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

The paper is devoted to a comprehensive study of smoothness of inertial manifolds for abstract semilinear parabolic problems. It is well known that in general we cannot expect more than $C^{1,\varepsilon}$-regularity for such manifolds (for…

Small steady-state deformational oscillations of a drop of a viscous magnetic liquid in a non-stationary uniform magnetic field are theoretically investigated for low Reynolds numbers. The drop is suspended in another viscous magnetic…

We study the magneto-rotational instability of an incompressible flow which rotates with angular velocity Omega(r)=a+b/r^2 where r is the radius and $a$ and b are constants. We find that an applied magnetic field destabilises the flow, in…

We extend the study of the inertial effects on the dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational…

Using a rotating flat layer heated from below as an example, we consider effects which lead to stabilizing an exponentially growing magnetic field in magnetostrophic convection in transition from the kinematic dynamo to the full non-linear…

This short article sets out some of the basic considerations that go into detecting the mass of quasiparticles with effective magnetic charge in solids. Effective magnetic charges may be appear as defects in particular magnetic textures. A…

We compute numerically the threshold for dynamo action in Taylor-Green swirling flows. Kinematic calculations, for which the flow field is fixed to its time averaged profile, are compared to dynamical runs for which both the Navier-Stokes…

Condensed matter systems can host emergent `vacua' with particles, fields and dimension different from that of the universe we inhabit. Motivated by the appearance of emergent gauge fields with both electric and magnetic charges, we…

Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear differential equations assuming a very general form of dichotomic behavior for the linear equation. Besides some new…

Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities…

These lecture notes are based on a tutorial given in 2017 at a plasma physics winter school in Les Houches. Their aim is to provide a self-contained graduate-student level introduction to the theory and modelling of the dynamo effect in…

A novel formulation of fluid dynamics as a kinetic theory with tailored, on-demand constructed particles removes any restrictions on Mach number and temperature as compared to its predecessors, the lattice Boltzmann methods and their…

Hamiltonian variational principles provided, since 60s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that…

The new proposed "energy gradient theory," which physically explains the phenomena of flow instability and turbulent transition in shear flows and has been shown to be valid for parallel flows, is extended to curved flows in this study.…

Two different approaches to the Roberts dynamo problem are considered. Firstly, the equations governing the magnetic field are specified to both harmonic and subharmonic solutions and reduced to matrix eigenvalue problems, which are solved…

The purpose of this note is to present an enhancement to a Maxey-Riley theory proposed in recent years for the dynamics of inertial particles on the ocean surface. This model upgrade removes constraints on the reserve buoyancy, defined as…

Hydromagnetic dynamo theory provides the prevailing theoretical description for the origin of magnetic fields in the universe. Here we consider the problem of kinematic, small-scale dynamo action driven by a random, incompressible,…

Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…

A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…