August 3, 2023, 12:30-1:30pm
Speaker: Pejman Sanaei (Georgia State University)
Title: On the applications of the immersed boundary method
July 27, 2023, 12:30-1:30pm
Speaker: Haniyeh Fattahpour (Georgia State University)
Title: A mathematical model for tissue growth in a tissue-engineering scaffold pore
Speaker: Lawan Wijayasooriya (Georgia State University)
Title: The Morris-Lecar model
July 20, 2023, 12:30-1:30pm
Speaker: Emeka Peter Mazi (Georgia State University)
Title: On mathematical modeling of erosion and deposition in complex porous media
Speaker: Sima Moshafi (Georgia State University)
Title: Mathematical modeling of flow and transport in pleated filters
June 7, 2023, 12:30-1:30pm
Speaker: Lawan Wijayasooriya (Georgia State University)
Title: The Morris-Lecar model
Abstract: I will give an update on the progress of my project.
June 1, 2023, 12:30-1:30pm
Speaker: Sima Moshafi (Georgia State University)
Title: Mathematical modeling of flow and transport in pleated filters
Abstract: I will give an update on the progress of my project.
May 25, 2023, 12:30-1:30pm
Speaker: Anand Oza (New Jersey Institute of Technology)
Title: Fluid-mediated active matter: capillary surfers and schooling wings
Abstract: In this talk I will describe my recent work on two active matter systems in which hydrodynamic interactions play a prominent role. The first is the capillary surfer system, which consists of objects that self-propel while floating on the surface of a vertically vibrating fluid bath. Recent experiments have demonstrated that multiple surfers may self-organize through the collective interfacial deformation in the form of propagating capillary waves. We derive and analyze a theoretical model for the surfer’s positional and orientational dynamics by modeling the capillary wave forces and torques that surfers exert on each other. The model predictions exhibit good agreement with experimentally observed interaction modes between two surfers.
The second system is motivated by the beautiful displays exhibited by fish schools and bird flocks, where there has been debate over the role of hydrodynamic interactions. I will present a model for flapping wings in orderly formations, wherein we explicitly solve the linearized Euler equations in a multiply-connected domain. The model predictions exhibit good agreement with experiments on schooling wings in a water tank. We then develop a one-dimensional continuum theory for a dense flock, which exhibits traveling wave solutions. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts.
May 19, 2023, 12:30-1:30pm
Speaker: Mohammad Nooranidoost (Florida State University)
Title: A mathematical model for biofilm viscoelasticity and its spatiotemporal organization
Abstract: Biofilms are initiated by individual bacteria and produce polysaccharides that form an extracellular polymeric network, which is essential in biofilm development and integrity. In this talk, we present a mathematical model to describe the rheology of biofilm structure and its components. First, we estimate the viscoelastic properties of different biofilm variants using a Bayesian framework and linear viscoelastic models. Then, we formulate a mathematical model to describe the spatiotemporal organization of biofilm components as a viscoelastic multiphase system where each volume in space is fractionally occupied by a polymeric network and a fluid solvent. Using numerical methods similar to those used to solve the Navier-Stokes equations, we investigate the dynamics and motion of the biofilm.
May 11, 2023, 12:30-1:30pm
Speaker: Haniyeh Fattahpour (Georgia State University)
Title: A mathematical model for tissue growth 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) developing 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) optimizing the initial configuration of the scaffold to obtain the maximum tissue growth.
May 4, 2023, 12:30-1:30pm
Speaker: Emeka Peter Mazi (Georgia State University)
Title: On mathematical modeling of erosion and deposition in complex porous media
Abstract: Erosion and deposition can have significant effects in the nurture, industrial applications and in general porous media. In this work, we study the deposition and erosion of solid particles at a microscale level and their direct consequence on the internal structure of porous media with complex internal morphology. We present an idealized model, in which a porous medium consists of bifurcating cylindrical channels. The flow and solid particles are modeled by Stokes and advection-diffusion equations, respectively. Finally, we investigate the erosion and deposition of solid particles and characterize the evolution of the internal geometry of porous media.