Related papers: Oscillatory mean-field dynamos with spherically sy…
The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field…
This paper reviews the dynamics of an isotropic and homogeneous cosmological scalar field. A general approach to the solution of the Einstein-Klein-Gordon equations is developed, which does not require slow-roll or other approximations.…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number…
The quasiradial wave functions and energy spectra of the alternative model of spherical oscillator on the $D$-dimensional sphere and two-sheeted hyperboloid are found.
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
Networks of coupled degrade-and-fire (DF) oscillators are simple dynamical models of assemblies of interacting self-repressing genes. For mean-field interactions, which most mathematical studies have assumed so far, every trajectory must…
A dynamo model is presented, based on a previously introduced kinematic model, in which the reaction of the magnetic field on the mass flow through the Lorentz force is included. Given the base mass flow corresponding to the case with no…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take…
We study some systems of interacting fields whose evolution is given by some singular stochastic partial differential equations of mean field type. We provide a robust setting for their study and prove a well-posedness result and a…
The possibility of fast dynamo action by collisionless kinetic Alfven Wave turbulence is demonstrated. The irreversibility necessary to lock in the generated field is provided by electron Landau damping, so the induced electric field does…
Parker's mean-field model includes two processes generating large-scale oscillatory dynamo waves: stretching of magnetic field lines by small-scale helical flows, and by differential rotation. In this work, we investigate the capacity of…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
A brief summary of the various observations and constraints that underlie solar dynamo research are presented. The arguments that indicate that the solar dynamo is an alpha-omega dynamo of the Babcock-Leighton type are then shortly…
Three closely related stumbling blocks of solar mean field dynamo theory are discussed: how dominant are the small scale fields, how is the alpha effect quenched, and whether magnetic and current helicity fluxes alleviate the quenching? It…
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation…
We show that for every ergodic and aperiodic probability preserving transformation and $\alpha\in (0,2)$ there exists a function whose associated time series is in the standard domain of attraction of a non-degenerate symmetric…
We discuss the static axially symmetric regular solutions, obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory [1]. These asymptotically flat solutions are characterized by the winding number $n>1$ and the node…