Topological properties of a self-assembled electrical network via ab initio calculation

Stephenson, Cory; Lyon, Dave; Hübler, Alfred

doi:10.1038/srep41621

Cited by 12 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following, the term morphology refers to the physical or space-dependent structure (how things are distributed in space), while the terms topology or network refer to the space-independent structure (how things are connected with each other). In this way, the structure of spatial networks has both physical and topological properties 12 , 13 .…”

Section: Introductionmentioning

confidence: 99%

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

Flores-Ortega,

Nicolás-Carlock,

Carrillo-Estrada

2023

Sci Rep

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Flores-Ortega,

Nicolás-Carlock,

Carrillo-Estrada

2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In the following and to avoid confusion, the term morphology refers to the physical or space-dependent structure (how things are distributed in space), while the terms topology and network refer to the space-independent structure (how things are connected with each other). In this way, structure is comprised of both physical and topological properties [17,18].…”

Section: Introductionmentioning

confidence: 99%

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

Flores-Ortega¹,

Nicolás-Carlock²,

Carrillo-Estrada³

2022

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…The differential equations play a prominent role in the disciplines of engineering, physics, economics and biology [2][3][4][5][6]. The nonlinear problems are difficult to solve analytically and efficient methods must be used to obtain either approximate or numerical solutions.…”

Section: Introductionmentioning

confidence: 99%

Efficient Iterative Methods for Solving the SIR Epidemic Model

Abed

AL-Jawary

2021

eijs

View full text Add to dashboard Cite

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods, namely the Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM), and the Banach contraction method (BCM), are used to obtain the approximate solutions. The results showed many advantages over other iterative methods, such as Adomian decomposition method (ADM) and the variation iteration method (VIM) which were applied to the non-linear terms of the Adomian polynomial and the Lagrange multiplier, respectively. Furthermore, numerical solutions were obtained by using the fourth-orde Runge-Kutta (RK4), where the maximum remaining errors showed that the methods are reliable. In addition, the fixed point theorem was used to show the convergence of the proposed methods. Our calculation was carried out with MATHEMATICA®10 to evaluate the terms of the approximate solutions.

show abstract

Topological properties of a self-assembled electrical network via ab initio calculation

Cited by 12 publications

References 24 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

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

Efficient Iterative Methods for Solving the SIR Epidemic Model

Contact Info

Product

Resources

About