Faculty Research Talks - Fall 2021
Talks will be held at 2:30PM on every other Monday (M) at 2:30PM in CULM 611 unless otherwise noted. Please see more information below:
September 27
Location: CULM 611
A Direct Approach to Periodic Fast Multipole Methods
Periodic Green’s functions arise naturally in boundary integral methods for the solution of partial differential equations on periodic domains. In general, there are no closed form expressions for these Green’s functions and they are computed by numerically approximating the sum over periodic images of the free space Green’s function. We will present a simple fast algorithm for evaluating these sums which is efficient even when the unit cell has a high aspect ratio and/or significant shear. We will also spend some time reviewing the underlying mathematics of these types of sums, which have some amusing features. Joint work with Ruqi Pei, Shidong Jiang, and Leslie Greengard.
October 11
Location: CULM 611
Soft Matter Systems: Big-data, Networks, Topology, Machine Learning
This project focuses on modeling soft matter systems using the 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 amount of dynamical data. The plan is to use various mathematical methods to simplify these data sets with focus on extracting physical mechanisms governing the behavior of underlying systems. The systems of interest include wet and dry granular matter 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 another modeling group at the Levich Institute at City College of New York, a group at Rutgers University focusing on topological methods, and a group at Oklahoma University implementing machine learning techniques.
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 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.
October 25
Location: CULM 611
A Latent State Space Model for Estimating Brain Dynamics from EEG Data
Modern neuroimaging technologies have substantially advanced the study of brain activity. Electroencephalogram (EEG) as a non-invasive neuroimaging technique measures changes in electrical voltage on the scalp induced by cortical activities. With its high temporal resolution, EEG has emerged as an increasingly useful tool to study brain connectivity. Challenges with modeling EEG signals of complex brain activities include interactions among unknown sources, low signal-to-noise ratio and substantial between-subject heterogeneity. We propose a state space model that jointly analyzes multi-channel EEG signals and learns dynamics of different sources corresponding to brain cortical activities. Our model borrows strength from spatially correlated measurements and uses low-dimensional latent sources to explain all observed channels. The model can account for patient heterogeneity and quantify the effect of a subject’s covariates on the latent space. The EM algorithm, Kalman filtering, and bootstrap resampling are used to fit the state space model and provide comparisons between patient diagnostic groups. We apply the developed approach to a case-control study of alcoholism and reveal significant attenuation of brain activities in response to visual stimuli in alcoholic subjects compared to healthy controls.
This is joint work with Qinxia Wang, Yuanjia Wang and Xiaofu He from Dept of Biostatistics and Dept of Psychiatry at Columbia University.
November 8
Location: Zoom
The Many Behaviors of Deformable Active Droplets
Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators. This is a collaboration with David Stein and Mike Shelley.
November 22
Location: WebEx
Density Interpolation Methods for the Evaluation of Helmholtz Layer Potentials
Boundary integral equations (BIE) methods, whenever applicable, are competitive numerical discretizations of wave equations posed in unbounded domains. A central challenge of BIE discretizations is the resolution of integral kernel singularities. I will present an overview of density interpolation methods (DIM) for the resolution of all types of kernel singularities in connection with Helmholtz layer potentials and their associated boundary integral operators. I will show a variety of numerical experiments concerning frequency as well as time domain scattering that showcase the versatility of DIM.
Updated: November 22, 2021