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Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 9 0 ∘. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.
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Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 9 0 ∘. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.
Data Types:
  • Dataset
Slime mould Physarum polycephalum is a single cell which physically oscillates via contraction of actomyosin in order to achieve motility. Several of its apparently ‘intelligent’ behaviour patterns such as anticipatory responses to periodic stimuli have recently been attributed as functions of the coupling between the oscillating intracellular reactions which drive its rhythmic muscular contraction, but the mechanisms that underlie these phenomena have not yet been experimentally verified. Through laboratory investigations in which we entrain the P. polycephalum plasmodium via periodic ultraviolet light exposure we find that this phenomenon is likely to result from biasing its various oscillating life processes through altering local concentration profiles of various allosteric molecules and their effectors. This temporarily overwrites the global streaming clock frequency and eradicates the wave packets usually observed in slime mould biomechanical oscillation. This response is likened to an intracellular chemical memory. We proceed to present a multi-agent model in which we demonstrate that travelling waves and oscillatory clock frequencies may emerge in the virtual organism’s biomechanical oscillator, although anticipatory responses cannot be replicated by simple mechanical interactions. We conclude by arguing that these phenomena are best characterised as analogue computation and discuss practical applications therein. The Physarum polycephalum actin network in a plasmodial tubule. SiR-actin staining, scale bar 200 μm.
Data Types:
  • Video
Slime mould Physarum polycephalum is a single cell which physically oscillates via contraction of actomyosin in order to achieve motility. Several of its apparently ‘intelligent’ behaviour patterns such as anticipatory responses to periodic stimuli have recently been attributed as functions of the coupling between the oscillating intracellular reactions which drive its rhythmic muscular contraction, but the mechanisms that underlie these phenomena have not yet been experimentally verified. Through laboratory investigations in which we entrain the P. polycephalum plasmodium via periodic ultraviolet light exposure we find that this phenomenon is likely to result from biasing its various oscillating life processes through altering local concentration profiles of various allosteric molecules and their effectors. This temporarily overwrites the global streaming clock frequency and eradicates the wave packets usually observed in slime mould biomechanical oscillation. This response is likened to an intracellular chemical memory. We proceed to present a multi-agent model in which we demonstrate that travelling waves and oscillatory clock frequencies may emerge in the virtual organism’s biomechanical oscillator, although anticipatory responses cannot be replicated by simple mechanical interactions. We conclude by arguing that these phenomena are best characterised as analogue computation and discuss practical applications therein. The Physarum polycephalum actin network in a plasmodial tubule. SiR-actin staining, scale bar 200 μm.
Data Types:
  • Video
The internal modes of the North Pacific can lead to climatic oscillations through ocean–atmosphere interactions and induce global climate responses. The best example is the Pacific Decadal Oscillation, but this fails to explain many climate phenomena. Here, another multidecadal variability over the North Pacific is described, found by analyzing reconstructed data covering the past 140 years. It is named the Pacific Multidecadal Oscillation (PMO), with anomalously high/low SSTs over the northeastern Pacific, and a quasi-60-year cycle. Related to this low-frequency variability of SST, the global mean temperature and precipitation present significant interdecadal differences. More importantly, the PMO index leads the global mean surface air temperature and SST by one to three years. The Arctic Oscillation pattern and atmospheric circulations are shown to change substantially with the transition of the PMO mode from positive to negative phases. This multidecadal oscillation improves the prospect for a long-term forecast of the global warming trend, since the PMO bears a remarkable relationship with global temperature.
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Figure S3. Influences on oscillation frequencies of the modules and hub nodes. For each of the 11 modules (1 plot per module), the influences on its frequencies of the modules and hub nodes (12 lines per plot corresponding to the modules and the hub nodes) are shown. The hub nodes become dominant in the process of global synchronization during the critical regime.
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  • Image
Figure S3. Influences on oscillation frequencies of the modules and hub nodes. For each of the 11 modules (1 plot per module), the influences on its frequencies of the modules and hub nodes (12 lines per plot corresponding to the modules and the hub nodes) are shown. The hub nodes become dominant in the process of global synchronization during the critical regime.
Data Types:
  • Image
The internal modes of the North Pacific can lead to climatic oscillations through ocean–atmosphere interactions and induce global climate responses. The best example is the Pacific Decadal Oscillation, but this fails to explain many climate phenomena. Here, another multidecadal variability over the North Pacific is described, found by analyzing reconstructed data covering the past 140 years. It is named the Pacific Multidecadal Oscillation (PMO), with anomalously high/low SSTs over the northeastern Pacific, and a quasi-60-year cycle. Related to this low-frequency variability of SST, the global mean temperature and precipitation present significant interdecadal differences. More importantly, the PMO index leads the global mean surface air temperature and SST by one to three years. The Arctic Oscillation pattern and atmospheric circulations are shown to change substantially with the transition of the PMO mode from positive to negative phases. This multidecadal oscillation improves the prospect for a long-term forecast of the global warming trend, since the PMO bears a remarkable relationship with global temperature.
Data Types:
  • Collection
Copyright information:Taken from "Distinguishing low frequency oscillations within the 1/spectral behaviour of electromagnetic brain signals"http://www.behavioralandbrainfunctions.com/content/3/1/62Behavioral and brain functions : BBF 2007;3():62-62.Published online 10 Dec 2007PMCID:PMC2235870.e 4 conditions forms the normalisation curve(-).
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Copyright information:Taken from "Distinguishing low frequency oscillations within the 1/spectral behaviour of electromagnetic brain signals"http://www.behavioralandbrainfunctions.com/content/3/1/62Behavioral and brain functions : BBF 2007;3():62-62.Published online 10 Dec 2007PMCID:PMC2235870.nding spectrograms.
Data Types:
  • Image
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