Materials Computation Center, University of Illinois

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Materials Computation Center, University of
Illinois Duane D. Johnson and Richard Martin, NSF
DMR-03-25939 Dynamically Driven Systems Alfred
Hubler, Karin Dahmen, Pascal Bellon
Systems subjected to external forcing open
dissipative systems E, H, F , time dependent or
time independent As forcing intensity increases
near equilibrium to far from equilibrium
Common objectives space and time scaling
fractals, self-organization, chaos, crackling
noise Techniques - atomistic simulations
RFIM, KMC, MD - comparisons w/ experiments and
theory (mean-field, renormalization group)
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The Growth of Fractal Transportation
Networks Alfred Hubler group
Research Understanding the dynamic processes
that form fractals and fractal-like trees remains
a key open problem in physical phenomena as
diverse as dielectric breakdown, viscous
fingering, fracturing, river formation and in
biological phenomena like branching in plants,
fungi, and blood vessels. There are two major
difficulties posed by studying the dynamics of
fractals by experiment 1) time scales are either
too fast (a bolt of lightning is an example of
dielectric breakdown) or too slow (as in river
formation) and 2) control of experimental
parameters are often out of the researchers
hands. We use graph theoretical models to predict
the growth of fractal transportation networks.
The geometry of the initial state can affect the
topology of the network. Because the binding of
particles to the boundary is strong, the network
does not reconfigure easily therefore, the way
the particles are distributed during stage II
largely determines how the particles connect to
one another. This constraint sets the relative
number of trunks, branches, and termini that the
network forms. This figure shows how different
initial states lead to different final
networks. Joseph K. Jun and Alfred W. Hubler,
Formation and structure of ramified charge
transportation networks in an electromechanical
system, PNAS 102, 536540 (2005). Alfred W.
Hubler, Predicting Complex Systems with a
Holistic Approach, Complexity 10, 11-16 (2005)
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Experimental Study of Adaptation to the Edge of
Chaos and Critical Scaling Alfred Hubler and
Alexander Scheeline
Research It was recently shown that
self-adjusting systems adapt to the edge of
chaos. We study the robustness of that adaptation
with respect to a controlling force. We find that
if the controlling has a periodic target
dynamics, the control is successful, if for very
small controlling forces. We also find, however,
that if the target dynamics is chaotic, the
self-adjustment resists the control and
adaptation to the edge of chaos occurs. Even when
the controlling force is very large, adaptation
to the edge of chaos is weaker, but still present
in the system. The theoretical results are in
good agreement with the experimental results from
a self-adjusting Chua circuit.
Fig. 1 Adaptation with small forcing in Chuas
circuit. The circuit diagram is shown on the
left. The plot on the upper right shows the
target resistance (dashed line) and the
experimentally value of resistance (cont. line).
When the target is in the chaotic regime (1770? lt
R lt 1750 ?) the control is unstable. The plot on
the lower right shows a histogram of the
experimental R-values. The population in the
chaotic regime is very small (see Melby, N.
Weber, A. Hubler, Robustness of Adaptation in
Controlled Self-Adjusting Chaotic Systems, Phys.
Fluctuation and Noise Lett. 2, L285-L292 (2002),
P. Melby, N. Weber, A. Hubler, Dynamics of
Self-Adjusting System with Noise, CHAOS 15,
033902 (2005), J.Xu, A. Hubler, Enhanced
Diffraction Pattern from a Fibonacci Chain,
Phys.Rev.B 67, 184202(2003)) .
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Dynamics of Disordered Nonequilibrium Systems
Hysteresis, Noise, and Domain Wall From Magnets
to Earthquakes Karin Dahmen group
Higher Order Spectra of Avalanche Noise
Approach Graduate student Amit Mehta developed
a new scaling theory for higher order spectra of
noise in systems with avalanches using mean field
theory and simulations. He compared the results
to new experiments done by graduate student
Andrea Mills with Prof. Michael Weissman on
Barkhausen noise in magnets and found good
agreement in almost all aspects. Higher order
spectra are useful to determine if noise in
systems is due to large avalanches of flipping
domains or many small domains switching back and
forth. Significant results To our knowledge
this represents the first scaling theory of
higher order spectra of crackling noise. The
results are expected to be relevant to a large
class of systems with avalanches and crackling
noise, ranging from magnets, to charge density
waves, to superconductors, to shape memory
alloys, and possibly even to earthquakes. This
work also supported by DMR 03-14279
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Dynamically driven alloys systems with competing
dynamics operating at different length
scales Pascal Bellon group
Irradiation Plastic deformation L from a
few atoms for EPKA 25-100 eV Lsh the grain
size to 104 atoms for EPKA 10 keV and
above (macroscopic) R mostly nearest
neighbor relocations, n 1 to 100 b but
medium range tail (nm) At finite temperature
Dynamical competition between Forced atomic
mixing and thermally activated
annealing mesoscale self-organization at steady
state
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Nanoscale Patterning of Chemical Order Induced By
Ion Beam Processing, graduate student Jia Ye
Binary alloy system with non-conserved order
parameter, L12 and L10 ordered phases MD
simulations -gt simulate the damage produced by
energetic ions (collab. w/ Averback) KMC
simulations -gt evaluate steady states f( T,
concentration, cascade frequency and size)
HRTEM contrast simulations -gt assess feasibility
of validation experiments (collab. w/
Zuo) If L gt Lc, possible
self-organization into random patterns PRB 70,
094104 094105 (2004) - new scaling of
steady-state structure factor to be submitted to
PRB - in progress temporal scaling of speckle
intensity (collab. w/ K. Dahmen) Possible
applications for nanoscale patterns of chemical
order - improve mechanical properties -
synthesize exchange spring magnets and
high-density magnetic storage media
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Summary of effects of external length scales R,
L(b), Lsh on patterning of composition and order
in driven alloys
Complementary roles of R and L on
cascade-induced patterning
Continuous transition from disordered state to
patterning state Tunable characteristic scale
of patterns up to R or L or Lsh