The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Magneto-dielectric and Magneto-resistive in the Mixed Spinel MgFe2O4

The mixed spinel, MgFe2O4 has been synthesized by ball-milling assisted sintering method. X-ray diffraction study confirms formation of cubic MgFe2O4 and the lattice parameter values calculated are a = b = c = 8.369(3) {\AA}. Vibrating sample magnetometer measurements at room temperature shows a soft ferrimagnetic nature. Magneto-Dielectric and Magneto-Restive plots confirm coupling at room temperature in the prepared MgFe2O4. The peak at 500 Oe in the MD plot is due to the canting of Fe3+ ions distributed in octahedral and tetrahedral sites.Comment: 3 pages 4 figur

A computational model for three-dimensional incompressible wall jets with large cross flow

A computational model for the flow field of three dimensional incompressible wall jets prototypic of thrust augmenting ejectors with large cross flow is presented. The formulation employs boundary layer equations in an orthogonal curvilinear coordinate system. Simulation of laminar as well as turbulen wall jets is reported. Quantification of jet spreading, jet growth, nominal separation, and jet shrink effects due to corss flow are discussed

Radio recombination lines from the largest bound atoms in space

In this paper, we report the detection of a series of radio recombination lines (RRLs) in absorption near 26 MHz arising from the largest bound carbon atoms detected in space. These atoms, which are more than a million times larger than the ground state atoms are undergoing delta transitions (n~1009, Delta n=4) in the cool tenuous medium located in the Perseus arm in front of the supernova remnant, Cassiopeia A. Theoretical estimates had shown that atoms which recombined in tenuous media are stable up to quantum levels n~1500. Our data indicates that we have detected radiation from atoms in states very close to this theoretical limit. We also report high signal-to-noise detections of alpha, beta and gamma transitions in carbon atoms arising in the same clouds. In these data, we find that the increase in line widths with quantum number (proportional to n^5) due to pressure and radiation broadening of lines is much gentler than expected from existing models which assume a power law background radiation field. This discrepancy had also been noted earlier. The model line widths had been overestimated since the turnover in radiation field of Cassiopeia A at low frequencies had been ignored. In this paper, we show that, once the spectral turnover is included in the modeling, the slower increase in line width with quantum number is naturally explained.Comment: 5 pages, 4 figures, accepted for publication in MNRA

The motion of bubbles inside drops in containerless processing

A theoretical model of thermocapillary bubble motion inside a drop, located in a space laboratory, due to an arbitrary axisymmetric temperature distribution on the drop surface was constructed. Typical results for the stream function and temperature fields as well as the migration velocity of the bubble were obtained in the quasistatic limit. The motion of bubbles in a rotating body of liquid was studied experimentally, and an approximate theoretical model was developed. Comparison of the experimental observations of the bubble trajectories and centering times with theoretical predictions lends qualified support to the theory

Brownian motion on disconnected sets, basic hypergeometric functions, and some continued fractions of Ramanujan

Motivated by L\'{e}vy's characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary closed subset of the line that is unbounded above and below: such a process will be a martingale, will have the identity function as its quadratic variation process, and will be ``continuous'' in the sense that its sample paths don't skip over points. We show that there is a unique such process, which turns out to be automatically a reversible Feller-Dynkin Markov process. We find its generator, which is a natural generalization of the operator $f\mapsto{1/2}f''$. We then consider the special case where the state space is the self-similar set $\{\pm q^k:k\in \mathbb{Z}\}\cup\{0\}$ for some $q>1$. Using the scaling properties of the process, we represent the Laplace transforms of various hitting times as certain continued fractions that appear in Ramanujan's ``lost'' notebook and evaluate these continued fractions in terms of basic hypergeometric functions (that is, $q$-analogues of classical hypergeometric functions). The process has 0 as a regular instantaneous point, and hence its sample paths can be decomposed into a Poisson process of excursions from 0 using the associated continuous local time. Using the reversibility of the process with respect to the natural measure on the state space, we find the entrance laws of the corresponding It\^{o} excursion measure and the Laplace exponent of the inverse local time -- both again in terms of basic hypergeometric functions. By combining these ingredients, we obtain explicit formulae for the resolvent of the process. We also compute the moments of the process in closed form. Some of our results involve $q$-analogues of classical distributions such as the Poisson distribution that have appeared elsewhere in the literature.Comment: Published in at http://dx.doi.org/10.1214/193940307000000383 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Tropical rainforest bird community structure in relation to altitude, tree species composition, and null models in the Western Ghats, India

Studies of species distributions on elevational gradients are essential to understand principles of community organisation as well as to conserve species in montane regions. This study examined the patterns of species richness, abundance, composition, range sizes, and distribution of rainforest birds at 14 sites along an elevational gradient (500-1400 m) in the Kalakad-Mundanthurai Tiger Reserve (KMTR) of the Western Ghats, India. In contrast to theoretical expectation, resident bird species richness did not change significantly with elevation although the species composition changed substantially (<10% similarity) between the lowest and highest elevation sites. Constancy in species richness was possibly due to relative constancy in productivity and lack of elevational trends in vegetation structure. Elevational range size of birds, expected to increase with elevation according to Rapoport's rule, was found to show a contrasting inverse U-shaped pattern because species with narrow elevational distributions, including endemics, occurred at both ends of the gradient (below 800 m and above 1,200 m). Bird species composition also did not vary randomly along the gradient as assessed using a hierarchy of null models of community assembly, from completely unconstrained models to ones with species richness and range-size distribution restrictions. Instead, bird community composition was significantly correlated with elevation and tree species composition of sites, indicating the influence of deterministic factors on bird community structure. Conservation of low- and high-elevation areas and maintenance of tree species composition against habitat alteration are important for bird conservation in the southern Western Ghats rainforests.Comment: 36 pages, 5 figures, two tables (including one in the appendix) Submitted to the Journal of the Bombay Natural History Society (JBNHS