Stable and unstable solutions in auto-parametric resonance zone of a non-holonomic system

2019 ◽  
Vol 99 (1) ◽  
pp. 299-312 ◽  
Author(s):  
Jiří Náprstek ◽  
Cyril Fischer
2015 ◽  
Vol 9 (3) ◽  
pp. 2487-2502 ◽  
Author(s):  
Igor V. Lebed

Scenario of appearance and development of instability in problem of a flow around a solid sphere at rest is discussed. The scenario was created by solutions to the multimoment hydrodynamics equations, which were applied to investigate the unstable phenomena. These solutions allow interpreting Stokes flow, periodic pulsations of the recirculating zone in the wake behind the sphere, the phenomenon of vortex shedding observed experimentally. In accordance with the scenario, system loses its stability when entropy outflow through surface confining the system cannot be compensated by entropy produced within the system. The system does not find a new stable position after losing its stability, that is, the system remains further unstable. As Reynolds number grows, one unstable flow regime is replaced by another. The replacement is governed tendency of the system to discover fastest path to depart from the state of statistical equilibrium. This striving, however, does not lead the system to disintegration. Periodically, reverse solutions to the multimoment hydrodynamics equations change the nature of evolution and guide the unstable system in a highly unlikely direction. In case of unstable system, unlikely path meets the direction of approaching the state of statistical equilibrium. Such behavior of the system contradicts the scenario created by solutions to the classic hydrodynamics equations. Unstable solutions to the classic hydrodynamics equations are not fairly prolonged along time to interpret experiment. Stable solutions satisfactorily reproduce all observed stable medium states. As Reynolds number grows one stable solution is replaced by another. They are, however, incapable of reproducing any of unstable regimes recorded experimentally. In particular, stable solutions to the classic hydrodynamics equations cannot put anything in correspondence to any of observed vortex shedding modes. In accordance with our interpretation, the reason for this isthe classic hydrodynamics equations themselves.


Author(s):  
Viktoriia Nozhenko ◽  
Dmytro Rodkin ◽  
Valerii Tytiuk ◽  
Kostyantin Bohatyrov ◽  
Evgeniia Burdilna ◽  
...  

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Mustafa A. Amin ◽  
Andrew J. Long ◽  
Zong-Gang Mou ◽  
Paul M. Saffin

Abstract We investigate the production of photons from coherently oscillating, spatially localized clumps of axionic fields (oscillons and axion stars) in the presence of external electromagnetic fields. We delineate different qualitative behaviour of the photon luminosity in terms of an effective dimensionless coupling parameter constructed out of the axion-photon coupling, and field amplitude, oscillation frequency and radius of the axion star. For small values of this dimensionless coupling, we provide a general analytic formula for the dipole radiation field and the photon luminosity per solid angle, including a strong dependence on the radius of the configuration. For moderate to large coupling, we report on a non-monotonic behavior of the luminosity with the coupling strength in the presence of external magnetic fields. After an initial rise in luminosity with the coupling strength, we see a suppression (by an order of magnitude or more compared to the dipole radiation approximation) at moderately large coupling. At sufficiently large coupling, we find a transition to a regime of exponential growth of the luminosity due to parametric resonance. We carry out 3+1 dimensional lattice simulations of axion electrodynamics, at small and large coupling, including non-perturbative effects of parametric resonance as well as backreaction effects when necessary. We also discuss medium (plasma) effects that lead to resonant axion to photon conversion, relevance of the coherence of the soliton, and implications of our results in astrophysical and cosmological settings.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ata Keşkekler ◽  
Oriel Shoshani ◽  
Martin Lee ◽  
Herre S. J. van der Zant ◽  
Peter G. Steeneken ◽  
...  

AbstractMechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.


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