Applied Mathematics Colloquium

Maria Deliyianni

Title: Semigroup Generation for a Flow-Cantilever System

Abstract: Motivated by alternative energy technologies such as piezoelectric energy harvesters, we examine a flow-structure interaction system modeling the aeroelastic flutter of a cantilevered beam. The fluid dynamics are governed by a perturbed hyperbolic equation representing potential flow, which interacts with a clamped-free beam. This coupling occurs along the beam’s surface, with a mixed dynamic boundary condition, known as the Kutta-Joukowsky condition, imposed in the beam’s wake.

In this talk, we discuss the semigroup framework for the system’s linearization, establishing well-posedness by decomposing the problem into a dissipative and a perturbation component. Building on these results, we employ a fixed-point scheme to construct strong solutions for the corresponding nonlinear problem, incorporating structural nonlinearities from a recent large-deflection cantilever model.

Ilaria Fontana 

TITLE: Adaptive Mesh Algorithm for Frictional Contact Problems Based on A Posteriori Error Analysis

ABSTRACT: Engineering teams often perform finite element numerical simulations to analyze the behavior of large hydraulic structures. The nonlinear behavior of concrete dams, particularly at the concrete-rock contact in the foundation or the interfaces between blocks, significantly influences their stability, generating significant numerical challenges. A mathematical approximation representing the behavior of these zones consists of the unilateral contact conditions with friction.

This talk focuses on frictional unilateral contact problems approximated using a finite element discretization with weak enforcement of contact conditions à la Nitsche. We present an a posteriori error analysis based on equilibrated stress reconstruction, providing a guaranteed and computable upper bound of the error. Local estimators are then used to introduce a fully automated adaptive algorithm for the refinement of the mesh with a stopping criterion for the linearization algorithm. 

Mete Demircigil

Title: Crowding Effects in Collective Cell Movement under Self-Generated Aerotactic Gradients.

Abstract: Using a self-generated hypoxic assay, it is shown that Acanthamoeba displays a remarkable collective aerotactic behavior: when a cell colony is covered, cells quickly consume the available oxygen and the population spreads outwards at constant speed, which is reminiscent of a similar behavior in Dictyostelium discoideum that we have studied. Yet, at high density only, we observe the emergence of an additional dense ring in Acanthamoeba, unlike in the latter experiment. By proposing a mesoscopic model for Acanthamoeba accounting for collisions, we are able to infer a new density-dependent macroscopic model, which shines light on the characterizing difference between the two experiments. The modeling inferences are confirmed by an experimental investigation of the cell behavior.