Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

Electronic transport in field-effect transistors of sexithiophene

The electronic conduction of thin-film field-effect-transistors (FETs) of sexithiophene was studied. In most cases the transfer curves deviate from standard FET theory; they are not linear, but follow a power law instead. These results are compared to conduction models of "variable-range hopping" and "multi-trap-and-release". The accompanying IV curves follow a Poole-Frenkel (exponential) dependence on the drain voltage. The results are explained assuming a huge density of traps. Below 200 K, the activation energy for conduction was found to be ca. 0.17 eV. The activation energies of the mobility follow the Meyer-Neldel rule. A sharp transition is seen in the behavior of the devices at around 200 K. The difference in behavior of a micro-FET and a submicron FET is shown. (C) 2004 American Institute of Physics.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

A rede de marcação e recaptura: o caso de borboletas do gênero heliconius

(The Mark and Recapture Network: a Heliconius case study). The current pace of habitat destruction, especially in tropical landscapes, has increased the need for understanding minimum patch requirements and patch distance as tools for conserving species in forest remnants. Mark recapture and tagging studies have been instrumental in providing parameters for functional models. Because of their popularity, ease of manipulation and well known biology, butterflies have become model in studies of spatial structure. Yet, most studies on butterflies movement have focused on temperate species that live in open habitats, in which forest patches are barrier to movement. This study aimed to view and review data from mark-recapture as a network in two species of butterfly (Heliconius erato and Heliconius melpomene). A work of marking and recapture of the species was carried out in an Atlantic forest reserve located about 20km from the city of Natal (RN). Mark recapture studies were conducted in 3 weekly visits during January-February and July-August in 2007 and 2008. Captures were more common in two sections of the dirt road, with minimal collection in the forest trail. The spatial spread of captures was similar in the two species. Yet, distances between recaptures seem to be greater for Heliconius erato than for Heliconius melpomene. In addition, the erato network is more disconnected, suggesting that this specie has shorter traveling patches. Moving on to the network, both species have similar number of links (N) and unweighed vertices (L). However, melpomene has a weighed network 50% more connections than erato. These network metrics suggest that erato has more compartmentalized network and restricted movement than melpomene. Thus, erato has a larger number of disconnected components, nC, in the network, and a smaller network diameter. The frequency distribution of network connectivity for both species was better explained by a Power-law than by a random, Poissom distribution, showing that the Power-law provides a better fit than the Poisson for both species. Moreover, the Powerlaw erato is much better adjusted than in melpomene, which should be linked to the small movements that erato makes in the network

DOING MORE WITH SHORT PERIOD DATA: DETERMINING MAGNITUDES FROM CLIPPED AND OVER-RUN SEISMIC DATA AT MOUNT ST. HELENS

How can we calculate earthquake magnitudes when the signal is clipped and over-run? When a volcano is very active, the seismic record may saturate (i.e., the full amplitude of the signal is not recorded) or be over-run (i.e., the end of one event is covered by the start of a new event). The duration, and sometimes the amplitude, of an earthquake signal are necessary for determining event magnitudes; thus, it may be impossible to calculate earthquake magnitudes when a volcano is very active. This problem is most likely to occur at volcanoes with limited networks of short period seismometers. This study outlines two methods for calculating earthquake magnitudes when events are clipped and over-run. The first method entails modeling the shape of earthquake codas as a power law function and extrapolating duration from the decay of the function. The second method draws relations between clipped duration (i.e., the length of time a signal is clipped) and the full duration. These methods allow for magnitudes to be determined within 0.2 to 0.4 units of magnitude. This error is within the range of analyst hand-picks and is within the acceptable limits of uncertainty when quickly quantifying volcanic energy release during volcanic crises. Most importantly, these estimates can be made when data are clipped or over-run. These methods were developed with data from the initial stages of the 2004-2008 eruption at Mount St. Helens. Mount St. Helens is a well-studied volcano with many instruments placed at varying distances from the vent. This fact makes the 2004-2008 eruption a good place to calibrate and refine methodologies that can be applied to volcanoes with limited networks.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Slow passage through thresholds in quantum dot lasers

A turn on of a quantum dot (QD) semiconductor laser simultaneously operating at the ground state (GS) and excited state (ES) is investigated both experimentally and theoretically. We find experimentally that the slow passage through the two successive laser thresholds may lead to significant delays in the GS and ES turn ons. The difference between the turn-on times is measured as a function of the pump rate of change and reveals no clear power law. This has motivated a detailed analysis of rate equations appropriate for two-state lasing QD lasers. We find that the effective time of the GS turn on follows an -1/2 power law provided that the rate of change is not too small. The effective time of the ES transition follows an -1 power law, but its first order correction in ln is numerically significant. The two turn ons result from different physical mechanisms. The delay of the GS transition strongly depends on the slow growth of the dot population, whereas the ES transition only depends on the time needed to leave a repellent steady state.

Search for VHE gamma-ray emission from Geminga pulsar and nebula with the MAGIC telescopes

The Geminga pulsar, one of the brighest gamma-ray sources, is a promising candidate for emission of very-high-energy (VHE > 100 GeV) pulsed gamma rays. Also, detection of a large nebula have been claimed by water Cherenkov instruments. We performed deep observations of Geminga with the MAGIC telescopes, yielding 63 hours of good-quality data, and searched for emission from the pulsar and pulsar wind nebula. We did not find any significant detection, and derived 95% confidence level upper limits. The resulting upper limits of 5.3 × 10^(−13) TeV cm^(−2)s^(−1) for the Geminga pulsar and 3.5 × 10^(−12) TeV cm^(−2)s^(−1) for the surrounding nebula at 50 GeV are the most constraining ones obtained so far at VHE. To complement the VHE observations, we also analyzed 5 years of Fermi-LAT data from Geminga, finding that the sub-exponential cut-off is preferred over the exponential cut-off that has been typically used in the literature. We also find that, above 10 GeV, the gamma-ray spectra from Geminga can be described with a power law with index softer than 5. The extrapolation of the power-law Fermi-LAT pulsed spectra to VHE goes well below the MAGIC upper limits, indicating that the detection of pulsed emission from Geminga with the current generation of Cherenkov telescopes is very difficult.

Heat Transfer in an Airfoil Shaped Strut

Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2016-08-31 09:37:50.239

Near-infrared polarimetry in the galactic center. On properties of Sagittarius A* and a dusty S-cluster object

Near-infrared polarimetry observation is a powerful tool to study the central sources at the center of the Milky Way. My aim of this thesis is to analyze the polarized emission present in the central few light years of the Galactic Center region, in particular the non-thermal polarized emission of Sagittarius~A* (Sgr~A*), the electromagnetic manifestation of the super-massive black hole, and the polarized emission of an infrared-excess source in the literature referred to as DSO/G2. This source is in orbit about Sgr~A*. In this thesis I focus onto the Galactic Center observations at $\lambda=2.2~\mu m$ ($K_\mathrm{s}$-band) in polarimetry mode during several epochs from 2004 to 2012. The near-infrared polarized observations have been carried out using the adaptive optics instrument NAOS/CONICA and Wollaston prism at the Very Large Telescope of ESO (European Southern Observatory). Linear polarization at 2.2 $\mu m$, its flux statistics and time variation, can be used to constrain the physical conditions of the accretion process onto the central super-massive black hole. I present a statistical analysis of polarized $K_\mathrm{s}$-band emission from Sgr~A* and investigate the most comprehensive sample of near-infrared polarimetric light curves of this source up to now. I find several polarized flux excursions during the years and obtain an exponent of about 4 for the power-law fitted to polarized flux density distribution of fluxes above 5~mJy. Therefore, this distribution is closely linked to the single state power-law distribution of the total $K_\mathrm{s}$-band flux densities reported earlier by us. I find polarization degrees of the order of 20\%$\pm$10\% and a preferred polarization angle of $13^o\pm15^o$. Based on simulations of polarimetric measurements given the observed flux density and its uncertainty in orthogonal polarimetry channels, I find that the uncertainties of polarization parameters under a total flux density of $\sim 2\,{\mathrm{mJy}}$ are probably dominated by observational uncertainties. At higher flux densities there are intrinsic variations of polarization degree and angle within rather well constrained ranges. Since the emission is most likely due to optically thin synchrotron radiation, the obtained preferred polarization angle is very likely reflecting the intrinsic orientation of the Sgr~A* system i.e. an accretion disk or jet/wind scenario coupled to the super-massive black hole. Our polarization statistics show that Sgr~A* must be a stable system, both in terms of geometry, and the accretion process. I also investigate an infrared-excess source called G2 or Dusty S-cluster Object (DSO) moving on a highly eccentric orbit around the Galaxy's central black hole, Sgr~A*. I use for the first time the near-infrared polarimetric imaging data to determine the nature and the properties of DSO and obtain an improved $K_\mathrm{s}$-band identification of this source in median polarimetry images of different observing years. The source starts to deviate from the stellar confusion in 2008 data and it does not show a flux density variability based on our data set. Furthermore, I measure the polarization degree and angle of this source and conclude based on the simulations on polarization parameters that it is an intrinsically polarized source with a varying polarization angle as it approaches Sgr~A* position. I use the interpretation of the DSO polarimetry measurements to assess its possible properties.

Effects of clouds on the surface shortwave radiation at a rural inland mid-latitude site

Seven years (2003–2010) of measured shortwave (SW) irradiances were used to obtain estimates of the 10 min averaged effective cloud optical thickness (ECOT) and of the shortwave cloud radiative effect (CRESW) at the surface in a mid-latitude site (Évora — south of Portugal), and its seasonal variability is presented. The ECOT, obtained using transmittance measurements at 415 nm, was compared with the correspondent MODIS cloud optical thickness (MODIS COT) for non-precipitating water clouds and cloud fractions higher than 0.25. This comparison showed that the ECOT represents well the cloud optical thickness over the study area. The CRESW, determined for two SW broadband ranges (300–1100 nm; 285–2800 nm), was normalized (NCRESW) and related with the obtained ECOT. A logarithmic relation between NCRESW and ECOT was found for both SW ranges, presenting lower dispersion for overcast-sky situations than for partially cloudy-sky situations. The NCRESW efficiency (NCRESW per unit of ECOT) was also related with the ECOT for overcast-sky conditions. The relation found is parameterized by a power law function showing that NCRESW efficiency decreases as the ECOT increases, approaching one for ECOT values higher than about 50.

Cyber bullying in schools and the law : is there an effective means of addressing the power imbalance?

Cyber bullying – or bullying through the use of technology – is a growing phenomenon which is currently most commonly experienced by young people and the consequences manifested in schools. Cyber bullying shares many of the same attributes as face-to-face bullying such as a power imbalance and a sense of helplessness on the part of the target. Not surprisingly, targets of face-to-face bullying are increasingly turning to the law, and it is likely that targets of cyber bullying may also do so in an appropriate case. This article examines the various criminal, civil and vilification laws that may apply to cases of cyber bullying and assesses the likely effectiveness of these laws as a means of redressing that power imbalance between perpetrator and target.

Continuous and pedagogically sound assessment : A new economy of power relations in Australian Law schools

In recent decades, assessment practices within Australian law schools have moved from the overwhelming use of end-of-year closed-book examinations to an increase in the use of a wider range of techniques. This shift is often characterised as providing a ‘better’ learning environment for students, contributing more positively to their own ‘personal development’ within higher education, or, considered along the lines of critical legal thought, as ‘liberating’ them from the ‘conservatising’ and ‘indoctrinating’ effects of the power relations that operate in law schools. This paper seeks to render problematic such liberal-progressive narratives about these changes to law school assessment practices. It will do so by utilising the work of French historian and philosopher Michel Foucault on power, arguing that the current range of assessment techniques demonstrates a shift in the ‘economy’ of power relations within the law school. Rather than ‘liberating’ students from relations of power, these practices actually extend the power relations through which students are governed. This analysis is intended to inform legal education research and assessment practice by providing a far more nuanced conceptual framework than one that seeks to ‘free’ law students from these ‘repressive’ practices, or hopes to ‘objectively’ contribute to their ‘personal development’.