Many medical therapies, such as thermal tumor detection and hypothermia cancer treatments, utilize heat transfer mechanisms of the body. The focus of this work is the development and experimental validation of a method to simultaneously estimate thermal conductivity, volumetric specific heat, and perfusion of in-vivo tissue. The heat transfer through the tissue was modeled using a modified Pennes' equation. Using a least-squares parameter estimation method with regularization, the thermal properties could be estimated from the temperature response to the known applied heat flux. The method was tested experimentally using a new agar-water tissue phantom designed for this purpose. A total of 40 tests were performed. The results of the experiments show that conductivity can be successfully estimated for perfused tissue phantoms. The values returned for volumetric specific heat are lower than expected, while the estimated values of perfusion are far greater than expected. It is believed that the mathematical model is incorrectly accounting between these two terms. Both terms were treated as heat sinks, so it is conceivable that it is not discriminating between them correctly. Although the method can estimate all three parameters simultaneously, but it seems that the mathematical model is not accurately describing the system. In the future, improvements to the model could be made to allow the method to function accurately. / Master of Science

We provide an L² theory for the local double Hilbert transform along an analytic surface (s, t ,φ(s, t )) in the Heisenberg group H¹, that is operator f ↦ Hφ f (x) := p.v.∫∣s∣,∣t∣≤1 f (x ∙ (s, t ,φ(s, t ))-¹) ds/s dt/t, where ∙ denotes the group operation in H1. This operator combines several features: it is amulti-parameter singular integral, its kernel is supported along a submanifold, and convolution is with respect to a homogeneous group structure. We reprove Hφ is always L²(H¹)→L²(H¹) bounded (a result first obtained in [Str12]) to illustrate the method and then refine it to characterize the largest class of polynomials P of degree less than d such that the operator HP is uniformly bounded when P ranges in the class. Finally, we provide examples of surfaces that can be treated by our method but not by the theory of [Str12].

The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth's subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the scattering integral method. Application to various synthetic and real data examples show accurate inversion results. I show that a good background ƞ model is required to accurately recover vh. For 3-D problems, I promote a hybrid approach, where efficient ray tracing is used to compute the sensitivity kernels. The proposed method highly reduces the computational cost.

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The electro-kinetic characteristics of different material bioreactor columns for treating water and waste water are experimentally studied. Separate columns of unsaturated gravels (~6mm) and ball clay were assessed for electro-kinetic characteristics by dosing water at a hydraulic loading rate of 50ml/min and 10ml/min. Similarly locally available organic materials such as sawdust, Moringa oleifera sheets and textile clothe pieces were also empirically analyzed. Size effects of the bio-reactor columns were also studied. The effluent from textile clothe and gravel reactor respectively showed an increase in pH while a depreciation in pH in the effluent was observed in the Moringa Oleifera reactor and sawdust reactor. This may be due to leaching of acidic organic components for sawdust and Moringa Oleifera . In gravels effluent pH depreciated with increase in flow rate but the general trend of the effluent pH curve showed an initial improvement before it slowed down to an asymptote for a specific constant dosage and height. A multi-parameter stochastic linear model for change in pH as a function of column height, dosage rate, time for specific volume discharge and change in electrical conductivity between influent and effluent was derived. A general stochastic model was also developed to characterize pH change in any bioreactor irrespective of the material media. Thirty centimeters of gravel exhibited an increase in conductivity with increase in flow rate while conductivity dipped with increasing flow rate when the gravel column height was halved. The measure of organic compounds in water decreased with increasing percolation rate through gravel. The chemical oxygen demand ratio within the gravel improved to unity showing increased containment of organic compounds with time. Organic textile clothes reactor also illustrated increased conductivity with increasing flow but conductivity dipped with increase in column height. For Moringa Oleifera reactors, a dosage of water at 10ml/min showed a significant improvement in conductivity with increase in column height. An initial depreciation in temperature curve was observed within clay and gravel reactor. With increase in depth there was an increase in temperature within the gravel as the saturation by water improved. In sawdust reactors this was not the trend. A birth process model is proposed to simulated temperature within a bioreactor as a function of time irrespective of any specific material used as bioreactor media.

The development and transition of optical fiber sensors from experimental stage to practical applications largely depends on manufacturing cost and simplicity. To date, in-fiber grating sensors are largely manufactured by ultraviolet lasers despite higher fabrication cost and complexity. Besides, ultraviolet radiation can only write gratings in doped fibers. Therefore, reaping the benefits of existing fibers such as pure silica fiber, photonics crystal fibers etc. cannot be achieved using this technique. In contrast, uses of ultra-fast lasers have the potential to eliminate or minimize those drawbacks. However, extensive fabrication and packaging research is required for ultrafast laser technology to mature and offer grating based sensors fabrication in industrial scale. This dissertation presents design and fabrication of fiber optic sensors using femtosecond laser for measurement of ambient refractive index and temperature. The femtosecond laser operating at 780 nm with pulse duration of 172 fs and pulse repetition rate of 1 kHz is used to study bulk index modification and fabricate fiber long period and short period gratings. Effective and reliable fabrication of in-fiber gratings requires spatial control of refractive index written in optical fiber. With an aim to better control spatial index modulation in direct ultrafast writing, primary focus of this work is given to write single-shot submicron periodic voids in bulk glass. Femtosecond pulse filamentation in glass is studied to understand the morphology of bulk index change written by ultrashort pulses. Laser writing parameters (such as beam diameter, pulse energy, scanning speed, depth of focus, etc.) are then further tuned to write pulse filamentation induced refractive index change in optical fibers suitable for fiber grating fabrication. In order to design and tailor grating’s spectrum, measurement of in-fiber index is introduced in this work. We propose fiber Bragg grating based Fabry-Perot cavity structure (cavity length, L= 10 mm) to characterize femtosecond pulse filamentation induced refractive index change in the core of standard SMF. In addition, Mach-Zehnder interferometer (MZI) is proposed as an alternative yet effective and low cost tool to measure in-fiber index change. Comsol simulation is used to validate the quantification of index change. Measured index change is used in Optiwave simulation to design fiber long period gratings in standard telecommunication and pure silica core fibers. To increase fabrication reliability, we introduce inscription of helical long period gratings using a custom made rotary stage. Tapered photonic crystal and microfiber based Mach-Zehnder interferometer is also investigated for ambient refractive index measurement. Miniature fiber Bragg grating written in microfiber Mach-Zehnder interferometer is used in this work for multi-parameter sensing as well as temperature compensated refractive index sensing. Microfiber Bragg gratings buried in materials of higher thermal expansion coefficient is also proposed to significantly enhance temperature sensitivity. / Graduate / 0548, 0794, 0775 / fariduvic@gmail.com

Next generation polymer composites that utilize the high electrical conductivity and tensile strength of carbon nanotubes are of interest. To effectively disperse carbon nanotubes into polymers, a more fundamental understanding of the polymer/nanotube interface is needed. This requires the development of new analytical methods and techniques for measuring the adhesion between a single molecule and the sidewalls of carbon nanotubes. Atomic Force Microscopy is an integral tool in the characterization of materials on the nanoscale. The objectives of this research were to: 1) characterize the binding force between single molecules and the backbone of a single walled carbon nanotube (SWNT), and 2) measure and interpret the mechanical response of carbon-based nano-objects to compressive loads using an atomic force microscope. To identify chemical moieties that bind strongly to the sidewall of the nanotubes, two experimental approaches have been explored. In the first, force volume images of SWNT paper were obtained using gold-coated AFM tips functionalized with terminally substituted alkanethiols and para-substituted arylthiols. Analysis of these images enabled quantification of the adhesive interactions between the functionalized tip and the SWNT surface. The resultant adhesive forces were shown to be dependent upon surface topography, tip shape, and the terminal group on the alkanethiol. The mechanical response of several single- and multi-walled carbon nanotubes under compressive load was examined with an AFM. When the scanner, onto which the substrate has been mounted, was extended and retracted in a cyclic fashion, cantilever deflection, oscillation amplitude and resonant frequency were simultaneously monitored. By time-correlating cantilever resonance spectra, deflection and scanner motion, precise control over the length of nanotube in contact with the substrate, analogous to fly-fishing was achieved. This multi-parameter force spectroscopy method is applicable for testing the mechanical and interfacial properties of a wide range of nanoscale objects. This research has led to a clearer understanding of the chemistry at the nanotube/polymer interface, as well as the mechanical response of nanoscale materials. A new force spectroscopic tool, multi-parameter force spectroscopy, should be extremely helpful in characterizing the mechanical response of a myriad of nanoscale objects and enable nanoscale devices to become a reality.

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