Related papers: A systematic route to subcritical dynamo branches
We prove some multiplicity results by means of a perturbation technique in critical point theory.
Analytical investigations of the critical state are carried out for a superconducting stripline consisting of two individual coplanar strips with an arbitrary distance between them. Two different cases are considered: a stripline with…
The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW-bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we…
Some features of the calculation of fluid dynamo systems in magnetohydrodynamics are studied. In the coupled set of the ordinary linear differential equations for the spherically symmetric $\alpha^2-$dynamos, the problem represented by the…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are…
Chains of resonators in the form of spring-mass systems have long been known to exhibiting interesting properties such as band gaps. Such features can be leveraged to manipulate the propagation of waves such as the filtering of specific…
In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most…
The question of whether a dynamo can be triggered by gravitational collapse is of great interest, especially for the early Universe. Here, we employ supercomoving coordinates to study the magnetic field amplification from decaying…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
Supernova remnants are expected to contain braided (or stochastic) magnetic fields, which are in some regions directed mainly perpendicular to the shock normal. For particle acceleration due to repeated shock crossings, the transport in the…
Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…
Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…
This paper addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order…
A non-linear, time-dependent, magnetically driven dynamo theory which shows how magnetically dominated configurations can relax to become helical on the largest scale available is presented. Coupled time-dependent differential equations for…
A current-carrying superconducting strip partly penetrated by magnetic flux and surrounded by a bulk magnet of high permeability is considered. Two types of samples are studied: those with critical current controlled by an edge barrier…