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One of the most common methods of strengthening concrete structures is the use of composite fibers such as FRP. These fibers have found a special place in structural retrofitting methods due to a number of specific ability including lightness and ease of performance. Reinforced concrete structures have long been considered by design engineers for the possibility of retrofitting high strength composite steel structures. In this study, twenty-two steel beam models were modeled by ANSYS software. Variable parameters studied in the modeled steel beams can be referred to the number, orientation and thickness of composite layers.

One of the factors affecting the dynamic state of the dams that may cause damages to the dam is the change under the spatial and temporal Excitation of the Heterogeneous ground Motion. Therefore, in different states the stress, strain, displacement and hydrostatic pressure indices are changed and led to serious damage to the dam. In this study, Karun 3 dam is investigated which is classified as one of the double curvature arch and gravity dams. For this purpose, using ABAQUS software, these indices have been investigated and controlled and the effectiveness of indices in this dam has been investigated in nonlinear dynamic seismic state. Northridge, Kobe, Bam, Hector, Chi-Chi and Manjil earthquakes are applied to the Karun 3 Dam. The results showed that due to the large amplitude and periodicity of the near-fault mappings, under the near-field earthquake, the deformation of the Karun 3 dam is greater than the far-field fault zone. As the height of the Karun 3 Dam rises, the effectiveness of far-field earthquakes declines and near-field earthquakes show more impact on the structure. In far-field earthquakes, stress changes due to earthquakes with maximum dynamic acceleration, the relative percentage of mises stress change is 15.5% and maximum dam crest change is 68.5 mm, and for near-field earthquakes is 25% and maximum dam crest change is 100 mm.

We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the plane. The probability density to find the walker at a given distance from the origin either in a line or in the plane geometry is exactly calculated as a function of time t. We find that the large time asymptotic behavior of the walker for any arbitrary number $n_l$ of lines is eventually governed by the plane geometry after a crossover time approximately given by $t_c\propto n_l^2$. We show that this competition can be changed in favor of the line geometry by switching on an arbitrarily small perturbation of a drift term in which even a weak biased walk is able to drain the whole probability density into the line at long time limit. We also present the results of our extensive simulations of the model which perfectly support our analytical predictions. Our method can, however, be simply extended to other crossing geometries with a single common point., Comment: 6 pages, 6 figures

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom (TW) distribution for p0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow., 5 pages, 6 figures, Phys. Rev. Lett. (2019) (accepted)

We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been carried out to measure the global interfacial width as a function of temperature for different lattice sizes which is shown to signal the criticality of the model at $T_c$ by forming a size-independent cusp in 3D, along with an emergent super-roughening at its 2D cross section. We find that the super-rough state is accompanied by an intrinsic anomalous scaling behavior in the local properties characterized by a set of geometric exponents which are the same as those for a pure 2D Ising model., Comment: 5 pages, 6 figures, to appear in Phys. Rev E(Rapid Communication)

The statistical properties of the carrier density profile of graphene in the ground state in the presence particle-particle interaction and random charged impurity in zero gate voltage has been recently obtained by Najafi \textit{et al.} (Phys. Rev E95, 032112 (2017)). The non-zero chemical potential ($\mu$) in gated graphene has non-trivial effects on electron-hole puddles, since it generates mass in the Dirac action and destroys the scaling behaviors of the effective Thomas-Fermi-Dirac theory. We provide detailed analysis on the resulting spatially inhomogeneous system in the framework of the Thomas-Fermi-Dirac theory for the Gaussian (white noise) disorder potential. We show that, the chemical potential in this system as a random surface, destroys the self-similarity, and the charge field is non-Gaussian. We find that the two-body correlation functions are factorized to two terms: a pure function of the chemical potential and a pure function of the distance. The spatial dependence of these correlation functions is double-logarithmic, e.g. the two-point density correlation $D_2(r,\mu)\propto \mu^2\exp\left[-\left(-a_D\ln\ln r^{\beta_D}\right)^{\alpha_D} \right]$ ($\alpha_D=1.82$, $\beta_D=0.263$ and $a_D=0.955$). The Fourier power spectrum function behaves like $\ln(S(q))=-\beta_S^{-a_S}\left(\ln q \right)^{a_S}+2\ln \mu$ ($a_S=3.0\pm 0.1$ and $\beta_S=2.08\pm 0.03$) in contrast to the ordinary Gaussian rough surfaces for which $a_S=1$ and $\beta_S=\frac{1}{2}(1+\alpha)^{-1}$, ($\alpha$ being the roughness exponent). The geometrical properties are however similar to the un-gated ($\mu=0$) case, with the exponents that are reported in the text., Comment: arXiv admin note: text overlap with arXiv:1609.07096

In many situations we are interested in the propagation of energy in some portions of a three dimensional system with dilute long-range links. In this paper sandpile model is defined on the three-dimensional small world network with real dissipative boundaries and the energy propagation is studied in three-dimensions as well as the two-dimensional cross sections. Two types of cross section are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long range links ($\alpha$) increases. This trend is numerically shown to be power law in a manner described in the paper. Two regimes of $\alpha$ are considered in this work. For sufficiently small $\alpha$s the dominant behavior of the system is just like that of the regular BTW, whereas for the intermediate values the behavior is non-trivial with some exponents that are reported in the paper. It is shown that the spatial extent up to which the statistics is similar to the regular BTW model scales with $\alpha$ just like the dissipative BTW model with the dissipation factor (mass in the corresponding ghost model) $m^2\sim \alpha$ for the three-dimensional system as well as its two-dimensional cross-sections.

The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections. We use the moment analysis to extract the exponents for two separate cases: the critical ($p=p_c\equiv p_c^{3D}$) and the off-critical ($p_c

We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension ${D}_{u}=4$. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the $d$-dimensional cross sections and the $d$-dimensional BTW model for $d=2$ and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops ${d}_{f}$, which is found to be $1.50\ifmmode\pm\else\textpm\fi{}0.02\ensuremath{\approx}\frac{3}{2}={d}_{f}^{\text{GFF}}$.

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature T_{c} the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to D_{f}^{SAW}=4/3. Also, the corresponding open curves has conformal invariance with the root-mean-square distance R_{rms}∼t^{3/4} (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T=T_{c} the model has some aspects compatible with the 2D BTW model (e.g., the 1/log(L)-dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1/L-dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T=T_{c}. In the off-critical temperatures in the close vicinity of T_{c} the exponents show some additional power-law behaviors in terms of T-T_{c} with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L^{1/2}, which is different from the regular 2D BTW model.

We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively in a percolation process, which leads to a sudden growth of the boundary domains. For two-dimensional square lattices of linear dimension L, independent of the models studied here, we find that the maximum of the boundary interface width, the susceptibility χ, exhibits the scaling χ ~ Lγ with the universal exponent γ = 1. The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the the universal scaling of χ.

Scientific Reports 6: Article number: 21110;10.1038/srep21110 published online February222016; updated: June232016 The original version of this Article contained errors. H. Dashti-Naserabadi and A. Abbasi were incorrectly listed as being affiliated with ‘Department of Physics, Plasma and Condensed Matter Computational Laboratory, Azarbaijan Shahid Madani University, Tabriz 53714-161, Iran’ and ‘Physics and Accelerators Research School, NSRTI 11365-3486, Tehran, Iran’ respectively. The correct affiliations are listed below: H. Dashti-Naserabadi Physics and Accelerators Research School, NSRTI 11365-3486, Tehran, Iran A. Abbasi Department of Physics, Plasma and Condensed Matter Computational Laboratory, Azarbaijan Shahid Madani University, Tabriz 53714-161, Iran In the Abstract, “The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the the universal scaling of χ.” now reads: “The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the universal scaling of χ.” In the legend of Figure 1, “The (bottom) boundary domain consists of a single cluster (light blue) that evolves by merging with other neighboring clusters from the initial set of the L bottom sites (i = 0 to i = L − 1; j = 0).” now reads: “The (bottom) boundary domain consists of a single cluster (light blue) that evolves by merging with other neighboring clusters from the initial set of the L bottom sites (i = 0 to L - 1; j = 0).” In the legend of Figure 5, “Size Δ of the largest gap in w for a collection of continuous and discontinuous cluster percolation models. Specifically, for rnd-rule (○ ), 2nd-max-rule (W), 3rd-max-rule (◇), fractional (Δ, f = 0.5), all yielding discontinuous percolation, and max-max-rule (select at random a cluster and merge the two largest clusters that are neighbors of each other among the selected cluster and all its neighbors), yielding continuous percolation, Δ as a function of lattice size L is shown. 800 realizations for each data point. Error bars are smaller than symbol size.” now reads: “The maximal gap in w. Size Δ of the largest gap in w for a collection of continuous and discontinuous cluster percolation models. Specifically, for fractional f= 0 (∘), max-rule (☆), rnd-rule (□), all yielding discontinuous percolation, and site-percolation (▿), yielding continuous percolation, Δ as a function of lattice size L is shown. 10^5 realizations for each data point. Error bars are smaller than symbol size.” These errors have now been corrected in the PDF and HTML versions of the Article.

We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively in a percolation process, which leads to a sudden growth of the boundary domains. For two-dimensional square lattices of linear dimension L, independent of the models studied here, we find that the maximum of the boundary interface width, the susceptibility χ, exhibits the scaling χ ~ Lγ with the universal exponent γ = 1. The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the universal scaling of χ., Scientific Reports, 6, ISSN:2045-2322

We consider the three-dimensional (3D) Bak-Tang-Wiesenfeld model in a cubic lattice. Along with analyzing the 3D problem, the geometrical structure of the two-dimensional (2D) cross section of waves is investigated. By analyzing the statistical observables defined in the cross sections, it is shown that the model in that plane (named as 2D-induced model) is in the critical state and fulfills the finite-size scaling hypothesis. The analysis of the critical loops that are interfaces of the 2D-induced model is of special importance in this paper. Most importantly, we see that their fractal dimension is D(f)=1.387±0.005, which is compatible with the fractal dimension of the external perimeter of geometrical spin clusters of 2D critical Ising model. Some hyperscaling relations between the exponents of the model are proposed and numerically confirmed. We then address the problem of conformal invariance of the mentioned domain walls using Schramm-Lowener evolution (SLE). We found that they are described by SLE with the diffusivity parameter κ=2.8±0.2, nearly consistent with observed fractal dimension.

Although fluctuations in the waiting time series have been studied for a long time, some important issues such as its long-range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied. Here we find that the ``waiting times'' series for a given increment level have long-range correlations with Hurst exponents belonging to the interval $1/2lHl1$. We also study positive-negative level asymmetry of the waiting time distribution. We find that the logarithmic difference of waiting times series has a short-range correlation, and then we study its stochastic nature using the Markovian method and determine the corresponding Kramers-Moyal coefficients. As an example, we analyze the velocity fluctuations in high Reynolds number turbulence and determine the level dependence of Markov time scales, as well as the drift and diffusion coefficients. We show that the waiting time distributions exhibit power law tails, and we were able to model the distribution with a continuous time random walk.

We study (2+1)-dimensional single step model (SSM) for crystal growth including both deposition and evaporation processes parametrized by a single control parameter $p$. Using extensive numerical simulations with a relatively high statistics, we estimate various interface exponents such as roughness, growth and dynamic exponents as well as various geometric and distribution exponents of height clusters and their boundaries (or iso-height lines) as function of $p$. We find that, in contrary to the general belief, there exists a critical value $p_c\approx 0.25$ at which the model undergoes a roughening transition from a rough phase with $pp_c$, asymptotically in the Edwards-Wilkinson (EW) class. We validate our conclusion by estimating the effective roughness exponents and their extrapolation to the infinite-size limit., Comment: 7 pages, 18 figures

Statistical behavior and scaling properties of isoheight lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution $({\text{SLE}}_{\ensuremath{\kappa}})$. We present some evidence that the isoheight lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently ${\text{SLE}}_{8/3}$. This leads to the conclusion that all these discrete growth models fall into the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in two dimensions.

Statistical behavior and scaling properties of isoheight lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE_{κ}). We present some evidence that the isoheight lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently SLE_{8/3}. This leads to the conclusion that all these discrete growth models fall into the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in two dimensions.

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_\kappa) with diffusivity of \kappa=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., Comment: 5 pages, 5 figures, accepted for publication in EuroPhysics Letters (EPL)

Appreciation of Stochastic Loewner evolution (SLE$_\kappa$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model (ASM) are numerically shown to be conformally invariant and can be described by SLE with diffusivity $\kappa=2$. This value is the same as value obtained for loop erased random walks (LERW). The fractal dimension and Schramm's formula for left passage probability also suggest the same result. We also check the same properties for Zhang's sandpile model., Comment: 6 pages, 4 figures

We insert some asymmetries in the continuous Abelian sandpile models, such as directedness and ellipticity. We analyze probability distribution of different heights and also find the field theory corresponding to the models. Also we find the fields associated with some height variables., 14 Pages, 11 Figures

We study numerically the statistics of curves which form the boundaries of toppling wave clusters in the deterministic Bak, Tang and Wiesenfeld sandpile model and stochastic Manna model on a square lattice. We consider the Abelian version of each model. Multiple tests show that the boundary of toppling wave clusters in both deterministic and stochastic models can be described by SLEκ curves with diffusivity κ = 2.

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2., 24 pages, 5 figures