Related papers: Delayed Babcock-Leighton dynamos in the diffusion-…
Most of the theoretical results on the kinematic amplification of small-scale magnetic fluctuations by turbulence have been confined to the model of white-noise-like advecting turbulent velocity field. In this work, the statistics of the…
In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some…
We point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in…
We begin with a review of the predictions for cycle~24 before its onset. After summarizing the basics of the flux transport dynamo model, we discuss how this model had been used to make a successful prediction of cycle~24, on the assumption…
Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behaviour but they are based on…
A magnetic flux tube may be considered both as a separate body and as a confined field. As a field, it is affected both by the cyclonic convection ($\alpha$-effect) and differential rotation ($\Omega$-effect). As a body, the tube…
The tachocline is important in the solar dynamo for the generation and the storage of the magnetic fields. A most plausible explanation for the confinement of the tachocline is given by the fast tachocline model in which the tachocline is…
We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time dependent model for alpha quenching in dynamo theory. For dynamos without shear, this approach…
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…
We want to study the connections between the magnetic field generated inside the Sun and the solar wind impacting Earth, especially the influence of north-south asymmetry on the magnetic and velocity fields. We study a solar-like 11-year…
In this paper we study a system of delay differential equations from the viewpoint of a finite time blow-up of the solution. We prove that the system admits a blow-up solution, no matter how small the length of the delay is. In the…
One of the most striking manifestations of orderly behavior emerging out of complex interactions in any astrophysical system is the 11-year cycle of sunspots. However, direct sunspot observations and reconstructions of long-term solar…
The Babcock-Leighton type of dynamo has received recent support in terms of the discovery in the observational records of systematic cycle-to-cycle variations in the tilt angle of sunspot groups. It has been proposed that these variations…
We present a simple semi-analytical model of nonlinear, mean-field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the `no-$z$' approximation to a nonlinear system…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
In this paper, we study the asymptotic behavior of solution to a non-autonomous diffusion equations with delay containing some hereditary characteristics and nonlocal diffusion in time-dependent space $C_{\mathcal{H}_{t}(\Omega)}$. When the…
Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the…
After emerging to the solar surface, the Sun's magnetic field displays a complex and intricate evolution. The evolution of the surface field is important for several reasons. One is that the surface field, and its dynamics, sets the…
We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as 10Be and 14C, using a fully non-linear Babcock-Leighton type flux-transport…