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We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid variables are defined on the nodes, and we leverage this framework to design novel spatial and temporal discretizations for the two-phase problem. The benefits of the nodal collocation framework are best exemplified through our novel discretizations, which employ a hybrid finite difference-finite volume methodology to treat the boundary and interfacial jump conditions in an entirely sharp manner. We demonstrate the capabilities of our novel approach using a variety of canonical two- and three-dimensional examples and outline how our framework can be extended to address more complicated physics. The overall algorithm achieves high accuracy with simplified data structures, making this solver ideal for scientific and engineering applications. 

Abstract The effect of thermal stress on beneficial symbiosis, in the face of rapid climate change, remains poorly understood. We investigate this using the model system, Euprymna scolopes (Es), the Hawaiian bobtail squid, and its bioluminescent symbiont, Vibrio fischeri (Vf), which enables the squid to camouflage itself through counter-illumination. Successful colonization of the squid by Vf must occur hours after hatching and is mediated by fluid flow due to respiration within the squid mantle cavity. To study this process, we develop a mathematical model using the method of regularized stokeslets to simulate the flow and resulting bacterial trajectories within the squid. We explore how thermal stress, mediated by physiological changes in respiration, ciliary dynamics and internal geometry, affects early colonization by analysing the time bacteria spend in regions crucial to the establishment of symbioses in these simulations. A variance-based sensitivity analysis of physiologically relevant parameters on these metrics demonstrated that changes in the breath cycle significantly affect and reduce the time bacteria spend in the critical zone within the squid, hindering colonization. 

Abstract Bacteria often develop distinct phenotypes to adapt to environmental stress. In particular, they can produce biofilms, dense communities of bacteria that live in a complex extracellular matrix. While previous studies have investigated how bacterial biofilms are regulated under laboratory conditions, they have not considered (1) the data requirements necessary to estimate model parameters and (2) how bacteria respond to recurring stressors in their natural habitats. To address (1), we adapted a mechanistic population model to explore the dynamics of biofilm formation in the presence of predator stress, using synthetic data. We used a Maximum Likelihood Estimation framework to measure crucial parameters underpinning the biofilm formation dynamics. We used genetic algorithms to propose an optimal data collection schedule that minimised parameter identifiability confidence interval widths. Our sensitivity analysis revealed that, within the explored regimes, we could simplify the binding dynamics and eliminate biofilm detachment. To address (2), we proposed a structured version of our model to capture the long-term behaviour and evolutionary selection. In our extended model, the subpopulations feature different maximal rates of biofilm formation. We compared the selection under different predator types and amounts and identified key parameters that affected the speed of selection via sensitivity analysis. 

Abstract Many problems in fluid mechanics require single-shot 3D measurements of fluid flows, but are limited by available techniques. Here, we design and build a novel flexible high-speed two-color scanning volumetric laser-induced fluorescence (H2C-SVLIF) technique. The technique is readily adaptable to a range of temporal and spatial resolutions, rendering it easily applicable to a wide spectrum of experiments. The core equipment consists of a single monochrome high-speed camera and a pair of ND: YAG lasers pulsing at different wavelengths. The use of a single camera for direct 3D imaging eliminates the need for complex volume reconstruction algorithms and easily allows for the correction of distortion defects. Motivated by the large data loads that result from high-speed imaging techniques, we develop a custom, open-source, software package, which allows for real time playback with correction of perspective defects while simultaneously overlaying arbitrary 3D data. The technique is capable of simultaneous measurement of 3D velocity fields and a secondary tracer in the flow. To showcase the flexibility and adaptability of our technique, we present a set of experiments: (1) the flow past a sphere, and (2) vortices embedded in laminar pipe flow. In the first experiment, two channel measurements are taken at a resolution of 512 × 512 × 512 with volume rates of 65.1 Hz. In the second experiment, a single-color SVLIF system is integrated on a moving stage, providing imaging at 1280 × 304 × 256 with volume rates of 34.8 Hz. Although this second experiment is only single channel, it uses identical software and much of the same hardware to demonstrate the extraction of multiple information channels from single channel volumetric images. 

Abstract In response to the COVID-19 pandemic, many higher educational institutions moved their courses on-line in hopes of slowing disease spread. The advent of multiple highly-effective vaccines offers the promise of a return to “normal” in-person operations, but it is not clear if—or for how long—campuses should employ non-pharmaceutical interventions such as requiring masks or capping the size of in-person courses. In this study, we develop and fine-tune a model of COVID-19 spread to UC Merced’s student and faculty population. We perform a global sensitivity analysis to consider how both pharmaceutical and non-pharmaceutical interventions impact disease spread. Our work reveals that vaccines alone may not be sufficient to eradicate disease dynamics and that significant contact with an infectious surrounding community will maintain infections on-campus. Our work provides a foundation for higher-education planning allowing campuses to balance the benefits of in-person instruction with the ability to quarantine/isolate infectious individuals. 

Abstract In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin’s immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library, IB2d , which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.