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 $\delta_c$ 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 $-\alpha$ with $\alpha \le 3/2$.Comment: 16 pages, 14 figures, 1 table, published versio

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.Comment: 4 pages, 7 figure

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

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, $\xi$, and perimeters, $\eta$, 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.Comment: 14 pages, 14 figures and 6 tables; V2: Added comments, references, table and major correction

Height Fluctuations and Intermittency of V2O5V_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. $C_q =$ 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.Comment: 6 pages (two columns), 11 eps. figures, late

Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models

© 2016 American Physical Society. We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal, or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that the PFC approach is able to predict realistic formation energies and defect structures of grain boundaries. We provide an in-depth comparison of the formation energies between PFC, DFT, and molecular dynamics (MD) calculations. The DFT and MD calculations are initialized using atomic configurations extracted from PFC ground states. Finally, we use the PFC approach to explicitly construct large realistic polycrystalline samples and characterize their properties using MD relaxation to demonstrate their quality