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Fractal Growth Phenomena
Tamás Vicsek,Harvey Gould +1 more
TLDR
In this paper, B. Mandelbrot introduced fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces cluster-cluster aggregation (CCA) computer simulations experiments on Laplacian growth new developments.Abstract:
Foreword, B. Mandelbrot introduction fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces cluster-cluster aggregation (CCA) computer simulations experiments on Laplacian growth new developments.read more
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Novel Type of Phase Transition in a System of Self-Driven Particles
TL;DR: Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.
Book
Rhythms of the brain
TL;DR: The brain's default state: self-organized oscillations in rest and sleep, and perturbation of the default patterns by experience.
Journal ArticleDOI
Traffic and related self-driven many-particle systems
Dirk Helbing,Dirk Helbing +1 more
TL;DR: This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic, including microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models.
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Collective Motion
Tamás Vicsek,Anna Zafeiris +1 more
TL;DR: In this paper, the basic laws describing the essential aspects of collective motion are reviewed and a discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, are provided.
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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.