Symmetry breaking in a driven and strongly damped pendulum

Isohätälä, Jukka; Alekseev, Kirill N.; Kurki, Lauri; Pietiläinen, Pekka

doi:10.1103/physreve.71.066206

Cited by 15 publications

(20 citation statements)

References 37 publications

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“…However, it appears that both the identification of global and local symmetries and the precise detection of chaotic-periodic, periodic-chaotic [5], chaotic-chaotic transitions [4], "symmetry-breaking" bifurcations [31,28,33,29] and "symmetry-increasing" bifurcations [27] constitute promising results that bode well for the future, particularly in fields such a meteorology, finance and biomedicine. Indeed, the assessment of symmetry descriptors could be advantageously introduced for direct detection of symmetry breaking phenomena from the phase space (or time series) when the symmetry parameter varies.…”

Section: Discussionmentioning

confidence: 99%

“…This very common theoretical concept that shows the spatio-temporal invariance properties of systems has been much studied through the phase space representation to observe symmetry breaking [27]. This is particularly the case for nonlinear dynamical systems such as systems having on-off intermittency [28], those with a strongly damped pendulum system [29] and the Helmholtz-Duffing oscillator [7]. There are a certain number of analytical tools to study symmetry bifurcations [30], [31], [32].…”

Section: Introductionmentioning

confidence: 99%

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Recurrence and symmetry of time series: Application to transition detection

Girault¹

2015

Chaos, Solitons & Fractals

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International audienceThe study of transitions in low dimensional, nonlinear dynamical systems is a complex problem for which there is not yet a simple, global numerical method able to detect chaos–chaos, chaos–periodic bifurcations and symmetry-breaking, symmetry-increasing bifurcations. We present here for the first time a general framework focusing on the symmetry concept of time series that at the same time reveals new kinds of recurrence. We propose several numerical tools based on the symmetry concept allowing both the qualification and quantification of different kinds of possible symmetry. By using several examples based on periodic symmetrical time series and on logistic and cubic maps, we show that it is possible with simple numerical tools to detect a large number of bifurcations of chaos–chaos, chaos–periodic, broken symmetry and increased symmetry types

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Recurrence and symmetry of time series: Application to transition detection

Girault¹

2015

Chaos, Solitons & Fractals

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“…In the natural world, little exists in a state of true equilibrium; in fact, most of the physics around us is far from equilibrium 1 . On both macroscopic and microscopic levels, driven systems exhibit rich and complex behaviour well beyond their equilibrium properties, due to the delicate balance between the external drive and the ‘internal' equilibrium behaviour opposing the drive 2 3 4 5 6 7 8 9 10 .…”

mentioning

confidence: 99%

Microscopic dynamics of synchronization in driven colloids

Juniper

Straube

Besseling³

et al. 2015

Nat Commun

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Synchronization of coupled oscillators has been scrutinized for over three centuries, from Huygens' pendulum clocks to physiological rhythms. One such synchronization phenomenon, dynamic mode locking, occurs when naturally oscillating processes are driven by an externally imposed modulation. Typically only averaged or integrated properties are accessible, leaving underlying mechanisms unseen. Here, we visualize the microscopic dynamics underlying mode locking in a colloidal model system, by using particle trajectories to produce phase portraits. Furthermore, we use this approach to examine the enhancement of mode locking in a flexible chain of magnetically coupled particles, which we ascribe to breathing modes caused by mode-locked density waves. Finally, we demonstrate that an emergent density wave in a static colloidal chain mode locks as a quasi-particle, with microscopic dynamics analogous to those seen for a single particle. Our results indicate that understanding the intricate link between emergent behaviour and microscopic dynamics is key to controlling synchronization.

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“…If the governing equations remain invariant in transformation S, we say that they are symmetric or have symmetry S. In our previous works we have focused on the appearance of a spontaneous dc voltage via dynamical symmetry breaking [21,18,29,40,28]. Let u 0 be the generated dc voltage:…”

Section: Effective Circuit Model With a DC Current Sourcementioning

confidence: 99%

Rectification of terahertz radiation in semiconductor superlattices in the absence of domains

Isohätälä¹,

Alekseev²

2012

J. Phys.: Condens. Matter

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Abstract. We study theoretically the dynamical rectification of a terahertz ac electric field, i.e. the dc current and voltage response to the incident radiation, in strongly coupled semiconductor superlattices. We address the problem of stability against electric field domains: A spontaneous dc voltage is known to appear exactly for parameters for which a spatially homogeneous electron distribution is unstable. We show that by applying a weak direct current bias the rectifier can be switched from a zero dc voltage state to one with a finite voltage in full absence of domains. The switching occurs near the conditions of dynamical symmetry breaking of an unbiased semiconductor superlattice. Therefore our scheme allows for the generation of dc voltages that would otherwise be unreachable due to domain instabilities. Furthermore, for realistic, highly doped wide miniband superlattices at room temperature the generated dc field can be nearly quantized, that is, be approximately proportional to an integer multiple of ω/ea where a is the superlattice period and ω is the ac field frequency.

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Symmetry breaking in a driven and strongly damped pendulum

Cited by 15 publications

References 37 publications

Recurrence and symmetry of time series: Application to transition detection

Recurrence and symmetry of time series: Application to transition detection

Microscopic dynamics of synchronization in driven colloids

Rectification of terahertz radiation in semiconductor superlattices in the absence of domains

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