arXiv subjects

S. M. Vaez Allaei

Publications and source records attributed to S. M. Vaez Allaei.

8 recordsLinked to original sources

arXiv2016

Crossing Statistics of Anisotropic Stochastic Surface

In this paper, we propose crossing statistics and its generalization, as a new framework to characterize the anisotropy in a 2D field, e.g. height on a surface, extendable to higher dimensions. By measuring $ν^+$, the number of up-crossing (crossing points with positive slope at a given threshold of height ($α$)), and $N_{tot}$ (the generalized roughness function), it is possible to distinguish the nature of anisotropy, rotational invariance and Gaussianity of any given surface. For the case of anisotropic correlated self- or multi-affine surfaces (even with different correlation lengths in various directions and/or directional scaling exponents), we analytically derive some relations between $ν^+$ and $N_{tot}$ with corresponding scaling parameters. The method systematically distinguishes the directions of anisotropy, at $3σ$ confidence interval using P-value statistics. After applying a typical method in determining the corresponding scaling exponents in identified anisotropic directions, we are able to determine the kind and ratio of correlation length anisotropy. To demonstrate capability and accuracy of the method, as well validity of analytical relations, our proposed measures are calculated on synthetic stochastic rough interfaces and rough interfaces generated from simulation of ion etching. There are good consistencies between analytical and numerical computations. The proposed algorithm can be mounted with a simple software on various instruments for surface analysis and characterization, such as AFM, STM and etc.

physics.comp-ph↗

arXiv2015

Highly Anistoropic Thermal Conductivity of Arsenene: An ab initio Study

Elemental 2D materials exhibit intriguing heat transport and phononic properties. Here we have investigated the lattice thermal conductivity of newly proposed arsenene, the 2D honeycomb structure of arsenic, using {\it ab initio} calculations. Solving the Boltzmann transport equation for phonons, we predict a highly anisotropic thermal conductivity, of $30.4$ and $7.8$ W/mK along the zigzag and armchair directions, respectively at room temperature. Our calculations reveal that phonons with mean free paths between $20$ nm and $1$ $μ$m provide the main contribution to the large thermal conductivity in the zig-zag direction, mean free paths of phonons contributing to heat transport in the armchair directions range between $20$ and $100$ nm. The obtained low and anisotropic thermal conductivity, and feasibility of synthesis, in addition to other reports on high electron mobility, make arsenene a promising material for a variety of applications, including thermal management and thermoelectric devices.

cond-mat.mtrl-sci↗

arXiv2013

Universality and conformal non-invariance in self-affine rough surfaces

We show numerically that the roughness and growth exponents of a wide range of rough surfaces, such as random deposition with relaxation (RDR), ballistic deposition (BD) and restricted solid-on-solid model (RSOS), are independent of the underlying regular (square, triangular, honeycomb) or random (Voronoi) lattices. In addition we show that the universality holds also at the level of statistical properties of the iso-height lines on different lattices. This universality is revealed by calculating the fractal dimension, loop correlation exponent and the length distribution exponent of the individual contours. We also indicate that the hyperscaling relations are valid for the iso-height lines of all the studied Gaussian and non-Gaussian self-affine rough surfaces. Finally using the direct method of Langlands et.al we show that the contour lines of the rough surfaces are not conformally invariant except when we have simple Gaussian free field theory with zero roughness exponent.

cond-mat.stat-mech↗

arXiv2012

Geometrical exponents of contour loops on synthetic multifractal rough surfaces: multiplicative hierarchical cascade p-model

In this paper, we study many geometrical properties of contour loops to characterize the morphology of synthetic multifractal rough surfaces, which are generated by multiplicative hierarchical cascading processes. To this end, two different classes of multifractal rough surfaces are numerically simulated. As the first group, singular measure multifractal rough surfaces are generated by using the $p$ model. The smoothened multifractal rough surface then is simulated by convolving the first group with a so-called Hurst exponent, $H^*$ . The generalized multifractal dimension of isoheight lines (contours), $D(q)$, correlation exponent of contours, $x_l$, cumulative distributions of areas, $ξ$, and perimeters, $η$, are calculated for both synthetic multifractal rough surfaces. Our results show that for both mentioned classes, hyperscaling relations for contour loops are the same as that of monofractal systems. In contrast to singular measure multifractal rough surfaces, $H^*$ plays a leading role in smoothened multifractal rough surfaces. All computed geometrical exponents for the first class depend not only on its Hurst exponent but also on the set of $p$ values. But in spite of multifractal nature of smoothened surfaces (second class), the corresponding geometrical exponents are controlled by $H^*$, the same as what happens for monofractal rough surfaces.

cond-mat.stat-mech↗

arXiv2009

Scaling Relations for Contour Lines of Rough Surfaces

Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of underlying phenomena. Here, we analyze scaling properties of the cumulative distribution of iso-height loops (i.e., contour lines) of rough self-affine surfaces in terms of loop area and system size. Inspired by the Coulomb gas methods, we find the generating function of the area of the loops. Interestingly, we find that, after sorting loops with respect to their perimeters, Zipf-like scaling relations hold for ranked loops. Numerical simulations are also provided in order to demonstrate the proposed scaling relations.

cond-mat.stat-mech↗

arXiv2005

Elastic properties of small-world spring networks

We construct small-world spring networks based on a one dimensional chain and study its static and quasistatic behavior with respect to external forces. Regular bonds and shortcuts are assigned linear springs of constant $k$ and $k'$, respectively. In our models, shortcuts can only stand extensions less than $δ_c$ beyond which they are removed from the network. First we consider the simple cases of a hierarchical small-world network and a complete network. In the main part of this paper we study random small-world networks (RSWN) in which each pair of nodes is connected by a shortcut with probability $p$. We obtain a scaling relation for the effective stiffness of RSWN when $k=k'$. In this case the extension distribution of shortcuts is scale free with the exponent -2. There is a strong positive correlation between the extension of shortcuts and their betweenness. We find that the chemical end-to-end distance (CEED) could change either abruptly or continuously with respect to the external force. In the former case, the critical force is determined by the average number of shortcuts emanating from a node. In the latter case, the distribution of changes in CEED obeys power laws of the exponent $-α$ with $α\le 3/2$.

cond-mat.dis-nn↗

arXiv2003

Stochastic Analysis and Regeneration of Rough Surfaces

We investigate Markov property of rough surfaces. Using stochastic analysis we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy.

cond-mat.stat-mech↗

arXiv2003

Height Fluctuations and Intermittency of $V_2 O_5$ Films by Atomic Force Microscopy

The spatial scaling law and intermittency of the $V_2 O_5$ surface roughness by atomic force microscopy has been investigated. The intermittency of the height fluctuations has been checked by two different methods, first, by measuring scaling exponent of q-th moment of height-difference fluctuations i.e. $C_q = < |h(x_1) - h(x_2)|^{q} >$ and the second, by defining generating function $Z(q,N)$ and generalized multi-fractal dimension $D_q$. These methods predict that there is no intermittency in the height fluctuations. The observed roughness and dynamical exponents can be explained by the numerical simulation on the basis of forced Kuramoto-Sivashinsky equation.

cond-mat.stat-mech↗