Archive : Applied Mathematics and Mathematical Medicine and Biology Seminar

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Binan Gu, Department of Mathematical Sciences, New Jersey Institute of Technology139Binan Gu, Department of Mathematical Sciences, New Jersey Institute of Technology336 Ewing Hall and on Zoom<p><strong>​Mode:</strong> In-person and <a href="https://udel.zoom.us/j/98758622578" target="_blank">Zoom​</a><br><strong></strong></p><p><strong>Title:</strong>  Graphical Representation of Membrane Filtration</p><p><strong>Abstract:</strong> We study the performance of a membrane filter represented by a pore network based on two criteria: 1) total volumetric throughput and 2) accumulated foulant concentration. We first formulate the governing equations of fluid flow on a general network, and we model adsorptive fouling by imposing an advection equation on each pore (edge) and imposing conservation of fluid and foulant volumetric flow rate at each pore junction (vertex), which yields a system of partial differential equations. We study the influence of three geometric network parameters on filter performance: 1) average number of neighbors of each vertex; 2) initial total void volume of the pore network; and 3) tortuosity of the network. We find that total volumetric throughput has a stronger dependence on the initial void volume than on average number of neighbors.  Tortuosity turns out to be a universal parameter, leading to almost perfect collapse of all results for a variety of different network architectures. In particular, the accumulated foulant concentration shows an exponential decay as tortuosity increases.​<br></p>12/3/2021 3:10:00 PM12/3/2021 3:55:00 PM
Riku Paananen, Helsinki Eye Lab, Ophthalmology, University of Helsinki and Helsinki University Hospital138Riku Paananen, Helsinki Eye Lab, Ophthalmology, University of Helsinki and Helsinki University HospitalZoom<b>​Mode: </b>Virtual (<a href="https://udel.zoom.us/j/98758622578" target="_blank">Zoom​</a>)<br><b><br></b><div><b>Title: </b>Insights into lipid structures from molecular dynamics simulations<br><b><br></b></div><div><b>Abstract:</b> Self-assembly of lipids gives rise to various structures such as micelles, bilayers, vesicles, monolayers, and other more complex systems. These lipid structures play a key role in various biological processes, such as acting as structural components of cells, or forming protective barriers in the skin or the surface of the eye. Molecular dynamics (MD) simulations are a powerful computational tool in studying such lipid systems, since they can provide atomic-level details, which are often difficult to access via experimental techniques.<br><br>This talk provides a general introduction into studying lipid systems with MD simulations, followed by specific examples of how these techniques have been utilized to study the different questions related to biological systems. Often the best results can be obtained when MD simulations are combined with experimental approaches to provide a more in-depth view of the system. Examples include utilizing MD simulations to study tear film lipid layer structure and evaporation resistance, lateral heterogeneity in lung surfactant monolayers, and nanoscale structure of cellular membranes.<br></div>11/12/2021 3:10:00 PM11/12/2021 3:55:00 PM
Hangjie Ji, Department of Mathematics, North Carolina State University137Hangjie Ji, Department of Mathematics, North Carolina State UniversityZoom<p><strong>​Mode:</strong> <a href="https://udel.zoom.us/j/98758622578" target="_blank" title="Zoom room">Zoom​</a> Only (pass code needed, contact organizer)<br><strong></strong><span class="wrap-text"><strong>Title:</strong> Dynamics of thin liquid films on vertical cylindrical fibers<br><strong>Abstract:</strong> Thin liquid films flowing down vertical fibers spontaneously exhibit complex interfacial dynamics, creating irregular wavy patterns and traveling liquid droplets. Such dynamics is a fundamental component in many engineering applications, including mass and heat exchangers for thermal desalination and water vapor and particle capture. Recent experiments present a wealth of new dynamics that illustrate the need for more advanced theory. In this talk, I will first present a study of a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This model better explains the observed velocity and stability of traveling droplets in experiments and their transition to isolated droplets. Next, I will discuss thermally-driven droplet coalescence induced by an inhomogeneous temperature field along the fiber. To characterize the flow regime transition caused by varying nozzle geometries, I will also present a study of a weighted residual integral boundary-layer model that incorporates moderate inertia. Analytical results on traveling wave solutions to the fiber coating models will also be discussed.</span><br></p>10/29/2021 2:10:00 PM10/29/2021 2:55:00 PM
Linda Cummings, Department of Mathematical Sciences, New Jersey Institute of Technology136Linda Cummings, Department of Mathematical Sciences, New Jersey Institute of TechnologyZoom<p><strong>​Mode:</strong> Virtual (<a href="https://udel.zoom.us/j/98758622578">Zoom​</a>)<br><strong></strong></p><p><strong>Title:</strong> Dewetting and dielectrowetting in thin films of nematic liquid crystals</p><p><strong>Abstract:</strong> Thin films of nematic liquid crystal (NLC) find widespread industrial use, in applications ranging from liquid crystal display devices to liquid lenses and optical shutters. Understanding how such films spread and flow is therefore important from an industrial perspective as well as being of fundamental scientic interest. We will describe how asymptotic methods (lubrication theory) can be applied to derive a simplied model for the free surface evolution of NLC films in a number of different settings. Of particular importance for film behavior is the orientation of the NLC molecules, both within the bulk film and at interfaces. The former is dictated by elastic effects and by the presence of applied external fields such as an electric field; while the latter depends primarily on interactions of the NLC with the adjacent material (a phenomenon known as anchoring). We will present simulations of our model that illustrate film behavior both without (dewetting) and with (dielectrowetting) an applied electric field, showing good qualitative agreement with available experimental data.​​<br></p>10/22/2021 2:10:00 PM10/22/2021 2:55:00 PM

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