On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

Social evolution - Has nature ever rewound the tape?

Social insects such as ants, bees, wasps and termites exhibit extreme forms of altruism where some individuals remain sterile and assist other individuals in reproduction. Hamilton's inclusive fitness theory provides a powerful framework for investigating the evolution of such altruism. Using the paper wasp Ropalidia marginata, we have quantified and delineated the role of ecological, physiological, genetic and demographic factors in social evolution. An interesting feature of the models we have developed is their symmetry so that either altruism or selfishness can evolve, depending on the numerical values of various parameters. This suggests that selfish/solitary behaviour must occasionally re-emerge even from the eusocial state, It is useful to contemplate expected intermediate states during such potential reversals. We can perhaps envisage three successive steps in such a hypothetical process: i) workers revolt against the hegemony of the queen and challenge her status as the sole reproductive, ii) workers stop producing queens and one or more of them function as egg layers (functional queen/s) capable of producing both haploid as well as diploid offspring and iii) social evolution reverses completely so that a eusocial species becomes solitary, at least facultatively. It appears that the third step, namely transition from eusociality to the solitary state, is rare and has been restricted to transitions from the primitively eusocial state only. The absence of transitions from the highly eusocial state to the solitary state may be attributed to a number of 'preventing mechanisms' such as (a) queen control of workers (b) loss of spermathecae and ability to mate (c) morphological specialization (d) caste polyethism and (e) homeostasis, which must each make the transition difficult and, taken together, perhaps very difficult. However, the discovery of a transition from the highly eusocial to the solitary state can hardly he ruled out, given that little or no effort has gone into its detection. In this paper I discuss social evolution and its possible reversal and cite potential examples of stages in the transition from the social to the solitary.

Narrowband Detection of Acoustic Source in Shallow Ocean using Vector Sensor Array

The problem of narrowband CFAR (constant false alarm rate) detection of an acoustic source at an unknown location in a range-independent shallow ocean is considered. If a target is present, the received signal vector at an array of N sensors belongs to an M-dimensional subspace if N exceeds the number of propagating modes M in the ocean. A subspace detection method which utilises the knowledge of the signal subspace to enhance the detector performance is presented in thisMpaper. It is shown that, for a given number of sensors N, the performance of a detector using a vector sensor array is significantly better than that using a scalar sensor array. If a target is detected, the detector using a vector sensor array also provides a concurrent coarse estimate of the bearing of the target.

Determination of activation energy for thermal regeneration of EL2 from its metastable state by thermally stimulated photocurrent measurements

It is shown that thermally stimulated photocurrent measurements provide a simple and effective method of determining the activation energy of thermal regeneration rate of EL2 from the metastable state to the normal state in undoped semi‐insulating GaAs. The thermal regeneration rate r is found to be 2.5×108 exp(−0.26 eV/kT) s−1.

Stereochemistry of 2'-5' linked nucleic acids: crystal and molecular structure of ammonium adenylyl-2',5'-adenosine tetrahydrate: a core fragment of 2'-5' oligo A's produced by interferon induced adenylate synthetase

The preponderance of 3'-5' phosphodiester links in nucleic acids is well known. Albeit less prevalent, the 2'-5' links are specifically utilised in the formation of 'lariat' in group II introns and in the msDNA-RNA junction in myxobacterium. As a sequel to our earlier study on cytidylyl-2',5'-adenosine we have now obtained the crystal structure of adenylyl-2',5'-adenosine (A2'p5'A) at atomic resolution. This dinucleoside monophosphate crystallizes in the orthorhombic space group P2(1)2(1)2(1) with a = 7.956(3) A, b = 12.212(3) A and c = 36.654(3) A. CuK alpha intensity data were collected on a diffractometer. The structure was sloved by direct methods and refined by full matrix least squares methods to R = 10.8%. The 2' terminal adenine is in the commonly observed anti (chi 2 = 161 degrees) conformation and the 5' terminal base has a syn (chi 1 = 55 degrees) conformation more often seen in purine nucleotides. A noteworthy feature of A2'p5'A is the intranucleotide hydrogen bond between N3 and O5' atoms of the 5' adenine base. The two furanose rings in A2'p5'A show different conformations - C2' endo, C3' endo puckering for the 5' and 2' ends respectively. In this structure too there is a stacking of the purine base on the ribose O4' just as in other 2'-5' dinucleoside structures, a feature characteristically seen in the left handed Z DNA. In having syn, anti conformation about the glycosyl bonds, C2' endo, C3' endo mixed sugar puckering and N3-O5' intramolecular hydrogen bond A2'p5'A resembles its 3'-5' analogue and several other 2'-5' dinucleoside monophosphate structures solved so far. Striking similarities between the 2'-5' dinucleoside monophosphate structures suggest that the conformation of the 5'-end nucleoside dictates the conformation of the 2' end nucleoside. Also, the 2'-5' dimers do not favour formation of miniature classical double helical structures like the 3'-5' dimers. It is conceivable, 2-5(A) could be using the stereochemical features of A2'p5'A which accounts for its higher activity.

Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

Comparison of CloudSat and TRMM radar reflectivities

Comparison of reflectivity data of radars onboard CloudSat and TRMM is performed using coincident overpasses. The contoured frequency by altitude diagrams (CFADs) are constructed for two cases: (a) only include collocated vertical profiles that are most likely to be raining and (b) include all collocated profiles along with cloudy pixels falling within a distance of about 50 km from the centre point of coincidence. Our analysis shows that for both cases, CloudSat underestimates the radar reflectivity by about 10 dBZ compared to that of TRMM radar below 15 km altitude. The difference is well outside the uncertainty value of similar to 2 dBZ of each radar. Further, CloudSat reflectivity shows a decreasing trend while that of TRMM radar an increasing trend below 4 km height. Basically W-band radar that CloudSat flies suffers strong attenuation in precipitating clouds and its reflectivity value rarely exceeds 20 dBZ though its technical specification indicates the upper measurement limit to be 40 dBZ. TRMM radar, on the other hand, cannot measure values below 17 dBZ. In fact combining data from these two radars seems to give a better overall spatial structure of convective clouds.

Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class

The curvature (T)(w) of a contraction T in the Cowen-Douglas class B-1() is bounded above by the curvature (S*)(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle E-T corresponding to the operator T in the Cowen-Douglas class B-1() which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B-1() for a bounded domain in C-m.

Structure, interactions and evolutionary implications of a domain-swapped lectin dimer from Mycobacterium smegmatis

Crystal structure determination of the lectin domain of MSMEG_3662 from Mycobacterium smegmatis and its complexes with mannose and methyl-alpha-mannose, the first effort of its kind on a mycobacterial lectin, reveals a structure very similar to beta-prism II fold lectins from plant sources, but with extensive unprecedented domain swapping in dimer formation. The two subunits in a dimer often show small differences in structure, but the two domains, not always related by 2-fold symmetry, have the same structure. Each domain carries three sugar-binding sites, similar to those in plant lectins, one on each Greek key motif. The occurrence of beta-prism II fold lectins in bacteria, with characteristics similar to those from plants, indicates that this family of lectins is of ancient origin and had evolved into a mature system before bacteria and plants diverged. In plants, the number of binding sites per domain varies between one and three, whereas the number is two in the recently reported lectin domains from Pseudomonas putida and Pseudomonas aeruginosa. An analysis of the sequences of the lectins and the lectin domains shows that the level of sequence similarity among the three Greek keys in each domain has a correlation with the number of binding sites in it. Furthermore, sequence conservation among the lectins from different species is the highest for that Greek key which carries a binding site in all of them. Thus, it would appear that carbohydrate binding influences the course of the evolution of the lectin.