On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Oscilador eletromagnético caótico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O uso da análise de Fourier, de Wavelets e dos expoentes de Lyapunov no estudo de um sistema dinâmico não-ideal com atrito seco e excitação externa

Pós-graduação em Física - IGCE

Análise dinâmica por Wavelets em um sistema com fricção seca e amortecimento

Pós-graduação em Física - IGCE

Influência das não linearidades geométricas em sistemas de suspensão com amortecimento assimétrico sob excitação harmônica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

On waveform analysis, the adaptive task technique, and the effect of vibration on manual control skill

A re-examination of fundamental concepts and a formal structuring of the waveform analysis problem is presented in Part I. eg. the nature of frequency is examined and a novel alternative to the classical methods of detection proposed and implemented which has the advantage of speed and independence from amplitude. Waveform analysis provides the link between Parts I and II. Part II is devoted to Human Factors and the Adaptive Task Technique. The Historical, Technical and Intellectual development of the technique is traced in a review which examines the evidence of its advantages relative to non-adaptive fixed task methods of training, skill assessment and man-machine optimisation. A second review examines research evidence on the effect of vibration on manual control ability. Findings are presented in terms of percentage increment or decrement in performance relative to performance without vibration in the range 0-0.6Rms'g'. Primary task performance was found to vary by as much as 90% between tasks at the same Rms'g'. Differences in task difficulty accounted for this difference. Within tasks vibration-added-difficulty accounted for the effects of vibration intensity. Secondary tasks were found to be largely insensitive to vibration except secondaries which involved fine manual adjustment of minor controls. Three experiments are reported next in which an adaptive technique was used to measure the % task difficulty added by vertical random and sinusoidal vibration to a 'Critical Compensatory Tracking task. At vibration intensities between 0 - 0.09 Rms 'g' it was found that random vibration added (24.5 x Rms'g')/7.4 x 100% to the difficulty of the control task. An equivalence relationship between Random and Sinusoidal vibration effects was established based upon added task difficulty. Waveform Analyses which were applied to the experimental data served to validate Phase Plane analysis and uncovered the development of a control and possibly a vibration isolation strategy. The submission ends with an appraisal of subjects mentioned in the thesis title.

Aspects of Chiral Symmetry Breaking in Lattice QCD

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

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochastic release events (calcium puffs or sparks) from spatially localised calcium stores. The aim of this paper is to analyse how the stochastic nature of individual receptors within these stores combines to create stochastic behaviour on long timescales that may ultimately lead to waves of activity in a spatially extended cell model. Techniques from asymptotic analysis and stochastic phase-plane analysis are used to show that a large cluster of receptor channels leads to a release probability with a sigmoidal dependence on calcium density. This release probability is incorporated into a computationally inexpensive model of calcium release based upon a stochastic generalization of the Fire-Diffuse-Fire (FDF) threshold model. Numerical simulations of the model in one and two dimensions (with stores arranged on both regular and disordered lattices) illustrate that stochastic calcium release leads to the spontaneous production of calcium sparks that may merge to form saltatory waves. Illustrations of spreading circular waves, spirals and more irregular waves are presented. Furthermore, receptor noise is shown to generate a form of array enhanced coherence resonance whereby all calcium stores release periodically and simultaneously.

Footwear modifies coronal plane forefoot and sagittal plane hallux kinematics during stance phase of walking gait

Footwear is designed to reduce injury, and enhance performance. However, the effect footwear has on foot and ankle kinematics currently remains unknown. Acknowledging the need for improved understanding, multi-segment models of the foot-shoe complex need to be established to both describe and quantify the effect footwear has on the foot and ankle during stance phase of gait. The purpose of this study was to quantify how footwear alters the kinematics of the foot inside the shoe during stance phase of walking gait.

A reliable phase unwrapping algorithm based on the local fitting plane and quality map

A fast and reliable phase unwrapping (PhU) algorithm, based on the local quality-guided fitting plane, is presented. Its framework depends on the basic plane-approximated assumption for phase values of local pixels and on the phase derivative variance (PDV) quality map. Compared with other existing popular unwrapping algorithms, the proposed algorithm demonstrated improved robustness and immunity to strong noise and high phase variations, given that the plane assumption for local phase is reasonably satisfied. Its effectiveness is demonstrated by computer-simulated and experimental results.

Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order

A set of recursive formulas for diffractive optical plates design is described. The pure-phase plates simulated by this method homogeneously concentrate more than 96% of the incident laser energy in the desired focal-plane region. The intensity focal-plane profile fits a lath-order super-Gaussian function and has a nearly perfect flat top. Its fit to the required profile measured in the mean square error is 3.576 x 10(-3). (C) 1996 Optical Society of America

Fast-switching phase gratings using in-plane addressed short-pitch polymer stabilized chiral nematic liquid crystals

We demonstrate a fast-switching (sub-millisecond) phase grating based upon a polymer stabilized short-pitch chiral nematic liquid crystal that is electrically addressed using in-plane electric fields. The combination of the short-pitch and the polymer stabilization enables the diffraction pattern to be switched “on” and “off” reversibly in 600 µs. Results are presented on the far-field diffraction pattern along with the intensity of the diffraction orders as a function of the applied electric field and the response times.