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To assess the ability of the pressure gradient between breast lesions and adjacent normal tissue estimated by 3D subharmonic-aided pressure estimation (SHAPE) to characterize indeterminate breast lesions. This prospective study enrolled patients scheduled for ultrasound-guided needle biopsies of a breast lesion. Before the biopsy, 3D SHAPE data were collected from the breast lesion during the infusion of an ultrasound contrast agent (Definity) as well as after clearance of the agent. Direct, invasive pressure measurements in the lesion and adjacent normal tissue were then obtained using an intracompartmental pressure monitoring system (C2DX) before tissue sampling as part of the biopsy procedure. The mean SHAPE gradient and invasive measurement gradient between the lesion and adjacent normal tissue were compared to the biopsy results. The SHAPE gradients were also compared to the invasive pressure gradients. There were 8 malignant and 13 benign lesions studied. The SHAPE gradients and invasive pressure gradients were significantly different between the benign and malignant lesions (2.86 ± 3.24 vs. -0.03 ± 1.72 a.u.; p = 0.03 and 9.9 ± 8.5 vs. 20.9 ± 8.0 mmHg; p = 0.008, respectively). The area under the curves, specificities, and sensitivities for detecting malignancy by SHAPE gradients and invasive pressure gradients were 0.79 and 0.88, 77% and 92%, and 88% and 50%, respectively. A weak negative correlation was found between the SHAPE and invasive pressure gradients (r = -0.2). The pressure gradient between a breast lesion and adjacent normal tissue estimated by 3D SHAPE shows potential for characterizing indeterminate breast lesions. [ABSTRACT FROM AUTHOR]

In the work, the 1/2 order subharmonic wave of two coupling cavitation bubbles is investigated numerically via Fourier spectrum analysis. By analyzing the dynamics of bubble, we find that the mutual interaction between bubbles can affect the appearance of 1/2 order subharmonic. The results of parameter dependence show that the intensity of 1/2 order subharmonic would be promoted or inhibited with the increase of mutual interaction. The higher the driving amplitude or the smaller the distance between bubbles, the stronger the mutual interaction is, and also the greater the promotion or suppression of the 1/2 order subharmonic is. Moreover, while the 1/2 order subharmonic occurs, the energy of bubble would alternate between two different peaks, and the temperature inside bubble has a similar fluctuation while the bubble collapses. This qualitative analysis suggests that the bubble′s dynamics for multi-bubble case is complex. Understanding the generation of subharmonic of bubble′s dynamics is of great significance for helpful applying of cavitation bubble.

A direct proof of Oka’s lemma on the relation of holomorphic convexity and the properties of the distance to the boundary function is provided. Some related problems for subharmonicity properties of this function are also studied. A new geometric property of pseudoconvex domains is described. [ABSTRACT FROM AUTHOR]

The use of the subharmonic signal from microbubbles exposed to ultrasound is a promising safe and cost-effective approach for the non-invasive measurement of blood pressure. Achieving a high sensitivity of the subharmonic amplitude to the ambient overpressure is crucial for clinical applications. However, currently used microbubbles have a wide size distribution and diverse shell properties. This causes uncertainty in the response of the subharmonic amplitude to changes in ambient pressure, which limits the sensitivity. The aim of this study was to use monodisperse microbubbles to improve the sensitivity of subharmonic-based pressure measurements. With the same shell materials and gas core, we used a flow-focusing microfluidic chip and a mechanical agitation method to fabricate monodisperse (∼2.45-µm mean radius and 4.7 % polydisperse index) and polydisperse microbubbles (∼1.51-µm mean radius and 48.4 % polydisperse index), respectively. We varied the ultrasound parameters (i.e., the frequency, peak negative pressure (PNP) and pulse length), and found that there was an optimal excitation frequency (2.8 MHz) for achieving maximal subharmonic emission for monodisperse microbubbles, but not for polydisperse microbubbles. Three distinct regimes (occurrence, growth, and saturation) were identified in the response of the subharmonic amplitude to increasing PNP for both monodisperse and polydisperse microbubbles. For the polydisperse microbubbles, the subharmonic amplitude decreased either monotonically or non-monotonically with ambient overpressure, depending on the PNP. By contrast, for the monodisperse microbubbles, there was only a monotonic decrease at all PNPs. The maximum sensitivity (1.18 dB/kPa, R2 = 0.97) of the subharmonic amplitude to ambient overpressure for the monodisperse microbubbles was ∼6.5 times higher than that for the polydisperse microbubbles (0.18 dB/kPa, R2 = 0.88). These results show that monodisperse microbubbles can achieve a more consistent response of the subharmonic signal to changes in ambient overpressure and greatly improve the measurement sensitivity.

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler–Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors. [ABSTRACT FROM AUTHOR]

Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too.

This paper deals with the modeling and theoretical study of an average-current-mode-controlled photovoltaic power conversion chain. It should be noted that current mode control is a superior scheme for controlling DC–DC power electronic converters for photovoltaic applications. Bifurcation diagrams, largest Lyapunov exponents, Floquet theory, and time series are used to study the dynamics of the system. The theoretical results show the existence of subharmonic oscillations and period-1 oscillations in the system. The results of the numerical simulations showed that when the battery voltage at the output of the converter is fixed and ramp amplitude is taken as a control parameter, the photovoltaic power system exhibits the phenomenon of period doubling leading to chaotic dynamics. Furthermore, bifurcation diagrams showed that both the critical value of ramp amplitude for the occurrence of border collision bifurcation and the critical value of ramp amplitude for the occurrence of period-1 in the proposed system increased with the value of the battery terminal voltage. The numerical results are in accordance with the theoretical ones. Finally, an external control based on a non-adaptive controller having a sinusoidal function as a target is applied to the overall system for the suppression of chaotic behavior. [ABSTRACT FROM AUTHOR]

Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too. [ABSTRACT FROM AUTHOR]

In this study, a piezoelectric MEMS (Micro-Electro-Mechanical-System) speaker with thoughtfully selected resonant frequencies of dual cantilever units is designed and implemented. Based on the lead zirconium titanate (PZT) thin film with superior piezoelectric coefficient, the cantilever diaphragm is designed through the modal analysis. In the 1.5 mm by 1.5 mm cantilever array, a high-frequency actuation unit with resonance of 13.1 kHz and a low-frequency actuation unit with resonance of 6.35 kHz constitute the proposed piezoelectric MEMS speaker. The boost of sound pressure level (SPL) due to the resonant mode of low-frequency actuation unit reduces the total harmonic distortion (THD) around the subharmonic frequency of high-frequency actuation unit. Meanwhile, the asymmetric triangle diaphragm reduces the maximum stress in the structure when operating at the resonant frequency, thereby mitigating the THD spikes resulting from the nonlinear structural behavior. In pressure-field measurements, the proposed design can reach SPL ≥ 70.0 dB from 2.7 kHz to 15.0 kHz with only 0.179 V rms input. At the same time, THD remains below 3.0 % from 3.2 kHz to 20 kHz. The outstanding performance under larger input signal and bias voltage is also verified. Actuated by 0.354 V rms and 2 V DC bias, the maximum SPL achieves 111.9 dB and the SPL is higher than 80.0 dB from 3.3 kHz to 14.1 kHz. Furthermore, THD is lower than 3.0 % from 1.0 kHz to 8.9 kHz. A promising solution of piezoelectric MEMS speaker for in-ear applications is demonstrated in this study. [Display omitted] • A dual-cantilever-unit MEMS speaker with thoughtfully designed resonances. • The low-frequency unit decreases subharmonic THD of the high-frequency unit. • The asymmetric triangle design reduces the maximum stress in diaphragms. • Comprehensive investigation on the characteristics of both SPL and THD. • Good potential for integration with DD to fulfill a high-quality in-ear product. [ABSTRACT FROM AUTHOR]

This work investigates the primary and secondary resonances of an electrostatically excited double-clamped microbeam and its feasibility to be used for sensing applications. The sensor design can be excited directly in the vicinity of the primary and secondary resonances. This excitation mechanism would portray certain nonlinear phenomena and it would certainly lead in increasing the sensitivity of the device. To achieve this, a nonlinear beam model describing transverse deflection based on the Euler–Bernoulli beam theory was utilized. Then, a reduced-order model (ROM) considering all geometric and electrical nonlinearities was derived. Three different techniques involving time domain, fast Fourier transforms (FFTs), and frequency domain (FRCs) were used to examine the appearance of subharmonic resonance of order of one-half under various excitation waveforms. The results show that higher forcing levels and lower damping are required to activate this resonance. We note that as the forcing increases, the size of the instability region grows fast and the size of the unstable region increases rapidly. This, in fact, is an ideal place for designing bifurcation inertia MEMS sensors.

This paper proposes a dual-mode brushless wound rotor synchronous machine (DBL-WRSM) for high starting torque. The proposed DBL-WRSM consists of two modes: induction and brushless (BL)-synchronous modes. First, the induction mode operates as a wound rotor induction machine (WRIM) to achieve a high starting torque. Second, the BL-synchronous mode operates as a brushless wound rotor synchronous machine (BL-WRSM) using the subharmonic of the stator magnetomotive force (MMF) in the steady state. To realize the dual-mode topology of the proposed machine, the stator is composed of two divided armature windings and two inverters that can produce subharmonics. The rotor has five switches that convert the rotor winding configuration between the two modes. To verify the proposed topology of DBL-WRSM, finite element analysis (FEA) was performed. Through the FEA results of the transient electromagnetic torque for the voltage source, it was confirmed that the proposed DBL-WRSM not only operates as a BL-WRSM in a steady state but also has a sufficiently high starting torque even under a full-load condition.

This paper presents a 220‐GHz subharmonic downconverter with high conversion gain (CG) and low noise figure (NF) implemented in 28 nm bulk CMOS, including a core mixer and an intermediate frequency (IF) amplifier. Based on the traditional quasi‐subharmonic mixer, new gate‐shorted technology is presented to improve NF and CG by adding a source inductor to reduce the loss of radiofrequency signals. In addition, the impedance transformation network provides passive voltage gain to suppress the noise of the IF amplifier. The downconverter achieves a minimum single‐sidebandNF of 15.5 dB and a maximum CG of 21.3 dB when the IF frequency is 10 MHz. The 1 dB compression point of the downconverter is −30 dBm and consumes 8 mA current with an operating voltage of 0.9 V. The core area of the chip is 200 × 160 µm2 [ABSTRACT FROM AUTHOR]

Objectives: Subharmonic aided pressure estimation (SHAPE) has been shown effective for noninvasively measuring hydrostatic fluid pressures in a variety of clinical applications. The objective of this study was to explore potential improvements in SHAPE sensitivity using monodisperse microbubbles. Methods: Populations of monodisperse microbubbles were created using a commercially available microfluidics device (Solstice Pharmaceuticals). Size distributions were assessed using a Coulter Counter and stability of the distribution following fabrication was evaluated over 24 hours. Attenuation of the microbubble populations from 1 to 10 MHz was then quantified using single element transducers to identify each formulation's resonance frequency. Frequency spectra over increasing driving amplitudes were investigated to determine the nonlinear phases of subharmonic signal generation. SHAPE sensitivity was evaluated in a hydrostatic pressure‐controlled water bath using a Logiq E10 scanner (GE Healthcare). Results: Monodisperse lipid microbubble suspensions ranging from 2.4 to 5.3 μm in diameter were successfully created and they showed no discernable change in size distribution over 24 hours following activation. Calculated resonance frequencies ranged from 2.1 to 6.3 MHz and showed excellent correlation with microbubble diameter (R2 > 0.99). When investigating microbubble frequency response, subharmonic signal occurrence was shown to begin at 150 kPa peak negative pressure, grow up to 225 kPa, and saturate at approximately 250 kPa. Using the Logiq E10, monodisperse bubbles demonstrated a SHAPE sensitivity of −0.17 dB/mmHg, which was nearly twice the sensitivity of the commercial polydisperse microbubble currently being used in clinical trials. Conclusions: Monodisperse microbubbles have the potential to greatly improve the sensitivity of SHAPE for the noninvasive measurement of hydrostatic pressures. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in giving sufficient conditions of a quaternionic plurisubharmonic function defined on a bounded quaternionic hyperconvex domain such that it can be approximated by a decreasing sequence of smooth functions. As an application, we study the geometric property of quaternionic B-regular domains. [ABSTRACT FROM AUTHOR]

During the production and application of bonding structures, non-uniform adhesive coatings and deterioration of adhesive materials often lead to weak bonding damage at crucial interfaces, significantly impacting structural robustness. In this paper, a novel subharmonic ultrasonic resonance method is developed for damage identification in the interfacial weak bonding. Based on a nonlinear spring model of imperfect adhesive interfaces, the multi-scale method is used to explain the mechanism and the conditions for the generation of the subharmonic resonance. The ultrasonic resonance is employed to enhance the nonlinear response of imperfect adhesive interfaces efficiently, as nonlinear characteristics are not readily apparent in cases of the interfacial weak bonding damage. By analyzing the subharmonic ultrasonic resonance phenomenon in the spectrum, the interfacial weak bonding damage identification experiment for a carbon fiber reinforced plastic-aluminum plate bonding structure is carried out. The results demonstrate that ultrasonic resonance can lower the threshold for generating subharmonic resonance and the subharmonic ultrasonic resonance method significantly amplifies the nonlinear response at the damaged area, improving detection capabilities amidst noise interference. Moreover, the efficacy of the subharmonic ultrasonic resonance method in detecting and locating weak bonding damage is confirmed. [ABSTRACT FROM AUTHOR]

In the work, the 1/2 order subharmonic wave of two coupling cavitation bubbles is investigated numerically via Fourier spectrum analysis. By analyzing the dynamics of bubble, we find that the mutual interaction between bubbles can affect the appearance of 1 / 2 order subharmonic. The results of parameter dependence show that the intensity of 1 / 2 order subharmonic would be promoted or inhibited with the increase of mutual interaction. The higher the driving amplitude or the smaller the distance between bubbles, the stronger the mutual interaction is, and also the greater the promotion or suppression of the 1 / 2 order subharmonic is. Moreover, while the 1/2 order subharmonic occurs, the energy of bubble would alternate between two different peaks, and the temperature inside bubble has a similar fluctuation while the bubble collapses. This qualitative analysis suggests that the bubble′s dynamics for multi-bubble case is complex. Understanding the generation of subharmonic of bubble′s dynamics is of great significance for helpful applying of cavitation bubble. [ABSTRACT FROM AUTHOR]

[Display omitted] [ABSTRACT FROM AUTHOR]

• A novel beam-spring 2-DOF magnetically coupled bistable energy harvester is proposed. • The operating bandwidth is improved by approximately 60 % compared with a CBEH. • The subharmonic responses are characterized by the coexistence of two coupling modes. • Reasonable spring stiffness design is helpful to further enhance the bandwidth. • The excitation threshold peak effect of the 2-DOF coupled system is studied. Introducing the magnetic coupling effect with multiple degrees of freedom to a conventional bistable energy harvester is helpful to further enhance its operating bandwidth. However, it is not straightforward to design due to its extremely complicated dynamic characteristics, meanwhile, some underlying mechanisms also need to be explored ulteriorly. This paper proposes a novel beam-spring two-degree-of-freedom magnetically coupled bistable energy harvester, combining the advantages of multistable and multimodal harvesters. Based on the theoretical model validated by experiments, the complex nonlinear dynamic behaviors of the system are investigated in detail, as well as the effects of key parameters on power generation capacity. It is found that the working bandwidth is improved by more than 60 % because of the additional contribution from the 2nd resonance region. And there are abundant interwell ultraharmonic and subharmonic responses characterized by the coexistence of out-of-phase and in-phase coupling modes. Under appropriate spring stiffness or certain initial conditions, the snap-through motion can be successfully triggered to enter a high-energy orbit. The parameter study shows that the magnet distance and spring stiffness significantly affect the effective bandwidth. Furthermore, the excitation threshold peak effect that hinders the connection of the two resonant frequency bands is also observed. Fortunately, it can be eliminated by the reasonable design of the 1st and 2nd natural frequencies to achieve a consecutive and broad effective bandwidth. This research provides a theoretical case for designing and developing wide-band and low-threshold bistable energy harvester. [Display omitted] [ABSTRACT FROM AUTHOR]

A 27–44 GHz subharmonic up-conversion mixer using 65 nm CMOS technology is presented. For subharmonic scheme and wide RF/IF bandwidth, a dual-ring topology is developed in this mixer design. To increase the linearity and conversion gain (CG) without adding additional local oscillator (LO) power, a LO boosting linearization technique is adopted. The subharmonic up-conversion mixer achieves a measured CG of −12 dB ± 1.5 dB from a wide RF frequency of 27 to 44 GHz. The 3-dB IF bandwidth is from dc to 10 GHz. After adopting the linearization technique, the output 1-dB compression point (OP1 dB) of the subharmonic up-conversion mixer can be improved from −12 to −9 dBm at 38 GHz with zero addition dc consumption. [ABSTRACT FROM AUTHOR]

We present an analytical proof that certain natural metric universal covers are Hadamard metric spaces. If ρ d s induces a complete distance d on a plane domain Ω , and ρ = φ ∘ u where u is (locally Lipschitz and) subharmonic in Ω , φ is positive and increasing on an interval containing u (Ω) with log φ convex, then (Ω , d) has a universal cover (Ω ~ , d ~) which is a Hadamard metric space (with geodesics that have Lipschitz continuous first derivatives). [ABSTRACT FROM AUTHOR]

The development of microbubble contrast agents has broadened the scope of medical ultrasound imaging. Along with dedicated imaging techniques, these agents provide enhanced echoes from the blood pool and have enabled diagnostic ultrasound to assess and quantify microvascular blood flow. Contrast-enhanced ultrasound is currently used worldwide with clinical indications in cardiology and radiology, and it continues to evolve and develop through innovative technological advancements. In this review article, we present an overview of the basic microbubble physics and bubble-specific imaging techniques that enable this modality, and follow this with a discussion on new and emerging applications.

Harmonic distortions caused by non-linear loads (NLLs) affect the behavior of electrical systems, creating harmonics in the fundamental signal. As a result, this deteriorates the power quality. Therefore, this work proposes the implementation of a hybrid filter based on an artificial neural network (ANN) control system, focused on subharmonic, interharmonic and odd harmonic distortions generated by a three-pulse cycloconverter. In addition, a passive double tuned filter was implemented to damp even and odd harmonics. As a result, the simulation performed in MATLAB/SIMULINK showed that the responses produced by the ANN are approximate to the distortions present in the electrical system. Consequently, the levels of total voltage distortions (THDV) and total current distortions (THDI) are reduced. Therefore, the ANN control system improves the quality in the electrical network because the current and voltage harmonics comply with the electrical standards. [ABSTRACT FROM AUTHOR]

• A flow-focusing microfluidic chip for monodisperse microbubbles (MM) generation. • An optimal frequency was identified for achieving maximal subharmonic for MM. • Three distinct regimes were found in subharmonic-PNP relationship for MM. • Subharmonic amplitude decreased monotonically with overpressure at all PNPs for MM. • MM can greatly improve the sensitivity of subharmonic-based pressure measurements. The use of the subharmonic signal from microbubbles exposed to ultrasound is a promising safe and cost-effective approach for the non-invasive measurement of blood pressure. Achieving a high sensitivity of the subharmonic amplitude to the ambient overpressure is crucial for clinical applications. However, currently used microbubbles have a wide size distribution and diverse shell properties. This causes uncertainty in the response of the subharmonic amplitude to changes in ambient pressure, which limits the sensitivity. The aim of this study was to use monodisperse microbubbles to improve the sensitivity of subharmonic-based pressure measurements. With the same shell materials and gas core, we used a flow-focusing microfluidic chip and a mechanical agitation method to fabricate monodisperse (∼2.45-µm mean radius and 4.7 % polydisperse index) and polydisperse microbubbles (∼1.51-µm mean radius and 48.4 % polydisperse index), respectively. We varied the ultrasound parameters (i.e., the frequency, peak negative pressure (PNP) and pulse length), and found that there was an optimal excitation frequency (2.8 MHz) for achieving maximal subharmonic emission for monodisperse microbubbles, but not for polydisperse microbubbles. Three distinct regimes (occurrence, growth, and saturation) were identified in the response of the subharmonic amplitude to increasing PNP for both monodisperse and polydisperse microbubbles. For the polydisperse microbubbles, the subharmonic amplitude decreased either monotonically or non-monotonically with ambient overpressure, depending on the PNP. By contrast, for the monodisperse microbubbles, there was only a monotonic decrease at all PNPs. The maximum sensitivity (1.18 dB/kPa, R 2 = 0.97) of the subharmonic amplitude to ambient overpressure for the monodisperse microbubbles was ∼6.5 times higher than that for the polydisperse microbubbles (0.18 dB/kPa, R 2 = 0.88). These results show that monodisperse microbubbles can achieve a more consistent response of the subharmonic signal to changes in ambient overpressure and greatly improve the measurement sensitivity. [ABSTRACT FROM AUTHOR]

Dual-perspective high-speed imaging and acoustic detection is used to characterise cavitation activity at the tip of a commercial 20 kHz (f0) ultrasonic horn, over 2 s sonications across the range of input powers available (20 – 100%). Imaging at 1 × 105 frames per second (fps) captures cavitation-bubble cluster oscillation at the horn-tip for the duration of the sonication. Shadowgraphic imaging at 2 Mfps, from an orthogonal perspective, probes cluster collapse and shock wave generation at higher temporal resolution, facilitating direct correlation of features within the acoustic emission data generated by the bubble activity. f0/m subharmonic collapses of the primary cavitation cluster directly beneath the tip, with m increasing through integer values at increasing input powers, are studied. Shock waves generated by periodic primary cluster collapses dominate the non-linear emissions of the cavitation noise spectra. Transitional input powers for which the value of m is indistinct, are identified. Overall shock wave content within the emission signals collected during sonications at transitional input powers are reduced, relative to input powers with distinct m. The findings are relevant for the optimisation of applications such as sonochemistry, known to be mediated by bubble collapse phenomena.

In this letter, we propose a novel wideband subharmonically pumped fully differential I–Q resistive mixer architecture, which eliminates the necessity for on-chip dc-blocking capacitors to integrate IF amplifiers. The proposed differential subharmonic mixer topology is verified by presenting a CMOS millimeter-wave monolithic integrated circuit (MMIC), which includes the mixer and two on-chip differential IF amplifiers at the mixer’s I- and Q-channels. The 3-dB IF frequency bandwidth is measured from 0.01 to 5 GHz with a peak conversion gain (CG) of −2 dB and an image rejection ratio (IRR) of more than 25 dB over the IF frequency range. The proposed mixer covers the input signal (RF) frequency from 170 to 185 GHz. The mixer has also been tested with an on-chip voltage-controlled oscillator (VCO) and shows −4.7-dB CG with a 3-dB IF bandwidth from 0.01 to 4.5 GHz. [ABSTRACT FROM AUTHOR]

We examine the stability of the elliptic solutions of the focusing nonlinear Schrödinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spectral stability of the elliptic solutions, establishing that solutions of smaller amplitude are stable with respect to larger classes of perturbations. We show that spectrally stable solutions are orbitally stable by constructing a Lyapunov functional using higher-order conserved quantities of NLS. [ABSTRACT FROM AUTHOR]

This article presents a multi-subharmonic switching (SHS) digital power amplifier (PA) architecture for enhancing power back-off (PBO) efficiency while achieving watt-level output power. The proposed phase-interleaved architecture provides the inherent cancellation of the subharmonic components in the PBO region, alleviating the burden of the matching network. The proposed multi-SHS scheme can be further combined with a class-G operation to create a greater number of efficiency peaks in the PBO region. A transformer-based, three-way power combiner and a triple-stacking class-D driver are utilized to obtain watt-level output power. The proof-of-concept PA prototype is implemented with a switched-capacitor PA (SCPA) architecture in 65-nm CMOS and achieved 30-dBm peak power at 1.9 GHz, with 45.9%/41.3%/35.3%/32.2%/24.2% drain efficiency located at 0-, −3.5-, −7.0-, −9.5-, and −12-dB PBO, respectively. The average efficiency was 31.4% in real-time operation with a 7.2-dB peak-to-average power ratio (PAPR) modulated signal. [ABSTRACT FROM AUTHOR]

The short pulse (SP) equation describes the propagation of ultrashort optical pulses in nonlinear media and possesses a Lax pair of the Wadati–Konno–Ichikawa (WKI) type. In this paper, using integrability, we examine the spectral stability of elliptic solutions to the SP equation. Firstly, we analytically give an explicit description of the spectrum of the WKI-Lax operator to the SP equation for elliptic potentials. Then, by constructing the squared-eigenfunction connection between the non-standard linear stability problem (L Z = Λ Z ′ ) and the Lax spectral problem, we prove that the elliptic solutions are spectrally stable with respect to subharmonic perturbations. • We analytically give an explicit description of the Lax spectrum of the SP equation. • We construct the squared-eigenfunction connection. • We prove that the elliptic solutions are spectrally stable. [ABSTRACT FROM AUTHOR]

The novel drug delivery system refers to the formulations and technologies for transporting a pharmaceutical compound in the body as it is needed to safely achieve its desired therapeutic effects. In this study, the onset vibrational amplitude of capillary surface waves for ultrasonic atomization spray is explained based on Faraday instability. Using ultrasonic frequency, the vibrational amplitude approached a critical point, and the liquid surface broke up into tiny drops. The micro-droplets were are steadily and continuously formed after the liquid feeding rate was optimized. The simulation study reported a minimum vibrational amplitude or onset value of 0.38 μm at 500 kHz frequency. The required minimum energy to atomize the drops was simulated by COMSOL Multiphysics simulation software. The simulation result agreed well with the numerical results of a subharmonic vibrational model that ocurred at 250 kHz frequency on the liquid surface. This newly designed single frequency ultrasonic atomizer showed its true physical characteristic of resonance on the fluid surface plane. Hence, this research will contribute to the future development of a single-frequency ultrasonic nebulizer and mechatronics for the generation of uniform atomized droplets.

In this study, the onset amplitude of the initial capillary surface wave for ultrasonic atomization of fluids has been implemented. The design and characterization of 485 kHz microfabricated silicon-based ultrasonic nozzles are presented for the concept of economic energy development. Each nozzle is composed of a silicon resonator and a piezoelectric drive section consisting of three Fourier horns. The required minimum energy to atomize liquid droplets is verified by COMSOL Multiphysics simulation software to clarify experimental data. The simulation study reports a minimum vibrational amplitude (onset) of 0.365 μm at the device bottom under the designated frequency of 485 kHz. The experimental study agrees well with the suggested frequency and the amplitude concerning the corresponding surface vibrational velocity in simulation. While operating, the deionized water was initially atomized into microdroplets at the given electrode voltage of 5.96 V. Microdroplets are steadily and continuously formed after the liquid feeding rate is optimized. This newly designed ultrasonic atomizer facilitates the development of capillary surface wave resonance at a designated frequency. A required vibrational amplitude and finite electric driving voltage promote not only the modern development in the green energy industry, but also the exploration of noninvasive, microencapsulated drug delivery and local spray needs.

The flicker electroretinogram (ERG) is typically analyzed in terms of peak-to-trough amplitude and implicit time. However, additional important information may be captured by spectral-domain analysis of the ERG harmonics (responses that occur at multiples of the stimulus frequency). This study describes an approach to analyze the harmonic components of the flicker ERG and its application to patients who have early-stage non-proliferative diabetic retinopathy (NPDR). Of particular interest were the sub-harmonic components occurring at 1.5x and 2.5x the stimulus frequency that produce cycle-to-cycle variation in amplitude termed "period doubling." Twenty visually-normal subjects, 20 diabetic subjects who have no clinically-apparent retinopathy (NDR), and 20 diabetic subjects who have mild NPDR participated. ERGs were recorded in response to sinusoidal flicker (27-63 Hz) and Fourier analysis was performed to extract fundamental and harmonic response amplitudes. Linear quantile mixed models (LQMMs) were used to compare the amplitude of the response components among the three subject groups. Results indicated that the maximum sub-harmonic amplitude occurred in the stimulus frequency range of 33-38 Hz for all subjects. The LQMMs showed a significant sub-harmonic amplitude reduction for the mild NPDR subjects compared to the controls; sub-harmonic amplitude for the NDR subjects did not differ significantly from the controls. In contrast, the fundamental response did not differ among the groups for stimulus frequencies between 33 and 38 Hz. Modeling these results indicated that subharmonic amplitude loss in mild NPDR subjects may be attributed to attenuated feedback occurring early in the retina, possibly at the synapse of cone photoreceptors and OFF bipolar cells. [ABSTRACT FROM AUTHOR]

Time-delay displacement and velocity feedback of different types of active control in a cantilever beam carrying an lumped mass is investigated in this paper. Based on Euler–Bernoulli beam theory, the nonlinear governing equation is studied with damping, harmonic distribution, displacement delay, velocity delay and two time delays. The multiple scales perturbation method is applied to obtain the frequency response equations near primary, superharmonic and subharmonic resonances. A thorough study on the stability is proposed, with a particular emphasis on delay feedback. The results show that the hardening and softening behaviors of the system depend on the location of lumped mass. Furthermore, the displacement feedback gain coefficient only makes the peak amplitude move to the low frequency, yet velocity feedback coefficient and their time delays can be used to effectively enhance the stability and quench the nonlinear vibration of the cantilever beam. Thus, reasonable selection of the control system parameters can effectively improve the level of vibration control for the mechanical system. [ABSTRACT FROM AUTHOR]

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This paper presents a subharmonic switching (SHS) digital power amplifier (PA) architecture that enhances power efficiency in the power back-off (PBO) region. The proposed technique can be combined with the class-G operation. By using either SHS or dual-power supply switching, it can provide several peak efficiency points, located at 0, −3.5, −9.5, and, −13 dB PBO. By judiciously choosing the optimal operation mode between SHS and dual supplies for each PA cell at different output power levels, we can further improve the efficiency between peaks. The SHS PA prototype is implemented with a switched-capacitor PA (SCPA) architecture in 65-nm CMOS to validate the effectiveness of the proposed technique, which achieves a 26.8-dBm peak output power with a 49.3% peak drain efficiency (DE) at 2.25 GHz and a 27% DE at −13-dB PBO. [ABSTRACT FROM AUTHOR]

Ultrasound contrast agent microbubbles have expanded the utility of biomedical ultrasound from anatomic imaging to the assessment of microvascular blood flow characteristics and ultrasound-assisted therapeutic applications. Central to their effectiveness in these applications is their resonant and non-linear oscillation behaviour. This article reviews the salient physics of an oscillating microbubble in an ultrasound field, with particular emphasis on phospholipid-coated agents. Both the theoretical underpinnings of bubble vibration and the experimental evidence of non-linear encapsulated bubble dynamics and scattering are discussed and placed within the context of current and emerging applications. [ABSTRACT FROM AUTHOR]

It is known that the occurrence and existence of ferroresonant oscillations at the subharmonic frequency (SHC) in power transmission lines (TL) and in power supply systems is extremely undesirable, since they cause ferroresonant overvoltages at different frequencies. At the same time, there is a wide class of nonlinear electrical circuits, in which the excitation of autoparametric oscillations (AIC) at the frequency of the SHC forms the basis of frequency converting devices serving as secondary power sources. It is shown that three-phase nonlinear systems are in one way or another equivalent circuits for power transmission lines, the main elements of which are: longitudinal compensation capacitors, transverse compensation reactors, and transformers with a nonlinear characteristic. To study the regularities of the excitation and maintenance of SHC at a frequency in three-phase electro-ferromagnetic circuits (EFMC), theoretical and experimental studies of an equivalent model of a three-phase circuit with nonlinear inductance were carried out. For the analysis of the steady-state mode of the SHC at the frequency, the method of a small parameter (averaging) was applied. A shortened differential equation of motion for a three-phase nonlinear circuit is obtained. By solving them, the regions of existence of the SHC and the critical parameters of the chain were determined. The obtained results of theoretical research are confirmed by experimental studies.

Summary: Noncumulative higher and subharmonic Lamb wave modes generated as a result of partial de‐bonding of piezoelectric wafer transducers (PWT) is numerically investigated and experimentally validated. The influence of excitation frequency on the extent of nonlinear interaction as a result of partially de‐bonded PWTs is discussed. A set of specific frequency ranges is arrived at based on the eigenvalue and harmonic analyses of PWTs used in this study. These are the frequency ranges in which resonant width direction modes of a square PWT or radial modes of a circular PWT are seen. In these frequency ranges, significantly high amplitudes of higher and subharmonics are observed. It is also seen that in these frequency ranges, subharmonic and higher harmonic amplitudes are dependent on de‐bond length and location. Signal processing is carried out using normalized fast Fourier transform for relative comparisons. [ABSTRACT FROM AUTHOR]

In order to provide a serious alternative to chemical batteries for the energy supply of isolated sensors, bistable generators have been enthusiastically highlighted in recent years for their ability to harvest vibration energy over a wider frequency range compared to linear generators. Nevertheless, these bistable harvesters are generally characterized through a frequency sweep which does not reveal all the steady-state behaviors they can reach and therefore their full energy harvesting potential. Among such behaviors, subharmonic motions are hidden by this classical characterization and therefore had not received a lot of attention. This study proposes an original complete analytical analysis of subharmonic orbits for energy harvesting to predict their contribution to the global bandwidth of bistable generators. In addition, a new criterion, referred as stability robustness, is introduced to estimate the sensitivity of those behaviors to disturbances of different levels, allowing to finely and accurately estimate suitable behaviors for energy harvesting purposes in realistic conditions (behaviors easy to reach and maintain in time). Experimental results conducted with a buckled beam based electromagnetic generator confirm the relevance of this criterion showing good agreement with the analytical predictions. Subharmonic behaviors finally appear, both theoretically and experimentally, to be of significant interest, as exploiting them leads to a 180 % increase of the global operating frequency range of the considered bistable energy harvester, for which more than 100  µW are generated on a 70  Hz bandwidth at 0.5  g. [ABSTRACT FROM AUTHOR]

In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space Rd, on the torus Td and on the sphere Sd. The crucial regularity property that these maximal functions share is that they are subharmonic in the corresponding detachment sets. [ABSTRACT FROM AUTHOR]

In this brief, a current ripple recovery (CRR) model is proposed for voltage-mode control converters. By adding a duty cycle sample-hold effect, the inductor current ripple can be recovered so that the high-frequency dynamical information in the inductor current compensates for a conventional averaged model. The CRR model can be used to judge the system stability and, more importantly, identify the subharmonic oscillation. These theoretical results are in good agreement with experimental ones, which demonstrates the validity of the CRR model. [ABSTRACT FROM AUTHOR]

Subharmonic-perturbed shear flow downstream of a two-dimensional backward-facing step was experimentally investigated. The Reynolds number was Re = 2.0 ×10, based on free-stream velocity and step height. Planar 2D-2C particle image velocimetry was employed to measure the separating and reattaching flow in the horizontal-vertical plane in the center position. The subharmonic perturbations were generated by an oscillating flap which was implemented over the step edge and driven by periodic Ampere force. The subharmonic frequency was 55 Hz as the half of the fundamental frequency of the turbulent shear layer. As a result of the subharmonic perturbations, the size of recirculation region behind the backward-facing step is reduced and the time-averaged reattachment length is 31.0% shorter than that of the natural flow. The evolution of vortices, including vortex roll-up, growth and breakdown process, is analyzed by using phase-averaging, cross-correlation function and proper orthogonal decomposition. It is found that Reynolds shear stress is considerably increased in which the vortices roll up and then break down further downstream. In particular, rapid growth of vortices based on the 'step mode' occurs at approximate half of the recirculation region, caused by in interaction between the shear layer and the recirculation region. Furthermore, the coherent structures, which are represented by a phase-correlated POD mode pair, are reconstructed in phases in order to show regular patterns of the subharmonic-perturbed coherent structures. [ABSTRACT FROM AUTHOR]

In recent years, the nonlinear ultrasonic technique has been widely utilized for detecting fatigue crack, one of the most common forms of damage. However, one of limitations associated with this technique is that nonlinearities can be produced not only by damage but also by various intrinsic effects such as boundary conditions. The objective of this paper is to demonstrate the application of a nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as two elastic, frictionless half spaces that enter into contact during vibration and where the contact obeys the basic Hertz contact law. The nonlinear ordinary differential equation drawn from the developed model was solved with the method of multiple scales. The threshold of subharmonic generation was studied. Different threshold behaviors between the nonlinear boundary condition and the fatigue crack were found that can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments using an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The experimental results demonstrated that the subharmonic component of the sensing signal could be used to detect the fatigue crack and further to distinguish it from inherent nonlinear boundary conditions. [ABSTRACT FROM AUTHOR]

Subharmonic signals backscattered from gas-filled lipid-shelled microbubbles have generated significant research interest because they can improve the detection and sensitivity of contrast-enhanced ultrasound imaging. However, the emission of subharmonic signals is strongly characterized by a temporal dependence, the origins of which have not been sufficiently elucidated. The features that influence subharmonic emissions need to be identified not only to better develop next-generation microbubble contrast agents, but also to develop more efficient subharmonic imaging (SHI) modes and therapeutic strategies. We examined the effect of microbubble filling gas on subharmonic emissions. Phospholipid shelled-microbubbles with different gaseous compositions such as sulfur hexafluoride (SF6), octafluoropropane (C3F8) or decafluorobutane (C4F10), nitrogen (N2)/C4F10 or air were insonated using a driving frequency of 10 MHz and peak negative pressure of 450 kPa, and their acoustic responses were tracked by monitoring both second harmonic and subharmonic emissions. Microbubbles were first acoustically characterized with their original gas and then re-characterized after substitution of the original gas with air, SF6 or C4F10. A measureable change in intensity of the subharmonic emissions with a 20- to 40-min delayed onset and increasing subharmonic emissions of the order 12-18 dB was recorded for microbubbles filled with C4F10. Substitution of C4F10 with air eliminated the earlier observed delay in subharmonic emissions. Significantly, substitution of SF6 for C4F10 successfully triggered a delay in the subharmonic emissions of the resultant agents, whereas substitution of C4F10 for SF6 eliminated the earlier observed suppression of subharmonic emissions, clearly suggesting that the type of filling gas contained in the microbubble agent influences subharmonic emissions in a time-dependent manner. Because our agents were dispersed in air-stabilized phosphate-buffered saline, these results suggest that the diffusivity of the gas from the agent to the surrounding medium is correlated with the time-dependent evolution of subharmonic emissions. [ABSTRACT FROM AUTHOR]

The paper considers the degenerate parametric interaction of an intense acoustic pumping beam and a weak signal beam at the subharmonic. The use of a special emitter system with independent signal emission at the harmonic and subharmonic made it possible to study the features of nonlinear interaction both for different amplitude levels and arbitrary phase relations of the fields at these frequencies. Just as predicted in the theory, the experiment showed that signal amplification at the subharmonic hardly occurs at all. It is shown that the use of odd field harmonics, which are absent for a zero amplitude of the signal wave, makes it possible to substantially increase the efficiency of isolating a weak signal wave. The interaction of beams for large and small acoustic Reynolds numbers of the signal wave is studied. [ABSTRACT FROM AUTHOR]

Bolted joint structures are prone to bolt loosening under environmental and operational vibrations, which may severely affect the structural integrity. This paper presents a bolt looseness recognition method based on the subharmonic resonance analysis. The bolted joint structure was simplified to a two-degree-of-freedom nonlinear model, and a multiple timescale method was used to explain the phenomenon of the subharmonic resonance and conditions for the generation of subharmonics. Numerical simulation predictions for the generation of the subharmonics and conditions for the subharmonics can be found with respect to the excitation frequency and the excitation amplitude. Experiments were performed on a bolt-joint aluminum beam, where the damage was simulated by loosening the bolts. Two surface-bonded piezoelectric transducers were utilized to generate continuous sinusoidal excitation and to receive corresponding sensing signals. The experimental results demonstrated that subharmonic components would appear in the response spectrum when the bolted structure was subjected to the excitation of twice its natural frequency. This subharmonic resonance method was found to be effective on bolt looseness detection. [ABSTRACT FROM AUTHOR]

We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic functions. It is shown that the sum of two quasinearly subharmonic functions may not be quasinearly subharmonic. Moreover, we characterize the harmonicity via quasinearly subharmonicity. [ABSTRACT FROM AUTHOR]

Let a and b be elements of a semisimple, complex and unital Banach algebra A . Using subharmonic methods, we show that if the spectral containment σ ( a x ) ⊆ σ ( b x ) holds for all x ∈ A , then ax belongs to the bicommutant of bx for all x ∈ A . Given the aforementioned spectral containment, the strong commutation property then allows one to derive, for a variety of scenarios, a precise connection between a and b . The current paper gives another perspective on the implications of the above spectral containment which was also studied, not long ago, by J. Alaminos, M. Brešar et al. [ABSTRACT FROM AUTHOR]

The subharmonic threshold for ultrasound contrast agents has been defined as a 20–25 dB difference between the fundamental and subharmonic (2/1) spectral components of the backscatter signal. However, this Fourier-based criterion assumes a linear time-invariant signal. A more appropriate criterion for short cycle and frequency-modulated waveforms is proposed with an adaptive signal-processing approach based on the empirical mode decomposition (EMD) method. The signal is decomposed into an orthogonal basis known as intrinsic mode functions (IMFs) and a subharmonic threshold is defined with respect to the energy ratio of the subharmonic IMF component to that of the incident signal. The method is applied to backscatter data acquired from two polymer-shelled contrast agents, Philips (#38, mean diameter 2.0 \mu \textm ) and Point Biomedical (#12027, mean diameter 3.9 \mu \textm ). The acoustic backscatter signals are investigated for a single contrast agent subjected to monofrequency (20 MHz, 20 cycles) and chirp (15–25 MHz, 20 cycles) forcing for incident pressures ranging from 0.5 to 2.4 MPa. In comparison to the spectral peak difference (20 dB) criterion, the EMD method is more sensitive in determining subharmonic signals. [ABSTRACT FROM PUBLISHER]

In this article, we study the existence of periodic and subharmonic solutions for a class of non-autonomous first-order Hamiltonian systems such that the nonlinearity has a growth at infinity faster than $|x|^{\alpha}$, $0\leq\alpha < 1$. We also study the minimality of periods for such solutions. Our results are illustrated by specific examples. The proofs are based on the least action principle and a generalized saddle point theorem.

Recently, many publications reported the generation of subharmonic frequency (f0/2) and its potential use in imagingfrom ultrasound contrast agent (UCA). Subharmonic imaging (SHI) has provided better contrast resolution over the secondharmonic signals due to the lack of subharmonic generation in the tissue region. However, subharmonic separation in SHIutilizes linear bandpass filtering only. In this paper, we compare the subharmonic separation capability of linear band filter(LBF), pulse inversion (PI), and their combination (PILBF) based on contrast-to-tissue ratio (CTR). Results show that theCTR values from the LBF, the PI, and the PILBF are 20.30, 40.30, and 52.74 dB, respectively. The optimal stopband attenuation and fractional bandwidth for the PILBF method are 50 dB and 10%, respectively. This high CTR value indicates thefeasibility of the PILBF method in creating high quality ultrasound image from subharmonic frequency.