stress

STRESS Sponsors

STRESS 1 - A working group co-sponsored by:

National Center for Earth-surface Dynamics (NCED), University of Illinois, Hydrologic Synthesis Activities, and the Desert Research Institute (DRI)

TAHOE CENTER FOR ENVIRONMENTAL RESEARCH
INCLINE VILLAGE, NV
NOV  4-7, 2007

Workshop Objectives

Many of the classical differential equations used to describe physical phenomena arise as the scaling limits of stochastic models. These models use probability theory to predict the outcome of physical processes that contain random elements. If the random components of a physical process are characterized by frequent extreme events and best fit by a power-law distribution, then classical stochastic theory does not apply. The inclusion of heavy-tailed distributions in a stochastic model requires a generalization of the limit theorems used to obtain long time governing distributions. Similarly, equations governing scaling limits of heavy-tailed stochastic processes are a generalization of classical PDEs they include fractional derivatives. These non-integer order derivatives acting on equation parameters, are useful tools for treating seemingly scale-dependent physical processes. For example, fractional advection-dispersion equations have been used to model super- and sub-diffusive contaminant transport in both aquifers and rivers. In these applications, the scale dependence of dispersivity was eliminated because fractional derivatives can scale the dispersion coefficient appropriately.

Power-laws and scaling are frequently observed in Earth surface morphology suggesting that heavy-tailed stochastic models and fractional PDEs may be powerful tools for describing processes and transport laws that take place on the Earth’s surface from the hillslope to the whole river network. We propose to create a working group to explore ideas, in research and applications, in the area of stochastic transport and emergent scaling in earth-surface processes. By convening experts in Earth-surface processes and mathematicians and scientists who have successfully applied heavy-tailed stochastic theory and fractional differential equations in other disciplines, we will identify:

  1. Geomorphic and hydrologic transport laws to which existing heavy-tailed stochastic theories and fractional calculus tools can be immediately applied
  2. Outstanding theory required for the development of novel scale-invariant models for Earth surface processes

Workshop Participants

Foufoula-Georgiou, Efi (co-organizer)
Department of Civil Engineering
University of Minnesota
2 - 3rd Ave SE
Minneapolis, MN 55414
Tel: +1.612.626.0369
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Schumer, Rina (co-organizer)
Division of Hydraulic Sciences
Desert Research Institute
2215 Raggio Parkway
Reno, NV 89512
Tel: +1.775.673.7414
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Ancey, Christophe
Environmental Hydraulics Laboratory
EPF Lausanne
Station 18
CH - 1015 Lausanne
Switzerland
Tel: +41.21.693.32.87
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Baumer, Boris
Department of Mathematics and Statistics
University of Otago
Science III Building
730 Cumberland St.
Dunedin, New Zealand
Tel: +03.479.7763
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Benson, David
Department of Geology and Geological Engineering
Colorado School of Mines
Golden, CO 80401
Tel: +1.303.273.3806
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Bradley, Nate
Department of Geological Sciences
University of Colorado, Boulder
Campus Box 399
Boulder, CO 80309
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Chen, Dong
Division of Hydrologic Sciences
Desert Research Institute
755 E. Flamingo Rd.
Las Vegas, NV 89119
Tel: +1.702.862.5541
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Cushman, John
Center for Applied Mathematics
Purdue University
550 Stadium Mall Drive
West Lafayette, IN 47907-2051
Tel: +1.765.494.8040
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Ganti, Vamsi
National Center for Earth-surface Dynamics
University of Minnesota
2 - 3rd Ave SE
Minneapolis, MN 55414
Tel: +1.612.624.4629
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Harman, Ciaran
Department of Geography
University of Illinois, Urbana/Champaign
607 South Mathews Avenue
Urbana, IL 61801-3671
Tel: +1.217.721.8381
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Jerolmack, Douglas
Department of Earth and Environmental Science
University of Pennsylvania
240 S. 33rd Street
Hayden Hall
Philadelphia, PA 19104-6316
Tel: +1.215.746.2823
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Hill, Kimberly
Department of Civil Engineering
University of Minnesota
2 - 3rd Ave SE
Minneapolis, MN 55414
Tel: +1.612-626-0311
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Kumar, Praveen
Department of Civil and Environmental Engineering
University of Illinois, Urbana/Champaign
205 N. Mathews Avenue
Urbana, IL 61801
Tel: +1.217.333.4688
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Mantha, Satish
Dept of Civil and Environmental Engineering
University of Illinois, Urbana/Champaign
205 N. Mathews Avenue
Urbana, IL 61801
Tel: +1.504.452.7560
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Meerschaert, Mark
Department of Statistics and Probability
Michigan State University
A416 Wells Hall
Michigan State University
East Lansing, MI 48823
Tel: +1.517.432.7097
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Packman, Aaron
Department of Civil and Environmental Engineering
Northwestern University
A314 Technological Institute
2145 Sheridan Road
Evanston, IL 60208-3109 
Tel: +1.847.4912.9902
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Passalacqua, Paola
National Center for Earth-surface Dynamics
University of Minnesota
2 - 3rd Ave SE
Minneapolis, MN 55414
Tel: +1.612.624.4675
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Reeves, Matt
Division of Hydrologic Sciences
Desert Research Institute
2215 Raggio Parkway
Reno, NV 89512 
Tel: +1.775.673.7605
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Rentschler, Martin
Environmental Hydraulics Lab
EPF Lausanne
Station 18
CH - 1015 Lausanne
Switzerland
Tel: +41.21.693.23.84
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Schmeeckle, Mark
Department of Geography
Arizona State University
P.O. Box 870104
Tempe, AZ 85287-0104
Tel: +1.480.965.7246
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Sivapalan, Siva
Department of Geography
Department of Civil and Environmental Engineering
University of Illinois, Urbana/Champaign
607 South Mathews Avenue
Urbana, IL 61801-3671
Tel: +1.217.333.2675
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Stark, Colin
Lamont-Doherty Earth Observatory
Columbia University
305A Oceanography
61 Route 9W - PO Box 1000
Palisades, NY 10964
Tel: +1.845.365.8742
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
Tucker, Greg
Department of Geological Sciences
University of Colorado, Boulder
2200 Colorado Ave.
Boulder, CO 80309-0399
Tel: +1.303.492.6985
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.
  Zhang, Yong
Division of Hydrologic Sciences
Desert Research Institute
775 E. Flamingo Rd.
Las Vegas, NV 89119
Tel: +1.702.862.5314
Email: This email address is being protected from spambots. You need JavaScript enabled to view it.

Workshop Presentations

Christophe Ancey: Intermittent motion and sediment transport -- experimental and theoretical insight


Boris Baeumer: Scaling limits and subordination


David Benson: Fractional Calculus in (underneath) Our Backyard - An Abstracted Introductory Overview Summary Résumé


John Cushman: A universal field equation for dispersion: turbulence, porous media, nano-films and microbial dynamics


Efi Foufoula-Georgiou: 1) Stochastic transport on the Earth's surface: new physical-statistical formalisms?

Efi Foufoula-Georgiou: 2) Experimental evidence for intermittency and scaling in sediment transport


Kimberly Hill: Particle size dependence of bedload transport of gravel particles


Douglas Jerolmack: Thresholds and heavy tails in sediment-transporting systems


Praveen Kumar: Emergence of binary tree networks and their inevitable self-similar topology


Mark Meerschaert: 1) Scaling limits and governing equations

Mark Meerschaert: 2)Tail Estimation


Aaron Packman: Linking surface topography, subsurface structure, and solute transport in rivers


Matt Reeves: Operator-stable densities and solute transport in fractured media


Mark Schmeeckle: A Fokker-Planck model of bedload transport and morphodynamics


Rina Schumer: Extreme value models for processes with heavy-tailed interarrivals


Siva Sivapalan and Ciaran Harman: The closure problem in watershed hydrology


Colin Stark: A review of some outstanding problems in mountain geomorphology and their possible treatment with fractional calculus and similar tools


Gregory Tucker and Nathan Bradley: Landscape evolution models and challenges in formulating earth-surface transport laws


Workshop Location, Accommodations, and Travel Information

Daily meetings will be held at the Tahoe Environmental Research Center(TERC) in Incline Village, Nevada.

TheHyatt Regency Lake Tahoeis located on the east shore of Lake Tahoe, a five-minute walk from the TERC.  Hotel reservations under each invited participant’s name from Sunday November 4 through Wednesday November 7 will be paid in advance.  A map and directions to the hotel can be foundhere.  Please send us your arrival/departure information so we can arrange transportation from the Reno-Tahoe airport to the Hyatt on Sunday and back to the airport on Wednesday. 

Travel Reimbursement

Travel expenses can be reimbursed up to $800 for international and $500 for domestic air travel.  To obtain travel reimbursement, send receipts and a Participant Expense Worksheet to:
National Center for Earth-surface Dynamics 
Attn: David Olsen 
2 - 3rd Ave SE RM 379 
Minneapolis, MN 55414