Related papers: Oscillatory mean-field dynamos with spherically sy…
Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that…
We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter alpha, with alpha=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or…
In this article, we study domains $\Omega \subset \mathbb{S}^2$ that support positive solutions of the overdetermined problem $$ \Delta u + f(u,|\nabla u|)=0 \quad \text{in } \Omega, $$ subject to the boundary conditions $u=0$ on…
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact…
Kinney et al [PPL \textbf{1},(1994)] have investigated plasma filamentary structure dynamics. More recently, Wilkin et al [Phys Rev Lett \textbf{99}:134501,(2007)] have shown that kinetic energy spectrum of magnetic structures in…
We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped…
To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the…
We discuss the static and kinetic properties of a Ginzburg-Landau spherically symmetric $O(N)$ model recently introduced (Phys. Rev. Lett. {\bf 75}, 2176, (1995)) in order to generalize the so called Phase field model of Langer. The…
Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique…
The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\odot}$ rotating with period of 10 days. For the intermediate value of the parameter of the turbulent magnetic Prandl…
The scale separation approximation, which is in the base of the solar mean field dynamo models, can be hardly justified both by observations and theoretical applications to astrophysical dynamos.{ The general expression for the mean…
A new class of semi-analytically solvable MHD alpha^2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside…
We present a counterexample to the statement of convergence of the mean-field Langevin descent-ascent flow on $\mathbb{R}^2$. We consider payoff functions that are shaped as a double well in each coordinate, and for which the deterministic…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
The coefficients defining the mean electromotive force in a Galloway-Proctor flow are determined. This flow shows a two-dimensional pattern and is helical. The pattern wobbles in its plane. Apart from one exception a circular motion of the…
We investigate cellular automata where some global quantity varies periodically or quasiperiodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We…
Increasing evidence is becoming available about not only the surface differential rotation of rapidly rotating cool stars but, in a small number of cases, also about temporal variations, which possibly are analogous to the solar torsional…
Using three-dimensional convection simulations it is shown that a sinusoidal variation of horizontal shear leads to a kinematic \alpha effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises…