1,672 research outputs found
Interplay between phase ordering and roughening on growing films
We study the interplay between surface roughening and phase separation during
the growth of binary films. Renormalization group calculations are performed on
a pair of equations coupling the interface height and order parameter
fluctuations. We find a larger roughness exponent at the critical point of the
order parameter compared to the disordered phase, and an increase in the upper
critical dimension for the surface roughening transition from two to four.
Numerical simulations performed on a solid-on-solid model with two types of
deposited particles corroborate some of these findings. However, for a range of
parameters not accessible to perturbative analysis, we find non-universal
behavior with a continuously varying dynamic exponent.Comment: 10 pages, 8 figure
Dynamic Scaling Phenomena in Growth Processes
Inhomogeneities in deposition may lead to formation of rough surfaces, whose
height fluctuations can be probed directly by scanning microscopy, or
indirectly by scattering. Analytical or numerical treatments of simple growth
models suggest that, quite generally, the height fluctuations have a
self-similar character. The roughness and dynamic exponents are expected to be
universal; depending only on the underlying mechanism that generates
self-similar roughness. Despite its ubiquitous occurrence in theory and
simulations, experimental confirmations of dynamic scaling have been rare. I
shall briefly review the theoretical foundations of dynamic scaling, and
suggest possible reasons for discrepancies with experimental results.Comment: Plain TEX, 10 pages, no figures. For the Proceedings of the "Fourth
International Conference on Surface X-Ray and Neutron Scattering," Lake
Geneva, June 1995. To be published in a special issue of Physica
Probability distributions for directed polymers in random media with correlated noise
The probability distribution for the free energy of directed polymers in
random media (DPRM) with uncorrelated noise in dimensions satisfies the
Tracy-Widom distribution. We inquire if and how this universal distribution is
modified in the presence of spatially correlated noise. The width of the
distribution scales as the DPRM length to an exponent , in good (but not
full) agreement with previous renormalization group and numerical results. The
scaled probability is well described by the Tracy-Widom form for uncorrelated
noise, but becomes symmetric with increasing correlation exponent. We thus find
a class of distributions that continuously interpolates between Tracy-Widom and
Gaussian forms
Coalescence Model for Crumpled Globules Formed in Polymer Collapse
The rapid collapse of a polymer, due to external forces or changes in
solvent, yields a long-lived `crumpled globule.' The conjectured fractal
structure shaped by hierarchical collapse dynamics has proved difficult to
establish, even with large simulations. To unravel this puzzle, we study a
coarse-grained model of in-falling spherical blobs that coalesce upon contact.
Distances between pairs of monomers are assigned upon their initial
coalescence, and do not `equilibrate' subsequently. Surprisingly, the model
reproduces quantitatively the dependence of distance on segment length,
suggesting that the slow approach to scaling is related to the wide
distribution of blob sizes
Attractive and repulsive polymer-mediated forces between scale-free surfaces
We consider forces acting on objects immersed in, or attached to, long
fluctuating polymers. The confinement of the polymer by the obstacles results
in polymer-mediated forces that can be repulsive (due to loss of entropy) or
attractive (if some or all surfaces are covered by adsorbing layers). The
strength and sign of the force in general depends on the detailed shape and
adsorption properties of the obstacles, but assumes simple universal forms if
characteristic length scales associated with the objects are large. This occurs
for scale-free shapes (such as a flat plate, straight wire, or cone), when the
polymer is repelled by the obstacles, or is marginally attracted to it (close
to the depinning transition where the absorption length is infinite). In such
cases, the separation between obstacles is the only relevant macroscopic
length scale, and the polymer mediated force equals ,
where is temperature. The amplitude is akin to a critical
exponent, depending only on geometry and universality of the polymer system.
The value of , which we compute for simple geometries and ideal
polymers, can be positive or negative. Remarkably, we find for
ideal polymers at the adsorption transition point, irrespective of shapes of
the obstacles, i.e. at this special point there is no polymer-mediated force
between obstacles (scale-free or not).Comment: RevTeX, 10 pages, 10 figure
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