The hybrid scheme treatment based on

The hybrid scheme treatment based on HC by using Ecowirl reactor (20°C, 2.0bar, pH 2.0 or 4.0) and NaOCl (minimal dose 0.5mgL−1) was found to be the most energy efficient and environmental friendly method to treat wastewater containing RhB. The combined process HC and NaOCl increased the efficiency of RhB degradation as compared to the HC alone or to the NaOCl oxidation process implying an acceleration of the kinetic of RhB degradation and resulting in a decrease of treatment time and hence of treatment costs. Swirling jet-induced cavitation by using Ecowirl combined with NaOCl was more energy efficient if compared to other hydrodynamic and acoustic cavitation based processes.
The aim of the designers should be to maximize further the energy efficiency. This can be done based on manipulation of the operating conditions and geometric parameters of the reactor, resulting in optimal ΔPHC and rapid pressure increase, to give the desired effect in terms of the observed chemical change. Finally, further studies, in particular modelling studies, are needed to better understand the fluid dynamic of swirling jet induced cavitation devices.

Acknowledgements

Introduction
Silicon MLN2238 are today’s most popular commercialized solar cells, ruling all the photovoltaic industry with highest 24.7% efficiency for single-crystal silicon solar cells [1]. However, silicon solar cells are expensive for large scale production. It is known that the organic solar cells are much cheaper than the inorganic ones because of the low cost of the components and the ease of fabrication. In the past decade the perovskite-type compounds methylammonium lead trihalides CH3NH3PbX3 (X=Cl, Br, I) gained more interest in solar-energy application (“perovkite solar sells”). The rapid advances and breakthroughs in the organic–inorganic hybrid photovoltaic materials make the field attractive and promising for the solar cell industry [2–7]. Recently, improvement in the efficiency of the perovskite solar cell has been reported [7,8]. The fabrication costs of the perovskite solar cells are much lower than those of any other photovoltaic device [6]. CH3NH3PbI3 has a very high absorption coefficient in the visible region and a band gap of about 1.4–1.5eV [9]. This material is of the crystal structure of perovskite ABX3 with distortion in the octahedral center, breaking the inversion center and resulting in an octahedral tilt of the system [3]. The Pb atom is located in the corner of the cage whereas the iodine atom shares a bond between two Pb ions and the methyl amine ion, present at the center of the cage, acts as a rotating dipole. Solar cells made of this material work effectively in both mesoscopic and thin film configurations. The highest reported efficiency of this material, according to Seok, was 20.4% [10]. CH3NH3PbI3 exhibits a very high charge carrier diffusion length of about 1 micron which is extremely good for photovoltaic cells [10]. A thin film of perovskite shows very high polarizability, ferroelectric property and ionic movement in the system. Current researches are focusing on finding an efficient fabrication method of the perovskite material to make the solar cells and light emitting diode (LED) devices cheaper and easier to produce [8].
Quantum dots (QD) of perovskite are also one of the targets of current research as an additional means for increasing the efficiency of the solar devices. Easy exciton formation and charge-separation are remarkably efficient in QD. These nanocrystals are mainly used in the areas of fluorescent labeling, probing, LED and solar points [11]. The fabrication of stable quantum dot of perovskites was previously reported [11–13] by several groups but commercial application of perovskite-QD is still under investigation. Few reports described the synthesis of CH3NH3PbI3 by one-step deep coating and/or other methods without using any catalyst [14–18]. Perovskite nanoparticles (NPs) have attracted attention due to their easy synthesis for highly luminescent colloidal quantum dot materials which are highly demanding in the field of LED devices and solar cell fabrication.

br Acknowledgements This work was supported by the National

Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B4009122). We also thank Miss Migyeong Kim, a graduate student, in the Department of Environmental Engineering, Kyungpook National University for his valuable supports.

Introduction
The risks arising from extensive production of pesticides such as insecticides, acaricides, herbicides and fungicides for agricultural applications are a great environmental concern due to their hazardous effects on the living organisms [1–3]. Based on the studies carried out in this area, only 0.1% of the pesticide used reaches the target pest and 99.9% is dispersed in the environment, which could pollute the water resources, which, in turn, could be a great threat to both humans and aquatic organisms [4,5]. Among the various types of pesticides, abamectin is a broad-spectrum pesticide that has been widely used in agriculture fields and has hazardous impacts especially on human beings [2,6]. Thus, the development of an efficient and effective treatment technology to remove pesticides such as these is necessary. The conventional techniques such as physical, chemical and biological treatment methods have failed to mineralize or destroy the pesticides and only transfer them to another phase which requires further separation process, leading to additional costs of operation unit [7–9]. Therefore, applying more powerful and efficient technologies is necessary for treating such hazardous pollutants. Recently, considerable attention has been paid to the application of advanced LY2584702 processes (AOPs), as an effective technology based on the production of powerful oxidative free radicals [10–12]. AOPs include various methods such as Fenton, photo-Fenton, sonolysis, photocatalysis and ozonation, etc. which operate based on the generation of hydroxyl radicals (OH) [13–19]. In order to improve the degradation efficiency, hybrid methods including two or more individual AOPs processes have been applied [20]. Among hybrid systems, sonophotocatalytic degradation which uses the combination of ultrasonic sound waves, light radiation and a catalyst, is an alternative, low-cost and effective technique for wastewater treatment [21,22]. Combination of photocatalysis and ultrasound has showed synergistic effects on the degradation of many organic compounds [23–28]. Deaggregation and cleaning of photocatalyst particles due to acoustic cavitation phenomenon caused by ultrasound waves lead to mass transfer improvement between the solution phase and photocatalyst surface [29]. The phenomenon of acoustic cavitation includes the nucleation, growth, and sudden collapse of gas or vapor-filled microbubbles which is caused by the acoustical wave induced compression/rarefaction in a body of liquid [30,31]. In this condition, the hot spots with extreme temperature up to 5000°C and pressures of about 2000atm are formed with lifetimes of a few microseconds which causes higher reaction rate [32,33]. Thus, coupling of ultrasonic environment with photocatalytic process leads to the cleavage of dissolved oxygen molecules and water molecules, which subsequently leads to generation of a greater number of oxidative free radicals as follows, thereby increasing the rates of reaction [34–38]:where e−, h+ and OH− are the electron, hole and the hydroxide ion adsorbed on the photocatalyst surface, respectively, and 〉〉〉〉 represents ultrasound.
This study discusses the application of sonophotocatalytic as a sufficient technique for degradation of abamectin (ABM), using a novel visible-driven photocatalyst. Conventional photocatalysts such as TiO2, ZnO, Fe2O3, CdS, etc. is not efficient due to small surface area for sufficient radical generation, also most of them need UV irradiation for activation due to their large band gap, and these properties limit their large scale applications. Therefore, exploring for new photocatalyst materials with desired properties which can activate under visible light is an essential step in sonophotocatalytic process [1]. Among these, Cu, Zn and Bi based materials, serving as one kind of noble metal-based compound, have emerged due to their unique crystal structures, and fascinating photocatalytic properties. While, the drawbacks such as the serious deactivation, low efficiency, high electron hole recombination rate and short stability, have hindered its practical application in simultaneous photocatalysis process [12]. Thus, modification, composite and hybrid of this material with other materials such as MOFs and S2−, O2− and PO43− anions need to be put into effect to make an efficient, LY2584702 visible light active and stable photocatalyst. In this case, PO43− anion with cling to Cu can be exhibit high stability under successive blue LED illumination [39]. Also, metal–organic frameworks (MOFs) known as group of organic–inorganic hybrid materials possess three dimensional porous network and crystalline structures based on an organic linkers and metal-oxo clusters [9]. Among this, MOFs based Cu cluster exposure to light lead to initiating of their photocatalyst activity that favored due to large specific surface area, high pore volume and structural adaptivity. Therefore, in this work, Cu2(OH)PO4-HKUST-1 MOF as a new photocatalyst was synthesized and its application in blue LED irradiation for simultaneous sonophotocatalytic degradation of binary mixture of abamectin pesticide was investigated.

br Equipment and computer modelling of the oscillations In

Equipment and computer modelling of the oscillations
In order to demonstrate the effects of shock waves and verify the combined shockwave and ultrasonic method for water wells regeneration, special equipment was developed. The equipment included downhole and surface blocks. The downhole equipment consisted of a downhole tool with an electrohydraulic (shockwave) and an ultrasonic block and a pump. The blocks could be used as one single tool, or could be disassembled into two separate tools (ultrasonic and shockwave). Normally the ultrasonic block was attached above the shockwave block and connected to a geophysical cable with seven cores through a cable lug. If the ultrasonic block worked separately, its connection part was sealed with the protective cover. In case of separate operation of the shockwave block, it simvastin was connected directly to the cable lug. The downhole equipment included also a pump (Grundfos SQE7-40 1X200-240V 1.68kW 1.5M MOD.BB). The pump had a maximum flow of about 8–9 cubic meter per hour, it was put into the well on a separate cable and was used to create depression during or after the treatment. The downhole tool was connected to the surface equipment via the 7-cored geophysical cable (which was spooled on an automatic winch): the ultrasonic block to an ultrasonic generator and the shockwave block to a pulse generator. The pulse and ultrasonic generator were assembled in the same housing. A power station powered both generators and the pump. An operating scheme of the equipment is shown in Fig. 2.
The set of equipment had the following technical characteristics:
The ultrasonic block is described in detail in [28]. It was developed for operation in oil wells, however is also suitable for water wells. The verification of its characteristics was carried out during field tests, described in [28].
To verify the effect of the electrical discharge the electrohydraulic block of the downhole tool was checked in a transparent tank in laboratory conditions (under normal pressure and temperature). The block contained a multiplier scheme and pulse capacitors, which enabled us to create an electrical pulse between the two electrodes. The duration of the pulse was between 5 and 10μs. The energy was enough to achieve a discharge between the two electrodes. A discharge with the maximum energy was created and photographs were made in order to verify the process of shockwave creation. The photographs of the simvastin discharge zone during a discharge are shown in Fig. 3.
The photographs demonstrate the cavity, created during the discharge (Fig. 3a) and its collapse (Fig. 3b and c). The photographs (d) of Fig. 3 demonstrate also the cavitation, caused by the shockwave in the liquid; which is an evidence of the generated oscillations.
In order to estimate the penetration depth of the generated shockwave the parameters of the pressure pulse were measured in the vicinity of the device. A pressure sensor, which was placed 150mm from the discharge zone, was used. The experiments were performed in water. The shape of the pulse, which was measured, is shown in Fig. 4. The pressure sensor was connected to the fourth channel of the oscilloscope. The vertical scale is 30bar in a field. Channels 1 and 2 show the voltage between the electrodes (5kV in a field) and the discharge current (260 A in a field) respectively.
To model the temporal behavior of the signal near the borehole, a Fourier analysis was performed. The signal was modelled by the following equation (as a pulse with a fading sinusoidal signal, where the coefficients were obtained empirically):where P is the pressure in bar and t is the time. The form of the modelled signal at the starting point near the discharge zone is shown on Fig. 5.
The spectrum of the signal was determined by means of Fourier analysis. In detail the procedure is described in [31].
The pressure amplitude Pr (for each component of the spectrum) as a function of the distance r can be determined by the following equation:

br Mathematical models and numerical methods br

Mathematical models and numerical methods

Numerical validation

Results and discussion
To investigate the effect of ultrasound wave on the flow structure and behaviors of RBCs, Fig. 9 shows the scheme of microvessel with ultrasound source with area of 225×60 lattice nodes (45μm×12μm). The periodic boundary condition is applied and SBI-0206965 flow moves directly from left boundary to right one. The ultrasound source (D=50 lattice nodes) locates at the top boundary of the microvessel. A region of interest (ROI) is selected, which fits a square of 15×15 lattice nodes for visualization of vector measurement. To investigate the effect of the ultrasound on the RBC behaviors, three different intensity of ultrasound cases are elected (I=0, 0.2 and 0.3). In addition, the detail plasma and RBC parameters employed in this section are listed in Table 1 from Refs. [18,31].

Conclusion
An immersed boundary lattice Boltzmann method considering ultrasonic effect is proposed to simulate red blood cell (RBC) aggregation and deformation in ultrasonic field. Numerical examples involving the lid driven flow and typical RBC behaviors in shear flow are presented to verify the method. In the following, the typical streamline, normalized out-of-plane vorticity contours and vector fields in pure plasma under three different ultrasound intensities are presented. Meanwhile, the corresponding transient aggregation behavior of RBCs, with special emphasis on the detailed process of the RBC deformation, is shown. The normalized vorticity profiles with/without RBC are also investigated, respectively. The primary findings include:
Regarding future directions, additional research through IB-LBM considering the thermal effect is needed to further advance the understanding of the effect of temperature on the dynamics of RBCs aggregation, as well as shape deformation. Additional numerical studies used by IB-LBM are also needed to improve the understanding of the interplay between inflow and cantilever beam, particularly for cases with spatial/temporally varying inflow, and for cases with rigid and/or elastic body motion [43,46]. Such research is important because accurate prediction of fluid-structure interaction is critical when analyzing the noise, vibration, and hydroelastic stability of hydraulic machineries.

Acknowledgments
The authors gratefully acknowledge the support by the National Natural Science Foundation of China (Grant Nos.: 51679005, 51306020 and 51479002), and the Open Foundation of State Key Laboratory of Hydraulics and Mountain River Engineering (Sichuan University, China). Additionally, the assistance of Yuanqing Xu in simulating the red blood cell is gratefully acknowledged.

Introduction
From ancient times, people were attracted to perfumes and other fragrant materials. Nowadays, there is a growing need for high-quality textiles and packaging materials with antimicrobial properties for food safety, hygienic clothing, active wear, and wound healing [1]. Therefore, properly designed edible fragrant antimicrobial coating on textiles and packaging materials, would provide a significant contribution to the food, textile, medical, cleaning and toiletries industries. Several pathogenic bacteria and fungi were chosen for the antimicrobial testing due to their abundance as a community contaminator.
Ultrasound radiation is an excellent technique for the formation and adherence of organic [2,3] or inorganic [1] nanoparticles (NPs) to a large variety of substrates and for the deposition of NPs on flat and curved surfaces of ceramic [4–8], polymers [9,10], metals [11], and paper.
The edible fragrant solid flavors, Vanillin, RK, and camphor, inheritably possess antimicrobial properties, which have been known and used for centuries. Vanillin (4-hydroxy-3-ethoxybenzaldehyde), a pleasant smelling aromatic compound, is the world’s most popular flavor and fragrance compound [12,13]. It is widely used as flavoring agent in foods, beverages, pharmaceuticals, perfumes and cleaning products [14,15]. Vanillin is slowly oxidized on exposure to air and is slightly water soluble (10g/L) [12,16]. It displays antioxidant property [17,18] and gives antibacterial and antifungal activity against pathogenic microorganisms [12,18,19].

Most studies have shown successful USMB guided

Most studies have shown successful USMB guided drug delivery using already available clinical ultrasound imaging systems; however, the reported delivery efficiency is inconsistent [11], likely due to there being so far no standardization of the acoustic parameters. Although there are certain studies that have investigated microbubble parameters, including MB concentration, sound intensity, irradiation time, fundamental transmission frequency, duty cycle [19–23], most of these studies did not investigate the different combinations of various levels of parameters. What’s more, most of these studies investigate only one cell line and did not compare the sonoporation between tumor cell lines derived from different tissue.
Therefore, in this study, four kinds of human tumor cell line derived from different tissue including breast tumor (MCF-7), liver tumor (Bel7402), ovarian tumor (A2780) and thyroid tumor (ARO) were selected to reveal the effect of different tumor cell lines on sonoporation efficiency, and meanwhile use the orthogonal experimental design method to determine the impact of therapeutic parameters on sonoporation and determine the optimum parameter combination for each tumor cell line. To count the SBI-0206965 that are sonoporated, fluorescent dye (FD500) was used and counted by cytometry to evaluate transference percentage. It has been shown that sonoporated cells might undergo apoptosis, have poor cloning efficiency or can suffer from malfunction [24]. Therefore, safety remains an important factor to be addressed, and the cell survival rate was calculated with MTT test.

Materials and methods

Results

Discussion
Ultrasound-guided microbubble destruction has great potential for clinical translation in oncology because it is a safe, non-invasive, cost-effective and non-ionizing modality [29]. Importantly, this approach can create temporary and reversible openings in vessel walls and cellular membranes through a process called “sonoporation”, allowing enhanced transport of therapeutic agents across these biological barriers in the insonated region [10,30]. A number of molecules have transferred into cells with sonoporation including small fluorescent molecules, RNA, plasmid DNA, plasmid lipoplexes, nanoparticles, anti-cancer drugs, anti-bodies and viruses [7,31,32]. SonoVue is a suspension of stabilized sulfur hexafluoride (SF6) microbubbles which is isotonic to human plasma and very stable and resistant to pressure [33], and it is a commonly used microbubble to investigate sonoporation.
Most studies have shown successful USMB guided drug delivery using already available clinical ultrasound systems; however, the reported delivery efficiency is inconsistent [11], this phenomenon may have a variety of reasons, one of those may likely due to that the sonoporation maybe influenced by tumor cell lines from different tissue, and there being little research for this. It is also expected that optimized treatment schedules may need to be assessed for different tumor types to enable maximum treatment effects. Pichardo et al. has reported that various cell lines from the same tumor tissue (cervical-carcinoma-derived cells) impact the sonoporation [34]. Lamanauskas et al. has reported that human glioblastoma astrocytoma (U-87 MG) and colon cancer (HCT-116) cell lines showed different sonoporation efficiency of bleomycin under USMB treatment [28].
In this study, in order to assess whether the sonoporation efficiency is affected by tumor cell lines derived from different tissue, we selected four kinds of human tumor cell lines including breast tumor (MCF-7), liver tumor (Bel7402), ovarian tumor (A2780) and thyroid tumor (ARO). FD500 uptake assay was performed to assess cell membrane permeability changes. In addition, an orthogonal array experimental design based on three levels L9 (33) of three parameters (MB concentration, sound intensity and irradiation time) was employed to optimize the sonoporation efficiency for each tumor cell line. Finally, cell survival rate is also an important concern when carrying out the sonoporation experiment, therefore, MTT experiment for each group was also carried out.

The model is used to investigate also the

The model is used to investigate also the nonlinear attenuation experienced by the total field. The subject is discussed in relation to a recent investigation [12], in which a novel criterion to discriminate diverse forms of hysteretic damage is proposed. Like DAET, even this method employs the dependence of an acoustic quantity, specifically nonlinear AC220 inhibitor cost loss, on the excitation amplitude. Data are acquired without displacing the transducers, freeing the results from variations caused by the transducers’ coupling with the material under inspection. Here, confirming the result in [12], it is shown that the exponent of a power law fitting the dependence of the total nonlinear attenuation on the amplitude of the incident wave may be indeed introduced for the purpose of discriminating dislocations from microcracks.

Constitutive relationships

Theory
The equation of motion that describes the propagation of a one-dimensional stress wave iswhere ρ is the mass density of the material, and e=eel+ean is the total strain field. Introducing Eq. (2) in Eq. (12) yields
This equation has to be solved imposing the following boundary conditionsThe first term in AC220 inhibitor cost Eq. (14) describes an harmonic incident wave with amplitude at x=0, angular frequency ω, and wavenumber k, which propagates from −∞ to +∞. The two series represent the fields scattered by the region of damage. The symbol j represents the imaginary unit. In this model, damage is assumed to occupy a neighborhood of the origin of the system of reference. The viscoelastic nature of the material renders the wavenumber k complex with positive real and imaginary parts, implying that the boundary conditions in Eq. (14) describe an incident field with an infinite amplitude at −∞ and scattered waves with evanescent amplitude at infinity. Although the former condition is physically impossible, the stress waves which are obtained from solving this problem may still represent physically meaningful solutions within the limited spatial domain where experiments are carried out.
Eq. (13) is solved by means of a perturbation approach which decomposes the total stress wave into two terms, σ=+σ1, the first of which having norm much greater than the second one, ≫ σ1 . Introducing this decomposition in Eq. (13), and separating terms according to their magnitude, the following two equations are obtained
Note that, consistently with the assumption ≫ σ1 , the dependence of Γ on σ has been approximated so that Γ(· σ)≅Γ(· ). The first equation includes no scattering source. Thus, its solution must describe only the incident field which satisfies the following boundary conditions
Introducing Eq. (17) in Eq. (15), expressing the convolution integral in terms of the Fourier transforms of the integrand functions, and using the harmonic nature of this solution, the following characteristic equation is found which links the wave number k to ω,In Eq. (18), the complex function S(ω)=S′(ω)−jS″(ω) is given bywhich, considering that the creep function J is null for negative values of τ, coincides with the Fourier transform of ∂J/∂τ. In the next section, this function is assigned ad-hoc to model the linear dispersive properties of the material.
To solve Eq. (16), the field σ1 and the source term are first expanded in Fourier series of harmonics of ω,and
Making use of Eq. (20) and Eq. (21), the equation governing the spatial evolution of the pth harmonic component of σ1 iswhere
Each component σ1, must satisfy the following boundary conditionswhere the amplitudes A±(p) depend on the physical properties of the scatterer. The solution of Eq. (20) has the following structure:
Recall that outside a finite domain in which the medium is damaged, the characteristic function U(x) is null. Furthermore, the function (x,x′) is the Greens function satisfying the boundary conditions in Eq. (24), and it is given by

In this section we examine the

In this section, we examine the tendency of delaminated layers to start vibrating at one of their own resonance frequencies. In particular, we want to know if defect resonances are only observed when corresponding to an ultraharmonic frequency (as was the case in the previous section) or not. We do this by studying the influence of the delamination depth on the defect resonances. For a delamination at depth h, the LDR is attributed to the resonance vibrations of the material layer above the defect, which can be identified with flexural vibrations of a thin plate clamped around the boundaries. In case of a circular plate with thickness h and radius a, for instance, the nth order resonance frequency is given by:where E is Young’s modulus, is Poisson’s ratio, is the density of the material and is a constant depending on the different vibrational ion channel of the plate [26,27]. Changing the delamination depth (while keeping the excitation frequency constant), will therefore change the resonance frequencies and LDR frequencies may not correspond to ultraharmonic frequencies anymore.
In order to study if a particular defect resonance is still being generated when the delamination is located closer to the surface or deeper into the sample, we again consider the 5mm thick composite plate with ellipsoidal delamination that was excited at 25kHz, and use the defect resonances obtained at the ultraharmonic frequencies and (Fig. 6) as a reference. The position of the delamination now varies from 1.5mm to 2.5mm below the top surface of the sample, in steps of 0.1mm. In order to find all clapping-induced frequencies, we first calculate the normalized maximum amplitude responses for each configuration. The results are plotted in Fig. 7. The fundamental frequency is clearly visible in the figure. Other spectral ranges where high amplitude values occur, reflect the generation of harmonic, subharmonic or ultraharmonic frequencies and LDR frequencies. At 2mm depth for instance, the highest amplitudes (apart from the fundamental frequency) occur at the ultraharmonic frequencies and , which were found to be local defect resonances. At other depths, these two defect resonances seem to be generated again, however, shifted to higher or lower frequencies as the delamination depth is respectively larger or smaller, in correspondence with Eq. (1).
Figs. 8 and 9 show xy-plane visualizations (i.e. maximum pressure values) of the acoustic radiation generated by the ellipsoidal delaminations at different depths in the composite sample, at the high amplitude spectral ranges, corresponding to the first and second local defect resonances indicated in Fig. 7. The figures confirm that, varying the delamination depth, the defect resonances that showed up earlier for a 2mm deep delamination, are still observed. However, the resonances occur at different amplitudes and at slightly different frequencies, as mentioned earlier. At 2.4mm depth, the layer above the delamination becomes to heavy, making it harder to open the delamination for a longer period and initiate clapping.

Conclusions
Using the combined numerical model, we studied the radiation patterns in three different orientation planes. The simulations confirmed that the concept of detecting delaminations using nonlinear air-coupled emission (NACE) is achievable in practice. Defects can be clearly detected by studying the radiation patterns of (higher order) subharmonic frequencies and harmonic frequencies of the excitation frequency. A good determination potential of the defect location, size and, in some cases, shape is found at a range of distances approximately 5–15mm from the top surface of the sample, suggesting that robust manual scanning will be feasible. Also, it was demonstrated that the efficiency of NACE depends on the excitation frequency, and that delaminations become most visible when the clapping-induced frequency matches the defect resonances. Therefore, in experiments, it would be beneficial to search for frequencies able to excite the defect resonances by analyzing the response of sweep excitation.

br Numerical results and discussions The numerical determination of the

Numerical results and discussions
The numerical determination of the acoustic radiation force function in Bessel vortex beams with emphasis on the transition from the progressive to the standing wave behavior requires the evaluation of the (yet unknown) scattering coefficients . These coefficients are obtained by solving the truncated system of linear equations system
A MATLAB program code is developed to solve initially the system of linear equations given by Eq. (15), then evaluate the integrals in Eq. (11) using a standard numerical tubocurarine procedure based on the fast trapezoidal method with a sampling step of δθ=10−5 which ensures adequate convergence and accuracy of the results. In the computations, =πb2, kh=π/4 (which is the correct parameter also used in Ref. [33], and not =π/4), and the non-dimensional size parameter kb is varied in the range 0sized by varying the aspect ratio a/b (which is the ratio of the major axis to the minor axis of the spheroid). When a=b, the spheroid corresponds to a sphere. At low kb values (< 2), the radiation force function is larger the more prolate the spheroid becomes. This behavior changes as kb increases (> 2) where the opposite behavior occurs; that is, the radiation force function decreases the more prolate the spheroid becomes, as shown in panels (a) and (b). Nevertheless, for larger half-cone angles, some exceptions occur; the radiation force function does not show a general similar behavior with the change in kb, as shown in panel (c). Moreover, there exists a kb-range (), over which the radiation force function for progressive waves is negative, which induces an attractive (instead of a repulsive) force on the spheroid (i.e. “tractor beam” [51] behavior for a spheroid). This phenomenon has been initially observed for a rigid sphere in Bessel vortex beams of any order (or topological charge) [41]. Notice also, that for a small half-cone angle β (= 1°), the radiation force function is weaker as compared to the plots of panels (b) and (c). As β increases, the central hollow (intensity null) region diameter decreases, and the spheroid is illuminated by a larger portion of the beam leading to the increase in the radiation force function plots. Notice that in the absence of absorption, the radiation force is strongly affected by diffraction/scattering of the Franz waves circumnavigating the surface of the spheroid [48], where an explicit dependence on the scattering efficiency [67] was previously established for a sphere, and for the rigid elliptical cylinder [69]. In the present case, the scattering by the spheroids with variable aspect ratios is highly sensitive to the variations of the size parameter kb (see for example Fig. 7 in [47]), which mainly causes the variations in the radiation force function plots. Moreover, the half-cone angle of the incident Bessel vortex beam influences the scattering (see for example Fig. 5 in [48]), and subsequently the radiation force would be altered accordingly.

br Experimental The lens to generate the

Experimental
The lens to generate the Bessel-like beam was made of a 1D periodical structure with two elements: glass (density: 2203kgm−3, Young’s modulus: 73.1 GPa, Poisson’s ratio: 0.23) and water (density: 998kgm−3; sound speed: 1482ms−1). In our previous paper, we identified the backward propagation of acoustic waves in this structure [19]. A schematic diagram of the backward propagation in the glass plate is shown in (a). The acoustic waves propagate from the upper side of the glass plate with a certain angle of incidence. After the waves pass through the glass plate, the transmitted wave is shifted backward. This behavior is ascribed to the negative group velocity in the plate. In the plate, Lamb waves are formed by the reflection and interference of the incident waves from liquid. The acoustic casin propagates with the group velocity along the plate. The accumulation of the acoustic energy in the plate induces the plate radiates acoustic energy into liquid. Thus, the shift of the leaky wave is dependent on the group velocity. When the group velocity is negative (at frequency of 2.76MHz), the leaky wave moves backward.
In this study, we focused backward-shifted waves in the plate with different angles of incidence. The calculated results, which are presented in (b), reveal that the backward shift linearly increases with increasing angles of incidence for angles below 8°; the backward shift increases nonlinearly with increasing angle of incidence above 8°. The formation of the Bessel beam with the axicon and with the 1D periodical structure is illustrated in Fig. 1(c) and (d), respectively. It is evident from (d) that the formation of the Bessel beam depends on the backward shift of the wave in the periodical structure, and that the backward-shifted wave does not contribute appreciably to the formation of the Bessel beam at angles of incidence greater than 8°. Thus, the pass and stop bands of the periodical structure were carefully adjusted such that waves with angles of incidence greater than 8° were reflected, because the incident wave was in the stop band of the periodical structure. Our lens was made of six layers of the water/glass structure. The thickness of the water and glass layers were 1 and 1.1mm, respectively.
Visualization of the acoustic fields was conducted using the Schlieren method, which is based on the acousto-optic effect. A schematic diagram of the experimental setup is shown in Fig. 2 (the experimental details are described in our previous paper [19]). In this experiment, a line-focused transducer (2.76MHz) is used to generate a divergent beam and the periodical structure is placed behind the focal zone.

Results and discussion
The propagation process of the divergent beam through the lens is shown in Fig. 3, in which the color indicates the acoustic intensity. As can be seen in (a), the divergent waves propagate from the upper side of the structure. After the waves reach the lens, divergent waves from both sides simultaneously shift backward in every layer of the glass. In the fourth layer of the lens ((c)), the incident waves from both sides move into the central axis. In the fifth and sixth layers, the waves shift to the side opposite to the side of incidence.
The intensity of the transmitted waves, as shown in Fig. 3(d–f), was greater than that of the incident waves. This is because the transmitted waves are the superposition of the incident waves from both sides and form a Bessel-like beam. In contrast to the incident waves, the main lobe of the transmitted beam has a very high directivity. Moreover, the first and second side lobes, which can also be observed in the transmitted waves in Fig. 3(d–f), are also characteristic of a Bessel beam.
The radial distribution of the experimental pressure amplitude is plotted in Fig. 4 together with the Bessel function for comparison. The pressure distribution in the main lobe is in good agreement with the Bessel function and the positions of the side lobes are close to the peak of the Bessel function. However, the pressure amplitude of the side lobes is smaller than the Bessel function. We attribute this to the different parameters of the transmitted beam and the Bessel beam. For example, the transmitted beam had an arbitrary angle distribution from −8° to 8°, whereas the Bessel beam was superposed by two beams with fixed angles. It is also possible that the sensitivity of the iCCD camera contributed to this discrepancy.

The Morlet wavelet function is where s denotes the

The Morlet wavelet function is [18]where s denotes the scale of Morlet wavelet function, denotes the center frequency.
In the light of signal theory, the analytic function of Morlet wavelet function can be expressed aswhere is the Hilbert transform of the Morlet wavelet function, , the asterisk indicates convolution operation.
Then the envelope function of the Morlet wavelet function is
As discussed above, when an SAW device, whose input IDT is weighted by the envelope function , and the output IDT designed as uniform IDT, it can be regarded as a WTP, then the WTP using SAW devices can be designed and fabricated.
From formula (3), we can define the lengths of the apertures [4]:where n is an inter, defines the serial number of the apertures, k is constant.

Two-port network and its admittance parameters of the WTP using SAW devices

The applications of the two-port network
As shown in Fig. 1, input signal voltage is related to by , where denotes source impedance, while load voltage across load impedance is . From formula (5) the impulse response function in frequency domain is
Supposes that impedance and is resistive, that is and , the lpl receptor loss (IL) is defined aswhere is the impulse response function in frequency domain, which can be computed by formula (12).
In the matching circuit network of the WTP using SAW devices, the source and load resistance can be determined by its admittance parameters, and it can be calculated by the following formulawhere denotes a conjugate operation.

Results and discussion
In order to verify the two-port network analysis tool of the WTP using SAW devices presented in this paper, we have designed a WTP using SAW devices with the center frequency and the scale , and fabricated it on the piezoelectric substrate with the electromechanical coupling coefficient , the SAW velocity and the static capacitance/finger pair/unit length .
According to the discussion in Section 2, we can obtain the number of finger pairs N and the aperture length of each finger . Then the number of channels J, the number finger pairs in each channel and the static capacitance of an interdigital period in each channel can also be computed by the method presented in Section 3. Through these parameters, we can calculate the admittance parameters of the WTP using SAW devices through the formula (6). Meanwhile, the admittance parameters can also be measured by the method discussed in literature [15]. All the admittance parameters can be illustrated in Table 1. From Table 1, we can find that the computed results and measured results are consistent with the admittance parameters.
Using the admittance parameters of the two-port network, we can get the theoretical parameters with the formula (12) and (13). Furthermore, we can measure the WTP using SAW devices by the network analyzer 5061A, and obtain its experimental parameters. All the parameters of this device are shown in Table 2.
According to Table 2, the relative error of center frequency for WTP using SAW devices designed in this paper iswhere is the center frequency obtained by the two-port network analysis tool, is the actual measurement center frequency.
Likewise the relative errors of and frequency bandwidth for this device arewhere and are the frequency bandwidths obtained by the two-port network analysis tool, and are the actual measurement frequency bandwidths.
Furthermore, the relative error of the absolute insertion loss value for this device iswhere IL is the absolute insertion loss value obtained by the two-port network analysis tool, is the actual measurement absolute insertion loss value.
According to the formula (15)–(17), the theoretical parameters obtained by the two-port network analysis tool are consistent with the actual measurement parameters.
The theoretical parameters of the WTP using SAW device designed in this paper, which can be obtained by the frequency domain expression of Morlet wavelet function, the delta function model and the crossed-field model can be shown in Table 3.