Related papers: Transition from rotating waves to modulated rotati…
We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…
Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is…
In the study of the periodic solutions of a $\Gamma$-equivariant dynamical system, the $H~\mathrm{mod}~K$ theorem gives all possible periodic solutions, based on group-theoretical aspects. By contrast, the equivariant Hopf theorem…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…
In the inclined layer convection system, thermal convection in a Rayleigh--B\'enard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle ($\gamma$) and Rayleigh number…
Star-planet tidal interactions play a significant role in the dynamical evolution of close-in planetary systems. We investigate the propagation and dissipation of tidal inertial waves in a stellar/planetary convective region. We take into…
We study the contributions of off-resonant transitions to the dynamics of a system of N multilevel atoms sharing one excitation and interacting with the quantized vector electromagnetic field. The Rotating Wave Approximation significantly…
In this work, we discuss the way in which electric and magnetic dipole resonances arising in the optical scattering spectrum of non-absorbing dielectric nanospheres can be accurately approximated by means of simple explicit expressions that…
Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
In turbulent flows subject to strong background rotation, the advective mechanisms of turbulence are superseded by the propagation of inertial waves, as the effects of rotation become dominant. While this mechanism has been identified…
Rotating wave approximation in a quantum spin system driven by a linearly polarized alternating magnetic field with quadrupole interaction presents is investigated in detail in this paper. The conventional way to employ the rotating wave…
The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic)…
We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire…
The homogenization procedure developed here is conducted on a laminate with periodic space-time modulation on the fine scale: at leading order, this modulation creates convection in the low-wavelength regime if both parameters are…
Surface curvature of magnetic systems can lead to many static and dynamic effects which are not present in flat systems of the same material. These emergent magnetochiral effects can lead to frequency nonreciprocity of spin waves, which has…
In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…
We present a simplified model for linearized perturbations in a fluid with both differential rotation and differential vorticity. Without the latter the model reduces to the classical Shearing Sheet used in the description of spiral density…
We report for the first time on triadic resonances in a rotating convection system. Using direct numerical simulations, we find that convective modes in a rotating spherical fluid can excite a pair of inertial modes whose frequencies and…