The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

Preparation of sonoactivated TiO2-DVDMS nanocomposite for enhanced antibacterial activity

Titanium dioxide (TiO₂) nanoparticle has good photo-/sono-catalytic features, the reunion of this particle in solution-phase generally limits the extensive biomedical application. In the present study, the aggregation of TiO₂ nanoparticles was alleviated by facile fabrication under different pH conditions. A novel TiO₂ nanocomposite was further synthesized by properly conjugation with trace amount of DVDMS sensitizer (named DFT). The characterization, sonoactivity, as well as the antibacterial efficiency were specially evaluated. The results showed that the sonochemical activity of DFT was greatly improved as compared with the simple surface modification of TiO₂ (F-TiO₂) and free DVDMS, regarding to the hydroxyl radicals and singlet oxygen yields using the same ultrasound exposure. Moreover, ultrasonic stimulation of DFT exhibited excellent bacterial eradication, with up to 92.41% of killing efficiency in S. aureus. The flow cytometry analysis indicated an increased intracellular ROS and membrane disturbance by combination of DFT and ultrasound. The findings suggest that the proper fabrication and DVDMS incorporation greatly improved the sonocatalytic process of TiO₂, and the ultrasound based biomedical applications of DFT deserve future deep investigation.     

Manothermosonication (MTS) treatment by a continuous-flow system: Effects on the degradation kinetics and microstructural characteristics of citrus pectin

Modified pectin (MP) was reported to have increased bioactivities compared with the original one. However, traditional modification methods such as using an acidic solvent with heating are not only costly but causing severe pollution as well. In this study, manothermosonication (MTS) with a continuous-flow system was utilized to modify citrus pectin. The citrus pectin (5 g/L) treated by MTS (3.23 W/mL, 400 kPa, 45 °C) exhibited lower molecular weight (Mw, 248.17 kDa) and PDI (2.76). The pectin treated by MTS (400 KPa, 45 °C, 5 min) exhibited a narrower Mw distribution and lowered more Mw (48.8%) than the ultrasound(US)-treated (23.8%). Pectin degradation data fitted well to kinetic model of 1/Mw_t −1/Mw₀ = kt (45–65 °C). A lower activation energy of 13.33 kJ/mol was observed in the MTS treatment compared with the US-treated (16.38 kJ/mol). The MTS-treated pectin lowered the degree of methoxylation (DM), mol% of rhamnose and galacturonic acid (GalA) while increased mol% of galactose (Gal), xylose (Xyl), and arabinose (Ara). The ¹H and ¹³C nuclear magnetic resonance showed that MTS could not alter the primary structures of citrus pectin. However, an elevated (Gal + Ara)/Rha and reduced GalA/(Rha + Ara + Gal + Xyl) molar ratios after MTS suggested that MTS resulted in more significant degradation on the main chains and less on the side chains of pectin, in agreement with the result of atomic force microscope. Moreover, the MTS-treated pectin exhibited a higher 1,1-diphenyl-2picryl hydrazyl radical scavenging capacity compared with original pectin.     

Fabrication of high-performance nickel/graphene oxide composite coatings using ultrasonic-assisted electrodeposition

Ultrasonic-assisted electrodeposition was used to fabricate the nickel/graphene oxide composite coatings with high hardness, low friction coefficient, and high wear resistance. In the present study, the effects of ultrasonic power and concentration of graphene oxide on the mechanical and tribological properties of the electrodeposited nickel/graphene oxide composite coatings were systematically studied. X-ray diffraction (XRD) analyses showed that the crystallite size of the nickel decreased with an increase of ultrasonic power (0–50 W, 40 KHz, square wave) and concentration of graphene oxide (0.1–0.4 g/L). Morphologies of the surface and cross-section of the composite coatings observed by Scanning Electron Microscopy (SEM) confirmed the existence of graphene oxide particles in the nickel matrix. The results from microhardness measurement demonstrated that the hardness was increased by 1.8 times using 50 W ultrasonic-assisted electrodeposition with the fixed concentration of graphene oxide (0.1 g/L), compared to the pure nickel coating. The hardness was increased by 4.4 times for the 0.4 g/L graphene oxide with the optimized ultrasonic power of 50 W in comparison to the pure nickel coating. Meanwhile, the friction coefficient decreased gradually with an increase in ultrasonic power and concentration of graphene oxide, respectively, where the effect of the concentration of graphene oxide played a more important role.     

Standing wave-assisted acoustic droplet vaporization for single and dual payload release in acoustically-responsive scaffolds

An ultrasound standing wave field (SWF) has been utilized in many biomedical applications. Here, we demonstrate how a SWF can enhance drug release using acoustic droplet vaporization (ADV) in an acoustically-responsive scaffold (ARS). ARSs are composite fibrin hydrogels containing payload-carrying, monodispersed perfluorocarbon (PFC) emulsions and have been used to stimulate regenerative processes such as angiogenesis. Elevated amplitudes in the SWF significantly enhanced payload release from ARSs containing dextran-loaded emulsions (nominal diameter: 6 μm) compared to the -SWF condition, both at sub- and suprathreshold excitation pressures. At 2.5 MHz and 4 MPa peak rarefactional pressure, the cumulative percentage of payload released from ARSs reached 84.1 ± 5.4% and 66.1 ± 4.4% under + SWF and -SWF conditions, respectively, on day 10. A strategy for generating a SWF for an in situ ARS is also presented. For dual-payload release studies, bi-layer ARSs containing a different payload within each layer were exposed to temporally staggered ADV at 3.25 MHz (day 0) and 8.6 MHz (day 4). Sequential payload release was demonstrated using dextran payloads as well as two growth factors relevant to angiogenesis: basic fibroblast growth factor (bFGF) and platelet-derived growth factor BB (PDGF-BB). In addition, bubble growth and fibrin degradation were characterized in the ARSs under +SWF and -SWF conditions. These results highlight the utility of a SWF for modulating single and dual payload release from an ARS and can be used in future therapeutic studies.     

Coexistence of the solitary and periodic waves in convecting shallow water fluid

The existence of a solitary wave for the shallow water model in convecting circumstance was established in previous works. It is still unknown that whether there exist periodic waves. In this paper, we prove that the models possess periodic waves with a fixed range of wave speed. The amplitude and wave speed are explicitly given. Moreover, the coexistence of the solitary wave and one periodic wave is established.     

Tail wavelets in merger of binary compact objects

We present a model for tail wavelets, a phenomenon known as "echo" in the literature. The tail wavelet may appear in signal reconnaissances in the merger of binary compact objects, including black holes and neutron stars. We show that the dark matter surrounding the compact objects lead to a speculated tail wavelet following the main gravitational wave(GW). We demonstrate that the radiation pressure of the main wave is fully capable of pushing away the surrounding matter to some altitude, and splashing down of the matter excites the tail wavelet after ringing down of the main wave. We illustrate this concept in a simplified model, where numerical estimations are conducted on the specific distribution of dark matter outside the black hole horizon and the threshold values in accordance with observations. We study the full back reaction of the surrounding dark matter to the metric and find that the effect on to the tail wavelets is insignificant. We reveal the fine difference between the tail wavelets of a dressed and a bare black hole. We demonstrate that the tail wavelet can appear as a natural phenomenon in the frame of general relativity, without invoking modified gravities or quantum effects.