Applied/ACMS/absF22

ACMS Abstracts: Fall 2022

James Hanna (UN-Reno)

Title: A snapping singularity

Abstract: I will discuss our preliminary work (with A. Dehadrai) on the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a string or chain. This brief but violent event, with its remarkably large spikes in velocity, acceleration, and tension, is an essentially unavoidable feature of flexible structure dynamics, induced by generic initial and boundary conditions. We are guided by an analytical solution for a geometrically singular limit that features a finite-time singularity in other quantities. Regularization of this singularity does not arise from discretization of the continuous string equations or, equivalently, from the physical discreteness of a chain. It is instead associated with a length scale arising from the geometry of the problem, which evolves according to an anomalously slow curvature scaling.

Thomas Chandler (UW)

Title: Fluid–body interactions in liquid crystals: A complex variable approach

Abstract: Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of swimming bacteria. A model fluid used to investigate such environments is a liquid crystal. Large colloidal bodies undergo shape-dependent interactions when placed in such an environment, whilst deformable bodies like red blood cells tend to be stretched, offering a passive means of measuring cell material properties. While numerous methods exist for studying the liquid crystalline configurations and fluid–body interaction for a single body, there are exceedingly few analytical results for the interaction of two or more bodies. In this talk, we will bring the power of complex variables to bear on this problem, presenting a simple methodology to analytically solve for the interactions inside a liquid crystalline environment. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body shape and orientation, liquid crystal anchoring conditions, and body deformability.

Jennifer Franck (UW)

Title: Predictive modeling of oscillating foil wake dynamics

Abstract: Swimming and flying animals rely on the fluid around them to provide lift or thrust forces, leaving behind a distinct vortex wake in the fluid. The structure and size of the vortex wake is a blueprint of the animal’s kinematic trajectory, holding information about the forces and also the size, speed and direction of motion. This talk will introduce a bio-inspired oscillating turbine, which can be operated to generate energy from moving water through lift generation, in the same manner as flapping birds or bats. This style of turbines offers distinct benefits compared with traditional rotation-based turbines such as the ability to dynamically shift its kinematics for changing flow conditions, thus altering its wake pattern. Current efforts lie in predicting the vortex formation and dynamics of the highly structured wake such that it can be utilized towards cooperative motion within arrays of oscillating foils. Using numerical simulations, this talk will discuss efforts towards linking the fluid dynamic wake signature to the underlying foil kinematics, and investigating how that effects the energy harvesting performance of downstream foils. Two machine learning methodologies are introduced to classify, cluster and identify complex vorticity patterns and modes of energy harvesting, and inform more detailed modeling of arrays of oscillating foils.

Jinlong Wu (UW)

Title: Data-Driven Closure Modeling Using Derivative-free Kalman Methods

Closure problems are critical in predicting complex dynamical systems, e.g., turbulence or cloud dynamics, for which numerically resolving all degrees of freedom remains infeasible in the foreseeable future. Although researchers have been advancing traditional closure models of those systems for decades, the performance of existing models is still unsatisfactory in many applications, mainly due to the limited representation power of existing models and the associated empirical calibration process. Recently, the rapid advance of machine learning techniques shows great potential for improving closure models of dynamical systems. In this talk, I will share some progress in data-driven closure modeling for complex dynamical systems. More specifically, I will demonstrate the use of derivative-free Kalman methods to learn closure models from indirect and limited amount of data. In addition to deterministic closures, examples of sparse identification of dynamical systems and the learning of stochastic closures will also be presented.

Jeffrey Weiss (CU Boulder)

Title: Vortex-gas models for 3d atmosphere and ocean turbulence

Abstract: Atmospheres and oceans self-organize into coherent structures such as fronts, jets, and long-lived vortices. It is useful to model vortex dominated geophysical flows as a vortex gas, where solutions are assumed to take the form of a population of interacting vortices. There are many vortex gas models of increasing complexity for both 2d flow and for purely horizontal, so-called quasigeostrophic, 3d flow. Atmospheres and oceans, however, have small, but important vertical velocities. The smallness of the vertical velocity is due to rapid planetary rotation, quantified by a small Rossby number. The asymptotic expansion of the governing equations for planetary turbulence capture this small vertical velocity when carried to second order in the Rossby number. Here we find a find a vortex gas solution to these equations in the form of point vortices. The nonlinear dynamics of small numbers of such vortices shows complex and geophysically interesting vertical transport. This new point vortex model provides a platform to revisit in 3d the myriad problems studied with 2d point vortices, and provides a tool for modeling important processes in atmospheres and oceans.

Kui Ren (Columbia)

Title: Some results on inverse problems to elliptic PDEs with solution data and their implications in operator learning

Abstract: In recent years, there have been great interests in discovering structures of partial differential equations from given solution data. Very promising theory and computational algorithms have been proposed for such operator learning problems in different settings. We will try to review some recent understandings of such a PDE learning problem from the perspective of inverse problems. In particularly, we will highlight a few analytical and computational understandings on learning a second-order elliptic PDE from single and multiple solutions.

Casian Pantea (WVU)

Title: Motifs of multistationarity in mass-action reaction networks

Abstract: The existence of multiple positive steady states in models of reaction networks, referred to as multistationarity, underlies switching behavior in biochemistry, and has been an important area of study over the last two decades. A recent approach to multistationarity of large networks relies on “lifting”  positive steady states from smaller network components which are themselves multistationary.  This led to an effort of cataloging small multistationary network structures (multistationary motifs). In this talk we introduce two new classes of multistationary networks (networks with 1D stoichiometric subspace, and networks with cyclic structure). As a consequence we prove a partial converse to the DSR graph theorem, i.e. a graph-theoretical sufficient condition for multistationarity based solely on the wiring diagram of the network.