The strength and stability properties of hierarchical load-bearing networks and their strengthened variants have been discussed in a recent work. Here, we study the avalanche time distributions on these load-bearing networks. The avalanche time distributions of the V-lattice, a unique realization of the networks, show power-law behaviour when tested with certain fractions of its trunk weights. All other avalanche distributions show Gaussian peaked behaviour. Thus the V-lattice is the critical case of the network. We discuss the implications of this result.

Neelima Gupte

Department Of Physics

AJAY DEEP KACHHVAH

AVALANCHE DISTRIBUTIONS

Critical behaviour

CRITICAL CASE

Gaussians

HIERARCHICAL LATTICE

Hierarchical network

LOAD-BEARING

Power-law

Stability properties

Time distribution

Physics

stability

Fulltext

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IIT Madras

Pramana - Journal of Physics

We identify the existence of microtransitions in the process of avalanche transmission on 2−d load bearing hierarchical networks. It has been seen in earlier work that typical realizations of this network exhibit a second order transition, whereas the critical realization of the network, shows a first order transition. The microtransitions can be used to predict the transition point for both cases. Microtransitions are also seen in the correlation function and scale in a similar way for the critical realisation. We compare the ratios of the peaks of the Fourier spectrum of the correlation function with the structure factor of the network to infer information about the network structure. © 2018 Elsevier B.V.

Physics Letters, Section A: General, Atomic and Solid State Physics

Microtransitions in a 2 − d load bearing hierarchical network

The prediction of the critical point of a phase transition is useful in many practical contexts. Therefore, the identification of precursors, or early warning signals of the critical point, has become the focus of current interest. Recent model studies have shown that a series of small transitions, which have been called microtransitions, act as precursors to the percolation transition. Here, we identify the existence of microtransitions in the process of avalanche transmission on a specific realisation of branching hierarchical networks. We note that microtransitions are seen clearly in this realization, which we call the V- lattice. Additionally, the positions of the microtransitions show scaling behaviour here. This can be used to calculate the position of the critical point, which is seen to be in agreement with the observed result. The correlation function of the time series of the weight transmission also shows interesting behaviour, which can be used to draw inferences about the structure and behaviour of the system. Additionally we utilise the structure factor, and the ratio of the heights of the peaks of the Fourier transform of the correlation function to infer information about the structure of the lattices. We discuss the utility of our results and generalisability to other contexts. © 2019, Springer Nature Switzerland AG.

Understanding Complex Systems

Microtransitions in a 2 - d load bearing hierarchical network

We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical two dimensional network and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity, and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell-Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V lattice, the critical case of the 2D lattice. The scaling behavior of the second-order percolation case is studied in detail. We discuss the implications of our analysis. © 2012 American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Transmission of packets on a hierarchical network: Statistics and explosive percolation

We investigate the statistics and dynamics of failure in a two-dimensional load-bearing network with branching hierarchical structure, and its variants. The variants strengthen the original lattice by using connectivity strategies which add new sites to the maximal cluster in top-to-bottom or bottom-to-top versions. We study the load-bearing capacity and the failure tolerance of all versions, as well as that of the strongest realization of the original lattice, the V lattice. The average number of failures as a function of the test load shows power-law behavior with power 5/2 for the V lattice, but sigmoidal behavior for all other versions. Thus the V lattice turns out to be the critical case of the load-bearing lattices. The distribution of failures is Gaussian for the original lattice, the V lattice, and the bottom-to-top strategy, but is non-Gaussian for the top-to-bottom one. The bottom-to-top strategy leads to stable and strong lattices, and can resist failure even when tested with weights which greatly exceed the capacity of its backbone. We also examine the behavior of asymmetric lattices and discover that the mean failure rates are minimized if the probability of connection p is symmetric with respect to both neighbors. Our results can be of relevance in the context of realistic networks. © 2011 American Physical Society.

Failure tolerance of load-bearing hierarchical networks

Chaos: An Interdisciplinary Journal of Nonlinear Science

Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization

Reviews of Modern Physics

Statistical mechanics of complex networks

Nature

Exploring complex networks

Annals of Biomedical Engineering

Mathematical Modeling of the First Inflation of Degassed Lungs

Avalanche transmission and critical behaviour in load-bearing hierarchical networks

Journal	Pramana - Journal of Physics
ISSN	03044289
Open Access	No