The Plastic Coupled Map Lattice: a Novel Image‐processing Paradigm

Coupled map lattices (CML) can describe many relaxation and optimization algorithms currently used in image processing. We recently introduced the ‘‘plastic‐CML’’ as a paradigm to extract (segment) objects in an image. Here, the image is applied by a set of forces to a metal sheet which is allowed to undergo plastic deformation parallel to the applied forces. In this paper we present an analysis of our ‘‘plastic‐CML’’ in one and two dimensions, deriving the nature and stability of its stationary solutions. We also detail how to use the CML in image processing, how to set the system parameters and present examples of it at work. We conclude that the plastic‐CML is able to segment images with large amounts of noise and large dynamic range of pixel values, and is suitable for a very large scale integration(VLSI) implementation.

Aspects of Chiral Symmetry Breaking in Lattice QCD

Thesis (Ph.D.)--University of Washington, 2016-08

Functional alkali tantalate 2D structures for microelectronics and related applications

Alkali tantalates and niobates, including K(Ta / Nb)O3, Li(Ta / Nb)O3 and Na(Ta / Nb)O3, are a very promising ferroic family of lead-free compounds with perovskite-like structures. Their versatile properties make them potentially interesting for current and future application in microelectronics, photocatalysis, energy and biomedics. Among them potassium tantalate, KTaO3 (KTO), has been raising interest as an alternative for the well-known strontium titanate, SrTiO3 (STO). KTO is a perovskite oxide with a quantum paraelectric behaviour when electrically stimulated and a highly polarizable lattice, giving opportunity to tailor its properties via external or internal stimuli. However problems related with the fabrication of either bulk or 2D nanostructures makes KTO not yet a viable alternative to STO. Within this context and to contribute scientifically to the leverage tantalate based compounds applications, the main goals of this thesis are: i) to produce and characterise thin films of alkali tantalates by chemical solution deposition on rigid Si based substrates, at reduced temperatures to be compatible with Si technology, ii) to fulfil scientific knowledge gaps in these relevant functional materials related to their energetics and ii) to exploit alternative applications for alkali tantalates, as photocatalysis. In what concerns the synthesis attention was given to the understanding of the phase formation in potassium tantalate synthesized via distinct routes, to control the crystallization of desired perovskite structure and to avoid low temperature pyrochlore or K-deficient phases. The phase formation process in alkali tantalates is far from being deeply analysed, as in the case of Pb-containing perovskites, therefore the work was initially focused on the process-phase relationship to identify the driving forces responsible to regulate the synthesis. Comparison of phase formation paths in conventional solid-state reaction and sol-gel method was conducted. The structural analyses revealed that intermediate pyrochlore K2Ta2O6 structure is not formed at any stage of the reaction using conventional solid-state reaction. On the other hand in the solution based processes, as alkoxide-based route, the crystallization of the perovskite occurs through the intermediate pyrochlore phase; at low temperatures pyrochlore is dominant and it is transformed to perovskite at >800 °C. The kinetic analysis carried out by using Johnson-MehlAvrami-Kolmogorow model and quantitative X-ray diffraction (XRD) demonstrated that in sol-gel derived powders the crystallization occurs in two stages: i) at early stage of the reaction dominated by primary nucleation, the mechanism is phase-boundary controlled, and ii) at the second stage the low value of Avrami exponent, n ~ 0.3, does not follow any reported category, thus not permitting an easy identification of the mechanism. Then, in collaboration with Prof. Alexandra Navrotsky group from the University of California at Davis (USA), thermodynamic studies were conducted, using high temperature oxide melt solution calorimetry. The enthalpies of formation of three structures: pyrochlore, perovskite and tetragonal tungsten bronze K6Ta10.8O30 (TTB) were calculated. The enthalpies of formation from corresponding oxides, ∆Hfox, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -203.63 ± 2.84 kJ/mol, - 358.02 ± 3.74 kJ/mol, and -1252.34 ± 10.10 kJ/mol, respectively, whereas from elements, ∆Hfel, for KTaO3, KTa2.2O6 and K6Ta10.8O30 are -1408.96 ± 3.73 kJ/mol, -2790.82 ± 6.06 kJ/mol, and -13393.04 ± 31.15 kJ/mol, respectively. The possible decomposition reactions of K-deficient KTa2.2O6 pyrochlore to KTaO3 perovskite and Ta2O5 (reaction 1) or to TTB K6Ta10.8O30 and Ta2O5 (reaction 2) were proposed, and the enthalpies were calculated to be 308.79 ± 4.41 kJ/mol and 895.79 ± 8.64 kJ/mol for reaction 1 and reaction 2, respectively. The reactions are strongly endothermic, indicating that these decompositions are energetically unfavourable, since it is unlikely that any entropy term could override such a large positive enthalpy. The energetic studies prove that pyrochlore is energetically more stable phase than perovskite at low temperature. Thus, the local order of the amorphous precipitates drives the crystallization into the most favourable structure that is the pyrochlore one with similar local organization; the distance between nearest neighbours in the amorphous or short-range ordered phase is very close to that in pyrochlore. Taking into account the stoichiometric deviation in KTO system, the selection of the most appropriate fabrication / deposition technique in thin films technology is a key issue, especially concerning complex ferroelectric oxides. Chemical solution deposition has been widely reported as a processing method to growth KTO thin films, but classical alkoxide route allows to crystallize perovskite phase at temperatures >800 °C, while the temperature endurance of platinized Si wafers is ~700 °C. Therefore, alternative diol-based routes, with distinct potassium carboxylate precursors, was developed aiming to stabilize the precursor solution, to avoid using toxic solvents and to decrease the crystallization temperature of the perovskite phase. Studies on powders revealed that in the case of KTOac (solution based on potassium acetate), a mixture of perovskite and pyrochlore phases is detected at temperature as low as 450 °C, and gradual transformation into monophasic perovskite structure occurs as temperature increases up to 750 °C, however the desired monophasic KTaO3 perovskite phase is not achieved. In the case of KTOacac (solution with potassium acetylacetonate), a broad peak is detected at temperatures <650 °C, characteristic of amorphous structures, while at higher temperatures diffraction lines from pyrochlore and perovskite phases are visible and a monophasic perovskite KTaO3 is formed at >700 °C. Infrared analysis indicated that the differences are due to a strong deformation of the carbonate-based structures upon heating. A series of thin films of alkali tantalates were spin-coated onto Si-based substrates using diol-based routes. Interestingly, monophasic perovskite KTaO3 films deposited using KTOacac solution were obtained at temperature as low as 650 °C; films were annealed in rapid thermal furnace in oxygen atmosphere for 5 min with heating rate 30 °C/sec. Other compositions of the tantalum based system as LiTaO3 (LTO) and NaTaO3 (NTO), were successfully derived as well, onto Si substrates at 650 °C as well. The ferroelectric character of LTO at room temperature was proved. Some of dielectric properties of KTO could not be measured in parallel capacitor configuration due to either substrate-film or filmelectrode interfaces. Thus, further studies have to be conducted to overcome this issue. Application-oriented studies have also been conducted; two case studies: i) photocatalytic activity of alkali tantalates and niobates for decomposition of pollutant, and ii) bioactivity of alkali tantalate ferroelectric films as functional coatings for bone regeneration. Much attention has been recently paid to develop new type of photocatalytic materials, and tantalum and niobium oxide based compositions have demonstrated to be active photocatalysts for water splitting due to high potential of the conduction bands. Thus, various powders of alkali tantalates and niobates families were tested as catalysts for methylene blue degradation. Results showed promising activities for some of the tested compounds, and KNbO3 is the most active among them, reaching over 50 % degradation of the dye after 7 h under UVA exposure. However further modifications of powders can improve the performance. In the context of bone regeneration, it is important to have platforms that with appropriate stimuli can support the attachment and direct the growth, proliferation and differentiation of the cells. In lieu of this here we exploited an alternative strategy for bone implants or repairs, based on charged mediating signals for bone regeneration. This strategy includes coating metallic 316L-type stainless steel (316L-SST) substrates with charged, functionalized via electrical charging or UV-light irradiation, ferroelectric LiTaO3 layers. It was demonstrated that the formation of surface calcium phosphates and protein adsorption is considerably enhanced for 316L-SST functionalized ferroelectric coatings. Our approach can be viewed as a set of guidelines for the development of platforms electrically functionalized that can stimulate tissue regeneration promoting direct integration of the implant in the host tissue by bone ingrowth and, hence contributing ultimately to reduce implant failure.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

Lattice pulling effect and strain relaxation in axial (In, Ga)N/GaN nanowire heterostructures grown on GaN-buffered Si(111) substrate

Transmission electron microscopy and spatially resolved electron energy-loss spectroscopy have been applied to investigate the indium distribution and the interface morphology in axial (In,Ga)N/GaN nanowire heterostructures. The ordered axial (In,Ga)N/GaN nanowire heterostructures with an indium concentration up to 80% are grown by molecular beam epitaxy on GaN-buffered Si(111) substrates. We observed a pronounced lattice pulling effect in all the nanowire samples given in a broad transition region at the interface. The lattice pulling effect becomes smaller and the (In,Ga)N/GaN interface width is reduced as the indium concentration is increased in the (In,Ga)N section. The result can be interpreted in terms of the increased plastic strain relaxation via the generation of the misfit dislocations at the interface.

Lattice Boltzmann Modeling and Specialized Laboratory Techniques to Determine the Permeability of Megaporous Karst Rock

The Pleistocene carbonate rock Biscayne Aquifer of south Florida contains laterally-extensive bioturbated ooltic zones characterized by interconnected touching-vug megapores that channelize most flow and make the aquifer extremely permeable. Standard petrophysical laboratory techniques may not be capable of accurately measuring such high permeabilities. Instead, innovative procedures that can measure high permeabilities were applied. These fragile rocks cannot easily be cored or cut to shapes convenient for conducting permeability measurements. For the laboratory measurement, a 3D epoxy-resin printed rock core was produced from computed tomography data obtained from an outcrop sample. Permeability measurements were conducted using a viscous fluid to permit easily observable head gradients (~2 cm over 1 m) simultaneously with low Reynolds number flow. For a second permeability measurement, Lattice Boltzmann Method flow simulations were computed on the 3D core renderings. Agreement between the two estimates indicates an accurate permeability was obtained that can be applied to future studies.

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions. The research was focused on fluid-structure interaction solutions in complex, mesh-resistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.

Shaken not stirred: creating exotic angular momentum states by shaking an optical lattice

We propose a method to create higher orbital states of ultracold atoms in the Mott regime of an optical lattice. This is done by periodically modulating the position of the trap minima (known as shaking) and controlling the interference term of the lasers creating the lattice. These methods are combined with techniques of shortcuts to adiabaticity. As an example of this, we show specifically how to create an anti-ferromagnetic type ordering of angular momentum states of atoms. The specific pulse sequences are designed using Lewis-Riesenfeld invariants and a fourlevel model for each well. The results are compared with numerical simulations of the full Schrodinger equation.

Finite group lattice gauge theories for quantum simulation

The present manuscript focuses on Lattice Gauge Theories based on finite groups. For the purpose of Quantum Simulation, the Hamiltonian approach is considered, while the finite group serves as a discretization scheme for the degrees of freedom of the gauge fields. Several aspects of these models are studied. First, we investigate dualities in Abelian models with a restricted geometry, using a systematic approach. This leads to a rich phase diagram dependent on the super-selection sectors. Second, we construct a family of lattice Hamiltonians for gauge theories with a finite group, either Abelian or non-Abelian. We show that is possible to express the electric term as a natural graph Laplacian, and that the physical Hilbert space can be explicitly built using spin network states. In both cases we perform numerical simulations in order to establish the correctness of the theoretical results and further investigate the models.

Thermodynamic Study Of The Micellization Of Zwitterionic Surfactants And Their Interaction With Polymers In Water By Isothermal Titration Calorimetry.

The micellization of a homologous series of zwitterionic surfactants, a group of sulfobetaines, was studied using isothermal titration calorimetry (ITC) in the temperature range from 15 to 65 °C. The increase in both temperature and the alkyl chain length leads to more negative values of ΔGmic(0) , favoring the micellization. The entropic term (ΔSmic(0)) is predominant at lower temperatures, and above ca. 55-65 °C, the enthalpic term (ΔHmic(0)) becomes prevalent, figuring a jointly driven process as the temperature increases. The interaction of these sulfobetaines with different polymers was also studied by ITC. Among the polymers studied, only two induced the formation of micellar aggregates at lower surfactant concentration: poly(acrylic acid), PAA, probably due to the formation of hydrogen bonds between the carboxylic group of the polymer and the sulfonate group of the surfactant, and poly(sodium 4-styrenesulfonate), PSS, probably due to the incorporation of the hydrophobic styrene group into the micelles. The prevalence of the hydrophobic and not the electrostatic contributions to the interaction between sulfobetaine and PSS was confirmed by an increased interaction enthalpy in the presence of electrolytes (NaCl) and by the observation of a significant temperature dependence, the latter consistent with the proposed removal of hydrophobic groups from water.

Polyphenol Extraction Optimisation From Ceylon Gooseberry (dovyalis Hebecarpa) Pulp.

Originally from Asia, Dovyalis hebecarpa is a dark purple/red exotic berry now also produced in Brazil. However, no reports were found in the literature about phenolic extraction or characterisation of this berry. In this study we evaluate the extraction optimisation of anthocyanins and total phenolics in D. hebecarpa berries aiming at the development of a simple and mild analytical technique. Multivariate analysis was used to optimise the extraction variables (ethanol:water:acetone solvent proportions, times, and acid concentrations) at different levels. Acetone/water (20/80 v/v) gave the highest anthocyanin extraction yield, but pure water and different proportions of acetone/water or acetone/ethanol/water (with >50% of water) were also effective. Neither acid concentration nor time had a significant effect on extraction efficiency allowing to fix the recommended parameters at the lowest values tested (0.35% formic acid v/v, and 17.6 min). Under optimised conditions, extraction efficiencies were increased by 31.5% and 11% for anthocyanin and total phenolics, respectively as compared to traditional methods that use more solvent and time. Thus, the optimised methodology increased yields being less hazardous and time consuming than traditional methods. Finally, freeze-dried D. hebecarpa showed high content of target phytochemicals (319 mg/100g and 1,421 mg/100g of total anthocyanin and total phenolic content, respectively).

Influence Of Substrate Steps On The Catalytic Properties Of Pt Layers: The Ethanol Electrooxidation Reaction.

The ethanol oxidation reaction (EOR) is investigated on Pt/Au(hkl) electrodes. The Au(hkl) single crystals used belong to the [n(111)x(110)] family of planes. Pt is deposited following the galvanic exchange of a previously deposited Cu monolayer using a Pt(2+) solution. Deposition is not epitaxial and the defects on the underlying Au(hkl) substrates are partially transferred to the Pt films. Moreover, an additional (100)-step-like defect is formed, probably as a result of the strain resulting from the Pt and Au lattice mismatch. Regarding the EOR, both vicinal Pt/Au(hkl) surfaces exhibit a behavior that differs from that expected for stepped Pt; for instance, the smaller the step density on the underlying Au substrate, the greater the ability to break the CC bond in the ethanol molecule, as determined by in situ Fourier transform infrared spectroscopy measurements. Also, we found that the acetic acid production is favored as the terrace width decreases, thus reflecting the inefficiency of the surface array to cleave the ethanol molecule.