Publication Data. ISSN print : Publisher: Society for Industrial and Applied Mathematics. Online access to the content you have requested requires one of the following:. Banner art adapted from a figure by Hinke M. You have requested the following content:. His current research deals with the roles played by time-delayed feedback in the neural control of balance and the generation of epileptic seizures.
His pedagogical efforts are focused on bringing mathematics to the bedside through the creation of cross-disciplinary teams. He did his internship at the Royal Victoria Hospital and then completed his neurology residency and epilepsy fellowship at the Montreal Neurological Institute. From he was the co-director of the adult epilepsy program at the University of Chicago. He has received numerous awards including the Richard Bellman prize in mathematical biosciences shared with A. He is the section editor for Dynamical Diseases for the Encyclopedia of Computational Neuroscience and serves on the editorial advisory board of Chaos.
He has more than publications and has written three books: Dynamics of small neural populations , Epilepsy as a dynamic disease with P.
Jung and Mathematics as a laboratory tool with T. In this talk, we review some recent advances in the analysis and design of algebraic flux correction AFC schemes for hyperbolic problems. In contrast to most variational stabilization techniques, AFC approaches modify the standard Galerkin discretization in a way which provably guarantees the validity of discrete maximum principles for scalar conservation laws and invariant domain preservation for hyperbolic systems.
The corresponding inequality constraints are enforced by adding diffusive fluxes, and bound-preserving antidiffusive corrections are performed to obtain nonlinear high-order approximations. After introducing the AFC methodology and the underlying theoretical framework in the context of continuous piecewise-linear finite element discretizations, we present some of the limiting techniques that we use in high-resolution AFC schemes.
As an alternative to flux-corrected transport FCT algorithms which apply limited antidiffusive corrections to bound-preserving low-order solutions, we propose a new limiting strategy based on representation of these solutions as convex combinations of "bar states" satisfying physical and numerical admissibility conditions.
Douglas P. Henderson
Each antidiffusive flux is limited so as to guarantee that the associated bar state remains in the convex invariant set and preserves appropriate local bounds. There is no free parameter, and the nonlinear discrete problem is well-defined even in the steady-state limit. In the case study for the Euler equations of gas dynamics, we enforce local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure.
The results of numerical studies for standard test problems illustrate the ability of the methods under investigation to resolve steep gradients without generating spurious oscillations.
Dissertations & Theses from 12222
In the last part of this talk, we discuss the design of AFC schemes for high-order finite elements. The approaches to be explored are based on the use of Bernstein basis functions and partitioned finite element spaces. September Tuesday, Sep Thursday, Sep Friday, Sep Computational cardiac models have gained increasing popularity and become an indispensable and powerful tool in elucidating the pathological process of different heart diseases.
They can be used to estimate important physiological and clinically relevant quantities that are difficult to directly measure in experiments. The broad goals of this thesis were to develop 1 a microstructure-b. Applications of geometrothermodynamics in non-standard theories of gravity S. Taj Tassaddiq Solvability of systems of differential equations by complex symmetry analysis, M. Safdar QAU ; Mechanics M. QAU ; Electromagnetism M. You may be trying to access this site from a secured browser on the server.
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University Distinguished Professor at City University of Hong Kong
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X Rev XII XIII XVI Qadir and K. XIX Afridi and A. XXII Afridi, A. Qadir and J. Zaki, Pak. XXIII Naqvi A. Qadir and A. XXIV XXV XXVI Quamar, Proc.
Third Marcel Grossmann Meeting, ed. Gotsman and G. Tauber, Cambridge University Press Qadir and M. Rafique, Proc. Fourth Marcel Grossmann Meeting, Ed. Ruffini Elsevier Science Publishers , pp.
Bokhari and A. Qadir, ibid. Khan and A. Qadir, Proc. Fifth Marcel Grossmann Meeting, eds. Blair and M. Buckingham World Scientific Qadir and H. Rizvi, ibid. Third Regional Conference on Mathematical Physics, eds. Hussain and A. Qadir World Scientific, pp. Qadir, M. Beg Memorial Volume, eds.
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Ali and P. Hoodbhoy World Scientific Ziad, Proc. Sixth Marcel Grossmann Meeting, eds.
Nakamura and H. Sato, World Scientific pp. Pervez and A. Ardalan, H. Arfaei and S. Rouhani, Sharif University Press , pp. De Paolis. Ali Qadir and A. Gurovich, Kzyrgzistan University Press, Hanif and A. Ninth Marcel Grossmann, eds.
Jantzen and R. Ruffini, World Scientific, Singapore, , pp Rahvar, N. Sadooghi and F. Shojai, World Scientific , F. De Paolis, G. Ingrosso, A.