Related papers: Phase Transitions on Fractals and Networks
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…
Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous…
We discuss numerical results presented in a recent ppublication about the critical properties of a two dimensional Ising model with exchange and dipolar interactions.
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…
The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic…
This document presents a Data Model to describe Spectral Line Transitions in the context of the Simple Line Access Protocol defined by the IVOA (c.f. Ref[13] IVOA Simple Line Access protocol) The main objective of the model is to integrate…
Contents: A. Introduction B. High Temperature Expansions for the Ising Model C. Characteristic Functions and Cumulants D. The One Dimensional Chain E. Directed Paths and the Transfer Matrix F. Moments of the Correlation Function G. The…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
I review (1) Physics of Star Formation & Open Questions; (2) Structure & Dynamics of Star-Forming Clouds & Young Clusters; (3) Star Formation Rates: Observations & Theoretical Implications.
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.