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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]

[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.

• 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]

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. [ABSTRACT FROM AUTHOR]