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.

Atmospheric boundary-layer across Hadley and Ferrel cells over the Indian Ocean

A Southern Ocean Pilot cruise covering the latitudes from 10 degrees N to 56 degrees S in the open Indian Ocean was carried out during January February 2004. Surface and upper air data collected during this cruise are reported here. It is shown that the broad features of the atmosphere, in particular that of temperature, follow the tropical and mid-latitude weather expected during January February in this region. However, the atmospheric boundary-layer shows large variations, both in its height and structure between tropics and high latitudes. Strong influence of the surface heat flux on boundary layer structure is clearly seen. Humidity field reveals several local maxima and minima, suggesting a laminated atmosphere with air from different sources moving almost unmixed in adjacent layers.

The mobility of oxygen ions in CaF2

The a.c. conductivity of CaF2 samples containing a fine dispersion of CaO particles has been measured in the temperature range 630 to 1100 K. The conductivity of the dispersed solid electrolyte is two orders of magnitude higher than that for pure polycrystalline CaF2 in the middle of the temperature range. Transport measurements on pure single crystals of CaF2 and polycrystalline samples, with and without CaO dispersion, using Fe+FeO and pure Fe as electrodes, clearly indicate that fluorine ions are the only migrating ionic species with a transport number of almost unity, contrary to the suggestion of Chou and Rapp [1, 2]. The enhanced conductivity of the dispersed solid electrolyte probably arises from two effects. A small solubility of oxygen in CaF2 results in an increase in the fluorine vacancy concentration and conductivity. Adsorption of fluorine ions on the surface of the dispersed particles of CaO results in a space charge region around each particle with enhanced conductivity. Measurements on a galvanic cell incorporating CaF2 as the solid electrolyte and oxide electrodes show that the e.m.f. is a function of the activity of CaO at the electrode/electrolyte interface. The response to an oxygen potential gradient is, therefore, through an exchange reaction, which establishes an equivalent fluorine potential at the electrode/electrolyte interface.

Structure of the Indian southwesterly pre-monsoon and monsoon boundary layers: Observations and numerical simulation

Characteristics of pre-monsoon and monsoon boundary layer structure and turbulence were studied in New Delhi and Bangalore, India during the summer of 1987. Micrometeorological towers were installed and instrumented at these locations to provide mean and turbulent surface layer measurements, while information on the vertical structure of the atmosphere was obtained using miniradiosondes. Thermal structures of the pre-monsoon and monsoon boundary layers were quite distinct. The daytime, pre-monsoon boundary layer observed over New Delhi was much deeper than that of the monsoon boundary layer observed over Bangalore and at times was characterized by multiple inversions. Surface, turbulent sensible heat fluxes at both sites were approximately the same (235 and 200 Wm−2 for New Delhi and Bangalore, respectively). Diurnal variations in the monsoon boundary layer at Bangalore were more regular compared to those under pre-monsoon conditions at New Delhi. One-dimensional numerical simulations of the pre-monsoon boundary layer using a turbulent energy closure scheme show good agreement with observations.

Nonsimilar boundary layers for non-Darcy mixed convection flow about a horizontal surface in a saturated porous medium

The nonsimilar non-Darcy mixed convection flow about a heated horizontal surface in a saturated porous medium has been studied when the surface temperature is a power function of distance (Tw = T∞ ± Axλ). The analysis is performed for the cases of parallel and stagnation flows with favourable induced pressure gradient. The partial differential equations governing the flow have been solved numerically using the Keller box method. The heat transfer is enhanced due to the buoyancy parameter and wall temperature, but the non-Darcy parameter reduces it. For non-Darcy flow, the similarity solution exists only for the case of parallel flow.

Non-Newtonian boundary layers on a moving cylinder

The analysis of steady laminar forced convection boundary layer of power-law non-Newtonian fluids on a continuously moving cylinder with the surface maintained at a uniform temperature or uniform heat flux is presented. Of interest were the effects of power-law viscosity index, transverse curvature, generalized Prandtl number and streamwise coordinate on the local Nusselt number as well as on the velocity and temperature profiles. The two thermal boundary conditions yield quite similar results. Comparison of the calculated results with available series expansion solutions for a Newtonian fluid shows a very good performance of the present numerical procedure.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.

A sufficient criterion for Kelvin–Helmholtz instability in the magnetopause boundary‐layer region

The Kelvin–Helmholtz instability has been investigated for the magnetopause boundary‐layer region by the linearized method. The plasma in magnetosheath and magnetopause is assumed to be semi‐infinitely extended homogeneous, nondissipative, and incompressible. It is observed that, if one relation of two plasma speeds on the two sides of the magnetopause, wave number, and boundary‐layer thickness exceeds a certain threshold, the instability sets in. This new analytically sufficient criterion for excitation of instability in the three‐layer plasma flow generalizes the corresponding Chandrasekhar’s instability criterion for two‐layer plasma flow. The known results have been recovered and modified, the new results have been discovered. It is proved that the velocity threshold for the onset of instability is low when the magnitude of the magnetosheath and boundary‐layer region magnetic field and the angle between them are small. Also the threshold depends on the direction of plasma flow. The following results are observed numerically. The growth of the instability is sensitive to the magnetic field direction in the magnetosheath. A slight variation in the magnetic field direction in the second region can substantially change the relative velocity threshold for instability. When the ratio of the density of the second and third layer (magnetosphere) increases or that of the first and third layer decreases, the threshold decreases. Apart from this a necessary criterion for instability is obtained for a particular case.

Development of atmospheric pressure ionization ion mobility spectrometry and ion mobility spectrometry mass spectrometry

This study is focused on the development and evaluation of ion mobility instrumentation with various atmospheric pressure ionization techniques and includes the following work. First, a high-resolution drift tube ion mobility spectrometer (IMS), coupled with a commercial triple quadrupole mass spectrometer (MS), was developed. This drift tube IMS is compatible with the front-end of commercial Sciex mass spectrometers (e.g., Sciex API-300, 365, and 3000) and also allows easy (only minor modifications are needed) installation between the original atmospheric pressure ion source and the triple quadrupole mass spectrometer. Performance haracteristics (e.g.,resolving power, detection limit, transmission efficiency of ions) of this IMS-MS instrument were evaluated. Development of the IMS-MS instrument also led to a study where a proposal was made that tetraalkylammonium ions can be used as chemical standards for ESI-IMS. Second, the same drift tube design was also used to build a standalone ion mobility spectrometer equipped with a Faraday plate detector. For this highresolution (resolving power about 100 shown) IMS device, a multi-ion source platform was built, which allows the use of a range of atmospheric pressure ionization methods, such as: corona discharge chemical ionization (CD-APCI), atmospheric pressure photoionization (APPI), and radioactive atmospheric pressure chemical ionization (R-APCI). The multi-ion source platform provides easy switching between ionization methods and both positive and negative ionization modes can be used. Third, a simple desorpion/ionization on silicon (DIOS) ion source set-up for use with the developed IMS and IMS-MS instruments was built and its operation demonstrated. Fourth, a prototype of a commercial aspiration-type ion mobility spectrometer was mounted in front of a commercial triple quadrupole mass spectrometer. The set-up, which is simple, easy to install, and requires no major modifications to the MS, provides the possibility of gathering fundamental information about aspiration mobility spectrometry.

Compressible MHD boundary layer in the stagnation region of a sphere

The steady laminar compressible boundary layer flow of an electrically conducting fluid in the stagnation region of a sphere with an applied magnetic field has been studied. The effects of the induced magnetic field, mass transfer, and viscous dissipation have been taken into account. Both isothermal and adiabatic wall conditions have been considered. The governing equations have been solved numerically using a shooting method. The skin friction and heat transfer are found to be strongly affected by the magnetic field, mass transfer, wall temperature and Mach number. It is found that the magnetic field reduces the heat transfer. This is a significant result which can be used in controlling the heat transfer rate. The boundary layer solutions break down as the magnetic parameter tends to a certain critical value.

Analysis of energy utilization in the grain mill sector in Karnataka

Energy is a major constituent of a small-scale industry such as grain mills. Based on a sample survey of several mills spread over Karnataka, a state in India, a number of energy analyses were conducted primarily to establish relationships and secondarily to look at them in more detail. Initially specific energy consumption (SEC) was computed for all industries so as to compare their efficiencies of energy use. A wide disparity exists in SEC among various grain mills. In order to understand the disparities better, regression analyses were performed on the variables energy and production, SEC and production, and energy/SEC with percentage production capacity utilization. The studies show that smaller range industries have lower capacity utilization. This paper also examines the energy savings possible by shifting industries from the lower production ranges to the next higher range (thereby utilizing installed production capacity optimally). This leads to an overall energy capacity saving of 23.12% for the foodgrain sector and 18.67% for the paddy dehusking subgroup. If this is extrapolated to the whole state, we obtain a saving of 55 million kWh.

Kinetic approach to dislocation bending in low-mobility films

A kinetic model has been developed for dislocation bending at the growth surface in compressively stressed low-mobility films such as III-V nitrides. It is based on a reduction in the number of atoms at the growth surface. Stress and nonstress sources of driving force for such a reduction are discussed. A comparison between the derived equations and experimentally measured stress evolution data yields good agreement between the predicted and observed angles through which dislocations bend.