Abstract
The combustion of candles exhibits a variety of dynamical behaviors. Binding several candles together will result in flickering of candle flames, which is generally described as a nonlinear oscillator. The impact on the frequency of the flame by several factors, such as the arrangement, the number and the asymmetry of the oscillators, is discussed. Experimental results show that the frequency gradually decreases as the number of candles increases in the case of an isolated oscillator, while alternation between the in-phase and the anti-phase synchronization appears in a coupled system of two oscillators. Moreover, envelopes in the amplitude of the oscillatory luminance are displayed when candles are coupled asymmetrically. Since the coupling between oscillators is dominated by thermal radiation, a “overlapped peaks model” is proposed to phenomenologically explain the relationship between temperature distribution, coupling strength and the collective behavior in coupled system of candle oscillators in both symmetric and asymmetric cases.
Highlights
The nonlinear oscillation of candle flames was introduced and analyzed with imaging technique by Chamberlin et al in 1948 for the first time[25]
The high speed camera is aligned with the center of candle flames with the distance between them fixed
For a coupled system of two identical oscillators, whether it will lead to the in-phase, anti-phase and incoherent oscillation depends on the distances between the flames
Summary
The nonlinear oscillation of candle flames was introduced and analyzed with imaging technique by Chamberlin et al in 1948 for the first time[25]. The in-phase synchronization was observed when two groups were closely placed, while a distance further enough led the system to the anti-phase synchronization. Okamoto et al.[3] investigated three candle groups with equilateral triangular arrangement in detail, and discovered four distinct oscillation modes: in-phase synchronization, partial in-phase synchronization, rotation and death. We analyzed the coupled system of two identical oscillators with an infrared camera to measure the temperature distribution in a flame and especially focus on the in-phase and anti-phase oscillation. In-phase mode appears only when the oscillators are close enough to maintain coupling with each other all the time. Other modes appear when coupling strength remains stable for a minimum amount of time, resulting in phase-locked synchronization. The model proposed aims to explain how the distance between candle oscillators leads to multiple different collective behaviors of them
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