Seminar in Applied Mathematics

Department of Mathematics and Statistics

Texas Tech University

Spring 2017 - Wednesday, 4-5 pm - Room MATH 016

image Wednesday, January 25
Mixed Boundary Value Problem for Non-divergence Elliptic Equation
Akif Ibraguimov
image Thursday, February 2, 3:30pm, CHEM 107
Colloquium Talk (Biomath)
Rebecca Everett
image Thursday, February 9, 3:30pm, CHEM 107
Colloquium Talk (Biomath)
Naveen Vaidya
image Wednesday, February 15
Mixed Boundary Value Problem for Non-divergence Elliptic Equation (part II)
Akif Ibraguimov
image Tuesday, February 21, 3:30pm, CHEM 107
Colloquium Talk (Computational Math)
Wei Guo
image Thursday, February 23, 3:30pm, CHEM 107
Colloquium Talk (Computational Math)
Youngjoon Hong
image Tuesday, February 28, 3:30pm, CHEM 107
Colloquium Talk
Vakhtang Poutkaradze
image Wednesday, March 8
Unfolding surprising dynamical behaviors in disease models via dynamical systems approach
Wenjing Zhang
Deterministic models arise in many contexts in the biology, economic and social science. In this talk, dynamical systems theory and bifurcation theory are applied to investigate a simple 2-dimensional infectious disease model. Such model exhibits an amazing array of dynamical behaviour, from single stable equilibrium, to two types of bistable states, to stable and unstable bifurcation limit cycles (periodic solutions), to relaxation oscillation (recurrent phenomenon). The high-order model can also be analyzed via computer algebra systems: Maple.
image Wednesday, March 22
Fluid-structure interaction simulations with applications to aneurysms modeling and magnetic drug targeting
Sara Calandrini and Giacomo Capodaglio
We present numerical simulations of fluid-structure interaction (FSI) problems applied to blood flow applications. First we illustrate the formulation of the FSI problem in an arbitrary Eulerian Lagrangian (ALE) framework with particular attention to the solver chosen. Then we present biomedical applications where the mutual interaction between fluid and solid is of major relevance for the description of the physics. The first application consists of modeling the effect of stents placed on the neck of cerebral aneurysms in order to study the pressure distribution on the aneurysm wall and the change in volume of the aneurysm. The second application consists of magnetic drug targeting (MDT) simulations where magnetically susceptible drug particles are injected in a blood flow and externally directed to target only a specific region of the blood vessel, where for example a thrombosis or a tumor can be located.
image Wednesday, March 29
Fracture Model Reduction and Optimization for Nonlinear Flows in Porous Media
Pushpi Paranamana
In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing fractures with complex geometries. We model the coupled fracture-porous media system where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside the fracture. The optimal length of the fracture is analyzed using “the diffusive capacity”, a functional that measures the performance of the reservoir. Also, we devise a model to address the complexity of the fracture geometry which examines the flow inside fractures with variable thickness on a general manifold. The fracture is represented as a parametric surface on Riemannian manifold where the thickness changes in the normal direction from the barycentric surface. Using Laplace Beltrami operator, we formulate an equation that describes the flow and then further simplifications were done. Using the model, pressure profile of a nonlinear flow is analyzed and compared with the actual pressure profile obtained numerically in order to validate the model.
image Thursday, April 6, 3:30pm, CHEM 107 (Colloquium)
Quantifying the Capabilities of Attackers in Cyber-Physical Systems
Justin Ruths
While the modernization of control processes has led to unprecedented levels of productivity and efficiency, the coupling of the physical processes with an overarching cyber communication control layer opens up new vulnerabilities in such so called Cyber-Physical Systems (CPS). While attacks can be viewed as unknown disturbances or faults in the system, the strategic nature of attacks raises altogether new research challenges. Chief among them is to quantify the effect that an attacker can have, which is determined by the dynamics of the system, the design of the controller and state estimator, and the form of the attack detection method. In this talk I describe our work to quantify the impact that an attacker can have, including the prerequisite step to optimally tune attack detectors to a desired level of performance. I consider two major classes of static and dynamic detectors and show experimental results on scaled-industrial control systems.
image Thursday, April 13, 3:30pm, Physics 234
The interaction between fluids and solids: modeling, discretization, simulations (Joint Physics-Math Colloquium)
Giorgio Bornia
Multiphysics problems attract an increasing attention in the mathematical community. In fact, their study leads to a deeper understanding of real-life processes. Among them, the interaction of fluids and solids is certainly one of the most interesting, with ubiquitous applications in fields such as aeroelasticity, biomechanics and civil engineering. We will explore the two-way coupling between fluid and solid mechanics in a broad perspective. The physical modeling, the definition of numerical algorithms and their computer implementation will be discussed, in order to highlight the main challenges as well as the effectiveness in the simulation of real-world phenomena.
image Tuesday, April 18, 3:30pm, CHEM 107
Decoding and Control of Dynamic Structures in Population Systems (SIAM Colloquium)
Jr-Shin Li
Numerous natural and engineered systems that consist of ensembles of isolated or interacting dynamical components exhibit levels of complexity that are beyond human comprehension. These complex systems often require an appropriate excitation, an optimal hierarchical organization, or a periodic dynamical structure, such as synchrony, to function as desired or operate optimally. In many applications, the dynamics of such ensemble systems can be regulated by the application of a single or sparsely distributed external inputs in order to alter their state configurations or dynamic structures; for example, applying electromagnetic fields to excite quantum ensembles for spectroscopy and imaging, and implementing invasive or noninvasive neurostimulation to desynchronize pathologically synchronized neuronal populations for the treatment of neurological disorders. This control paradigm gives rise to challenging problems regarding robust control and computation for underactuated ensembles. Moreover, valid and precise models for such complex systems are often elusive, while the measurement data are available. In this talk, I will address theoretical and computational challenges for engineering dynamic structures in population and networked systems through various compelling applications. I will introduce both model-based and data-driven approaches for the encoding, control, and computation of dynamic structures and patterns in population systems. Practical ensemble control designs, including synchronization waveforms for pattern formation in nonlinear oscillator networks and optimal pulses in quantum control will be illustrated along with their experimental realizations.
image Friday, April 28, 8:20-18:15, Student Union Building, Senate Room

West Texas Applied Math Graduate Minisymposium