Drum Modes Research Articles

Mechanical Mode Imaging of a High-Q Hybrid hBN/Si3N4 Resonator.

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si3N4 membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si3N4 membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si3N4 membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si3N4 membranes for optomechanical or sensing applications.

The evolution of drum modes with strike intensity: Analysis and synthesis using the discrete cosine transform

The synthesis of convincing acoustic drum sounds remains an open problem. In this paper, a method for analysing and synthesising pitch glide in drums is proposed, whereby the discrete cosine transform (DCT) of an unwindowed drum sound is modelled. This is an extension of the scheme initially proposed by Kirby and Sandler [(2020). Proceedings of the 23rd International Conference on Digital Audio Effects, Vienna, Austria, pp. 155-162], which was able to reproduce key components of drum sounds accurately enough that they could not be distinguished from the reference samples. Here, drum modes were analysed in greater detail for a tom-tom struck at 67 different intensities to investigate their evolution with strike velocity. A clear evolution was observed in the DCT features, and interpolation was used to synthesise the modes of intermediate velocity. These synthesised modes were evaluated objectively through null testing, which showed that a continuous blending of strike velocities could be achieved throughout the data set. An AB listening test was also performed, where 20 participants attempted to distinguish between pairs of real and synthesised sounds. Exactly 50% accuracy was achieved overall, which demonstrates that the synthesised samples were deemed to sound as realistic as genuine samples. These results demonstrate that the DCT representation is a valuable framework for analysis and synthesis of drum sounds. It is also likely that this approach could be applied to other instruments.

Gravitational Forces Between Nonclassical Mechanical Oscillators

Interfacing quantum mechanics and gravity is one of the great open questions in natural science. Micromechanical oscillators have been suggested as a plausible platform to carry out these experiments. We present an experimental design aiming at these goals, inspired by Schm\"ole et al., Class. Quantum Grav. 33, 125031 (2016). Gold spheres weighing on the order a milligram will be positioned on large silicon nitride membranes, which are spaced at submillimeter distances from each other. These mass-loaded membranes are mechanical oscillators that vibrate at $\sim 2$ kHz frequencies in a drum mode. They are operated and measured by coupling to microwave cavities. First, we show that it is possible to measure the gravitational force between the oscillators at deep cryogenic temperatures, where thermal mechanical noise is strongly suppressed. We investigate the measurement of gravity when the positions of the gravitating masses exhibit significant quantum fluctuations, including preparation of the massive oscillators in the ground state, or in a squeezed state. We also present a plausible scheme to realize an experiment where the two oscillators are prepared in a two-mode squeezed motional quantum state that exhibits nonlocal quantum correlations and gravity the same time. Although the gravity is classical, the experiment will pave the way for testing true quantum gravity in related experimental arrangements. In a proof-of-principle experiment, we operate a 1.7 mm diameter Si$_3$N$_4$ membrane loaded by a 1.3 mg gold sphere. At 10 mK temperature, we observe the drum mode with a quality factor above half a million at 1.7 kHz, showing strong promise for the experiments. Following implementation of vibration isolation, cryogenic positioning, and phase noise filtering, we foresee that realizing the experiments is in reach by combining known pieces of current technology.

Quantum back-action-evading measurement of motion in a negative mass reference frame.

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation-the so-called standard quantum limit-on the precision of sensing of position, velocity and acceleration. Here we show that QBA on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational 'drum' mode of a millimetre-sized dielectric membrane, and the spin oscillator is an atomic ensemble in a magnetic field. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by -1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

Electromagnetic coupling to centimeter-scale mechanical membrane resonators via RF cylindrical cavities

We present experimental and theoretical results for the excitation of a mechanical oscillator via radiation pressure with a room-temperature system employing a relatively low-(Q) centimeter-size mechanical oscillator coupled to a relatively low-Q standard three-dimensional radio-frequency (RF) cavity resonator. We describe the forces giving rise to optomechanical coupling using the Maxwell stress tensor and show that nanometer-scale displacements are possible and experimentally observable. The experimental system is composed of a 35 mm diameter silicon nitride membrane sputtered with a 300 nm gold conducting film and attached to the end of a RF copper cylindrical cavity. The RF cavity is operated in its mode and amplitude modulated on resonance with the fundamental drum modes of the membrane. Membrane motion is monitored using an unbalanced, non-zero optical path difference, optically filtered Michelson interferometer capable of measuring sub-nanometer displacements.

High-finesse Fabry\u2013Perot cavities with bidimensional Si3N4 photonic-crystal slabs

Light scattering by a two-dimensional photonic-crystal slab (PCS) can result in marked interference effects associated with Fano resonances. Such devices offer appealing alternatives to distributed Bragg reflectors and filters for various applications, such as optical wavelength and polarization filters, reflectors, semiconductor lasers, photodetectors, bio-sensors and non-linear optical components. Suspended PCS also have natural applications in the field of optomechanics, where the mechanical modes of a suspended slab interact via radiation pressure with the optical field of a high-finesse cavity. The reflectivity and transmission properties of a defect-free suspended PCS around normal incidence can be used to couple out-of-plane mechanical modes to an optical field by integrating it in a free-space cavity. Here we demonstrate the successful implementation of a PCS reflector on a high-tensile stress Si3N4 nanomembrane. We illustrate the physical process underlying the high reflectivity by measuring the photonic-crystal band diagram. Moreover, we introduce a clear theoretical description of the membrane scattering properties in the presence of optical losses. By embedding the PCS inside a high-finesse cavity, we fully characterize its optical properties. The spectrally, angular- and polarization-resolved measurements demonstrate the wide tunability of the membrane’s reflectivity, from nearly 0 to 99.9470±0.0025%, and show that material absorption is not the main source of optical loss. Moreover, the cavity storage time demonstrated in this work exceeds the mechanical period of low-order mechanical drum modes. This so-called resolved-sideband condition is a prerequisite to achieve quantum control of the mechanical resonator with light.

Underwater sound transmission through arrays of disk cavities in a soft elastic medium.

Scattering from a cavity in a soft elastic medium, such as silicone rubber, resembles scattering from an underwater bubble in that low-frequency monopole resonance is obtainable in both cases. Arrays of cavities can therefore be used to reduce underwater sound transmission using thin layers and low void fractions. This article examines the role of cavity shape by microfabricating arrays of disk-shaped air cavities into single and multiple layers of polydimethylsiloxane. Comparison is made with the case of equivalent volume cylinders which approximate spheres. Measurements of ultrasonic underwater sound transmission are compared with finite element modeling predictions. The disks provide a deeper transmission minimum at a lower frequency owing to the drum-type breathing resonance. The resonance of a single disk cavity in an unbounded medium is also calculated and compared with a derived estimate of the natural frequency of the drum mode. Variation of transmission is determined as a function of disk tilt angle, lattice constant, and layer thickness. A modeled transmission loss of 18 dB can be obtained at a wavelength about 20 times the three-layer thickness, and thinner results (wavelength/thickness ∼ 240) are possible for the same loss with a single layer depending on allowable hydrostatic pressure.

Nonlinear experiments of tuning curve resonances for the vibrational modes of a weakly stretched circular membrane

Nonlinear oscillations of a pre-stretched 11.5 cm diameter latex circular membrane clamped rigidly around the boundary were investigated. The relaxed membrane thickness was 0.4 mm. An 8 cm diameter loud speaker drove the membrane from below using a swept sinusoidal tone. Low drive tuning curve sweeps demonstrated resonant frequencies corresponded to the first three radially symmetric linear drum modes (56, 147.6, and 240.5 Hz) sweeping from 50 to 300 Hz. Regression yielded a transverse wave speed of 10.6 m/s. Incrementally increasing the speaker amplitude (after each sweep) showed the lowest resonant frequency at first decreases, then increases with increasing acoustic drive pressure. Higher modes exhibited frequency increases with drive level. Tuning curve responses were measured using a 6 mm diameter microphone 5 mm above the center of the membrane. Nonlinear tuning curves hysteresis effects occur for higher drive levels sweeping between 50 and 70 Hz. Here, the amplitude sharply falls from a high to a low microphone response at fa = 59 Hz. With the same drive level, a sweep tone starting from 70 Hz to 50 Hz exhibits at fa = 57.5 Hz, a jump from a lower to a higher microphone response. [Goncalves et al., J. Vib. Sound 327, 231 (2009).]

Normal modes of a circular drum head under nonuniform applied tension: Mode splitting with respect to perturbation symmetry.

The effect of nonuniform tension on the normal modes of single headed musical drums is examined. Using the common (m,n) designation, ideal circular membrane modes with m>0 are doubly degenerate. This degeneracy may be lifted by a perturbation to the circular symmetry. Of practical interest to drummers are perturbations caused by nonuniform tension applied at the rim of the drum in the tuning process, leading in some cases to audible frequency splitting. The symmetry of the perturbation determines which of the various two‐fold degenerate modes will split, and to what degree the two resulting frequencies will differ. A selection rule taken from group theory is used, along with principles of perturbation theory, to describe a general model of the frequency splitting of drum modes under the influence of nonuniform applied tension. This model is compared with results of finite element modeling of the membrane normal modes. Experimental results obtained using electronic speckle pattern interferometry (ESPI) are...

Béla Bartók’s Arab music research and composition

In 1913 Béla Bartók traveled to Algeria to research Arab folk music. He took with him the most modern technological device then available, the Edison phonograph, and recorded Arab peasants performing their music. Analysis of his ensuing scholarly documentation and free composition reveals the inspiration Bartók drew from Arab folk music, not only in his treatment of traditional musical elements — melody, rhythm, and harmony — but also in novel incorporation of exotic timbre, scales, drum modes, ululation, and exorcism. This paper elucidates diverse musical elements with examples from authentic folk music and Bartók’s compositions. What emerges is a remarkably comprehensive image of Arab music, seen through the lens of Béla Bartók’s unique scholarship and creativity.

Cyclic total reflux batch distillation with two reflux drums

The present work proposes a novel cyclic total reflux (CTR) operation of batch distillation with two reflux drums working alternatively. A mathematical model is set up for the process. The computational comparison of the novel policy with the regular constant reflux and non-cyclic total reflux (NCTR) operations is also presented. The experimental runs of the new mode show that it can be operated and controlled more easily. The novel operation is significantly time saving compared to the mode of regular constant reflux theoretically and experimentally. The two reflux drum mode of CTR is also suitable for the separation of the mixture containing a large amount of light component.

INDIRECT THERMAL DRYING OF LIGNITE: DESIGN ASPECTS OF A ROTARY DRYER

ABSTRACT An investigation of the thermal drying of lignite has been carried out, by using an indirect heat pilot rotary drum. The process aims at the production of dry lignite and clean steam as part of a gasification procedure. Both flighted and bare drum modes have been employed. Temperature profiles along the dryer length, the amount of evaporation (moisture conversion) and the solids residence time distribution (RTD) were measured. A non-isothermal model was tested under three different regimes of solids flow. Model integration, by taking account of experimental amount of evaporation at dryer exit and temperature profiles along the dryer length, has been utilized in the validation of drying kinetics and heat transfer correlations. Model predictions compare satisfactorily with the operating data of an indirect heat industrial lignite dryer. Overall heat transfer coefficients of the pilot rotary dryer were found to agree well with those reported for direct heat dryers.

The Four Modes of Drum: Popular Fiction and Social Control in South Africa

Literature is both an object and an agent of social control. Not only is it shaped by social constraints, but it is also a constraint on society. Ezekiel Mphahlele (1962: 186), the South African writer, has lamented the effect of society on literature in his homeland: During the last twenty years the political, social climate of South Africa has been growing viciously difficult for a non-white to write in. It requires tremendous organization of one's mental and emotional faculties before one can write a poem or a novel or a play. This has become all but impossible…[At one time,] oppression provided just a sufficient spur to adult creative writing. The spur is a paralysing one today. Although the short story is very demanding, it is often used as a short-cut to prose meaning. And so it has become the most common medium in African literary activity, barring the large volume of vernacular writing being produced for school use. Oppression constrains not only the structure of literature but also its content. Mphahlele suggests that the short story in such a racist setting goes through three stages: romance or escape, then protest, and finally irony. He calls irony “the meeting point of acceptance and rejection in the broadest terms: acceptance and protest in specific areas of black-white relations within implicit acceptance in a larger area” (Mphahlele, 1962: 188).