Narrow Results

The materials with a perovskite phase have been in the limelight due to their power conversion efficiency (PSC) in solar cells. New perovskite materials are essential to predict the abundant availability of efficient materials for technological applications. Mechanical properties can predict the mechanical stability of crystals. Therefore, it is very important to know their mechanical parameters. So, in this work, the elastic constants $C_{11}$, $C_{12}$ and $C_{44}$ of the cubic chloride perovskites (ABCl${}_3)$ have been determined through first principles study using density functional theory by using the Chirpan method integrated with WIEN2k. After calculating the elastic constants, we have also calculated different moduli like Shear, Bulk and Young moduli, different parameters like Kleinman’s constant, Lame constants, Chung–Buessem anisotropy index, universal anisotropic index, acoustic behavior and its anisotropy, hardness, melting temperature, Poisson ratios by using different formulas in connection with the elastic constants. It has been found that the studied compounds possess low resistance to the plastic deformations. It has also been found that the majority of the materials possess a central type of force because Poisson’s ratio is greater than 0.25. It has been studied that six out of eighteen new perovskites were brittle and the rest were ductile. The anisotropy of the materials was checked and found that all the materials are anisotropic elastically. This work is useful for the synthesis of these new perovskites.

In this work, we investigate the influence of substrate temperature on the surface morphology for substrate coverage below one monolayer. The model of film growth is based on random deposition enriched by limited surface diffusion. Also, anisotropy in the growth is involved. We found from computer simulations for the simple cubic lattice and solid-on-solid model that the surface morphology changes with increasing temperature from isotropically distributed isolated small islands through anisotropic 1D stripes to larger 2D anisotropic islands and again randomly distributed single atoms. The transition is also marked in height–height correlation function dependence on temperature as directly seen by snapshots from simulations. The results are in good qualitative agreement with already published results of kinetic Monte Carlo simulations as well as with some experimental data.

The Grüneisen parameter for covalent crystals is calculated by employing an angular force model with eight parameters and using a 6–12 potential [Lennard–Jones potential (L–J)] whereas for ionic crystals, it is calculated by employing the Daniel's method, which uses anisotropy factor tables f(s,t) of de Launay.

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B.

Two extended cooperative driving lattice hydrodynamic models are proposed by incorporating the intelligent transportation system and the backward-looking effect in traffic flow under certain conditions. They are the lattice versions of the hydrodynamic model of traffic: one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference-difference equation in which both time and space variables are discrete. In light of the real traffic situations, the appropriate forward and backward optimal velocity functions are selected, respectively. Then the stability conditions for the two models are investigated with the linear stability theory and it is found that the new consideration leads to the improvement of the stability of traffic flow. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations. Moreover, the anisotropy of traffic flow is further discussed through examining the negative propagation velocity as the effect of following vehicle is involved.

Site invasion percolation (IP) processes are combined with bond percolation model, to study the effects of size restriction on low capillary number immiscible displacement in heterogeneous nanoporous media. Both cases of compressible (NTIP) and incompressible defender fluid (TIP) are considered. It is found that in site IP the value of mass uptake increases with the size of invader particles, if the latter is not greater than a critical value. This occurs when the accessible porosity of the medium decreases as the size of fluid particles increases. We also investigate the effect of nanopore's concentration on the mass and the anisotropy of sample spanning cluster as well as the critical exponent of trap numbers.

In this paper, we have tried to point out the features of the correlation between the lanes of a two-lane road, created by the entry of this facility. For this purpose, we have adopted a quasi-one-dimensional system composed of a diverging node connecting two roads and where no lanes’ changing is allowed. Our study has highlighted the strong effect of a node. We have found that if we create a disturbance in one lane, a spontaneous symmetry breaking occurs in the whole system. In fact, a self-anisotropy is produced at the node, to which the system responds via a self-organization mechanism. Those results have urged us to investigate the anisotropy as an extrinsic parameter. By privileging one lane over the other at the node, we have been able to confirm that the system can always get self-organized and that three phases can be established: the symmetric high density phase, the asymmetric low density phase and the asymmetric phase of transition low density/high density. Finally, we have found that the system is strongly correlated when it is in a symmetric phase, and is not when in an asymmetric phase. This finding brought us to the assumption that the cross-correlation of the observables of a quasi-one-dimensional system can be considered as an order parameter that defines the phases’ transitions.

The equilibrium behaviors of the anisotropic XY ferromagnet, with nonmagnetic impurity, have been investigated in three dimensions by Monte Carlo simulation using Metropolis algorithm. Two different types of anisotropy, namely, the bilinear exchange type and single-site anisotropy are considered here. The thermodynamic behaviors of the components of the magnetizations (M), susceptibility ($\chi$) and the specific heat (C) have been studied systematically through extensive Monte Carlo simulations. The ferro–para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ($T_c^{\ast }$) has been found to decrease as the system gets more and more impure (impurity concentration p increases). In the case of bilinear exchange type of anisotropy ($\lambda$), the pseudocritical temperature ($T_c^{\ast }$) increases linearly with $\lambda$ for any given concentration of nonmagnetic impurity (p). The slope of this linear function has been found to depend on the impurity concentration (p). The slope decreases linearly with the impurity concentration (p). In the case of the single-site anisotropy (D), the pseudocritical temperature ($T_c^{\ast }$) has been found to decrease linearly with p for fixed D. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth-order Binder cumulants ($U_L$) for different system sizes (L). The critical magnetization ($M(T_c)$) and the maximum value of the susceptibility (${\chi }_p$) are calculated for different system sizes (L). The critical exponents for the assumed scaling laws, $M(T_c)\sim L^{-\frac{\beta }{\nu }}$ and ${\chi }_p\sim L^{\frac{\gamma }{\nu }}$, are estimated through the finite size analysis. We have estimated, $\frac{\beta }{\nu }$, equals $0.48\pm 0.05$ and $0.37\pm 0.04$ for bilinear exchange and single-site anisotropy, respectively. We have also estimated, $\frac{\gamma }{\nu }$ equals $1.78\pm 0.05$ and $1.81\pm 0.05$ for bilinear exchange and single-site anisotropy, respectively.

We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of self-similar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides — for simulations of texture as well as for detection of anisotropies in an image — a large class of models with controlled anisotropic geometries and structures.

The effect of model size on fluid flow through fractal rough fractures under shearing is investigated using a numerical simulation method. The shear behavior of rough fractures with self-affine properties was described using the analytical model, and the aperture fields with sizes varying from 25 to 200mm were extracted under shear displacements up to 20mm. Fluid flow through fractures in the directions both parallel and perpendicular to the shear directions was simulated by solving the Reynolds equation using a finite element code. The results show that fluid flow tends to converge into a few main flow channels as shear displacement increases, while the shapes of flow channels change significantly as the fracture size increases. As the model size increases, the permeability in the directions both parallel and perpendicular to the shear direction changes significantly first and then tends to move to a stable state. The size effects on the permeability in the direction parallel to the shear direction are more obvious than that in the direction perpendicular to the shear direction, due to the formation of contact ridges and connected channels perpendicular to the shear direction. The variances of the ratio between permeability in both directions become smaller as the model size increases and then this ratio tends to maintain constant after a certain size, with the value mainly ranging from 1.0 to 3.0.

This paper introduces a modified DLA model, based on a fractional diffusion mechanism, as a novel approach to modeling fractal growth. The specific memory performance of fractional operators can be reflected macroscopically in aggregated patterns eventually. The influence of the model’s order on the structure and behavior of its pattern is further quantitatively described by anisotropy index and fractal dimension. Some simulations are provided to illustrate the correctness and effectiveness of the main results.

Hydraulic tortuosity is one of the key parameters for evaluating effective transport properties of natural and artificial porous media. A pore-scale model is developed for fluid flow through porous media based on fractal geometry, and a novel analytical tortuosity–porosity correlation is presented. Numerical simulations are also performed on two-dimensional Sierpinski carpet model. The proposed fractal model is validated by comparison with numerical results and available experimental data. Results show that hydraulic tortuosity depends on both statistical and morphological characteristics of porous media. The exponents for the scaling law between tortuosity and porosity depend on pore size distribution and tortuous fractal dimension. It has been found that hydraulic tortuosity indicates evident anisotropy for asymmetrical particle arrangements under the same statistical characteristics of porous media. The present work may be helpful to understand the transport mechanisms of porous materials and provide guidelines for the development of oil and gas reservoir, water resource and chemical engineering, etc.

We used multifractals to analyze the Lebanese topography focusing on Mount Lebanon. The elevation data were obtained from NASA STRM Global Digital Elevation of Earth Land, spaced at 80m in the East-West direction, and at 90m in the North-South direction. After transforming the grid to be perpendicular and parallel to the range, we found anisotropic scaling from 500m to 10,000m, and it reflected the fact that the Lebanese topography was more correlated in the direction perpendicular to the mountain range, probably due to occurrence of valleys and ridges in that direction. We estimated the parameters of the Universal Multifractal (UM) model and found $\alpha =1.45$ and $c1=0.05$, consistent with values reported for topography. The UM parameter $H$ was found to be 0.72 across the range and 0.57 along the range, the latter value agrees with prior observations. However, the larger value across the range is consistent with the higher spatial correlation in that direction. We introduced a new expression for the 2D power spectral density, and we showed that it can decently capture the anisotropic scaling. We also generated multiple realizations and we showed that the generation of anisotropic scaling did not alter the underlying parameter values $\alpha$ and $c1$ of the UM model. We also proposed an approximate method for generating conditional simulations, and we showed that through a judicious selection of values, one may reproduce approximately the observed field values at the desired locations. We believe such an approach could be used to generate realistic simulations of fields that are time-invariants, such as topography and soil properties.

An in-depth understanding of the deterioration characteristics of porous rock materials in freeze–thaw (F–T) environments is very important for rock mass engineering in cold regions. However, quantitative descriptions of key rock indicators such as porosity, permeability, and anisotropy are lacking. In this paper, computed tomography (CT) was used to study saturated intact sandstone, saturated fractured sandstone, and ice-filled fractured sandstone under various F–T cycles and stress states. Meso-structural parameters were obtained by reconstructing the three-dimensional fracture networks from CT images. Then, based on fractal geometry theory, the fractal dimension ($D_F)$, tortuosity fractal dimension ($D_T)$, and anisotropic two-dimensional fractal dimension ($D_A)$ of the sandstone samples were analyzed quantitatively. The $D_F$ gradually increased during the F–T process, while $D_T$ gradually decreased. Compared with $D_F$, $D_T$ was found to describe changes in the absolute permeability of rocks under F–T cycling more accurately. Anisotropy in sandstone was enhanced by F–T cycling. After uniaxial compression, the $D_A$ value was the greatest in ice-filled fractured sandstone. In addition, the tree-like fracture structure produced by F–T cycling expanded the range of self-similarity, which enhanced the fractal characteristics of sandstone. However, due to the large frost heave pressure of ice-filled sandstone, fracture expansion accelerated in the later period of F–T cycling, which destroyed the self-similarity. These results assist in understanding the F–T characteristics of porous rock materials. The method described provides a new way to better evaluate and predict F–T-related engineering disasters.

In this study, two-dimensional (2D) fractal parameters ($D_{RL}$ and $A$ as well as $D_v$ and $K_v)$ calculated through the roughness length, and variogram methods, and a three-dimensional (3D) fractal parameter, $D_s$ calculated through the 3D modified divider method were used to investigate some important factors that could influence the accurate quantification of rock joint roughness. The results showed that nonstationarity resulting from a linear trend did not have any effect on $D_v$ and $K_v$ (variogram method). A significant effect of heterogeneity was found on all the computed 2D and 3D fractal roughness metrics; irrespective of the $X$ value, the $Y$(0–500mm) section of the joint surface was found to be relatively homogeneous with a low level of roughness while the $Y$(750–1000mm) section of the joint surface had a higher level of roughness. For the relatively homogeneous section, the 2D fractal parameters indicated no joint size effect. For the whole rock joint, which is somewhat heterogeneous, the results showed negligible joint size effect on $D_{RL}$ and $A$ for all investigated profiles while $D_v$ and $K_v$ values showed negligible joint size effect and small joint size effect for profiles in the $X$ and $Y$ directions, respectively. Also, the results showed a significant reduction in roughness variability with an increase in joint size. A negligible effect of joint size was found on $D_s$ for the joint surface. These findings indicated that the roughness heterogeneity is most likely the reason for the conflicting observations in the literature regarding the effect of scale on joint roughness. The studied joint surface exhibited anisotropy resulting from a shear joint.

The pores and fissures in loaded rock masses are the main channels for underground flow, and may cause serious accidents during the development of groundwater resources. This work presents an efficient method for analyzing the microstructure of the loaded rock mass using fractal theory and computed tomography (CT) scanning. A relation between the microstructure features of the sandstone porosity, fractal dimension, and loading stress is developed using an image identification technique. The results demonstrate that the distribution trends of sandstone samples’ slice porosities in the xz- and yz-directions are nearly identical, and the distribution in the xy-direction differs significantly from those in xz- and yz-directions. The total and connected porosities increase with the increase of stress, and the change can be fitted to straight lines. The fractal dimensions of the pores change significantly with stress or loading stress in the xy-direction.