Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method

In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the decomposition series solutions. The numerical results display that the Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.     

A convenient computational form for the Adomian polynomials

Recent important generalizations by G. Adomian (“Stochastic Systems”, Academic Press 1983) have extended the scope of his decomposition method for nonlinear stochastic operator equations (see also iterative method, inverse operator method, symmetrized method, or stochastic Green's function method) very considerably so that they are now applicable to differential, partial differential, delay, and coupled equations which may be strongly nonlinear and/or strongly stochastic (or linear or deterministic as subcases). Thus, for equations modeling physical problems, solutions are obtained rapidly, easily, and accurately. The methodology involves an analytic parametrization in which certain polynomials A_n, dependent on the nonlinearity, are derived. This paper establishes simple symmetry rules which yield Adomian's polynomials quickly to high orders.     

Travel Distance Through Transportation Terminals on a Rectangular Grid

The number of terminals used in a transportation network affects inventory, transportation and overhead costs. With few terminals, overhead and inventory costs tend to be small, but average travel distance through terminals is large. With many terminals, overhead and inventory costs are large, but average travel distance is small. As a first step toward analyzing this trade-off, this paper develops equations that quantify the relation between number of terminals and average travel distance. These equations are verified by applying them to an example involving the 37 largest cities in the United States. Average travel distance is shown to decrease slowly as the number of terminals increases, declining by no more than one third. Although adding terminals decreases travel distance somewhat, the marginal travel distance reduction quickly becomes quite small.     

Sparse matrix multiplication package (SMMP)

Routines callable fromFortran and C are described which implement matrix-matrix multiplication and transposition for a variety of sparse matrix formats. Conversion routines between various formats are provided.The algorithms and routines described here were developed while both authors were visiting the Center for Applied Mathematics, Department of Mathematics, Purdue University. This research was supported in part by the Office of Naval Research, Grant No. N00014-895-1440.     

Coupled differential equations and coupled boundary conditions

It is demonstrated that the high accuracy for approximations requiring only a few terms which is typical of the decomposition method for nonlinear stochastic operator equations, or special cases (linear or deterministic), holds for coupled equations and coupled boundary conditions as well.     

Molecular valence calculations on cyclohexasulfur,cycloheptasulfur, and cyclooctasulfur

A theoretical study of homocyclic sulfur species S₆, S₇, and S₈ was carried out using a molecular valence method involving stepwise approximations for orthogonality and core-valence interactions. The valence shell orbitals are described at the minimal basis level. The geometries of the molecules are predicted well as compared with other theoretical studies and the experimental values. The slight overestimation of the SS bond length is typical to the nonpolarized basis sets. The energies of the valence orbitals are well in accord with the conventional all-electron ab initio results. The trend in the stabilities of the three molecules is discussed. The present method provides an attractive possibility to study homocyclic and heterocyclic systems involving heavier chalcogens with no increase of the computing time.     

A time-differential measurement of the hyperfine structure of the 6.13 MeV state in highly ionized 16O atoms

A time-differential technique has been developed which makes possible the observation of time dependent effects produced by hyperfine interactions in highly ionized atoms during recoil into vacuum. Theoretical and experimental considerations of the technique are discussed and a value for |g_I| of 0.55 ± 0.03 has been obtained for the 6.13 MeV (3^?) state of ¹⁶O.     

Core-shell nanoparticles: characterization and study of their use for the encapsulation of hydrophobic fluorescent dyes

Core-shell nanocapsules intended to be used as drug scavengers were prepared using a surfactant mixture containing octadecyltrimethoxysilane (OTMS) as a reactive amphiphile, to form spherical templates. A siloxane shell was grown on the surface of the templates by reacting tetramethoxysilane (TMOS) with the silanol groups obtained after the hydrolysis and condensation of OTMS. Dynamic light scattering (DLS) showed that particles with diameters in the range of 100-200 nm were obtained, with core and shell sizes controlled by varying component compositions. Atomic force microscopy (AFM) was used to study the effect of the silica coating of the templates on their robustness after deposition on a substrate. Subsequently, we present studies on the encapsulation of two hydrophobic fluorescent dyes, which are sensors of polarity and rigidity. Steady-state fluorescence spectroscopy was used to examine the fluorescence response of the dyes before and after shell growth. Changes in the emission of the encapsulated dyes were related to changes in the polarity and rigidity of the microenvironment where the dyes were located and correlated to the AFM results. Finally, dye-free core-shell particles were used to sequester the dyes from aqueous suspensions. Fluorescence of the sequestered species was compared to the dye-loaded particles to determine the final fate of the fluorophores in the nanoparticles.