Neste trabalho fazemos um estudo do conceito de soma torcida de F-espaços. Apresentamos algumas propriedades e simplificações na construção de somas torcidas de F-espaços localmente limitados. Em particular, estudamos uma condição suficiente para que uma soma torcida de espaços de Banach seja um espaço de Banach. Finalmente aplicamos esses conceitos para definir o espaço construído por N. J. Kalton, que é um exemplo de um espaço de Banach não isomorfo ao conjugado complexo. Este espaço X de Kalton corresponde a uma soma torcida de espaços de Hilbert, isto é, X possui um subespaço fechado E tal que E e X/E são isomorfos a espaços de Hilbert. / In this work we study the concept of twisted sum of F-spaces. We also study some properties and simplifications in the construction of twisted sums of locally bounded F-spaces. In particular, we study a sufficient condition for a twisted sum of Banach spaces to be a Banach space. Finally we apply these concepts to define the space constructed by N. J. Kalton, which is an example of a Banach space not isomorphic to its complex conjugate. The Kalton space X is a twisted sum of Hilbert spaces, i.e. X has a closed subspace E such that E and X/E are isomorphic to Hilbert spaces.

The ability to isolate single atomic layers of van der Waals materials has led to renewed interest in the electronic and optical properties of these materials as they can be fundamentally different at the monolayer limit. Moreover, these 2D crystals can be assembled together layer by layer, with controllable sequence and orientation, to form artificial materials that exhibit new features that are not found in monolayers nor bulk. Twisted bilayer graphene is one such prototype system formed by two monolayer graphene layers placed on top of each other with a twist angle between their lattices, whose electronic band structure depends on the twist angle. This thesis presents the efforts to explore the electronic and optical properties of twisted bilayer graphene by Raman spectroscopy and scanning tunneling microscopy measurements. We first synthesize twisted bilayer graphene with various twist angles via chemical vapor deposition. Using a combination of scanning tunneling microscopy and Raman spectroscopy, the twist angles are determined. The strength of the Raman G peak is sensitive to the electronic band structure of twisted bilayer graphene and therefore we use this peak to monitor changes upon doping. Our results demonstrate the ability to modify the electronic and optical properties of twisted bilayer graphene with doping. We also fabricate twisted bilayer graphene by controllable stacking of two graphene monolayers with a dry transfer technique. For twist angles smaller than one degree, many body interactions play an important role. It requires eight electrons per moire unit cell to fill up each band instead of four electrons in the case of a larger twist angle. For twist angles smaller than 0.4 degree, a network of domain walls separating AB and BA stacking regions forms, which are predicted to host topologically protected helical states. Using scanning tunneling microscopy and spectroscopy, these states are confirmed to appear on the domain walls when inversion symmetry is broken with an external electric field. We observe a double-line profile of these states on the domain walls, only occurring when the AB and BA regions are gaped. These states give rise to channels that could transport charge in a dissipationless manner making twisted bilayer graphene a promising platform to realize controllable topological networks for future applications.

In the search for natural orbital angular momentum (OAM) effects, some of the first incoherent scatter experiments with twisted radar beams during aurora were conducted at Poker Flat Incoherent Scatter Radar (PFISR), Alaska, USA, in October 2012. Experimental data of scatter from beam configurations with opposite twists were investigated. By the use of hypothesis tests in combination with Monte Carlo simulations together with traditional estimations of the mean and confidence interval, asymmetries between scatter of radar beams with opposite twists were identified for an integration time of at least 30 minutes. Asymmetries were detected in the internal radar noise too, but not necessarily with the same signs as for the asymmetries from the ionospheric signals. The asymmetries identified could be due to amplified noise for signals coming from intense aurora or perhaps the rectangular-shaped antenna array used at PFISR. These two possible causes need to be ruled out before suggesting that the asymmetries identified are an outcome of OAM effects present in the ionosphere.

The objective of this research was to investigate the effects of twisted steel micro rebar (TSMR) fibers on 1) the mechanical properties of concrete used in bridge deck construction and 2) the early cracking behavior of concrete bridge decks. This research involved the evaluation of four newly constructed bridge decks through a series of laboratory and field tests. At each location, one deck was constructed using a conventional concrete mixture without TSMR, and one was constructed using the same conventional concrete mixture with an addition of 40 lb of TSMR per cubic yard of concrete. Regarding laboratory testing, the conventional and TSMR beam specimens exhibited similar average changes in height after 4 months of shrinkage testing. The electrical impedance measurements did not indicate a notable difference between specimens comprising concrete with TSMR and those comprising conventional concrete. Although no notable difference in behavior between conventional and TSMR specimens was apparent before initial cracking, the toughness of the TSMR specimens was substantially greater than that of the conventional concrete specimens. Regarding field testing, sensors installed in the bridge decks indicated that the addition of TSMR does not affect internal concrete temperature, moisture content, or electrical conductivity. The average Schmidt rebound number varied little between the TSMR decks and conventional decks; therefore, the stiffness of the TSMR concrete was very similar to that of conventional concrete. Distress surveys showed that the conventional decks exhibited notably more cracking than the TSMR decks. The TSMR fibers exhibited the ability to limit both crack density and crack width. For all of the decks, chloride concentrations increased every year as a result of the use of deicing salts on the bridge decks during winter. However, the chloride concentrations for samples collected over cracked concrete increased more rapidly than those for samples collected over non-cracked concrete. Although TSMR fibers themselves do not directly affect the rate at which chloride ions penetrated cracked or non-cracked concrete, the fibers do prevent cracking, which, in turn, limits the penetration of chloride ions into the decks. Therefore, the use of TSMR would be expected to decrease the area of a bridge deck affected by cracking and subsequent chloride-induced corrosion damage and thereby increase the service life of the bridge deck.

Thesis advisor: Solomon Friedberg / We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

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When nematic liquid crystals are placed between parallel glass plates with differing alignment directions, the bulk will twist in order to match the boundary conditions. This phenomenon of a twisted cell has been used extensively for the development of everyday liquid-crystal displays. However, there has been limited study of the twisted cell beyond the 90-degree twist case. In this thesis, I explore the behaviour of inhomogeneous liquid-crystal devices where the front and back alignment layers are uniquely and spatially patterned. This creates a non-symmetric device which can act on light differently depending on the orientation of the device and an externally applied voltage. The effect on the polarization of light is theoretically modelled using Jones matrices, and elastic continuum theory is employed to fully understand how the twist and tilt distributions of the liquid crystals change with field strength. Different pattern configurations were fabricated, tested, and characterized, revealing the complex behaviour that occurs with an applied electric field. Liquid-crystal devices provide a bespoke way of tailoring the spatial distribution of light and photons. A set of quantum key distribution experiments through underwater channels, leveraging these devices to encode information on structured photons, is also presented.

Current progress in mobility assistive devices revolves around traditional actuation methods including electric motors, hydraulics, and pneumatic cylinders to provide assistive joint torques to the user. While these mechanisms are effective at providing the torques needed, they are often bulky, heavy, and suffer from poor alignment with the joints of the user. These drawbacks have created a need for novel technologies that can provide a more compact and compliant form of actuation. Twisted and coiled polymers, under the thermomechanical class of smart material actuators, have emerged as a strong candidate for use as soft actuators in assistive devices due to their low cost, commercial availability, high stroke capacity, and power density. Progress to their development is currently limited by lack of proper standardization in the fabrication process, along with incomplete characterization of its quasi-static mechanical and thermal behaviours and how the performance is influenced by various design considerations. This thesis defined a fabrication process of twisted coiled polymer actuators and evaluated the trends between design considerations and their impacts on the final actuator performance. In this work, a fabrication rig was developed to manufacture consistent and repeatable actuators, while enabling the control of various identified design parameters. Subsequently, a comprehensive experimental evaluation was accomplished which resulted in a better understanding of the relationships between these parameters and the actuator performance including its tensile stroke, force generation, and variable stiffness properties. The results provided a foundation for designers to consider which variables should be controlled during both actuator fabrication and operation, in order to optimize its final performance to meet a set of prescribed requirements.

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No description available.