Oscillatory surface rheotaxis of swimming E. coli bacteria

Bacterial contamination of biological conducts, catheters or water resources is a major threat to public health and can be amplified by the ability of bacteria to swim upstream. The mechanisms of this rheotaxis, the reorientation with respect to flow gradients, often in complex and confined environments, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow with two complementary experimental assays, based on 3D Lagrangian tracking and fluorescent flagellar labelling and we develop a theoretical model for their rheotactic motion. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A full theoretical analysis explains these regimes and predicts the corresponding critical shear rates. The predicted transitions as well as the oscillation dynamics are in good agreement with experimental observations. Our results shed new light on bacterial transport and reveal new strategies for contamination prevention.Comment: 12 pages, 5 figure

Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data

The impact of pelvic lateral rotation on hindlimb kinematics and stride-length in the red-legged running frog, Kassina maculata

Some frog species, such as Kassina maculata (red-legged running frog), use an asynchronous walking/running gait as their primary locomotor mode. Prior comparative anatomy work has suggested that lateral rotation of the pelvis improves walking performance by increasing hindlimb stride length; however, this hypothesis has never been tested. Using non-invasive methods, experimental high-speed video data collected from eight animals were used to create two three-dimensional kinematic models. These models, each fixed to alternative local anatomical reference frames, were used to investigate the hypothesis that lateral rotation of the mobile ilio-sacral joint in the anuran pelvis plays a propulsive role in walking locomotion by increasing hindlimb stride length. All frogs used a walking gait (duty factor greater than 0.5) despite travelling over a range of speeds (0.04–0.23 m s−1). The hindlimb joint motions throughout a single stride were temporally synchronized with lateral rotation of the pelvis. The pelvis itself, on average, underwent an angular excursion of 12.71° (±4.39°) with respect to the body midline during lateral rotation. However, comparison between our two kinematic models demonstrated that lateral rotation of the pelvis only increases the cranio-caudal excursion of the hindlimb modestly. Thus, we propose that pelvic lateral rotation is not a stride length augmenting mechanism in K. maculata

Phreatic seepage flow through an earth dam with an impeding strip

New mathematical models are developed and corresponding boundary value problems are analytically and numerically solved for Darcian flows in earth (rock)–filled dams, which have a vertical impermeable barrier on the downstream slope. For saturated flow, a 2-D potential model considers a free boundary problem to Laplace’s equation with a traveling-wave phreatic line generated by a linear drawup of a water level in the dam reservoir. The barrier re-directs seepage from purely horizontal (a seepage face outlet) to purely vertical (a no-flow boundary). An alternative model is also used for a hydraulic approximation of a 3-D steady flow when the barrier is only a partial obstruction to seepage. The Poisson equation is solved with respect to Strack’s potential, which predicts the position of the phreatic surface and hydraulic gradient in the dam body. Simulations with HYDRUS, a FEM-code for solving Richards’ PDE, i.e., saturated-unsaturated flows without free boundaries, are carried out for both 2-D and 3-D regimes in rectangular and hexagonal domains. The Barenblatt and Kalashnikov closed-form analytical solutions in non-capillarity soils are compared with the HYDRUS results. Analytical and numerical solutions match well when soil capillarity is minor. The found distributions of the Darcian velocity, the pore pressure, and total hydraulic heads in the vicinity of the barrier corroborate serious concerns about a high risk to the structural stability of the dam due to seepage. The modeling results are related to a “forensic” review of the recent collapse of the spillway of the Oroville Dam, CA, USA