arXiv subjects

Abbas Ali Saberi

Publications and source records attributed to Abbas Ali Saberi.

40 records · Page 3Linked to original sources

arXiv2013

Percolation description of the global topography of Earth and Moon

Remarkable global correlations exist between geometrical features of terrestrial surface on the Earth, current mean sea level and its geological internal processes whose origins have remained an essential goal in the Earth sciences. Theoretical modeling of the ubiquitous self-similar fractal patterns observed on the Earth and their underlying rules is indeed of great importance. Here I present a percolation description of the global topography of the Earth in which the present mean sea level is automatically singled out as a critical level in the model. This finding elucidates the origins of the appearance of scale invariant patterns on the Earth. The criticality is shown to be accompanied by a continental aggregation, unraveling an important correlation between the water and long-range topographic evolution. To have a comparison point in hand, I apply such analysis onto the lunar topography which reveals various characteristic features of the Moon.

cond-mat.stat-mech↗

arXiv2011

Fractal structure of a three dimensional Brownian motion on an attractive plane

Consider a Brownian particle in three dimensions which is attracted by a plane with a strength proportional to some dimensionless parameter $α$. We investigate the fractal spatial structure of the visited lattice sites in a cubic lattice by the particle around and on the attractive plane. We compute the fractal dimensions of the set of visited sites both in three dimensions and on the attractive plane, as a function of the strength of attraction $α$. We also investigate the scaling properties of the size distribution of the clusters of nearest-neighbor visited sites on the attractive plane, and compute the corresponding scaling exponent $τ$ as a function of $α$. The fractal dimension of the curves surrounding the clusters is also computed for different values of $α$, which, in the limit $α\rightarrow\infty$, tends to that of the outer perimeter of planar Brownian motion i.e., the self-avoiding random walk (SAW). We find that all measured exponents depend significantly on the strength of attraction.

cond-mat.stat-mech↗

arXiv2010

Three Dimensional Ising Model, Percolation Theory and Conformal Invariance

The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the critical behavior of the 3d model. The fractal dimension and the winding angle statistics of the perimeter and external perimeter of the geometric spin clusters at the critical point suggest that, if conformally invariant in the scaling limit, they can be described by the theory of Schramm-Loewner evolution (SLE_κ) with diffusivity of κ=5 and 16/5, respectively, putting them in the same universality class as the interfaces in 2d tricritical Ising model. It is also found that the Fortuin-Kasteleyn (FK) clusters associated with the cross sections undergo a nontrivial percolation transition, in the same universality class as the ordinary 2d critical percolation.

cond-mat.stat-mech↗

arXiv2010

Geometrical Phase Transition on WO$_3$ Surface

A topographical study on an ensemble of height profiles obtained from atomic force microscopy techniques on various independently grown samples of tungsten oxide WO$_3$ is presented by using ideas from percolation theory. We find that a continuous 'geometrical' phase transition occurs at a certain critical level-height $δ_c$ below which an infinite island appears. By using the finite-size scaling analysis of three independent percolation observables i.e., percolation probability, percolation strength and the mean island-size, we compute some critical exponents which characterize the transition. Our results are compatible with those of long-range correlated percolation. This method can be generalized to a topographical classification of rough surface models.

cond-mat.stat-mech↗