3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Synergistic interaction between particular X-chromosome deletions andSex-lethal causes female lethality inDrosophila melanogaster

We studied the effect on female viability of trans-heterozygous combinations of X-chromosome deficiencies and Sxt-(fl), a null allele of Sex-lethal. Twentyfive deficiencies, which together covered 80% of the X chromosome, were tested. Seven of these trans-heterozygous combinations caused significant levels of female lethality. Two of the seven interacting deficiencies include the previously known sex determination genes sans fille and sisterless-a. Four of the remaining uncover X-chromosomal regions that were not hitherto known to contain sex determination genes. These newly identified regions are defined by deficiencies Df(1)RA2 (7D10; 8A4-5), Df(1)KA14 (7F1-2; 8C6), Df(1)C52 (8E; 9C-D) and Df(1)N19 (17A1; 18A2). These four deficiencies were characterized further to determine whether it was the maternal or zygotic dosage that was primarily responsible for the observed lethality of female embryos, daughterless and extra macrochaetae, two known regulators of Sxl, influence the interaction of these deficiencies with Sxl.

Statistical Methods for Accelerated Life Testing with Particular Reference to Resin Impregnated Paper Bushings

Electrical failure of insulation is known to be an extremal random process wherein nominally identical pro-rated specimens of equipment insulation, at constant stress fail at inordinately different times even under laboratory test conditions. In order to be able to estimate the life of power equipment, it is necessary to run long duration ageing experiments under accelerated stresses, to acquire and analyze insulation specific failure data. In the present work, Resin Impregnated Paper (RIP) a relatively new insulation system of choice used in transformer bushings, is taken as an example. The failure data has been processed using proven statistical methods, both graphical and analytical. The physical model governing insulation failure at constant accelerated stress has been assumed to be based on temperature dependent inverse power law model.