The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics

Nicolás-Carlock, J. R.; Solano-Altamirano, J. Manuel; Carrillo-Estrada, J. L.

doi:10.1016/j.chaos.2020.109649

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…The morphology of these systems seem to solve an adaptive exploration problem related to the maximization of the space that a connected structure can cover in order to retain or gain conditions for survival given limited amounts of matter, energy and information, and according to the demands of the environment 25 – 28 . One characteristic of these systems is their physical fractality, often quantified by the fractal dimension 19 , 29 – 31 . However, although the fractal dimension is a good global measure of morphological complexity, it does not provide a comprehensive account of the micro structural features that could make branched morphologies relevant at the macro level for the system’s biological function 22 , 32 – 34 .…”

Section: Discussionmentioning

confidence: 99%

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

Flores-Ortega,

Nicolás-Carlock,

Carrillo-Estrada

2023

Sci Rep

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The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal morphology. Under a geometric graphs approach, we quantify the effectiveness of the exchange of information in the system from center to perimeter and over the entire network structure. We mainly consider two paradigmatic models of disordered fractal formation, the Ballistic Aggregation and Diffusion-Limited Aggregation models, and complementary, the Viscek and Hexaflake fractals, and Kagome and Hexagonal lattices. First, we show that complex tree morphologies provide important advantages over regular configurations, such as an invariant structural cost for different fractal dimensions. Furthermore, although these systems are known to be scale-free in space, they have bounded degree distributions for different values of an euclidean connectivity parameter and, therefore, do not represent ordinary scale-free networks. Finally, compared to regular structures, fractal trees are fragile and overall inefficient as expected, however, we show that this efficiency can become similar to that of a robust hexagonal lattice, at a similar cost, by just considering a very short euclidean connectivity beyond first neighbors.

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Section: Discussionmentioning

confidence: 99%

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

Flores-Ortega,

Nicolás-Carlock,

Carrillo-Estrada

2023

Sci Rep

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“…Because the functionals

and

can be related to the entropy of dilute gases, either classical or quantum, the fact that these functionals are defined over a system divided into cells enables their use for defining the entropy of out-of-equilibrium systems, other than dilute gases. Specifically, and derived from our previous work (e.g., [ 30 , 31 ]), the

and

functionals may serve to describe the entropy, as well as the entropy generation, occurring during the growth of complex physical systems, such as fractals. Possibly, studying these systems might also shed light on the explicit functional form of

and

.…”

Section: Comments and Remarksmentioning

confidence: 99%

Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes

Medel-Portugal

Solano-Altamirano

Carrillo-Estrada

2021

Entropy

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We propose a novel framework to describe the time-evolution of dilute classical and quantum gases, initially out of equilibrium and with spatial inhomogeneities, towards equilibrium. Briefly, we divide the system into small cells and consider the local equilibrium hypothesis. We subsequently define a global functional that is the sum of cell H-functionals. Each cell functional recovers the corresponding Maxwell–Boltzmann, Fermi–Dirac, or Bose–Einstein distribution function, depending on the classical or quantum nature of the gas. The time-evolution of the system is described by the relationship dH/dt≤0, and the equality condition occurs if the system is in the equilibrium state. Via the variational method, proof of the previous relationship, which might be an extension of the H-theorem for inhomogeneous systems, is presented for both classical and quantum gases. Furthermore, the H-functionals are in agreement with the correspondence principle. We discuss how the H-functionals can be identified with the system’s entropy and analyze the relaxation processes of out-of-equilibrium systems.

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“…One characteristic of these systems is their physical fractality, often quantified by the fractal dimension [1,11,12,13]. However, although the fractal dimension is a good measure of morphological complexity, it does not provide a comprehensive account of the micro structural features that could make branched morphologies relevant at the macro level for the system's biological function [4,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Structural analysis of bio-inspired spatial systems: network efficiency of fractal morphologies

Flores-Ortega¹,

Nicolás-Carlock²,

Carrillo-Estrada³

2022

Preprint

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Biological systems with tree-like morphological features emerge as nature's solution to an adaptive spatial exploration problem. The morphological complexity of these systems is often described in terms of its fractality, however, the network topology plays a relevant role behind the system's biological function. Therefore, here we considered a structural analysis of bio-inspired spatial systems based on fractal and network approaches in order to identify the features that could make tree-like morphologies better at exploring space under limited matter, energy and information. We considered connected clusters of particles in two-dimensions: the Ballistic and Diffusion-Limited Aggregation stochastic fractals, the Viscek and Hexaflake deterministic fractals, and the Kagome and Hexagonal lattices. We characterized their structure in terms of the range (linear extension), coverage (plane-filling), cost (assembly connections), configurational complexity (local connectivity), and efficiency (network communication). We found that tree-like systems have a lower configurational complexity and an invariant structural cost for different fractal dimensions, however, they are also fragile and inefficient. Nevertheless, this efficiency can become similar to that of an hexagonal lattice, at a similar cost, by considering euclidean connectivity beyond first neighbors. These results provide relevant insights into the interplay between the morphological and network properties of complex spatial systems.

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The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics

Cited by 4 publications

References 31 publications

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

Network efficiency of spatial systems with fractal morphology: a geometric graphs approach

Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes

Structural analysis of bio-inspired spatial systems: network efficiency of fractal morphologies

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