Proceedings of the Indian Academy of Sciences - Mathematical Sciences

Bhattacharyya, S.; Abbas, M.

doi: 10.1007/BF02837243pmid: N/A

The conducting liquid interface is found to undulate in an alternating magnetic field. It was shown earlier that ifM =B 0 2/μηω, B0, ω, μ andη being the amplitude (complex) of the alternating longitudinal magnetic field imposed at the interface, the angular frequency of the field, the magnetic permeability and the viscosity respectively, and ifM c was the critical value ofM then the planar layer was stable or unstable according asM < M c orM > M c. In this paper we have determined the stability criterion when in addition to the alternating longitudinal field there acts a uniform field in the same direction. After comparing our results with those obtained earlier, in the absence of the uniform field, we find that the additional uniform field has a significant destabilizing effect.

Gupta, S.

doi: 10.1007/BF02837242pmid: N/A

By employing a new embedding technique, a short-time analytical solution for the axisymmetric melting of a long cylinder due to an infinite flux is presented in this paper. The sufficient condition for starting the instantaneous melting of the cylinder has been derived. The melt is removed as soon as it is formed. The method of solution is simple and straightforward and consists of assuming fictitious initial temperature for some fictitious extension of the actual region.

Somaraju, V.; Mohandas, D.; Balasubramanian, R.

doi: 10.1007/BF02837245pmid: N/A

The effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that whenE 1/2 ≪ Z ≪ E1/2/δ, whereE is the Ekman number, the stream lines are closely packed near the sidewall within a thickness ofO(E 1/2). The effect of stratification is unimportant within this depth range. In the depth rangeE 1/2 /δ ≪ Z ≪ 1/Eδ the vertical boundary layer in which the streamlines are packed is ofO(EZδ) 1/3. WhenZ ≫ 1/Eδ it is shown that the circulation decays algebraically with depth as 1/Z.

Nitsure, Nitin

doi: 10.1007/BF02837250pmid: N/A

The purpose of this paper is to compute the Betti numbers of the moduli space ofparabolic vector bundles on a curve (see Seshadri [7], [8] and Mehta & Seshadri [4]), in the case where every semi-stable parabolic bundle is necessarily stable. We do this by generalizing the method of Atiyah and Bott [1] in the case of moduli of ordinary vector bundles. Recall that (see Seshadri [7]) the underlying topological space of the moduli of parabolic vector bundles is the space of equivalence classes of certain unitary representations of a discrete subgroup Γ which is a lattice in PSL (2,R). (The lattice Γ need not necessarily be co-compact).

Bhat-Nayak, Vasanti; Wirmani-Prasad, Anjana

doi: 10.1007/BF02837248pmid: N/A

It is established that the exact covering numberg(1,5; 10) is 102. It is further shown that this configuration is unique. It can be obtained from the unique Steiner systemS(5, 6, 12).

Bhattacharyya, S.; Abbas, M.

doi: 10.1007/BF02837244pmid: N/A

The instability of a hot horizontal layer of ferromagnetic fluid rotating about a vertical axis has been investigated when the Prandtl numberP < 1. Earlier it was shown that forP > 1 the overstability cannot occur. In this paper the convective and overstable marginal states have been investigated separately forP < 1 and it is found that though convective marginal state is possible for alla, the non-dimensional wave number, and N the Taylor number, the overstability is possible only ifN > (1 +P)π 4/(1 −P) and in case the condition is satisfied, overstability is possible for all those values ofa which satisfya 2 < [N(1 −P)π 2/(1 +P)] 1/3 − π2. IfR c (con) andR c (o.s) are the critical values of the convective and the overstable marginal states respectively, then it is also found thatR c (con) <R c (o.s) providedN is not sufficiently large.