April 20, 2023, 12:30-1:30pm
Speaker: Arkady Wey (University of Oxford, Mathematical Institute)
Title: Two new frameworks for filtration modelling: A size-structured model and a network–continuum multiscale model
Abstract: Filtration is the removal of particles from a fluid suspension by forcing it through a porous material, which causes particles to become captured in pores, leading to clogging. Filtration using membranes is a well-studied industrial process with multiple important applications. Existing mathematical approaches often either ignore important microscale information, such as the particle- and pore-size distribution and the connectivity of pores, or are prohibitively computationally expensive.
In this talk, we discuss two novel approaches for filtration modelling:
(I) A size-structured model
Using ideas common in age-structured population models, we treat the particle and pore sizes as independent variables. This allows us to pose the blocking and deposition clogging mechanisms as relationships between the relative sizes of particles and pores, which gives rise to a system of partial integro–differential equations for the two size distributions. The solutions provide us with greater understanding of the filtration process;
(II) A network–continuum multiscale model
The pore scale of the filter is treated as a network of nodes and edges. Deposition is modelled as a continuous process that shrinks edges, altering their ability to conduct fluid, so that the structure of the network is dynamic. This gives rise to a system of ordinary algebraic–differential equations on the network, the solution of which may be prohibitively expensive when the network is large. We use a novel method of multiple scales to homogenise this model and arrive at a continuum macroscale approximation of it that is much more computationally feasible, despite the fact it is still coupled to the dynamics of the underlying microstructure.
April 13, 2023, 12:30-1:30pm
Speaker: Christopher Conklin (Donaldson Company)
Title: Industrial Filtration Applications and Challenges
Abstract: Donaldson Company is an industry leader in providing unique filtration solutions in industries such as aerospace, agriculture, food and beverage, manufacturing, and transportation. This talk will explore filtration needs from a customer perspective, how we address those needs from pore scale to system scale, and the role of mathematical modeling in the process.
April 6, 2023, 12:30-1:30pm
Speaker: Soheil Saghafi (NJIT)
Title: Deep hybrid modeling of neuronal dynamics using generative adversarial networks
Abstract: Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. Here we introduce a novel parameter inference technique that combines deep learning with mechanistic modeling to address these shortcomings. In particular, we will use conditional Generative Adversarial Networks (cGANs) to provide an inverse mapping of data to mechanistic models and identify the distributions of mechanistic modeling parameters coherent to the data.
March 30, 2023, 12:30-1:30pm
Speaker: Sima Moshafi (Georgia State University)
Title: Mathematical modeling of flow and transport in pleated filters
Abstract:
March 23, 2023, 12:30-1:30pm
Speaker: Pejman Sanaei (Georgia State University)
Title: Dynamic Entrainment: A deep learning and data-driven process approach for synchronization in the Hodgkin-Huxley model
Abstract: Resonance and synchronized rhythm are important phenomena and can be either constructive or destructive in dynamical systems in the nature, specifically in biology. There are many examples showing that the human's body organs must maintain their rhythm in order to function properly. For instance, in the brain, synchronized or desynchronized electrical activities can lead to neurodegenerative disorders such as Huntington's disease. In this work, we adopt a well known conductance based neuronal model known as Hodgkin-Huxley model describing the propagation of action potentials in neurons. Armed with the ``data-driven" process alongside the outputs of the Hodgkin-Huxley model, we introduce a novel Dynamic Entrainment technique, which is able to maintain the system to be in its entrainment regime dynamically by applying deep learning approaches.
March 16, 2023, 12:30-1:30pm
Speaker: Haniyeh Fattahpour, Emeka Peter Mazi (Georgia State University)
Title: 1) A mathematical model for tissue growth in a tissue-engineering scaffold pore
2) On mathematical modeling of erosion and deposition in complex porous media
March 2, 2023, 12:30-1:30pm
Speaker: Lanjing Bao
Title: Reduction to smooth maps for the global dynamics of a vibro-impact pair model
Abstract: Vibro-impact dynamic pairs appear in multiple engineering applications including vibro-impact harvesters. Such devices can harvester energy from vibro-impact motion of a ball moving freely within a driven cylindrical capsule with two dielectric elastomer membranes that cover its both ends. When the membranes are impacted and deformed by the ball, the capacitance change generates an extra charge to be harvested. Due to the complexity of the non-smooth interactions, there is a lack of mathematical approaches to analyzing the global dynamics of such vibro-impact systems. In this talk, we will present a computational method for reducing the non-smooth dynamics into smooth maps which represent the evolution of the system’s states from one impact to another. These maps allow for a semi-analytical study of the system’s global dynamics via an auxiliary 1D map approach for estimating the solutions’ basins of attraction. Our results may provide practical guidelines for designing vibro-impact energy harvesters with a desired globally stable dynamical regime that can maximize the energy gain.
February 23, 2023, 12:30-1:30pm
Speaker: Binan GU (Worcester Polytechnic Institute)
Title: Stochastic modeling of membrane filtration on pore networks
Abstract: Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport, and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this talk, we discuss several mathematical models of membrane filtration on a network of cylindrical pores, which capture various features observed in the manufacturing process of membrane filters. In particular, under the context of fluid flow, foulant particle transport, and adsorptive membrane fouling, we address the mathematical formulation of their governing PDEs on graphs with conservation laws at graph vertices (pore junctions). We analyze the performance of membrane filters represented by pore networks using two criteria: 1) total volumetric throughput of filtrate over the filter lifetime and 2) accumulated foulant concentration in the filtrate. We study the influence of membrane connectivity and geometric features such as tortuosity on these measures of performance. Lastly, we propose a new problem on membrane filtration under simultaneous adsorption and sieving, which pertains to several disciplines of applied mathematics.
February 16, 2023, 12:30-1:30pm
Speaker: Haniyeh Fattahpour, Emeka Peter Mazi (Georgia State University)
Title: 1) Effects of elasticity on cell proliferation in a tissue-engineering scaffold pore
2) Mathematical modeling of erosion and deposition in porous media
February 9, 2023, 12:30-1:30pm
Speaker: Pejman Sanaei (Georgia State University)
Title: On free streamline theory and flight stability of cones and wedges
Abstract: Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments, simulations and mathematical modeling (using free streamline theory) that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar flows at Reynolds numbers 100 to 1000. Slender wedges are statically unstable with apex leading and tend to flip over or tumble, and broad wedges oscillate or flutter due to dynamical instabilities, but those of apex half angles between about 40◦ and 55◦ maintain stable posture during flight. The existence of ‘‘Goldilocks’’ shapes that possess the ‘‘just right’’ angularity for flight stability is thus robust to dimensionality.
February 2, 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.
January 26, 2022, 12:30-1:30pm
Speaker: Haniyeh Fattahpour (Georgia State University)
Title: Effects of elasticity on cell proliferation in a tissue-engineering scaffold pore
Abstract: Scaffolds engineered for in vitro tissue engineering consist of multiple pores where cells can migrate along with nutrient-rich culture medium. The presence of the nutrient medium throughout the scaffold pores promotes cell proliferation and this process depends on several factors such as scaffold geometry, nutrient medium flow rate, shear stress, cell-scaffold focal adhesions and elastic properties of the scaffold material. While numerous studies have addressed the first four factors, the mathematical approach describe herein focuses on cell proliferation rate in elastic scaffolds, under constant flux of nutrients. As cells proliferate, the scaffold pores radius shrinks and thus, in order to sustain the nutrient flux, the inlet applied pressure on the upstream side of the scaffold pore must be increased. This results in expansion of the elastic scaffold pore, which in turn further increases the rate of cell proliferation. Considering the elasticity of the scaffold, the pore deformation allows further cellular growth beyond that of inelastic conditions. In this paper, our objectives are as follows: (i) develop a mathematical model for describing fluid dynamics, scaffold elasticity and cell proliferation for scaffolds consist of identical nearly cylindrical pores; (ii) solve the models and then simulate cellular proliferation within an elastic pore. The simulation can emulate real life tissue growth in a scaffold and offer a solution which reduces the numerical burdens. Lastly, our results demonstrated to be in qualitative agreement with experimental observations reported in the literature.