Stereo imaging velocimetry for microgravity applications

Stereo imaging velocimetry is the quantitative measurement of three-dimensional flow fields using two sensors recording data from different vantage points. The system described in this paper, under development at NASA Lewis Research Center in Cleveland, Ohio, uses two CCD cameras placed perpendicular to one another, laser disk recorders, an image processing substation, and a 586-based computer to record data at standard NTSC video rates (30 Hertz) and reduce it offline. The flow itself is marked with seed particles, hence the fluid must be transparent. The velocimeter tracks the motion of the particles, and from these we deduce a multipoint (500 or more), quantitative map of the flow. Conceptually, the software portion of the velocimeter can be divided into distinct modules. These modules are: camera calibration, particle finding (image segmentation) and centroid location, particle overlap decomposition, particle tracking, and stereo matching. We discuss our approach to each module, and give our currently achieved speed and accuracy for each where available

Estimating particle velocity from dual-camera mixed reality video images using 3D particle tracking velocimetry

Mixed reality (MR) systems integrate diverse sensors, allowing users to better visualize and quantify surrounding environmental processes. Some existing mixed reality headsets include synchronized front-facing cameras that, among other things, can be used to track naturally occurring tracer particles (such as dust or snowflakes) to estimate particle velocity field in real time. The current work presents a 3D particle tracking velocimetry (PTV) method for use with MR systems, which combines various monocular cues to match particles between corresponding stereo images. Binocular disparity is used to estimate particle distance from an observer. Individual particles are tracked through time and used to construct the vector field of a scene. A digital display of velocity vectors can be broadcasted into a user’s surrounding environment with the MR headset to be used as a flow visualization tool. The mixed reality particle tracking velocimetry (MR-PTV) approach was optimized to perform in natural conditions where particle size, particle color, and lighting are non-uniform. The approach was first tested using synthetic particle image data obtained by discrete element method simulations then experimentally validated for particles transported by a flume flow using the Microsoft HoloLens 2 MR headset. Uniform flow and flow around a body were considered experimentally. Experimental velocity measurements are compared to computational fluid dynamics results. The resulting MR-PTV system can be used for a variety of industry, scientific and recreational purposes for field-based measurement of particle velocities in real time

High-speed 3D imaging of liquid jets, surfaces and respiratory droplets

Sprays are commonly found in, among other, combustion, agriculture and food processing. For each of these applications, the understanding of spray liquid dynamics is crucial for optimization of efficiency, accuracy, and robustness of the spray­-system in use. Sprays are also found as a collection of respiratory droplets ejected when people are speaking, yelling, coughing etc. that is one of the main transmission routes for viral disease in the recent COVID­19 pandemic. The experimental research performed on these sprays is often in 2D and not seldom on average data. However, the spray dynamics of interest acts in 3D space, during very short timescales and are stochastically unique. Here, instantaneous high-­speed 3D imaging is required to fully characterize these events.This thesis applies and analyses three different laser­-based instantaneous high­-speed 3D imaging techniques on three different liquid dynamics. These include, (1) volumetric Laser Induced Fluorescence (LIF) imaging of liquid jets, (2) LIF structured illumination for surface 3D reconstruction of a liquid hollow cone sheet and (3) stereoscopic particle tracking velocimetry of respiratory droplets. The volumetric imaging was found to be challenging because of refractive effects at the liquid­-air interface. The structured illumination 3D reconstruction technique managed to reconstruct a transient 3D event where liquid breakups, ruptures, surface ­waves, and ejection angles were extracted. Simulations found that the used reconstruction was accurate to below 1% of the structure and could resolve small surface waves with a height up to 65% of the theoretical limit. Finally, the stereoscopic imaging extracted 3D tracks of respiratory droplets with found experimental average speed uncertainties around 0.3 m/s. In addition, this experiment enabled simultaneous estimation of speed and size of respiratory droplets that give valuable information on the risks of disease spreading.The presented instantaneous high­-speed 3D reconstruction techniques can provide data that paves the way towards a deeper understanding of liquid dynamics in general and sprays in particular. The data is advantageous partly since it can be directly applied by modellers to improve and validate their simulations. In the future, both more validation and application of the presented techniques are required which is enabled by the open-­sourced software and data that this thesis provides

Velocimetry-based pressure information for spray analysis – novel experimental, processing and evaluation strategies

In der vorliegenden Arbeit wurde der Spraytransport von komplexen Benzindirekteinspritzungssprays (GDI) mittels auf Geschwindigkeitmessung basierter Druckauswertung untersucht. Für diesen Zweck wurden neue Versuchs-, Verarbeitungs- und Auswertestrategien eingeführt, um eine Druckauswertung der Spray-induzierten Strömung zu befähigen und deren Möglichkeiten auszuweiten. Dies umfasst unter anderem ein statistisches Verfahren auf Basis der Unsteady Reynolds-Averaged Navier-Stokes (URANS) Gleichungen und Ensemble-Mittelung, welche die Druckauswertung transienter, statistisch stationärer Strömungen mittels konventioneller Particle Image Velocimetry (PIV) ermöglicht. Darüber hinaus wurde eine neuartige Technik namens Dual-Plane-Stereo-Astigmatismus (DPSA) entwickelt, die die Auswertung momentaner Druckfelder und damit die Analyse einzelner Einspritzereignisse unter Verwendung eines stereoskopischen Aufbaus und einer einzigen Lichtquelle ermöglicht. Abschließend wurde die Methode der Physics-Informed Neural Networks (PINNs) erfolgreich aus dem Bereich des Deep Learnings in die experimentelle Strömungsmechanik und Spray-Analyse übertragen. Das PINN-Verfahren weitet die Möglichkeiten der bisherigen auf Geschwindigkeitsmessung basierenden Druckauswertung aus und ermöglicht die Auswertung von bislang nicht auswertbaren Strömungsbereichen, sowohl in Raum und Zeit. Unter Verwendung der beschriebenen Methoden wurde die Wechselwirkung zwischen Spray und Umgebungsgasströmung für unterschiedliche Betriebsbedingungen und Sprayauslegungen untersucht. Es zeigte sich, dass der Impulsaustausch mit höherem Einspritzdruck, Gasdichte, Kraftstofftemperatur, größerer Relativgeschwindigkeit, Spray-Gas-Grenzfläche, Sprayexpansion und stärkerer Zerstäubung bzw. Flash-Boiling zunimmt. Als eine wesentliche Erkenntnis wurde festgestellt, dass die Ablenkung von Sprays bzw. das Phänomen der Strahl-zu-Strahl-Wechselwirkung und Spraykontraktion auf einen Nettoimpuls zurückzuführen ist, der auf einzelne Spraykeulen infolge von induzierten Druckkräften wirkt. In diesem Zusammenhang wurde das Vorhandensein eines Niederdruckgebiets im Zentrum von Mehrlochsprays experimentell bestätigt. Es wurde aufgezeigt, dass das Ausmaß der Strahl-zu-Strahl-Wechselwirkung und der Spraykontraktion durch eine enge Spritzlochanordnung und -ausrichtung, eine starke Zerstäubung und ein erhöhtes Tropfen-Folgeverhalten begünstigt wird

Investigation of turbulence modulation in solid-liquid suspensions using FPIV and micromixing experiments

The focus of this thesis is the study of turbulent solid-liquid stirred suspensions, which are involved in many common unit operations in the chemical, pharmaceutical and food industries. The studies of two-phase flows present a big challenge to researchers due to the complexity of experiments; hence there is a lack of quantitative solid and liquid hydrodynamic measurements. Therefore, an investigation of turbulence modulation by dispersed particles on the surrounding fluid in stirred vessels has been carried out, via two-phase fluorescent Particle Image Velocimetry (FPIV) and micromixing experiments. The main property of interest has been the local dissipation rate, as well as root-mean-square (rms) velocities and turbulent kinetic energy (TKE) of the fluid. Initially a single-phase PIV study was conducted to investigate the flow field generated by a sawtooth (EkatoMizer) impeller. The purpose of this study was to gain insight into various PIV techniques before moving on to more complex two-phase flows. Subsequently stereo-, highspeed and angle-resolved measurements were obtained. The EkatoMizer formed a good case study as information regarding its hydrodynamics is not readily available in literature, hence knowledge has been extended in this area. An analysis of the mean flow field elucidated the general structure of fluid drawn into the impeller region axially and discharged radially; the latter characterised the impeller stream. The radial rms velocity was considered to represent best the system turbulence, even though the tangential rms velocity was greater close to the blade; however the radial component was more prevalent in the discharge stream. Due to differences in rms velocities, TKE estimates obtained from two and three velocity components deviated, being greater in the latter case. Integral (1-D and 2-D) length scales were overestimated by the quantity W / 2 in the impeller region. Ratios of longitudinal-to-lateral length scales also indicated flow anisotropy (as they deviated from 2:1). The anisotropy tensor showed that the flow was anisotropic close to the blade, and returned to isotropy further away from the impeller. Instantaneous vector plots revealed vortices in the discharge stream, but these were not associated with flow periodicity. Alternatively, the vortex structures were interpreted as low frequency phenomena between 0-200 Hz; macro-instabilities were found to have a high probability of occurrence in the discharge stream. Dissipation is the turbulent property of most interest as it directly influences micromixing processes, and its calculation is also the most difficult to achieve. Its direct determination from definition requires highly resolved data. Alternative methods have been proposed in the literature, namely dimensional analysis, large eddy simulation (LES) analogy and deduction from the TKE balance. All methods were employed using 2-D and 3-D approximations from stereo-PIV data. The LES analogy was deemed to provide the best estimate, since it accounts for three-dimensionality of the flow and models turbulence at the smallest scales using a subgrid scale model. (Continues...)

Hydrolink 2019/1. Drone

Topic: Dron

Roadmap on signal processing for next generation measurement systems

Signal processing is a fundamental component of almost any sensor-enabled system, with a wide range of applications across different scientific disciplines. Time series data, images, and video sequences comprise representative forms of signals that can be enhanced and analysed for information extraction and quantification. The recent advances in artificial intelligence and machine learning are shifting the research attention towards intelligent, data-driven, signal processing. This roadmap presents a critical overview of the state-of-the-art methods and applications aiming to highlight future challenges and research opportunities towards next generation measurement systems. It covers a broad spectrum of topics ranging from basic to industrial research, organized in concise thematic sections that reflect the trends and the impacts of current and future developments per research field. Furthermore, it offers guidance to researchers and funding agencies in identifying new prospects.AerodynamicsMicrowave Sensing, Signals & System

Convective heat transfer control in turbulent boundary layers

Mención Internacional en el título de doctorThe sustainable development of our society opens up concerns in several fields of engineering, including energy management, production, and the impact of our technology, being thermal management a common issue to be addressed. The investigation reported in this manuscript focuses on understanding, controlling and optimizing the physical processes involving convective heat transfer in turbulent wall-bounded flows. The content is divided into two main blocks, namely the investigation of classic open-loop active-control techniques to control heat transfer, and the technological development of machine-learning strategies to enhance the performance of flow control in the field of convective heat transfer. The first block focuses on actuator technology, applying dielectric-barrier discharge (DBD) plasma actuators and a pulsed slot jet in crossflow (JICF), respectively, to control the convective heat transfer in a turbulent boundary layer (TBL) over a flat plate. In the former, an array of DBD plasma actuators is employed to induce pairs of counter-rotating, streamwise-aligned vortices embedded in the TBL to reduce heat transfer downstream of the actuation. The whole three-dimensional mean flow field downstream of the plasma actuator is reconstructed from stereoscopic particle image velocimetry (PIV). Infrared thermography (IR) measurements coupled with a heated thin foil provide ensemble-averaged convective heat transfer distributions downstream of the actuators. The combination of the flow field and heat transfer measurements provides a complete picture of the fluid-dynamic interaction of plasma-induced flow with local turbulent transport effects. The plasmainduced streamwise vortices are stationary and confined across the spanwise direction due to the action of the plasma discharge. The opposing plasma discharge causes a mass- and momentum-flux deficit within the boundary layer, leading to a low-velocity region that grows in the streamwise direction and which is characterised by an increase in displacement and momentum thicknesses. This low-velocity ribbon travels downstream, promoting streak-alike patterns of reduction in the convective heat transfer distribution. Near the wall, the plasma-induced jets divert the main flow due to the DBD-actuator momentum injection and the suction on the surrounding fluid by the emerging jets. The stationarity of the plasma-induced vortices makes them persistent far downstream, reducing the convective heat transfer. Conversely, the target of the second paper in this first block is to enhance convective heat transfer rather than reduce it. A fully modulated, pulsed, slot JICF is used to perturb the TBL. The slot-jet actuator, flush-mounted and aligned in the spanwise direction, is controlled based on two design parameters, namely the duty cycle (DC) and the pulsation frequency (f). Heat transfer and flow-field measurements are performed to characterise the control performance using IR thermography and planar PIV, respectively. A parametric study on f and DC is carried out to assess their effect on the heat transfer distribution. The vorticity fields are reconstructed from the Proper Orthogonal Decomposition (POD) modes, retrieving phase information. The flow topology is considerably altered by the jet pulsation, even compared to the case of a steady jet. The results show that both the jet penetration in the streamwise direction and the overall Nusselt number increase with increasing DC. However, the frequency at which the Nusselt number is maximised is independent of the duty cycle. A wall-attached jet rises from the slot accompanied by a pair of counter-rotating vortices that promote flow entrainment and mixing. Eventually, a simplified model is proposed which decouples the effect of f and DC in the overall heat transfer enhancement, with a good agreement with experimental data. The cost of actuation is also quantified in terms of the amount of injected fluid during the actuation, leading to conclude that the lowest duty cycle is the most efficient for heat transfer enhancement among the tested set. The second block of the thesis splits into a comparative assessment of machine learning (ML) methods for active feedback flow control and an application of linear genetic algorithms to an experimental convective heat transfer enhancement problem. First, the comparative study is carried out numerically based on a well-established benchmark problem, the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number (Re = 100). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylinder. The feedback employs several velocity sensors. Two probe configurations are evaluated: 5 and 11 velocity probes located at different points around the cylinder and in the wake. The control laws are optimized with Deep Reinforcement Learning (DRL) and Linear Genetic Programming Control (LGPC). Both methods successfully stabilize the vortex alley and effectively reduce drag while using small mass flow rates for the actuation. DRL features higher robustness with respect to variable initial conditions and noise contamination of the sensor data; on the other hand, LGPC can identify compact and interpretable control laws, which only use a subset of sensors, thus allowing reducing the system complexity with reasonably good results. The gained experience and knowledge of machine-learning methods motivated the last study enclosed in this thesis, which utilises linear genetic algorithm control (LGAC) to identify the best actuation parameters in an experimental application. The actuator is a set of six slot jets in crossflow aligned with the freestream. An open-loop optimal periodic forcing is defined by the carrier frequency (f), the duty cycle (DC) and the phase between actuators (ϕ) as control parameters. The control laws are optimised with respect to the unperturbed TBL and the steady-jet actuation. The cost function includes wall convective heat transfer and the cost of the actuation, thus leading to a multi-objective optimisation problem. Surprisingly, the LGAC algorithm converges to the same frequency and duty cycle for all the actuators. This frequency is equivalent to the optimal frequency reported in the second study of the first block of this thesis. The performance of the controller is characterised by IR thermography and PIV measurements. The action of the jets considerably alters the flow topology compared to the steady-jet actuation, yielding a slightly asymmetric flow field. The phase difference between multiple jet actuation has shown to be very relevant and the main driver of flow asymmetry. A POD analysis concludes the shedding phenomena characterising the steady-jet actuation, while the optimised controller exhibits an elongated large-scale structure just downstream of the actuator. The investigation carried out in this thesis sheds some light on the application of different flow control strategies to the field of convective heat transfer. From the utilisation of plasma actuators and a single jet in cross flow to the development of sophisticated control logic, the results point to the exceptional potential of machine learning control in unravelling unexplored controllers within the actuation space. Ultimately, this work demonstrates the viability of employing sophisticated measurement techniques together with advanced algorithms in an experimental investigation, paving the way towards more complex applications involving feedback information.El desarrollo sostenible de nuestra sociedad abre preocupaciones en varios campos de la ingeniería, incluyendo la gestión de la energía, la producción y el impacto de nuestra tecnología, siendo la gestión térmica un tema común a tratar. La investigación que se presenta en este manuscrito se centra en la comprensión, el control y la optimización de los procesos físicos que implican la transferencia de calor por convección en flujos turbulentos de pared. El contenido se divide en dos bloques principales: la investigación de las técnicas clásicas de control activo de lazo abierto para controlar la transferencia de calor, y el desarrollo tecnológico de estrategias de aprendizaje automático para mejorar el rendimiento del control del flujo en el campo de la transferencia de calor por convección. El primer bloque se centra en la tecnología de los actuadores, aplicando actuadores de plasma de descarga de barrera dieléctrica (dielectric barrier dicharge, DBD) y un chorro con forma de ranura pulsado en flujo cruzado (jet in crossflow, JICF), respectivamente, para controlar la transferencia de calor por convección en una capa límite turbulenta (turbulent boundary layer, TBL) sobre una placa plana. En el primero, se emplea un conjunto de actuadores de plasma DBD para inducir pares de vórtices contra-rotativos, alineados con la corriente e incrustados en la TBL para reducir la transferencia de calor aguas abajo de la actuación. El campo de flujo medio tridimensional completo aguas abajo del actuador de plasma se reconstruye a partir de la velocimetría de imagen de partículas estereoscópica (particle image velocimetry, PIV). Las mediciones de termografía infrarroja (IR) junto a una fina lámina calentada proporcionan distribuciones de transferencia de calor convectiva promediadas aguas abajo de los actuadores. La combinación de las mediciones del campo de flujo y de la transferencia de calor proporciona una imagen completa de la interacción fluido-dinámica del flujo inducido por el plasma con los efectos locales de transporte turbulento. Los vórtices en el sentido de la corriente inducidos por plasma son estacionarios y están confinados transversalmente debido a la acción de la descarga de plasma. La descarga de plasma en oposición causa un déficit de flujo de masa y de momento dentro de la capa límite, lo que conduce a una región de baja velocidad que crece en la dirección de la corriente y que se caracteriza por un aumento de los espesores de desplazamiento y de momento. Esta zona de baja velocidad se desplaza corriente abajo, promoviendo patrones de reducción similares a rayas en los que se reduce la transferencia de calor por convección. Cerca de la pared, los chorros inducidos por el plasma desvían el flujo principal debido a la inyección de momento del actuador DBD y a la succión sobre el fluido circundante por parte de los chorros emergentes. La estacionariedad de los vórtices inducidos por el plasma los hace persistentes aguas abajo, reduciendo la transferencia de calor por convección. Por el contrario, el objetivo del segundo trabajo de este primer bloque es mejorar la transferencia de calor por convección en lugar de reducirla. Se utiliza un JICF, pulsado y con forma de ranura, totalmente modulado para perturbar la TBL. El actuador de chorro, montado a ras y alineado en la dirección transversal, se controla en base a dos parámetros de diseño, a saber, el ciclo de trabajo (DC) y la frecuencia de pulsación (f). Se realizan mediciones de la transferencia de calor y del campo de flujo para caracterizar el rendimiento del control mediante termografía IR y PIV planar, respectivamente. Se lleva a cabo un estudio paramétrico de f y DC para evaluar su efecto en la distribución de la transferencia de calor. Los campos de vorticidad se reconstruyen a partir de los modos de descomposición ortogonal adecuada (POD), recuperando la información de fase. La topología del flujo se ve considerablemente alterada por la pulsación del chorro, incluso en comparación con el caso de un chorro estacionario. Los resultados muestran que tanto la penetración del chorro en la dirección de la corriente como el número Nusselt global aumentan con el incremento de DC. Sin embargo, la frecuencia a la que se maximiza el número Nusselt es independiente del ciclo de trabajo. Un chorro adherido a la pared sale de la ranura acompañado de un par de vórtices contrarrotantes que promueven el arrastre y la mezcla del flujo. Finalmente, se propone un modelo simplificado que desacopla el efecto de f y DC en la mejora global de la transferencia de calor, con un buen acuerdo con los datos experimentales. También se cuantifica el coste de la actuación en términos de la cantidad de fluido inyectado durante la actuación, llegando a la conclusión de que el ciclo de trabajo más bajo es el más eficiente para la mejora de la transferencia de calor entre el conjunto probado. El segundo bloque de la tesis se divide en una evaluación comparativa de los métodos de aprendizaje automático (machine learning, ML) para el control activo del flujo por retroalimentación y una aplicación de algoritmos genéticos lineales a un problema experimental de mejora de la transferencia de calor por convección. En primer lugar, el estudio comparativo se realiza numéricamente a partir de un problema de referencia bien establecido: la reducción de la resistencia aerodinámica de una calle de vórtices de Kármán bidimensional tras un cilindro circular a un número de Reynolds bajo (Re = 100). El flujo se manipula con dos actuadores de soplado/succión en la parte superior e inferior de un cilindro. La retroalimentación emplea varios sensores de velocidad. Se evalúan dos configuraciones de sondas: 5 y 11 sondas de velocidad situadas en diferentes puntos alrededor del cilindro y en la estela. Las leyes de control se optimizan con el aprendizaje profundo por refuerzo (Deep Reinforcement Learning, DRL) y el control por programación genética lineal (Linear Genetic Programming Control, LGPC). Ambos métodos estabilizan con éxito la calle de vórtices y reducen de manera efectiva la resistencia al tiempo que usan caudales másicos pequeños para la actuación. El DRL se caracteriza por una mayor robustez con respecto a la variación de la condición inicial y a la contaminación por ruido de los datos de los sensores; por otro lado, el LGPC puede identificar leyes de control compactas e interpretables, que sólo utilizan un subconjunto de sensores, lo que permite reducir la complejidad del sistema con resultados razonablemente buenos. La experiencia adquirida y el conocimiento de los métodos de aprendizaje automático motivaron el último estudio incluido en esta tesis, que utiliza el control por algoritmo genético lineal (Linear Genetic Algorithm Control, LGAC) para identificar los mejores parámetros de actuación en una aplicación experimental. El actuador es un conjunto de seis chorros con forma de ranura en flujo cruzado y alineados con la corriente principal. Se define una ley de forzado periódica en lazo abierto mediante la frecuencia portadora (f), el ciclo de trabajo (DC) y la fase entre actuadores (ϕ) como parámetros de control. Las leyes de control se optimizan con respecto a la TBL no perturbada y la actuación de chorro constante. La función de coste incluye la transferencia de calor por convección de la pared y el coste de la actuación, lo que da lugar a un problema de optimización multiobjetivo. Sorprendentemente, el algoritmo LGAC converge a la misma frecuencia y ciclo de trabajo para todos los actuadores. Esta frecuencia es equivalente a la frecuencia óptima reportada en el segundo estudio del primer bloque de esta tesis. El rendimiento del controlador se caracteriza mediante termografía IR y mediciones PIV. La acción de los chorros altera considerablemente la topología del flujo en comparación con la actuación de los chorros constantes, dando lugar a un campo de flujo ligeramente asimétrico. La diferencia de fase entre la actuación de múltiples chorros ha demostrado ser muy relevante y el principal impulsor de la asimetría del flujo. Un análisis POD concluye los fenómenos de desprendimiento de vórtices que caracterizan la actuación de chorro constante, mientras que el controlador optimizado muestra una estructura alargada a gran escala justo aguas abajo del actuador. La investigación llevada a cabo en esta tesis arroja algo de luz sobre la aplicación de diferentes estrategias de control de flujo en el campo de la transferencia de calor por convección. Desde la utilización de actuadores de plasma y un único chorro en flujo cruzado hasta el desarrollo de una sofisticada lógica de control, los resultados apuntan al excepcional potencial del control por aprendizaje automático para desentrañar controladores inexplorados dentro del espacio de actuación. En última instancia, este trabajo demuestra la viabilidad de emplear sofisticadas técnicas de medición junto con algoritmos avanzados en una investigación experimental, allanando el camino hacia aplicaciones más complejas que implican información de retroalimentación.The work enclosed in this thesis has been partially supported by the Universidad Carlos III de Madrid through a PIPF scholarship awarded on a competitive basis, and by the following research projects: ARTURO (Active contRol of Turbulence for sUstainable aiRcraft propulsiOn), ref. PID2019-109717RB-I00/AEI/10.13039/501100011033, funded by the Spanish State Research Agency (SRA); the 2020 Leonardo Grant for Researchers and Cultural Creators AEROMATIC (Active flow control of aerodynamic flows with machine learning), funded by the BBVA Foundation with grant number IN[20]_ING_ING_0163; and GloWing Starting Grant, funded by the European Research Council (ERC), under grant agreement ERC-2018.StG-803082.Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i VirgiliPresidente: Octavio Armas Vergel.- Secretario: Manuel García-Villalba Navaridas.- Vocal: Gioacchino Cafier

Dynamic discrete tomography

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This particular particle tracking problem, with applications, e.g., in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.Comment: In Pres