Modeling for Process Control: High-Dimensional Systems Page: 2 of 5
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Our research within this grant has been devoted to the modeling of complex temporal and
extended spatio-temporal high-dimensional systems with the aim of applying these models
for controlling the corresponding physical processes. The main direction of our research was
modeling of complex dynamics of granular materials.
Among the highlights of our research in this area during the lifetime of the grant (2004-
2006) are the advances in understanding the behavior of anisotropic granular matter under
external driving, theoretical description of granular impact, modeling of the thermal collapse
of hot granular gas under gravity, as well as development of theory for pattern formation by
microtubules and molecular motors.
1 Partial fluidization theory and applications
In this part of work we applied our previously developed theory of partial fluidization to
various problems of granular dynamics. In particular, we studied the stick-slip dynamics of
a sold body moved over a granular bed, and found a good agreement between our theoretical
modeling and direct molecular dynamics simulations as well as the earlier experiments. This
work was published in Ref. .
In collaboration with French group of Dr. Anne Mangeney (Paris University) we applied
the theory of partial fluidization to the problem of erosion of granular mass in order to com-
pare and validate the Saint-Venant modeling approach and develop novel order-parameter
based modeling tools. Using these new tools we studied avalanche dynamics in realistic geo-
physical conditions. In particular we addressed the problem of enhanced avalanche mobility
in erodible bed conditions and explained it by entrainment of granular material underneath
the avalanche. Our results on this subject were published in [9, 10].
2 Modeling of anisotropic granular dynamics
We discovered the novel mechanism of transport of granular medium related to the anisotropic
shape of the grains. In our prior DOE-funded work we elucidated the mechanisms of collec-
tive motion of rods on a vibrating plate and developed phenomenological continuum model
which demonstrated the transition to directed motion and onset of vortices. In our work
within the grant period we focused on more specific properties of the inelastic frictional in-
teraction between the anisotropic grains and the vibrating bottom. In particular, we studied
the various regimes of motion of a bouncing dimer comprised of two spheres connected with
a rigid rod. The first excited mode has a novel horizontal drift in which one end of the
dimer stays on the plate during most of the cycle, while the other end bounces in phase with
the plate. The speed and direction of the drift depend on the aspect ratio of the dimer.
We employed both a novel soft-particle molecular dynamics algorithm and the event-driven
simulations based on the detailed treatment of frictional interactions between the dimer and
the plate in order to elucidate the nature of the transport mechanism in the drift mode. This
work has been done in collaboration with experimental groups of Arshad Kudrolli (Clark
University) and Igor Aranson (Argonne). This work has been published in [13, 6, 5, 81.
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Tsimring, Lev S. Modeling for Process Control: High-Dimensional Systems, report, September 15, 2008; United States. (digital.library.unt.edu/ark:/67531/metadc898293/m1/2/: accessed November 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.