Spring 2006 Visiting Scientists

Fedrik Andersson, Centre for Mathematical Sciences, Lund Institute of Technology, Lund University, Sweden

Thematic Visiting Scholars Program

The Center for Computational and Applied Mathematics designates a research theme every semester. Experts in the subject are invited to speak at speak at Purdue. The theme for Spring, 2006 is Porous Media. Below is information about the speakers invited to Purdue. The organizer for this semester is Dr. John Cushman.

Spring 2006 Theme: Porous Media

Visitor

Home Insitition

Date of Talk*

 
Wojbor A. Woyczynski Case Western March 1 details
TBA   March 8  
Spring Break   March 15  
George Papanicolaou Stanford March 22 details
Alexandre Chorin UC-Berkley April 5 details
Mary Wheeler UT-Austin April 12 details
Howard Brenner MIT April 19 details

* each speaker will arrive the day before their talk and depart the day after their talk

March 1

Seminar at in 3:30 p.m. MTHW 304

Title: "Growing interfaces in the presence of hopping surface diffusion and fractional Hamilton-Jacobi-KPZ equations"

Wojbor A. Woyczynski, Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and Technology Case Western Reserve University, Cleveland, Ohio

Abstract: Ballistic deposition of particles on a growing interface, accompanied by surface diffusion that has both the brownian and the jump components, leads to nonlocal and nonlinear evolution equations involving infinitesimal generators of Levy stochastic processes such as the fractional Laplacian. I will describe asymptotic behavior of mild solutions to such equations.

References:

  • J.A. Mann and W.A. Woyczynski, Growing fractal interfaces in the presence of self-similar hopping surface diffusion, Physica A. Statistical Mechanics and Its Applications   291(2001), 159-183.
  • P. Biler, G. Karch and W.A. Woyczynski, Critical nonlinearity exponent and self-similar asymptotics for Levy conservation laws, Annales d'Institute H. Poincare- Analyse Nonlineaire (Paris) 18(2001), 613-637
  • B. Jourdain,   S. Meleard and W.A. Woyczynski, A probabilistic approach for nonlinear equations involving fractional Laplacian and singular operator, Potential Analysis   23(2005), 55-81.
  • G. Karch and W.A. Woyczynski, Fractal Hamilton-Jacobi-KPZ equations, 2006 preprint, 27 pp., to appear.

March 22

Seminar at in 3:30 p.m. MTHW 304

Title: "Imaging in random media"

George Papanicolaou, Stanford University

Abstract: Imaging in its many forms is a very rapidly advancing interdisciplinary science that is deeply rooted in modern applied mathematics: In wave propagation (migration or back-propagation methods), diffusion, impedance and x-ray tomography, statistical denoising and classification, as well as in fast compuational methods for dealing with very large data sets. I will present some recently developed methods for imaging with array and distributed sensors when the environment between the objects to be imaged and the sensors is complex and only partially known to the imager. This brings in modeling and analysis in random media, and the need for statistical algorithms that increase the computational complexity of imaging. I will illustrate the theory with applications from non-destructive testing and from other areas.

April 5

Seminar at in 3:30 p.m. UNIV 303

Title: "Problem reduction and Brenormalization."

Alexandre Chorin, Department of Mathematics, University of California - Berkley

Abstract: I will present methods for the reduction of the complexity of computational problems, both time-dependent and stationary, together with connections to renormalization, scaling, and irreversible statistical mechanics, and with applications in fluid mechanics and molecular dynamics. The key points are: (i) in time dependent problems, it is not in general legitimate to average equations without taking into account memory effects and noise; (ii) problem reduction is a search for hidden similarities; (iii) mathematical tools developed in physics for carrying out renormalization group transformations yield effective block Monte-Carlo methods; (iv) the Mori-Zwanzig formalism, which in principle yields exact reduction methods but is often hard to use, can be tamed by approximation; (v) the case of long memory (=long support for the autocorrelations of the noise) is important in applications, and can be handled by a
straightforward expansion formalism.

Reference:

  • Chorin and Hald, Stochastic tools for mathematicsand science, Springer 2005.

April 12

Seminar at in 3:30 p.m. MTHW 304

Title: "Computational Environments for Coupling Multiphase Flow, Trancsport, and Mechanics in Porous Media"

Mary Wheeler, Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, University of Texas - Austin

Abstract: Cost-effective management of remediation of contamination sites and production from oil and gas reservoirs is driving development of a new generation of subsurface simulators. The central challenge is to minimize costs of cleanup or maximize economic benefit from an environment whose properties are only poorly known and in which a variety of complex chemical and physical phenomena take place. In order to address this challenge a robust reservoir simulator comprised of coupled programs that together account for multi-component, multi-phase flow and transport through porous media and through wells is required. The coupled programs must be able to treat different physical processes occurring simultaneously in different parts of the domain, and for computational accuracy and efficiency, should also accomodate multiple numerical schemes. We present a "wish list" for simulator capabilities as well as describe the methodology employed in the IPARS software developed at The University of Texas at Austin.

April 19

Seminar at in 3:30 p.m. MTHW 304

Title: "Measuring Darcy Permeability Without Flow "

Howard Brenner, Department of Chemical Engineering, MIT

Abstract: This talk will summarize recent work by the speaker on the subject of (gravity-free) fluid motion in continua generated by the presence of "slip" occurring at solid-fluid surfaces arising from an externally-imposed temperature gradient along the surface.   An application of the general concept to porous media will show that it is possible, in principle, to experimentally measure the Darcy permeability of a porous medium without requiring that fluid flow through its pores. The notions apply equally to gases and liquids.

References:

  • Bielenberg, J. R. and Brenner, H. "A continuum model of thermal transpiration." J. Fluid Mech.   546, 1-23 (2006).
  • Brenner, H, "Nonisothermal Brownian motion. Thermophoresis as the molecular manifestation of thermally-biased molecular motion. " Phys. Rev. E 72, 061201-1 to 16 (2005).
  • Bielenberg, J. R. and Brenner, H. "A hydrodynamic/Brownian motion model of thermal diffusion in liquids. " Physica A 356, 279-293 (2005).
  • Brenner, H. and Bielenberg, J. R., "A continuum approach to phoretic motions.   Thermophoresis. " Physica A   355, 251-273 (2005).
  • Brenner, H., "Navier-Stokes revisited." Physica A 349, 60-132 (2005).
  • Brenner, H., "Kinematics of volume transport" Physica A 349, 11-59 (2005) flow around a sphere." Phys. Fluids 17, 038107-1 to 4 (2005).
  • Brenner, H. "Is the tracer velocity of a fluid continuum equal to its mass velocity? " Phys. Rev. E. 70, 061201-1 to 10   (2004).
  • Yariv, E. and Brenner, H. "Flow animation by unsteady temperature fields." Phys. Fluids 16, L95-L98   (2004).