Farooq Ahmad

Statistical Mechanics of the Cosmological Many-Body Problem. II. Results of Higher Order Contributions

We calculate the irreducible triplet contribution to galaxy clustering in the cosmological many-body problem. These triplets generally represent short-lived configurations in which three close objects interact with pairwise gravitational forces. From the resulting grand canonical partition function, we obtain higher order analytical expressions for thermodynamic quantities such as specific heats, isothermal compressibility, and thermal expansion in the system. Compared with previous analyses, which included reducible but not irreducible triplets, the additional terms are usually small, especially in the limit of large N. This confirms the thermodynamic results. We also derive the modified spatial distribution functions and show that they agree with recent observational results. The inclusion of triplet and higher order irreducible clusters does not significantly modify the results of the reducible terms in the partition function or of its thermodynamic consequences such as the distribution function.

DISTRIBUTION FUNCTION OF GALAXIES FOR TWO-COMPONENT SYSTEMS

We extend the statistical mechanical theory of cosmological many-body problem to a system consisting of two kinds of galaxies with different masses. The general partition function for such a two-component system, in the grand canonical ensemble, is developed. From this partition function various thermodynamical quantities and distribution functions are evaluated. A quantity bm, called the clustering parameter for the two-component system, which inherently takes into account the ratio of the number of particles (galaxies) of each kind and their masses, emerges directly from the calculations. Various clustering phenomena can be explained on the basis of this parameter. We find these results in agreement with the available N-body simulation results as well as the observational distribution function determined from the 2MASS survey. Besides, our distribution function, for the two-component system, makes these comparisons more objective and easily comprehensible.

Transesterification of oil extracted from different species of algae for biodiesel production.

In the current study, biodiesel production efficiency of C hlorella vulgaris, Rhizoclonium hieroglyphicum and mixed algae culture was measured by transesterification process. Growth rate of algal species was measured on the basis of increase in their dry matter in various media. Protein, carbohydrates and lipids in all selected algae were measured on dry matter basis. Extracted oil was analyzed for water contents, iodine value, saponification value, acid number and fatty acid composition. Transesterification of algal oil was performed by using sodium methoxide as a catalyst. Yield of biodiesel from extracted oil was calculated for C. vulgaris (95%), R. hieroglyphicum (91%) and mixed algae culture (92%). Produced biodiesel was analyzed for kinematic viscosity (4.9, 5.0 and 4.7 mm2/s), flash point (160, 156 and 155°C), specific gravity (0.91, 0.914 and 0.912 g/ml), cetain number (51, 49 and 47 min), iodine value (47, 53 and 49 mg/g), acid number (0.49, 0.5 and 0.46 mg.KOH/g), carbon residue (0.01, 0.02 and 0.01 mass%), sulfated ash (0.007, 0.003 and 0.004 mass%), sulphur (0.013, 0.012 and 0.01 wt%) and water contents (15, 23 and 17 mg/kg) for C. vulgaris, R. hieroglyphicum and mixed algae culture, respectively. Properties of biodiesel were compared with ASTM standards and it was found with high quality biodiesel. Key words: Biodiesel, oil extraction, algae, transesterification.

Extended structure of galaxies and cosmic energy equation

We derive the cosmic energy equation for extended mass structures (i.e., galaxies with halos) which cluster gravitationally in the expanding universe. From this cosmic energy equation, we study the quasi-static evolution for nonpoint mass system of galaxies. Using this cosmic energy equation, we examine the growth of correlation potential energy for the extended masses. We also derive the expression for virial mass and try to account for the dark matter present in the halos of the galaxies.

Gravitational Clustering of Galaxies in an Expanding Universe

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of thermodynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in combination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem.

Gravitational potential energy of a pair of overlapping galaxies

The interaction of the gravitational potential energy of a pair of overlapping Plummer-model galaxies is determined exactly for various separationsr of their centres. It is shown that the results can be well represented by the simple relationW(r)=−GM1M2/(r2+ɛ2)1/2, where 1/ε is the average reciprocal distance between the stars of two galaxies of massesM1 andM2 when they have zero separation.

Forces between Overlapping Plummer-Model Galaxies

In groups and clusters of galaxies interpenetrating collisions are common.In the coma cluster, for example, a typical galaxy may undergo three interpenetrating collisions in IO10 yrs. It has been found convenient to represent density distribution in galaxies(Fujimoto et al I977) and in clusters of galaxies(White 1976) by Plummer-model. Estimates for energy transfer in a collision between two identical Plummer-model galaxies was made by Toomre(I977), and Ahmad(l979) extended this work for non-identical cases.

Challenges, Problems, and Issues Faced in Language-Specific Synset Creation and Linkage in the Kashmiri WordNet

The first half of the present paper highlights some of the issues that are faced while creating language-specific synsets in Kashmiri. It also discusses the necessity of the standards and guidelines for group work. It thoroughly describes some of the issues of untranslatability and transliteration. It focuses on the need of field work while creating language-specific synsets in the language. The second half of the paper discusses the problems faced while linking synsets with the Hindi WordNet. It gives some description regarding the areas where problems are faced which include domains such as concept creation, example translation, maintenance of category, and English–Hindi linking.

ERRATUM: "STATISTICAL MECHANICS OF GALAXY CLUSTERING FOR A TWO-COMPONENT SYSTEM: EFFECT OF THE EXTENDED NATURE OF GALAXIES"

We develop a more general theory of the two-component system of galaxies by treating the galaxies as extended structures. We make use of the softened potential (r2 + ∊2)-1/2, with ∊ as a measure of the finite size of the galaxies, to evaluate the partition function, various thermodynamic properties of the system and the distribution function. Our analysis shows that the distribution function is not too greatly altered by the softening, thus vindicating our earlier claim1 besides making the theory more elaborate as all the earlier results1,2 are retrieved exactly from the new distribution function. Also, an attempt is made to account for the dark matter in the universe.