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Concept: Harmonic oscillator


The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

Concepts: Quantum mechanics, Physics, Laser, Interaction, Oscillation, Wave, Normal mode, Harmonic oscillator


The newly proposed in-plane resonant nano-electro-mechanical (IP R-NEM) sensor, that includes a doubly clamped suspended beam and two side electrodes, achieved a mass sensitivity of less than zepto g/Hz based on analytical and numerical analyses. The high frequency characterization and numerical/analytical studies of the fabricated sensor show that the high vacuum measurement environment will ease the resonance detection using the capacitance detection technique if only the thermoelsatic damping plays a dominant role for the total quality factor of the sensor. The usage of the intrinsic junction-less field-effect-transistor (JL FET) for the resonance detection of the sensor provides a more practical detection method for this sensor. As the second proposed sensor, the introduction of the monolithically integrated in-plane MOSFET with the suspended beam provides another solution for the ease of resonance frequency detection with similar operation to the junction-less transistor in the IP R-NEM sensor. The challenging fabrication technology for the in-plane resonant suspended gate field-effect-transistor (IP RSG-FET) sensor results in some post processing and simulation steps to fully explore and improve the direct current (DC) characteristics of the sensor for the consequent high frequency measurement. The results of modeling and characterization in this research provide a realistic guideline for these potential ultra-sensitive NEM sensors.

Concepts: Transistor, Resonance, Harmonic oscillator, Optical cavity, Electronics terms, Damping, RLC circuit, Q factor


This paper focuses on several aspects extending the dynamical efficiency of a cantilever beam vibrating in the third mode. A few ways of producing this mode stimulation, namely vibro-impact or forced excitation, as well as its application for energy harvesting devices are proposed. The paper presents numerical and experimental analyses of novel structural dynamics effects along with an optimal configuration of the cantilever beam. The peculiarities of a cantilever beam vibrating in the third mode are related to the significant increase of the level of deformations capable of extracting significant additional amounts of energy compared to the conventional harvester vibrating in the first mode. Two types of a piezoelectric vibrating energy harvester (PVEH) prototype are analysed in this paper: the first one without electrode segmentation, while the second is segmented using electrode segmentation at the strain nodes of the third vibration mode to achieve effective operation at the third resonant frequency. The results of this research revealed that the voltage generated by any segment of the segmented PVEH prototype excited at the third resonant frequency demonstrated a 3.4-4.8-fold increase in comparison with the non-segmented prototype. Simultaneously, the efficiency of the energy harvester prototype also increased at lower resonant frequencies from 16% to 90%. The insights presented in the paper may serve for the development and fabrication of advanced piezoelectric energy harvesters which would be able to generate a considerably increased amount of electrical energy independently of the frequency of kinematical excitation.

Concepts: Wave, Frequency, Classical mechanics, Resonance, Vibration, Harmonic oscillator, Standing wave, Energy harvesting


The dielectric properties of Z-type hexaferrite Sr3Co2Fe24O41 (SCFO) have been investigated as a function of temperature from 153 to 503 K between 1 and 2 GHz. The dielectric responses of SCFO are found to be frequency dependent and thermally activated. The relaxation-type dielectric behavior is observed to be dominating in the low frequency region and resonance-type dielectric behavior is found to be dominating above 10(8) Hz. This frequency dependence of dielectric behavior is explained by the damped harmonic oscillator model with temperature dependent coefficients. The imaginary part of impedance (Z″) and modulus (M″) spectra show that there is a distribution of relaxation times. The scaling behaviors of Z″ and M″ spectra further suggest that the distribution of relaxation times is temperature independent at low frequencies. The dielectric loss spectra at different temperatures have not shown a scaling behavior above 10(8) Hz. A comparison between the Z″ and the M″ spectra indicates that the short-range charges motion dominates at low temperatures and the long-range charges motion dominates at high temperatures. The above results indicate that the dielectric dispersion mechanism in SCFO is temperature independent at low frequencies and temperature dependent at high frequencies due to the domination of resonance behavior.

Concepts: Optics, Fundamental physics concepts, Wave, Physical quantities, Hertz, Resonance, Harmonic oscillator, Dielectric


This paper introduces a modern version of the classical Huygens' experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks-ad hoc designed and fabricated-which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit ‘sympathetic’ motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

Concepts: Scientific method, Science, Theory, Harmonic oscillator, Simple harmonic motion, Pendulum clock, Christiaan Huygens, Escapement


Acquired nystagmus, a highly symptomatic consequence of damage to the substrates of oculomotor control, often is resistant to pharmacotherapy. Although heterogeneous in its neural cause, its expression is unified at the effector-the eye muscles themselves-where physical damping of the oscillation offers an alternative approach. Because direct surgical fixation would immobilize the globe, action at a distance is required to damp the oscillation at the point of fixation, allowing unhindered gaze shifts at other times. Implementing this idea magnetically, herein we describe the successful implantation of a novel magnetic oculomotor prosthesis in a patient.

Concepts: Eye, Amputation, Harmonic oscillator, Pupil, Simple harmonic motion


Tapping or clapping to an auditory beat, an easy task for most individuals, reveals precise temporal synchronization with auditory patterns such as music, even in the presence of temporal fluctuations. Most models of beat-tracking rely on the theoretical concept of pulse: a perceived regular beat generated by an internal oscillation that forms the foundation of entrainment abilities. Although tapping to the beat is a natural sensorimotor activity for most individuals, not everyone can track an auditory beat. Recently, the case of Mathieu was documented (Phillips-Silver et al. 2011 Neuropsychologia 49, 961-969. (doi:10.1016/j.neuropsychologia.2011.02.002)). Mathieu presented himself as having difficulty following a beat and exhibited synchronization failures. We examined beat-tracking in normal control participants, Mathieu, and a second beat-deaf individual, who tapped with an auditory metronome in which unpredictable perturbations were introduced to disrupt entrainment. Both beat-deaf cases exhibited failures in error correction in response to the perturbation task while exhibiting normal spontaneous motor tempi (in the absence of an auditory stimulus), supporting a deficit specific to perception-action coupling. A damped harmonic oscillator model was applied to the temporal adaptation responses; the model’s parameters of relaxation time and endogenous frequency accounted for differences between the beat-deaf cases as well as the control group individuals.

Concepts: Quantum mechanics, Oscillation, Resonance, Normal mode, Harmonic oscillator, Simple harmonic motion, Pendulum, Ordinary differential equations


Coupling a microscopic mechanical resonator to a nanoscale quantum system enables control of the mechanical resonator via the quantum system and vice-versa. The coupling is usually achieved through functionalization of the mechanical resonator, but this results in additional mass and dissipation channels. An alternative is an intrinsic coupling based on strain. Here we employ a monolithic semiconductor system: the nanoscale quantum system is a semiconductor quantum dot (QD) located inside a nanowire. We demonstrate the resonant optical driving of the QD transition in such a structure. The noise spectrum of the resonance fluorescence signal, recorded in the single-photon counting regime, reveals a coupling to mechanical modes of different types. We measure a sensitivity to displacement of 65 fm/[Formula: see text] limited by charge noise in the device. Finally, we use thermal excitation of the different modes to determine the location of the QD within the trumpet, and calculate the contribution of the Brownian motion to the dephasing of the emitter.Resonant driving of a nanoscale quantum system coupled to a microscopic mechanical resonator may have uses in precision sensing and quantum information. The authors realize this by tailoring the geometry of a semiconductor nanowire embedding a quantum dot, detecting sub-picometre displacements.

Concepts: Electron, Photon, Quantum mechanics, Resonator, Wave, Resonance, Harmonic oscillator, Albert Einstein


There is evidence that vibrations of soft tissue compartments are not appropriately described by a single sinusoidal oscillation for certain types of locomotion such as running or sprinting. This paper discusses a new method to quantify damping of superimposed oscillations using a wavelet-based time-frequency approach. This wavelet-based method was applied to experimental data in order to analyze the decay of the overall power of vibration signals over time. Eight healthy subjects performed sprinting trials on a 30m runway on a hard surface and a soft surface. Soft tissue vibrations were quantified from the tissue overlaying the muscle belly of the medial gastrocnemius muscle. The new methodology determines damping coefficients with an average error of 2.2% based on a wavelet scaling factor of 0.7. This was sufficient to detect differences in soft tissue compartment damping between the hard and soft surface. On average, the hard surface elicited a 7.02s(-1) lower damping coefficient than the soft surface (p<0.05). A power spectral analysis of the muscular vibrations occurring during sprinting confirmed that vibrations during dynamic movements cannot be represented by a single sinusoidal function. Compared to the traditional sinusoidal approach, this newly developed method can quantify vibration damping for systems with multiple vibration modes that interfere with one another. This new time-frequency analysis may be more appropriate when an acceleration trace does not follow a sinusoidal function, as is the case with multiple forms of human locomotion.

Concepts: Muscle, Tissues, Wave, Vibration, Harmonic oscillator, Simple harmonic motion, Damping, Mechanical vibrations


Mechanical oscillators are present in almost every electronic device. They mainly consist of a resonating element providing an oscillating output with a specific frequency. Their ability to maintain a determined frequency in a specified period of time is the most important parameter limiting their implementation. Historically, quartz crystals have almost exclusively been used as the resonating element, but micromechanical resonators are increasingly being considered to replace them. These resonators are easier to miniaturize and allow for monolithic integration with electronics. However, as their dimensions shrink to the microscale, most mechanical resonators exhibit nonlinearities that considerably degrade the frequency stability of the oscillator. Here we demonstrate that, by coupling two different vibrational modes through an internal resonance, it is possible to stabilize the oscillation frequency of nonlinear self-sustaining micromechanical resonators. Our findings provide a new strategy for engineering low-frequency noise oscillators capitalizing on the intrinsic nonlinear phenomena of micromechanical resonators.

Concepts: Laser, Resonator, Oscillation, Wave, Feedback, Periodic function, Beat, Harmonic oscillator