Online social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online, the content that spreads on online social networks can have important consequences on public opinion, policy, and voting. To better understand the online content spread, mathematical modeling of opinion dynamics is becoming […]
In this talk, we will talk about the thin film model derived for liquid film resulting from a distributed source on a vertical wall and some distinct properties about the model. We will discuss the different behavior and properties of the model with and without considering surface tension. When the surface tension is neglected, a […]
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, which have been proposed recently as a framework for global solutions for multi-dimensional hyperbolic systems of conservation laws. We […]
In this talk, we will present a recent study of the Maxwell-Bloch equations that model the nonlinear interactions of light and matter, where the light is modeled classically by the […]
Abstract: We consider the problem of minimizing the first nonzero eigenvalue of an elliptic operator with Neumann boundary conditions with respect to the distribution of two conducting materials with a […]
Abstract: In the presentation we will discuss our research program concerning the search for the most singular behaviors possible in viscous incompressible flows. These events are characterized by extremal growth […]
The immersed boundary method was first developed in the 1970s to model the motion of heart valves and has since been utilized to study many different biological systems. While the IB method has seen countless modifications and advancements from the perspective of fluid-structure interaction, the use of a Newtonian fluid model remains a fundamental component […]
We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound. Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain […]
Abstract: The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the “shortest path” between two nodes, this talk will explore the properties of the recently proposed measure, the heatmap centrality, by comparing the farness of a node […]
Abstract: The Landau-de Gennes theory is a type of continuum theory that describes nematic liquid crystal configurations in the framework of the Q-tensor order parameter. In the free energy, there is a singular bulk potential which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. In this […]
Abstract The COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency […]
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