Browsing by Subject "topology"
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Item Broken Lefschetz fibrations on smooth four-manifolds(2010-05) Williams, Jonathan Dunklin; Gompf, Robert E., 1957-; Etnyre, John B.; Luecke, John; Reid, Alan; Sadun, Lorenzo A.It is known that an arbitrary smooth, oriented four-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken Lefschetz fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken Lefschetz fibration in a given homotopy class of smooth maps. One notable application is that adding an additional projection move generates all broken Lefschetz fibrations, regardless of homotopy class. The paper ends with further applications and open problems.Item Fiberedness of almost-Montesinos knots(2015-05) Miller, Maggie; Gordon, CameronIn this paper we begin to classify fiberedness of "Almost-Montesinos" knots, a generalization of Montesinos knots. We employ the method used in the classification of fiberedness of Montesinos knots due to Hirasawa and Murasugi. To achieve this classification, we find minimal-genus surfaces of "skew pretzel links" (a generalization of pretzel links) via sutured manifold decompositions, following Gabai's method for pretzel links. We end by stating three remaining cases.Item Helix Capping in RNA Structure(PLOS One, 2014-04-01) Lee, Jung C.; Gutell, Robin R.Helices are an essential element in defining the three-dimensional architecture of structured RNAs. While internal basepairs in a canonical helix stack on both sides, the ends of the helix stack on only one side and are exposed to the loop side, thus susceptible to fraying unless they are protected. While coaxial stacking has long been known to stabilize helix ends by directly stacking two canonical helices coaxially, based on analysis of helix-loop junctions in RNA crystal structures, herein we describe helix capping, topological stacking of a helix end with a basepair or an unpaired nucleotide from the loop side, which in turn protects helix ends. Beyond the topological protection of helix ends against fraying, helix capping should confer greater stability onto the resulting composite helices. Our analysis also reveals that this general motif is associated with the formation of tertiary structure interactions. Greater knowledge about the dynamics at the helix-junctions in the secondary structure should enhance the prediction of RNA secondary structure with a richer set of energetic rules and help better understand the folding of a secondary structure into its three-dimensional structure. These together suggest that helix capping likely play a fundamental role in driving RNA folding.Item Mass Customization: Reuse of Topology Information to Accelerate Slicing Process for Additive Manufacturing(University of Texas at Austin, 2016) Ye, Hang; Zhou, Chi; Xu, WenyaoAdditive manufacturing (AM) can build objects with complex features with little extra effort, opening up potentials to realize mass customization. Continuous Liquid Interface Production (CLIP) prints object in a continuous fashion, leading to extremely high productivity and consequently enabling mass customization. CLIP adopts a large number of images as input, which poses a fundamental challenge in layer generation. The slicing procedure for a single customized model can take tens of minutes or even hours to complete, and the time consumption becomes more prominent in mass customization context. Motivated by the similarities among the customized products, we proposed a new slicing paradigm. It reuses topology information obtained from the template model for other customized products from the same category. The idea of topology information reuse is implemented at three levels, including self reuse, intra-model reuse, and inter-model reuse. Experimental results show that the proposed slicing paradigm can significantly reduce the time consumption on pre-fabrication computation, and ultimately fulfill mass customization enabled by AM.Item Multi-Objective Topology Optimization of Additively Manufactured Heat Exchangers(University of Texas at Austin, 2019) Paudel, Basil J.; Masoomi, Mohammad; Thompson, Scott M.The higher design flexibility offered by additive manufacturing (AM) allows for radical improvements in the design and functionality of legacy parts. In this study, a flat-plate heat exchanger is designed and optimized using the ANSYS topology optimization module. Unlike conventional numerical optimization tools, the current optimization approach employs multiple objective functions, including mass reduction and maximization of heat transfer efficiency. Two unique, initial designs were used for ‘seeding’ the multi-objective topology optimization (TO) routines and the results are compared and discussed. Topology design and operating (boundary condition) variables were varied to elucidate major design sensitivities. The predicted heat transfer within the topology-optimized parts was validated using separate numerical methods. Constraints related to flow pressure drops and additive manufacturability were enforced. In both cases, the optimal design performed significantly better than the conventional heat exchanger in terms of thermal efficiency per unit mass.Item Next-Generation Fibre-Reinforced Lightweight Structures for Additive Manufacturing(University of Texas at Austin, 2018) Plocher, J.; Panesar, A.In an attempt to realise next-generation lightweight parts and to fully utilize the inherent design freedom of AM, we propose a topology optimization based design procedure that includes the anisotropic considerations for continuous fibre printing of variable stiffness composites. In this paper, we aim to improve the normalized compliance of a beam in a three-point bending scenario, using a skeletal reinforcement for a topology in which the change in fibre orientation is derived from the medial axis information. FDM with a dual-nozzle system printing nylon and carbon fibre filaments were utilized for fabrication. The toolpath i.e. reinforcement strategy available from the commercial software Eiger® was chosen to imitate the proposed strategy. The numerical investigation is complemented with experimental tests and a general benchmarking is conducted using standard pedants. The results have shown improved specific flexural stiffness for samples with skeletal reinforcement. The skeletal information is therefore considered as important tool for the retrieval of fibre angles which align with the principle stresses and therefore allow for a more efficient fibre placement in AM parts for future lightweight end-use parts.Item Photonic topological insulators: Building topological states of matter(2013-05) Berdanier, William; Shvets, GennadyThe discovery of topological insulators -- materials which are conventional insulators in the bulk but support dissipationless, "topologically protected" edge states -- has revolutionized condensed matter physics in recent years. Indeed, topological insulators have been of interest to physicists as much for their unique physics as for their plethora of potential applications, which run the gamut from nano-scale electronic circuits to the realization of Majorana fermions and large-scale quantum computers. However, the main drawback of topological insulators is that they are currently difficult to produce experimentally, and only a handful of materials supporting the topological insulator state are known. The Shvets group recently proposed an analogue of the topological insulator state in photonic crystals. In contrast to the topological insulator state in conventional materials, in which we must simply take what nature gives us, in photonics we can literally build a topological insulator. In order for this photonic topological insulator state to occur, non-zero bianisotropy is introduced. Bianisotropy simply adds another coupling $\chi$ to the constitutive relations for the crystal: $\v{D} = \hat\epsilon \cdot \v{E} + \hat\chi \cdot \v{H}$, $\v{B} = \hat{\chi}^\dagger \cdot \v{E}+\hat\mu \cdot \v{H}$. A photonic crystal composed of a hexagonal lattice of rods has a Dirac point crossing in its band structure at the K-point, and in the presence of a non-zero bianisotropy, this Dirac point becomes gapped, supporting topologically protected edge states. This thesis seeks to extend the photonic topological insulator model originally proposed by Shvets et. al. by adding another important term from photonics, a so-called "magneto-optic" (MO) term. This term is produced by applying an external magnetic field to the crystal, which is interesting theoretically because magnetic-fields are not time-reversal symmetric. Thus this research has a twofold purpose: (1) to determine the effects of another important photonic property on the photonic topological insulator structure and potentially exploit those effects in novel applications, thereby \emph{building} topologically insulating structures, and (2) to investigate the role of time-reversal symmetry breaking in topological insulators via photonic crystals. For the photonic topological insulator structure, I derive an effective Dirac Hamiltonian that describes the two bands of the Dirac crossing. I show that this Hamiltonian, when no MO term is present, is identical to the famous Kane-Mele Hamiltonian that introduced the topological insulator state in conventional materials. Here, bianisotropy plays the role of spin-orbit coupling, with the states $\Psi^+=E_z + H_z$ and $\Psi^-= E_z - H_z$ playing the roles of spin-up and spin-down, respectively. I demonstrate that these states are immune to disorder -- a consequence of their topological protection -- by calculating the Chern numbers of the edge states, calculating their band diagrams, and by launching these states in simulations and showing that they propagate one-way through various obstacles with no backscattering. I also calculate the new terms added by the time-reversal-symmetry-breaking MO term and calculate analytically what becomes of the system's eigenstates. As well, a weak form of Maxwell's equations is derived for use in finite-element-method simulations in COMSOL, then implemented for band-structure calculations. I find that MO adds a second mass term to the Dirac Hamiltonian which has no natural analogue in conventional topological insulators, as this mass term is not time-reversal invariant. The system's eigenstates are shown to be an admixture of spin-up and spin-down, which I refer to as $\Phi^+$ and $\Phi^-$, which become $\Psi^+$ and $\Psi^-$ in the limit of bianisotropy being much stronger than MO and become just $E_z$ and $H_z$ (TE and TM modes) in the limit of MO being much stronger than bianisotropy. MO's effect on the band structure is shown to be that it splits the gap caused by bianisotropy alone, dividing it into two gaps, one larger than the other. As the magnitude of the MO term increases, one of the gaps becomes smaller indefinitely while the other grows, a consistent result with previous literature in photonics which predicts that the MO term alone only opens \emph{one} gap (only TM waves are affected by the MO term). Several types of interfaces are explored in order to investigate the edge states in the presence of MO and bianisotropy. Remarkably, it is found that if the ratio of the MO term and the bianisotropy is kept constant across two interfacing photonic crystals, then the edge states survive. More remarkable still, they retain their topological protection, demonstrated via propagating $\Phi^\pm$ through disordered interfaces. This result is truly unexpected, as the topological protection of the edge states of topological insulators is fundamentally dependent on the system being time-reversal invariant.Item A Second-Order Bias Model For The Logarithmic Halo Mass Density(2012-07) Jee, Inh; Park, Changbom; Kim, Juhan; Choi, Yun-Yong; Kim, Sungsoo S.; Jee, InhWe present an analytic model for the local bias of dark matter halos in a Lambda CDM universe. The model uses the halo mass density instead of the halo number density and is searched for various halo mass cuts, smoothing lengths, and redshift epochs. We find that, when the logarithmic density is used, the second-order polynomial can fit the numerical relation between the halo mass distribution and the underlying matter distribution extremely well. In this model, the logarithm of the dark matter density is expanded in terms of log halo mass density to the second order. The model remains excellent for all halo mass cuts (from M-cut = 3 x 10(11) to 3 x 10(12) h (1) M-circle dot), smoothing scales (from R = 5 h(-1) Mpc to 50h(-1) Mpc), and redshift ranges (from z = 0 to 1.0) considered in this study. The stochastic term in the relation is found to be not entirely random, but a part of the term can be determined by the magnitude of the shear tensor.Item Simple Genetic Selection Protocol For Isolation Of Overexpressed Genes That Enhance Accumulation Of Membrane-Integrated Human G Protein-Coupled Receptors In Escherichia Coli(2010-09) Skretas, Georgios; Georgiou, George; Skretas, Georgios; Georgiou, GeorgeThe efficient production of membrane proteins in bacteria remains a major challenge. In this work, we sought to identify overexpressed genes that enhance the yields of recombinant membrane proteins in Escherichia coli. We developed a genetic selection system for bacterial membrane protein production, consisting of membrane protein fusions with the enzyme beta-lactamase and facile selection of high-production strains on ampicillin-containing media. This system was used to screen the ASKA library, an ordered library of plasmids encoding all the known E. coli open reading frames (ORFs), and several clones with the ability to accumulate enhanced amounts of recombinant membrane proteins were selected. Notably, coexpression of ybaB, a gene encoding a putative DNA-binding protein of unknown function, was found to enhance the accumulation of a variety of membrane-integrated human G protein-coupled receptors and other integral membrane proteins in E. coli by up to 10-fold. The results of this study highlight the power of genetic approaches for identifying factors that impact membrane protein biogenesis and for generating engineered microbial hosts for membrane protein production.Item Trapezoidality and the Alexander polynomial(2012) Cameron, James; Gordon, CameronWe study the Alexander polynomial of a class of alternating Montesinos links, and show that this class of links satisfies a conjecture of Ralph Fox that states that alternating links have trapezoidal polynomials.