An OpenMP version of the parallel algorithm for calculation of unsteady gas flow through porous objects with energy sources: Analysis and application

Gas flows in the gravity field through the porous objects with energy sources, which may originate from the natural or man-caused disasters, are investigated. An OpenMP version of the parallel algorithm has been developed for calculating unsteady 2D gas flows through porous self-heating media of complex subsurface geometries. The structure of the sequential algorithm and the transition from it to the OpenMP version are described; the performance and efficiency of parallelization are analyzed. Unsteady gas flows through axisymmetric porous self-heating objects with a partial closure of the object outlet (with a top cover) are investigated by means of the developed parallel algorithm. The influence of the partial closure of the object outlet on the cooling process of the porous objects with a nonuniform distribution of heat sources is analyzed.     

Scanning electron-microscopic study of the structureof oxidized “carbon — carbon” composite materials

Scanning electron microscopy is used to study the structure and failure process of “carbon—carbon” composites under the action of flows of gas containing oxygen. Failure is shown to be caused by the successive oxidation of the carbon matrix and the reinforcing fibers, giving rise to the collapse of the bond between the matrix and the fibers and, thus, to a weakening of the composite. Ways of increasing the heat resistance of the composites by building up an additional heat-resistant coating on the surface of articles made of the composites is proposed.     

Sorption-desorption hysteresis in fibrous silica gel (Santocel C) with isomeric monohydric aliphatic alcohols

By employing the quartz fibre spring technique, sorption-desorption hysteresis at 35° has been studied of Iso-propyl, Iso-Butyl, Sec-Butyl, Tert-Butyl, Active Amyl and Iso-Amyl alcohols on fibrous silica gel (Santocel C) activated at 250°. The isotherms of all the alcohols have clearly defined “knees”. By the application of BET theory, the monolayer capacities are determined. Knowing the specific surface area of fibrous silica gel, assuming oriented sorption of the isomeric alcohols with the OH group attached to surface; the cross-sections of the alcohol molecules are calculated. Excepting Iso-Propyl and Sec-Butyl alcohols, all others have cross-sections greater than that of normal aliphatic alcohols. These higher values are to be expected in view of the side CH₃ groups. The exceptional behaviour of Iso-Propyl and Sec-Butyl alcohols is not clear. Permanent and reproducible hysteresis loops have been obtained in all the cases. Cohan’s theory of hysteresis cannot explain the observations satisfactorily. Cavity theory however explains all the cases of hysteresis. The shapes of the isotherms of the different alcohols in the high relative vapour pressure region indicate a variation in contact angles of the alcohols.     

Acidity function in dipolar aprotic media

The H₀ acidity function has been determined for hydrochloric and trichloroacetic acids in dimethyl sulphoxide (DMSO) and acetonitrile using three amine class of indicators. The variation of H₀ with solvent composition at a fixed concentration of 0.1 M HCI in DMSO-water, acetonitrile-water and DMSO acetonitrile mixtures was also studied. Approximate medium effects on the proton in all these solvents were computed from the H₀ data and the results are discussed.     

Extendability of Contractible Configurations for Nowhere-Zero Flows and Modulo Orientations

Let H be a connected graph and G be a supergraph of H. It is trivial that for any k-flow (D, f) of G, the restriction of (D, f) on the edge subset E(G / H) is a k-flow of the contracted graph G / H. However, the other direction of the question is neither trivial nor straightforward at all: for any k-flow \((D',f')\) of the contracted graph G / H, whether or not the supergraph G admits a k-flow (D, f) that is consistent with \((D',f')\) in the edge subset E(G / H). In this paper, we will investigate contractible configurations and their extendability for integer flows, group flows, and modulo orientations. We show that no integer flow contractible graphs are extension consistent while some group flow contractible graphs are also extension consistent. We also show that every modulo \((2k+1)\)-orientation contractible configuration is also extension consistent and there are no modulo (2k)-orientation contractible graphs.     

A numerical study of an MPI/OpenMP implementation based on asynchronous threads for a three-dimensional splitting scheme in heat transfer problems

We present the results of a study of the parallel algorithms based on MPI and OpenMP for vector splitting schemes in heat transfer problems. We compare the three parallel implementations: MPI, “simple” MPI/OpenMP (#pragma omp directives applied to MPI-based code), and MPI/OpenMP with “postman” threads. The main idea of the last algorithm is to assign one thread within each computational node to perform the data transfer. This approach allows us to implement overlapping of useful computations and data transfer. The results show that the introducing postman threads can significantly improve the performance of an MPI/OpenMP implementation; nevertheless, for the considered class of numerical algorithms, it is more reasonable to use an MPI implementation.     

The Cuboid Lemma and Mal’tsev Categories

We prove that a regular category ? is a Mal’tsev category if and only if a strong form of the denormalised 3 × 3 Lemma holds true in ?. In this version of the 3 × 3 Lemma, the vertical exact forks are replaced by pullbacks of regular epimorphisms along arbitrary morphisms. The shape of the diagram it determines suggests to call it the Cuboid Lemma. This new characterisation of regular categories that are Mal’tsev categories (= 2-permutable) is similar to the one previously obtained for Goursat categories (= 3-permutable). We also analyse the “relative” version of the Cuboid Lemma and extend our results to that context.     

Thermodynamics of binary liquid mixtures

Excess volumes, V^E, of binary liquid mixtures (1) Toluene-Bromo-benzene, (2) Toluene-Nitrobenzene, (3) Toluene-Cyclohexanone, (4) Cyclo-hexane-Nitrobenzene, (5) Cyclohexane-Cyclohexanone were measured at 30° C. The results were analysed in terms of Flory’s theory. It is found that the theory, in general, is applicable to the mixtures studied.     

A simple proof of Ramanujan’s summation of the1ψ1

A simple proof by functional equations is given for Ramanujan’s₁ ψ ₁ sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.     

Pick Matricies and Quaternionic Power Series

It is well known that a non-constant complex-valued function f defined on the open unit disk \({\mathbb{D}}\) of the complex plane is an analytic self-mapping of \({\mathbb{D}}\) if and only if Pick matrices \({\left[ (1 - f(z_i)\overline{f(z_j)})/\right.\left.(1 - z_i\overline{z}_j)\right]_{i,j=1}^n}\) are positive semidefinite for all choices of finitely many points \({z_{i} \in \mathbb{D}}\) . A stronger version of the “if” part was established by Hindmarsh (Pac J Math 27:527–531, 1968): if all 3 × 3 Pick matrices are positive semidefinite, then f is an analytic self-mapping of \({\mathbb{D}}\) . In this paper, we extend this result to the non-commutative setting of power series over quaternions.     

Faraday rotation tensor-extraction of components

This paper reports methods of obtaining the components of Faraday rotation tenser in anisotropic crystals, using longitudinal and transverse Faraday rotation along the optic axis. It is found that in crystals belonging to triclinic, monoclinic and orthorhombic symmetry, one can get 6 out of 9, 3 or 4 out of 5, and 2 out of 3 components respectively. In the case of uniaxial crystals only 1 component can be obtained. By measuring Faraday rotation in a randomly oriented polycrystal one more component in all the above classes can be obtained.     

A cellular-automata model of population dynamics of three species of organisms in Lake Baikal

A cellular automata model of population dynamics of three species of organisms in Lake Baikal is proposed and investigated. Each species is subdivided into age and prey-predator groups. There are eight groups altogether. The model takes into account the spatial distribution of the organisms, seasonal birth rate variation, possible habitat pollution, and water streams. A computational experiment has been carried out for pollution in a southern area of Lake Baikal. It demonstrates that the population dynamics tends to an oscillating process with a period of one year. The minimum pollution at total extinction and maximum pollution not affecting the population dynamics are estimated. The model has been verified with production-to-biomass and occurrence frequency ratios.     

There exist no Ramanujan congruences mod 6912

Let τ(n) be Ramanujan's function, $$x\prod _{m = 1}^\infty (1 - x^m )^{24} = \sum\nolimits_{n = 1}^\infty {\tau (n)x^n .} $$ In this paper it is shown that the Ramanujan congruence τ(n)=σ_d/nd¹¹ mod 691 cannot be improved mod 691². The following result is proved: for arbitrary r, s mod 691 the set of primes such that p ≡ r mod 691,τ (p) ≡ p¹¹+1+691 · s mod 691² has positive density.     

Solas cycle theory of pulsars

The plausibility of the Solar Cycle type of mechanism for pulsar phenomenon is examined. The relevant time scales are found to be within the range of the observed pulsar periods.     

Averages of Ramanujan sums: note on two papers by E. Alkan

We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd’s, the Gamma function, the Bernoulli polynomials, and binomial coefficients.     

Measurements of total electron content over Ahmedabad and Bombay from Beacon satellite data

The paper outlines the method used at Ahmedabad for determining the total electron content in the ionosphere from differential Faraday rotations of plane polarised radio waves on 40.010 and 41.010 Mc./s. transmitted by NASA satellite 64-64A. The observations made during the period October 1964 to April 1965 are utilised to determine the diurnal variation of the total electron content up to the satellite height which was about 1,000 km. over Ahmedabad and Bombay latitudes. The curve of total electron content up to the satellite height shows similarity to the curve of maximum electron density at the F2 peak. The total electron contents over Bombay are in general higher than those over Ahmedabad.     

Vibrational spectra and normal vibrations of acetanilide and N-deuterated acetanilide

The Raman and infra-red spectra of acetanilide and N-methylacetamide and of their N-deuterated compounds have been recorded. The vibrational frequencies of acetanilide have been assigned and the nature of the Amide I, II and III bands in acetanilide and N-methylacetamide has been investigated by the study of the changes in the frequencies of these bands in the spectra of their deuterated compounds. Acetanilide and deuterated acetanilide molecules have been subjected to normal co-ordinate treatment and the mixing up of the skeletal frequencies arising out of the in-plane vibrations has been determined. These results indicate that as in secondary amides, the amide II and amide III bands in acetanilide are due to the combined contribution ofδ (NH) andν (C-N) vibrations, but the contribution ofν (C-N) to the amide II band is less in acetanilide and deuterated acetanilide than in cases of N-methylacetamide and deuterated N-methylacetamide.     

Some point set properties of merotopic spaces and their cohomology groups

Connectedness properties of merotopic spaces (resp. topological spaces, uniform spaces, metric spaces) and the relations to simplicial complexes and cohomology groups (these groups were defined in 1952 byC. H. Dowker [9]) are studied. Furthermore, a cohomological characterization of zero-dimensionality for proximity spaces is proved.