239 research outputs found

    Computation of Implicit Representation of Volumetric Shells with Predefined Thickness

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    We propose and validate a method to find an implicit representation of a surface placed at a distance h from another implicit surface. With two such surfaces on either side of the original surface, a volumetric shell of predefined thickness can be obtained. The usability of the proposed method is demonstrated through providing solid models of triply periodic minimal surface (TPMS) geometries with a predefined constant and variable thickness. The method has an adjustable order of convergence. If applied to surfaces with spatially varying thickness, the convergence order is limited to second order. This accuracy is still substantially higher than the accuracy of any contemporary 3D printer that could benefit from the function as an infill volume for shells with predefined thicknesses

    The lattice size of a lattice polygon

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    We give upper bounds on the minimal degree of a model in P2\mathbb{P}^2 and the minimal bidegree of a model in P1×P1\mathbb{P}^1 \times \mathbb{P}^1 of the curve defined by a given Laurent polynomial, in terms of the combinatorics of the Newton polygon of the latter. We prove in various cases that this bound is sharp as soon as the polynomial is sufficiently generic with respect to its Newton polygon

    Time-Resolved Studies and Nanostructure Formation in Sb2Te3 Films Using Femtosecond Lasers.

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    Antimony telluride (Sb2Te3) is an important material with a wide range of applications in thermoelectrics, data storage devices and topological insulator research. Our work on femtosecond laser studies of Sb2Te3 films has significance for insights into femtosecond laser interaction with Sb2Te3 above the damage threshold, as well as providing a new pathway for novel fabrication of highly-ordered nanostructured Sb2Te3. These new developments are made possible by careful control of the laser scanning conditions, opening the way to future nanoscale studies and materials applications. The pump-probe scheme for the time-resolved studies employed a novel asynchronous optical sampling (ASOPS) technique, which has distinctive advantages over the traditional mechanical-delay scheme including superior stability of beam alignment during scans, faster data acquisition rates, and the ability to monitor a much wider range of dynamics up to ten nanoseconds. With ASOPS, it is shown that a sequence of connected processes can be studied in Sb2Te3 films, from coherent optical phonons and acoustic echoes at picosecond timescale, through thermal transport at nanosecond timescale. In particular, the coherent phonons were used, for the first time, to monitor the element segregation in Sb2Te3 films under high-fluence pump laser irradiation conditions. These results are important for the ultrafast spectroscopy research community: they highlight the need for careful interpretation of coherent phonon spectra in tellurides, which are susceptible to fs laser damage. Femtosecond laser irradiation of Sb2Te3 above ~6 mJ/cm2 was also found to produce highly-ordered nanotracks with a periodicity an order of magnitude below the laser wavelength. A variety of characterization techniques identified these nanotracks as single crystalline Sb2Te3 nanowires separated by polycrystalline phases including a large amount of the insulating Sb2O3. Laser irradiation in different gas environments revealed the sensitivity of the Sb2Te3 surface morphology to the surrounding gas species, especially O2, highlighting the critical role of the ambient environment interactions with Sb2Te3 for nanostructure formation in the thin films. These results provide valuable experimental input for the future analysis of the generation mechanism of these nanostructures. Additionally, the results open up new opportunities for fabrication of in-plane Sb2Te3 nanowires for planar applications.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/108790/1/yuweili_1.pd

    Combinatorics of Pisot Substitutions

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    Siirretty Doriast

    Electronic Transport Behavior of Adatom- and Nanoparticle-Decorated Graphene

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    To induce a non-negligible spin-orbit coupling in monolayer graphene, for the purposes of realizing the Kane-Mele Hamiltonian, transition metal adatoms have been deposited in dilute amounts by thermal evaporation in situ while holding the device temperature near 4K. Electronic transport studies including measurements such as gate voltage dependent conductivity and mobility, weak localization, high field magnetoresistance (Shubnikov de Haas oscillations), quantum Hall, and nonlocal voltage were performed at low temperature before and after sequential evaporations. Studies of tungsten adatoms are consistent with literature regarding other metal adatoms on graphene but were unsuccessful in producing a spin-orbit signature, at least partially due to lithography residue inhibiting the adatoms’ ability to dope the graphene. Osmium adatoms on graphene behave differently from other adatoms in several ways. While all other measured adatoms donate electrons to graphene, osmium is observed to donate holes to graphene. In addition, tungsten and other adatoms directly affect the scattering potentials by causing a dominant Coulomb-like potential from isolated point charges. Osmium, on the other hand, does not obey this simple model. Separately, a claim was made in a recent study of Bi2Te3 nanoparticles on graphene showing tantalizing evidence of quantization in resistance coinciding with predictions for edge channel conduction. Our attempts to reproduce these observations have not been successful so far

    Acousto-Optic Filter Device Using Proton-Exchanged Waveguides

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    This thesis describes an investigation of the acoustic and optical properties of waveguides fabricated by proton-exchange from dilute melts. Initially a narrow-band acousto-optic filter, based on the Integrated Optical Spectrum Analyser, is investigated. The device is proposed to detect and separate two acoustic frequencies and it was envisaged that the angular separation of the acoustically diffracted optical beams could be performed within a channel waveguide structure. However, analysis has indicated the impracticality of the device when operational requirements are considered. The dilute melt proton-exchange process for waveguide fabrication on LiNbO3 substrates is characterised. The waveguides have step-index profiles and are stable immediately after exchange. The waveguide depth increases as a t function of exchange time, so a temperature dependent diffusion coefficient can be assigned and this coefficient fits an Arrhenius law. In comparison with pure melt proton-exchange waveguides, dilute melt waveguides exhibit less in-plane scattering and Rutherford Back-Scattering Spectrometry (RBS) measurements indicate a significantly lower level of latice disorder. Close agreement is found between optical measurements of waveguide depth (assuming a step-index profile) and RBS data for a range of melt dilutions, thus supporting the step-index model as an appropriate profile for the refractive index. Multi-mode waveguides are fabricated on Y-cut LiNbO3 substrates without surface damage, though short post annealing is necessary to relieve induced strain. Planar optical waveguides are fabricated on X-cut and Z-cut LiTaO3 substrates from dilute melts without the need for prolonged post annealing. High quality waveguides with low in-plane scattering levels are produced. The refractive index change is similar to that achieved with titanium indiffused LiNbO3 and RBS measurements indicate a region of lattice disorder similar to that observed with LiNbO3. A line-focus-beam Scanning Acoustic Microscope is used to investigate the acoustical properties of dilute melt proton-exchanged LiNbO3 waveguides. Substantial changes (as much as 5%) in the surface acoustic wave (SAW) propagation velocity due to proton-exchange are observed on all three major-axis crystal cuts, with both increases and decreases in velocity occurring, depending on propagation direction. Changes in acoustic attenuation are also observed. A simple model is used to calculate the 'true' velocity change for a proton-exchange region without the infulence of a virgin LiNbO3 base and the acoustic anisotropy exhibited by the X-and Y-cut LiNbO3 appears greater than that of virgin LiNbO3. A theoretical analysis based on the quasi-static approximation is used to determine the overlap integral between the acoustic and optical waves in proton-exchange waveguides. The overlap integral falls with variations in index profile from step-index to graded-index and the domination of the acousto-optic interaction by the electro-optic effect is emphasized. The analysis indicates that shallow (~3mum) step-index waveguides are required for maximum interaction efficiency and that prolonged annealing results in reduced interaction efficiencies. Acousto-optic devices are fabricated on dilute melt proton-exchanged LiNbO3 and LiTaO3 waveguides using simple, non-optimal, electrode structures. For 7. 5 minutes exchange in 0.5% dilute melt on X-cut LiNbO3 at 22

    Near-integrable behaviour in a family of discretised rotations

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    We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and show that the limit of vanishing discretisation is described by an integrable piecewise-affine Hamiltonian flow, whereby the plane foliates into families of invariant polygons with an increasing number of sides. Considered as perturbations of the flow, the lattice maps assume a different character, described in terms of strip maps: a variant of those found in outer billiards of polygons. Furthermore, the flow is nonlinear (unlike the original rotation), and a suitably chosen Poincare return map satisfies a twist condition. The round-off perturbation introduces KAM-type phenomena: we identify the unperturbed curves which survive the perturbation, and show that they form a set of positive density in the phase space. We prove this considering symmetric orbits, under a condition that allows us to obtain explicit values for densities. Finally, we show that the motion at infinity is a dichotomy: there is one regime in which the nonlinearity tends to zero, leaving only the perturbation, and a second where the nonlinearity dominates. In the domains where the nonlinearity remains, numerical evidence suggests that the distribution of the periods of orbits is consistent with that of random dynamics, whereas in the absence of nonlinearity, the fluctuations result in intricate discrete resonant structures.Comment: PhD Thesis, Queen Mary University of London, 117 page

    Studies of coated and polycrystalline superconductors using the time dependant Ginzburg-Landau equations

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    Time-dependent Ginzburg-Land au equations are used to model 2D and 3D systems containing both superconductors and normal metals, in which both T(_c) and normal-state resistivity are spatially dependent. The equations are solved numerically using an efficient semi-implicit Crank-Nicolson algorithm. The algorithm, is used to model flux entry and exit in homogenous superconductors with metallic coatings of different resistivities. For an abrupt boundary there is a minimum field of initial vortex entry occurring at a kappa-dependent finite ratio of the normal-state resistivities of the superconductor and the normal metal. Highly reversible magnetization characteristics are achieved using a diffusive layer several coherence lengths wide between the superconductor and the normal metal. This work provides the first TD GL simulation in both 2D and 3D of current flow in polycrystalline superconductors, and provides some important new results both qualitative and quantitative. Using a magnetization method we obtain Jc for both 2D and 3D systems, and obtain the correct field and kappa dependences in 3D, given by F = 3.6 x 10-4 B}l (T) (1- b)2. The pre-factor is different (about 3 to 5 times smaller) from that observed in technological superconductors, but evidence is provided showing that this prefactor depends on the details of 1կ effects at the edges of superconducting grains. In 2D, the analytic flux shear calculation developed by Pruymboom in his thin-film work gives good agreement with our computational results.Visualization of Iぜ and dissipation (including movies in the 2D case) shows that in both 2D and 3D, Jc is determined by flux shear along grain boundaries. In 3D the moving fluxons are confined to the grain boundaries, and cut through stationary fluxons which pass through the grains and are almost completely straight
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