Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPercolation in deposits for competitive models in (1+1)-dimensions
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry. These models are based on the combination of ballistic deposition (BD) and random deposition (RD) models or BD and Family deposition (FD) models. Numerically we find, that for pure RD, FD or BD models the mean height of the percolation deposit $bar h$ grows with the substrate length $L$ according to the generalized logarithmic law $bar hpropto (ln (L))^gamma$, where $gamma=1.0$ (RD), $gamma=0.88pm 0.020$ (FD) and $gamma=1.52pm 0.020$ (BD). For BD model, the scaling law between deposit density $p$ and its mean height $bar h$ at the point of percolation of type $p-p_infty propto bar h^{-1/ u_h}$ are observed, where $ u_h =1.74pm0.02$ is a scaling coefficient. For competitive models the crossover, %in $h$ versus $L$ corresponding to the RD or FD -like behaviour at small $L$ and the BD-like behaviour at large $L$ are observed.
rate research
Read More
We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented triangular lattice shows a continuous transition at a non-trivial p_c. On the augmented triangular lattice we find, by extensive numerical simulation, that the directed rigidity percolation transition belongs to the same universality class as directed percolation. The same conclusion is reached by studying its surface critical behavior, i.e. the spreading of rigidity from finite clusters close to a non-rigid wall. Near the discontinuous transition at p=1 on the triangular lattice, we are able to calculate the finite-size behavior of the density of rigid sites analytically. Our results are confirmed by numerical simulation.
Consider nearest-neighbor oriented percolation in $d+1$ space-time dimensions. Let $rho,eta, u$ be the critical exponents for the survival probability up to time $t$, the expected number of vertices at time $t$ connected from the space-time origin, and the gyration radius of those vertices, respectively. We prove that the hyperscaling inequality $d ugeeta+2rho$, which holds for all $dge1$ and is a strict inequality above the upper-critical dimension 4, becomes an equality for $d=1$, i.e., $ u=eta+2rho$, provided existence of at least two among $rho,eta, u$. The key to the proof is the recent result on the critical box-crossing property by Duminil-Copin, Tassion and Teixeira (2017).
We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation is given. The process is an alternative to a recently proposed spatiotemporal correlated model process [J. Garcia-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate explicitely the hitherto not known autocorrelation function in real space.
We derive a selection rule among the $(1+1)$-dimensional SU(2) Wess-Zumino-Witten theories, based on the global anomaly of the discrete $mathbb{Z}_2$ symmetry found by Gepner and Witten. In the presence of both the SU(2) and $mathbb{Z}_2$ symmetries, a renormalization-group flow is possible between level-$k$ and level-$k$ Wess-Zumino-Witten theories only if $kequiv k mod{2}$. This classifies the Lorentz-invariant, SU(2)-symmetric critical behavior into two symmetry-protected categories corresponding to even and odd levels,restricting possible gapless critical behavior of translation-invariant quantum spin chains.
We construct Holographic Space-time models that reproduce the dynamics of $1 + 1$ dimensional string theory. The necessity for a dilaton field in the $1 + 1$ effective Lagrangian for classical geometry, the appearance of fermions, and even the form of the universal potential in the canonical $1$ matrix model, follow from general HST considerations. We note that t Hoofts ansatz for the leading contribution to the black hole S-matrix, accounts for the entire S-matrix in these models in the limit that the string scale coincides with the Planck scale, up to transformations between near horizon and asymptotic coordinates. These $1 + 1$ dimensional models are describable as decoupling limits of the near horizon geometry of higher dimensional extremal black holes or black branes, and this suggests that deformations of the simplest model are equally physical. After proposing a notion of relevant deformations, we describe deformations, which contain excitations corresponding to linear dilaton black holes, some of which can be considered as UV completions of the CGHS model. We study the question of whether the AMPS paradox can be formulated in those models. It cannot, because the classical in-fall time to the singularity of linear dilaton black holes, is independent of the black hole mass. This result is reproduced by our HST models. We argue that it is related to the absence of quasi-normal modes of these black hole solutions, which is itself related to the fact that the horizon has zero area. This is compatible with the resolution of the AMPS paradox proposed in previous work with Fischler, according to which the compatibility conditions of HST identify the long non-singular sojourn of observers behind the horizon, with the dynamics of equilibration on the horizon as seen by a detector which has not yet fallen through the horizon.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
