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For simple mechanical systems, bifurcating branches of relative equilibria with trivial symmetry from a given set of relative equilibria with toral symmetry are found. Lyapunov stability conditions along these branches are given.
For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show,…
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…
Galaxies and galaxy clusters are observed to have a rather non-trivial radial behaviour. The observations show that the radial profiles change from one power-law profile near the centre to another power-law profile in the outer region. We…
Branched flow is an interesting phenomenon that can occur in diverse systems. It is usually linear in the sense that the flow does not alter the medium properties. Branched flow of light on thin films was recently discovered. A question of…
A new kinetic instability which results in formation of charge density waves is proposed. The instability is of a purely classical nature. A spatial period of arising space-charge and field configuration is inversely proportional to…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to…
The problem of describing optical turbulent structures, arising in resonant media with high Fresnel numbers, is reviewed. The consideration is based on the probabilistic approach to pattern selection, ascribing a probability distribution of…
We discuss a specific circumstance in which the topology of the communication network of a robotic swarm has to change during the movement. The variation is caused by a topological obstruction which emerges from certain geometric…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…
A new form of the well known Lin equation for the energy balance in isotropic turbulence is given which takes account of the filtered-partitioned transfer spectra which were used to resolve the scale paradox. It is argued that this new…
In the full-orbit particle simulations of energetic particle transport in plasmas, the plasma turbulence is typically described as a homogeneous superposition of linear Fourier modes. The turbulence evolution is, however, typically a…
The crucial part of electromagnetic phenomena in many atmospheric processes is verified by systematized data. The multilayered charged system of clouds represents some dynamically equilibrium structure kept by the ionic and polarization…
To this day, the two-slit electron interference pattern remains shrouded in an inordinate mystery. It continues to defy a logical and rational explanation. This paper will postulate a new "characteristic" pertaining to the electron. If this…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
We examine the transport behaviour of non-interacting particles in a simple channel billiard, at equilibrium and in the presence of an external field. The channel walls are constructed from straight line-segments. We observe a sensitive…
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…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…