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The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
Light scattering in random media is usually considered within the framework of the three-dimensional Anderson universality class, with modifications for the vector nature of electromagnetic waves. We propose that the linear dispersiveness…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A…
We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet…
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent…
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose…
The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize…
The last 20 years have seen an explosion in our understanding of the large-scale distribution and motions of galaxies in the nearby universe. The field has moved from a largely qualitative, morphological description of the structures seen…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…
A concentration difference of particles across a membrane perforated by pores will induce a diffusive flux. If the diffusing objects are of the same length scale as the the pores, diffusion may not be simple, objects can move into the pore…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…