Generation of a train of ultrashort pulses using periodic waves in tapered photonic crystal fibres

Funding This work was supported by the Ministry of Education , Nigeria for financial support through the TETFUND scholarship 55 scheme; CSIR [grant number 03(1264)/12/EMR-II].

A new method to calculate the periodic steady state of sequencing batch reactors for biological wastewater treatment : model development and applications

Peer reviewed

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Periodic Breathing and Behavioral Awakenings at High Altitude.

Objectives. To study the relationship between nocturnal periodic breathing episodes and behavioral awakenings at high altitude. Methods. Observational study. It is 6-day ascent of 4 healthy subjects from Besisahar (760 meters) to Manang (3540 meters) in Nepal in March 2012. A recording pulse oximeter was worn by each subject to measure their oxygen saturation and the presence of periodic breathing continuously through the night. An actigraph was simultaneously worn in order to determine nocturnal behavioral awakenings. There were no interventions. Results. 187-hour sleep at high altitude was analyzed, and of this, 145 hours (78%) had at least one PB event. At high altitude, 10.5% (95% CI 6.5-14.6%) of total sleep time was spent in PB while 15 out of 50 awakenings (30%, 95% CI: 18-45%) occurring at high altitudes were associated with PB (P < 0.001). Conclusions. Our data reveals a higher than expected number of behavioral awakenings associated with PB compared to what would be expected by chance. This suggests that PB likely plays a role in behavioral awakenings at high altitude.

THE DESIGN AND SYNTHESIS OF SILOXANE PRECURSORS FOR CHIRAL PERIODIC MESOPOROUS ORGANOSILICA MATERIALS

The development of cost-effective and reliable methods for the synthesis and separation of asymmetric compounds is paramount in helping to meet society’s ever-growing demand for chiral small molecules. Of these methods, chiral heterogeneous supports are particularly appealing as they allow for the reuse of the chiral source. One such support, based on the synergy between chiral organic units and structurally stable inorganic silicon scaffolds are periodic mesoporous organosilicas (PMOs). In the work described herein, I examine some of the factors governing the transmission of chirality between chiral dopants and prochiral bulk phases in chiral PMO materials. In particular, the exploration of 1,1’-binaphthalene-bridged chiral dopants with a focus on the point of attachment into the materials. Moreover, the effects of ordering in the materials are examined and reveal that chirality transfer is more facile in materials with molecular-scale order then those containing amorphous walls. Secondly, the issues surrounding the synthesis and purification of aryl-triethoxysilanes as siloxane precursors are addressed. Both the introduction of a two-carbon linker and the direct attachment of allyl and mixed allyldiethoxysilane species are explored. This work demonstrates that allyldiethoxysilanes are ideal, in that they are stable enough to permit facile synthesis, while still being able to hydrolyze completely to produce well-ordered materials. Lastly, the production of new bulk phases for chiral PMO materials is examined by introducing new prochiral nitrogen-containing siloxane precursors. Biphenyldiamine and bipyridine-bridged siloxane precursors are readily synthesized on reasonable scales. Their use as the bulk siloxane precursor in the production of PMO materials however, is precluded by insufficient gelation and additional siloxane precursors are necessary for the production of ordered materials. In addition to the research detailed above that forms the body of this thesis, two short works are appended. The first details the production of polythiophene assemblies mediated through coordination nanospaces, while the second explores the production of N-heterocyclic carbene functionalized gold nanoparticles through ligand exchange.

UPTAKE OF THE PERIODIC HEALTH EXAM AMONG ADULTS WITH INTELLECTUAL AND DEVELOPMENTAL DISABILITIES FROM 2003 TO 2015

Background: Over the past decade, annual heath exams have been de-emphasized for the general population but emphasized for adults with intellectual and developmental disabilities (IDD). The purpose of this project was to determine if there has been an increase in the uptake of the health exam among adults with IDD in Ontario, to what extent, and the effect on the quality of preventive care provided. Methods: Using administrative health data, the proportion of adults (18-64 years old) with IDD who received a health exam (long appointment, general assessment, and “true” health exam), a high value on the primary care quality composite score (PCQS), and a health exam or high PCQS each year was compared to the proportion in a propensity score matched sample of the general population. Negative binomial and segmented negative binomial regression controlling for age and sex were used to determine the relative risk of having a health exam/high PCQS/health exam or PCQS over time. Results: Pre joinpoint, the long appointment and general assessment health exam definitions saw a decrease and the “true” health exam saw an increase in the likelihood of adults having a health exam. Post joinpoint, all health exam definitions saw a decrease in the likelihood of adults having a health exam. Pre joinpoint, all PCQS measures (high PCQS, long appointment or high PCQS, “true” health exam or high PCQS) saw an increase in the likelihood for adults to achieve a high PCQS or high PCQS/have a health exam. Post joinpoint, all PCQS measures saw a decrease in the likelihood for adults to achieve a high PCQS or high PCQS/have a health exam. Achieving a high PCQS was strongly associated with having a health exam regardless of health exam definition or IDD status. Conclusions: Despite the publication of guidelines, only a small proportion of adults with IDD are receiving health exams. This indicates that the publication of guidelines alone was not sufficient to change practice. More targeted measures, such as the implementation of an IDD-specific health exam fee code, should be considered to increase the uptake of the health exam among adults with IDD.

THE MICROSTRUCTURES OF ZR-EXCEL ALLOY: EFFECTS OF HEAVY ION IRRADIATION, PLASTIC DEFORMATION, THERMAL TREATMENT AND IN-SITU HEATING

Zr-Excel alloy (Zr-3.5Sn-0.8Nb-0.8Mo) is a dual phase (α + β) alloy in the as-received pressure tube condition. It has been proposed to be the pressure tube candidate material for the Generation-IV CANDU-Supercritical Water Reactor (CANDU-SCWR). In this dissertation, the effects of heavy ion irradiation, deformation and heat treatment on the microstructures of the alloy were investigated to enable us to have a better understanding of the potential in-reactor performance of this alloy. In-situ heavy ion (1 MeV) irradiation was performed to study the nucleation and evolution of dislocation loops in both α- and β-Zr. Small and dense type dislocation loops form under irradiation between 80 and 450 °C. The number density tends to saturate at ~ 0.1 dpa. Compared with the α-Zr, the defect yield is much lower in β-Zr. The stabilities of the metastable phases (β-Zr and ω-Zr) and the thermal-dynamically equilibrium phase, fcc Zr(Mo, Nb)2, under irradiation were also studied at different temperatures. Chemi-STEM elemental mapping was carried out to study the elemental redistribution caused by irradiation. The stability of these phases and the elemental redistribution are strongly dependent on irradiation temperature. In-situ time-of-flight neutron diffraction tensile and compressive tests were carried out at different temperatures to monitor lattice strain evolutions of individual grain families during these tests. The β-Zr is the strengthening phase in this alloy in the as-received plate material. Load is transferred to the β-Zr after yielding of the α-Zr grains. The temperature dependence of static strain aging and the yielding sequence of the individual grain families were discussed. Strong tensile/compressive asymmetry was observed in the {0002} grain family at room temperature. The microstructures of the sample deformed at 400 °C and the samples only subjected to heat treatment at the same temperature were characterized with TEM. Concentration of β phase stabilizers in the β grain and the morphology of β grain have significant effect on the stability of β- and ω-Zr under thermal treatment. Applied stress/strain enhances the decomposition of isothermal ω phase but suppresses α precipitation inside the β grains at high temperature. An α → ω/ZrO phase transformation was observed in the thin foils of Zr-Excel alloy and pure Zr during in-situ heating at 700 °C in TEM.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

Report on the Status of Findings and Recommendations from the City of Lambs Grove Periodic Examination Report dated September 4, 2014 for the period June 1, 2015 through February 29, 2016

Report on the Status of Findings and Recommendations from the City of Lambs Grove Periodic Examination Report dated September 4, 2014 for the period June 1, 2015 through February 29, 2016

Modélisation de la dispersion chromatique et de l’atténuation dans les fibres microstructurées à coeur suspendu

D’abord, nous présentons les principes physiques nous permettant de modéliser et comprendre le phénomène de propagation linéaire des impulsions lumineuses dans un milieu homogène, dans les guides d’ondes planaires et enfin dans les fibres optiques microstructurées. Ensuite, nous faisons une analyse mathématique rigoureuse des équations linéaires de propagation et posons le problème comme celui de la recherche de valeurs propres d’opérateurs auto-adjoints dans un espace de Hilbert. On verra que ces résultats théoriques s’appliquent aux équations simulées dans le logiciel Comsol Multiphysics. Enfin, nous recensons et proposons différentes façons de prédire les valeurs de dispersion chromatique et d’atténuation dans les fibres microstructurées à coeur suspendu en utilisant les notions et équations discutés dans les deux premiers chapitres. Le choix de la géométrie, du matériau et de la longueur d’onde de la lumière transmise sont parmi les variables étudiées numériquement. Nous ferons également un exemple détaillé d’utilisation du logiciel Comsol Multiphysics pour construire un modèle de fibre optique microstructurée.

A Periodic State Space Model to Monthly Long-term Temperature Data

This work presents a periodic state space model to model monthly temperature data. Additionally, some issues are discussed, as the parameter estimation or the Kalman filter recursions adapted to a periodic model. This framework is applied to monthly long-term temperature time series of Lisbon.