Refined secondary Bjerknes force equation for double bubbles with pulsation, translation, and deformation.

The secondary Bjerknes force (SBF) is the time-averaged interaction between two bubbles driven in a sound field. We derived a refined formula for the interaction force, incorporating the radial vibration and translational and deformational motions of the bubble. The coupling of pulsation, translation, and deformation enhances the interaction between bubbles but also weakens their stability, making it easier for bubbles to merge or break during motion. The effects of the coupling mode on the magnitude and direction of SBFs coupled with pulsation, translation, and deformation were numerically analyzed and studied. Under certain sound-field conditions, the SBF increased with increasing pressure amplitude, initial radius, and initial velocity, while decreased as the distance increased. In addition, the SBF irregularly increased with increasing frequency.

Dynamics of three cavitation bubbles with pulsation and symmetric deformation.

A new system of dynamical equations was obtained by using the perturbation and potential flow theory to couple the pulsation and surface deformation of the second-order Legendre polynomials (P2) of three bubbles in a line. The feasibility and effectiveness of the model were verified by simulating the radial oscillations, surface deformation with P2, and shape evolution of three bubbles. The spherical radial pulsation and surface deformation of the three bubbles exhibit periodic behavior. The maximum secondary Bjerknes forces (SBFs) on the three bubbles are found not to depend on the system's resonance frequency. Within a stable region, the SBFs of the three bubbles increase with increasing sound pressure amplitude but decrease with increasing distance between the bubbles. The primary Bjerknes force (PBF) on a bubble is significantly higher than the SBF on it.

Dynamics of twin bubbles formed by ultrasonic cavitation in a liquid.

Based on potential flow and perturbation theory, a theoretical model is derived to describe the pulsation, translation, and deformation of twin bubbles in an ultrasound field. The amplitudes of radial oscillation, translation, and deformation of twin bubbles are found to depend on initial translation velocities. The radii, translation, and deformation of twin bubbles also exhibit periodic behavior. As the initial translation velocities increase, the periods of two bubbles' oscillations reduce, and the instable area in the phase space of R01-R02 enlarges because of the interaction between bubbles.

[Recognition of S1 and S2 heart sounds with two-stream convolutional neural networks].

Auscultation of heart sounds is an important method for the diagnosis of heart conditions. For most people, the audible component of heart sound are the first heart sound (S1) and the second heart sound (S2). Different diseases usually generate murmurs at different stages in a cardiac cycle. Segmenting the heart sounds precisely is the prerequisite for diagnosis. S1 and S2 emerges at the beginning of systole and diastole, respectively. Locating S1 and S2 accurately is beneficial for the segmentation of heart sounds. This paper proposed a method to classify the S1 and S2 based on their properties, and did not take use of the duration of systole and diastole. S1 and S2 in the training dataset were transformed to spectra by short-time Fourier transform and be feed to the two-stream convolutional neural network. The classification accuracy of the test dataset was as high as 91.135%. The highest sensitivity and specificity were 91.156% and 92.074%, respectively. Extracting the features of the input signals artificially can be avoid with the method proposed in this article. The calculation is not complicated, which makes this method effective for distinguishing S1 and S2 in real time.

Controllable and reversible sensing cyanide ion using dual-functional Cu(II)-based ensemble.

In this work, a dual-functional Cu2+-based ensemble (2S·Cu2+) was well designed and characterized. Then, the successional and discriminating sensing for CN- over other competitive species (H2PO4- and biothiols) was achieved based on the disaggregation of 2S·Cu2+ ensemble and the deprotonation of imidazole NH of regenerated sensor S in aqueous solution, respectively. The visual sensing mechanism could be clearly demonstrated by 1H NMR, HRMS and energy changes between the HOMO-LUMO band gaps. Furthermore, the reversibility and reusability of S and 2S·Cu2+ upon alternating addition of CN-/H+ and CN-/Cu2+ were studied. Interestingly, the sequential sensing for biothiols (cysteine, glutathione and homocysteine) and CN- was also realized through spectroscopic methodology and test paper strips. This work may provide a feasible strategy to discriminate CN- over H2PO4- and biothiols with high selectivity and sensitivity through Cu2+-based ensembles.

Tb(III) line intensities in multibubble sonoluminescence.

We observed the line emissions of trivalent terbium [Tb(III)] ions during multibubble sonoluminescence (MBSL) in the aqueous solutions of terbium chloride (TbCl3) under argon gas atmosphere. The line intensities of excited Tb(III) ions increased with TbCl3 concentration(mass percentage) in aqueous solutions. This phenomenon was interpreted qualitatively by numerically computing the Tb(III) line intensities in one sonoluminescing bubble among the cavitation bubbles in a liquid. The driving pressure for this sonoluminescing bubble was obtained by numerically solving the cavitation dynamic equation and bubble-pulsation equation. The Tb(III) ion line intensities obtained from the sonoluminescing bubble were attained by solving computing fluid dynamics equations and the spectral radiation formula.

Asymmetric transmission of sound wave in cavitating liquids.

Two modes of the asymmetric sound transmission are observed experimentally in a one-dimensional system composed of coupled two layers of liquids. Their cavitation thresholds are different from each other. When the sound wave propagates from the high-threshold liquid to the low-threshold liquid, the two liquids can avoid the cavitation for a medium driving pressure. When it propagates from the low-threshold liquid to the high-threshold liquid, however, the low-threshold liquid can be cavitated by the same driving pressure, though the high-threshold liquid remains uncavitated. Therefore, there is a sound transmission asymmetry, or sound rectification in this double-layer liquid. Furthermore, when the system is driven by a high pressure, cavitation can take place in both high- and low-threshold liquids in the sound transmission from the high-threshold liquid to the low-threshold liquid, but only the low-threshold liquid can be cavitated in the opposite transmission. This mechanism gives an asymmetry with reversed rectifying direction. The efficiency of rectification is related to the driving sound pressure and the cavitation thresholds of the two liquids based on experimental results. Finally, the experimental observations are reproduced by the numerical simulation based on the modified two-phase fluid mechanics.

Publisher's Note: Asymmetric transmission of sound wave in cavitating liquids [Phys. Rev. E 95, 033118 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.033118.

Computational investigation of Tb(III) ion line intensities in single-bubble sonoluminescence.

We perform a computational fluid dynamics simulation of trivalent terbium [Tb(III)] ion line emissions from single-bubble sonoluminescence (SBSL). Our simulation includes dynamic boundary conditions as well as the effects of gas properties and quenching by species, such as nitrite ion (NO_{2}^{-}). Simulation results demonstrate that when the maximum temperature inside a dimly luminescing bubble is relatively low, emission peaks from excited Tb(III) ions are prominent within the emission spectra. As the maximum temperature of the bubble increases, emission peaks of Tb(III) ions fade away relative to the continuum background emission. These calculations match observations of Tb(III) line emissions from SBSL occurring in aqueous solutions of terbium nitrate [Tb(NO_{3})_{3}] under an argon gas atmosphere. The evolution of the radiation energy spectrum over time for sonoluminescing bubbles provides a clear mechanism explaining Tb(III) emission peaks gradually merging into the continuous background emission as the radiation power increases.

Dynamics of two interacting bubbles in a nonspherical ultrasound field.

In this paper, we present and analyze a model of the oscillations of a pair of gas bubbles driven by nonspherical ultrasound. We derived our model based on the perturbation and potential flow theories and use it to study three cases of oscillation of two bubbles under driving ultrasound with different initial phases, different separation distances between the bubbles and different sound pressure amplitudes. For the driving ultrasound with different initial phases, we obtain the in-phase and anti-phase radial pulsations of the bubbles in incompressible liquid. We also study the effect of the secondary Bjerknes force on the oscillation of bubbles separated by different relative distances. Lastly, we analyze the ratio of a nonspherical to a spherical partial quantity, and the results show that the bubbles survive longer with decreases in both the pressure amplitude of nonspherical ultrasound and the initial bubbles radii.