1,093 research outputs found
A periodic elastic medium in which periodicity is relevant
We analyze, in both (1+1)- and (2+1)- dimensions, a periodic elastic medium
in which the periodicity is such that at long distances the behavior is always
in the random-substrate universality class. This contrasts with the models with
an additive periodic potential in which, according to the field theoretic
analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the
random manifold class dominates at long distances in (1+1)- and
(2+1)-dimensions. The models we use are random-bond Ising interfaces in
hypercubic lattices. The exchange constants are random in a slab of size
and these coupling constants are periodically repeated
along either {10} or {11} (in (1+1)-dimensions) and {100} or {111} (in
(2+1)-dimensions). Exact ground-state calculations confirm scaling arguments
which predict that the surface roughness behaves as: and , with in
-dimensions and; and , with in -dimensions.Comment: Submitted to Phys. Rev.
Intermittence and roughening of periodic elastic media
We analyze intermittence and roughening of an elastic interface or domain
wall pinned in a periodic potential, in the presence of random-bond disorder in
(1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the
typical behavior of a large sample is intermittent, and does not self-average
to a smooth behavior. Instead, large fluctuations occur in the mean location of
the interface and the onset of interface roughening is via an extensive
fluctuation which leads to a jump in the roughness of order , the
period of the potential. Analytical arguments based on extreme statistics are
given for the number of the minima of the periodicity visited by the interface
and for the roughening cross-over, which is confirmed by extensive exact ground
state calculations.Comment: Accepted for publication in Phys. Rev.
Disorder-induced roughening in the three-dimensional Ising model
Using an exact method, we numerically study the zero-temperature roughness of interfaces in the random bond, cubic lattice, Ising model (of size L3, with L<~80). Interfaces oriented along the {100} direction undergo a roughening transition from a weak disorder phase, which is almost flat, to a strong disorder phase with interface width w∼cL0.42 (c is a function of the disorder). For random dilution we find the roughening threshold p∗=0.89±0.01 and c∼p∗−p for p<~p∗ (p is the volume fraction of present bonds). In contrast {111} interfaces are algebraically rough for all disorder.Peer reviewe
Structural compliance, misfit strain and stripe nanostructures in cuprate superconductors
Structural compliance is the ability of a crystal structure to accommodate
variations in local atomic bond-lengths without incurring large strain
energies. We show that the structural compliance of cuprates is relatively
small, so that short, highly doped, Cu-O-Cu bonds in stripes are subject to a
tensile misfit strain. We develop a model to describe the effect of misfit
strain on charge ordering in the copper oxygen planes of oxide materials and
illustrate some of the low energy stripe nanostructures that can result.Comment: 4 pages 5 figure
Self-Attracting Walk on Lattices
We have studied a model of self-attracting walk proposed by Sapozhnikov using
Monte Carlo method. The mean square displacement
and the mean number of visited sites are calculated for
one-, two- and three-dimensional lattice. In one dimension, the walk shows
diffusive behaviour with . However, in two and three dimension, we
observed a non-universal behaviour, i.e., the exponent varies
continuously with the strength of the attracting interaction.Comment: 6 pages, latex, 6 postscript figures, Submitted J.Phys.
Extremal statistics in the energetics of domain walls
We study at T=0 the minimum energy of a domain wall and its gap to the first
excited state concentrating on two-dimensional random-bond Ising magnets. The
average gap scales as , where , is the energy fluctuation exponent, length scale, and
the number of energy valleys. The logarithmic scaling is due to extremal
statistics, which is illustrated by mapping the problem into the
Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of
domain walls has also a logarithmic dependence on system size.Comment: Accepted for publication in Phys. Rev.
Quasi-static cracks and minimal energy surfaces
We compare the roughness of minimal energy(ME) surfaces and scalar
``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces
have the same roughness scaling, w sim L^zeta (L is system size) with zeta =
2/3. The 3-d ME and SQF results at strong disorder are consistent with the
random-bond Ising exponent zeta (d >= 3) approx 0.21(5-d) (d is bulk
dimension). However 3-d SQF surfaces are rougher than ME ones due to a larger
prefactor. ME surfaces undergo a ``weakly rough'' to ``algebraically rough''
transition in 3-d, suggesting a similar behavior in fracture.Comment: 7 pages, aps.sty-latex, 7 figure
Random-field Ising model on complete graphs and trees
We present exact results for the critical behavior of the RFIM on complete
graphs and trees, both at equilibrium and away from equilibrium, i.e., models
for hysteresis and Barkhausen noise. We show that for stretched exponential and
power law distributions of random fields the behavior on complete graphs is
non-universal, while the behavior on Cayley trees is universal even in the
limit of large co-ordination.Comment: 4 pages, 4 figure
The true reinforced random walk with bias
We consider a self-attracting random walk in dimension d=1, in presence of a
field of strength s, which biases the walker toward a target site. We focus on
the dynamic case (true reinforced random walk), where memory effects are
implemented at each time step, differently from the static case, where memory
effects are accounted for globally. We analyze in details the asymptotic
long-time behavior of the walker through the main statistical quantities (e.g.
distinct sites visited, end-to-end distance) and we discuss a possible mapping
between such dynamic self-attracting model and the trapping problem for a
simple random walk, in analogy with the static model. Moreover, we find that,
for any s>0, the random walk behavior switches to ballistic and that field
effects always prevail on memory effects without any singularity, already in
d=1; this is in contrast with the behavior observed in the static model.Comment: to appear on New J. Phy
Strength Reduction in Electrical and Elastic Networks
Particular aspects of problems ranging from dielectric breakdown to metal
insu- lator transition can be studied using electrical o elastic networks. We
present an expression for the mean breakdown strength of such networks.First,
we intro- duce a method to evaluate the redistribution of current due to the
removal of a finite number of elements from a hyper-cubic network of
conducatances.It is used to determine the reduction of breakdown strength due
to a fracture of size .Numerical analysis is used to show that the
analogous reduction due to random removal of elements from electrical and
elastic networks follow a similar form.One possible application, namely the use
of bone density as a diagnostic tools for osteorosporosis,is discussed.Comment: one compressed file includes: 9 PostScrpt figures and a text fil
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