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 Events
IBM TJ Watson Research Center
Mon 2 Feb 2015, 4:00pm
Department Colloquium
LSK 200
A conjugate IP approach for large scale non smooth programs
LSK 200
Mon 2 Feb 2015, 4:00pm-5:00pm

Abstract

Many scientific computing applications can be formulated as large-scale optimization problems, including inverse problems, medical and seismic imaging, classification in machine learning, data assimilation in weather prediction, and sparse difference graphs. While first-order methods have proven widely successful in recent years, recent developments suggest that matrix-free second-order methods, such as interior-point methods, can be competitive.

This talk has three parts. We first develop a modeling framework for a wide range of problems, and show how conjugate representations can be exploited to design a uniform interior point approach for this class. We then show a range of applications, focusing on modeling and special problem structure. Finally, we preview some recent work, which suggests that the conjugate representations admit very efficient matrix free methods in important special cases, and present some recent results for large scale extensions.   


Note for Attendees

Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.
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NYU
Tue 3 Feb 2015, 4:00pm
Department Colloquium
MATH 100
Multiscale modeling and simulation in active fluids
MATH 100
Tue 3 Feb 2015, 4:00pm-5:00pm

Abstract


Active fluids, the novel class of non-equilibrium materials made up of self-driven constituents, is attracting growing interest due to its impact on cell biology, condensed matter physics, and nanotechnology. Despite their differences in composition, active fluids orchestrate cooperative actions across various length and time scales, and accompany energy conversion from one form to another. In this talk, I focus on a recent study of nonlinear dynamics and pattern formation of microtubule/motor-protein assemblies using multiscale modeling and simulation. I explain how the local microtubule-motor and microtubule-microtubule interactions manifest themselves at macroscopic scales through hydrodynamic instability, as well as the connections between the coherent flow structures and topological defects observed in active nematics. I also briefly discuss the new physics and phenomena in other systems, and numerical and theoretical tool development for the quantitative study of general complex fluids.


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UT Austin
Thu 5 Feb 2015, 12:30pm
Department Colloquium
MATX 1100
Applications and Numerical Methods for Optimal Transportation
MATX 1100
Thu 5 Feb 2015, 12:30pm-1:30pm

Abstract

The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. However, the numerical solution of this problem remains extremely challenging. After surveying several current applications, we describe a numerical method for the widely-studied case when the cost is quadratic. The solution is obtained by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to anon-standard implicit boundary condition. Expressing this problem in terms of weak (viscosity) solutions enables us to construct a monotone finite difference approximation that provably converges to the correct solution. A range of challenging computational examples demonstrate the effectiveness of this method.

Note for Attendees

Sushi will be served.
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Los Alamos National Laboratory
Thu 5 Feb 2015, 4:00pm
Department Colloquium
ESB 2012 (note changed time and place)
Low Reynolds number flows through shaped and deformable conduits
ESB 2012 (note changed time and place)
Thu 5 Feb 2015, 4:00pm-5:00pm

Abstract

Unconventional fossil energy resources are revolutionizing the US energy market. While the techniques developed over the last 50 years lead to viable and profitable extraction of, e.g., trapped gas and hydrocarbons from almost-impermeable rock formations via hydraulic fracturing, the abysmal extraction rates (typically 15%) suggest the fluid mechanics of these processes is not well understood. In this talk, I will describe three basic theoretical fluid mechanics problems inspired by unconventional fossil fuel extraction. The first problem is flow in a deformable microchannel. Fluid-structure interaction couples the shape of the conduit to the flow through it, drastically altering the flow rate--pressure drop relation. Using perturbation methods, we show that the flow rate is a quartic polynomial of pressure drop for shallow channels, in contrast to the linear relation for rigid conduits. The second problem involves two-phase (gas-liquid) displacement in a horizontal Hele-Shaw cell with an elastic membrane as the top boundary. This problem arises at the pore-scale in enhanced oil recovery for large injection pressures. Once again, fluid-structure interaction alters the problem, leading to stabilization of the Saffman--Taylor (viscous fingering) instability below a critical flow rate. Using lubrication theory, we derive the stability threshold and show that it agrees well with recent experiments. The third problem involves the spread of a viscous liquid in a vertical Hele-Shaw cell with a variable thickness in the flow-wise direction, as a model for the spread of a plume of supercritical carbon dioxide through the non-uniform passages created by hydraulic fracturing. We show that the propagation regimes in such a shaped conduit are set by the direction of propagation. While the rate of spread in the direction of increasing gap thickness (and, hence, permeability) can be obtained by standard scaling techniques, the reverse scenario requires the construction of a so-called second-kind self-similar solution, leading to nontrivial exponents in the rate of spread.

Note for Attendees

Refreshments will be served at 3:45pm in the PIMS Lounge.
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McGill University
Wed 11 Feb 2015, 3:00pm
Department Colloquium
ESB 2012
Some new numerical techniques to some old PDE problems
ESB 2012
Wed 11 Feb 2015, 3:00pm-4:00pm

Abstract

Problems involving complicated deforming time-dependent boundaries or interfaces (i.e. codim-1 surfaces) are ubiquitous in the modeling of physical systems. The resulting Partial Differential Equations (PDEs) often have irregular, and even discontinuous solutions along these surfaces. In turn, the solution of these PDEs couples back to flow and hence deform the surfaces in question. The numerical approximation of such systems isnotoriously challenging.

In a regular Cartesian grid setting, I propose to replace the original PDE by another PDE which better approximates, in the discrete setting, the exact solution to the original PDE. I will provide 3 examples of this approach.

First, in the active penalty method one does not enforce the PDE boundary conditions directly, but rather solves the PDE in a larger domain without boundary (e.g. a flat torus) and adds a carefully constructed source or penalty term that mimics boundary conditions. I will show how to systematically construct  penalty terms which improve the convergence rates of the penalized PDE, thereby allowing for higher-order finite-difference or Fourier-spectral numerical schemes to be applied to problems withnon-conforming boundaries.

Second, in the correction function method I tackle the problem of solving PDEs with jump discontinuities across a codim-1 surface, i.e. an interface. This is achieved by formulating an auxiliary local PDE which solution smoothly extends across the interface while enforcing the jump conditions. I will show that this approach is general, and can achieve arbitrary order of convergence while incurring (asymptotically) no additional computational cost.

Third, I will present methods for evolving in time arbitrary geometric objects such as boundaries or interfaces, but also general open/closed
surfaces with possibly no regularity (e.g. fractals). This is achieved by evolving in time the flow map and composing it with the initial conditions. This method fit naturally within the gradient-augmented level set framework and enables use of  a two-grid approach to achieve arbitrary order of convergence and optimal efficiency.

Throughout the talk I will illustrate these approaches with simulations of various physical systems including problems from fluid dynamics,
electromagnetism, solid mechanics for which these methods may need to be combined.

Note for Attendees

PIMS Afternoon Tea will be served at 2:45 p.m. in the PIMS Lounge (ESB 4133).
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Anthony Wachs
IFP Energies nouvelles France
Thu 12 Feb 2015, 4:00pm
Department Colloquium
ESB 2012
Particulate flow across multi-scales: numerical strategies for momentum, heat and mass transfer
ESB 2012
Thu 12 Feb 2015, 4:00pm-5:00pm

Abstract

Particulate flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by the momentum transfer between the continuous fluid phase and the dispersed particulate phase. When significant temperature differences exist between the fluid and particles and/or chemical reactions take place at the fluid/particle interfaces, the phases also exchange heat and/or mass, respectively. While some multi-phase processes may be successfully modelled at the continuum scale through closure approximations, an increasing number of applications require resolution across scales, e.g. dense suspensions, fluidized beds. Within a multi-scale micro/meso/macro-framework, we develop robust numerical models at the micro and meso-scales, based on a Distributed Lagrange Multiplier/Fictitious Domain method and a two-way Euler/Lagrange method, respectively. Particles, assumed to be of finite size, potentially collide with each other and these collisions are modeled with a Discrete Element Method. We discuss the mathematical issues related to modeling this type of flows and present the main numerical and computational features of our simulation methods. We also illustrate what can be gained from massively parallel computations performed with our numerical code PeliGRIFF, in terms of physical insight into both fundamental questions and applications from the chemical engineering and process industry. Finally, we explain how knowledge gained at the micro scale can cascade upwards and contribute to the development of enhanced meso and macro-scale models.

 Speaker Biography: Dr Anthony Wachs received BS & MS degrees from University Louis Pasteur, Strasbourg and his PhD from the Institut National Polytechnique of Grenoble in 2000. He joined Institut Français du Pétrole in 2001 (now IFP Energies Nouvelles), passed his HDR in 2010 and is currently both scientific advisor and project manager.  He leads a team of researchers that develop both mathematical models and robust computational algorithms for the resolution of multi-phase flows (www.peligriff.com). His main research interests are non-Newtonian Flows, Multiphase Flows and High Performance Computing. He collaborates extensively with academic groups in Canada, Brazil, France and Germany.

 

Note for Attendees

Refreshments will be served in the PIMS Lounge (ESB 4133) at 3:15p.m. before this colloquium.
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Stanford U. and UC Irvine
Mon 16 Feb 2015, 3:30pm
Department Colloquium
ESB 2012 (PIMS)
Special PIMS colloquium: New results on the Bartnik mass
ESB 2012 (PIMS)
Mon 16 Feb 2015, 3:30pm-4:30pm

Abstract

We will introduce the Bartnik mass and survey the progress toward its understanding. We will then present a new upper bound which is sharp in certain cases. It is contained in a recent joint work with C. Mantoulidis and has relevance to a conjecture of G. Gibbons.
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Northwestern University
Mon 23 Feb 2015, 4:00pm
Department Colloquium
LSK 200
Math Department Colloquium/Fluids Seminar: Sessile drop dynamics
LSK 200
Mon 23 Feb 2015, 4:00pm-5:00pm

Abstract

Oscillations of the sessile drop are of fundamental interest in a number of industrial applications, such as ink-jet printing and drop atomization. We generalize the stability analysis for the free inviscid drop (Rayleigh, 1879), focusing on the wetting properties of the solid substrate and mobility of the three-phase contact-line.  We report oscillation frequencies and modal structures for the `symmetry-broken’ Rayleigh drop that display spectral splitting/reordering and compare with experiments. To organize and explain the hierarchy of frequencies, we construct a corresponding `periodic table of mode shapes’ from the spectral data. In addition to the oscillatory spectrum, we report a new hydrodynamic instability that has fundamental implications for fluid transport.


Profile:  Dr Joshua Bostwick received bachelors degrees in Physics and Civil Engineering from University of Wisconsin-Milwaukee in 2005, and his PhD from Cornell University in 2011. He worked as a postdoctoral researcher at North Carolina State University and is currently Golovin Assistant Professor in the Department of Engineering Science and Applied Mathematics at Northwestern University. His research interests span surface tension, hydrodynamic instability, wetting and spreading, elastocapillarity, dynamical systems, constrained variational principles, symmetry methods.


Note for Attendees

Refreshments will be served at 3:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Caltech
Fri 27 Feb 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
PIMS-UBC distinguished colloquium: Blowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations.
ESB 2012 (PIMS)
Fri 27 Feb 2015, 3:00pm-4:00pm

Abstract

Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities.  To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order 10^12 in each direction. A careful local analysis also suggests that the solution develops a highly anisotropic self-similar profile which is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity.

This is a joint work of Prof. Guo Luo.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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