Search results for "Nonlinear system"
showing 10 items of 1446 documents
Size effect in phase transition kinetics
1988
The growth of a spontaneous lattice average magnetization in a magnetic system which is suddenly brought below the transition temperature is a stochastic process in which the very small fluctuations of the initial magnetization are amplified to a macroscopic size. The initial magnetization fluctuates in time around the zero average value because of the finite size of the system. As a consequence of the fluctuation-amplification phenomenon the nonlinear relaxation of the finite system is qualitatively different from that of the infinite one. The present paper studies this feature of phase-transition kinetics in the framework of a very simple model: the dynamical generalization of the spheric…
Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles
2015
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with …
Optomechanical systems close to the conservative limit
2017
In dissipative optomechanical systems, the total damping hits negative values at the parametric instability point. This also corresponds to the phonon lasing threshold, where the mechanical resonator enters in the self-induced oscillations regime. This paper shows that the two mentioned phenomena are delayed from each other when the optomechanical systems operate close to their conservative limit, where the mechanical damping is very small. In fact, the total damping can be negative and very small for a while before the phonon lasing happens. As a result, the linearized theory is extended over the negative damping region where the mechanical displacements remain very small. It follows that …
Integrated Generation of High-dimensional Entangled Photon States and Their Coherent Control
2017
Exploiting a frequency-domain approach, we demonstrate the generation of high-dimensional entangled quantum states with a Hilbert-space dimensionality larger than 100 from an on-chip nonlinear microcavity, and introduce a coherent control platform using standard telecommunications components.
Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance
2014
5 pags.; 4 figs.; PACS number(s): 05.45.Yv, 47.20.Ky, 47.35.−i, 47.54.−r
NON-LINEAR MECHANICAL, ELECTRICAL AND THERMAL PHENOMENA IN PIEZOELECTRIC CRYSTALS
2003
Mechanical, electrical and thermal phenomena occurring in piezoelectric crystals were examined by non-linear approximation. For this purpose, use was made of the thermodynamic function of state, which describes an anisotropic body. Considered was the Gibbs function. The calculations included strain tensor εij = f(σkl , En, T), induction vector Dm = f(σkl , En, T) and entropy S = f(σkl , En, T) as function of stress σkl , field strength En and temperature difference T. The equations obtained apply to anisotropic piezoelectric bodies provided that the “forces” σkl , En, T acting on the crystal are known. Механічні, електричні та термічні явища у п’єзоелектричних кристалах вивчаються у неліній…
Isotope separation by nonlinear resonances in a Paul trap
1996
Deviations from the ideal quadrupole potential in a Paul ion trap create nonlinear resonances at certain operating points inside the stability diagram, where in the absence of potential pertubations storing times are very long. In the presence of those pertubations, however, the ions are lost from the trap. Since these resonances are mass dependent and the mass resolution is of the order of 100 it can be used to separate isotopes of a given element by choosing suitable trap operating conditions. Experiments on a natural mixture of Eu+ ions of mass 151 and 153 show that in a simple way, by proper choice of the operating point, the ions can be completely separated and laser-induced optical sp…
Amplification of nonlinear currents generation at harmonics frequencies of submillimeter radiation
2006
The conditions are found when rapid heating of the electrons of a degenerate semiconductor in the presence of two electric fields, one constant and the other variable, is accompanied by the formation of a distribution function significantly departing from the Fermi one. It is also shown that the newly found modification of the electron distribution yields a relative amplification of nonlinear currents generation.
Controlling stability and transport of magnetic microswimmers by an external field
2019
We investigate the hydrodynamic stability and transport of magnetic microswimmers in an external field using a kinetic theory framework. Combining linear stability analysis and nonlinear 3D continuum simulations, we show that for sufficiently large activity and magnetic field strengths, a homogeneous polar steady state is unstable for both puller and pusher swimmers. This instability is caused by the amplification of anisotropic hydrodynamic interactions due to the external alignment and leads to a partial depolarization and a reduction of the average transport speed of the swimmers in the field direction. Notably, at higher field strengths a reentrant hydrodynamic stability emerges where t…
A multiscale approach to liquid flows in pipes I: The single pipe
2012
Abstract In the present paper we study the propagation of pressure waves in a barotropic flow through a pipe, with a possibly varying cross-sectional area. The basic model is the Saint–Venant system. We derive two multiscale models for the cases of weak and strong damping, respectively, which describe the time evolution of the piezometric head and the velocity. If the damping is weak, then the corresponding first-order hyperbolic system is linear but contains an additional integro-differential equation that takes into account the damping. In the case of strong damping, the system is nonlinear. The full and multiscale models are compared numerically; we also discuss results obtained by a lar…