In this paper, we recover the amplitude of a seismic image by approximating the normal (demigrationmigration) operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigen-vectors. Subsequently, we propose an approximate non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse-time ’wave-equation’ migration code simulating the acoustic wave equation on the SEG-AA salt model.

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response.

No description available.

No description available.

Faculty of Engineering & Built Environment, School of Electrical & Info Engineering, Dissertation / The primary objective of this paper is to present results regarding data obtained from Eskom’s Lightning Positioning and Tracking System (LPATS) and is a continuation of the work presented at the two SAUPEC Conferences in Pretoria and Stellenbosch [1, 2]. LPATS provides some useful information regarding the lightning field measurements around the Brixton and Hillbrow Towers, in Johannesburg, for the two seasons of June 2001 to June 2003. The results suggest that there is a significant increase in apparent ground flash density in the vicinity of the towers when compared to the surrounding areas. The observation of mean current values in the order of -20kA suggests that the increased contribution of upward flashes to the total incidence of flashes in tall structures should lead to a decrease in measured current amplitudes.

To Kin Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 99-104). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multi-carrier Communication Systems --- p.1 / Chapter 1.2 --- Objective of the Thesis --- p.4 / Chapter 1.3 --- Thesis Outline --- p.5 / Chapter 2 --- Wavelet Packet Division Multiplexing (WPDM) --- p.7 / Chapter 2.1 --- "Wavelets, Wavelet Packets and Multiresolution Analysis (MRA)" --- p.8 / Chapter 2.2 --- Application of Wavelet Packets in Multiple Signal Transmission --- p.14 / Chapter 2.3 --- Summary --- p.20 / Chapter 3 --- Nonlinear System Theories --- p.22 / Chapter 3.1 --- Characteristics of Memoryless Nonlinearities --- p.23 / Chapter 3.1.1 --- Memoryless Baseband Nonlinearities --- p.23 / Chapter 3.1.2 --- Memoryless Bandpass Nonlinearities --- p.24 / Chapter 3.2 --- Volt err a Series for Nonlinearities with Memory --- p.26 / Chapter 3.2.1 --- Baseband Nonlinearities with Memory --- p.26 / Chapter 3.2.2 --- Bandpass Nonlinearities with Memory --- p.27 / Chapter 3.3 --- High Power Amplifier (HPA) Models --- p.28 / Chapter 3.3.1 --- Traveling Wave Tube Amplifier (TWTA) --- p.28 / Chapter 3.3.2 --- Solid State Power Amplifier (SSPA) --- p.28 / Chapter 3.3.3 --- Input and Output Backoff Ratios --- p.29 / Chapter 3.4 --- Summary --- p.29 / Chapter 4 --- WPDM in the Presence of Amplifier Nonlinearities --- p.30 / Chapter 4.1 --- System Model --- p.31 / Chapter 4.2 --- Derivation of Channel Models --- p.32 / Chapter 4.2.1 --- Single-carrier WPDM --- p.32 / Chapter 4.2.2 --- Multi-carrier WPDM --- p.34 / Chapter 4.3 --- Performance Analysis --- p.35 / Chapter 4.3.1 --- Conditional Mean --- p.36 / Chapter 4.3.2 --- Conditional Variance --- p.41 / Chapter 4.3.3 --- Power Spectral Density (PSD) --- p.44 / Chapter 4.4 --- Probability of Symbol Error --- p.48 / Chapter 4.5 --- Simulation Results --- p.52 / Chapter 4.6 --- Summary --- p.56 / Chapter 5 --- Nonlinear Compensation (The pth-Order Inverse) --- p.57 / Chapter 5.1 --- Data Predistortion --- p.58 / Chapter 5.2 --- Predistorter Structure --- p.62 / Chapter 5.3 --- Complexity --- p.63 / Chapter 5.4 --- Simulation Results --- p.66 / Chapter 5.5 --- Summary --- p.78 / Chapter 6 --- Conclusions and Suggestions for Future Research --- p.79 / Chapter 6.1 --- Conclusions --- p.79 / Chapter 6.2 --- Suggestions for Future Research --- p.82 / Appendices --- p.83 / Chapter A --- Derivation of (4.14) --- p.83 / Chapter B --- Derivation of (4.16) --- p.85 / Chapter C --- Evaluation of higher order expectations --- p.86 / Chapter D --- Derivation of φ ss(T) in (4.32) --- p.90 / Chapter E --- Derivation of φsi(T) in(4.32) --- p.93 / Chapter F --- Derivation of φ is(T) in (4.32) --- p.95 / Chapter G --- Derivation of φii(T) in (4.32) --- p.97 / Bibliography --- p.99

The asymptotic behavior of the wave functions of three charged particles has been investigated. There are two different types of three-body scattering wave functions. The first type of scattering wave function evolves from the incident three-body wave of three charged particles in the continuum. The second type of scattering wave function evolves from the initial two-body incident wave. In this work the asymptotic three-body incident wave has been derived in the asymptotic regions where two particles are close to each other and far away from the third particle. This wave function satisfies the Schrodinger equation up to terms O(1/3pa), where pa is the distance between the center of mass of two particles and the third particle. The derived asymptotic three-body incident wave transforms smoothly into Redmond’s asymptotic incident wave in the asymptotic region where all three particles are well separated. For the scattering wave function of the second type the asymptotic threebody scattered wave has been derived in all the asymptotic regions. In the asymptotic region where all three particles well separated, the derived asymptotic scattered wave coincides with the Peterkop asymptotic wave. In the asymptotic regions where two particles are close to each other and far away from the third one, this is a new expression which is free of the logarithmically diverging phase factors that appeared in the Peterkop approach. The derived asymptotic scattered wave resolves a long-standing phase-amplitude ambiguity. Based on these results the expressions for the exact prior and post breakup amplitudes have been obtained. The post breakup amplitude for charged particles has not been known and has been derived for the first time directly from the prior form. It turns out that the post form of the breakup amplitude is given by a surface integral in the six dimensional hyperspace, rather than a volume integral, with the transition operator expressed in terms of the interaction potentials. We also show how to derive a generalized distorted-wave-Born approximation amplitude (DWBA) from the exact prior form of the breakup amplitude. It is impossible to derive the DWBA amplitude from the post form. The three-body Coulomb incident wave is used to calculate the reaction rates of 7Be(ep, e)8B and 7Be(pp, p)8B nonradiative triple collisions in stellar environments.

No description available.

A non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness and continuity constraints is proposed. The applied formalism explores curvelets as a directional frame that, by their sparsity on the image, and their invariance under the imaging operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation of the normal operator in the form of an ’eigenvalue’ decomposition with curvelets as the ’eigenvectors’. Subsequently, we propose an inversion method that derives from estimation of the normal operator and is formulated as a convex optimization problem. Sparsity in the curvelet domain as well as continuity along the reflectors in the image domain are promoted as part of this optimization. Our method is tested with a reverse-time ’wave-equation’ migration code simulating the acoustic wave equation.

The Project in Canada to Search for Supersymmetric Objects (PICASSO) searches for cold dark matter through the direct detection of Weakly Interacting Massive Particles (WIMPs) via spin-dependent and spin independent interactions with 19F nuclei. The detection principle is based on the superheated droplet technique; the detectors consist of a gel matrix with millions of liquid droplets of superheated fluorocarbon (C4F10) dispersed in it. In order to reduce the background, it is essential to distinguish the signature of different background particles interacting in the detector. A dedicated setup was developed in order to study the response of the C4F10 droplets in the presence of different backgrounds. The main objectives of this research are to identify the actual size (diameter) of the droplet increases due to phase transition and to check and establish the correlation between the droplet size and the maximum amplitude of the signal. In addition, the alpha-neutron discrimination was studied by observing each event’s image frames and the associated acoustic signal to get the amplitude distribution. The mean ratio of bubble size to droplet size was found to be 5.48, independent of temperature and type of interacting particle. Furthermore, no correlation was found between the droplet size and the maximum amplitude of the signal. As for the discrimination studies, the analysis of the signal events has confirmed that alphas generated outside the active liquid in the gel are much more difficult to discriminate from neutron than when alphas are generated inside the active liquid.