Related papers: Complexity perspectives: an anomalous diffusion ap…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
Cosmic structures at large scales represent the earliest and most extended form of matter condensation. In this lecture we review the application of the methods and concepts of modern statistical physics to these structures. This leads to a…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems,…
Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light…
Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction…
The question of the nature of galaxy clustering and the possible homogeneity of galaxy distribution is one of the fundamental problem of cosmology. It is well established that galaxy structures are characterized, up to a certain scale, by…
Since the famous 1926 paper by Richardson, the relative diffusion of two particles in a turbulent liquid has attracted a lot of interest. The motion of a single particle on the other hand is usually considered not to be especially…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
A qualitatively new, much more liberal and efficient organisation of science is proposed and justified, in connection with growing debate about further role and development of fundamental science. Although the key ideas can be explained…
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
We consider Brownian particles immersed in the fluid which flow is turbulent. We study the limit where the particles' inertia is weak and their velocity relaxes fast to the velocity of the flow. The trajectories of the particles in this…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Nature hosts a wealth of materials showcasing intricate structures intertwining order, disorder, and hierarchy, delivering resilient multifunctionality surpassing perfect crystals or simplistic disordered materials. The engineering of such…