Part I. Influence of membrane morphology on ion-exchange and charge propagation in composite polyelectrolyte electrode coatings. Part II. Dynamic surface tension measurements of polarization relaxation at mercury pool electrodes by the method of Wilhelmy.

Part I. Novel composite polyelectrolyte materials were developed that exhibit desirable charge propagation and ion-retention properties. The morphology of electrode coatings cast from these materials was shown to be more important for its electrochemical behavior than its chemical composition.

Part II. The Wilhelmy plate technique for measuring dynamic surface tension was extended to electrified liquid-liquid interphases. The dynamical response of the aqueous NaF-mercury electrified interphase was examined by concomitant measurement of surface tension, current, and applied electrostatic potential. Observations of the surface tension response to linear sweep voltammetry and to step function perturbations in the applied electrostatic potential (e.g., chronotensiometry) provided strong evidence that relaxation processes proceed for time-periods that are at least an order of magnitude longer than the time periods necessary to establish diffusion equilibrium. The dynamical response of the surface tension is analyzed within the context of non-equilibrium thermodynamics and a kinetic model that requires three simultaneous first order processes.

Measurement of the Polarization of the Cosmic Microwave Background with the BICEP2 and Keck Array Telescopes

Precision polarimetry of the cosmic microwave background (CMB) has become a mainstay of observational cosmology. The ΛCDM model predicts a polarization of the CMB at the level of a few μK, with a characteristic E-mode pattern. On small angular scales, a B-mode pattern arises from the gravitational lensing of E-mode power by the large scale structure of the universe. Inflationary gravitational waves (IGW) may be a source of B-mode power on large angular scales, and their relative contribution to primordial fluctuations is parameterized by a tensor-to-scalar ratio r. BICEP2 and Keck Array are a pair of CMB polarimeters at the South Pole designed and built for optimal sensitivity to the primordial B-mode peak around multipole l ~ 100. The BICEP2/Keck Array program intends to achieve a sensitivity to r ≥ 0.02. Auxiliary science goals include the study of gravitational lensing of E-mode into B-mode signal at medium angular scales and a high precision survey of Galactic polarization. These goals require low noise and tight control of systematics. We describe the design and calibration of the instrument. We also describe the analysis of the first three years of science data. BICEP2 observes a significant B-mode signal at 150 GHz in excess of the level predicted by the lensed-ΛCDM model, and Keck Array confirms the excess signal at > 5σ. We combine the maps from the two experiments to produce 150 GHz Q and U maps which have a depth of 57 nK deg (3.4 μK arcmin) over an effective area of 400 deg² for an equivalent survey weight of 248000 μK². We also show preliminary Keck Array 95 GHz maps. A joint analysis with the Planck collaboration reveals that much of BICEP2/Keck Array's observed 150 GHz signal at low l is more likely a Galactic dust foreground than a measurement of r. Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance.

The polarization of the recoil proton in ETA photoproduction

We measured the recoil proton polarization in the process γp → pη at the 1.5 GeV Caltech electron synchrotron, at photon energies from 0.8 to 1.1 GeV, and at center-of-mass production angles around 90°. A counter-spark chamber array was used to determine the kinematics of all particles in the final state of the partial mode γp → pη (η → 2γ). The protons' polarization was determined by measuring an asymmetry in scattering off carbon. Analysis of 280,000 pictures yielded 2400 useful scatters with a background which was 30% of the foreground. The polarization results show a sizeable opposite parity interference at 830 MeV, 950 MeV, and 1100 MeV.

Some uses of the spontaneous polarization method

As a partial fulfillment of the requirements in obtaining a Professional Degree in Geophysical Engineering at the California Institute of Technology. Spontaneous Polarization method of electrical exploration was chosen as the subject of this thesis. It is also known as "self potential electrical prospecting" and "natural currents method."

The object of this thesis is to present a spontaneous polarization exploration work done by the writer, and to apply analytical interpretation methods to these field results.

The writer was confronted with the difficulty of finding the necessary information in a complete paper about this method. The available papers are all too short and repeat the usual information, giving the same examples. The decision was made to write a comprehensive paper first, including the writer's experience, and then to present the main object of the thesis.

The following paper comprises three major parts:

1 - A comprehensive treatment of the spontaneous polarization method.

2 - Report of the field work.

3 - Analytical interpretation of the field work results.

The main reason in choosing this subject is that this method is the most reliable, easiest and requires the least equipment in prospecting for sulphide orebodies on unexplored, rough terrains.

The intention of the writer in compiling the theoretical and analytical information has been mainly to prepare a reference paper about this method.

The writer wishes to express his appreciation to Dr. G. W. Potapenko, Associate Professor of Physics at California Institute of Technology, for his generous help.

New technologies driving decade-bandwidth radio astronomy : quad-ridged flared horn and compound-semiconductor LNAs

Among the branches of astronomy, radio astronomy is unique in that it spans the largest portion of the electromagnetic spectrum, e.g., from about 10 MHz to 300 GHz. On the other hand, due to scientific priorities as well as technological limitations, radio astronomy receivers have traditionally covered only about an octave bandwidth. This approach of "one specialized receiver for one primary science goal" is, however, not only becoming too expensive for next-generation radio telescopes comprising thousands of small antennas, but also is inadequate to answer some of the scientific questions of today which require simultaneous coverage of very large bandwidths.

This thesis presents significant improvements on the state of the art of two key receiver components in pursuit of decade-bandwidth radio astronomy: 1) reflector feed antennas; 2) low-noise amplifiers on compound-semiconductor technologies. The first part of this thesis introduces the quadruple-ridged flared horn, a flexible, dual linear-polarization reflector feed antenna that achieves 5:1-7:1 frequency bandwidths while maintaining near-constant beamwidth. The horn is unique in that it is the only wideband feed antenna suitable for radio astronomy that: 1) can be designed to have nominal 10 dB beamwidth between 30 and 150 degrees; 2) requires one single-ended 50 Ohm low-noise amplifier per polarization. Design, analysis, and measurements of several quad-ridged horns are presented to demonstrate its feasibility and flexibility.

The second part of the thesis focuses on modeling and measurements of discrete high-electron mobility transistors (HEMTs) and their applications in wideband, extremely low-noise amplifiers. The transistors and microwave monolithic integrated circuit low-noise amplifiers described herein have been fabricated on two state-of-the-art HEMT processes: 1) 35 nm indium phosphide; 2) 70 nm gallium arsenide. DC and microwave performance of transistors from both processes at room and cryogenic temperatures are included, as well as first-reported measurements of detailed noise characterization of the sub-micron HEMTs at both temperatures. Design and measurements of two low-noise amplifiers covering 1--20 and 8—50 GHz fabricated on both processes are also provided, which show that the 1--20 GHz amplifier improves the state of the art in cryogenic noise and bandwidth, while the 8--50 GHz amplifier achieves noise performance only slightly worse than the best published results but does so with nearly a decade bandwidth.

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

CMB as a probe of new physics and old times

Cosmic birefringence (CB)---a rotation of photon-polarization plane in vacuum---is a generic signature of new scalar fields that could provide dark energy. Previously, WMAP observations excluded a uniform CB-rotation angle larger than a degree.

In this thesis, we develop a minimum-variance--estimator formalism for reconstructing direction-dependent rotation from full-sky CMB maps, and forecast more than an order-of-magnitude improvement in sensitivity with incoming Planck data and future satellite missions. Next, we perform the first analysis of WMAP-7 data to look for rotation-angle anisotropies and report null detection of the rotation-angle power-spectrum multipoles below L=512, constraining quadrupole amplitude of a scale-invariant power to less than one degree. We further explore the use of a cross-correlation between CMB temperature and the rotation for detecting the CB signal, for different quintessence models. We find that it may improve sensitivity in case of marginal detection, and provide an empirical handle for distinguishing details of new physics indicated by CB.

We then consider other parity-violating physics beyond standard models---in particular, a chiral inflationary-gravitational-wave background. We show that WMAP has no constraining power, while a cosmic-variance--limited experiment would be capable of detecting only a large parity violation. In case of a strong detection of EB/TB correlations, CB can be readily distinguished from chiral gravity waves.

We next adopt our CB analysis to investigate patchy screening of the CMB, driven by inhomogeneities during the Epoch of Reionization (EoR). We constrain a toy model of reionization with WMAP-7 data, and show that data from Planck should start approaching interesting portions of the EoR parameter space and can be used to exclude reionization tomographies with large ionized bubbles.

In light of the upcoming data from low-frequency radio observations of the redshifted 21-cm line from the EoR, we examine probability-distribution functions (PDFs) and difference PDFs of the simulated 21-cm brightness temperature, and discuss the information that can be recovered using these statistics. We find that PDFs are insensitive to details of small-scale physics, but highly sensitive to the properties of the ionizing sources and the size of ionized bubbles.

Finally, we discuss prospects for related future investigations.

Testing inflationary cosmology with the BICEP1 and BICEP2 experiments

Recent observations of the temperature anisotropies of the cosmic microwave background (CMB) favor an inflationary paradigm in which the scale factor of the universe inflated by many orders of magnitude at some very early time. Such a scenario would produce the observed large-scale isotropy and homogeneity of the universe, as well as the scale-invariant perturbations responsible for the observed (10 parts per million) anisotropies in the CMB. An inflationary epoch is also theorized to produce a background of gravitational waves (or tensor perturbations), the effects of which can be observed in the polarization of the CMB. The E-mode (or parity even) polarization of the CMB, which is produced by scalar perturbations, has now been measured with high significance. Con- trastingly, today the B-mode (or parity odd) polarization, which is sourced by tensor perturbations, has yet to be observed. A detection of the B-mode polarization of the CMB would provide strong evidence for an inflationary epoch early in the universe’s history.

In this work, we explore experimental techniques and analysis methods used to probe the B- mode polarization of the CMB. These experimental techniques have been used to build the Bicep2 telescope, which was deployed to the South Pole in 2009. After three years of observations, Bicep2 has acquired one of the deepest observations of the degree-scale polarization of the CMB to date. Similarly, this work describes analysis methods developed for the Bicep1 three-year data analysis, which includes the full data set acquired by Bicep1. This analysis has produced the tightest constraint on the B-mode polarization of the CMB to date, corresponding to a tensor-to-scalar ratio estimate of r = 0.04±0.32, or a Bayesian 95% credible interval of r < 0.70. These analysis methods, in addition to producing this new constraint, are directly applicable to future analyses of Bicep2 data. Taken together, the experimental techniques and analysis methods described herein promise to open a new observational window into the inflationary epoch and the initial conditions of our universe.

Geometric quantization and foliation reduction

A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.

In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kähler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or “admissible”, values of momentum.

We first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.

We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.

Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.

A significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.

Wnt and FGF signaling in C. elegans vulval cell lineage polarity

The interpretation of extracellular cues leading to the polarization of intracellular components and asymmetric cell divisions is a fundamental part of metazoan organogenesis. The C. elegans vulva, with its invariant cell lineage and interaction of multiple cell signaling pathways, provides an excellent model for the study of cell polarity within an organized epithelial tissue. Herein I discuss the interaction of Wnt and FGF signaling in controlling vulval cell lineage polarity with emphasis on the posterior-most cell that forms the vulva, P7.p.

The mirror symmetry of the C. elegans vulva is achieved by the opposite division orientation of the vulval precursor cells (VPCs) flanking the axis of symmetry. Opposing Wnt signals control the division patterns of the VPCs by controlling the localization of SYS-1/ β-catenin toward the direction of the Wnt gradient. Multiple Wnt signals, expressed at the axis of symmetry, promote the wild-type, anterior-facing, P7.p orientation, whereas Wnts EGL-20 and CWN-1 from the tail and posterior body wall muscle, respectively, promote the daughter cells of P7.p to face the posterior. EGL-20 acts through a member of the LDL receptor superfamily, LRP-2, along with Ror/CAM-1 and Van Gogh/VANG-1. All three transmembrane proteins control orientation through the localization of the SYS-1.

The Fibroblast Growth Factor (FGF) pathway acts in concert with LIN-17/Frizzled to regulate the localization of SYS-1. The source of the FGF ligand is the 1° VPC, P6.p, which controls the polarity of the neighboring 2° VPC, P7.p, by signaling through the sex myoblasts (SMs), activating the FGF pathway. The Wnt, cwn-1, is expressed in the posterior body wall muscle of the worm as well as the SMs, making it the only Wnt expressed on the posterior and anterior sides of P7.p at the time of the polarity decision. Both sources of cwn-1 act instructively to influence P7.p polarity in the direction of the Wnt gradient. The FGF pathway leads to the regulation of cwn-1 transcripts in the SMs. These results illustrate the first evidence of the interaction between FGF and Wnt in C. elegans development and vulval cell lineage polarity as well as highlight the promiscuous nature of Wnt signaling within C. elegans.