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"A Discrete Curvature Approach to the Drill String Bending Problem" by Arthur Mills and "Modeling Traffic with ``Traffic Awareness" of Multiple Species in an Urban Environment" by Madison Phelps

"A Discrete Curvature Approach to the Drill String Bending Problem" by Arthur Mills and "Modeling Traffic with ``Traffic Awareness" of Multiple Species in an Urban Environment" by Madison Phelps

Start: 
Friday, May 5, 2023 12:00 pm
End: 
Friday, May 5, 2023 12:50 pm
Location: 
Strand Agriculture Hall 113
Arthur Mills and Madison Phelps
Oregon State University

Abstract of talk by Arthur Mills

In the drilling of a well, the drill string may come into contact with the well bore. The curvature of the well bore determines where these contact points arise. As the drill bit turns, potential contact points are created along the wall of the well. These candidates then become realized as contact points once the bit passes threshold distances related to the surface features of these points. Beyond a certain distance these contact points become permanent in the sense that the drill string will remain in contact with these points for the entirety of the drilling operation. We will use standard techniques from the differential geometry of curves and surfaces to determine these points of contact and compute them in a MATLAB implementation.

Abstract of talk by Madison Phelps

We consider traffic flow of multiple species in an urban environment such as mixed-use campus network. The species are humans and robots, and humans on bicycles, and some species move only on paved paths, while some are allowed to move off the paths to avoid (possible) congestion. The model is a coupled system of hyperbolic PDE conservation laws, and the couplings are in the flux functions and in the trajectories for the species for which we solve a flow model. Behavior of species is incorporated in the flux functions and flow models: in particular, we fully explore ``traffic awareness" and ``traffic un-awareness" for which we assume the species to not ``care" about their respective positions and those of other species. Our ``traffic awareness" model is inspired by the well known LWR traffic flow for density of cars which was later interpreted by [Rossa, D'Angelo, Quarteroni et al, 2010] as a continuous limit of a stochastic network model, where the mean values and standard deviations of transitional probabilities at each time step are linked to the preferred direction of movement and speed of each species. However, this model does not allow for coupled interactions between multiple species. Other extended models that allow interactions between multiple species are individual based models, but come with a high computational cost on complex networks. We build our computational model with CCFD and Godunov scheme, discuss convergence, and show examples in 1d and 2d.

Contact: 
Malgorzata Peszynska