2,977 research outputs found
Comment on: "Roughness of Interfacial Crack Fronts: Stress-Weighted Percolation in the Damage Zone"
This is a comment on J. Schmittbuhl, A. Hansen, and G. G. Batrouni, Phys.
Rev. Lett. 90, 045505 (2003). They offer a reply, in turn.Comment: 1 page, 1 figur
Entanglement transition of elastic lines in a strongly disordered environment
We investigate by exact optimization the geometrical properties of
three-dimensional elastic line systems with point disorder and hard-core
repulsion. The line 'forests' become entangled due to increasing line wandering
as the system height is increased, at fixed line density. There is a transition
height at which a cluster of pairwise entangled lines spans the system,
transverse to average line orientation. Numerical evidence implies that the
phenomenon is in the ordinary percolation universality class.Comment: 11 pages RevTeX, eps-figs included; one figure and some references
adde
Oscillations and patterns in interacting populations of two species
Interacting populations often create complicated spatiotemporal behavior, and
understanding it is a basic problem in the dynamics of spatial systems. We
study the two-species case by simulations of a host--parasitoid model. In the
case of co-existence, there are spatial patterns leading to noise-sustained
oscillations. We introduce a new measure for the patterns, and explain the
oscillations as a consequence of a timescale separation and noise. They are
linked together with the patterns by letting the spreading rates depend on
instantaneous population densities. Applications are discussed.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. E as a
Rapid Communicatio
Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature
We study the effect of an external field on (1+1) and (2+1) dimensional
elastic manifolds, at zero temperature and with random bond disorder. Due to
the glassy energy landscape the configuration of a manifold changes often in
abrupt, ``first order'' -type of large jumps when the field is applied. First
the scaling behavior of the energy gap between the global energy minimum and
the next lowest minimum of the manifold is considered, by employing exact
ground state calculations and an extreme statistics argument. The scaling has a
logarithmic prefactor originating from the number of the minima in the
landscape, and reads ,
where is the roughness exponent and is the energy fluctuation
exponent of the manifold, is the linear size of the manifold, and is
the system height. The gap scaling is extended to the case of a finite external
field and yields for the susceptibility of the manifolds . We also present a mean field argument
for the finite size scaling of the first jump field, .
The implications to wetting in random systems, to finite-temperature behavior
and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are
discussed.Comment: 20 pages, 22 figures, accepted for publication in Eur. Phys. J.
Low Temperature Properties of the Random Field Potts Chain
The random field q-States Potts model is investigated using exact
groundstates and finite-temperature transfer matrix calculations. It is found
that the domain structure and the Zeeman energy of the domains resembles for
general q the random field Ising case (q=2), which is also the expectation
based on a random-walk picture of the groundstate. The domain size distribution
is exponential, and the scaling of the average domain size with the disorder
strength is similar for q arbitrary. The zero-temperature properties are
compared to the equilibrium spin states at small temperatures, to investigate
the effect of local random field fluctuations that imply locally degenerate
regions. The response to field pertubabtions ('chaos') and the susceptibility
are investigated. In particular for the chaos exponent it is found to be 1 for
q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is
studied for correlated random fields.Comment: 11 pages RevTeX, eps-figs include
Financial interaction networks inferred from traded volumes
In order to use the advanced inference techniques available for Ising models,
we transform complex data (real vectors) into binary strings, by local
averaging and thresholding. This transformation introduces parameters, which
must be varied to characterize the behaviour of the system. The approach is
illustrated on financial data, using three inference methods -- equilibrium,
synchronous and asynchronous inference -- to construct functional connections
between stocks. We show that the traded volume information is enough to obtain
well known results about financial markets, which use however the presumably
richer price information: collective behaviour ("market mode") and strong
interactions within industry sectors. Synchronous and asynchronous Ising
inference methods give results which are coherent with equilibrium ones, and
more detailed since the obtained interaction networks are directed.Comment: 14 pages, 6 figure
- …