Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneration of spatiotemporal correlated noise in 1+1 dimensions
71
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
Simple analytically solvable models are proposed exhibiting 1/f spectrum in wide range of frequency. The signals of the models consist of pulses (point process) which interevent times fluctuate about some average value, obeying an autoregressive process with very small damping. The power spectrum of the process can be expressed by the Hooge formula. The proposed models reveal possible origin of 1/f noise, i.e., random increments of the time intervals between pulses or interevent time of the process (Brownian motion in the time axis).
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.
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.
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.
Zero temperature limit in (1+1) directed polymers with finite range correlated random potential is studied. In terms of the standard replica technique it is demonstrated that in this limit the considered system reveals the one-step replica symmetry breaking structure similar to the one which takes place in the Random Energy Model. In particular, it is shown that at the temperature $T_{*} sim (u R)^{1/3}$ (where $u$ and $R$ are the strength and the correlation length of the random potential) there is a crossover from the high- to the low-temperature regime. Namely, in the high-temperature regime at $T >> T_{*}$ the model is equivalent to the one with the $delta$-correlated potential where the non-universal prefactor of the free energy is proportional to $T^{-2/3}$, while at $T << T_{*}$ this non-universal prefactor saturates at a finite (temperature independent) value.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
