Measure synchronization and clustering in a coupled-pendulum system suspended from a common beam

Abstract

In this paper, we investigate measure synchronization (MS) in a nondissipative coupled-pendulum system suspended from a common beam. The system consists of several identical pendula hanging from a common beam that are indirectly coupled through the movements of the beam. We find that as the ratio R of the mass of the common beam to the mass of each pendulum decreases, which, in turn, increases the coupling strength between the pendula, the coupled-pendulum can achieve MS, including partial MS and complete MS, below certain threshold values of Rc. The energy characteristics of the MS are discussed. It is found that the pendula reach frequency locking at the MS transitions. Furthermore, by employing Poincaré section analysis, we reveal the dynamical mechanism of MS transitions.

Measure synchronization in hybrid quantum–classical systems

“…This feature is shared by measure synchronization in two coupled classical Hamiltonian system, where two subsystems get frequency-locked with very few frequencies being involved. [19] In contrast, for quantum measure synchronization, we have found that the frequency locking involves multiple frequencies.…”

“…[9] Being identical, the only difference in between the coupled Hamiltonian systems are their initial conditions. [9,[15][16][17][18][19][20] Even though for coupled quantum Hamiltonian and classical Hamiltonian systems, Ĥa and H b , the two Hamiltonian systems are intrinsic different. Here we shall relax the requirement by setting the classical Hamiltonian system and quantum Hamiltonian system in exact correspondence except for their initial conditions.…”

“…Up to now, classical MS behavior have been revealed in different model systems, i.e., φ 4 model, [15] Duffing model, [16] coupled bosonic Josephson junction [17,18] and more recently in non-dissipative Huygens' pendulum. [19] The classical concept of MS has been extended into quantum regime. We have revealed that quantum MS appears in coupled quantum many body systems, and quantum MS will manifest itself in a purely quantum mechanical way, i.e., collapses and revivals dynamics will get synchronized once the system reaching quantum MS. [20] More recently, quantum MS has also been found in a pair of Harper systems [21] and in between two scattering modes in Bose-Einstein condensates.…”

Flow-mediated interaction between a forced-oscillating cylinder and an elastically mounted cylinder in less regular regimes

“…Although the geometry is simple, this problem involves abundant flow physics, including vortex shedding, resonance, harmonics and synchronisation. The present problem setup is also relevant to the Huygens' pendulum of two synchronised oscillators (Huygens, 1660;Peña Ramirez et al, 2014;Tian et al, 2019) and the interacting tuning forks (Klein et al, 2012).…”