindrical solar collector for adsorption refrigeration system

In the present communication, the unglazed cylindrical solar adsorber module is suggested for refrigeration and theoretical models for the heat and mass transfer in the cylindrical adsorber with heat balance equations in the collector components have been developed. It has been found that, both the SCP and COP_solar raises with increasing the evaporation temperature and drop off with the increase of the condensation temperature. The COP_solar increased from 0.15 to 0.52 with the increase of the total solar energy absorbed by the collector while the COP_cycle varied in the range of 0.57–0.73. The efficiency of unglazed solar collector varied from 36 to 44 %. The cost of current unglazed adsorption refrigeration system is compared with the glazed system, and it is 33 to 50 % less than the cost of glazed system.     

Simultaneous behaviour of the Fourier coefficients of two Hilbert modular cusp forms

Archiv der Mathematik - In this article, we study simultaneous sign changes of the Fourier coefficients of two Hilbert cusp forms of different non-parallel weights. We also study simultaneous...     

Solid-state decomposition studies on fluoroperoxo species of transition metals. Part VI. Kinetics of isothermal decomposition of M2Zr2(O2)2F6 · 2 H2O (M = Rb+, or Cs+)

The decomposition of solid fluoroperoxozirconates of alkali metals, M₂Zr₂(O₂)₂F₆ · 2 H₂O (M = Rb⁺, Cs⁺), is carried out in vacuum under isothermal conditions. The stoichiometry of the reaction may be represented by the equation, M₂Zr₂(O₂)₂F₆ · 2 H₂O(S) — M₂Zr₂O₂F₆(s) + O₂(g) + 2 H₂ O(g) (condensed). The fractional decomposition α is determined by measuring the pressure of oxygen evolved during pyrolysis with a McLeod gauge. The α values range from 0.06 to 0.70 for the rubidium and from 0.06 to 0.79 for the caesium species in the temperature ranges 107–202°C and 101–219°C, respectively. The α—time data for both compounds show that the kinetics are deceleratory throughout the course of the decomposition reaction. In both compounds, the initial stages of decomposition are described by a unimolecular decay law, while the later stages obey a contracting volume equation at all temperatures. The activation energies from Arrhenius plots are 14.0 and 10.9 kcal mole^?1 for the rubidium and 12.9 and 11.2 kcal mole^?1 for the caesium compound.