Related papers: On the Dynamical Stability of the Hovering Magneti…
Recent advancements with trapped nano- and micro-particles have enabled the exploration of motional states on unprecedented scales. Rotational degrees of freedom stand out due to their intrinsic non-linearity and their coupling with…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
Stability properties of magnetic-field configurations containing the toroidal and axial field are considered. The stability is treated by making use of linear analysis. It is shown that the conditions required for the onset of instability…
In this work I outline a general procedure for dynamic modeling and stability analysis of a magnetic bearing, which is a rotating shaft confined inside a chamber through electromagnetic forces alone. I consider the simplest type of…
Recently, a novel magnetic levitation phenomenon involving two magnetically equivalent neodymium permanent magnets has been reported. In this work, we propose that this system functions as a scaled-up analog of the Levitron. The key…
Using a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions, the dynamics of magnetized, rigidly rotating neutron stars are studied. Beginning with fully consistent…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
In stably stratified stars, numerical magneto-hydrodynamics simulations have shown that arbitrary initial magnetic fields evolve into stable equilibrium configurations, usually containing nearly axisymmetric, linked poloidal and toroidal…
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that…
The dynamical equations for a gliding Lagrange top are not integrable. They have 5 dynamical variables and admit one integral of motion. We show that all solutions go to one of the two vertical spinning solutions and determine conditions of…
The dynamics of an active walker in a harmonic potential is studied experimentally, numerically and theoretically. At odds with usual models of self-propelled particles, we identify two dynamical states for which the particle condensates at…
Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9,…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
In the absence of an active dynamo, purely poloidal magnetic field configurations are unstable to large-scale dynamical perturbations, and decay via reconnection on an Alfvenic timescale. Nevertheless, a number of classes of dynamo-free…
We prove that the stability problem of a vertical uniform rotation of a heavy top is completely solved by using the linearization method and the conserved quantities of the differential system which describe the rotation of the heavy top.
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or…
This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a…
This study examines the stability of Vlasov equilibrium solutions for magnetically confined plasmas, derived through the principle of maximum entropy. By treating the toroidal limit as a perturbation from an analytical cylindrical solution,…