Psychobiophysics of transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that stimulates the brain using a magnetic coil placed on the scalp. Since it is applicable to humans non-invasively, directly interfering with neural electrical activity, it is potentially a good tool to study the direct relationship between perceptual experience and neural activity. However, it has been difficult to produce a clear perceptible phenomenon with TMS of sensory areas, especially using a single magnetic pulse. Also, the biophysical mechanisms of magnetic stimulation of single neurons have been poorly understood.

In the psychophysical part of this thesis, perceptual phenomena induced by TMS of the human visual cortex are demonstrated as results of the interactions with visual inputs. We first introduce a method to create a hole, or a scotoma, in a flashed, large-field visual pattern using single-pulse TMS. Spatial aspects of the interactions are explored using the distortion effect of the scotoma depending on the visual pattern, which can be luminance-defined or illusory. Its similarity to the distortion of afterimages is also discussed. Temporal interactions are demonstrated in the filling-in of the scotoma with temporally adjacent visual features, as well as in the effective suppression of transient visual features. Also, paired-pulse TMS is shown to lead to different brightness modulations in transient and sustained visual stimuli.

In the biophysical part, we first develop a biophysical theory to simulate the effect of magnetic stimulation on arbitrary neuronal structure. Computer simulations are performed on cortical neuron models with realistic structure and channels, combined with the current injection that simulates magnetic stimulation. The simulation results account for general and basic characteristics of the macroscopic effects of TMS including our psychophysical findings, such as a long inhibitory effect, dependence on the background activity, and dependence on the direction of the induced electric field.

The perceptual effects and the cortical neuron model presented here provide foundations for the study of the relationship between perception and neural activity. Further insights would be obtained from extension of our model to neuronal networks and psychophysical studies based on predictions of the biophysical model.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

Parylene-C as a new piezoelectric material

The goal of this thesis is to develop a proper microelectromechanical systems (MEMS) process to manufacture piezoelectric Parylene-C (PA-C), which is famous for its chemical inertness, mechanical and thermal properties and electrical insulation. Furthermore, piezoelectric PA-C is used to build miniature, inexpensive, non-biased piezoelectric microphones.

These piezoelectric PA-C MEMS microphones are to be used in any application where a conventional piezoelectric and electret microphone can be used, such as in cell phones and hearing aids. However, they have the advantage of a simplified fabrication process compared with existing technology. In addition, as a piezoelectric polymer, PA-C has varieties of applications due to its low dielectric constant, low elastic stiffness, low density, high voltage sensitivity, high temperature stability and low acoustic and mechanical impedance. Furthermore, PA-C is an FDA approved biocompatible material and is able to maintain operate at a high temperature.

To accomplish piezoelectric PA-C, a MEMS-compatible poling technology has been developed. The PA-C film is poled by applying electrical field during heating. The piezoelectric coefficient, -3.75pC/N, is obtained without film stretching.

The millimeter-scale piezoelectric PA-C microphone is fabricated with an in-plane spiral arrangement of two electrodes. The dynamic range is from less than 30 dB to above 110 dB SPL (referenced 20 µPa) and the open-circuit sensitivities are from 0.001 – 0.11 mV/Pa over a frequency range of 1 - 10 kHz. The total harmonic distortion of the device is less than 20% at 110 dB SPL and 1 kHz.

Identification of thermally-tagged coherent structures in the zero pressure gradient turbulent boundary layer

A zero pressure gradient boundary layer over a flat plate is subjected to step changes in thermal condition at the wall, causing the formation of internal, heated layers. The resulting temperature fluctuations and their corresponding density variations are associated with turbulent coherent structures. Aero-optical distortion occurs when light passes through the boundary layer, encountering the changing index of refraction resulting from the density variations. Instantaneous measurements of streamwise velocity, temperature and the optical deflection angle experienced by a laser traversing the boundary layer are made using hot and cold wires and a Malley probe, respectively. Correlations of the deflection angle with the temperature and velocity records suggest that the dominant contribution to the deflection angle comes from thermally-tagged structures in the outer boundary layer with a convective velocity of approximately 0.8U∞. An examination of instantaneous temperature and velocity and their temporal gradients conditionally averaged around significant optical deflections shows behavior consistent with the passage of a heated vortex. Strong deflections are associated with strong negative temperature gradients, and strong positive velocity gradients where the sign of the streamwise velocity fluctuation changes. The power density spectrum of the optical deflections reveals associated structure size to be on the order of the boundary layer thickness. A comparison to the temperature and velocity spectra suggests that the responsible structures are smaller vortices in the outer boundary layer as opposed to larger scale motions. Notable differences between the power density spectra of the optical deflections and the temperature remain unresolved due to the low frequency response of the cold wire.

Geometric elasticity for graphics, simulation, and computation

We develop new algorithms which combine the rigorous theory of mathematical elasticity with the geometric underpinnings and computational attractiveness of modern tools in geometry processing. We develop a simple elastic energy based on the Biot strain measure, which improves on state-of-the-art methods in geometry processing. We use this energy within a constrained optimization problem to, for the first time, provide surface parameterization tools which guarantee injectivity and bounded distortion, are user-directable, and which scale to large meshes. With the help of some new generalizations in the computation of matrix functions and their derivative, we extend our methods to a large class of hyperelastic stored energy functions quadratic in piecewise analytic strain measures, including the Hencky (logarithmic) strain, opening up a wide range of possibilities for robust and efficient nonlinear elastic simulation and geometry processing by elastic analogy.

Spectroscopic investigations of inter- and intramolecular processes in crystalline benzene

I. Introductory Remarks

A brief discussion of the overall organization of the thesis is presented along with a discussion of the relationship between this thesis and previous work on the spectroscopic properties of benzene.

II. Radiationless Transitions and Line broadening

Radiationless rates have been calculated for the ³B_1u→¹A_1g transitions of benzene and perdeuterobenzene as well as for the ¹B_2u→¹A_1g transition of benzene. The rates were calculated using a model that considers the radiationless transition as a tunneling process between two multi-demensional potential surfaces and assuming both harmonic and anharmonic vibrational potentials. Whenever possible experimental parameters were used in the calculation. To this end we have obtained experimental values for the anharmonicities of the carbon-carbon and carbon-hydrogen vibrations and the size of the lowest triplet state of benzene. The use of the breakdown of the Born-Oppenheimer approximation in describing radiationless transitions is critically examined and it is concluded that Herzberg-Teller vibronic coupling is 100 times more efficient at inducing radiationless transitions.

The results of the radiationless transition rate calculation are used to calculate line broadening in several of the excited electronic states of benzene. The calculated line broadening in all cases is in qualitative agreement with experimental line widths.

III. ³B_1u←¹A_1g Absorption Spectra

The ³B_1u←¹A_1g absorption spectra of C₆H₆ and C₆D₆ at 4.2˚K have been obtained at high resolution using the phosphorescence photoexcitation method. The spectrum exhibits very clear evidence of a pseudo-Jahn-Teller distortion of the normally hexagonal benzene molecule upon excitation to the triplet state. Factor group splitting of the 0 – 0 and 0 – 0 + v exciton bands have also been observed. The position of the mean of the 0 – 0 exciton band of C₆H₆ when compared to the phosphorescence origin of a C₆H₆ guest in a C₆D₆ host crystal indicates that the “static” intermolecular interactions between guest and hose are different for C₆H₆ and C₆D₆. Further investigation of this difference using the currently accepted theory of isotopic mixed crystals indicates that there is a 2cm^-1 shift of the ideal mixed crystal level per hot deuterium atom. This shift is observed for both the singlet and triplet states of benzene.

IV. ³E_1u←¹A_1g, Absorption Spectra

The ³E_1u←¹A_1g absorption spectra of C₆H₆ and C₆D₆ at 4.2˚K have been obtained using the phosphorescence photoexcitation technique. In both cases the spectrum is broad and structureless as would be expected from the line broadening calculations.

A study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas

This thesis is a study of nonlinear phenomena in the propagation of electromagnetic waves in a weakly ionized gas externally biased with a magnetostatic field. The present study is restricted to the nonlinear phenomena rising from the interaction of electromagnetic waves in the ionized gas. The important effects of nonlinearity are wave-form distortion leads to cross modulation of one wave by a second amplitude-modulated wave.

The nonlinear effects are assumed to be small so that a perturbation method can be used. Boltzmann’s kinetic equation with an appropriate expression for the collision term is solved by expanding the electron distribution function into spherical harmonics in velocity space. In turn, the electron convection current density and the conductivity tensors of the nonlinear ionized gas are found from the distribution function. Finally, the expression for the current density and Maxwell’s equations are employed to investigate the effects of nonlinearity on the propagation of electromagnetic waves in the ionized gas, and also on the reflection of waves from an ionized gas of semi-infinite extent.

Effects produced in GaAs by MeV ion bombardment

Presented in the first part of this thesis is work performed on the ionizing energy beam induced adhesion enhancement of thin (~ 500 Angstrom) Au films on GaAs substrates. The ionizing beam, employed in the present thesis, is the MeV ions (i.e., ¹⁶O, ¹⁹F, and ³⁵Cl), with energies between 1 and 20 MeV. Using the "Scratch" test for adhesion measurement, and ESCA for chemical analysis of the film-substrate interface, the native oxide layer at the interface is shown to play an important role in the adhesion enhancement by the ionizing radiation. A model is discussed which explains the experimental data on the the dependence of adhesion enhancement on the energy which was deposited into electronic processes at the interface. The ESCA data indicate that the chemical bonds (or compounds), which are responsible for the increase in the thin film adherence, are hydroxides rather than oxides.

In the second part of the thesis we present a research performed on the radiation damage in GaAs crystals produced by MeV ions. Lattice parameter dilatation in the surface layers of the GaAs crystals becomes saturated after a high dose bombardment at room temperature. The strain produced by nuclear collisions is shown to relax partially due to electronic excitation (with a functional dependence on the nuclear and electronic stopping power of bombarding ions). Data on the GaAs and GaP crystals suggest that low temperature recovery stage defects produce major crystal distortion. The x-ray rocking curve technique with a dynamical diffraction theory analysis provides the depth distribution of the strain and damage in the MeV ion bombarded crystals.

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.

A scaling technique for the design of idealized electromagnetic lenses

A technique is developed for the design of lenses for transitioning TEM waves between conical and/or cylindrical transmission lines, ideally with no reflection or distortion of the waves. These lenses utilize isotropic but inhomogeneous media and are based on a solution of Maxwell's equations instead of just geometrical optics. The technique employs the expression of the constitutive parameters, ɛ and μ, plus Maxwell's equations, in a general orthogonal curvilinear coordinate system in tensor form, giving what we term as formal quantities. Solving the problem for certain types of formal constitutive parameters, these are transformed to give ɛ and μ as functions of position. Several examples of such lenses are considered in detail.

The structure of liquid argon as determined by x-ray diffraction

X-ray diffraction measurements and subsequent data analyses have been carried out on liquid argon at five states in the density range of 0.91 to 1.135 gm/cc and temperature range of 127 to 143°K. Duplicate measurements were made on all states. These data yielded radial distribution and direct correlation functions which were then used to compute the pair potential using the Percus-Yevick equation. The potential minima are in the range of -105 to -120°K and appear to substantiate current theoretical estimates of the effective pair potential in the presence of a weak three-body force.

The data analysis procedure used was new and does not distinguish between the coherent and incoherent absorption factors for the cell scattering which were essentially equal. With this simplification, the argon scattering estimate was compared to the gas scattering estimate on the laboratory frame of reference and the two estimates coincided, indicating the data normalized. The argon scattering on the laboratory frame of reference was examined for the existence of the peaks in the structure factor and the existence of an observable third peak was considered doubtful.

Numerical studies of the effect of truncation, normalization, the subsidiary peak phenomenon in the radial distribution function, uncertainties in the low angle data relative to errors in the direct correlation function and the distortion phenomenon are presented.

The distortion phenomenon for this experiment explains why the Mikolaj-Pings argon data yielded pair potential well depths from the Percus-Yevick equation that were too shallow and an apparent slope with respect to density that was too steep compared to theoretical estimates.

The data presented for each measurement are: empty cell and cell plus argon intensity, absorption factors, argon intensity, smoothed argon intensity, smoothed argon intensity corrected for distortion, structure factor, radial distribution function, direct correlation function and the pair potential from the Percus-Yevick equation.