The instanton method and its numerical implementation in fluid mechanics

A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of instanton methods to turbulence. Instantons are saddle point configurations of the underlying path integrals. They are equivalent to minimizers of the related Freidlin-Wentzell action and known to be able to characterize rare events in such systems. While there is an impressive body of work concerning their analytical description, this review focuses on the question on how to compute these minimizers numerically. In a short introduction we present the relevant mathematical and physical background before we discuss the stochastic Burgers equation in detail. We present algorithms to compute instantons numerically by an efficient solution of the corresponding Euler-Lagrange equations. A second focus is the discussion of a recently developed numerical filtering technique that allows to extract instantons from direct numerical simulations. In the following we present modifications of the algorithms to make them efficient when applied to two- or three-dimensional fluid dynamical problems. We illustrate these ideas using the two-dimensional Burgers equation and the three-dimensional Navier-Stokes equations

Theory, design and application of gradient adaptive lattice filters

SIGLELD:D48933/84 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Adaptive notch filtering for tracking multiple complex sinusoid signals

This thesis is related to the field of digital signal processing; where the aim of this research is to develop features of an infinite impulse response adaptive notch filter capable of tracking multiple complex sinusoid signals. Adaptive notch filters are commonly used in: Radar, Sonar, and Communication systems, and have the ability to track the frequencies of real or complex sinusoid signals; thus removing noise from an estimate, and enhancing the performance of a system. This research programme began by implementing four currently proposed adaptive notch structures. These structures were simulated and compared: for tracking between two and four signals; however, in their current form they are only capable of tracking real sinusoid signals. Next, one of these structures is developed further, to facilitate the ability to track complex sinusoid signals. This original structure gives superior performance over Regalia's comparable structure under certain conditions, which has been proven by simulations and results. Complex adaptive notch filter structures generally contain two parameters: the first tracks a target frequency, then the second controls the adaptive notch filter's bandwidth. This thesis develops the notch filter, so that the bandwidth parameter can be adapted via a method of steepest ascent; and also investigates tracking complex-valued chirp signals. Lastly, stochastic search methods are considered; and particle swarm optimisation has been applied to reinitialise an adaptive notch filter, when tracking two signals; thus more quickly locating an unknown frequency, after the frequency of the complex sinusoid signal jumps

Antenna near-field wave studies in magnetized plasmas as part of the optimization of auxiliary heating in fusion devicesAntenna near-field wave studies in magnetized plasmas as part of the optimization of auxiliary heating in fusion devices

C

Adaptive techniques for signal enhancement in the human electroencephalogram

This thesis describes an investigation of adaptive noise cancelling applied to human brain evoked potentials (EPs), with particular emphasis on visually evoked responses. The chief morphological features and signal properties of EPs are described. Consideration is given to the amplitude and spectral properties of the underlying spontaneous electroencephalogram and the importance of noise reduction techniques in EP studies is empnasised. A number of methods of enhancing EP waveforms are reviewed in the light of the known limitations of coherent signal averaging. These are shown to oe generally inadequate for enhancing individual EP responses. The theory of adaptive filters is reviewed with particular reference to adaptive transversal filters usiny the Widrow-Hoff algorithm. The theory of adaptive noise cancelling using correlated reference sources is presented, and new work is described which relates canceller performance to the magnitude-squared coherence function of the input signals. A novel filter structure, the gated adaptive filter, is presented and shown to yield improved cancellation without signal distortion when applied to repetitive transient signals in stationary noise under the condition of fast adaption. The signal processing software available is shown to be inadequate, and a comprehensive Fortran program developed for use on a PDP-11 computer is described. The properties of human visual evoked potentials and the EEO are investigated in two normal adults using a montage of 7 occipital electrodes. Signal enhancement of EPs is shown to be possible oy adaptive noise cancelling, and improvements in signal to noise in the range 2-10 dB are predicted. A discussion of filter strategies is presented, and a detailed investiyation of adaptive noise cancel liny performed usiny a ranye of typical EP data. Assessment of the results confirms the proposal that substantial improvement in sinyle EP response recoynition is achieved by this technique

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Measuring cellular traction forces on non-planar substrates

Animal cells use traction forces to sense the mechanics and geometry of their environment. Measuring these traction forces requires a workflow combining cell experiments, image processing and force reconstruction based on elasticity theory. Such procedures have been established before mainly for planar substrates, in which case one can use the Green's function formalism. Here we introduce a worksflow to measure traction forces of cardiac myofibroblasts on non-planar elastic substrates. Soft elastic substrates with a wave-like topology were micromolded from polydimethylsiloxane (PDMS) and fluorescent marker beads were distributed homogeneously in the substrate. Using feature vector based tracking of these marker beads, we first constructed a hexahedral mesh for the substrate. We then solved the direct elastic boundary volume problem on this mesh using the finite element method (FEM). Using data simulations, we show that the traction forces can be reconstructed from the substrate deformations by solving the corresponding inverse problem with a L1-norm for the residue and a L2-norm for 0th order Tikhonov regularization. Applying this procedure to the experimental data, we find that cardiac myofibroblast cells tend to align both their shapes and their forces with the long axis of the deformable wavy substrate.Comment: 34 pages, 9 figure

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Spatial and temporal background modelling of non-stationary visual scenes

PhDThe prevalence of electronic imaging systems in everyday life has become increasingly apparent in recent years. Applications are to be found in medical scanning, automated manufacture, and perhaps most significantly, surveillance. Metropolitan areas, shopping malls, and road traffic management all employ and benefit from an unprecedented quantity of video cameras for monitoring purposes. But the high cost and limited effectiveness of employing humans as the final link in the monitoring chain has driven scientists to seek solutions based on machine vision techniques. Whilst the field of machine vision has enjoyed consistent rapid development in the last 20 years, some of the most fundamental issues still remain to be solved in a satisfactory manner. Central to a great many vision applications is the concept of segmentation, and in particular, most practical systems perform background subtraction as one of the first stages of video processing. This involves separation of ‘interesting foreground’ from the less informative but persistent background. But the definition of what is ‘interesting’ is somewhat subjective, and liable to be application specific. Furthermore, the background may be interpreted as including the visual appearance of normal activity of any agents present in the scene, human or otherwise. Thus a background model might be called upon to absorb lighting changes, moving trees and foliage, or normal traffic flow and pedestrian activity, in order to effect what might be termed in ‘biologically-inspired’ vision as pre-attentive selection. This challenge is one of the Holy Grails of the computer vision field, and consequently the subject has received considerable attention. This thesis sets out to address some of the limitations of contemporary methods of background segmentation by investigating methods of inducing local mutual support amongst pixels in three starkly contrasting paradigms: (1) locality in the spatial domain, (2) locality in the shortterm time domain, and (3) locality in the domain of cyclic repetition frequency. Conventional per pixel models, such as those based on Gaussian Mixture Models, offer no spatial support between adjacent pixels at all. At the other extreme, eigenspace models impose a structure in which every image pixel bears the same relation to every other pixel. But Markov Random Fields permit definition of arbitrary local cliques by construction of a suitable graph, and 3 are used here to facilitate a novel structure capable of exploiting probabilistic local cooccurrence of adjacent Local Binary Patterns. The result is a method exhibiting strong sensitivity to multiple learned local pattern hypotheses, whilst relying solely on monochrome image data. Many background models enforce temporal consistency constraints on a pixel in attempt to confirm background membership before being accepted as part of the model, and typically some control over this process is exercised by a learning rate parameter. But in busy scenes, a true background pixel may be visible for a relatively small fraction of the time and in a temporally fragmented fashion, thus hindering such background acquisition. However, support in terms of temporal locality may still be achieved by using Combinatorial Optimization to derive shortterm background estimates which induce a similar consistency, but are considerably more robust to disturbance. A novel technique is presented here in which the short-term estimates act as ‘pre-filtered’ data from which a far more compact eigen-background may be constructed. Many scenes entail elements exhibiting repetitive periodic behaviour. Some road junctions employing traffic signals are among these, yet little is to be found amongst the literature regarding the explicit modelling of such periodic processes in a scene. Previous work focussing on gait recognition has demonstrated approaches based on recurrence of self-similarity by which local periodicity may be identified. The present work harnesses and extends this method in order to characterize scenes displaying multiple distinct periodicities by building a spatio-temporal model. The model may then be used to highlight abnormality in scene activity. Furthermore, a Phase Locked Loop technique with a novel phase detector is detailed, enabling such a model to maintain correct synchronization with scene activity in spite of noise and drift of periodicity. This thesis contends that these three approaches are all manifestations of the same broad underlying concept: local support in each of the space, time and frequency domains, and furthermore, that the support can be harnessed practically, as will be demonstrated experimentally