Image Analysis of Microfluidic Flows Using Partial Differential Equations

This thesis deals with advanced models to characterize microfluidic flows from image sequences. The governing equations and boundary conditions for viscous flows are introduced as a global model in order to impose physically sound motion results. The connection between the computational fluid simulations and experimental measurement data is established by using constrained optimization. This framework also allows to introduce control variables, which are determined in agreement with the underlying data. In this context, the thesis focuses on the study of the influence of i) the image data, ii) the underlying motion and iii) the boundary conditions on the estimation of the control variables and the corresponding physical quantities. These questions are assessed by the application to synthetic images that allow to measure the induced errors. It is shown that the application of physically motivated differential equations as global motion models increase the robustness and accuracy of the motion estimation. Control variables are used to change the equations in a modeled manner, so that the solution describes the processes that are inherent in the images. The strength of global models lies in the combination with sparsely distributed information in the images, where common state-of- the-art methods have extreme difficulties to obtain reasonable results. It is demonstrated that the optimal control framework allows to relax the governing equations in order to model uncertainty of the measurement setting parameters, such as wall-slip. And finally, such a parameter model is extended to three dimensions and allows to estimate the pressure drop of the flow and the diffusion coefficient of the trace substance caged Q-rhodamine dextran in water

Novel learning-based techniques for dense fluid motion measurements

In this thesis novel learning-based approaches are presented for the estimation of dense fluid flow velocity fields from particle image sequences. The developed methods apply prior knowledge in form of typical spatio-temporal motion models. These motion models are obtained with methods of unsupervised learning using proper orthogonal decomposition (POD). The POD modes reveal dominant flow structures and contain relevant information of complex relations between neighboring flow vectors. The first high-energy POD modes obtained from appropriate training vector fields are used as typical motion models. Meaningful local flow structures can be expressed in the orthogonal space spanned by the motion models. Additional information about dominant flow events is gained by the motion models and related parameters. The proposed approaches are embedded in well-established local parametric and variational optical flow frameworks but are contrasted with these common techniques by the inclusion of prior knowledge. Further extensions of the methods use available information, which is generally discarded in other methods, to obtain robust motion estimations. The methods can easily be tuned for different flow applications by choice of training data and, thus, are universally applicable. Beyond their simple implementation, the approaches are very efficient, accurate and easily adaptable to all types of flow situations. All methods were tested on synthetic and real particle image sequences and the influence of the relevant parameters was investigated. For typical use cases of optical flow, such as small image displacements, they were more accurate compared to all competing methods including particle image velocimetry (PIV) and common optical flow techniques

Sensing animal group behavior and bio-clutter in the ocean over continental shelf scales

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 267-294).Fish populations often comprise the largest biomass in a productive marine ecosystem. They typically play an essential role in inter-trophic energy transport, and serve as a mainstay for human consumption comprising roughly 16% of the animal protein consumed by the world's population. Despite their ecological importance, there is substantial evidence that fish populations are declining worldwide, motivating the need for an ecosystem approach to fisheries management through ecosystem scale sensing of fish populations and behavior. In this Thesis, it is shown how the recently developed Ocean Acoustic Waveguide Remote Sensing (OAWRS) technique can be used to (1) quantify the acoustic scattering response of fish and remotely infer their physiological characteristics to enable species classification, and (2) remotely assess shoaling populations and quantify their group behavior in a variety of oceanic ecosystems. Shoal dynamics is studied by developing a novel Minimum Energy Flow (MEF) method to extract velocity and force fields driving motion from time-varying density images describing compressible or incompressible motion. The MEF method is applied to experimentally obtained density images, spanning spatial scales from micrometers to several kilometers. Using density image sequences describing cell splitting, for example, we show that cell division is driven by gradients in apparent pressure within a cell. By applying MEF to fish population density image sequences collected during the OAWRS 2003 experiment in the New Jersey strataform, we quantify (1) inter-shoal dynamics such as coalescence of fish groups over tens of kilometers, (2) fish mass flow between different parts of a large shoal and (3) the stresses acting on large fish shoals. Observations of fish shoals made during the OAWRS 2006 experiment in the Georges Bank are used to confirm general theoretical predictions on group behavior believed to apply in nature irrespective of animal species. By quantifying the formation processes of vast oceanic fish shoals during spawning, it is shown that (1) a rapid transition from disordered to highly synchronized behavior occurs as population density reaches a critical value; (2) organized group migration occurs after this transition; and (3) small sets of leaders significantly influence the actions of much larger groups. Several species of fish, birds, insects, mammals and other self propelled particles (SPPs) are known to group in large numbers and exhibit orderly migrations. The stability of this orderly state of motion in large SPP-groups is studied by developing a fluid-dynamic theory for flocking behavior based on perturbation analysis. It is shown that an SPP group where individuals assume the average velocity of their neighbours behaves as a fluid over large spatial scales. The existence of a critical population density above which perturbations to the orderly state of motion are damped is also shown. Further, it is shown that disturbances can propagate within mobile groups at speeds much higher than that of the individuals, facilitating rapid information transfer. These findings may explain how large shoals of fish and flocks of birds are able to stay together and migrate over large distances without breaking up. Fish shoals are ubiquitous in continental shelf environments and so are a major cause of acoustic clutter in long-range Navy sonars. It is shown that man-made airfilled cylindrical targets have very different spectral acousic scattering response than fish, so that they can be distinguished using multi-frequency measurements. It is also shown that the use of the Sonar Equation to model scattering from the man-made targets leads to large errors differing by up to an order of magnitude from measurements. A Greens' Theorem-based full-field model that describes scattering from vertically extended cylindrical targets in range-dependent ocean waveguides is shown to accurately describe the statistics of the targets' scattered field measured during OAWRS 2001, 2003 and 2006 experiments. Measurements of infrasound made during the 2004 Indian Ocean Tsunami event that occured on December 26, 2004 have suggested that large-scale tsunamis may produce deep-infrasonic signals that travel thousands of kilometers in the atmosphere. By developing an analytical model to describe air-borne infrasound generation by tsunamis and applying it to the 2004 Indian Ocean Tsunami, it is shown that the mass flow of air caused by changes in sea-level due to a tsunami can generate infrasound of sufficient amplitude to be picked up thousands of kilometers away. The possibility of detecting tsunamis via seismic means is also examined by developing an analytical model for quantifying very low frequency (0.01-0.1 Hz) Rayleigh waves generated by a tsunami.by Srinivasan Jagannathan.Ph.D