Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.

A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers

Using a modified Green's function technique the two well-known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the “jump” and “sum” of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.

DNA binding properties of novel dansylated distamycin analogues in which the fluorophore is directly conjugated to the N-methyl-pyrrole carboxamide backbone

Polyamides that are structural analogues of the naturally occurring DNA minor groove binding antibiotic distamycin (Dst) are promising candidates as gene modulators. Developing strategies for the large scale screening and monitoring of the cellular distribution of such ligands would aid the faster discovery of molecules, which would have eventual utility in molecular biology and medicine. Attachment of fluorescent tags would be a useful step towards this end. A fundamental question in this connection is whether the tag modifies the DNA binding affinity of the parent compounds. Towards answering this question, we have developed two oligopeptides that bear the dansyl (N, N-dimethylaminonaphthalene sulfonamido fluorophore) coupled directly to the N-terminus of the conjugated N-methylpyrrole carboxamide network, and possess three or four N-methyl pyrrole carboxamide units (abbreviated as Dn3 and Dn4 respectively). DNA binding abilities of these molecules were assessed from fluorescence titration experiments, duplex-DNA T-m analysis (employing both UV and fluorescence spectroscopy), induced circular dichroism measurements (ICD), salt dependence of ICD and apparent binding constant measurements (K-app) employing ethidium bromide (EtBr) displacement assay. Both these molecules 'reported' DNA binding in the form of an enhanced fluorescence emission. As judged from the ICD measurements, salt dependence of ICD, T-m analysis and K-app measurements, the binding affinities of the molecules that possessed dansyl group at their N-termini were lower than the ones with equivalent number of amide units, but possessed N-methylpyrrole carboxamide unit at their N-termini. These results would have implications in the future design of fluorescent polyamides.

Turbulent free convection above a heated plate inclined at a small angle to the horizontal Journal

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion. Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments. The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

Spin State Selective Excitation of Single Quantum Transitions Using Multiple Quantum Spectroscopy- an Aid to Analyse Complex Proton NMR spectra of Oriented Molecules

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)−single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.