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Browsing Department of Mathematics by Department "Biomedical Engineering and Mechanics"
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- Computational tools for inversion and uncertainty estimation in respirometryCho, Taewon; Pendar, Hodjat; Chung, Julianne (PLoS, 2021-05-21)In many physiological systems, real-time endogeneous and exogenous signals in living organisms provide critical information and interpretations of physiological functions; however, these signals or variables of interest are not directly accessible and must be estimated from noisy, measured signals. In this paper, we study an inverse problem of recovering gas exchange signals of animals placed in a flow-through respirometry chamber from measured gas concentrations. For large-scale experiments (e.g., long scans with high sampling rate) that have many uncertainties (e.g., noise in the observations or an unknown impulse response function), this is a computationally challenging inverse problem. We first describe various computational tools that can be used for respirometry reconstruction and uncertainty quantification when the impulse response function is known. Then, we address the more challenging problem where the impulse response function is not known or only partially known. We describe nonlinear optimization methods for reconstruction, where both the unknown model parameters and the unknown signal are reconstructed simultaneously. Numerical experiments show the benefits and potential impacts of these methods in respirometry.
- How soap bubbles freezeAhmadi, S. Farzad; Nath, Saurabh; Kingett, Christian M.; Yue, Pengtao; Boreyko, Jonathan B. (Springer Nature, 2019-06-18)Droplets or puddles tend to freeze from the propagation of a single freeze front. In contrast, videographers have shown that as soap bubbles freeze, a plethora of growing ice crystals can swirl around in a beautiful effect visually reminiscent of a snow globe. However, the underlying physics of how bubbles freeze has not been studied. Here, we characterize the physics of soap bubbles freezing on an icy substrate and reveal two distinct modes of freezing. The first mode, occurring for isothermally supercooled bubbles, generates a strong Marangoni flow that entrains ice crystals to produce the aforementioned snow globe effect. The second mode occurs when using a cold stage in a warm ambient, resulting in a bottom-up freeze front that eventually halts due to poor conduction along the bubble. Blending experiments, scaling analysis, and numerical methods, the dynamics of the freeze fronts and Marangoni flows are characterized.
- Lagrangian Reduced Order Modeling Using Finite Time Lyapunov ExponentsXie, Xuping; Nolan, Peter J.; Ross, Shane D.; Mou, Changhong; Iliescu, Traian (MDPI, 2020-10-23)There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose two new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct two new Lagrangian ROMs, which we denote α-ROM and λ-ROM. We show that both Lagrangian ROMs are more accurate than the standard Eulerian ROMs, that is, ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). In particular, the α-ROM can be orders of magnitude more accurate than the standard Eulerian ROMs. We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs’ accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis.
- Transfer Entropy Analysis of Interactions between Bats Using Position and Echolocation DataShaffer, Irena; Abaid, Nicole (MDPI, 2020-10-19)Many animal species, including many species of bats, exhibit collective behavior where groups of individuals coordinate their motion. Bats are unique among these animals in that they use the active sensing mechanism of echolocation as their primary means of navigation. Due to their use of echolocation in large groups, bats run the risk of signal interference from sonar jamming. However, several species of bats have developed strategies to prevent interference, which may lead to different behavior when flying with conspecifics than when flying alone. This study seeks to explore the role of this acoustic sensing on the behavior of bat pairs flying together. Field data from a maternity colony of gray bats (Myotis grisescens) were collected using an array of cameras and microphones. These data were analyzed using the information theoretic measure of transfer entropy in order to quantify the interaction between pairs of bats and to determine the effect echolocation calls have on this interaction. This study expands on previous work that only computed information theoretic measures on the 3D position of bats without echolocation calls or that looked at the echolocation calls without using information theoretic analyses. Results show that there is evidence of information transfer between bats flying in pairs when time series for the speed of the bats and their turning behavior are used in the analysis. Unidirectional information transfer was found in some subsets of the data which could be evidence of a leader–follower interaction.