Related papers: Fractal transit networks: self-avoiding walks and …
Disruptions are an inherent feature of transportation systems, occurring unpredictably and with varying durations. Even after an incident is reported as resolved, disruptions can induce irregular train operations that generate substantial…
The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of…
The method of approximate automodel solution for the Green's function of the time-dependent superdiffusive (nonlocal) transport equations (J. Phys. A: Math. Theor. 49 (2016) 255002) is extended to the case of a finite velocity of carriers.…
We analyze simple models of quantum chaotic scattering, namely quantized open baker's maps. We numerically compute the density of quantum resonances in the semiclassical r\'{e}gime. This density satisfies a fractal Weyl law, where the…
We investigate the behavior of extended urban traffic networks within the framework of percolation theory by using real and synthetic traffic data. Our main focus shifts from the statistical properties of the cluster size distribution…
In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in…
Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of…
Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…
Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by…
Spatially extended chaotic systems with power-law decaying interactions are considered. Two coupled replicas of such systems synchronize to a common spatio-temporal chaotic state above a certain coupling strength. The synchronization…
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
What is the analogue of L\'evy processes for random surfaces? Motivated by scaling limits of random planar maps in random geometry, we introduce and study L\'evy looptrees and L\'evy maps. They are defined using excursions of general L\'evy…
A wide class of non-stationary superdiffusive transport on a uniform background with a power-law decay, at large distances, of the step-length probability distribution function (PDF) is shown to possess an automodel solution. The solution…
The results of transportation infrastructure network analyses have been used to analyze complex networks in a topological context. However, most modeling approaches, including those based on complex network theory, do not fully account for…
The city is a complex system that evolves through its inherent social and economic interactions. Mediating the movements of people and resources, urban street networks offer a spatial footprint of these activities; consequently their…
We review some of the theory relevant to passage times of one-dimensional L\'evy processes out of bounded regions, highlighting results that are useful in physical phenomena modelled by heavy-tailed L\'evy flights. The process is…
We report measurements and analysis of the voltage noise due the to vortex motion, performed in superconducting Niobium micro-bridges. Noise in such small systems exhibits important changes from the behavior commonly reported in macroscopic…