* Soft condensed matter physics, granular physics, nonlinear dynamics and pattern formation;
Welcome to my webpage! I hope you find the materials and brief discussions presented here interesting. This page is being regularly updated, so please feel free to come back soon! Also, if you have any questions or have some related or unrelated ideas or suggestions for potential collaborations, please do not hesitate to get in touch with me. My contact details are in blue color below.
I am Behrooz Ferdowsi, currently a Hess Fellow and Postdoctoral Research Associate at the Department of Geosciences, Princeton University. I am primarily working with Prof. Allan M. Rubin on constitutive laws for earthquake fault friction (also known as rate- and state-dependent friction laws) over the earthquake cycle, and on the physics of the seismic cycle. I further collaborate with Prof. Troy Shinbrot (Rutgers University) on several problems in granular physics, including pattern formation in granular flows, and wave-matter interaction in granular materials.
Since fall 2018, I also have started a collaboration with Prof. Blair Schoene (Princeton Geosciences) and Enrique Del Castillo (Princeton Geosciences) on revisiting Critical Taper Wedge theory for describing orogenic zone processes. As of summer 2018, I also collaborate with Prof. Jane Willenbring (Scripps Institution of Oceanography, and the University of California San Diego) and Emma Harrison (Scripps Institution of Oceanography, and the University of California San Diego) on granular physics of soil production, soil mixing and transport across the scales and environments. In all these lines of research, I work on using physics and mechanics of granular, disodered, and amorphous media, to connect with geomorphology, geochemistry, geochronology, fault mechanics, and seismology. Ultimately, I use this unique set of tools to develop physics-based frameworks that will enable us to explore and answer fundmental and outstanding questions about Earth and planetary surface, near-surface and subsurface processes over short and long (geological) timescales.
Before coming to Princeton, I was a Postdoctoral Researcher at the University of Pennsylvania, Sediment Dynamics Laboratory (PennSeD) and a Synthesis Postdoctoral Fellow of the National Center for Earth-Surface Dynamics (NCED). At PennSeD, I worked with Prof. Douglas J. Jerolmack (UPenn, Earth and Environmental Science) on bimodal sediment transport, subsurface to surface evolution of riverbeds and also granular controls of hillslope creep and landscape evolution. I received my PhD (Dr. sc.) from ETH Zurich (Switzerland), Department of Civil, Environmental and Geomatic Engineering. For my PhD research, I studied the influence of vibrations on the frictional behavior of sheared granular layers and implcations of the phenomenon for triggering of earthquakes by other (seismic) sources.
I have a broad research interest in several (and expanding) areas of geosciences and geophysics, including (i) constitutive laws for earthquake fault friction, fault zone processes, rock mechanics, and the physics and the mathematical modelings of the seismic cycle, (ii) hillslope and landscape evolution, geohazards and their environmental implications, (iii) sediment transport, fluvial geomorphology and aeolian transport, and (iv) sedimentology. I am further curious and excited about ways that surfacial, remote, and seismic observations can complement each other, and help with a better understanding of Earth-surface and subsurface processes in isolation and in coupling. I am also interested in broad engineering applications and implications of these research areas including implementation of the latest scientific discoveries in hazard assessment and mitigation methods. The unifying concept of my research and scientific interests however lies in soft condensed matter physics and the statistical physics of particles and fields. I search for laws (preferrably universal but they could be also non-universal) that can describe spatiotemporal evolution of different sections (and cross-sections) of the Earth and other planets across the scales of time (sub-second to million years) and space (asperities and grains to geo/log/phy/ical scales). For my works, I often use a combination of laboratory-scale experiments, numerical (Discrete Element Method and Molecular Dynamics) simulations, and analytical (sometimes continuum) modeling, with continuous inspiration and insight from direct (by myself) and indirect (previously published, collected, documented) field observations.
News, short notes and views
- At the AGU Annual Meeting 2018: my contributions are as following:
T11E-0208 Using granular physics to model rate- and state-dependent frictional behavior of earthquake fault zones
Behrooz Ferdowsi, Allan M. Rubin
Monday, 10 December 2018 08:00 - 12:20
Convention Ctr - Hall A-C (Poster Hall)
TEP24B-048 A Dynamical and Topographic Imprint of the Creep-to-Landslide Transition on Hillslopes
Douglas J Jerolmack, Behrooz Ferdowsi, Carlos P. Ortiz
Tuesday, 11 December 2018 16:45 - 17:00
Convention Ctr - 147A
TEP34A-108 Granular physics of soil production and creep
Emma Jayne Harrison, Behrooz Ferdowsi, Jane Willenbring
Wednesday, 12 December 2018 17:15 - 17:30
Convention Ctr - 147A
TEP41B-26718 Soil creep without gophers and other complications: Experiments probing sub-yield creep in the (near-)absence of disturbances
Nakul Deshpande, Behrooz Ferdowsi, Carlos P. Ortiz, Douglas J. Jerolmack
Thursday, 13 December 2018 08:00 - 12:20
Convention Ctr - Hall A-C (Poster Hall)
- 12-05-2018: I will give a seminar at the School of Earth and Atmospheric Sciences, Georgia Institute of Technology, on February 19, 2019.
- 09-20-2018: I will give a geodynamics seminar at the Lamont-Doherty Earth Observatory, Columbia University, on October 15, 2018.
- 09-04-2018: I will give a departmental seminar at the Department of Geology and Geophysics, College of Geosciences, Texas A&M University on February 15, 2019.
- 09-04-2018: I will give a talk on "soft matter physics of earthquake fault friction and nucleation processes" at Soft Materials Coffee Hour (SMatCH) Meeting at Princeton University. The talk is scheduled for December 4, 2018 at 2pm.
- 08-06-2018: I will be participating in the Workshop on Modeling Earthquake Source Processes to be held at the Seismological Laboratory, California Institute of Technology, October 8-10, 2018. I am grateful for the acceptance of my participation and the financial support provided by the workshop organizors and the National Science Foundation.
- 08-01-2018: We will give an invited talk at American Geophysical Union Annual Meeting in December 2018, on our most recent work on soft matter physics of soil production, soil creep and soil transport across environments. The first author of the talk is Emma Harrison, PhD student at the research group of Professor Jane Willenbring at Scripps Institute of Oceanography and at the University of California San Diego. I will post time and location of the talk (session EP018) here as soon as AGU schedule is available. We are grateful for the invitation from session chairs and organizors, Professor Kimberly Hill, Dr. Matteo Saletti, and Professor Philippe Frey.
- 07-23-2018: I will give an invited talk at the Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum GFZ, Germany. The talk will be on August 8, 2018. Since I cannot travel outside the USA due to the US government Travel Ban on my nationality, I will deliver the talk with video-conferencing!!!
- 07-23-2018: I will give an invited talk in the final plenary session (Early Investigator Presentations) of the 2018 Rock Deformation Gordon Research Conference. I am very grateful to the Chair of the GRC meeting, Professor Julia Morgan, for her invitation: 2018 Rock Deformation Gordon Research Conference
- 06-08-2018: I will be presenting at the 3rd Annual Soft Matter Day on July 27, 2018, at the Physics Department at UMass Amherst: 3rd Annual Soft Matter Day. This is an event especially designed for undergraduate students and graduate researchers (it's free!) in soft condensed matter physics broadly (Physics, Chemistry, Mechanical and Chemical Engineering, Biomedical Engineering, Civil and Environmental Engineering, and Geophysics). My talk will be on soft matter physics for geosciences, and I will discuss about applications of condensed matter physics in various areas of geosciences from landslide hazard prediction, riverbed geomorphology and landscape dynamics, to friction and fracture for earthquake source and rupture processes. I am grateful for the invitation from the event organziers, and look forward to an exciting day of lectures and discussions!
- 04-28-2018: Our latest paper is now published (open access) at Proceedings of the National Academy of Sciences of the USA. You can see the paper in this link: Glassy dynamics of landscape evolution
- 03-01-2018: I will be attending the annual Geoprocesses, geohazards - CSDMS 2018
meeting on May 22-24, 2018 at CU-Boulder. Thank you Sediment Experimentalist Network (SEN) for inviting me! I am very grateful for their support, and I look forward to the meeting and discussions!
- 02-21-2018: I will be visiting and giving a talk at the Department of Civil and Environmental Engineering, Carnegie Mellon University, on March 22, 2018 (time for the talk TBD).
- 02-14-2018: I will be visiting and giving a talk at the Department of Civil and Environmental Engineering, Duke University, on March 7, 2018, 12:00pm local time.
- 01-22-2018: A new revised version of our manuscript on landscape dynamics is now online on arXiv and ResearchGate. Please see here for a PDF: Glassy Dynamics of landscape evolution.
- 12-25-2017: I now have a blog where I write in it whenever I have a chance.
- 11-12-2017: I will be attending the UNAVCO short-course @ AGU - Using GPS data in undergraduate courses: from tectonic motions to water resources and climate change issues on December 10, 2017 at New Orleans, LA. Thank you for the supports of GEodetic Tools for Societal Issues (GETSI), AGU, UNAVCO, and NAGT (National Association of Geoscience Teachers) that make this short-course possible.
- 11-08-2017: Our new paper is out and online in Nature Communications: River-bed armouring as a granular segregation phenomenon, https://www.nature.com/articles/s41467-017-01681-3.
- 10-25-2017: I will be attending the American Geophysical Union Annual Meeting in New Orleans, USA, December 11-15, 2017. I will give a talk on earthquake (fault friction) physics scheduled for Friday, 15 December 2017 15:10 - 15:25, session S53D-07, at New Orleans Ernest N. Morial Convention Center - 217-219. This earthquake-related talk abstract is available here: "Toward a physics-based rate and state friction law for earthquake nucleation processes in fault zones with granular gouge". I am also contributer to an invited talk on landscape evolution by my postdoctoral advisor at Univ Pennsylvania, Prof. Jerolmack. This second talk is scheduled for Wednesday, 13 December 2017 08:15 - 08:30, session EP31F-02, at New Orleans Ernest N. Morial Convention Center - 353-355. The abstract for this geomorphology-related talk is available here: "A Physical Interpretation of Hillslope Soil Creep as Deformation of an Amorphous Solid".
Brief summary on current and past research
a) Evolution of riverbed surface in gravel-bed rivers (2015-2017)
In collaboration with Dr. Carlos P. Ortiz and Dr. Morgane Houssais and under direction of Prof. Douglas J. Jerolmack, I worked on sediment transport in bimodal (two major grain size) systems in an idealized laboratory river. Separation or segregation of grains with different size (and shape, mass, surface characteristics, etc.) is a frequently observed phenomenon in rivers, streams (where it is commonly known as sorting, coarsening, or armoring when larger grains cover the riverbed surface, and is known as gravel bars and fans when segregation and separation takes place intermittently) and all forms of granular materials and systems! Geologists and geomorphologists tend to think that formation of a coarse surface layer shields the finer underlying grains from erosion. They also traditionally assume that armor develops due to sorting of surficial grains by the fluid flow. In this research, we showed how motion of grains deep beneath the surface delivers larger grains to the surface. Using experiments in a laboratory river, and discrete and continuum models, we further demonstrated that river-bed armoring is driven by vertical granular segregation and that the fluid has little effect. Results also revealed different segregation mechanisms for deep (creeping) versus shallow (dense and rapidly flowing) grains, which has broader implications for all manner of granular flows. Please see our Nature Communications (2017) paper and University of Pennsylvania News article: `Brazil Nut Effect` Helps Explain How Rivers Resist Erosion on this work for more information.
↑ Phenomenology and setup. (A) Bed sediment of the River Wharfe, U.K., that shows a pronounced surface armor. Photo courtesy D. Powell [1
]. (B) Sketch of the experiment, showing position of the camera and laser plane used for imaging inside the granular bed. (C-E) Snapshots during armor development for τs*
. Also shown is the fluid boundary stress, which is computed as τ = ηUf
] where Uf
are the top-plate speed and flow depth, respectively. The red curve shows the long-term-averaged streamwise particle velocity ux
(z), where I and II correspond to the bed load and creep zones, respectively. The directions x and z are indicated. (F) Temporal evolution of the thickness of the armored layer at different Shields number. Legend indicates Shields number associated with each curve. The brighter continuous lines are predictions from a modified version -to account for creep (slow flow) segregation- of advection-diffusion model
[ Gray and Ancey, 
, Gray and Thornton, 
], , commonly used to model size-segregation phenomenon in granular mixing. Note the first rapid stage of armoring, which is dependent on Shields number and is associated with bed-load transport, and the second slower stage that exhibits a nearly constant rate for all Shields numbers and is the result of creep.
b) Hillslope evolution and landscape dynamics over geological timescales (2016-present)
Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed upon model that captures the full range of behavior. In this work, we have examined the granular origins of hillslope soil transport by Discrete Element Method simulations, studying deformation and transport in an experimental hillslope using dynamic light scattering technique, and re-analysis of sediment flux versus gradient measurements in natural landscapes around the world. We found creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical there is a continuous transition to a dense-granular flow rheology, consistent with previous laboratory experiments and theoretical developments in amorphous Earth materials and disordered media [ Fisher, 1998, Chauve et al., 2000, Dauchot et al., 2005, Reddy et al., 2011, Reichhardt and Reichhardt, 2016]. Slow earthflows and landslides thus exhibit glassy dynamics that is a characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales.
↑ Landslide and creep phenomenology. (A) Rapid landslide in San Salvador, El Salvador; and (B) Slow earthflow in Osh, Kyrgyzstan. (C) Ranges of surface velocities observed for various types of slow and rapid landslides. The datapoints in red, brown, magenta, and green correspond to the observations reported or documented by Cruden and Varnes, [1996
], Hungr et al., [2001
], Hilley et al., [2004
], and Saunders and Young, [1983
], respectively. (D) Schematic cross section of a soil-mantled hillslope. Photo credits: (A) Associated Press/Wide World Photos, (B) Joachim Lent.
↑ General flow behavior and the glassy flux model. (A) DEM results showing normalized local downslope velocity ([(ux
))]) as a function of normalized local friction coefficient ([(μ)/(μc
)]) for four different inclinations, below and above the bulk angle of repose. (B) Field data of normalized flux qs
- equivalent to normalized velocity us
- versus normalized gradient (S/Sc
) for five different studies of natural hillslopes. Data cloud color represents the probability of all field observations, that takes into account not only the probability of an observation at a given value of flux-gradient in the collected datasets, but also the number of sites/hillslopes collected and involved in each study (please see this arXiv:1708.06032
submission for methods and details of the analysis, and Figs. S5 & S6 therein). Dashed line illustrates an exponential scaling for creep regime with critical gradient Sc
= 0.4 and a power-law scaling for the range of large flux. The chosen values of exponential and power law scaling coefficients are not a fit to the data, because of inherent variability of the observations. They represent a qualitative comparison between expectations from theory, numerical simulations, and the field.
↑ Hillslope topography of the Oregon Coast Range (OCR) derived from this publicly available airborne lidar data on opentopography platform (link to lidar data
). (A) Regional perspective view, showing locations of two example hillslopes. (B) The elevation-distance and (C) gradient-distance relationships for representative profiles of hillslopes (1) (black dots) and (2) (red dots) in panel (A). Blue dashed line is the prediction of the "glassy" flux model with Sc
= 0.5 and β = 5/2. Please see supplementary information in this arXiv:1708.06032
submission for more examples.
c) Physics of rate- and state-dependent friction laws for Earth materials with a focus on earthquake fault gouge and earthquake source (2015-present)
This is an ongoing study under supervision and in collaboration with Professor Allan M. Rubin (Department of Geosciences, Princeton University).
Numerical simulations of earthquake nucleation rely on constitutive rate and state evolution laws to model earthquake initiation and propagation processes. In these laws, the frictional response of an interface is described as:
where a and b in equation (1) are the coefficients of the rate- and-state "direct" and "evolution" effects, respectively, σ is the effective normal stress, f* and V* are reference (initial) values of the friction coefficient and sliding velocity, respectively, V is the current value of the sliding velocity, and θ is the "state" variable. Two empirical forms for the evolution of the state variable θ have been previously proposed by Ruina, , and are used more frequently:
τ = σ||⎡|
f* + a ln ||
+ b ln||
= 1 − ||
In equations (2) and (3), Dc is a characteristic slip distance. The "state" variable θ is designed so as to reflect the product of the true contact area of asperities of the frictional interface and the intrinsic strength of the contacts in touch.
↑ (A) Most empirical frictional laws deal with the evolution of frictional resistance between two solid blocks pressed together and pulled (sometimes with a spring attached to one of the blocks) at a constant velocity or force parallel to solid-solid interface. The effective contact between the two interface is made of small localized patches whose total area is significantly less that the nominal area of contact. (B) The actual fault-fault interface is usually comprised of weak and fragmented rocks called "fault gouge". The rate- and state-dependent friction laws are supposedly designed to work for both solid-solid interface friction and the granular-interface friction. Despite decades of rigorous experimental, numerical, computational, observational and theoretical research by a broad group of researchers from geophysics to physics and tribology, the fundamental physics of frictional interfaces (including for fault physics) remain illusive for both types of interfaces until nowadays. The image is the courtesy of Kristie Bradford, http://geology1403.blogspot.com. (C) The figure shows the transient ("direct") and (toward "evolution") steady-state effect on friction of a change in loading velocity for a 3-mm–thick layer of quartz gouge sheared under nominally dry conditions at 25-MPa normal stress [Marone, 1998
]. (D) The figure shows the behavior of velocity-step experiments (four order of magnitude velocity change compared to the initial imposed velocity) on a simulated granular layer, subject to confining pressure 5-MPa. The Hertzian normal contact law and Coulomb friction law govern the grain-grain contact interactions, and the mean grain diameter is 3 mm (polydisperse grain size distribution). Note that no time-dependent plasticity is implemented at the grain contact scale. One of our goals in this research program is to separate complex though important contributions of contact plasticity, then design a granular-physics based friction law for fault and Earth materials friction. We will next revisit the problem and contributions of contact plasticity on frictional behavior as related to wide range of geoscience problems including earthquake source and physics in collaboration with physicists, geophysicists, and tribologists.
The response of different state evolution laws to large velocity increases is an important feature of these constitutive relations that can significantly change the style of earthquake nucleation in numerical models. However, currently there is not a rigorous understanding of the physical origins of the response of bare rock or gouge-filled fault zones to large velocity increases. This in turn hinders our ability to design physics-based friction laws that can appropriately describe those responses. In this research program, we argue that most fault zones form a granular gouge after an initial shearing phase and that it is the behavior of the gouge layer that controls the fault friction. We perform numerical experiments of a confined sheared granular gouge under a range of confining stresses and driving velocities relevant to fault zones and apply 1-3 order of magnitude velocity steps to explore dynamical behavior of the system from grain- to macro-scales. We compare our numerical observations with experimental data from biaxial double-direct-shear fault gouge experiments under equivalent loading and driving conditions. Our intention is to first investigate the degree to which these numerical experiments, with Hertzian normal and Coulomb friction laws at the grain-grain contact scale and without any time-dependent plasticity, can reproduce experimental fault gouge behavior. We next compare the behavior observed in numerical experiments with predictions of the Dieterich (Aging) and Ruina (Slip) friction laws. Ultimately, the numerical observations at the grain and meso-scales will be used for designing a rate and state evolution law that takes into account recent advances in rheology of granular systems, including local and non-local effects [DeGiuli and Wyart, 2017,Zhang and Kamrin, 2017,Henann and Kamrin, 2013], for a wide range of shear rates and slow and fast deformation regimes of the fault gouge.
d) Soft matter physics of soil production and creep across environments (2018-present)
This is an ongoing study in collaboration with Emma Harrison (PhD student at Scripps Institute of Oceanography and University of California San Diego) and Professor Jane Willenbring (Professor at Scripps Institute of Oceanography and University of California San Diego).
In many mountainous landscapes, soil is underlain by chemically altered saprolite. The production of soil from saprolite occurs via chemical and physical processes working on porous rocks and aggregated granular materials under shear, flow, and confinement. Empirical findings from field studies in Northern California, Oregon, Australia, and New Zealand suggest that there is an exponential relationship between the rate of soil production and soil depth. The observation of an exponential soil production rate has been associated with diffusive processes, like the penetration of oxygen or fluid into pore space, decreasing with depth. However, a physical understanding of the mechanism for soil production variation with depth remains elusive. On the other hand, the exponential decay of flux with depth is a ubiquitous observation in creep and slow deformation of disordered, amorphous and granular materials under gravity and shear. The decay rate of velocity (mass flux/mass density) in granular materials, is called the granular shear rate. In one theoretical framework for dense granular flows known as local granular rheology, the granular shear rate feeds into a non-dimensional number, known as Inertial number, together with grain size, local normal effective stress, and mass density, thus relating grain size with soil depth and deformation (transport and creep) dynamics. Despite these similarities, creep phenomena in granular materials hasn't yet been connected to soil flux and soil production rate functions. Here we work to do just that, by combining computational physics models of amorphous and disordered granular materials, with field observations of soil production obtained from in situ produced cosmogenic 10Be concentrations in saprolite sampled under soils of different ages. The field measurements are carried out in the Luquillo Experimental Forest in Puerto Rico, where existing research has demonstrated that spatial variations in erosion rate correspond to differences in saprolite thickness, soil composition, and above-ground forest structure. We compare measured soil production rates from Puerto Rico and other published works with calculations of soil flux from granular shear and creep, and the resulting vertical mixing and diffusivity. The computational model is using grains of different size and size distributions to accommodate size variability that is often related to environmental effects. Our work elucidates the primary physical controls of soil flux and mixing due to anomalous diffusion, and unifies granular physics with soil sciences. In addition to obtaining a physics-based relationship for variation of soil flux with depth at different environments, the findings could have important implications for understanding the relationship between chemical and physical erosion rates, and roles of these processes in driving landscape evolution, nutrient transport and global carbon cycle.
For more information about this work, please see Emma Harrison (UCSD) invited talk at AGU Annual Meeting December 2018. I will advertise the talk in "News, short notes and views" section above on my website as soon as we have information about location and time of the talk.
e) Pattern formation in vibrated granular beds and implications for landforms on Earth and other planets (2017-present)
f) Role of dynamic stress and perturbation in triggering slip in frictional amorphous systems (2011-2014)
- [Chauve et al. 2000]
Pascal Chauve, Thierry Giamarchi, and Pierre Le Doussal.
Creep and depinning in disordered media.
Physical Review B, 62 (10): 6241, 2000.
- [Cruden and Varnes 1996]
David M Cruden and David J Varnes.
Landslides: investigation and mitigation. chapter 3-landslide types
Transportation research board special report, (247),
- [Dauchot et al. 2005]
Olivier Dauchot, Guillaume Marty, and Giulio Biroli.
Dynamical heterogeneity close to the jamming transition in a sheared
Physical review letters, 95 (26): 265701,
- [DeGiuli and Wyart 2017]
E. DeGiuli and M. Wyart.
Friction law and hysteresis in granular materials.
Proceedings of the National Academy of Sciences, 2017.
- [Fisher 1998]
Daniel S Fisher.
Collective transport in random media: from superconductors to
Physics reports, 301 (1): 113-150, 1998.
- [Gray and Ancey 2015]
JMNT Gray and C Ancey.
Particle-size and-density segregation in granular free-surface flows.
Journal of Fluid Mechanics, 779: 622-668, 2015.
- [Gray and Thornton 2005]
JMNT Gray and AR Thornton.
A theory for particle size segregation in shallow granular
In Proceedings of the Royal Society of London A: Mathematical,
Physical and Engineering Sciences, volume 461, pages 1447-1473. The Royal
- [Henann and Kamrin 2013]
David L Henann and Ken Kamrin.
A predictive, size-dependent continuum model for dense granular
Proceedings of the National Academy of Sciences, 110
(17): 6730-6735, 2013.
- [Hilley et al. 2004]
George E Hilley, Roland Bürgmann, Alessandro Ferretti, Fabrizio Novali, and
Dynamics of slow-moving landslides from permanent scatterer analysis.
Science, 304 (5679): 1952-1955, 2004.
- [Houssais et al. 2015]
Morgane Houssais, Carlos P Ortiz, Douglas J Durian, and Douglas J Jerolmack.
Onset of sediment transport is a continuous transition driven by
fluid shear and granular creep.
Nature communications, 6, 2015.
- [Hungr et al. 2001]
Oldrich Hungr, SG Evans, MJ Bovis, and JN Hutchinson.
A review of the classification of landslides of the flow type.
Environmental & Engineering Geoscience, 7
(3): 221-238, 2001.
- [Marone 1998]
Laboratory-derived friction laws and their application to seismic
Annual Review of Earth and Planetary Sciences, 26
(1): 643-696, 1998.
- [Powell 1998]
D Mark Powell.
Patterns and processes of sediment sorting in gravel-bed rivers.
Progress in Physical Geography, 22 (1):
- [Reddy et al. 2011]
KA Reddy, Y Forterre, and O Pouliquen.
Evidence of mechanically activated processes in slow granular flows.
Physical Review Letters, 106 (10): 108301,
- [Reichhardt and Reichhardt 2016]
Charles Reichhardt and CJ Olson Reichhardt.
Depinning and nonequilibrium dynamic phases of particle assemblies
driven over random and ordered substrates: a review.
Reports on Progress in Physics, 80 (2):
- [Ruina 1983]
Slip instability and state variable friction laws.
Journal of Geophysical Research: Solid Earth, 88
(B12): 10359-10370, 1983.
- [Saunders and Young 1983]
Ian Saunders and Anthony Young.
Rates of surface processes on slopes, slope retreat and denudation.
Earth Surface Processes and Landforms, 8
(5): 473-501, 1983.
- [Zhang and Kamrin 2017]
Qiong Zhang and Ken Kamrin.
Microscopic description of the granular fluidity field in nonlocal
Physical Review Letters, 118 (5): 058001,
File translated from
On 5 December 2018, 10:45 EST