A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

Various algorithms for optimization and learning in adaptive systems

This thesis discusses various methods for learning and optimization in adaptive systems. Overall, it emphasizes the relationship between optimization, learning, and adaptive systems; and it illustrates the influence of underlying hardware upon the construction of efficient algorithms for learning and optimization. Chapter 1 provides a summary and an overview.

Chapter 2 discusses a method for using feed-forward neural networks to filter the noise out of noise-corrupted signals. The networks use back-propagation learning, but they use it in a way that qualifies as unsupervised learning. The networks adapt based only on the raw input data-there are no external teachers providing information on correct operation during training. The chapter contains an analysis of the learning and develops a simple expression that, based only on the geometry of the network, predicts performance.

Chapter 3 explains a simple model of the piriform cortex, an area in the brain involved in the processing of olfactory information. The model was used to explore the possible effect of acetylcholine on learning and on odor classification. According to the model, the piriform cortex can classify odors better when acetylcholine is present during learning but not present during recall. This is interesting since it suggests that learning and recall might be separate neurochemical modes (corresponding to whether or not acetylcholine is present). When acetylcholine is turned off at all times, even during learning, the model exhibits behavior somewhat similar to Alzheimer's disease, a disease associated with the degeneration of cells that distribute acetylcholine.

Chapters 4, 5, and 6 discuss algorithms appropriate for adaptive systems implemented entirely in analog hardware. The algorithms inject noise into the systems and correlate the noise with the outputs of the systems. This allows them to estimate gradients and to implement noisy versions of gradient descent, without having to calculate gradients explicitly. The methods require only noise generators, adders, multipliers, integrators, and differentiators; and the number of devices needed scales linearly with the number of adjustable parameters in the adaptive systems. With the exception of one global signal, the algorithms require only local information exchange.

Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice

In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Nanostructured tungsten trioxide photoanodes for solar energy conversion

Nanostructured tungsten trioxide (WO₃) photoelectrodes are potential candidates for the anodic portion of an integrated solar water-splitting device that generates hydrogen fuel and oxygen from water. These nanostructured materials can potentially offer improved performance in photooxidation reactions compared to unstructured materials because of enhancements in light scattering, increases in surface area, and their decoupling of the directions of light absorption and carrier collection. To evaluate the presence of these effects and their contributions toward energy conversion efficiency, a variety of nanostructured WO₃ photoanodes were synthesized by electrodeposition within nanoporous templates and by anodization of tungsten foils. A robust fabrication process was developed for the creation of oriented WO₃ nanorod arrays, which allows for control nanorod diameter and length. Films of nanostructured WO₃ platelets were grown via anodization, the morphology of the films was controlled by the anodization conditions, and the current-voltage performance and spectral response properties of these films were studied. The observed photocurrents were consistent with the apparent morphologies of the nanostructured arrays. Measurements of electrochemically active surface area and other physical characteristics were correlated with observed differences in absorbance, external quantum yield, and photocurrent density for the anodized arrays. The capability to quantify these characteristics and relate them to photoanode performance metrics can allow for selection of appropriate structural parameters when designing photoanodes for solar energy conversion.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering

This dissertation consists of two parts. The first part presents an explicit procedure for applying multi-Regge theory to production processes. As an illustrative example, the case of three body final states is developed in detail, both with respect to kinematics and multi-Regge dynamics. Next, the experimental consistency of the multi-Regge hypothesis is tested in a specific high energy reaction; the hypothesis is shown to provide a good qualitative fit to the data. In addition, the results demonstrate a severe suppression of double Pomeranchon exchange, and show the coupling of two "Reggeons" to an external particle to be strongly damped as the particle's mass increases. Finally, with the use of two body Regge parameters, order of magnitude estimates of the multi-Regge cross section for various reactions are given.

The second part presents a diffraction model for high energy proton-proton scattering. This model developed by Chou and Yang assumes high energy elastic scattering results from absorption of the incident wave into the many available inelastic channels, with the absorption proportional to the amount of interpenetrating hadronic matter. The assumption that the hadronic matter distribution is proportional to the charge distribution relates the scattering amplitude for pp scattering to the proton form factor. The Chou-Yang model with the empirical proton form factor as input is then applied to calculate a high energy, fixed momentum transfer limit for the scattering cross section, This limiting cross section exhibits the same "dip" or "break" structure indicated in present experiments, but falls significantly below them in magnitude. Finally, possible spin dependence is introduced through a weak spin-orbit type term which gives rather good agreement with pp polarization data.

Topics in LIGO-related physics: interferometric speed meters and tidal work

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors, one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. The most straightforward design for a speed-meter interferometer that accomplishes this is described and analyzed in Chapter 2. This design (due to Braginsky, Gorodetsky, Khalili, and Thorne) is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and used to show (in accord with the speed being a quantum nondemolition observable) that in principle the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies . However, in practice, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation.

Chapter 3 proposes a more sophisticated version of a speed meter. This new design requires only a modest input power and appears to be a fully practical candidate for third-generation LIGO. It can beat the SQL (the approximate sensitivity of second-generation LIGO interferometers) over a broad range of frequencies (~ 10 to 100 Hz in practice) by a factor h/h_SQL ~ √W^(SQL)_(circ)/W_circ. Here W_circ is the light power circulating in the interferometer arms and W_SQL ≃ 800 kW is the circulating power required to beat the SQL at 100 Hz (the LIGO-II power). If squeezed vacuum (with a power-squeeze factor e^-2R) is injected into the interferometer's output port, the SQL can be beat with a much reduced laser power: h/h_SQL ~ √W^(SQL)_(circ)/W_circe^-2R. For realistic parameters (e^-2R ≃ 10 and W_circ ≃ 800 to 2000 kW), the SQL can be beat by a factor ~ 3 to 4 from 10 to 100 Hz. [However, as the power increases in these expressions, the speed meter becomes more narrow band; additional power and re-optimization of some parameters are required to maintain the wide band.] By performing frequency-dependent homodyne detection on the output (with the aid of two kilometer-scale filter cavities), one can markedly improve the interferometer's sensitivity at frequencies above 100 Hz.

Chapters 2 and 3 are part of an ongoing effort to develop a practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising third- generation interferometric gravitational-wave detector that entails low laser power.

Chapter 4 is a contribution to the foundations for analyzing sources of gravitational waves for LIGO. Specifically, it presents an analysis of the tidal work done on a self-gravitating body (e.g., a neutron star or black hole) in an external tidal field (e.g., that of a binary companion). The change in the mass-energy of the body as a result of the tidal work, or "tidal heating," is analyzed using the Landau-Lifshitz pseudotensor and the local asymptotic rest frame of the body. It is shown that the work done on the body is gauge invariant, while the body-tidal-field interaction energy contained within the body's local asymptotic rest frame is gauge dependent. This is analogous to Newtonian theory, where the interaction energy is shown to depend on how one localizes gravitational energy, but the work done on the body is independent of that localization. These conclusions play a role in analyses, by others, of the dynamics and stability of the inspiraling neutron-star binaries whose gravitational waves are likely to be seen and studied by LIGO.

Dynamic response of structures with uncertain parameters

This thesis presents a technique for obtaining the response of linear structural systems with parameter uncertainties subjected to either deterministic or random excitation. The parameter uncertainties are modeled as random variables or random fields, and are assumed to be time-independent. The new method is an extension of the deterministic finite element method to the space of random functions.

First, the general formulation of the method is developed, in the case where the excitation is deterministic in time. Next, the application of this formulation to systems satisfying the one-dimensional wave equation with uncertainty in their physical properties is described. A particular physical conceptualization of this equation is chosen for study, and some engineering applications are discussed in both an earthquake ground motion and a structural context.

Finally, the formulation of the new method is extended to include cases where the excitation is random in time. Application of this formulation to the random response of a primary-secondary system is described. It is found that parameter uncertainties can have a strong effect on the system response characteristics.

The combinatorics of transcriptional regulation

The ability to regulate gene expression is of central importance for the adaptability of living organisms to changes in their internal and external environment. At the transcriptional level, binding of transcription factors (TFs) in the vicinity of promoters can modulate the rate at which transcripts are produced, and as such play an important role in gene regulation. TFs with regulatory action at multiple promoters is the rule rather than the exception, with examples ranging from TFs like the cAMP receptor protein (CRP) in E. coli that regulates hundreds of different genes, to situations involving multiple copies of the same gene, such as on plasmids, or viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in coupling ("entanglement") between transcription of different genes. The last few decades have seen rapid advances in our ability to quantitatively measure such effects, which calls for biophysical models to explain these data. Here we develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression and the resulting correlation in transcription rates for a general set of promoters. To test these predictions experimentally, we create genetic constructs with known TF copy number, binding site affinities, and gene copy number; hence avoiding the need to use free fit parameters. Our results clearly prove the TF titration effect and that the statistical mechanical model can accurately predict the fold change in gene expression for the studied cases. We also generalize these experimental efforts to cover systems with multiple different genes, using the method of mRNA fluorescence in situ hybridization (FISH). Interestingly, we can use the TF titration affect as a tool to measure the plasmid copy number at different points in the cell cycle, as well as the plasmid copy number variance. Finally, we investigate the strategies of transcriptional regulation used in a real organism by analyzing the thousands of known regulatory interactions in E. coli. We introduce a "random promoter architecture model" to identify overrepresented regulatory strategies, such as TF pairs which coregulate the same genes more frequently than would be expected by chance, indicating a related biological function. Furthermore, we investigate whether promoter architecture has a systematic effect on gene expression by linking the regulatory data of E. coli to genome-wide expression censuses.

I. The effects of variations in certain parameters upon the efficiency of in vivo hemodialysis with a Kiil dialyzer. II. Interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube.

Part I

Regression analyses are performed on in vivo hemodialysis data for the transfer of creatinine, urea, uric acid and inorganic phosphate to determine the effects of variations in certain parameters on the efficiency of dialysis with a Kiil dialyzer. In calculating the mass transfer rates across the membrane, the effects of cell-plasma mass transfer kinetics are considered. The concept of the effective permeability coefficient for the red cell membrane is introduced to account for these effects. A discussion of the consequences of neglecting cell-plasma kinetics, as has been done to date in the literature, is presented.

A physical model for the Kiil dialyzer is presented in order to calculate the available membrane area for mass transfer, the linear blood and dialysate velocities, and other variables. The equations used to determine the independent variables of the regression analyses are presented. The potential dependent variables in the analyses are discussed.

Regression analyses were carried out considering overall mass-transfer coefficients, dialysances, relative dialysances, and relative permeabilities for each substance as the dependent variables. The independent variables were linear blood velocity, linear dialysate velocity, the pressure difference across the membrane, the elapsed time of dialysis, the blood hematocrit, and the arterial plasma concentrations of each substance transferred. The resulting correlations are tabulated, presented graphically, and discussed. The implications of these correlations are discussed from the viewpoint of a research investigator and from the viewpoint of patient treatment.

Recommendations for further experimental work are presented.

Part II

The interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube in the wavy flow regime has been measured using resistance wave gages. The median water depth, r.m.s. wave height, wave frequency, extrema frequency, and wave velocity have been measured as functions of air and water flow rates. Reynolds numbers, Froude numbers, Weber numbers, and bulk velocities for each phase may be calculated from these measurements. No theory for wave formation and propagation available in the literature was sufficient to describe these results.

The water surface level distribution generally is not adequately represented as a stationary Gaussian process. Five types of deviation from the Gaussian process function were noted in this work. The presence of the tube walls and the relatively large interfacial shear stresses precludes the use of simple statistical analyses to describe the interfacial structure. A detailed study of the behavior of individual fluid elements near the interface may be necessary to describe adequately wavy two-phase flow in systems similar to the one used in this work.

MEMS for Diabetic Retinopathy

As the worldwide prevalence of diabetes mellitus continues to increase, diabetic retinopathy remains the leading cause of visual impairment and blindness in many developed countries. Between 32 to 40 percent of about 246 million people with diabetes develop diabetic retinopathy. Approximately 4.1 million American adults 40 years and older are affected by diabetic retinopathy. This glucose-induced microvascular disease progressively damages the tiny blood vessels that nourish the retina, the light-sensitive tissue at the back of the eye, leading to retinal ischemia (i.e., inadequate blood flow), retinal hypoxia (i.e., oxygen deprivation), and retinal nerve cell degeneration or death. It is a most serious sight-threatening complication of diabetes, resulting in significant irreversible vision loss, and even total blindness.

Unfortunately, although current treatments of diabetic retinopathy (i.e., laser therapy, vitrectomy surgery and anti-VEGF therapy) can reduce vision loss, they only slow down but cannot stop the degradation of the retina. Patients require repeated treatment to protect their sight. The current treatments also have significant drawbacks. Laser therapy is focused on preserving the macula, the area of the retina that is responsible for sharp, clear, central vision, by sacrificing the peripheral retina since there is only limited oxygen supply. Therefore, laser therapy results in a constricted peripheral visual field, reduced color vision, delayed dark adaptation, and weakened night vision. Vitrectomy surgery increases the risk of neovascular glaucoma, another devastating ocular disease, characterized by the proliferation of fibrovascular tissue in the anterior chamber angle. Anti-VEGF agents have potential adverse effects, and currently there is insufficient evidence to recommend their routine use.

In this work, for the first time, a paradigm shift in the treatment of diabetic retinopathy is proposed: providing localized, supplemental oxygen to the ischemic tissue via an implantable MEMS device. The retinal architecture (e.g., thickness, cell densities, layered structure, etc.) of the rabbit eye exposed to ischemic hypoxic injuries was well preserved after targeted oxygen delivery to the hypoxic tissue, showing that the use of an external source of oxygen could improve the retinal oxygenation and prevent the progression of the ischemic cascade.

The proposed MEMS device transports oxygen from an oxygen-rich space to the oxygen-deficient vitreous, the gel-like fluid that fills the inside of the eye, and then to the ischemic retina. This oxygen transport process is purely passive and completely driven by the gradient of oxygen partial pressure (pO₂). Two types of devices were designed. For the first type, the oxygen-rich space is underneath the conjunctiva, a membrane covering the sclera (white part of the eye), beneath the eyelids and highly permeable to oxygen in the atmosphere when the eye is open. Therefore, sub-conjunctival pO₂ is very high during the daytime. For the second type, the oxygen-rich space is inside the device since pure oxygen is needle-injected into the device on a regular basis.

To prevent too fast or too slow permeation of oxygen through the device that is made of parylene and silicone (two widely used biocompatible polymers in medical devices), the material properties of the hybrid parylene/silicone were investigated, including mechanical behaviors, permeation rates, and adhesive forces. Then the thicknesses of parylene and silicone became important design parameters that were fine-tuned to reach the optimal oxygen permeation rate.

The passive MEMS oxygen transporter devices were designed, built, and tested in both bench-top artificial eye models and in-vitro porcine cadaver eyes. The 3D unsteady saccade-induced laminar flow of water inside the eye model was modeled by computational fluid dynamics to study the convective transport of oxygen inside the eye induced by saccade (rapid eye movement). The saccade-enhanced transport effect was also demonstrated experimentally. Acute in-vivo animal experiments were performed in rabbits and dogs to verify the surgical procedure and the device functionality. Various hypotheses were confirmed both experimentally and computationally, suggesting that both the two types of devices are very promising to cure diabetic retinopathy. The chronic implantation of devices in ischemic dog eyes is still underway.

The proposed MEMS oxygen transporter devices can be also applied to treat other ocular and systemic diseases accompanied by retinal ischemia, such as central retinal artery occlusion, carotid artery disease, and some form of glaucoma.

Neutron-neutron scattering parameters from the ^3He(d,t)2p and ^3H(d,^3He)2n reactions

The energy spectra of tritons and Helium-3 nuclei from the reactions ³He(d,t)2p, ³H(d,³He)2n, ³He(d,³He)pn, and ³H(d,t)pn were measured between 6° and 20° at a bombarding energy of 10.9 MeV. An upper limit of 5 μb/sr. was obtained for producing a bound di-neutron at 6° and 7.5°. The ³He(d,t)2p and ³H(d,³He)2n data, together with previous measurements at higher energies, have been used to investigate whether one can unambiguously extract information on the two-nucleon system from these three-body final state reactions. As an aid to these theoretical investigations, Born approximation calculations were made employing realistic nucleon-nucleon potentials and an antisymmetrized final state wave function for the five-particle system. These calculations reproduce many of the features observed in the experimental data and indicate that the role of exchange processes cannot be ignored. The results show that previous attempts to obtain information on the neutron-neutron scattering length from the ³H(d,³He)2n reaction may have seriously overestimated the precision that could be attained.

Spontaneous and stimulated light emission due to radiative recombination in forward biased lead telluride P-N junctions

Since the discovery in 1962 of laser action in semiconductor diodes made from GaAs, the study of spontaneous and stimulated light emission from semiconductors has become an exciting new field of semiconductor physics and quantum electronics combined. Included in the limited number of direct-gap semiconductor materials suitable for laser action are the members of the lead salt family, i.e . PbS, PbSe and PbTe. The material used for the experiments described herein is PbTe . The semiconductor PbTe is a narrow band- gap material (E_g = 0.19 electron volt at a temperature of 4.2°K). Therefore, the radiative recombination of electron-hole pairs between the conduction and valence bands produces photons whose wavelength is in the infrared (λ ≈ 6.5 microns in air).

The p-n junction diode is a convenient device in which the spontaneous and stimulated emission of light can be achieved via current flow in the forward-bias direction. Consequently, the experimental devices consist of a group of PbTe p-n junction diodes made from p –type single crystal bulk material. The p - n junctions were formed by an n-type vapor- phase diffusion perpendicular to the (100) plane, with a junction depth of approximately 75 microns. Opposite ends of the diode structure were cleaved to give parallel reflectors, thereby forming the Fabry-Perot cavity needed for a laser oscillator. Since the emission of light originates from the recombination of injected current carriers, the nature of the radiation depends on the injection mechanism.

The total intensity of the light emitted from the PbTe diodes was observed over a current range of three to four orders of magnitude. At the low current levels, the light intensity data were correlated with data obtained on the electrical characteristics of the diodes. In the low current region (region A), the light intensity, current-voltage and capacitance-voltage data are consistent with the model for photon-assisted tunneling. As the current is increased, the light intensity data indicate the occurrence of a change in the current injection mechanism from photon-assisted tunneling (region A) to thermionic emission (region B). With the further increase of the injection level, the photon-field due to light emission in the diode builds up to the point where stimulated emission (oscillation) occurs. The threshold current at which oscillation begins marks the beginning of a region (region C) where the total light intensity increases very rapidly with the increase in current. This rapid increase in intensity is accompanied by an increase in the number of narrow-band oscillating modes. As the photon density in the cavity continues to increase with the injection level, the intensity gradually enters a region of linear dependence on current (region D), i.e. a region of constant (differential) quantum efficiency.

Data obtained from measurements of the stimulated-mode light-intensity profile and the far-field diffraction pattern (both in the direction perpendicular to the junction-plane) indicate that the active region of high gain (i.e. the region where a population inversion exists) extends to approximately a diffusion length on both sides of the junction. The data also indicate that the confinement of the oscillating modes within the diode cavity is due to a variation in the real part of the dielectric constant, caused by the gain in the medium. A value of τ ≈ 10^-9 second for the minority- carrier recombination lifetime (at a diode temperature of 20.4°K) is obtained from the above measurements. This value for τ is consistent with other data obtained independently for PbTe crystals.

Data on the threshold current for stimulated emission (for a diode temperature of 20. 4°K) as a function of the reciprocal cavity length were obtained. These data yield a value of J’_th = (400 ± 80) amp/cm² for the threshold current in the limit of an infinitely long diode-cavity. A value of α = (30 ± 15) cm^-1 is obtained for the total (bulk) cavity loss constant, in general agreement with independent measurements of free- carrier absorption in PbTe. In addition, the data provide a value of n_s ≈ 10% for the internal spontaneous quantum efficiency. The above value for n_s yields values of t_b ≈ τ ≈ 10^-9 second and t_s ≈ 10^-8 second for the nonradiative and the spontaneous (radiative) lifetimes, respectively.

The external quantum efficiency (n_d) for stimulated emission from diode J-2 (at 20.4° K) was calculated by using the total light intensity vs. diode current data, plus accepted values for the material parameters of the mercury- doped germanium detector used for the measurements. The resulting value is n_d ≈ 10%-20% for emission from both ends of the cavity. The corresponding radiative power output (at λ = 6.5 micron) is 120-240 milliwatts for a diode current of 6 amps.

Estimation of catalyst activity profiles and deactivation parameters from reactor operating data with applications to naphtha reforming

Techniques are developed for estimating activity profiles in fixed bed reactors and catalyst deactivation parameters from operating reactor data. These techniques are applicable, in general, to most industrial catalytic processes. The catalytic reforming of naphthas is taken as a broad example to illustrate the estimation schemes and to signify the physical meaning of the kinetic parameters of the estimation equations. The work is described in two parts. Part I deals with the modeling of kinetic rate expressions and the derivation of the working equations for estimation. Part II concentrates on developing various estimation techniques.

Part I: The reactions used to describe naphtha reforming are dehydrogenation and dehydroisomerization of cycloparaffins; isomerization, dehydrocyclization and hydrocracking of paraffins; and the catalyst deactivation reactions, namely coking on alumina sites and sintering of platinum crystallites. The rate expressions for the above reactions are formulated, and the effects of transport limitations on the overall reaction rates are discussed in the appendices. Moreover, various types of interaction between the metallic and acidic active centers of reforming catalysts are discussed as characterizing the different types of reforming reactions.

Part II: In catalytic reactor operation, the activity distribution along the reactor determines the kinetics of the main reaction and is needed for predicting the effect of changes in the feed state and the operating conditions on the reactor output. In the case of a monofunctional catalyst and of bifunctional catalysts in limiting conditions, the cumulative activity is sufficient for predicting steady reactor output. The estimation of this cumulative activity can be carried out easily from measurements at the reactor exit. For a general bifunctional catalytic system, the detailed activity distribution is needed for describing the reactor operation, and some approximation must be made to obtain practicable estimation schemes. This is accomplished by parametrization techniques using measurements at a few points along the reactor. Such parametrization techniques are illustrated numerically with a simplified model of naphtha reforming.

To determine long term catalyst utilization and regeneration policies, it is necessary to estimate catalyst deactivation parameters from the the current operating data. For a first order deactivation model with a monofunctional catalyst or with a bifunctional catalyst in special limiting circumstances, analytical techniques are presented to transform the partial differential equations to ordinary differential equations which admit more feasible estimation schemes. Numerical examples include the catalytic oxidation of butene to butadiene and a simplified model of naphtha reforming. For a general bifunctional system or in the case of a monofunctional catalyst subject to general power law deactivation, the estimation can only be accomplished approximately. The basic feature of an appropriate estimation scheme involves approximating the activity profile by certain polynomials and then estimating the deactivation parameters from the integrated form of the deactivation equation by regression techniques. Different bifunctional systems must be treated by different estimation algorithms, which are illustrated by several cases of naphtha reforming with different feed or catalyst composition.