相关论文: On some recent results about inertial manifolds an…

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is…

Pitch angles $p$ of the large-scale magnetic fields $\overline{\bf{\it{B}}}$ of spiral galaxies have previously been inferred from observations to be systematically larger in magnitude than predicted by standard mean-field dynamo theory.…

We give a critical analysis of the conceptual foundations of special relativity. We formulate a simple operational criterion for distinguishing between noninertial and inertial frames which is introduced prior to geometry. We associate the…

New additional equations for the Newtonian dynamical systems on Riemannian manifolds are found. They supplement the previously found weak normality conditions up to the complete normality conditions for Newtonian dynamical systems.

Several recent advances in turbulent dynamo theory are reviewed. High resolution simulations of small-scale and large-scale dynamo action in periodic domains are compared with each other and contrasted with similar results at low magnetic…

Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary…

With materials of anisotropic electrical conductivity, it is possible to generate a dynamo with a simple velocity field, of the type precluded by Cowling's theorems with isotropic materials. Following a previous study by Ruderman and…

The effect of precession in a rotating sphere filled with fluid was studied with direct numerical simulations, both in the incompressible hydrodynamics (HD) and magnetohydrodynamics (MHD) scenarios. In both cases the asymptotic state and…

Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…

The effect of non periodic boundary conditions on decaying two-dimensional magnetohydrodynamic turbulence is investigated. We consider a circular domain with no-slip boundary conditions for the velocity and where the normal component of the…

With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust…

In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in $\mathbf{R}^N$. Applying a nonlinear change of variables, we rewrite the equation as a diffusion on a…

Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…

Let M be a closed 3-manifold that supports a partially hyperbolic diffeomorphism f. If $\pi_1(M)$ is nilpotent, the induced action of f on $H_1(M, R)$ is partially hyperbolic. If $\pi_1(M)$ is almost nilpotent or if $\pi_1(M)$ has…

We review the results obtained by three successful fluid dynamo experiments and discuss what has been learnt from them about the effect of turbulence on the dynamo threshold and saturation. We then discuss several questions that are still…

Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…

Describing effects of small but finite inertia on suspended particles is a fundamental fluid dynamical problem that has never been solved in full generality. Modern microfluidics has turned this academic problem into a practical challenge…

The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated…

Efficiency of collective beam-plasma interaction strongly depends on the growth rates of dominant instabilities excited in the system. Nevertheless, exact calculations of the full unstable spectrum in the framework of relativistic kinetic…

We establish a variational framework for nonlinear instabilities in a setting of the ideal magnetohydrodynamic (MHD) equations. We apply a variational method to various kind of smooth steady states which are shown to be nonlinearly unstable…