Inverse problem for the wave equation : partial data and novel boundary sources

An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

Novel kinetic scheme for the ammonium perchlorate gas phase

A novel gas-phase kinetic scheme for ammonium perchlorate (AP) deflagration involving 22 reactions among 18 species is developed. The kinetic scheme is based on a study of the effect of initial conditions on the solution of the differential equations of adiabatic constant-pressure combustion kinetics. The existence of condensed-phase reaction products providesalternate pathways for the consumption of NH3 and HCIOl produced by gas-phase dissociation of AP. Theoretically obtained temperature-time profiles of the novel scheme do not change when the conventional reaction pathways are included, indicatingthat the novel scheme is a substantially faster rate process. The new scheme does not involve the species CIO, which has long been considered a critical component of the AP gas phase and which is included in the conventional reaction pathways.The new scheme develops faster overall reaction rates, steeper temperature-time profiles, and in a deflagration model will result in higher heat-transfer rates from gas phase to the condensed phase.

Human Ecology in India Some Historical Perspectives

Before the spread of extensive settled cultivation, the Indian subcontinent would have been inhabited by territorial hunter–gatherers and shifting cultivators with cultural traditions of prudent resource use. The disruption of closed material cycles by export of agricultural produce to centres of non-agricultural population would have weakened these traditions. Indeed, the fire-based sacrificial ritual and extensive agricultural settlements might have catalysed the destruction of forests and wildlife and the suppression of tribal peoples during the agricultural colonization of the Gangetic plains. Buddhism, Jainism and later the Hindu sects may have been responses to the need for a reassertion of ecological prudence once the more fertile lands were brought under cultivation. British rule radically changed the focus of the country's resource use pattern from production of a variety of biological resources for local consumption to the production of a few commodities largely for export. The resulting ecological squeeze was accompanied by disastrous famines and epidemics between the 1860s and the 1920s. The counterflows to tracts of intensive agriculture have reduced such disasters since independence. However, these are quite inadequate to balance the state-subsidized outflows of resources from rural hinterlands. These imbalances have triggered serious environmental degradation and tremendous overcrowding of the niche of agricultural labour and marginal cultivator all over the country.

A New Improved Procedure for the Synthesis of 4-Formylcarane - Precursor to Sandatrile, a Novel Perfumery Chemical

Stereospecific synthesis of 4-formylcarane (2) has been achieved through hydroboration-carbonylation of DELTA-3-carene. Both the reactions are optimised using sodium borohydride. The method is utilised for the synthesis of sandatrile (3), a novel perfumery chemical.

A norbornadiene–cyclobutadiene cycloaddition cascade: novel intramolecular σ2+π2 trapping of a cyclobutane ring

Norbornadiene and 1,2-bismethoxycarbonylcyclobutadiene furnish a novel heptacyclic system 3(whose X-ray crystal structure has been determined)and an annulated pterodactylane derivative 4 in a single step.

A novel metal binding mode of a pyrimidine nucleotide. Crystal structure of [Cu(5′-UMP)(im)2(H2O)]·4H2O

X-ray analysis of the ternary complex [Cu(5′-UMP)(im)2(H2O)]·4H2O, where 5′-UMP uridine-5′-monophosphate and IM = imidazole, reveals a novel metal binding mode of pyrimidine nucleotide through the ribose group.

A Novel Method for the Uniform Incorporation of Grain-Boundary Layer Modifiers in Positive Temperature Coefficient of Resistivity Barium Titanate

The presently developed two-stage process involves diping the prefired porous disks of n-BaTiO3 in nonaqueous solutions containing Al-buty rate, Ti-isopropoxide, and tetraethyl silicate and subsequent sintering. This leads to uniform distribution of the grain-boundary layer (GBL) modifiers (Al2O3+ TiO2+ SiO2) and better control of the grain size as well as the positive temperature coefficient of resistivity characteristics. The technique is particularly suited for GBL modifiers in low concentrations (< 1%).

A novel laser direct write technique for fabrication of thin film MICs

A technique for fabrication of thin-film circuits for microwave integrated circuit (MIC) application is presented. This low-cost fabrication technique utilizes laser direct write of copper patterns on alumina substrates. The method obviates the need for photomasks and photolithography. The film deposition mechanism, deposit film analysis, and MIC fabrication sequence are presented. Performance evaluation of MICs fabricated using this technique is also included

A novel phenomenon of burst of oxygen uptake during decavanadate-dependent oxidation of NADH

Oxidation of NADH by decavanadate, a polymeric form vanadate with a cage-like structure, in presence of rat liver microsomes followed a biphasic pattern. An initial slow phase involved a small rate of oxygen uptake and reduction of 3 of the 10 vanadium atoms. This was followed by a second rapid phase in which the rates of NADH oxidation and oxygen uptake increased several-fold with a stoichiometry of NADH: O2 of 1ratio1. The burst of NADH oxidation and oxygen uptake which occurs in phosphate, but not in Tris buffer, was prevented by SOD, catalase, histidine, EDTA, MnCl2 and CuSO4, but not by the hydroxyl radical quenchers, ethanol, methanol, formate and mannitol. The burst reaction is of a novel type that requires the polymeric structure of decavanadate for reduction of vanadium which, in presence of traces of H2O2, provides a reactive intermediate that promotes transfer of electrons from NADH to oxygen.