AZ - Los Alamos Days
DateSaturday, April 20, 2019 (All day) to Sunday, April 21, 2019 (All day)
AbstractOn April 20-21, 2019, the Program in Applied Mathematics will host the Arizona Los Alamos - Days. The event will be held at the Biosphere 2 in Tucson, Arizona. There will be 7 topic sessions: Biology, Astronomy, Materials, Energy Systems, Fluid Mechanics, Geosciences, and Optimization/Inference/Learning (OIL). Please see http://appliedmath.arizona.edu/calendar/arizona-los-alamos-days for the schedule and more information.
Discrete geometry and mechanics of leaves, flowers, and sea slugs
DateTuesday, April 23, 2019 - 12:30pm
AbstractThe edges of growing leaves, blooming flowers, torn plastic sheets, and frilly sea slugs all exhibit intricate wrinkled patterns. Why is this so? We argue that the mechanics of these so-called non-Euclidean elastic sheets are influenced by non-trivial geometric considerations (i.e., non-smooth defects) which may be explored by new methods using discrete differential geometry (DDG). Wrinkled morphologies appear as an optimization of many topological/geometric degrees of freedom underlying its microstructure. I will motivate the need for DDG-inspired methods to study the mechanics of hyperbolic sheets, i.e., soft/thin objects with negative Gauss curvature. And, I will share results obtained from them, including energetic impacts from non-smooth defects, the role of weak external forces, and associated scaling laws. Ultimately, these modeling techniques have the potential to explain rippled shapes in leaves, flowers, etc. and to enable the control/design of slender elastic materials, e.g., for soft robotics. This is joint work with Shankar Venkataramani.
How biodiversity gradients are made: speciation, extinction, and colonization
DateTuesday, April 23, 2019 - 4:00pm
AbstractHow were hotspots of biodiversity formed? I take a macroevolutionary approach to understand which processes generated present-day biodiversity gradients and how long these processes have operated over deep time scales. In my talk I will focus on three global-scale biodiversity patterns: the peak in marine richness at the Central Indo-Pacific region, the latitudinal biodiversity gradient on land, and the difference between terrestrial and marine richness. Species can be added to a region through in-situ speciation or colonization from elsewhere, and removed through local or global extinction. To understand the relative roles of these processes, I reconstructed past biogeography on time-calibrated molecular phylogenies of vertebrates. A common link between these three biodiversity patterns is that species-rich regions have provided stable habitats for their occupants for much longer than species-poor regions.
Fractal Dimension for Measures via Persistent Homology
DateThursday, April 25, 2019 - 12:30pm
AbstractFractal dimensions give a way to describe objects that display multiscale complexity in their structure. Fractal objects appear in a wide variety of contexts from chaotic dynamical systems to distributions of earthquakes. While fractal dimensions are most classically defined for a space, there are a variety of fractal dimensions for measures, like the Hausdorff dimension. In this talk, I will define a fractal dimension based on persistent homology. This fractal dimension can be estimated computationally and works for arbitrary probability measures on metric spaces. We will look at examples and will discuss several interesting related conjectures.
Nest architecture influences the colony organization of ants
DateFriday, April 26, 2019 - 12:30pm
AbstractFor some organisms, a near sessile life history mandates a strategic placement of where they live. Environmental constraints can be solved with an organism’s ‘extended phenotype’, or traits that extend into the environment: for example, in social insects, the nest, built by the colony, protects the colony from the external environment. Ants can thus change their local environments to the benefit of colony survival. Much attention has been given how organisms shape their extended phenotypes (e.g. nest architecture), while largely ignoring how organisms interpret them. The ant Temnothorax rugatulus provides an ideal model system to investigate the effects of nest architecture on colony organization, thus providing insight into the interactions between nest environment and its occupant. We tested the hypotheses that (i) nest architecture affects worker and brood spatial distribution, in particular (ii) that nest architecture would determine extent and distribution of spatial fidelity zones (‘micro-territories’) of workers in the nest, and that (iii) nest architectures promote different worker movement patterns. We use space syntax theory (structural accessibility) from human architectural research to determine the influence of spatial properties of the nest on the colony organization. Besides investigating the feedback between nest architecture and colony organization, our results may provide implications of nest accessibility on the behavior of the colony.