# Applied Mathematics and Mathematical Physics Seminar 2009/2010 (sponsored by MITACS and PIMS)

This is the web page for the Applied Mathematics and Mathematical Physics Seminar at the Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Canada. This seminar is organized and jointly run by J. Brooke, G. Patrick, J. Szmigielski (Applied Mathematics/ Mathematical Physics) and R. Spiteri (Department of Computer Science).

For inquiries concerning the seminar send email to Jacek Szmigielski, szmigiel@math.usask.ca.

The seminar takes place in McLean Hall rm 242.1 on Thursdays at 2:00 till 3:00 unless advertised differently.

Next meetings:

### September 18, 2008

Chih-Che Chueh, PhD student Department of Mechanical Engineering Institute for Integrated Energy Systems University of Victoria, Victoria BC, Canada

Place: Thorv 105

Time: 2:00-3:00 pm

Computational Modeling and Optimization of Proton Exchange Membrane Fuel Cells

#### Abstract

Fuel cells offer the possibility of a low-emission power source for automotive, stationary, and portable applications but face a number of technical challenges that must be surmounted in order to compete against internal combustion and batteries. One type of the fuel cell devices is called proton exchange membrane fuel cell (PEMFC). The success of PEMFC as a comprehensive energy conversion device will depend upon the advances made in the next decade in PEMFC design; therefore, much research in this area is required. PEMFC design is not an easy task because PEMFC performance depends on a large number of coupled physical phenomena such as fluid flow, heat, mass and charge transport, and electrochemistry. How to increase the performance of PEMFC is very important for both engineers and scientists. In this talk, the basic fuel cell operation and PEMFC fuel cell numerical modeling and optimization will be present. And some numerical results for fuel cell modeling as well as two phase flows in porous media will be shown as well.

### September 25, 2008

Rainer Dick, Department of Physics and Engineering Physics

Place: MCLH 242.1

Time: 2:30-3:30 pm

Cosmic rays through the Higgs portal

#### Abstract

Minimal dark matter models are models in which gauge singlets couple to standard matter only indirectly through their coupling to the Higgs particle.One of my current research interests concerns the question whether annihilation of gauge singlets in the galactic dark matter halo yields an observable gamma ray signal.

### October 2, 2008

George Patrick , Department of Mathematics and Statistics

Place: MCLH 242.1

Time: 2:30-3:30 pm

Local error analysis of variational integrators

#### Abstract

Discretizations of variational principles of physical systems are towards discrete models that have a status equivalent to the continuous models. For Hamilton's principle of mechanics, such discretizations lead to a class of numerical methods called variational integrators. Existence and uniqueness, and accuracy, of variational integrators, cannot be correctly established without due consideration of their singularities at zero time-step. We show existence and uniqueness for variational integrators by blowing up the variational principle at zero time-step. This gives an accuracy one less than is observed in simulations, a deficit that is recovered by a past--future symmetry of the blown-up principle.

### October 16, 2008

Ryan Dean, Department of Computer Science

Place: MCLH 242.1

Time: 2:30-3:30 pm

#### Abstract

Numerical methods for simulation of electrical activity in the heart Mathematical models of the electrophysiological properties of the heart can be used to simulate the electrical behaviour of the heart. For simulations in two or three dimensions, both ordinary differential equations (ODEs) and partial differential equations (PDEs) are usually coupled together in the models. A model consisting of ODEs describes the electrical properties of the individual cells, and a model consisting of PDEs describes the flow of electricity across the heart. Typically these equations are solved separately using a technique called operator splitting. This makes the solution process easier, but sophisticated numerical methods are still needed to solve the two models efficiently. In this talk, I will give an overview the models and methods commonly used in practice and then discuss recent work we have done in the area. I will discuss the use of Implicit-Explicit Runge-Kutta methods to solve the ODE models and show they are more efficient than the most commonly used techniques for four popular ODE cell models. I will then discuss the use of a second-order L-Stable SDIRK method to solve the PDE model, comparing it in terms of efficiency and stability to two commonly used methods.

### October 30, 2008

Sergei Panasiuk, Wardrop Engineering Inc., Saskatoon

Place: Physics Bldg 103

Time: 3:30-4:30 pm

Joint Seminar with the College of Engineering

#### Abstract

This presentation discusses in situ leach (ISL) mining which is defined as the extraction of target mineral from underground by chemical solutions and the recovery at the surface. This method is appliablel for all three major minerals of Saskatchewan (potash, uranium and bitumen). ISL methods have a number of critical advantages over traditional open pit and underground shaft mining technologies which tend to generate large volumes of waist and require direct contact of the personnel with dangerous environments. ISL is used in the world primarily for uranium extraction, but so far had very limited applications in Canada. Only potash (KCl) is currently extracted by ISL on a relatively small scale (Belle Plaine near Regina). One of the main reasons is lack of special knowledge that is a combination of nonlinear fluid mechanics, hydrogeology, geochemistry, rock mechanics and nuclear physics (for uranium ISL). It also involves fairly complicated mathematical methods for the description of flows in porous medium, nonlinear diffusion and convention, etc. As a whole, this is a complex interdisciplinary area with a significant amount of advanced scientific knowledge and require an integrated science and technology group of researchers. As such it is deserved to be seriously addressed by an intensive research group such as the University of Saskatchewan. In this talk, specific details for ISL uranium mining will be discussed, however it has much broader application for all mining industry and outside of ISL method. E.g. similar problem occur in the problem of treatment and containment of liquid waist, long tern underground water interactions with planned storage of radioactive materials, and many others.

### October 30, 2008

Sergei Panasiuk, Wardrop Engineering Inc., Saskatoon

Place: Physics Bldg 103

Time: 3:30-4:30 pm

Joint Seminar with the College of Engineering

#### Abstract

This presentation discusses in situ leach (ISL) mining which is defined as the extraction of target mineral from underground by chemical solutions and the recovery at the surface. This method is appliablel for all three major minerals of Saskatchewan (potash, uranium and bitumen). ISL methods have a number of critical advantages over traditional open pit and underground shaft mining technologies which tend to generate large volumes of waist and require direct contact of the personnel with dangerous environments. ISL is used in the world primarily for uranium extraction, but so far had very limited applications in Canada. Only potash (KCl) is currently extracted by ISL on a relatively small scale (Belle Plaine near Regina). One of the main reasons is lack of special knowledge that is a combination of nonlinear fluid mechanics, hydrogeology, geochemistry, rock mechanics and nuclear physics (for uranium ISL). It also involves fairly complicated mathematical methods for the description of flows in porous medium, nonlinear diffusion and convention, etc. As a whole, this is a complex interdisciplinary area with a significant amount of advanced scientific knowledge and require an integrated science and technology group of researchers. As such it is deserved to be seriously addressed by an intensive research group such as the University of Saskatchewan. In this talk, specific details for ISL uranium mining will be discussed, however it has much broader application for all mining industry and outside of ISL method. E.g. similar problem occur in the problem of treatment and containment of liquid waist, long tern underground water interactions with planned storage of radioactive materials, and many others.

### November 6, 2008

Raymond Spiteri

Place: Thorvaldson 105

Time: 2:30

Title: New Computational Approaches for the Simulation of Electrical Activity in Cardiac Tissue Joint Seminar with Department of Computer Science

#### Abstract

The electrocardiogram (ECG) is perhaps the most recognized method for representing the function of heart. Doctors are able to diagnose various pathologies of the heart including heart attacks, arrhythmias, and ventricular hypertrophy simply by studying the ECG patterns of their patients. It is truly amazing that these same ECG patterns can be faithfully reproduced using mathematical models based on fundamental physiological principles.Mathematical models of electric activity in cardiac tissue are often based on ordinary differential equations that describe the ionic currents at the cell level coupled with partial differential equations that describe how the electricity flows at the tissue level. Because the models are so large, the physiological accuracy of tissue-scale models is often limited by the efficiency of the numerical solution process. In this talk, I relate our experiences with numerical methods for the efficient solution of various cardiac electrophysiological models.

### November 13, 2008

Alexei Cheviakov, Department of Mathematics and Statistics

Place: MCLH 242.1

Time: 2:30-3:30 pm

Title: A Two-Dimensional Metastable Flame-Front

#### Abstract

A two-dimensional model for upward flame propagation in a vertical channel (Berestycki et al, 1995) involves a nonlinear evolutionary PDE with a small parameter and a nonlocal term. We use a nonlinear transformation to map this problem into a quasilinear degenerate parabolic PDE problem without nonlocal terms, and show that the latter has an exact localized spike-type equilibrium solution. We study the metastable behavior associated with this model using formal asymptotic analysis. In particular, we demonstrate that in the asymptotic limit, the flame-front interface assumes a roughly paraboloidal shape (which was observed in experiments and numerical simulations), and the flame tip drifts asymptotically exponentially slowly towards the closest point on the wall of the channel. Asymptotic estimates for the exponentially small eigenvalues responsible for this metastable behavior are derived together with an explicit ODE for the slow motion of the tip of the paraboloid. The subsequent motion of the tip along the channel wall is also characterized explicitly. The results are confirmed by direct numerical solution of the full PDE problem. This is a joint work with M.Ward (UBC).

### November 20, 2008

Simone Ludwig, Department of Computer Science

Place: MCLH 242.1

Time: 2:30-3:30 pm

Title: Applications of Evolutionary Optimization Techniques in Grid Computing

#### Abstract

Evolutionary Computing is the umbrella term for a range of problem-solving techniques based on the principles of biological evolution, such as natural selection and genetic inheritance. In this presentation, the application of evolutionary techniques such as Genetic algorithms, Ant Colony and Particle Swarm in the area of Grid Computing are investigated. Two projects have been explored using the above mentioned optimization techniques. The service selection project addresses the assignment of multiple services to users, whereby users are requesting services depending on specific Quality of Service parameters. The Grid job scheduling project addresses the problem of load balancing. Prior work has addressed the problem of load balancing with a centralized approach, however, as this can lead to a single point of failure, distributed load balancing using ant colony and particle swarm approaches have been investigated. This presentation will outline how the optimization techniques are applied to the different areas and deliver the research results obtained.

### January 20, 2009

Samuel Butler, Department of Geological Sciences

Place: THORV 125

Time: 3:00-4:00 pm

Title: Modeling band-forming instabilities in compacting, ductile porous media: applications to melt flow in Earth's mantle

#### Abstract

Oceanic crust is formed from solidified melt that is extracted from Earth's mantle at mid-ocean ridges. Melt forms below ridges in rising convective mantle flows that undergo decompression melting. Melting occurs over roughly 100 km laterally but volcanism almost entirely occurs within 1 km of the ridge axis. Petrological studies also indicate that the magma must be extracted very quickly, indicating that some form of channeling instability must occur to extract the magma quickly and focus it towards the ridge axis. The magma and ductile solid rock can be modeled as two inter-penetrating fluids of very different viscosity. If the viscosity of the matrix decreases with porosity, then an instability occurs that concentrates the low viscosity phase in bands whose orientation is controlled by the stress field. The orientation of the bands is also a function of the stress-dependence of the matrix viscosity and the effects of buoyancy of the melt phase cause oscillations and waves. In this presentation, I will outline the theory of a compacting, ductile porous layer. I will then show a number of numerical solutions where a compacting porous layer is subjected to an externally driven stress and where buoyancy oscillations are present. The numerical solutions will also be compared with some linear theory. I will demonstrate that melt bands form under mantle-like conditions and that magma flow is channelized within these. When buoyancy is significant, however, there may be two orientations of melt bands and only one these is in the correct orientation to channel melt towards a ridge axis.

### February 12, 2009 (cancelled)

Kai Wunderle, Department of Physics and Engineerig Physics

Place: MCHL 242.1

Time: 2:00-3:00 pm

Title: TBA

TBA

### March 19, 2009 (cancelled)

Michael P. Bradley, Department of Physics and Engineerig Physics

Place: MCHL 242.1

Time: 2:30-3:30 pm

Title: Modelling Silicon Photonic Devices: A Tool for Rational Design

#### Abstract

Recent advances in developing light-emitting silicon may open the door to on-chip CMOS-compatible silicon-based lasers. Such devices will allow-on chip optical interconnect with significant higher bandwidth and significantly reduced I2R losses. Rational design of these devices will be heavily dependent on developing accurate models. Such models do not currently exist as silicon was until recently not considered to be a useful material for optoelectronic applications. This talk will discuss some recent developments in this field at the U of S and elsewhere, and will lay out some of the anticipated challenges which can be expected in modelling new silicon-based photonic devices.

### April 2, 2009

Marc Secanell (University of Alberta)

Place: Phys 165

Time: 2:00-3:00 pm

Title: Moving Beyond Trial-and-Error Design: Using Computational Methods to Develop the Energy Systems of the Future

#### Abstract

Energy systems present some of the most exciting research challenges of the 21st century. In order to improve these complex systems, all the disciplines involved in their design (such as fluid mechanics, structures, heat and charge transfer and economics) must be analyzed and optimized simultaneously. Solving such intricate problems remains an elusive and challenging endeavour because these systems are too complex to be designed by trial-and-error approaches. Research on computational design tools to achieve energy systems that are efficient, reliable and minimize environmental impact is required. In this presentation, several design problems are presented that illustrate the benefits of using numerical (computational) optimization for designing complex systems involving several objectives, parameters and disciplines. In particular, numerical optimization is applied to: a) obtain optimal membrane electrode assembly compositions for a polymer electrolyte fuel cell, b) obtain the optimal operating conditions for an integrated fuel cell system and, c) find the optimal shape for a low Reynolds number airfoil in order to minimize drag. Future areas of research in computational analysis and optimization of energy systems will also be discussed.

Dr. Marc Secanell received his Ph.D. in Mechanical Engineering from the University of Victoria in 2007. During his career he has worked in a variety of projects such as the transient analysis of three-phase transformers, aerodynamic shape optimization of low Reynolds number airfoils and analysis and optimization of fuel cells. In 2008, he was a research assistant in the modeling group at the National Research Council Institute for Fuel Cell Innovation. In 2009, he joined the Mechanical Engineering Department at the University of Alberta where is currently setting up a new laboratory on Energy Systems Design. His research interests include: analysis and design of fuel cells, multi-phase/multi-component/reactive transport in porous media, multidisciplinary design optimization, analysis and design of renewable energy systems and energy system integration.

### April 9, 2009

Zhengrong Li, Department of Mathematics and Statistics

Place: MCHL 242.1

Time: 10:00-11:00 pm

Title: A New Clustering Method with Unknown Number of Components

#### Abstract

Cluster analysis is concerned with partitioning cases into > clusters such that the cases in a cluster are similar in terms of a set of variables. K-means is a popular clustering method, which starts with a random partition, and then search a reasonable partition by alternating refining the model parameters given a partition and allocations of cases into groups given the parameters. In K-means, the number of clusters has to be supplied in advance, which may be difficult in practice. A new method, X-means, is proposed to solve this problem, which starts with an initial partition, then recursively runs a local K-means in each cluster to split it until a lower Bayesian Information Criterion (BIC) value is reached compared with the previous larger cluster. However, this method would introduce a more severe local mode problem, that is, the previous inappropriate partition of cases cannot be corrected in the following local splitting. In this work, we develop a new method which is similar to X-means, but each time after splitting a cluster, we run EM algorithm with all the cases to find a tentative partition. By this way, the previous inappropriate partitions still have the chance of being corrected, for example, some clusters may be merged again. We have tested this method with a vehicle data. In this data, for each vehicle data of variables axle spacings and axle weights can be gathered easily by some sensor. People are interested in clustering the > vehicles according to these data. Using t-distribution modelling each variable in each cluster, we obtained good results of clustering, which corresponds to types of vehicles such as cars, minivans, and trucks.

### April 16, 2009

Andrew Kroshko, Numerical Simulation Lab, Dept of Computer Science, UofS

Place: MCHL 242.1

Time: 2:30-3:30 pm

Title: Numerical Simulation and Optimization of CH4+CO2 Chemistry Over Palladium

#### Abstract

The chemistry of methane (CH4) and carbon dioxide(CO2) over a palladium catalyst is important to the process of the sequestering the CO2 emitted when fossil fuels are burnt. We derive the Arrhenius rate constants for the surface reactions involving this system when it is simulated using a plug flow reactor. We perform a numerical optimization to find the partial pressures and temperature which produce the maximum amount of desirable products. The method used for optimization is the evolutionary algorithm, particle swarm optimization. We look at the stability properties as well as some experimental results from applying this algorithm.

### April 27, 2009

Jean-Francois Ganghoffer (LEMTA ENSEM, Nancy, France)

Place: MCHL 242.1

Time: 2:00-3:00 pm

Title: Mechanical behaviour of an adhering cell with consideration of damping

#### Abstract

The purpose of this contribution is the description of the rolling of a single cell by a stochastic approach of the cell-extracellular wall interface behaviour, in both cases of an elastic and a viscous interface.Cell rolling corresponds to the slowing down of the cell during its motion (along the wall of an extracellular matrix, e.g. an artery) followed by the capture of the cell. These stages are greatly influenced by the molecular rupture and adhesion kinetics, occurring at the interface between the cell and the wall of the ECM. Those kinetics correspond to the succession of creation and rupture of molecular bonds, under the effects of mechanical and chemical external actions. The molecular connections (ligand receptor pairs) are modelled as elastic springs in association with a viscous analogical element.A three-dimensional model of these interfacial kinetic events is developed in the present contribution, as an extension of a 2D model, considering an elastic behaviour of the connections (Mefti et al. Int. J. Solids Struc., 2006). This model describes the behaviour of the cell-wall interface in terms of the time evolution of the creation of new molecular connections and the rupture of the existing connections, under the combined effects of the fluid pressure and physical interactions (Van der Waals forces, electrostatic repulsion). From a mechanical point of view, we assume that the cell-wall interface is composed of two elastic shells, namely the wall and the cell membrane, linked by rheological viscous elements, which represent the molecular connections. Both the time and space fluctuations of several parameters (amongst of them the rupture threshold of the bonds) are described by the stochastic field theory. Numerical simulations emphasize the rolling phenomenon, in terms of the time evolution of the number of molecular connections - broken or created - and of the rolling angle. The influence of the mechanical damping of the connections on the behaviour of the contact interface is further highlighted. Finally, the motion of the cell (modelled as an elastic shell) is analysed, considering a modification of the cell membrane due to internal forces modelled as a stochastic field in the context of stochastic finite element methods.

#### References

Mechanical modeling of the rolling phenomenon at the cell scale. N. Mefti, B. Haussy, J.-F. Ganghoffer. Int. J. Solids and Struct. 43, Issue 24, 2006, 7378-7392.

Modelling of the behaviour of cell-wall interface during the rolling of a single cell: a probabilistic approach. N. Mefti, J.F. Ganghoffer, B. Haussy. Comptes Rendus Acadmie des Sciences, Paris. 334, Issue 4, 2006, 230-237.

Probabilistic mechanisms of adhesive contact formation and interfacial processes. J.F. Ganghoffer, B. Haussy. Arch. Appl. Mech., 75, 2006, 338-354. Influence of the mechanical damping on the rolling of a single biological cell: A stochastic approach. N. Mefti, B. Haussy, J.F. Ganghoffer. Journal de Physique IV, 134, Issue 1, 2006, 453-460.

A 3D modelling of the protrusion and retraction of a single cell during the motility and the rolling. N. Mefti, B. Haussy, J.F. Ganghoffer. J. Phys. IV, 134, 2006, 449-452.

### May 1, 2009

Professor Daryl Geller, Mathematics Department State University of New York at Stony Brook

Place: MCHL 242.1

Time: 10:30-11:30 pm

Title: Spin Wavelets on the Sphere for CMB Polarization Data Analysis

#### Abstract

The cosmic background radiation (CMB), which was emitted only 400,000 years after the Big Bang, has attracted an enormous amount of attention. Physics was very simple then, so an analysis of the data can be used, to confirm or eliminate various physical theories which have been proposed concerning the universe, and to estimate numerous physical parameters, such as the amount of dark matter in the universe. In order to do this, however, one must have a way of extracting statistically valid estimators from the data. Since CMB cannot be observed in a large portion of the sky, owing to interference from the Milky Way, it is not possible to use spherical harmonic coefficients as such estimators. Spherical wavelet coefficients can be used effectively instead. Because wavelets are well-localized, one can to a great extent avoid the unobserved region. CMB has both temperature and polarization. Almost all work to date has been on temperature, for which precise data is available. We study polarization, for which precise data should be available soon. Polarization data is not an ordinary function on the sphere, but rather a (random) section of a line bundle. Starting with the spin spherical harmonics of Newman and Penrose, we construct spin wavelets on the sphere, which are appropriate for analyzing sections of this line bundle. We show that spin wavelet coefficients have the required statistical properties, under reasonable assumptions. (The needlets of Narcowich, Petrushev and Ward were earlier used by Baldi, Kerkyacharian, Marinucci and Picard for similar purposes, in studying CMB temperature.) One hopes to use CMB polarization to provide the first direct evidence of gravitational waves.

### August 21, 2009

Tyler Helmuth, Department of Mathematics, University of British Columbia

Place: MCHL 242.1

Time: 10:00-11:30 am

Title: Newman's Central Limit Theorem

#### Abstract

In this talk I'll describe the basic setup for many models in mathematical statistical mechanics. After introducing the idea of scaling limits, which describe the limiting behaviour of discrete models, I will present Newman's central limit theorem. This theorem describes the scaling limit of so-called FKG systems which are non-critical; these terms will be defined. Colloquially, the theorem describes the behaviour of the average spins of small regions of magnetic material, provided the system is not undergoing a phase change.

### September 21, 2009

Peter Miller, Department of Mathematics, University of Michigan, Ann Arbor, USA

Place: ARTS 217

Time: 3:30

Title: The Benjamin-Ono Equation in the Small Dispersion Limit

#### Abstract

The Benjamin-Ono equation is a model for several physical phenomena, including gravity-driven internal waves in certain density-stratified fluids. It has the features of being a nonlocal equation (the dispersion term involves the Hilbert transform of the disturbance profile) and also of having a Lax pair and an associated inverse-scattering algorithm for the solution of the Cauchy initial-value problem. We will review known phenomena associated with this equation in the limit when the dispersive effects are nominally small, and compare with the better-known Korteweg-de Vries equation. Then we will present a new result (joint with Zhengjie Xu) establishing the zero-dispersion limit of the solution of the Benjamin-Ono Cauchy problem for certain initial data, in the topology of weak convergence. The proof relies on aspects of the method of moments from probability theory.

About the Speaker: Prof. Miller works generally in the area of applied analysis, with specific interests in integrable systems, nonlinear waves, and random matrix theory. Asymptotic methods play a central role in his work. He is currently serving as the Director of the graduate program in Applied and Interdisciplinary Mathematics. For more info check: Peter Miller

### October 5, 2009

Ron Steer, Department of Chemistry, University of Saskatchewan

Place: MCLH 242.1

Time: 2:45

Title: FAST UPPER SINGLET STATE RELAXATION IN METALLOPORPHYRINS: IMPLICATIONS FOR NIR SOLAR ENERGY HARVESTING

#### Abstract

Research on the photophysics and spectroscopy of the highly excited valence electronic states of polyatomic molecules (thiones, nonalternant aromatic hydrocarbons, tetrapyrroles) carried out at the University of Saskatchewan over the past 30 years has found recent application in understanding and controlling solar photon upconversion processes. The predictive structure – photophysical property relationships developed - using ultrafast laser techniques - for the upper excited singlet states of d0 and d10 metalloporphyrins will be described. These relationships, together with recent experiments on the mechanism of excited state annihilation (the key step in photon upconversion), will be used to assess the viability of using non-coherent near-infrared photon upconversion as a means of improving the efficiency of dye-sensitized solar photovoltaic cells.

### November 16, 2009

Masoud Ghezelbash, Department of Physics and Engineering Physics, UofS

Place: MCLH 242.1

Time: 3:30

Title: Self-Dual Geometries in M-theory

#### Abstract

We present new M2 and M5 brane solutions in M-theory based on transverse self-dual geometries. All the recently known M2 and M5 branes, constructed on transverse self-dual Taub-NUT, Egughi-Hanson and Atiyah-Hitchin spaces are special cases of this solution. The solution provides a smooth transition from Eguchi-Hanson type I based M branes to corresponding branes based on Eguchi-Hanson type II space. All the solutions preserve some supersymmetries and can be reduced down to ten dimensional fully localized intersecting brane configurations in type IIA supergravity.

### November 23, 2009

Masoud Ghezelbash, Department of Physics and Engineering Physics, UofS

Place: MCLH 242.1

Time: 3:00

Title: Self-Dual Geometries in M-theory (Part II)

#### Abstract

We present new M2 and M5 brane solutions in M-theory based on transverse self-dual geometries. All the recently known M2 and M5 branes, constructed on transverse self-dual Taub-NUT, Egughi-Hanson and Atiyah-Hitchin spaces are special cases of this solution. The solution provides a smooth transition from Eguchi-Hanson type I based M branes to corresponding branes based on Eguchi-Hanson type II space. All the solutions preserve some supersymmetries and can be reduced down to ten dimensional fully localized intersecting brane configurations in type IIA supergravity.

### November 30, 2009

Jason J. Boisvert, Department of Computer Science (joint work with Paul H. Muir and Raymond J. Spiteri)

Place: MCLH 242.1

Time: 2:30

Title: Methods for Global Error Estimation in Defect-Control BVODE Codes

#### Abstract

Some of the most popular boundary value ordinary differential equa- tions (BVODEs) codes ensure that the defect, i.e., the amount by which the continuous numerical solution fails to satisfy the BVODE, is less than a user-specified tolerance. Examples include bvp4c, bvp5c written in MATLAB and MIRKDC, BVP SOLVER written in Fortran. Other BVODE codes ensure that the global error, i.e., the amount by which the numerical and ex- act solution differ, fails to satisfy a user-specified tolerance. COLSYS is an example of one such code. Because users are usually more familiar with the concept of global error, it is useful for defect-control BVODE codes to offer an a posteriori global error estimate. At present, BVP SOLVER is the only defect-control code known to do this. The code uses Richardson extrapolation to estimate the global error. In this presentation, I explore three additional methods to estimate global error within BVP SOLVER, namely the use of higher-order discretiza- tion formulas, deferred correction, and a BVODE conditioning constant. All methods are compared through several numerical experiments. In the end, higher-order and deferred-correction methods are shown to perform better than Richardson extrapolation. The use of a conditioning constant is shown to be faster than the other three methods but suffers in terms of accuracy. The implication of these results on BVODE codes is that they should use higher-order or deferred-correction methods rather than Richardson extrapolation to estimate global error.

### January 11, 2010

Alexander Moewes, Department of Physics and Engineering Physics, UofS (joint work with T.D. Boyko and J.A. McLeod)

Place: MCLH 242.1

Time: 3:30

Title: Understanding Bandgap and Electronic Structure of crystalline materials

#### Abstract

The bandgap or energy gap in a solid is the energy difference between the top of the valence band the bottom of the conduction band. The bandgap and the promotion of electrons across it, is exploited in the design of most modern electronic devices such as transistors, laser and photo diodes and solar cells. Key electronic parameters like conductivity and key mechanical parameters like hardness strongly depend on the bandgap, which is one of the reasons why tailoring the bandgap of materials is an important field in materials science. We will discuss various methods to determine the bandgap. We use synchrotron-based soft X-ray spectroscopy to measure the bandgap. In the excitation process a photon is absorbed leaving the atom in an excited state with a core hole. The presence of the core hole alters the occupancy of the bands and therefore needs to be accounted for. It will be discussed how to account for the core and a number of systems are studied: (1) Solid solutions of silicon nitride (γ-Si3N4) and germanium nitride (γ-Ge3N4): γ-[Si1-x, Gex]3N4, (for 0 ≤ x ≤ 1). The bandgap of these materials changes non-linearly with concentration x. The experimentally determined bandgaps agree quite well with the trends of our calculations. (2) The luminescence material Ba3Si6O12N2: Eu. (3) A series of alkaline metal, transition metal and post transition metal oxides. We conclude that soft X-ray spectroscopy with synchrotron radiation and Density functional theory calculations provide a reliable way to determine the bandgap of solid-state materials.

### March 16, 2010 (joint with the Analysis Seminar)

Ion Nechita, University of Ottawa and Universite de Lyon

Place: MCLH 242.2

Time: 2:30

Title: Random matrix techniques in quantum information theory

#### Abstract

I will discuss some recent results about random constructions related to quantum information. My focus will be on the additivity conjecture for the capacity of quantum channels, and how random matrix results were used to construct counterexamples. Various techniques will be outlined, such as the moment method, unitary integration, concentration of measure and free probability. This is joint work with Benoit Collins and Serban Belinschi.

### March 19, 2010

Peter Olver, School of Mathematics, University of Minnesota, USA

Place: Arts 217

Time: 3:30

Title: Moving Frames in Applications

#### Abstract

The classical method of moving frames was developed by Elie Cartan into a powerful tool for studying the geometry of submanifolds under certain geometrical transformation groups. In this talk, I will present a new foundation for moving frame theory based on equivariant maps. The method is completely algorithmic, and can be readily applied to completely general Lie group and even infinite-dimensional pseudo-group actions. The resulting theory and applications are remarkably wide-ranging, and include classification of differential invariants, construction and analysis of invariant variational problems and invariant differential equations, the design of symmetry-preserving numerical algorithms, and symmetry and object recognition in computer vision.

### March 23, 2010

Mark Ablowitz, Department of Applied Mathematics, University of Colorado, Boulder, CO, USA

Place: Arts 134

Time: 3:30

Title: Nonlinear waves: from beaches to lasers

#### Abstract

The study of localized waves has a long history dating back to the discoveries in the 1800s by Russell, Boussinesq and Korteweg-deVries(KdV) describing water waves in shallow water. In the 1960s researchon the KdV equation led to the concept of solitons which are solitary waves which interact elastically’’. More recently both in fluid dynamics and nonlinear optics there has been considerable interest invarious aspects of localized waves. Some of the topics that will be briefly discussed include: cross-wave interactions in water waves,ultra-short pulse dynamics in lasers and nonlinear waves in optical lattices.

### March 29, 2010

Richard Bowles, Department of Chemistry, UofS

Place: MCLH 242.1

Time: 2:30

Title: The glass transition from a particle packing perspective

#### Abstract

The characterisation and enumeration of jammed packings in hard core particle systems such as hard discs and hard spheres is a long-standing problem which holds the key to understanding the nature of glassy dynamics in these systems. A simple model consisting of hard discs trapped in a narrow channel exhibits the slow relaxation and heterogeneous dynamics at high densities, that are charecteristic of glassy systems. We show that for some cases, all the collectively jammed packings of the system can be constructed from a small set of locally jammed structures. As a result, we can exactly enumerate the entire jamming landscape of the system and explore how this landscape is connected to the thermodynamics and dynamics of the glassy system.

### April 8, 2010 (Joint with the Random Matrix Theory Seminar)

Donald Richards, Department of Statistics Penn State University, University Park, USA

Place: MCLH 242.1

Time: 2:30

Title: Integrals of Characteristic Polynomials of Unitary Matrices, and Applications to the Riemann Zeta Function

#### Abstract

In recent research on the Riemann zeta function and the Riemann Hypothesis, it is necessary to calculate certain integrals involving the characteristic functions of $N \times N$ unitary matrices and to develop asymptotic expansions of these integrals as $N \to \infty$. In this talk, I will derive exact formulas for several of these integrals, verify that the leading coefficients in their asymptotic expansions are non-zero, and relate these results to conjectures about the distribution of the zeros of the Riemann zeta function on the critical line. Finally, I will explain how these integrals are related to mathematical statistics and to the hypergeometric functions of Hermitian matrix argument.

### April 9, 2010

Donald Richards, Department of Statistics Penn State University, University Park, USA

Place: Arts 134

Time: 3:30

Title: Constant Proportion Debt Obligations, Zeno's Paradox, and the Spectacular Financial Crisis of 2008

#### Abstract

We analyze a coin-tossing model used to justify the sale of constant proportion debt obligations (CPDOs) and prove that it was impossible for CPDOs to achieve the Cash-In Event. In the best-case scenario in which the coin is two-headed, we show that the goal of attaining the Cash-In Event in a finite lifetime is precisely the goal, described more than two thousand years ago in Zeno's Paradox of the Dichotomy, of evaluating the sum of an infinite geometric series with only a finite number of terms. In the case of a fair coin, we show that a CPDO player operating on 9X margin (and hence subject to margin calls) has, approximately, an 89% chance of bankruptcy; moreover, even if the margin broker is infinitely wealthy and infinitely patient, his CPDO customers who lose on the first or any given toss are doomed, with high probability, to suffer losses for hundreds of successive tosses. In light of these results, we are dismayed by many of the mathematical models propagated over the past decade by financial engineers'' and experts'' in structured finance, and it heightens our fears about the durability of the on-going worldwide financial crisis.

### May 20, 2010

Speaker: Professor Jean-François Ganghoffer LEMTA, Nancy, France

Place: Arts 134

Time: 3:30

Title: Homogenization techniques for discrete media: from the virial approach to discrete asymptotic homogenization