AM-seminars

APPLIED MATHEMATICS SEMINAR
(contact: Arian NOVRUZI)

I have organized AM seminars during 2003-2006. For an updated list of seminars follow departmental seminars link

List of seminars 2005-2006, 200 4-2005, 2003-2004, 2002-2003, 2001-2002

2006

2005

List of seminars 2005-2006
May 4, 2005, 15:00, B015, Math. Dep.
Traian Iliescu, Department of Mathematics at Virginia Tech
Title: A Bounded Artificial Viscosity Large Eddy Simulation Model
Abstract:
In this talk, we present a rigorous numerical analysis for a bounded artificial viscosity model for the numerical simulation of turbulent flows. In practice, the commonly used Smagorinsky model is overly dissipative, and yields unphysical results. To date, several methods for ``clipping'' the Smagorinsky viscosity have proved useful in improving the physical characteristics of the simulated flow. However, such heuristic strategies rely strongly upon a priori knowledge of the flow regime. The bounded artificial viscosity model relies on a highly nonlinear, but monotone and smooth, semilinear elliptic form for the artificial viscosity. For such a bounded model, we have introduced a variational computational strategy, provided finite element error convergence estimates, and included several computational examples indicating its improvement over the overly diffusive Smagorinsky model. The presentation will be at a general level. Graduate students are strongly encouraged to attend.

Apr. 11, 2006, 15:00, B015, Math Dept. (cancelled)
Michel Delfour, FRSC Centre de recherches mathématiques et Département de mathématiques et de statistique Université de Montréal
Title:Simulation and Design of Coated Stents in Interventional Cardiology
Abstract: Stents are used in interventional cardiology to keep a diseased vessel open. New stents are coated with a medicinal agent to prevent early reclosure due to the proliferation of smooth muscle cells. It is recognized that it is the dose of the agent that effectively controls the cells in the wall of the vessel. This talk will focus on the effect of the number of struts and the ratio between the coated area of the struts and the targeted zone of the vessel on the design problem under set therapeutic bounds on the dose. It introduces mathematical models of the dose for a family of zero-thickness periodic stents and their associated asymptotic stent that are playing a central role in our analysis. Theoretical and numerical results are presented along with their impact on the design process.

Feb. 23, 2006, 14:00, B015 Math. Dept.
Thomas Hillen, University of Alberta
Title: Mathematical Models for Cell Movement in Fibre Tissues
Abstract : Mesenchymal motion is a form of cellular movement that occurs in three-dimensions through tissues formed from fibre networks, for example the invasion of tumor metastases through collagen networks. The movement of cells is guided by the directionality of the network and in addition, the network is degraded by proteases.
I derive mathematical models for mesenchymal motion in a timely varying network tissue. The models are based on transport equations and their drift-diffusion limits. It turns out that the mean drift velocity is given by the mean orientation of the tissue and the diffusion tensor is given by the variance-covariance matrix of the tissue orientations. I will discuss relations to existing models and future applications.

Feb. 14, 2006, B015, Math. Dept
Sara Deriviere, University of Sherbrooke
Title: Dynamical systems : from localisation toward existence of chaotic attractors
Abstract: Many systems of first order differential equations have the property to be extremely sensitive to the initial conditions and reveal a chaotic behavior. The study of such systems is often delicate and there never exists analytical solutions of chaotic attractors. Their study is thus limited. In this talk, we will discuss a method based on an extension of the LaSalle invariance principle allowing to locate (chaotics) attractors. To do this, one determines a bounded region of the phase space necessarily containing the attractor. Then, we will develop the first steps towards the rigorous proof of the chaotic behavior of the dynamic systems by using concepts of algebraic topology, computation of homology and the Conley theory.

Feb. 07, 2006, B015, Math. Dept.
Mads Kaern, Canada Research Chair in Systems Biology

Ottawa Institute of Systems Biology

Department of Cellular and Molecular Medicine

Department of Physics

University of Ottawa

Title:Mathematical Challenges in Systems Biology
Abstract: Systems biology is an emergent scientific approach that seeks to address multifaceted biological and medical problems by integrating mathematical and computational methodologies with molecular and cellular biology. In this talk, I will highlight different areas of my research program that has benefited from applied mathematics as well as areas where additional input is needed.

Jan. 31, 2006, B015, Math. Dept.
Tore Ftatten, University of Oslo
Title: Wave characteristics of unsteady 1-dimensional two-phase flow models
Abstract: Large-scale industrial simulations of two-phase pipe flow problems requires simplified models, typically obtained by averaging in space. Models thus obtained may be represented as systems of hyperbolic partial differential equations. In this talk, we will focus on three such models, constituting a hierarchy in terms of mathematical simplification. In particular, we will study the various wave phenomena inherent in the various models. By this, we aim to shed light on the physical relevance of the various simplifications, as well as the difficulties of obtaining a complete description of two-phase flow dynamics within a unified framework.

Jan. 24, 2006, B015, Math. Dept.
Patrick Boily, University of Ottawa
Title: Spiral Wave Dynamics Under Full Euclidean Symmetry-Breaking
Abstract: The spiral is one of Nature's more ubiquitous shape: it can be seen in various media, from galactic geometry to cardiac tissue. In the literature, very specific models are used to explain some of the observed incarnations of these dynamic entities. Barkley first noticed that the range of possible spiral behaviour is caused by the Euclidean symmetry that these models possess. In experiments however, the physical domain is never perfectly Euclidean. The heart, for instance, is finite, anisotropic and littered with inhomogeneities. To capture this loss of symmetry and as a result model the physical situation with a higher degree of accuracy, LeBlanc and Wulff introduced forced Euclidean symmetry-breaking (FESB) in the analysis, via two basic types of perturbations: translational symmetry-breaking (TSB) and rotational symmetry-breaking terms. They show that phenomena such as anchoring and quasi-periodic meandering can be explained by combining Barkley's insight with FESB. In this talk, we provide a characterization of spiral anchoring by studying the effects of full FESB, combining RSB terms with simultaneous TSB terms.

Dec. 14, 2005
Youssef Belhamadia, University of Calgari
Titre: Adaptation de maillage pour des applications biomdicales

Nov. 16, 2005
Frithjof Lutscher, UofOttawa
Title Life in the flow: Persistence, Invasions and Competition in Rivers
Abstract
The question how populations in rivers can persist despite flow-induced washout, has been termed the "drift paradox". More generally, systems with unidirectional flow include rivers, plug-flow reactors, prevailing wind directions, and climate-change models. A first simple model in the form of a reaction-advection-diffusion equation explored persistence criteria by looking at the minimal domain size (Speirs and Gurney (2001), Ecology). Starting from this simple model, I will report on several extensions, namely: vertical structure in the population (drift and benthic state), spatial heterogeneity and the influence on channel geometry, effects of resource gradients, and competition of two species. I will focus on the minimal domain size, on speeds of upstream invasions, and on spatially mediated coexistence.

Nov. 02, 2005
Xianguo Li, Uof Waterloo

Title: A Consistent, Systematic and Comprehensive Analysis of PEMFC Cells and Stacks

Abstract
Polymer electrolyte membrane (PEM) fuel cell has increasingly become the potential choice of zero-emission power source for portable, mobile and stationary co-generation applications. However, technical barriers need to be overcome before its widespread commercialization; cost reduction and performance improvement including reliability are the two key areas, that can be realized through better cell/stack design and improved understanding of the transport processes occurring inside the individual cells and stacks. In this presentation, we will provide an overview of various cell/stack models that are available in the literature, their strength and weakness, and then present a comprehensive multi-species, multi-phase and multi-dimensional formulation of a single PEM fuel cell, with consistent and systematic formulation for all the regions involved, including the solid bipolar plates, gas flow channels, the electrode backing layers, the catalyst layers and the electrolyte membrane. Such a detailed approach allows us to extract sufficient information to the analysis of a stack of PEM fuel cells. Stack model will be presented that investigates the various stack designs and flow configurations, and the optimal stack design based on the present study will be described. Also some innovative cell/stack designs will be featured.

Oct., 16, 2005
Charles Pierre, Uof Nantes
Title: The direct problem in electrocardioloy, modeling of the fully coupled heart+torso system : toward the simulation of the electrocardiogram.
Abstract:
The purpose of that talk will be to present some ideas, numerical technics and simulations in the field of the bio mathematics; precisely the description of the electrical activity generated by the (human) heart. In a first time we shall introduce a model for that electrical activity which is consistent with physiological facts and well adapted for the reconstruction of electrocardiograms (ECGs). A finite volume technic for the resolution of that model will be detailed and numerical simulatioms for the electrical activity of the heart and ECG's reconstitutions im 2D and 3D will be discussed, both for normal and pathological behaviours of the heart.

Oct. 12, 2005
Paul Arminjon, Uof Montreal
Title Finite volume methods for hyperbolic systems . Applications to Aerodynamics and Magnetohydrodynamics
Abstract
We present three-dimensional central finite volume methods for solving systems of hyperbolic equations. Based on the Lax-Friedrichs and Nessyahu-Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve an original and a staggered grid in order to avoid the resolution of the Riemann problems at the cell interfaces. The cells of the original grid are Cartesian (cubes with faces parallel to the axes) while those of the staggered grid are either Cartesian or diamond-shaped. We apply these methods and solve some ideal magnetohydrodynamics problems. To satisfy the solenoidal property of the magnetic field in the numerical solution, we present an adaptation of Evans and Hawley¡Çs constrained transport method for central schemes which we call ¡ÈCTCS¡É. The CTCS method is easy to implement, it deals directly with the computed solution and does not require any additional staggering for the magnetic field components; furthermore, it preserves the second-order accuracy of the base scheme. Even without the application of the CTCS procedure, our numerical base schemes do not break down, and may even in some cases deliver reasonable results. The diamond dual cell scheme has a slight advantage for shocks and contact discontinuities. Our numerical results are in good agreement with corresponding results appearing in the recent literature.

Sep. 29, 2005
Arian Novruzi, University of Ottawa, KED B015, 15:00
Title Some problems and mathematical results related to hydrogen fuel cells dynamics
Abstract:
Hydrogen fuel cells are devices that produce electrical current by a chemical reaction. The electrical current is produced on the
membrane and its uniform distribution increases the life of fuel cell. We consider a dry model of fluid dynamics in a free air domain
(channel) coupled with a porous domain (gas diffusive layer).
The model consits of a system of nonlinear PDEs including Stokes equations, Dacry, mass and heat conservation laws. For this PDEs system
we prove an existence and regularity results, and different estimations. Moreover, we prove that there exists an optimal (channel)
shape minimizing a (membrane) cost functional which measures the membrane current oscillation.

Sep. 15, 2005
Victor LeBlanc, University of Ottawa, KED B015, 11:00
Title Toroidal normal forms for delay-differential equations
Abstract We will present some recent results on the realisability and restrictions of normal forms for parametrized scalar delay-differential equations undergoing either non-resonant multiple Hopf bifurcation, or steady-state/non-resonant multiple Hopf interaction. Our results fully exploit the toroidal equivariance of the normal forms for these bifurcations. This allows for the development of a framework in which generic cases, degenerate cases, and unfoldings can be treated systematically.

List of seminars (2004-2005)
2005

2004

Rebecca Tyson
The codling moth is a major pest for apple and pear growers worldwide. Until recently, the standard method of control involved extensive use of chemical sprays. Now a Sterile Insect Technique (SIT) has been developed which provides orchardists with a viable alternative to pesticides. The programme is expensive however, and so it is important to understand exactly how the sterile and wild insects disperse in heterogeneous landscapes, in order to make the SIT as effective as possible. I will present a diffusion-based model for codling moth dispersal, along with field data being gathered in the Okanagan Valley. Our main goal is to understand the effect of heterogeneous landscapes on codling moth dispersal behaviour.

Katarina Jegdic, University of Huston, 14:30, B015
Title: Convergence of a spacetime discontinuous Galerkin method for systems of conservation laws.
Abstract:
We consider a spacetime discontinuous Galerkin (SDG) method for one-dimensional systems of conservation laws. The method is based on spacetime partitions of the spacetime domain and the Galerkin basis consists of piecewise polynomials. The values of approximate functions across element boundaries are coupled through the Godunov flux. We present mathematical study of the SDG method under assumptions that the spacetime partitions satisfy a causality constraint and that the Galerkin basis is piecewise constant. In the case of strictly hyperbolic and genuinely nonlinear systems we prove that given a causal spacetime mesh, if a SDG approximation exists, then it must satisfy certain discrete entropy inequalities. Convergence of the SDG approximations to a weak solution is shown for genuinely nonlinear Temple class systems (such as equations of multicomponent chromatography). Our computational results will be presented for two systems of conservation laws with singular and transitional shock solutions

Robert Owens, Universite de Montreal
Title: A Fokker-Planck-based numerical method for modelling non-homogeneous flows of dilute polymeric solutions
Abstract:
An original mixed finite-difference/spectral method based upon a Fokker-Planck equation is proposed for the numerical simulation of non-homogeneous flows of suspensions of finitely extensible nonlinear elastic (FENE) dumbbells. Since the configuration distribution function $\psi$ for the dumbbells varies as a function of time and in both physical and configuration space careful attention has been paid to the discretization scheme for derivatives of $\psi$ in these variables, the domains of definition of the physical and configuration coordinates being inter-dependent. Numerical results for start-up planar Poiseuille flow are in excellent quantitative agreement with those of a stochastic simulation and, for comparable levels of accuracy, are much less CPU expensive. Theoretical results for the polymeric stress fields under equilibrium conditions are verified numerically and generalize earlier results for Hookean dumbbells by Brunn and Grisafi [P. O. Brunn and S. Grisafi, Chem. Eng. Commun., 36 (1985) 367-383]. Some interesting parallels with micro-channel blood flow will be highlighted.

Dhavide Aruliah, UOIT
Title: An analysis of partitioned systems of nonlinear equations
Abstract:
Preconditioning techniques for Krylov subspace iterations have become a major focus of research in scientific computing. This trend has been driven largely by the growth in computing power and the development of iterative methods for solving linear and nonlinear systems of equations over the last fifteen years. For nonlinear systems of equations, effective preconditioning is essential for inner iterations of inexact Newton-Krylov methods. In practice, however, preconditioners are largely application-dependent. Specific heuristics are hard to find and deeper theoretical analyses tend to apply under fairly restrictive physical or geometric properties of the problem at hand. For instance, fast Poisson solvers, domain decomposition techniques, and multigrid methods are used with great success to precondition linear systems that arise from the discretisation of elliptic partial differential equations. I will present some recent work looking at preconditioning for a fairly general family of partitioned systems of nonlinear equations that seems to occur in numerous applications (e.g., discretisation of partial differential equations). In such systems, various analytic problem formulations exist based on a natural partitioning of the unknowns or introduction of auxiliary unknowns. The existence of distinct analytic formulations prompts the question of which analytic system should be solved. While the problems are mathematically equivalent, once fed into appropriate variants of Newton's method (e.g., quasi-Newton methods, inexact Newton methods), distinct discrete dynamical systems result. I will present some examples of such systems and some suggestions of how to choose between alternative equivalent formulations of nonlinear systems of equations that arise in practical applications. While some familiarity with iterative methods and issues in modern scientific computing will be helpful, my presentation is suitable for a general mathematics audience. Graduate students are encouraged to attend

Peter Berg , UOIT
Title: Spatio-temporal patterns in traffic flow

Jose Manuel Urquiza, Univrsity of Montreal
Title: Transport of macromolecules through the arterial wall: Some mathematical and numerical issues.
Abstract:
After an introduction to the pathologies of unhealthy arteries we briefly describe the mechanisms involved in atherosclerosis and we describe the architectural composition of artery walls. Then we present the most basic and popular equations in the modelling of macromolecular transport through the arterial wall. Finally we discuss some issues about the modelling equations and their mathematical analysis as well as about the numerical treatment of the partial differential equations that govern the transport mechanisms

Bartosz Protas, Department of Mathematics and Statistics, McMaster University,
Title:TOWARDS A MULTI-SCALE FRAMEWORK FOR COMPUTATIONAL FLOW CONTROL AND ESTIMATION
Abstract:
In this talk we will discuss a range of issues related to numerical solution of optimal control and estimation problems for systems governed by the Navier-Stokes equation. The physical objective that a control or estimation strategy seeks to achieve is represented by a suitably selected cost functional which is minimized with respect to the control variable. We will first derive an optimality system and show how an optimal solution can be found in computations using a gradient-based approach. The sensitivity of the cost functional to control (i.e. the gradient) can be conveniently expressed using an adjoint field. This method is applied to the problem of wake control for drag reduction in the laminar regime. In the numerical simulations, the Navier-Stokes system and the adjoint system are both solved using a Vortex Method which is briefly outlined and benchmarked. Application of this control strategy to multi-scale systems, such as high Reynolds number turbulence, requires some form of regularization. It may be introduced into an optimization problem by modifying the form of the evolution equation and the forms of the norms, duality pairings, and inner products used to frame the adjoint analysis. Typically, L_2 brackets are used in the definition of the cost functional, the adjoint operator, and the cost functional gradient. If instead we adopt the more general Sobolev brackets, the various fields involved in the adjoint analysis may be made smoother and therefore easier to resolve numerically. We will identify several relationships which illustrate how the different regularization options fit together to form a general framework. Many commonly-used strategies for regularization, including implicit Tikhonov regularization and ad hoc smoothing of the gradient with the inverse Laplacian, are shown to fit into the present framework as special cases. The regularization strategies proposed are exemplified using control and estimation problems for the Kuramoto-Sivashinsky equation and the Navier-Stokes equation in various configurations. Computational examples will be provided to exhibit utility of the presented strategies. Future directions will also be discussed.

List of seminars (2003-2004)

Sue Ann Campbell, University of Waterloo
April 2, 14:00, B004, DMS

Ramon J. Cova
March 5, 14:00, B004, DMS
Title: Harmonic Maps and topological solitions

Kokou Dossou, University of Laval
February 6, 14:00, B004, DMS0

Title: Finite Element Modeling of Electromagnetic Wave Propogations in Periodic Dielectric Structures

Daniel LeRoux, University of Laval
January 30, 14:00, B004, DMS
Title: Numerical models in shallow-water systems: the P1 NC - P1 element

January 16, 14:00, B004, DMS
Remi Vaillancourt, University of Ottawa
Title:Detecting Singularities with Continuous Wavelet Transforms

November 28, 14:15, B004, DMS
Yves Coudiere, University of Nantes
Title: Analyse numerique et calcul 3D pour un modele de propagation du potentiel d'action dans le myocarde.

November 19, 14:30, B004, DMS
Pierre-Emmanual Jabin, ENS, France
Title:Kinetic Equations: a short presentation

November 14, 14:15, B004, DMS
Brian Ingalls, University of Waterloo
Title: Sensitivity of Biochemical Networks: a Control Theoretic Approach

November 7, 14:15, B004, DMS
Andre Garon, Ecole Polytechnique de Montreal
Title: CFD design and optimisation of heart pumps

October 24, 14:15, B004, DMS
Lucy Cambell, Carleton University
Title: Gravity waves in the atmosphere and their representation in large-scale models

October 17, 14:15, B004, DMS
Mary Pugh, University of Toronto
Title: Blowing-up exact solutions of long-wave unstable thin film equations

October 3, 3:30, B005, DMS
Gerard Philippin, University of Laval
Title: Applications of the maximum principle to a variety of problems involving elliptic and parabolic equations

September 26, 14:15, B004, DMS
Huaxiong Huang, York University
Title: A Perturbation Model for the Growth of ZnS Crystals

September 19, 14:15, B004, DMS
Anne Bourlioux, University of Montreal
Title:Effective Hamiltonians for large scale simulations of premixed turbulent flames

September 12, 14:15, B004, DMS
Arian Novruzi, University of Ottawa
Title: Shape optimization of free air-porous domain transmission coefficient

List of seminars (2002-2003)

May 9, 14:00, B004, DMS
Brian Wetton, University of British Columbia
Title: A simple but comprehensive proton exchange membrane unit cell model.

May 2, 14:00, B004, DMS
A. Tamassan, University of Toronto
Title: An inverse boundary problem in transport theory

April 25, 14:00, B004, DMS
Ph. Sharp, University of Auckland, NZ
Title: Close approaches in N-body simulations of the Solar Systems

April 11, 14:00, B004, DMS A. Hajji, DMS, University of Ottawa Title: An introduction to wavelets and their applications.

April 4, 14:00, B004, DMS
David Amundsen, DM, University of Carleton
Title: Efficient Simulation of Optical Fibre Communication

March 28, 13:30, B004, DMS
Yves Bourgault
Title: Simulation of electropysiological waves

March 21st, 15:30, B006, DMS
Michel Delfour, CRM and DMS, Univesity of Montreal
Title: Shapes and geometries; retrospective, applications and perspectives

March 14, 13:30, B004, DMS
Eric Matsui, UofO
Title: On some numerical results on spiral waves and their applications

March 7, 13:30, B004, DMS
Victor LeBlanc, DMS, UofO
Title: Versal unfoldings for linear retarded functionals differential equations

List of seminars (2001-2002)

Laurent Cohen,Directeur de Recherche au CNRS CEREMADE, Universite Paris IX Dauphine
www.ceremade.dauphine.fr/~cohen
August 1, 2002
Title: Minimal Paths and Deformable Models in Image Analysis
Abstract: We present an overview of our work on minimal paths. Introduced first as a way to find the minimal energy of active contours and based on Fast Marching, we have used them afterwards for multiple contour finding in order to make contour completion in 2D and 3D images. Many variations allow improving time computation, simplifying initialization, or centering the path in a tubular structure. Fast Marching is also an efficient way to solve evolution of the balloon model through level sets. We show applications, mainly for medical images, in particular for vascular segmentation and Virtual Endoscopy.

Marc Thiriet, INRIA, France
Tuesday, 13 November, 2001
Title: Numerical simulations of bio-fluid flows as pedagogical models or as element of medical tools

Marcus Pivato
March 30, 2001
Title: Limit Measures for Affine Cellular Automata

Zhu Huaiping, Department of Mathematics & Statistics, McMaster University
Tuesday, 13 March, 2001
Title: A predator-prey model and seasonal perturbation

Pietro-Luciano Buono, CRM, Universite de Montreal
Jeudi, 8 mars, 2001
Title: Bifurcations d'equilibres dans les systemes dynamiques avec equivariance et reversibilite du temps

Alain Charbonneau, UQAH
Jeudi, 22 fevrier, 2001
Title: Analyse vectorielle des modes propres d'un guide d'ondes optiques par une m?thode adaptative d'elements finis

Aziz Madrane
Thursday, 7 December, 2000
Title: Finite element-finite volume method for conservation laws

Steve Desjardins
Thursday, 16 November, 2000
Title: Introduction to Image Processing