December 1, 2022, 12:30-1:30pm
Speaker: Ling Xu (North Carolina A&T State University)
Title: Dynamics of elliptical vortices in 2D inviscid fluid flow
Abstract: We examine the dynamics of elliptical vortices in 2D ideal fluid using an adaptively refined and remeshed vortex method. Four cases are considered: the compact MMZ and POLY vortices, and noncompact Gaussian and smooth Kirchhoff vortices (SK). The vortices have the same maximum vorticity and 2:1 initial aspect ratio, but unlike the top-hat Kirchhoff vortex, they have continuous profiles with different regularity. In all cases, the co-rotating phase portrait has two hyperbolic points. For all four cases, at the early time two filaments emerge and form a halo around the core as vorticity is advected along the unstable manifold of each hyperbolic point. However, the dynamics of these four vortices are also different depending on the relative locations of the vortex in the phase portrait.
November 17, 2022, 12:30-1:30pm
Speaker: Daniel Fong (US Merchant Marine Academy)
Title: Modeling of tissue growth in a spatially-varying permeability engineering scaffold
Abstract: Tissue engineering is a rapidly growing field, attracting a huge concentration of research effort. An important subfield of tissue engineering focuses on the use of bioreactors, devices that attempt to simulate a physiological environment in order to promote the growth of functional cell or tissue in vivo. In this talk we present a mathematical model to simulate both nutrient transport and cell proliferation within a spatially-varying permeability scaffold inside a perfusion bioreactor, and compare results from this model with experimental results from the literature.
November 10, 2022, 12:30-1:30pm
Speaker: Yi Jiang (Georgia State University)
Title: Shape of cell migration: the single and the collective
Abstract: After decades (centuries?) of accumulation of qualitative and quantitative observations, can we begin to derive fundamental laws of biology as we have so successfully done in physics? If yes, what mathematical tools do we need to get it right? I plan to describe two systems, single cell migration and collective cancer invasion, where the movement of cells resemble fluid flow. Can we write / derive Navier-Stokes type of governing equations for single cell migration and collective cell migration? Needless to say, both phenomena are crucially important for biology, from single cellular survival, development, immune response, wound healing, to cancer invasion, just to name a few. I hope this informal presentation will stir up further discussions.
November 3, 2022, 12:30-1:30pm
Speaker: Yixuan Sun (University of Oxford)
Title: Filtration with multiple species of particles
Abstract: Membrane filtration of feed containing multiple species of particles is a common process in the industrial setting. In this work we propose a model for filtration of a suspension containing multiple particle species (concrete examples of our model are shown in two and three species), each with different affinities for the material of the porous filter membrane. Using the pore shape within the membrane as a design objective, we formulate a number of optimization problems pertaining to effective separation of desired and undesired particles in the special case of two particle species and we present results showing how properties such as feed composition affect the optimal filter design. In addition, we propose a novel multi-stage filtration strategy, which provides a significant mass yield improvement for the desired particles, and, surprisingly, higher purity of the product as well.
October 27, 2022, 12:30-1:30pm
Speaker: Maryam Yashtini (Georgetown University)
Title: Counting Objects by Diffused Index: geometry-free and training-free approach
Abstract: Counting objects is a fundamental but challenging problem. In this work, we propose diffusion-based, geometry-free, and learning-free methodologies to count the number of objects in images. The main idea is to represent each object by a unique index value regardless of its intensity or size, and to simply count the number of index values. First, we place different vectors, referred to as seed vectors, uniformly throughout the mask image. The mask image has boundary information of the objects to be counted. Secondly, the seeds are diffused using an edge-weighted harmonic variational optimization model within each object. We propose an efficient algorithm based on an operator splitting approach and alternating direction minimization method, and theoretical analysis of this algorithm is given. An optimal solution of the model is obtained when the distributed seeds are completely diffused such that there is a unique intensity within each object, which we refer to as an index. For computational efficiency, we stop the diffusion process before a full convergence, and propose to cluster these diffused index values. We refer to this approach as Counting Objects by Diffused Index (CODI). We explore scalar and multi-dimensional seed vectors. For Scalar seeds, we use Gaussian fitting in histogram to count, while for vector seeds, we exploit a high-dimensional clustering method for the final step of counting via clustering. The proposed method is flexible even if the boundary of the object is not clear nor fully enclosed. We present counting results in various applications such as biological cells, agriculture, concert crowd, and transportation. Some comparisons with existing methods are presented.
October 20, 2022, 12:30-1:30pm
Speaker: Emeka Mazi (Georgia State University)
Title: Dynamic Entrainment for the Hodgkin Huxley model
Abstract: The Hodgkin-Huxley (HH) model is a mathematical model which aims at determining the law that governs the movement of ions in nerve cells during action potentials. In this work, we investigate the 1:1 Dynamic Entrainment of the HH model under the square periodic forcing, which captures its predictor and response features. Furthermore, we investigate the reduced analytical version of the HH model known as the Morris-Lecar model, which captures key phenomena of the HH model.
October 13, 2022, 12:30-1:30pm
Speaker: Haniyeh Fattahpour (Georgia State University)
Title: Mathematical modeling and simulation of cell proliferation in a tissue-engineering scaffold pore
Abstract: Tissue-engineering scaffolds contain pores lined by cells that allow nutrient-rich culture medium to pass through to encourage cell proliferation. Several factors have significant impacts on the tissue growth, including the nutrient flow rate and concentration in the feed, scaffold elasticity as well as cell properties. Several studies have investigated these effects separately; however, in this work, we examine all of them simultaneously. Our objectives in this work are as follows: (i) the development of a mathematical model describing the nutrient fluid dynamics and concentration, scaffold elasticity and cell proliferation; (ii) solving the model and then simulating the cell proliferation process; (iii) developing a `reverse algorithm' that determines the initial configuration of the scaffold based on the desired geometry of the final tissue.
October 6, 2022, 12:30-1:30pm
Speaker: Carter Hinsley (Georgia State University)
Title: Existence criteria for utilitarian preference relations
Abstract: Expected utility theory extends the notion of outcome preferences in game theory to probabilistic games with uncertain outcomes. Even if multiple choices present equal expected utility, an agent’s attitude towards uncertainty may result in one choice being preferred to others. We investigate the consequences of von Neumann-Morgenstern rationality in expected utility theory and attempt to establish criteria for the existence of certain preference relations on collections of choices with probabilistic outcomes. A brief review of the Arrow-Pratt measures of risk aversion is provided, followed by a discussion of their insufficiency as invariants of equivalence classes of utility functions.
September 29, 2022, 12:30-1:30pm
Speaker: Hamad El Kahza (University of Delaware)
Title: Mathematical modeling of erosion and deposition in porous media
Abstract: Erosion and deposition are represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surfaces, which both often lead to reconfiguration and change of the topology and structure of porous media. These processes are notably very complicated and challenging to study in reality. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow-networks in the setting of cylindrical channels, undergoing a unidirectional flow, by using asymptotic and numerical techniques. Starting from the Stokes and continuity equations combined with the advection-diffusion equation for solid transport, we propose a model to construct a complete analysis of both the erosion and deposition. The considered approach is of the form of threshold laws: the fluid-solid interface erosion and deposition occur, when the total shear stress is respectively, greater and lower than some specific critical values, depending on the solid material. As a consequence of the erosion and deposition, the structure channels' radii expand and shrink, respectively, due to several key parameters, which we further investigate in this work. We also perform a parametric study to quantify the correlation between these threshold values and the particles concentration in the flow. A complete parametric study of the constructed model reveals that the final configuration of the structure can be predicted from the system parameters.
September 22, 2022, 12:30-1:30pm
Speaker: Pejman Sanaei (Georgia State University)
Title: Simulating liquid–gas interfaces and moving contact lines with the immersed boundary method
Abstract: In this work, we use the immersed boundary method with four extensions to simulate a moving liquid–gas interface on a solid surface. We first define a moving contact line model and implements a static-dynamic friction condition at the immersed solid boundary. The dynamic contact angle is endogenous instead of prescribed, and the solid boundary can be non-stationary with respect to time. Second, we simulate both a surface tension force and a Young’s force with one general equation that does not involve estimating local curvature. In the third extension, we splice liquid–gas interfaces to handle topological changes, such as the coalescence and separation of liquid droplets or gas bubbles. Finally, we re-sample liquid–gas interface markers to ensure a near-uniform distribution without exerting artificial forces. We demonstrate empirical convergence of our methods on non-trivial examples and apply them to several benchmark cases, including a slipping droplet on a wall and a rising bubble.
September 15, 2022, 12-1pm
Speaker: Sima Moshafi (Georgia State University)
Title: Wetting and drying in membrane filters
Abstract: Throughout its lifespan, a filter membrane is subjected to repeated cycles of wetting and drying processes. The fluid molecules or contaminant concentration, distribution, and the medium internal morphology change over these cycles. As a result, after several cycles, the filter performance deteriorates. In this work, we develop a mathematical model for the dynamics of wetting and drying in a porous medium. Our model takes into account the internal architecture of the porous medium, the deposition of contaminants, and the development of wet/dry interfaces as a result of evaporation. Using asymptotic analysis based on the small aspect ratio of the porous medium, our model is able to predict the proper time to change the filter based on their best performance and offers insights into the wetting/drying processes over time. We have built a numerical model in order to verify the accuracy of our analytical asymptotic approach. Using COMSOL Multiphysics, we compare our asymptotic model with direct numerical simulations of the governing equations. It is established that the asymptotic model is adequate for describing the wetting/drying events and offers tremendously less computational cost.
September 8, 2022, 12-1pm
Speaker: Hoseyn Akhoundpour Amiri (Georgia State University)
Title: Flight stability simulation in static mode
Abstract: Flight stability of objects with arbitrary shapes is one of the most fundamental problems in the concept of fluid-solid interaction (FSI). Regardless of their surrounding environments in which they move, objects follow the same principle: the generalized equations of motion. As a result, their physical characteristics such as geometry, the center of mass, and density play significant roles in their movement by altering the force/torque distributions over surfaces. In this presentation, we tackle this problem by analyzing various conditions via numerical modeling. For this purpose, COMSOL Multiphysics was utilized, and its results will be compared with the previous observations. Followed by that, a step-by-step implementation of the problem will be provided during the presentation.