||Title and Abstract
||Longhua Zhao (Case Western Reserve
||Title: Fluid-structure interactions
with biological applications
Abstract: Fluid-structure interactions have drawn intense attention due to their biological applications. In this talk, two types of problems will be discussed. The first is fluid-structure interactions between fluid flow and structures such as cilia, helical flagella, micro-fluidic tweezers in the low Reynolds number regime. We utilize the singularity method to explore flow fields induced by ‘carpets’ of rotating flagella, processing nodal cilia and micro-fluidic tweezers. Using our model system, we are able to capture the phenomena observed in experimental studies. To better understand the transport of microscale loads or to achieve accurate control of micro-beads, we model a fully coupled helix (tweezers)-vesicle system by placing a finite-sized vesicle held together by elastic springs. The second problem is about simulating and modeling the dynamics of spider ballooning. The detailed physics driving this ballooning process remains little understood. We develop a mathematical model to identify the crucial physical phenomena that drive this unique mode of dispersal. The immersed boundary method has been used to solve this complex multi-scale problem.
||Mingji Zhang (New Mexico Tech)
||Title: Mathematical studies of
Poisson-Nernst-Planck systems: qualitative properties of
ionic flows without electroneutrality conditions
Abstract: We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flow through a membrane channel. We consider two ion species, one positively charged and one negatively charged, assume zero permanent charge, and include a local hard-sphere potential depending pointwise on ion concentrations to account for effects on ionic flows from ion size. The model problem is treated as a boundary value problem of a singularly perturbed differential system. Critical potentials are identified, which plays an important role in characterizing the ion size effects on ionic flows. Rich interplays among the physical parameters are observed and analyzed in great details. Throughout our analysis, electroneutrality conditions are NOT assumed, and this is the novelty of this work.
||Ivan A. Sudakov (University of Dayton)
102 Weir Hall 3:30pm
|Title: The mathematics of arctic tipping
Abstract: A tipping element for the Earth's cryosphere may be the melting of the summer Arctic sea ice pack, which is occurring at a precipitous rate that has far outpaced the projections of large-scale climate models. Also, permafrost melting could release considerable amounts of greenhouse gases into the atmosphere. Methane emission from tundra permafrost lakes is a significant positive feedback mechanism to the atmosphere in a changing climate. This is another potential tipping point in the climate system.
These types of critical phenomena in the cryosphere are of increasing interest as the climate system warms, and are crucial for predicting its stability. In this lecture I will give examples of how bifurcation and stochastic theories are powerful tools that can be used to address such questions. Ultimately this work will advance the representation of tipping elements in climate models, which will provide better predictions of the fate of Earth's cryosphere and the response of ecosystems.
||Gilberto C. González Parra (University of Los
||Title: Mathematical modeling of viral and
immune system dynamics: tools and challenges
Abstract: Mathematical modeling is an important tool to understand the spread and control of infectious diseases in different type of population. Mathematical models have been increasing exponentially for the last decades, in order to deal with different emerging and re-emerging infectious disease that cause morbidity and mortality around the world. In this talk, a description of some mathematical and computational models used to study viral dynamics is presented. We will discuss some parameter estimation techniques that are a key tool to analyze viral kinetics and antivirals. We show how mathematical modeling can be used to estimate several important parameters such as virus clearance, infectious lifespan, eclipse phase, infecting time and drug efficacy. Moreover, we provide some examples of how data-oriented mathematical models can help to design in vivo and in vitro experiments that can be used to provide an insightful view of the viral processes.
5:00pm 102 Weir Hall
|PhD final defense
Abstract: In this study a mathematical modeling and analysis of wind turbine’s dynamics is presented. The model represented by control blocks and transfer
functions, taken from recognized papers and studies, is translated to a system of nonlinear differential algebraic equations. For the resulted system, we presented possible reductions to the size of the system based on the wind speed range and activated controls. For computational and numerical studies, we proved the existence of a unique terminal voltage solution, which eliminated the algebraic constraint. Numerically, we found the steady states as functions of the wind speed and computed the eigenvalues to study local stability. Steady states and stability in grid parameter space (R and X) were studied as well. We studied the sensitivity of the state variables and eigenvalues to wind speed and other parameters. Our study provides proofs of boundedness, existence, and uniqueness for the initial value problem of the system. A safe region in R and X space was defined, in which existence and uniqueness were guaranteed. We found a Hopf bifurcation in the safe region. Eventually, we used time scale analysis and simulations to simulate the system. Some of the simulations aimed to capture the system’s response to time dependent wind speed profiles, a drop-clear case for the terminal voltage, and a drop-clear case for the reactance passing through the bifurcation point. Other simulations intend to test attraction limits versus control limits, as well as the Q Drop’s function effect on the reactive power control dynamics.
||Yaozhong Hu (possibly )(University
||Spring break! No talks!
||Title: Coupling of Electromagnetic Fields from Lightning Strikes to Metallic Objects in Coal Mines
Abstract: It is known that fields generated from lightning strikes can couple to metallic objects in coal mines and if conditions are right an arc formed between metal objects can ignite a mixture of methane gas and air. This talk considers the numerical modeling of fields generated from an engineering model of a lightning strike and their coupling to metallic objects as vent pipes and roof meshes that are typically present in coal mines via integral equations. A brief discussion of the problem formulation in terms of integral equations and dyadic Green’s function’s for layered media, code validation via another numerical solution, comparison to experiment, and well as numerical results and insights relevant to coal mine safety will be presented.
||Hanchun Yang (Yunnan University, China &
Title: Developments and Applications of Delta Shock Waves
Abstract: The delta shock wave is a type of nonclassical wave whichrepresents the phenomenon of concentration of the mass. In this talk, we are concerned with the delta shock waves with Dirac delta functions developing in both state variables for a class of nonstrictly hyperbolic systems of conservation laws. We also show the generality and practicability of our theory on the delta shock waves which can be successfully applied to those systems investigated by Korchinski (1977), Tan, Zhang and Zheng (1991), Ercole (2000), Cheng and Yang (2011), as well as the equations of geometrical optics by Engquist and Runborg (1996), etc, and we give a simplified approach to solve a two-dimensional Riemann problem for the Burgers-type equations considered by Tan and Zhang (1990) for the 4Js’ case. Finally, we present the numerical simulations coinciding with theoretical analysis.