Search results for "Critical frequency"
showing 7 items of 7 documents
Dynamics of a flexible magnetic chain in a rotating magnetic field.
2004
The model of an elastic magnetic rod is applied for a study of a behavior of the flexible magnetic particle chain in a rotating magnetic field. By numerical simulation it is shown that behavior of a flexible magnetic chain is characterized by the existence of a critical frequency beyond which the dynamics of the rod is periodic with subsequent stages of bending and straightening. The value of the critical frequency found is explained by a simple model. Below the critical frequency the chain is bent and rotates synchronously with a field. It is illustrated that in particular cases the considered model reproduces phenomena observed experimentally and numerically for the magnetic particle chai…
Stability of an electromagnetically levitated spherical sample in a set of coaxial circular loops
2005
This paper presents a theoretical study of oscillatory and rotational instabilities of a solid spherical body, levitated electromagnetically in axisymmetric coils made of coaxial circular loops. We apply our previous theory to analyze the static and dynamic stability of the sample depending on the ac frequency and the position of the sample in the coils for several simple configurations. We introduce an original analytical approach employing a gauge transformation for the vector potential. First, we calculate the spring constants that define the frequency of small-amplitude oscillations. For static stability, the spring constants must be positive. Dynamic instabilities are characterized by …
Dynamics of an active magnetic particle in a rotating magnetic field.
2006
The motion of an active (self-propelling) particle with a permanent magnetic moment under the action of a rotating magnetic field is considered. We show that below a critical frequency of the external field the trajectory of a particle is a circle. For frequencies slightly above the critical point the particle moves on an approximately circular trajectory and from time to time jumps to another region of space. Symmetry of the particle trajectory depends on the commensurability of the field period and the period of the orientational motion of the particle. We also show how our results can be used to study the properties of naturally occurring active magnetic particles, so-called magnetotacti…
Quantum resonant activation
2017
Quantum resonant activation is investigated for the archetype setup of an externally driven two-state (spin-boson) system subjected to strong dissipation by means of both analytical and extensive numerical calculations. The phenomenon of resonant activation emerges in the presence of either randomly fluctuating or deterministic periodically varying driving fields. Addressing the incoherent regime, a characteristic minimum emerges in the mean first passage time to reach an absorbing neighboring state whenever the intrinsic time scale of the modulation matches the characteristic time scale of the system dynamics. For the case of deterministic periodic driving, the first passage time probabili…
3D motion of flexible ferromagnetic filaments under a rotating magnetic field.
2020
Ferromagnetic filaments in a rotating magnetic field are studied both numerically and experimentally. The filaments are made from micron-sized ferromagnetic particles linked with DNA strands. It is found that at low frequencies of the rotating field a filament rotates synchronously with the field and beyond a critical frequency it undergoes a transition to a three dimensional regime. In this regime the tips of the filament rotate synchronously with the field on circular trajectories in the plane parallel to the plane of the rotating field. The characteristics of this motion found numerically match the experimental data and allow us to obtain the physical properties of such filaments. We als…
On ( p ( x ), q ( x ))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition
2021
In the present work, we consider a (p(x), q(x))-elliptic equation describing the behavior of a double-phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti-Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler-Lagrange functional …
Modulation instability scenario in negative index materials
2010
We present an investigation of the critical frequency windows permitting modulation instability in negative index materials. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective dispersive magnetic permeability in addition to the effective dielectric permittivity determining the propagation model for ultrashort pulses in negative index materials. We emphasize the influence of nonlinear dispersion terms, arising out of the combinatorial effect of the dispersive permeability with the nonlinear polarization, over the MI phenomena, the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has be…