Asymptotic Hyperstability of a Class of Linear Systems under Impulsive Controls Subject to an Integral Popovian Constraint

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Analysis of switched capacitor DC-DC step down converter

A 5V/1 V Switched Capacitor (SC) dc-dc converter designed for a 0.18μm CMOS process is analysed in detail, in this paper. Analytical equations are derived for the voltages and currents through the main components of the SC converter. The model includes switches, capacitors, equivalent series resistances and the load. The switches in the converter are represented by MOSFETs in the UMC 0.18μm CMOS process. The impact of system parameters on output voltage ripple are studied using the analytical expressions.

Effects of pedestal suppression on gain-switched laser sources for 40 Gbit/s OTDM transmission

The performance of 40 Gbit/s optical time-division multiplexed (OTDM) communication systems can be severely limited when the extinction ratio of the optical pulses is low. This is a consequence of the coherent interference noise between individual OTDM channels. When taken alone, the multiple quantum well-distributed feedback laser+dispersion compensating fiber source exhibits a relatively poor extinction ratio which impairs its potential for use in a 40 Gbit/s OTDM system. However, with the addition of an electroabsorption modulator to suppress the pulse pedestals to better than 30 dB extinction, coherent interference noise is reduced, the bit-error-rate performance is greatly improved, and the source shows good potential for 40 Gbit/s OTDM communication.

Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

High speed optical communication systems: From modulation formats to radically new fibres

High volumes of data traffic along with bandwidth hungry applications, such as cloud computing and video on demand, is driving the core optical communication links closer and closer to their maximum capacity. The research community has clearly identifying the coming approach of the nonlinear Shannon limit for standard single mode fibre [1,2]. It is in this context that the work on modulation formats, contained in Chapter 3 of this thesis, was undertaken. The work investigates the proposed energy-efficient four-dimensional modulation formats. The work begins by studying a new visualisation technique for four dimensional modulation formats, akin to constellation diagrams. The work then carries out one of the first implementations of one such modulation format, polarisation-switched quadrature phase-shift keying (PS-QPSK). This thesis also studies two potential next-generation fibres, few-mode and hollow-core photonic band-gap fibre. Chapter 4 studies ways to experimentally quantify the nonlinearities in few-mode fibre and assess the potential benefits and limitations of such fibres. It carries out detailed experiments to measure the effects of stimulated Brillouin scattering, self-phase modulation and four-wave mixing and compares the results to numerical models, along with capacity limit calculations. Chapter 5 investigates hollow-core photonic band-gap fibre, where such fibres are predicted to have a low-loss minima at a wavelength of 2μm. To benefit from this potential low loss window requires the development of telecoms grade subsystems and components. The chapter will outline some of the development and characterisation of these components. The world's first wavelength division multiplexed (WDM) subsystem directly implemented at 2μm is presented along with WDM transmission over hollow-core photonic band-gap fibre at 2μm. References: [1]P. P. Mitra, J. B. Stark, Nature, 411, 1027-1030, 2001 [2] A. D. Ellis et al., JLT, 28, 423-433, 2010.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Generic low-latency NoC router architecture for FPGA computing systems

A novel cost-effective and low-latency wormhole router for packet-switched NoC designs, tailored for FPGA, is presented. This has been designed to be scalable at system level to fully exploit the characteristics and constraints of FPGA based systems, rather than custom ASIC technology. A key feature is that it achieves a low packet propagation latency of only two cycles per hop including both router pipeline delay and link traversal delay - a significant enhancement over existing FPGA designs - whilst being very competitive in terms of performance and hardware complexity. It can also be configured in various network topologies including 1-D, 2-D, and 3-D. Detailed design-space exploration has been carried for a range of scaling parameters, with the results of various design trade-offs being presented and discussed. By taking advantage of abundant buildin reconfigurable logic and routing resources, we have been able to create a new scalable on-chip FPGA based router that exhibits high dimensionality and connectivity. The architecture proposed can be easily migrated across many FPGA families to provide flexible, robust and cost-effective NoC solutions suitable for the implementation of high-performance FPGA computing systems. © 2011 IEEE.

Modelling and Control of a Variable-Speed Switched Reluctance Generator based Wind Turbine

This paper studies the system modelling and control aspects of switched reluctance generator (SRG) based variable speed wind turbines. A control system is implemented to provide proper operation of the SRG as well as power tracking capabilities for varying wind speeds. The control system for the grid side inverter that will allow the SRG to properly generate power to the system is also presented. Studies are presented of both the SRG and inverter control systems capabilities during a balanced three-phase fault. The paper will demonstrate that the SRG based wind turbine presents a feasible variable wind speed solution with good fault response capabilities.

Switched Diversity Techniques for Indoor Off-body Communications Channels: An Experimental Analysis and Modeling

This paper investigates the potential improvement in signal reliability for indoor off-body communications channels operating at 5.8 GHz using switched diversity techniques. In particular we investigate the performance of switch-and-stay combining (SSC), switch-and-examine combining (SEC) and switch-and-examine combining with post-examining selection (SECps) schemes which utilize multiple spatially separated antennas at the base station. During the measurements a test subject, wearing an antenna on his chest, performed a number of walking movements towards and then away from a uniform linear array. It was found that all of the considered diversity schemes provided a worthwhile signal improvement. However, the performance of the diversity systems varied according to the switching threshold that was adopted. To model the fading envelope observed at the output of each of the combiners, we have applied diversity specific equations developed under the assumption of Nakagami-$m$ fading. As a measure of the goodness-of-fit, the Kullback-Leibler divergence between the empirical and theoretical probability density functions (PDFs) was calculated and found to be close to 0. To assist with the interpretation of the goodness-of-fit achieved in this study, the standard deviation, $\sigma$, of a zero-mean, $\sigma^2$ variance Gaussian PDF used to approximate a zero-mean, unit variance Gaussian PDF is also presented. These were generally quite close to 1 indicating that the theoretical models provided an adequate fit to the measured data.

Detection of quasi-periodic processes in complex systems: how do we quantitatively describe their properties?

It has been shown that in reality at least two general scenarios of data structuring are possible: (a) a self-similar (SS) scenario when the measured data form an SS structure and (b) a quasi-periodic (QP) scenario when the repeated (strongly correlated) data form random sequences that are almost periodic with respect to each other. In the second case it becomes possible to describe their behavior and express a part of their randomness quantitatively in terms of the deterministic amplitude–frequency response belonging to the generalized Prony spectrum. This possibility allows us to re-examine the conventional concept of measurements and opens a new way for the description of a wide set of different data. In particular, it concerns different complex systems when the ‘best-fit’ model pretending to be the description of the data measured is absent but the barest necessity of description of these data in terms of the reduced number of quantitative parameters exists. The possibilities of the proposed approach and detection algorithm of the QP processes were demonstrated on actual data: spectroscopic data recorded for pure water and acoustic data for a test hole. The suggested methodology allows revising the accepted classification of different incommensurable and self-affine spatial structures and finding accurate interpretation of the generalized Prony spectroscopy that includes the Fourier spectroscopy as a partial case.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Development and parametric studies of pulsed nitrogen and d-switched nd:glass lasers and some of their applications

Laser engineering is an area in which developments in the existing design concepts and technology appear at an alarming rate. Now—a-days, emphasis has shifted from innovation to cost reduction and system improvement. To a major extent, these studies are aimed at attaining larger power densities, higher system efficiency and identification of new lasing media and new lasing wavelengths. Todate researchers have put to use all the ditferent Forms of matter as lasing material. Laser action was observed For the first time in a gaseous system - the He-Ne system. This was Followed by a variety of solidstate and gas laser systems. Uarious organic dyes dissolved in suitable solvents were found to lase when pumped optically. Broad band emission characteristics of these dye molecules made wavelength tuning possible using optical devices. Laser action was also observed in certain p-n junctions of semiconductor materials and some of these systems are also tunable. The recent addition to this list was the observation of laser action from certain laser produced plasmas. The purpose of this investigation was to examine the design and Fabrication techniques of pulsed Nitrogen lasers and high power Nd: Glass laserso Attempt was also made to put the systems developed into certain related experiments

Ideotyping integrated aquaculture systems to balance soil nutrients

Due to growing land scarcity and lack of nutrient inputs, African farmers switched from shifting cultivation to continuous cropping and extended crop area by bringing fragile lands such as river banks and hill slopes into production. This accelerated soil fertility decline caused by erosion, harvesting and insufficient nutrient replenishment. We explored the feasibility to reduce nutrient depletion by increasing nutrient utilization efficiencies, while diversifying and increasing food production through the development of integrated aquaculture – agriculture (IAA). Considering the climatic conditions prevailing in Kenyan highlands, aquaculture production scenarios were ideotyped per agro-ecological zone. These aquaculture production scenarios were integrated into existing NUTrient MONitoring (NUTMON) farm survey data for the area. The nutrient balances and flows of the resulting IAA-systems were compared to present land use. The effects of IAA development on nutrient depletion and total food production were evaluated. With the development of IAA systems, nutrient depletion rates dropped by 23–35%, agricultural production increased by 2–26% and overall farm food production increased by 22–70%. The study demonstrates that from a bio-physical point of view, the development of IAA-systems in Africa is technically possible and could raise soil fertility and total farm production. Further studies that evaluate the economic feasibility and impacts on the livelihood of farming households are recommended.