Research interests

Currently I'm working on experimental and theoretical aspects of surface growth and trying to Use of Schramm-Loewner Evolution (SLE) for of grown nanostructure surfaces, however some of my interests that I like to work are as follows :

• CFT & critical phenomena

• Growing and etching of surface

• Nanotechnology and Nanoscience

• Thermoelectric Phenomena

• Thermodynamics and Statistical Physics in small systems

Selected Publications:

• Watersheds are Schramm-Loewner Evolution curves

E Daryaei, NAM Araujo, KJ Schrenk, S Rouhani, HJ Herrmann, Physical Review Letters 109 (21), 218701 ( pdf )

Abstract:

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLEκ, with κ=1.734±0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c≈-7/2.

• Loop erased random walk on percolation cluster: Crossover from Euclidean to fractal geometry

E Daryaei, and S Rouhani, arXiv preprint, arXiv:1308.5692 ( pdf )

Abstract:

We study loop erased random walk (LERW) on the percolation cluster, with occupation probability p>pc, in two and three dimensions. We find that the fractal dimensions of LERW_p is close to normal LERW in Euclidean lattice, for all p > pc. However our results reveal that LERW on critical incipient percolation clusters is fractal with df =1.217±0.0015 for D = 2 and 1.44±0.03 for D = 3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERW_p crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to pc. For the finite systems, two crossover exponents and a scaling relation can be derived. This work opens up a new theoretical window regarding diffusion process on fractal and random landscapes.

• Loop erased random walk on percolation cluster is compatible with Schramm-Loewner Evolution, E. Daryaei, Physical Review E 90 (2), 022129 (2014). ( pdf )

We study the scaling limit of planar loop-erased random walk (LERW) on the percolation cluster‎, ‎with occupation probability p>p_c. ‎We numerically demonstrate that the scaling limit of planar LERW_p curves‎, ‎for all p>p_c, ‎can be described by Schramm-Loewner evolution (SLE) with a single parameter k that is close to the normal LERW in a Euclidean lattice‎. ‎However‎, ‎our results reveal that the LERW on critical incipient percolation clusters is compatible with SLE‎, ‎but with another diffusivity coefficient k. ‎Several geometrical tests are applied to ascertain this‎. ‎All calculations are consistent with SLE_k, ‎where k=1.732. ‎This value of the diffusivity coefficient is outside of the well-known duality range 2<k< 8. ‎We also investigate how the winding angle of the LERW_p crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to p_c. ‎For finite systems‎, ‎two crossover exponents and a scaling relation can be derived‎. ‎This finding should‎, ‎to some degree‎, ‎help us to understand and to predict the existence of conformal invariance in disordered and fractal landscapes‎.

• Surface roughness analysis of the hydrophilic SiO_2/TiO_2 nano bi-layers by Level crossing approach

E Daryaei, M Reza Rahimi Tabar, AZ Moshfegh, Physica A: Statistical Mechanics and its Applications 392 (9), 2175-2181 ( pdf )

Abstract:

The effect of etching time on the statistical properties of hydrophilic surfaces of SiO2/TiO2/glass nano bilayers has been studied using atomic force microscopy (AFM) and a stochastic approach based on a level crossing analysis. We have created rough surfaces of the hydrophilic SiO2/TiO2 nano bilayer system by using 26% potassium hydroxide (KOH) solution. Measuring the average apparent contact angle allowed us to assess the degree of hydrophilicity, and the optimum condition was determined to be 10 min etching time. A level crossing analysis based on AFM images provided deeper insight into the microscopic details of the surface topography. With different etching times, it has been shown that the average frequency of visiting a height with positive slope behaves in a Gaussian manner for heights near the mean value and obeys a power law for heights far away from the mean value. Finally, by applying the generalized total number of crossings with positive slope, it was found that the both high heights and deep valleys of the surface have a great effect on the hydrophilic degree of the SiO2/TiO2/glass nano bilayer investigated system.