Happening @ Michigan https://events.umich.edu/group/4882/rss RSS Feed for Happening @ Michigan Events at the University of Michigan. AIM Seminar: Spatiotemporal dynamics in neural systems: from data to mathematical models and computation (March 29, 2024 3:00pm) https://events.umich.edu/event/114770 114770-21833585@events.umich.edu Event Begins: Friday, March 29, 2024 3:00pm
Location: East Hall
Organized By: Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics

Abstract: Neurons in cortex are connected in intricate patterns, with local- and long-range connections and distance-dependent time delays for transmitting signals. In recent work, we have found that spontaneous and stimulus-driven waves of neural activity travel over these networks, sparsely modulating the spiking activity of the local network as they pass. The waves represent changes in the moment-by-moment activity state of these networks, which in turn directly shapes neuronal responses to incoming visual input and causes measurable effects in visual perception.

Understanding how the networks of cortex generate these sophisticated dynamics, however, remains an open problem. This is due, in part, to the fact that connecting the specific structure of networks to the resulting nonlinear dynamics is a difficult problem in general. Experiments suggest one mechanism for these waves could be the distance-dependent time delays due to transmitting spikes along the axons connecting neurons across these networks. Analyzing the underlying network mechanism for these waves thus represents an additional mathematical challenge, as we need to consider systems with many time delays.

In this talk, I will present recent results from my group connecting the structure of individual networks to the resulting dynamics in systems of nonlinear Kuramoto oscillators. We introduce a complex-valued approach that allows linking the precise structure of connections in the network to the spatiotemporal patterns that will occur in individual simulations. This approach allows understanding these activity patterns in terms of a modification of the eigenspectrum of the graph adjacency matrix. This, in turn, leads to analytical predictions for the precise traveling wave patterns that will emerge in these systems. Finally, I will present our latest efforts to understand computation with spatiotemporal dynamics in neural systems using these nonlinear network models.

Contact: Guanhua Sun

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Lecture / Discussion Thu, 21 Mar 2024 14:32:57 -0400 2024-03-29T15:00:00-04:00 2024-03-29T16:00:00-04:00 East Hall Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics Lecture / Discussion East Hall
AIM Seminar: Filtered volume fraction fluctuations in dilute, non-collisional, particle-laden flow (April 5, 2024 3:00pm) https://events.umich.edu/event/114771 114771-21833586@events.umich.edu Event Begins: Friday, April 5, 2024 3:00pm
Location: East Hall
Organized By: Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics

Abstract: Turbulent particle-laden flows give rise to spatial heterogeneity (e.g. clustering) characterized by two-point statistics. Most coarse-grained (i.e. two fluid) models only solve for one-point moments, limiting reproduction of important two-phase flow statistics. In this talk, we present set of equations describing the evolution of these flows that include fluctuating components of filtered fields --- a description of the level of clustering present in these flows. For dilute heavy particles settling in homogeneous isotropic turbulence, the averaged filtered drag and filtered Reynolds-stress like term that dictates enhanced settling is correlated to this description of volume fraction fluctuation. A data-driven approach that efficiently traverses parameter space in direct numerical simulations to inform closures is proposed, providing both descriptive insights and directions for future modeling. Further, a numerical crossflow experiment is proposed, yielding several advantages over traditional forced homogeneous isotropic turbulence for the study of turbulent particle-laden flows. The filtered volume fraction is shown to be valuable in that it may enable better fits for unclosed quantities related to particle drag and particle-phase momentum flux in coarse-grained simulations.


Contact: Silas Alben

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Lecture / Discussion Wed, 20 Mar 2024 10:41:59 -0400 2024-04-05T15:00:00-04:00 2024-04-05T16:00:00-04:00 East Hall Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics Lecture / Discussion East Hall
AIM/MICDE/MCAIM Seminar: Immersed methods for fluid-structure interaction (April 12, 2024 3:00pm) https://events.umich.edu/event/114758 114758-21833573@events.umich.edu Event Begins: Friday, April 12, 2024 3:00pm
Location: East Hall
Organized By: Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics

Abstract: The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure interacts with a viscous incompressible fluid. The fundamental feature of the IB approach to such fluid-structure interaction (FSI) problems is its combination of an Eulerian formulation of the momentum equation and incompressibility constraint with a Lagrangian description of the structural deformations and resultant forces. In conventional IB methods, Eulerian and Lagrangian variables are linked through integral equations with Dirac delta function kernels, and these singular kernels are replaced by regularized delta functions when the equations are discretized for computer simulation. This talk will focus on three related extensions of the IB method. I first detail an IB approach to structural models that use the framework of large-deformation nonlinear elasticity. I will focus on efficient numerical methods that enable finite element structural models in large-scale simulations, with examples focusing on models of the heart and its valves. Next, I will describe an extension of the IB framework to simulate soft material failure using peridynamics, which is a nonlocal structural mechanics formulation. Numerical examples demonstrate constitutive correspondence with classical mechanics for non-failure cases along with essentially grid-independent predictions of fluid-driven soft material failure. Finally, I will introduce a reformulation of the IB large-deformation elasticity framework that enables accurate and efficient fluid-structure coupling through a version of the immersed interface method, which is a sharp-interface IB-type method. Computational examples demonstrate the ability of this methodology to simulate a broad range of fluid-structure mass density ratios without suffering from artificial added mass instabilities, and to facilitate subgrid contact models. I will also present biomedical applications of the methodology, including models of clot capture by inferior vena cava filters.

Bio: Boyce Griffith is a Professor in the Department of Mathematics and of Biomedical Engineering at the University of North Carolina, where he is also an Adjunct Professor of Applied Physical Sciences and Associate Chair for Research in the Department of Mathematics. His research group focuses on the development and application of numerical methods for simulating fluid-structure interaction with a particular focus on models of the heart and its valves. Their core approach is based on extensions of the immersed boundary method fluid-structure interaction.

Event will be in-person and on Zoom: https://umich.zoom.us/j/98734707290

Contact: S. Alben

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Lecture / Discussion Tue, 19 Mar 2024 13:17:21 -0400 2024-04-12T15:00:00-04:00 2024-04-12T16:00:00-04:00 East Hall Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics Lecture / Discussion Boyce Griffith, University of North Carolina, Chapel Hill
AIM Seminar: Title TBA (April 19, 2024 3:00pm) https://events.umich.edu/event/114772 114772-21833587@events.umich.edu Event Begins: Friday, April 19, 2024 3:00pm
Location: East Hall
Organized By: Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics

Abstract: TBA

Contact: Robert Krasny

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Lecture / Discussion Wed, 14 Feb 2024 14:18:11 -0500 2024-04-19T15:00:00-04:00 2024-04-19T16:00:00-04:00 East Hall Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics Lecture / Discussion East Hall