Method for generating long-range correlations for large systems.

@article{Makse1996MethodFG,
  title={Method for generating long-range correlations for large systems.},
  author={Makse and Havlin and Schwartz and Stanley},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={53 5},
  pages={
          5445-5449
        }
}
  • Makse, Havlin, +1 author Stanley
  • Published 4 December 1995
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation. 
ON GENERATING RANDOM POTENTIALS
The study of transport and diffusion of Brownian particles in disorder media needs the generation of random potentials with well prescribed statistical properties. Here we present a straightforward
Regular Article: Generation of Short and Long Range Temporal Correlated Noises
We present the implementation of an algorithm to generate Gaussian random noises with prescribed time correlations that can be either long or short ranged. Examples of Langevin dynamics with short
Long-Range Temporal Correlations in Kinetic Roughening
We introduce a class of generalized Langevin-type growth equations exhibiting long-ranged temporal correlations in kinetic roughening, and investigate memory effects and dynamic scaling behavior
Percolation in networks with long-range connections
Two-dimensional lattices of points are connected with long-range links, whose lengths are distributed according to P(r)∼r-α. By changing the decay exponent α one can go from d-dimensional short-range
Generation of correlated binary sequences from white noise.
We suggest a method for generation of random binary sequences of elements 0 and 1, with prescribed correlation properties. It is based on a modification of the widely used convolution method of
Recent advances and open challenges in percolation
TLDR
A very brief overview of more than 60 years of work inercolation is presented and several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation are discussed.
Role of short-range correlation in facilitation of wave propagation in a long-range ladder chain
Abstract We extend a new method for generating a random chain, which has a kind of short-range correlation induced by a repeated sequence while retaining long-range correlation. Three distinct
Generation of long-range correlations in large systems as an optimization problem.
  • H. Hamzehpour, M. Sahimi
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
TLDR
This work formulate the problem of generating the long-range correlations as one of optimization, and utilize simulated annealing to generate a d-dimensional array which contains the correlations and honors the existing data.
Power-law correlated processes with asymmetric distributions.
TLDR
A stochastic process is proposed that can model power-law correlations together with an asymmetry in the probability distribution and is applied to air humidity data and finds that the statistical properties of the process are in a good agreement with those observed in the data.
Anderson localization in a correlated landscape near the band edge
We study the Anderson localization in a potential landscape with long-range power-law correlations in one dimension. We find that, for energies E close to the band edge of the unperturbed energy
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 15 REFERENCES
Fractal Growth Phenomena
Foreword, B. Mandelbrot introduction fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces
The science of fractal images
TLDR
Fractal Modelling of Real World Images and a Unified Approach to Fractal Curves and Plants are studied.
Fundamentals of Statistical and Thermal Physics
This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical
Numerical Recipes: FORTRAN
TLDR
The Diskette v 2.04, 3.5'' (720k) for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
Fundamental Algorithms for Computer Graphics
TLDR
Theoretical and Linguistic methods for Describing Straight Lines, and an application of Euclid's Algorithm to Drawing Straight Lines.
͓1͔ Dynamics of Fractal Surfaces
  • ͓1͔ Dynamics of Fractal Surfaces
  • 1991
Rev. Lett. Nature
  • Rev. Lett. Nature
  • 1438
0ϽHϽ1/2) cannot be obtained using ͑4͒. In this case, the correlation function must satisfy C(l )ϳϪl Ϫ␥ , for l →ϱ, and ͐ 0 ϱ C(l )dl ϭ0 ͓13͔
  • ͓15͔ Antipersistent behavior
387 ͑1984͒. 53 5449 METHOD FOR GENERATING LONG-RANGE CORRELATIONS
  • 387 ͑1984͒. 53 5449 METHOD FOR GENERATING LONG-RANGE CORRELATIONS
...
1
2
...