A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation

In this work, we apply a particle filter with three additional procedures (model reduction, tempering and jittering) to a damped and forced incompressible 2D Euler dynamics defined on a simply connected bounded domain. We show that using the combined algorithm, we are able to successfully assimilate data from a reference system state (the ``truth") modelled by a highly resolved numerical solution of the flow that has roughly $3.1\times10^6$ degrees of freedom for $10$ eddy turnover times, using modest computational hardware. The model reduction is performed through the introduction of a stochastic advection by Lie transport (SALT) model as the signal on a coarser resolution. The SALT approach was introduced as a general theory using a geometric mechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows on the numerical implementation for SALT presented by Cotter et al, SIAM Multiscale Model. Sim. (2019) for the flow in consideration. The model reduction is substantial: The reduced SALT model has $4.9\times 10^4$ degrees of freedom. Forecast reliability and estimated asymptotic behaviour of the particle filter are also presented

Multilevel ensemble data assimilation

This thesis aims to investigate and improve the efficiency of ensemble transform methods for data assimilation, using an application of multilevel Monte Carlo. Multilevel Monte Carlo is an interesting framework to estimate statistics of discretized random variables, since it uses a hierarchy of discretizations with a refinement in resolution. This is in contrast to standard Monte Carlo estimators that only use a discretization at a fine resolution. A linear combination of sub-estimators, on different levels of this hierarchy, can provide new statistical estimators to random variables at the finest level of resolution with significantly greater efficiency than a standard Monte Carlo equivalent. Therefore, the extension to computing filtering estimators for data assimilation is a natural, but challenging area of study. These challenges arise due to the fact that correlation must be imparted between ensembles on adjacent levels of resolution and maintained during the assimilation of data. The methodology proposed in this thesis, considers coupling algorithms to establish this correlation. This generates multilevel estimators that significantly reduce the computational expense of propagating ensembles of discretizations through time and space, in between stages of data assimilation. An effective benchmark of this methodology is realised by filtering data into high-dimensional spatio-temporal systems, where a high computational complexity is required to solve the underlying partial differential equations. A novel extension of an ensemble transform localisation framework to finite element approximations within random spatio-temporal systems is proposed, in addition to a multilevel equivalent.Open Acces

Modification of spintronic terahertz emitter performance through defect engineering

Spintronic ferromagnetic/non-magnetic heterostructures are novel sources for the generation of THz radiation based on spin-to-charge conversion in the layers. The key technological and scientific challenge of THz spintronic emitters is to increase their intensity and frequency bandwidth. Our work reveals the factors to engineer spintronic Terahertz generation by introducing the scattering lifetime and the interface transmission for spin polarized, non-equilibrium electrons. We clarify the influence of the electron-defect scattering lifetime on the spectral shape and the interface transmission on the THz amplitude, and how this is linked to structural defects of bilayer emitters. The results of our study define a roadmap of the properties of emitted as well as detected THz-pulse shapes and spectra that is essential for future applications of metallic spintronic THz emitters.Comment: 33 pages, 13 figure

Explicit energy-conserving modification of relativistic PIC method

The use of explicit particle-in-cell (PIC) method for relativistic plasma simulations is restricted by numerical heating and instabilities that may significantly constrain the choice of time and space steps. To eliminate these limitations we consider a possibility to enforce exact energy conservation by altering the standard time step splitting. Instead of particle advancement in a given field followed by field advancement with current, we split the step so that each particle is coupled with the field at the nearby nodes and this coupling is accounted for with enforced energy conservation sequentially for all particles. Such a coupling method is compatible with various advances, ranging from accounting for additional physical effects to the use of numerical-dispersion-free field solvers, high-order weighting shapes and particle push subcycling. To facilitate further considerations and use, we provide a basic implementation in a 3D, relativistic, spectral code $\pi$-PIC, which we make publicly available. The method and its implementations are verified using simulations of cold plasma oscillations, Landau damping and relativistic two-stream instability. The capabilities of the method to deal with large time and space steps are demonstrated in the problem of plasma heating by intense incident radiation

Robust and real-time hand detection and tracking in monocular video

In recent years, personal computing devices such as laptops, tablets and smartphones have become ubiquitous. Moreover, intelligent sensors are being integrated into many consumer devices such as eyeglasses, wristwatches and smart televisions. With the advent of touchscreen technology, a new human-computer interaction (HCI) paradigm arose that allows users to interface with their device in an intuitive manner. Using simple gestures, such as swipe or pinch movements, a touchscreen can be used to directly interact with a virtual environment. Nevertheless, touchscreens still form a physical barrier between the virtual interface and the real world. An increasingly popular field of research that tries to overcome this limitation, is video based gesture recognition, hand detection and hand tracking. Gesture based interaction allows the user to directly interact with the computer in a natural manner by exploring a virtual reality using nothing but his own body language. In this dissertation, we investigate how robust hand detection and tracking can be accomplished under real-time constraints. In the context of human-computer interaction, real-time is defined as both low latency and low complexity, such that a complete video frame can be processed before the next one becomes available. Furthermore, for practical applications, the algorithms should be robust to illumination changes, camera motion, and cluttered backgrounds in the scene. Finally, the system should be able to initialize automatically, and to detect and recover from tracking failure. We study a wide variety of existing algorithms, and propose significant improvements and novel methods to build a complete detection and tracking system that meets these requirements. Hand detection, hand tracking and hand segmentation are related yet technically different challenges. Whereas detection deals with finding an object in a static image, tracking considers temporal information and is used to track the position of an object over time, throughout a video sequence. Hand segmentation is the task of estimating the hand contour, thereby separating the object from its background. Detection of hands in individual video frames allows us to automatically initialize our tracking algorithm, and to detect and recover from tracking failure. Human hands are highly articulated objects, consisting of finger parts that are connected with joints. As a result, the appearance of a hand can vary greatly, depending on the assumed hand pose. Traditional detection algorithms often assume that the appearance of the object of interest can be described using a rigid model and therefore can not be used to robustly detect human hands. Therefore, we developed an algorithm that detects hands by exploiting their articulated nature. Instead of resorting to a template based approach, we probabilistically model the spatial relations between different hand parts, and the centroid of the hand. Detecting hand parts, such as fingertips, is much easier than detecting a complete hand. Based on our model of the spatial configuration of hand parts, the detected parts can be used to obtain an estimate of the complete hand's position. To comply with the real-time constraints, we developed techniques to speed-up the process by efficiently discarding unimportant information in the image. Experimental results show that our method is competitive with the state-of-the-art in object detection while providing a reduction in computational complexity with a factor 1 000. Furthermore, we showed that our algorithm can also be used to detect other articulated objects such as persons or animals and is therefore not restricted to the task of hand detection. Once a hand has been detected, a tracking algorithm can be used to continuously track its position in time. We developed a probabilistic tracking method that can cope with uncertainty caused by image noise, incorrect detections, changing illumination, and camera motion. Furthermore, our tracking system automatically determines the number of hands in the scene, and can cope with hands entering or leaving the video canvas. We introduced several novel techniques that greatly increase tracking robustness, and that can also be applied in other domains than hand tracking. To achieve real-time processing, we investigated several techniques to reduce the search space of the problem, and deliberately employ methods that are easily parallelized on modern hardware. Experimental results indicate that our methods outperform the state-of-the-art in hand tracking, while providing a much lower computational complexity. One of the methods used by our probabilistic tracking algorithm, is optical flow estimation. Optical flow is defined as a 2D vector field describing the apparent velocities of objects in a 3D scene, projected onto the image plane. Optical flow is known to be used by many insects and birds to visually track objects and to estimate their ego-motion. However, most optical flow estimation methods described in literature are either too slow to be used in real-time applications, or are not robust to illumination changes and fast motion. We therefore developed an optical flow algorithm that can cope with large displacements, and that is illumination independent. Furthermore, we introduce a regularization technique that ensures a smooth flow-field. This regularization scheme effectively reduces the number of noisy and incorrect flow-vector estimates, while maintaining the ability to handle motion discontinuities caused by object boundaries in the scene. The above methods are combined into a hand tracking framework which can be used for interactive applications in unconstrained environments. To demonstrate the possibilities of gesture based human-computer interaction, we developed a new type of computer display. This display is completely transparent, allowing multiple users to perform collaborative tasks while maintaining eye contact. Furthermore, our display produces an image that seems to float in thin air, such that users can touch the virtual image with their hands. This floating imaging display has been showcased on several national and international events and tradeshows. The research that is described in this dissertation has been evaluated thoroughly by comparing detection and tracking results with those obtained by state-of-the-art algorithms. These comparisons show that the proposed methods outperform most algorithms in terms of accuracy, while achieving a much lower computational complexity, resulting in a real-time implementation. Results are discussed in depth at the end of each chapter. This research further resulted in an international journal publication; a second journal paper that has been submitted and is under review at the time of writing this dissertation; nine international conference publications; a national conference publication; a commercial license agreement concerning the research results; two hardware prototypes of a new type of computer display; and a software demonstrator

A cloudy Vlasov solution

We propose to integrate the Vlasov-Poisson equations giving the evolution of a dynamical system in phase-space using a continuous set of local basis functions. In practice, the method decomposes the density in phase-space into small smooth units having compact support. We call these small units ``clouds'' and choose them to be Gaussians of elliptical support. Fortunately, the evolution of these clouds in the local potential has an analytical solution, that can be used to evolve the whole system during a significant fraction of dynamical time. In the process, the clouds, initially round, change shape and get elongated. At some point, the system needs to be remapped on round clouds once again. This remapping can be performed optimally using a small number of Lucy iterations. The remapped solution can be evolved again with the cloud method, and the process can be iterated a large number of times without showing significant diffusion. Our numerical experiments show that it is possible to follow the 2 dimensional phase space distribution during a large number of dynamical times with excellent accuracy. The main limitation to this accuracy is the finite size of the clouds, which results in coarse graining the structures smaller than the clouds and induces small aliasing effects at these scales. However, it is shown in this paper that this method is consistent with an adaptive refinement algorithm which allows one to track the evolution of the finer structure in phase space. It is also shown that the generalization of the cloud method to the 4 dimensional and the 6 dimensional phase space is quite natural.Comment: 46 pages, 25 figures, submitted to MNRA