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It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…
A numerical simulation of kinetic plasma turbulence is performed to assess the applicability of critical balance to kinetic, dissipation scale turbulence. The analysis is performed in the frequency domain to obviate complications inherent…
Prominent examples of longitudinal phase separation in elastic systems include elastic necking, the propagation of a bulge in a cylindrical party balloon and the beading of a gel fiber subject to surface tension. Here we demonstrate that,…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device…
The effect of concentration on coil-stretch hysteresis in extensional flows of polymer solutions is examined with insights from Brownian dynamics simulations of isolated chains and scaling theory for non-dilute solutions. In the hysteresis…
Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is…
The non-equilibrium dynamics of the critical behaviour of the Boson system undergoing the second order quantum phase transition is discussed. The analysis is carried out using the Keldysh technique of the non-equilibrium dynamics…
The present paper gives an overview of the recent developments in the description of critical behavior for Hamiltonian perturbations of hyperbolic and elliptic systems of partial differential equations. It was conjectured that this behavior…
We study anharmonic localization in a periodic five atom chain with quadratic-quartic spring potential. We use discrete symmetries to eliminate the degeneracies of the harmonic chain and easily find periodic orbits. We apply linear…
We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of…
Stationary whirling of slender and homogeneous (continuous) elastic shafts rotating around their axis, with pin-pin boundary condition at the ends, is revisited by considering the complete deformations in the cross section of the shaft. The…
We study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the winding number of a vortex is naturally extended…
Anomaly detection is crucial in industrial product quality inspection. Failing to detect tiny defects often leads to serious consequences. Existing methods face a structure-semantics trade-off: structure-oriented models (such as…
In a recent work, a new numerical method (the lifespan method) has been introduced to study the critical properties of epidemic processes on complex networks [Phys. Rev. Lett. \textbf{111}, 068701 (2013)]. Here, we present a detailed…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…