Growing Order out of Randomness
In my Ph.D. thesis, I study a class of statistical patterns in
Nature arising from local stochastic activity and leading to large-scale
patterns and order.
I study the formation of extremely periodic patterns which are
usually observed in
sedimentary structures. In this case, Nature separates previously mixed
granular materials of different sizes by a selective sieve during
transport by wind and avalanching during sedimentation.
I address the longstanding question of how the process forms the
I also consider the patterns observed in surfaces and interfaces
generated in various non-equilibrium systems. A very general feature of
these surfaces is that they typically present scale-invariant
power-law correlations ---statistical patterns that apply across the
whole object--- both in space and in time, so that their study shares
many features with that of critical phenomena.
STRATIFICATION IN SAND AND ROCKS
I present a new type of size segregation in granular matter.
I show that
a mixture of small and large grains is poured
between two transparent
slabs, a size
segregation of the mixture in successive layers of small
I propose a theoretical explanation for the formation of the layers,
which is related to the different angles of repose entering in the
The formation of periodic layers of small and large grains
is reminiscent of
the stratified patterns observed in aeolian rocks.
NON-EQUILIBRIUM KINETIC ROUGHENING
I study a subset of non-equilibrium
phenomena and disordered systems. I explore
the scaling properties of driven surfaces and interfaces
in disordered media, and the dynamical
properties of surface erosion via ion-sputtering.
In particular, I
formulate a discrete stochastic model which includes the essential
features of large classes of sputter etching processes. The model
reproduces dynamical instabilities encountered in several experiments on
sputtered surfaces, whereas it displays scaling behavior at later stages
of the dynamical evolution.
CHARACTERIZING SPATIAL PATTERNS IN POROUS MEDIA
I consider porous media, such as
sedimentary rocks, which
have complex correlated patterns that influence the
flow of fluids and hydrocarbons.
I quantify these patterns using
long-range correlated percolation models.
- CORRELATED AND UNCORRELATED PERCOLATION MODELS OF ROCKS
PATTERN FORMATION IN URBAN GROWTH
I consider the fractal patterns formed by human agglomerations.