ACMS Abstracts: Spring 2018
Thomas Fai (Harvard)
The Lubricated Immersed Boundary Method
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.
Lee Panetta (Texas A&M)
Traveling waves and pulsed energy emissions seen in numerical simulations of electromagnetic wave scattering by ice crystals
The numerical simulation of single particle scattering of electromagnetic energy plays a fundamental role in remote sensing studies of the atmosphere and oceans, and in efforts to model aerosol "radiative forcing" processes in a wide variety of models of atmospheric and climate dynamics, I will briefly explain the main challenges in the numerical simulation of single particle scattering and describe how work with 3-d simulations of scattering of an incident Gaussian pulse, using a Pseudo-Spectral Time Domain method to numerically solve Maxwell’s Equations, led to an investigation of episodic bursts of energy that were observed at various points in the near field during the decay phase of the simulations. The main focus of the talk will be on simulations in dimensions 1 and 2, simple geometries, and a single refractive index (ice at 550 nanometers). The periodic emission of pulses is easy to understand and predict on the basis of Snell’s laws in the 1-d case considered. In much more interesting 2-d cases, simulations show traveling waves within the crystal that give rise to pulsed emissions of energy when they interact with each other or when they enter regions of high surface curvature. The time-dependent simulations give a more dynamical view of "photonic nanojets" reported earlier in steady-state simulations in other contexts, and of energy release in "morphology-dependent resonances."
Michael Herty (RWTH-Aachen)
Opinion Formation Models and Mean field Games Techniques
Mean-Field Games are games with a continuum of players that incorporate the time dimension through a control-theoretic approach. Recently, simpler approaches relying on reply strategies have been proposed. Based on an example in opinion formation modeling we explore the link between differentiability notions and mean-field game approaches. For numerical purposes a model predictive control framework is introduced consistent with the mean-field game setting that allows for efficient simulation. Numerical examples are also presented as well as stability results on the derived control.
Molei Tao (Georgia Tech)
Explicit high-order symplectic integration of nonseparable Hamiltonians: algorithms and long time performance
Symplectic integrators preserve the phase-space volume and have favorable performances in long time simulations. Methods for an explicit symplectic integration have been extensively studied for separable Hamiltonians (i.e., H(q,p)=K(p)+V(q)), and they lead to both accurate and efficient simulations. However, nonseparable Hamiltonians also model important problems, such as non-Newtonian mechanics and nearly integrable systems in action-angle coordinates. Unfortunately, implicit methods had been the only available symplectic approach for general nonseparable systems.
This talk will describe a recent result that constructs explicit and arbitrary high-order symplectic integrators for arbitrary Hamiltonians. Based on a mechanical restraint that binds two copies of phase space together, these integrators have good long time performance. More precisely, based on backward error analysis, KAM theory, and some additional multiscale analysis, a pleasant error bound is established for integrable systems. This bound is then demonstrated on a conceptual example and the Schwarzschild geodesics problem. For nonintegrable systems, some numerical experiments with the nonlinear Schrodinger equation will be discussed.
Boualem Khouider (UVic)