Faculty Research Talks - Fall 2024
Talks will be held at 2:30PM on every other Monday (M) at 2:30PM in CULM 611 unless otherwise noted.
September 16
Location: CULM 611
Spatially Quasi-Periodic Gravity-Capillary Waves
For linearized gravity-capillary waves, it is possible that two periodic waves with different wave numbers travel at the same speed. If the ratio of their wave numbers is irrational, the motion of the superposition of the two waves is spatially quasi-periodic. We present a framework for computing and studying two-dimensional spatially quasi-periodic gravity-capillary water waves. Specifically, we adopt a conformal mapping formulation of the water wave equation and represent quasi-periodic water waves by periodic functions on a higher-dimensional torus. We will also discuss an approach to extend this study to three dimensions. This is based on joint works with Jon Wilkening and David Nicholls.
September 30
Professor Zoi-Heleni Michalopoulou
Location: CULM 611
Inverse Problems in Ocean Acoustics
In this talk, we will present the nature of inverse problems in ocean acoustic applications. We will focus on localizing a sound transmitting source and on estimating properties related to the propagation medium. New work in our group features denoising acoustic signals for better inversion results and developing Machine Learning algorithms for seabed classification. We will describe open problems in the field and seek solutions, including the optimization of interpolation approaches, the design of stochastic Decision Trees, and the use of Optimal Transport in waveguide characterization.
October 14
Location: CULM 611
Applied Math in Fluid Dynamics and Biophysics
In this talk, I will present two examples to illustrate the mathematical modeling of physics applied to fluid dynamics and biophysics. One example is the fluid dynamics of an active nematic droplet, often used as a model system for live cells. The other example is developing and analyzing a geometric coarse-grained model for the dynamics of motor-driven centrosomal asters in C elegans cells.
October 28
Location: CULM 611
Soft Matter Systems: Big-data, Networks, Topology, Machine Learning
This project focuses on modeling soft matter systems using methods that include modeling, discrete element simulations, network analysis using computational topology methods, and machine learning. The considered setups are typical for big-data problems involving large amounts of dynamic data. The plan is to use various mathematical methods to simplify these data sets, focusing on extracting physical mechanisms governing the behavior of underlying systems. The systems of interest include porous media flow, as well as wet and dry granular systems that are of relevance to a number of soft matter systems, such as suspensions, including active matter ones, among others. The part of the project at NJIT focuses on modeling and simulations and will be carried out in close collaboration with the groups focusing on physical experiments.
The presentation will provide an overview of various approaches being used, as well as of specific problems that have been explored recently. In addition, we will briefly discuss a few other projects that are currently considered by Complex Flow and Soft Matter Group members; more information about current and past projects can be found at the group page, cfsm.njit.edu.
December 9
Location: CULM 611
Pattern Formation and Noise-Induced Transitions in High Dimensional Inhomogeneous Neural Networks
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuron. We find conditions for Turing-like bifurcations in a system where the cortex is modelled as a ring, and we produce numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. The joint effects of clustering / spatial structure of the connectivity on pattern formation is also explored. Finally, we compute the most likely transitions paths between attractors induced by finite-size effects by proving a Large Deviation Principle and using this to compute the most likely transition path.
Last updated: December 6, 2024