Deviation from standard inflationary cosmology and the problems in ekpyrosis

There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $\langle a_{lm}a_{l'm'}^*\rangle$ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.

Holistic Design In High-Speed Optical Interconnects

Integrated circuit scaling has enabled a huge growth in processing capability, which necessitates a corresponding increase in inter-chip communication bandwidth. As bandwidth requirements for chip-to-chip interconnection scale, deficiencies of electrical channels become more apparent. Optical links present a viable alternative due to their low frequency-dependent loss and higher bandwidth density in the form of wavelength division multiplexing. As integrated photonics and bonding technologies are maturing, commercialization of hybrid-integrated optical links are becoming a reality. Increasing silicon integration leads to better performance in optical links but necessitates a corresponding co-design strategy in both electronics and photonics. In this light, holistic design of high-speed optical links with an in-depth understanding of photonics and state-of-the-art electronics brings their performance to unprecedented levels. This thesis presents developments in high-speed optical links by co-designing and co-integrating the primary elements of an optical link: receiver, transmitter, and clocking.

In the first part of this thesis a 3D-integrated CMOS/Silicon-photonic receiver will be presented. The electronic chip features a novel design that employs a low-bandwidth TIA front-end, double-sampling and equalization through dynamic offset modulation. Measured results show -14.9dBm of sensitivity and energy efficiency of 170fJ/b at 25Gb/s. The same receiver front-end is also used to implement source-synchronous 4-channel WDM-based parallel optical receiver. Quadrature ILO-based clocking is employed for synchronization and a novel frequency-tracking method that exploits the dynamics of IL in a quadrature ring oscillator to increase the effective locking range. An adaptive body-biasing circuit is designed to maintain the per-bit-energy consumption constant across wide data-rates. The prototype measurements indicate a record-low power consumption of 153fJ/b at 32Gb/s. The receiver sensitivity is measured to be -8.8dBm at 32Gb/s.

Next, on the optical transmitter side, three new techniques will be presented. First one is a differential ring modulator that breaks the optical bandwidth/quality factor trade-off known to limit the speed of high-Q ring modulators. This structure maintains a constant energy in the ring to avoid pattern-dependent power droop. As a first proof of concept, a prototype has been fabricated and measured up to 10Gb/s. The second technique is thermal stabilization of micro-ring resonator modulators through direct measurement of temperature using a monolithic PTAT temperature sensor. The measured temperature is used in a feedback loop to adjust the thermal tuner of the ring. A prototype is fabricated and a closed-loop feedback system is demonstrated to operate at 20Gb/s in the presence of temperature fluctuations. The third technique is a switched-capacitor based pre-emphasis technique designed to extend the inherently low bandwidth of carrier injection micro-ring modulators. A measured prototype of the optical transmitter achieves energy efficiency of 342fJ/bit at 10Gb/s and the wavelength stabilization circuit based on the monolithic PTAT sensor consumes 0.29mW.

Lastly, a first-order frequency synthesizer that is suitable for high-speed on-chip clock generation will be discussed. The proposed design features an architecture combining an LC quadrature VCO, two sample-and-holds, a PI, digital coarse-tuning, and rotational frequency detection for fine-tuning. In addition to an electrical reference clock, as an extra feature, the prototype chip is capable of receiving a low jitter optical reference clock generated by a high-repetition-rate mode-locked laser. The output clock at 8GHz has an integrated RMS jitter of 490fs, peak-to-peak periodic jitter of 2.06ps, and total RMS jitter of 680fs. The reference spurs are measured to be –64.3dB below the carrier frequency. At 8GHz the system consumes 2.49mW from a 1V supply.

Experimental and theoretical developments in extended x-ray absorption fine structure (EXAFS) spectroscopy

To obtain accurate information from a structural tool it is necessary to have an understanding of the physical principles which govern the interaction between the probe and the sample under investigation. In this thesis a detailed study of the physical basis for Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy is presented. A single scattering formalism of EXAFS is introduced which allows a rigorous treatment of the central atom potential. A final state interaction formalism of EXAFS is also discussed. Multiple scattering processes are shown to be significant for systems of certain geometries. The standard single scattering EXAFS analysis produces erroneous results if the data contain a large multiple scattering contribution. The effect of thermal vibrations on such multiple scattering paths is also discussed. From symmetry considerations it is shown that only certain normal modes contribute to the Debye-Waller factor for a particular scattering path. Furthermore, changes in the scattering angles induced by thermal vibrations produces additional EXAFS components called modification factors. These factors are shown to be small for most systems.

A study of the physical basis for the determination of structural information from EXAFS data is also presented. An objective method of determining the background absorption and the threshold energy is discussed and involves Gaussian functions. In addition, a scheme to determine the nature of the scattering atom in EXAFS experiments is introduced. This scheme is based on the fact that the phase intercept is a measure of the type of scattering atom. A method to determine bond distances is also discussed and does not require the use of model compounds or calculated phase shifts. The physical basis for this method is the absence of a linear term in the scattering phases. Therefore, it is possible to separate these phases from the linear term containing the distance information in the total phase.

Palladium-Catalyzed Decarboxylative and Decarbonylative Transformations in the Synthesis of Fine and Commodity Chemicals

Decarboxylation and decarbonylation are important reactions in synthetic organic chemistry, transforming readily available carboxylic acids and their derivatives into various products through loss of carbon dioxide or carbon monoxide. In the past few decades, palladium-catalyzed decarboxylative and decarbonylative reactions experienced tremendous growth due to the excellent catalytic activity of palladium. Development of new reactions in this category for fine and commodity chemical synthesis continues to draw attention from the chemistry community.

The Stoltz laboratory has established a palladium-catalyzed enantioselective decarboxylative allylic alkylation of β-keto esters for the synthesis of α-quaternary ketones since 2005. Recently, we extended this chemistry to lactams due to the ubiquity and importance of nitrogen-containing heterocycles. A wide variety of α-quaternary and tetrasubstituted α-tertiary lactams were obtained in excellent yields and exceptional enantioselectivities using our palladium-catalyzed decarboxylative allylic alkylation chemistry. Enantioenriched α-quaternary carbonyl compounds are versatile building blocks that can be further elaborated to intercept synthetic intermediates en route to many classical natural products. Thus our chemistry enables catalytic asymmetric formal synthesis of these complex molecules.

In addition to fine chemicals, we became interested in commodity chemical synthesis using renewable feedstocks. In collaboration with the Grubbs group, we developed a palladium-catalyzed decarbonylative dehydration reaction that converts abundant and inexpensive fatty acids into value-added linear alpha olefins. The chemistry proceeds under relatively mild conditions, requires very low catalyst loading, tolerates a variety of functional groups, and is easily performed on a large scale. An additional advantage of this chemistry is that it provides access to expensive odd-numbered alpha olefins.

Finally, combining features of both projects, we applied a small-scale decarbonylative dehydration reaction to the synthesis of α-vinyl carbonyl compounds. Direct α-vinylation is challenging, and asymmetric vinylations are rare. Taking advantage of our decarbonylative dehydration chemistry, we were able to transform enantioenriched δ-oxocarboxylic acids into quaternary α-vinyl carbonyl compounds in good yields with complete retention of stereochemistry. Our explorations culminated in the catalytic enantioselective total synthesis of (–)-aspewentin B, a terpenoid natural product featuring a quaternary α-vinyl ketone. Both decarboxylative and decarbonylative chemistries found application in the late stage of the total synthesis.

Entrainment of fine sediments by turbulent flows

A study was made of the means by which turbulent flows entrain sediment grains from alluvial stream beds. Entrainment was considered to include both the initiation of sediment motion and the suspension of grains by the flow. Observations of grain motion induced by turbulent flows led to the formulation of an entrainment hypothesis. It was based on the concept of turbulent eddies disrupting the viscous sublayer and impinging directly onto the grain surface. It is suggested that entrainment results from the interaction between fluid elements within an eddy and the sediment grains.

A pulsating jet was used to simulate the flow conditions in a turbulent boundary layer. Evidence is presented to establish the validity of this representation. Experiments were made to determine the dependence of jet strength, defined below, upon sediment and fluid properties. For a given sediment and fluid, and fixed jet geometry there were two critical values of jet strength: one at which grains started to roll across the bed, and one at which grains were projected up from the bed. The jet strength K, is a function of the pulse frequency, ω, and the pulse amplitude, A, defined by

K = Aω^-s

Where s is the slope of a plot of log A against log ω. Pulse amplitude is equal to the volume of fluid ejected at each pulse divided by the cross sectional area of the jet tube.

Dimensional analysis was used to determine the parameters by which the data from the experiments could be correlated. Based on this, a method was devised for computing the pulse amplitude and frequency necessary either to move or project grains from the bed for any specified fluid and sediment combination.

Experiments made in a laboratory flume with a turbulent flow over a sediment bed are described. Dye injection was used to show the presence, in a turbulent boundary layer, of two important aspects of the pulsating jet model and the impinging eddy hypothesis. These were the intermittent nature of the sublayer and the presence of velocities with vertical components adjacent to the sediment bed.

A discussion of flow conditions, and the resultant grain motion, that occurred over sediment beds of different form is given. The observed effects of the sediment and fluid interaction are explained, in each case, in terms of the entrainment hypothesis.

The study does not suggest that the proposed entrainment mechanism is the only one by which grains can be entrained. However, in the writer’s opinion, the evidence presented strongly suggests that the impingement of turbulent eddies onto a sediment bed plays a dominant role in the process.