Summary: In this talk, we will briefly introduce the nonlinear elasticity equations to understand the language of large deformations modeling. After this, we will focus on the much less studied “Inverse Elasticity Problem”, whose solution is sometimes referred to as the reference configuration, or stress-free configuration. This problem can be stated as follows: Given a set of known external forces and a *deformed* configuration, find an initial (or reference) configuration such that, when the given forces are applied to it, we recover the deformed configuration. As we will...

Read More## Generalized Quasi-Geostrophy for Moist Spatially Anisotropic Atmospheric Flows with Phase Changes.

Summary: Traditionally, the simulation of precipitating convection use a non-Boussinesq dynamical core such as the anelastic equations, and would incorporate water substance in all of its phases: vapour (cloud and rain), liquid and ice. Furthermore, the liquid water phase would be separated into cloud water (small droplets suspended in air) and rain water (larger droplets that fall). Depending on environmental conditions, the moist convection may organize itself on multiple length and time scales. One of the minimal representations of water substance and dynamics that still reproduces the...

Read More## Caminos de Santiago: small separating path systems for complete graphs.

Summary: In a communication network of n nodes, each linked to every other, a single link fails. How can we discover which link is broken without going through the burdensome process of examining separately all \(\Theta(n^2)\) of them? A quick way to determine the faulty link would be to propagate messages through a designated set of paths S, such that for every two links there exists a path in S that contains exactly one of them. We say that such a set S (weakly) separates the network. It is known that a separating path system for a network of n nodes must contain at least n-1 paths....

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