| Giovanna Guidoboni, University of Missouri | Giovanna Guidoboni, University of Missouri | EWG336 | Title: Physically-based modeling for a virtual laboratory in Science and
Engineering: theory and applications<br><br>
Description: Physically-based models combine fundamental principles of physics,
engineering, mathematics and scientific computing to provide qualitative
and quantitative assessments of the mechanisms governing the behavior of
complex systems. The utilization of physically-based models to study
living systems helps disentangle the interaction among coexisting (often
competing) factors that is not possible to single out in experimental
and clinical studies. Thus, physically-based models can serve as a
virtual laboratory where multiple scenarios can be simulated,
conjectures can be tested and new hypotheses can be formulated.
This talk will present two particular applications of physically-based
models. The first application aims at characterizing changes in ocular
hemodynamics due to alterations in intraocular pressure (IOP), blood
pressure (BP) and vascular autoregulation (AR) of each individual. The
knowledge on interacting factors gained via physically-based models can
also be used as a guide for the statistical analysis of clinical data
for more informative outcomes, as shown by the Singapore Epidemiology of
Eye Diseases study, where our theoretical predictions on the interplay
between IOP and BP have been confirmed on nearly 10,000 people. The
second, more recent, application aims at elucidating the cardiovascular
mechanisms giving rise to the ballistocardiogram (BCG). BCG is a signal
generated by the repetitive motion of the human body due to sudden
ejection of blood into the great vessels with each heartbeat. Main
cardiovascular diseases, such as hypertension and congestive heart
failure, have been shown to alter the BCG signal, which then yields a
great potential for passive, noncontact monitoring of the cardiovascular
status (e.g. through sensors positioned under the bed or on an
armchair). Our work aims at standardizing BCG measurements in order to
achieve a consistent clinical interpretation of the BCG signal across
sensing devices.
Interestingly, the need to address specific questions arising in the
applied sciences calls for the theoretical study of new mathematical
problems and computational methods. Examples discussed in this talk
include: (i) well-posedness of partial differential equations of mixed
parabolic/elliptic type with nonhomogeneous boundary conditions utilized
to describe the perfusion of deformable tissues; and the (ii)
energy-preserving numerical algorithms based on operator splitting to
simulate multiscale problems.
| 12/3/2019 8:30:00 PM | 12/3/2019 9:30:00 PM | False | |
| Shawn Walker, Louisiana State University | Shawn Walker, Louisiana State University | EWG336 | Title: The Uniaxially Constrained Q-tensor Model for Nematic Liquid Crystals<br><br>
Abstract: We consider the one-constant Landau-de Gennes (LdG) model for nematic
liquid crystals with traceless tensor field Q as the order parameter
that seeks to minimize a Dirichlet energy plus a double well potential
that confines the eigenvalues of Q (examples/applications will be
described). Moreover, we constrain Q to be uniaxial, which involves a
rank-1 constraint. Building on similarities with the one-constant
Ericksen energy, we propose a structure-preserving finite element method
for the computation of equilibrium configurations. We prove stability
and consistency of the method without regularization, and
$\Gamma$-convergence of the discrete energies towards the continuous one
as the mesh size goes to zero. We also give a monotone gradient flow
scheme to find minimizers. We illustrate the method's capabilities with
several numerical simulations in two and three dimensions including
non-orientable line fields. In addition, we do a direct comparison
between the standard LdG model, and the uniaxially constrained model. | 11/19/2019 8:30:00 PM | 11/19/2019 9:30:00 PM | False | |
| Daniela Egas, EPFL | Daniela Egas, EPFL | EWG336 | Title: Topology and neuroscience<br><br>
Abstract: I will broadly present some of the applications of topology and topological data analysis to neuroscience through an exploration of the collaboration between the applied topology group at EPFL and the Blue Brain Project. In particular, I will describe how we are using topology to further understand brain architectures, learning and neuroimaging techniques.
| 11/18/2019 8:30:00 PM | 11/18/2019 9:30:00 PM | False | |
| Shailesh Shah | Shailesh Shah | EWG336 | Title: A Mathematician’s Journey
</br></br>
Abstract:
I will provide a personal account of a forty year non-academic career spanning from mathematical modeling in a gas utility to risk modeling and management in global financial institutions. The talk will describe the transition from academia to industrial R&D to providing decision support for senior management, and discuss leveraging technical skills and building new "soft" skills to succeed in Business. Using select examples from industry (Demand Forecasting and Network Simulation) and Finance (Risk and Capital), I will provide insight into how mathematical models and related techniques such as scenario analysis and stress testing are used to guide decision making. In particular, I will touch upon their advantages, limitations and related challenges in data, models, systems and operational complexity - particularly focusing on the Great Financial Crisis and its aftermath.
| 11/5/2019 8:30:00 PM | 11/5/2019 9:30:00 PM | False | |
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