Amy Buchmann, Mathematics and CCS, Tulane
"Mathematical and Computational Modeling of Bacterial Motility and Swarming"
Computational models play an important role in understanding bacterial movement. For example, the very social Myxococcus xanthus, a bacterium commonly found in soil and known for its multicellular interactions, can be modeled using the subcellular element method. I will present an implementation of this model and show how it can be used to study the effects of cell flexibility, cell-cell adhesion, and cellular reversal periods on cell-cell interactions. To characterize cell-cell interactions, the contacts between cells in simulations are analyzed to determine how these properties influence the populations' ability to form and keep cell-cell connections. Bacterial flagella may also play an important role in the development of microfluidics devices. Recent experimental work has suggested that the flagella of bacteria may be used as motors in microfluidics devices by creating a bacterial carpet. I will show how the flow induced by bacterial carpets can be modeled and analyzed using the method of regularized Stokeslets, and also examine the transport of vesicles of finite size by arrays of rotating flagella.
Alex Hoover, Mathematics and CCS, Tulane
"From Pacemaker to Vortex Ring: Modeling Jellyfish Propulsion and Maneuvering"
Joanna Gyory, EEB and CCS, Tulane
"Simulations of blue crab larval dispersal in the northern Gulf of Mexico"
The commercial blue crab fishery is the 9th most valuable in the United States. In 2013, fishers harvested more than 60,000 metric tons of crabs that sold for $191 million. However, blue crab abundance varies greatly from year to year, and the causes are not fully understood. One important driver of this variability may be the dispersal dynamics of the larval stage. Blue crab larvae spend ~30-60 days at the ocean surface, where they are transported by currents until they metamorphose into juvenile crabs. We coupled an ocean circulation model with a particle-tracking model to simulate larval dispersal in the northern Gulf of Mexico, and then used network metrics to determine how blue crab populations from different estuaries may be interconnected. We found that the Mississippi River Delta is a barrier to larval dispersal, and that a high percentage of larvae were retained near the parental estuary. Population connectivity declines throughout the spawning season, probably due to changes in near-shore ocean circulation patterns. We also investigated the potential impacts of the Deepwater Horizon oil spill, and found that more than 96% of larvae east of the Mississippi River Delta may have been exposed to oil. We are now using the models to examine how the annual low-oxygen Dead Zone in the Gulf of Mexico might change larval dispersal patterns by restricting the spawning sites available to adult females.
Howard Elman, Computer Science and Institute for Advanced Computer Studies, University of Marylandhttps://www.cs.umd.edu/users/elman/
We consider new computational methods for solving partial differential equations (PDEs) when components of the problem such as diffusion coefficients or boundary conditions are not known with certainty but instead are represented as random fields. In recent years, several computational techniques have been developed for such models that offer potential for improved efficiencies compared with traditional Monte-Carlo methods. These include stochastic Galerkin methods, which use an augmented weak formulation of the PDE derived from averaging with respect to expected value, and stochastic collocation methods, which use a set of samples relatively small in cardinality that captures the character of the solution space. We give an overview of the relative advantages of these two methods and present efficient computational algorithms for solving the algebraic systems that arise from them. In addition, we show that these algorithms can be combined with techniques of reduced-order modeling to significantly enhance efficiency with essentially no loss of accuracy.
Nicole Gasparini, Earth and Environmental Sciences, Tulane University
"Landlab: An open-source landscape evolution model"
The Landlab project creates an environment in which scientists can build a numerical landscape model without having to code all of the individual components. Landscape models compute flows of mass, such as water, sediment, glacial ice, volcanic material, or landslide debris, across a gridded terrain surface. Landscape models have a number of commonalities, such as operating on a grid of points and routing material across the grid. Scientists who want to use a landscape model often build their own unique model from the ground up, re-coding the basic building blocks of their landscape model rather than taking advantage of codes that have already been written.
Whereas the end result may be novel software programs, many person-hours are lost rewriting existing code, and the resulting software is often idiosyncratic and not able to interact with programs written by other scientists in the community. This individuality in software programs leads to lost opportunity for exploring an even wider array of scientific questions than those which can be addressed using a single model. The Landlab project seeks to eliminate these redundancies and lost opportunities by creating a user- and developer-friendly numerical landscape modeling environment which provides scientists with the fundamental building blocks needed for modeling landscape processes. The model code is written in Python, an open-source language that is a relatively easy language for casual programmers to learn.
Noa Marom, Physics & Engineering Physics, Tulane
"Structure Matters More Than Size: Tuning the Electronic Properties of TiO2 Clusters"
Atomic clusters comprising up to few tens of atoms offer exciting prospects for designing nano-catalysts, owing to their high reactivity and the strong dependence of their electronic properties on their size and structure. Quantum mechanical atomistic simulations may be used for computer-aided design of cluster-based nano-catalysts.
The vast majority of computational studies of clusters have focused on finding their global minimum structure, using various global optimization techniques. However, the most stable structures of atomic clusters are not necessarily optimal for catalysis. Rather, the presence of an active site may enhance the reactivity and/or selectivity of a cluster-based nano-catalyst. The presence of such an active site may be associated with certain electronic properties. For example, clusters with a high electron affinity or a low ionization potential would be more likely to accept or donate an electron.
We use a basin hopping algorithm based on density functional theory (DFT) in combination with many-body perturbation theory to show that photoemission spectroscopy (PES) experiments on (TiO2)2-10 anions select for clusters with a high electron affinity, rather than the most stable isomers. We then develop a suite of property-based genetic algorithms (GA) tailored to optimize for low-energy (EGA), high vertical electron affinity (VEA-GA), and low vertical ionization potential (VIP-GA). Analysis of the best structures found by the VEA-GA and VIP-GA reveals structure-property relations and explains the absence of the expected size trends. A high VEA is associated with a large number of dangling O atoms. A low VIP is associated with a low connectivity between dangling O atoms. These structural features become less probable with increasing cluster size, explaining why some smaller clusters have higher VEAs, lower VIPs, and narrower fundamental gaps than larger clusters.
 N. Marom, M. Kim, and J. R. Chelikowsky, Phys. Rev. Lett. 108, 106801 (2012)
 N. Marom, J. E. Moussa, X. Ren, A. Tkatchenko, and J. R. Chelikowsky, Phys. Rev. B 84, 245115 (2011)
 S. Bhattacharya, B. H. Sonin, C. J. Jumonville, L. M. Ghiringhelli, N. Marom, to be published
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