Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption

We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745].     

Topological defects and cosmology

Many particle physics models of matter admit solutions corresponding to stable or long-lived topological defects. In the context of standard cosmology it is then unavoidable that such defects will form during phase transitions in the very early Universe. Certain types of defects lead to disastrous consequences for cosmology, others may play a useful role, as possible seeds for the formation of structure in the Universe, or in mediating baryon number violating processes. In all cases, topological defects lead to a fruitful interplay between particle physics and cosmology.     

The spin density distribution in some phenyl substituted imidazyl and pyrryl radicals

ENDOR spectroscopy has been used to interpret the E.S.R. spectra of the 2,4,5-triphenylimidazyl, tetraphenylpyrryl, tetrakis (p-tolyl) pyrryl, tetrakis (p-anisyl) pyrryl radicals. Using the hyperfine coupling constants thus obtained in conjunction with a McLachlan-type HMO calculation the spin density distribution in these radicals is calculated. The configuration of the phenyl rings and the deviation of their bond lengths from hexagonal symmetry is inferred from the MO parameters required to fit the experimental couplings.     

Studies of Hindered Rotation and Magnetic Anisotropy by 1H, 13C and 19F NMR. The Diels-Alder Adduct of N- Pentafluorophenylmaleimide and Phencyclone: A Model for Drugs.

The potent Diels-Alder diene, phencyclone, 1, reacts with N-pentafluorophenylmaleimide, 2, to form an adduct, 3, characterized by ¹H, ¹³C, and ¹⁹F NMR at 300, 75 and 282 MHz, respectively. The one-dimensional (1D) and two-dimensional (2D) ¹H and ¹³C NMR spectra of 3 at ambient temperatures imply a slow exchange limit (SEL) regime with respect to rotation of the unsubstituted bridgehead phenyl groups about severely hindered C(sp²)-C(sp³) bonds. Major non-bonded interactions are expected between the ortho protons of the C₆H₅ groups and H-1, 8 of the phenanthrenoid moiety of 3. ¹⁹F 1D and 2D (COSY) NMR spectra show that the SEL regime also obtains for rotation about the N-C₆F₅ bond of 3, with five separate fluorine signals seen, consistent with a preferred conformation in which the C₆F₅ may lie roughly perpendicular to the plane of the pyrrolidinedione moiety, and may be in the mirror symmetry plane of 3. The results are considered relevant to hindered aryl rotations in numerous Pharmaceuticals. Selected spectral data for 2 and precursors are also presented.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.     

Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard Metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model.     

Symplectic integration of Hamiltonian wave equations

Summary The numerical integration of a wide class of Hamiltonian partial differential equations by standard symplectic schemes is discussed, with a consistent, Hamiltonian approach. We discretize the Hamiltonian and the Poisson structure separately, then form the the resulting ODE's. The stability, accuracy, and dispersion of different explicit splitting methods are analyzed, and we give the circumstances under which the best results can be obtained; in particular, when the Hamiltonian can be split into linear and nonlinear terms. Many different treatments and examples are compared.     

Extensions of the Levine-Nahikian method for constructing involutory matrices

Various characterizations for sums of matrices over arbitrary fields to be involutions are established. Applications of these results in constructing involutions of matrices with elements from finite fields are considered.     

A simple version of Karzanov's blocking flow algorithm

Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n ? 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the best time bound known for the blocking flow problems is O(n²). Karzanov devised the first O(n²)-time blocking flow algorithm, which unfortunately is rather complicated. Later Malhotra, Kumar and Maheshwari devise another O(n²)-time algorithm, which is conceptually very simple but has some other drawbacks. In this paper we propose a simplification of Karzanov's algorithm that is easier to implement than Malhotra, Kumar and Maheshwari's method.