ARTICLE | doi:10.20944/preprints202103.0299.v2
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Multifractals, Self-similarity, Hurst exponent (H), High-speed computer networks, Traffic models.
Online: 12 March 2021 (09:36:16 CET)
This paper proposes a multifractal model, with the aim of providing a possible explanation for the locality phenomenon that appears in the estimation of the Hurst exponent in stationary second order temporal series representing self-similar traffic flows in current high-speed computer networks. It is shown analytically that this phenomenon occurs if the network flow consists of several components with different Hurst exponents.
ARTICLE | doi:10.20944/preprints202105.0502.v2
Subject: Physical Sciences, General & Theoretical Physics Keywords: deterministic chaos; multifractals; effective field theory; Lyapunov exponents; Renormalization Group; selfsimilarity
Online: 24 May 2021 (15:16:54 CEST)
Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.
ARTICLE | doi:10.20944/preprints202104.0654.v1
Subject: Keywords: Multifractals, measure theory, Rényi entropy, generalized dimension, geodesic trajectories, relativistic spacetime.
Online: 26 April 2021 (10:56:12 CEST)
As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.
ARTICLE | doi:10.20944/preprints202011.0518.v1
Subject: Physical Sciences, General & Theoretical Physics Keywords: Self-organized criticality, multifractals, Lagrangian field theory, non-equilibrium dynamics, complexity theory.
Online: 19 November 2020 (16:18:10 CET)
Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.
ARTICLE | doi:10.20944/preprints201710.0096.v1
Subject: Earth Sciences, Environmental Sciences Keywords: complex catchment; weather X-band radars; flash floods; multifractals; spatio-temporal variability
Online: 14 October 2017 (03:10:07 CEST)
This paper presents a comparison between rain gauges, C-band and X-band radar data over an instrumented and regulated catchment of the Paris region, as well as their respective hydrological impacts with the help of flow observations and a semi-distributed hydrological model. Both radars confirm the high spatial variability of the rainfall down to their space resolution (respectively one kilometer and 250 m) and therefore underscore limitations of semi-distributed simulations. The use of the polarimetric capacity of the Météo-France C-band radar was limited to corrections of the horizontal reflectivity and its rainfall estimates are adjusted with the help of a rain gauge network. On the contrary, neither calibration was performed for the polarimetric X-band radar of the Ecole des Ponts ParisTech (below called ENPC X-band radar), nor any optimization of its scans. In spite of that and the non-negligible fact that the catchment was much closer to the C-band radar than to the X-band radar (20 km vs. 40 km), the latter seems to perform at least as well as the former, but with a higher scale resolution. This characteristic was best highlighted with the help of a multifractal analysis of the respective radar data, which also shows that the X-band radar was able to pick up a few extremes that were smoothed out by the C-band radar.
Subject: Physical Sciences, Particle & Field Physics Keywords: Complex Dynamics; Ginzburg-Landau (GL) equation; Chaos and Bifurcations; Multifractals; Self-organized Criticality (SOC); Minimal Fractal Manifold; Fractional Field Theory
Online: 9 November 2020 (08:38:02 CET)
This work is a top-level summary of several contributions published in the last three decades. It makes the case that complex dynamics of nonlinear systems lies at the heart of foundational physics.