Quantum Teichm\"uller space from quantum plane

We derive the quantum Teichm\"uller space, previously constructed by Kashaev and by Fock and Chekhov, from tensor products of a single canonical representation of the modular double of the quantum plane. We show that the quantum dilogarithm function appears naturally in the decomposition of the tensor square, the quantum mutation operator arises from the tensor cube, the pentagon identity from the tensor fourth power of the canonical representation, and an operator of order three from isomorphisms between canonical representation and its left and right duals. We also show that the quantum universal Teichm\"uller space is realized in the infinite tensor power of the canonical representation naturally indexed by rational numbers including the infinity. This suggests a relation to the same index set in the classification of projective modules over the quantum torus, the unitary counterpart of the quantum plane, and points to a new quantization of the universal Teichm\"uller space.Comment: 41 pages, 9 figure

A noncontact measurement technique for the density and thermal expansion coefficient of solid and liquid materials

A noncontact measurement technique for the density and the thermal expansion coefficient of refractory materials in their molten as well as solid phases is presented. This technique is based on the video image processing of a levitated sample. Experiments were performed using the high-temperature electrostatic levitator (HTESL) at the Jet Propulsion Laboratory in which 2–3 mm diam samples can be levitated, melted, and radiatively cooled in vacuum. Due to the axisymmetric nature of the molten samples when levitated in the HTESL, a rather simple digital image analysis can be employed to accurately measure the volumetric change as a function of temperature. Density and the thermal expansion coefficient measurements were made on a pure nickel sample to test the accuracy of the technique in the temperature range of 1045–1565 °C. The result for the liquid phase density can be expressed by rho=8.848+(6.730×10^−4)×T (°C) g/cm^3 within 0.8% accuracy, and the corresponding thermal expansion coefficient can be expressed by beta=(9.419×10^−5) −(7.165×10^−9)×T (°C) K^−1 within 0.2% accuracy

Scheduling of Multicast and Unicast Services under Limited Feedback by using Rateless Codes

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications

Doctor of Philosophy

dissertationThis work studied the relationship between surfactant, oil, and water, by building ternary phase diagrams, the goal of which was to identify the oil-in-water phase composition. The resulting nano-sized emulsion was coated with dicalcium phosphate by utilizing the ionic affinity between calcium ions and the emulsion surface. Since the desired function of the particle is as an oxygen carrier, the particle stability, oxygen capacity, and oxygen release rate were investigated. The first step in the process was to construct ternary phase diagrams with 1,2-dioleoyl-sn-glycero-3-phosphate (DOPA) and soy derived lecithin. The results showed that the lecithin surfactant formed an oil-in-water phase region that was 36 times greater than that of DOPA. With the desired phase composition set, the lecithin emulsion was extruded, resulting in a well-dispersed nanosized particle. A pH titration study of the emulsion found an optimized calcium phosphate coating condition at pH 8.8, at which, the calcium ion had a greater affinity for the emulsion surface than phosphate. A Hill plot was used to show calcium cooperativeness on the emulsion surface which suggested one calcium ion binds to one lecithin molecule. The lecithin emulsion particles were then coated with calcium phosphate using a layering technique that allowed for careful control of the coating thickness. The overall particle hydrodynamic radius was consistent with the growth of the calcium phosphate coating, from 8 nm to 28 nm. This observation was further supported with cryo-TEM measurements. The stability of the coated emulsion was tested in conditions that simulate practical thermal, physical, and time-dependent conditions. Throughout the tests, the coated emulsion exhibited a constant mono-dispersed particle size, while the uncoated emulsion size fluctuated greatly and exhibited increased polydispersion. The fast mixing method with the stopped-flow apparatus was employed to test the product as an oxygen carrier, and it was shown that particles with thicker calcium phosphate coatings released smaller amounts of oxygen in a given timeframe. This study proved the hypothesis by showing a fundamental understanding of emulsion science, coating the flexible emulsion surface with a biocompatible material, and a strong particle performance with regard to stability and as an oxygen carrier

Understanding Anticipatory Time Perception in Consumers’ Time-Related Decisions

Anticipatory time (e.g., prospective duration into the future) is one of the key pieces of information to be processed in intertemporal decisions - decisions requiring a tradeoff between smaller sooner and larger delayed outcomes. Extensive research has examined human and animal perception of time as it is currently passing (i.e., experienced time) and time that has already passed (i.e., retrospective time). However, the nature of anticipatory time perception and its role in consumers’ judgment and decision making have been largely neglected. In my dissertation, I aim to demonstrate that considering subjective anticipatory time estimates offers a new perspective to understand intertemporal decisions. For this purpose, first, I propose that both diminishing sensitivity to longer time horizons (i.e., how long individuals perceive short time horizons to be relative to long time horizons) and the level of time contraction overall (i.e., how long or short individuals perceive time horizons to be overall) contribute to how much individuals discount the value of delayed outcomes, and, then, examine factors influencing intertemporal decisions by changing subjective time perception. Specifically, in the first and third essays, I demonstrate that sexually arousing images and auditory tempo (which has been shown to influence judgment of elapsed time) influence anticipatory time perception and subsequent intertemporal preferences. These results indicate that anticipatory time perception shares the property of perceptual inputs (e.g., people process anticipatory time as if they “perceive” elapsed time). In the second and fourth essays, I demonstrate that cognitive information available at the time of judging anticipatory time such as spatial distance and perceived life span influence individuals’ intertemporal preferences by changing their subjective perception of anticipatory time, which suggests that anticipatory time perception also has the property of embodied cognitions. Taken together, my dissertation incorporate both time perception research and consumer research on time-related judgment and decision making and sheds light on both domains

Time Perception and Retirement Saving: Lessons from Behavioral Decision Research

This chapter provides a behavioral decision perspective on the implications of intertemporal choice research for retirement savings. In particular, we focus on two cognitive mechanisms explaining how and why future monetary outcomes are discounted: (1) changes in the perception of delayed outcomes due to changes in mental representations and perceived slack, and (2) changes in the perception of temporal distance to delayed outcomes. Relevant recent findings are reviewed and the implications for retirement savings are discussed

Schwinger Pair Production at Finite Temperature in Scalar QED

In scalar QED we study the Schwinger pair production from an initial ensemble of charged bosons when an electric field is turned on for a finite period together with or without a constant magnetic field. The scalar QED Hamiltonian depends on time through the electric field, which causes the initial ensemble of bosons to evolve out of equilibrium. Using the Liouville-von Neumann method for the density operator and quantum states for each momentum mode, we calculate the Schwinger pair-production rate at finite temperature, which is the pair-production rate from the vacuum times a thermal factor of the Bose-Einstein distribution.Comment: RevTex 10 pages, no figure; replaced by the version accepted in Phys. Rev. D; references correcte

Enhancing 2D Growth of Organic Semiconductor Thin Films with Macroporous Structures via a Small-Molecule Heterointerface

The physical structure of an organic solid is strongly affected by the surface of the underlying substrate. Controlling this interface is an important issue to improve device performance in the organic electronics community. Here we report an approach that utilizes an organic heterointerface to improve the crystallinity and control the morphology of an organic thin film. Pentacene is used as an active layer above, and m-bis(triphenylsilyl) benzene is used as the bottom layer. Sequential evaporations of these materials result in extraordinary morphology with far fewer grain boundaries and myriad nanometre-sized pores. These peculiar structures are formed by difference in molecular interactions between the organic layers and the substrate surface. The pentacene film exhibits high mobility up to 6.3 cm(2)V(-1)s(-1), and the pore-rich structure improves the sensitivity of organic-transistor-based chemical sensors. Our approach opens a new way for the fabrication of nanostructured semiconducting layers towards high-performance organic electronics.X116049Nsciescopu

Jamming transition in a highly dense granular system under vertical vibration

The dynamics of the jamming transition in a three-dimensional granular system under vertical vibration is studied using diffusing-wave spectroscopy. When the maximum acceleration of the external vibration is large, the granular system behaves like a fluid, with the dynamic correlation function G(t) relaxing rapidly. As the acceleration of vibration approaches the gravitational acceleration g, the relaxation of G(t) slows down dramatically, and eventually stops. Thus the system undergoes a phase transition and behaves like a solid. Near the transition point, we find that the structural relaxation shows a stretched exponential behavior. This behavior is analogous to the behavior of supercooled liquids close to the glass transition.Comment: 5 pages, 5 figures, accepted by Phys. Rev.