106 research outputs found
An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution
We compute exactly the asymptotic distribution of scaled height in a
(1+1)--dimensional anisotropic ballistic deposition model by mapping it to the
Ulam problem of finding the longest nondecreasing subsequence in a random
sequence of integers. Using the known results for the Ulam problem, we show
that the scaled height in our model has the Tracy-Widom distribution appearing
in the theory of random matrices near the edges of the spectrum. Our result
supports the hypothesis that various growth models in dimensions that
belong to the Kardar-Parisi-Zhang universality class perhaps all share the same
universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde
From Vicious Walkers to TASEP
We propose a model of semi-vicious walkers, which interpolates between the
totally asymmetric simple exclusion process and the vicious walkers model,
having the two as limiting cases. For this model we calculate the asymptotics
of the survival probability for particles and obtain a scaling function,
which describes the transition from one limiting case to another. Then, we use
a fluctuation-dissipation relation allowing us to reinterpret the result as the
particle current generating function in the totally asymmetric simple exclusion
process. Thus we obtain the particle current distribution asymptotically in the
large time limit as the number of particles is fixed. The results apply to the
large deviation scale as well as to the diffusive scale. In the latter we
obtain a new universal distribution, which has a skew non-Gaussian form. For
particles its asymptotic behavior is shown to be
as and
as .Comment: 37 pages, 4 figures, Corrected reference
Interface Scaling in the Contact Process
Scaling properties of an interface representation of the critical contact
process are studied in dimensions 1 - 3. Simulations confirm the scaling
relation beta_W = 1 - theta between the interface-width growth exponent beta_W
and the exponent theta governing the decay of the order parameter. A scaling
property of the height distribution, which serves as the basis for this
relation, is also verified. The height-height correlation function shows clear
signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett.
83, 4594 (1999)], but no evidence of multiscaling.Comment: 10 pages, 9 figure
Moving glass phase of driven lattices
We study periodic lattices, such as vortex lattices, driven by an external
force in a random pinning potential. We show that effects of static disorder
persist even at large velocity. It results in a novel moving glass state with
topological order analogous to the static Bragg glass. The lattice flows
through well-defined, elastically coupled, {\it % static} channels. We predict
barriers to transverse motion resulting in finite transverse critical current.
Experimental tests of the theory are proposed.Comment: Revised version, shortened, 8 pages, REVTeX, no figure
Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
We provide a comprehensive report on scale-invariant fluctuations of growing
interfaces in liquid-crystal turbulence, for which we recently found evidence
that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1
dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here
we investigate both circular and flat interfaces and report their statistics in
detail. First we demonstrate that their fluctuations show not only the KPZ
scaling exponents but beyond: they asymptotically share even the precise forms
of the distribution function and the spatial correlation function in common
with solvable models of the KPZ class, demonstrating also an intimate relation
to random matrix theory. We then determine other statistical properties for
which no exact theoretical predictions were made, in particular the temporal
correlation function and the persistence probabilities. Experimental results on
finite-time effects and extreme-value statistics are also presented. Throughout
the paper, emphasis is put on how the universal statistical properties depend
on the global geometry of the interfaces, i.e., whether the interfaces are
circular or flat. We thereby corroborate the powerful yet geometry-dependent
universality of the KPZ class, which governs growing interfaces driven out of
equilibrium.Comment: 31 pages, 21 figures, 1 table; references updated (v2,v3); Fig.19
updated & minor changes in text (v3); final version (v4); J. Stat. Phys.
Online First (2012
Vortex wandering in a forest of splayed columnar defects
We investigate the scaling properties of single flux lines in a random
pinning landscape consisting of splayed columnar defects. Such correlated
defects can be injected into Type II superconductors by inducing nuclear
fission or via direct heavy ion irradiation. The result is often very efficient
pinning of the vortices which gives, e.g., a strongly enhanced critical
current. The wandering exponent \zeta and the free energy exponent \omega of a
single flux line in such a disordered environment are obtained analytically
from scaling arguments combined with extreme-value statistics. In contrast to
the case of point disorder, where these exponents are universal, we find a
dependence of the exponents on details in the probability distribution of the
low lying energies of the columnar defects. The analytical results show
excellent agreement with numerical transfer matrix calculations in two and
three dimensions.Comment: 11 pages, 9 figure
Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
We study the statistics of thermodynamic quantities in two related systems
with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in
a random potential and the 2-dimensional random bond dimer model. The first
system is examined by a replica-symmetric Bethe ansatz (RBA) while the latter
is studied numerically by a polynomial algorithm which circumvents slow glassy
dynamics. We establish a mapping of the two models which allows for a detailed
comparison of RBA predictions and simulations. Over a wide range of disorder
strength, the effective lattice stiffness and cumulants of various
thermodynamic quantities in both approaches are found to agree excellently. Our
comparison provides, for the first time, a detailed quantitative confirmation
of the replica approach and renders the planar line lattice a unique testing
ground for concepts in random systems.Comment: 16 pages, 14 figure
The Global Forest Transition as a Human Affair
Forests across the world stand at a crossroads where climate and land-use changes are shaping their future. Despite demonstrations of political will and global efforts, forest loss, fragmentation, and degradation continue unabated. No clear evidence exists to suggest that these initiatives are working. A key reason for this apparent ineffectiveness could lie in the failure to recognize the agency of all stakeholders involved. Landscapes do not happen. We shape them. Forest transitions are social and behavioral before they are ecological. Decision makers need to integrate better representations of people’s agency in their mental models. A possible pathway to overcome this barrier involves eliciting mental models behind policy decisions to allow better representation of human agency, changing perspectives to better understand divergent points of view, and refining strategies through explicit theories of change. Games can help decision makers in all of these tasks
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