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This paper investigates a class of planar Schrödinger–Poisson systems with critical exponential growth. The conditions for the local well‐posedness of the Cauchy problem in the energy space are defined. By introducing innovative ideas and relaxing some of the classical growth assumptions on nonlinearity, this study shows that such a system has at least two standing waves with a prescribed mass. One wave is a ground‐state standing wave with positive energy, and another one is a high‐energy standing wave with positive energy. In addition, with the help of the local well‐posedness, it is shown that the set of ground‐state standing waves is orbitally stable. [ABSTRACT FROM AUTHOR]

In order to study the supercritical flow in a curved channel of a rectangular cross section, the classical shallow water equations in a cylindrical coordinate system based on the mass and momentum laws that take into account the friction and bottom slope are used. The obtained mathematical model forms nonlinear partial differential equations of first-order. For simplification, a linearization of the partial differential equations (PDEs) set is performed using small perturbation approach valid for weak bends (axial curvature radius extremely larger than the channel width). The governing equations with well-posed initial and boundary conditions were solved for a rectangular bend channel flow by applying the method of characteristics that is capable of transforming the hyperbolic partial differential equations to a system of ordinary differential equations (ODEs). The proposed model is tested and validated by comparing the results with broad available experimental data reported in the literature, and particular attention was paid to the wave maximum and its location. Comparisons indicate a reasonable agreement between the results obtained for the maximum flow depth along the outer channel wall. However, the model prediction is only reliable for a small relative curvature. Despite the model limitations, the results show the reliability and accuracy of the proposed approach for practical design purposes. [ABSTRACT FROM AUTHOR]

We investigate the existence and blow-up profile of normalized solutions to the fractional nonlinear Schrödinger equation$ \begin{align} \begin{cases} (-\Delta)^su+V(x)u+\lambda u = |u|^{\frac{4s}{N}}u, \ \text{in}\ \mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2\mathrm{d}x = \alpha, \end{cases} \end{align} $with $ N\ge 2, s\in(0, 1), \alpha>0 $, $ \lambda\in\mathbb{R} $, and negative potentials $ V(x) $. Firstly, we prove the existence and nonexistence of normalized solutions for negative potentials $ V\in L^p(\mathbb{R}^N)+L^{q}(\mathbb{R}^N) $ with $ \frac{N}{2s}\le p

The thermoacoustic engine is an eco-friendly technology capable of harnessing solar and waste energy for electricity generation, in conjunction with a linear alternator, and can function as a heat pump. This engine type holds significant appeal due to its simplistic design, devoid of any mechanical moving components, comprising only a stack sandwiched between heat exchangers within a resonator. When the temperature gradient across the stack reaches the critical threshold (onset temperature), the working gas undergoes spontaneous oscillation. Typically, a high onset temperature is necessary to induce gas oscillation in a thermoacoustic engine due to viscous losses within the system. A method to lower the onset temperature by increasing the number of unit stages consisting of stacks and heat exchangers so that the engine can utilize low-grade thermal sources has been developed to overcome this challenge. However, this method has only been applied to traveling-wave thermoacoustic engines. Its application in standing-wave engines, which offer a more compact and straightforward structure, remains unexplored. This research aims to examine how the number of unit stages in a standing-wave thermoacoustic engine influences the onset temperature and acoustic field. The onset temperature is estimated using a fundamental hydrodynamics equation and the investigation of the acoustic field throughout the engine using DeltaEC software. Results showed that the strategic positioning of multiple unit stages is essential to achieve a low onset temperature. The minimum onset temperature, approximately 92°C, is obtained when three- or four-unit stages are installed. Additionally, increasing the number of unit stages does not affect the acoustic impedance and phase difference between pressure and velocity in the stack, while simultaneously enhancing both acoustic power output and thermal efficiency.

Self‐excited thermoacoustic instability (SETAI) is a dangerous phenomenon in combustion equipment. While it is widely acknowledged that SETAI behavior is determined by the couple between pressure and heat release oscillation, their phase difference is difficult to predict, which impedes the development of SETAI control technology. With the aim of passive control technology development, this paper conducted experiment on a premixed hedge combustor to explore the mechanism whereby premixed chamber length (LP) and equivalence ratio (φ) collaboratively influence SETAI behavior. Results showed LP mainly affects the pressure mode shape within premixed chamber and consequently alters the phase difference between pressure and flowrate oscillation at combustion chamber inlet. Changing φ gives rise to different reaction time‐lag (τ), thus altering the phase difference between flowrate and reaction heat release oscillation. By introducing this flowrate oscillation, how LP and φ collaboratively determine phase difference between pressure oscillation and heat release oscillation was clarified. The mechanisms identified in this study are consistent with the emerging rationalization of the factors contributing to SETAI, and also provides better understanding on Rayleigh criterion and guidance for SETAI control. With further work on heat release and flow rate measurement, as well as the development on τ description, SETAI can be better predicted and controlled. [ABSTRACT FROM AUTHOR]

When David Kemp discovered "spontaneous ear noise" in 1978, it opened up a whole new perspective on how the cochlea works. The continuous tonal sound emerging from most healthy human ears, now called spontaneous otoacoustic emissions or SOAEs, was an unmistakable sign that our hearing organ must be considered an active detector, not just a passive microphone, just as Thomas Gold had speculated some 30 years earlier. Clearly, something is oscillating as a byproduct of that sensitive inbuilt detector, but what exactly is it? Here, we give a chronological account of efforts to model SOAEs as some form of oscillator, and at intervals, we illustrate key concepts with numerical simulations. We find that after many decades there is still no consensus, and the debate extends to whether the oscillator is local, confined to discrete local sources on the basilar membrane, or global, in which an assembly of micro-mechanical elements and basilar membrane sections, coupled by inner ear fluid, interact over a wide region. It is also undecided whether the cochlear oscillator is best described in terms of the well-known Van der Pol oscillator or the less familiar Duffing or Hopf oscillators. We find that irregularities play a key role in generating the emissions. This paper is not a systematic review of SOAEs and their properties but more a historical survey of the way in which various oscillator configurations have been applied to modelling human ears. The conclusion is that the difference between the local and global approaches is not clear-cut, and they are probably not mutually exclusive concepts. Nevertheless, when one sees how closely human SOAEs can be matched to certain arrangements of oscillators, Gold would no doubt say we are on the right track. [ABSTRACT FROM AUTHOR]

In this paper, we study the Rosenzweig–MacArthur predator–prey model with predator-taxis and time delay defined on a disk. Theoretically, we studied the equivariant Hopf bifurcation around the positive constant steady-state solution. Standing and rotating waves have been investigated through the theory of isotropic subgroups and Lyapunov–Schmidt reduction. The existence conditions, the formula for the periodic direction and the periodic variation of bifurcation periodic solutions are obtained. Numerically, we select appropriate parameters and conduct numerical simulations to illustrate the theoretical results and reveal quite complicated dynamics on the disk. Different types of rotating and standing waves, as well as more complex spatiotemporal patterns with random initial values, are new dynamic phenomena that do not occur in one-dimensional intervals. [ABSTRACT FROM AUTHOR]

Standing wave (SW) microscopy is a method that uses an interference pattern to excite fluorescence from labelled cellular structures and produces high‐resolution images of three‐dimensional objects in a two‐dimensional dataset. SW microscopy is performed with high‐magnification, high‐numerical aperture objective lenses, and while this results in high‐resolution images, the field of view is very small. Here we report upscaling of this interference imaging method from the microscale to the mesoscale using the Mesolens, which has the unusual combination of a low‐magnification and high‐numerical aperture. With this method, we produce SW images within a field of view of 4.4 mm × 3.0 mm that can readily accommodate over 16,000 cells in a single dataset. We demonstrate the method using both single‐wavelength excitation and the multi‐wavelength SW method TartanSW. We show application of the method for imaging of fixed and living cells specimens, with the first application of SW imaging to study cells under flow conditions. LAY DESCRIPTION: With a standard microscope, it is possible to interfere two or more beams of light and produce a contour map of cell structures using a technique known as standing wave microscopy. This method is usually applied with high power objective lenses, and only a tiny area can be studied, usually showing structural detail from one or two cells at most. The Mesolens is a unique objective lens that has been designed and manufactured to image large populations of cells in a single image. Two‐dimensional images of cells can be obtained with the Mesolens using regular illumination methods, but the cell topography is lost. Here we have combined standing wave illumination with the Mesolens to perform topographical imaging of large numbers of cells in a single image. We first proved the method with a non‐biological specimen comprised of a glass lens, and then we applied the technique to imaging of fixed and living cells: in the case of red blood cells, we showed that we can study the topography of more than 16,000 cells in a single image. With the much larger area of study afforded by the Mesolens, we also used standing wave illumination for the first time monitor red blood cell topography when the cells are subject to flow environment. This new application of standing wave imaging at unusually large spatial scales may prove useful for studying behaviour in the circulatory system. [ABSTRACT FROM AUTHOR]

The aim of this paper is to deal with the standing wave problems in coupled nonlinear fractional Klein–Gordon equations. First, we establish the constrained minimizations for a single nonlinear fractional Laplace equation. Then we prove the existence of a standing wave with a ground state using a variational argument. Next, applying the potential well argument and the concavity method, we obtain the sharp criterion for blowing up and global existence. Finally, we show the instability of the standing wave. [ABSTRACT FROM AUTHOR]

Circular domains frequently appear in mathematical modeling in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a two-dimensional disk. The properties of these bifurcations at equilibriums are analyzed rigorously by studying the equivariant normal forms. Two reaction–diffusion systems with discrete time delays are selected as numerical examples to verify the theoretical results, in which spatially inhomogeneous periodic solutions including standing waves and rotating waves, and spatially homogeneous periodic solutions are found near the bifurcation points. [ABSTRACT FROM AUTHOR]

In the 21st century, students' higher-order thinking skills (HOTS) are crucial, as they focus on students' capacity to identify problems and think analytically to solve them. Therefore, students were required to have higher-order thinking skills. The purpose of this research was to assess the impact of e-scaffolding in problem-based learning (PBL) on students' HOTS in the context of standing waves. This study utilized a quasi-experimental approach employing a non-equivalent control group design. The experimental group, which was taught with e-scaffolding in PBL, consisted of 31 students, while the control group, taught only with the PBL model, had 29 students. A total of eight multiple-choice questions that had been proven valid with a reliability of 0.752 were used to assess students' HOTS. The data were then analyzed using ANCOVA, with pretest scores as covariates. The results showed statistically significant differences among students with increased higher-order thinking skills in favor of using e-scaffolding in PBL: 0.000 (α < 0.005). The eta squared statistic (0.785) indicates a large effect size. By employing PBL with electronic scaffolding, students actively participate in collaborative activities focused on successful problem-solving, resulting in a high success rate. Consequently, it is recommended to consider e-scaffolding as a primary method for developing higher-order thinking skills. [ABSTRACT FROM AUTHOR]

In a number of studies, it has been shown that the geometry of an acoustic resonator strongly affects its resonant frequencies, as well as the nonlinear shape of the standing pressure waves generated inside the cavity. In this paper, we consider three resonators with different wall shapes (cone, exponential and bulb-shaped resonators) in which gas vibrations are formed due to an external periodic force. The acoustic field in the resonators is generated by the vibration of the left wall of the enclosure. The oscillation frequency of this wall is chosen so that the lowest acoustic mode can propagate along the resonator. The fully compressible form of the Navier–Stokes equations is used, and the explicit time-stepping algorithm is employed for modeling the motion of acoustic waves. The structure of acoustic flows of the second order, resulting from the interaction between the wave field and viscous effects on the walls, leads to the formation of flow patterns. These patterns can be revealed by averaging solutions over a specific period of time. To evaluate the performance of resonators, the pressure amplitude gain factor is used. This is defined as the ratio of pressure amplitude at the small end of the resonator to the pressure amplitude at its large end. It has been found that the best performance is observed in a flask-shaped resonator. [ABSTRACT FROM AUTHOR]

We study the dynamics of solutions of nonlinear Schrödinger equation (NLS) near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is proved. The novelty of our result is that we allow the existence of internal modes. [ABSTRACT FROM AUTHOR]

We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [9]. There are some well-posedness results for the equation, however there is no ill-posedness result. We focus on the scale critical space and obtain the ill-posedness in the super-critical or at the critical space under certain condition. The proofs in the super-critical space are based on the argument established by Christ, Colliander and Tao [4]. More precisely, we analyze dispersionless equation with smooth initial data, namely the Schwartz function and it is locally well-posed in some weighted Sobolev space. We construct the solution for the half wave Schrödinger equation by using the solution for the dispersionless equation and we can exploit the norm inflation or the decoherence properties. For the critical space, we use the standing wave solution, which was proved the existence by Bahri, Ibrahim and Kikuchi [1]. [ABSTRACT FROM AUTHOR]

Real-time characterization of microresonator dynamics is important for many applications. In particular, it is critical for near-field sensing and understanding light--matter interactions. Here, we report camera-facilitated imaging and analysis of standing wave patterns in optical ring resonators. The standing wave pattern is generated through bidirectional pumping of a microresonator, and the scattered light from the microresonator is collected by a short-wave infrared (SWIR) camera. The recorded scattering patterns are wavelength dependent, and the scattered intensity exhibits a linear relation with the circulating power within the microresonator. By modulating the relative phase between the two pump waves, we can control the generated standing waves' movements and characterize the resonator with the SWIR camera. The visualized standing wave enables subwavelength distance measurements of scattering targets with nanometer-level accuracy. This work opens broad avenues for applications in on-chip near-field (bio) sensing, real-time characterization of photonic integrated circuits, and backscattering control in telecom systems. [ABSTRACT FROM AUTHOR]

The interaction between electro-physiology and the geomagnetic field generates bio-waves within the body, which are conducted through the spaces between tissues. Meridians (Jing Luo) act as channels for these bio-waves. Inserting needles into the body creates "standing waves" that excite the body, enhancing membrane fluidity and facilitating the influx of calcium ions into cells from the interstitial space. Calcium ions (Ca++) play a crucial role in both physiology and pathology. The standing wave produces a "Synapse-Block" effect, which inhibits the production and movement of cytocysts, increases the threshold, and converts EPSPs into IPSPs, thereby achieving anesthesia and analgesia. [ABSTRACT FROM AUTHOR]

This paper describes an experiment designed to observe potential changes in electromagnetic propagation velocity. It has been widely demonstrated that if the frequency of an electromagnetic wave is fixed, then the associated wavelength is causally related to c. Furthermore, the logical conclusion related to this known association (of frequency, wavelength, and light speed) is that, if the generated frequency during an experiment remains the same, and there is a velocity change in c, there would be causally related expansion or reduction in the associated wavelength. With the use of a Lecher line and a standing electromagnetic wave, the experimenter can measure changes in wavelength by measuring electrical output at an assigned position on a Lecher line. Results of this experiment demonstrated an obvious and experimentally repeatable phase change associated with rotation of the Lecher line. This phase change was demonstrated by a change in electrical output measured at the assigned location on the Lecher line. This experiment was repeated using various frequencies and voltage inputs into the Lecher line with obvious results that demonstrated an anisotropic difference. Further experiments were completed attempting to find an alternative hypothesis for the phase change noted in the original experiment, but these experiments were unable to identify an alternative cause of the phase change and consequently support the hypothesis that the phase change was directly related to anisotropy secondary to a change in the measured wavelength of the electromagnetic wave. Based upon the logical conclusions associated with this experiment and the results obtained, this experiment appears to demonstrate variable speed light. Furthermore, this discovery brings into question the theory that electromagnetic propagation though space is at the constant of c. [ABSTRACT FROM AUTHOR]

Insulin therapy is integral to the treatment of diabetes mellitus. Epidemiologic studies have shown its benefits both in terms of improving glycemic control and reducing the risk for long-term diabetic complications for both type 1 and type 2 diabetes. Despite these benefits, barriers to insulin therapy are well documented and include perceived inconvenience, needle anxiety, and portability of device in case of insulin pumps. Therefore, this study aims to design and simulate a low frequency sonophoretic array for transdermal insulin delivery. This study utilizes COMSOL Multiphysics software to simulate the transducer used to increase the skin permeability for delivering drugs. It consists of $8\times 5$ array of a piezoelectric elements operated at 100 kHz and 1 volt. To evaluate the effectiveness of the transducer, an intricate skin model has been developed that includes all anatomical layers extending to the bone. The skin layers, particularly muscle and bone, exhibit reflective properties, leading to the formation of a standing wave. This phenomenon arises from the impedance mismatch between muscle and bone. Standing wave served to promote the transportation of the drug into the dermal layer, rich with capillary networks. We found that applying standing wave with 100 kHz the achieved pressure of 0.3 MPa induced acoustic streaming for the drug flow of $1605~\frac {\mathrm {\mu g}}{{\mathrm {cm}}^{2}}$ per 24 hours. Also, the precise modulation of ultrasound frequency and voltage is key to controlling peak acoustic pressure, thereby regulating the rate of insulin delivery through the skin.

Dielectric Assist Accelerating (DAA) structures based on ultralow-loss ceramic are being studied as an alternative to conventional disk-loaded copper cavities. This accelerating structure consists of dielectric disks with irises arranged periodically in metallic structures working under the TM02-w mode. In this paper, the numerical design of an S-band DAA structure for low beta particles, such as protons or carbon ions used for Hadrontherapy treatments, is shown. Four dielectric materials with different permittivity and loss tangent are studied as well as different particle velocities. Through optimization, a design that concentrates most of the RF power in the vacuum space near the beam axis is obtained, leading to a significant reduction of power loss on the metallic walls. This allows to fabricate cavities with an extremely high quality factor, over 100,000, and shunt impedance over 300 ΗΩ/m at room temperature. During the numerical study, the design optimization has been improved by adjusting some of the cell parameters in order to both increase the shunt impedance and reduce the peak electric field in certain locations of the cavity, which can lead to instabilities in its normal functioning. [ABSTRACT FROM AUTHOR]

This work reports that the flame oscillation induced by acoustic excitation can effectively suppress soot generation in Rijke-type burners. When the acoustic frequency is close to the natural frequency of the burner system, it can produce resonance resulting in intense oscillation of the flame. The relationship between the soot suppression efficiency and the acoustic field of standing wave at different flame positions is discussed. Compared with that under self-excited oscillation, when there is external forced acoustic force introduced to the flame, oscillation combustion occurred in a lager zone in the glass tube. The fundamental cause of different soot suppression efficiency at different positions is that the standing wave acoustic field causes the particles to move at different speeds in different positions of the glass tube. The axial particle velocity difference results in the formation of acoustic vortexes and the change of the flame shape. The high particle velocity causes the air in the glass tube to turn into the turbulent condition and make the flame temperature rise. Simulation results show that the surface growth rate of soot is reduced, while the oxidation rate of soot is enhanced, which result in the soot suppression under acoustic oscillation. This study can provide some reference for the practical application of oscillate combustion in soot suppression. [ABSTRACT FROM AUTHOR]

The work presents short characteristics of the X-ray fluxes waveguide-resonance propagation phenomenon. There is described peculiarities of the X-ray nanophotonics base device functioned in frame of the phenomenon – the planar X-ray waveguide-resonator and denoted directions of its development. X-ray waveguide-resonance devices elaboration in the process of base construction modification are discussed. [ABSTRACT FROM AUTHOR]

The results of a previously performed survey of steel cables of a cable-stayed crossing where the tension force was determined based on the frequency of their transverse vibrations are considered. The features of the methodology for measuring the natural frequencies of rope vibrations are revealed concerning the method of excitation ща vibrations, their orientation, and the volume of an informative sample of recorded frequencies. The physical model underlying the measurement technique does not take into account the elastic bending reaction of the cable and viscous friction. It is shown that taking into account these factors allows one not only to increase the accuracy of measuring the tension force, but also opens up a possibility for detecting cable defects. For example, the breakage of cable fibers, its thinning as a result of corrosion or abrasion could lead to a decrease in bending stiffness. A change in the state of the cable lubricant or the penetration of liquid into the cable leads to a change in the damping coefficient of its vibrations. The results of the study can be used to create systems for monitoring the condition of steel cables. [ABSTRACT FROM AUTHOR]

The statistics suggest that extreme waves cause more damage in shallow waters and at the coast than in the deep sea. In the linear theory of the formation of extreme waves, their existence is interpreted as a local superposition of surface monochromatic waves. The event of excitation of extreme waves can be understood as an increase in natural oscillations of the water basin. The conditions for the excitation and sustaining of natural oscillations are the proximity of the periods of exciting traveling waves to the period of traveling waves and the speed of movement of the exciting current to the phase speed of propagation of traveling waves of the reservoir. Examples of stimulating natural oscillations are presented. We determined the range of expected periods of natural oscillations, which range from 30 seconds to 24 hours. Synchronously and in common-mode with the oscillations of standing waves between their antinodes, a ''standing'' current occurs with a measured speed of up to 11 km/h. We presented a hypothesis about the possibility of stimulating natural oscillations of water bodies by a standing current, which changes its direction due to the movement of the water surface from the trough of the wave to its crest, and back. A model of stimulating oscillations by the waves with a constant period and currents with constant and variable speeds has been developed.

Dielectric Assist Accelerating (DAA) structures based on ultralow-loss ceramic are being studied as an alternative to conventional disk-loaded copper cavities. This accelerating structure consists of dielectric disks with irises arranged periodically in metallic structures working under the TM02-π mode. In this paper, the numerical design of an S-band DAA structure for low beta particles, such as protons or carbon ions used for Hadrontherapy treatments, is shown. Four dielectric materials with different permittivity and loss tangent are studied as well as different particle velocities. Through optimization, a design that concentrates most of the RF power in the vacuum space near the beam axis is obtained, leading to a significant reduction of power loss on the metallic walls. This allows to fabricate cavities with an extremely high quality factor, over 100,000, and shunt impedance over 300 MΩ/m at room temperature. During the numerical study, the design optimization has been improved by adjusting some of the cell parameters in order to both increase the shunt impedance and reduce the peak electric field in certain locations of the cavity, which can lead to instabilities in its normal functioning.

A non-destructive inspection technique using infrared thermography and ultrasound excitation (ultrasound-excited thermography method) was focused on in this study. Although this method is effective in the detection of closed defects, the standing waves are generated in the inspection object, and this causes periodic heat distribution in the non-defective area. Such standing wave heat distribution can lead to the misdetection of defects and result in a reduction in inspection capability. In this study, in order to suppress the influence of standing wave heat distribution, we examined a method to average thermal images obtained under different ultrasonic excitation conditions. The experimental results showed that averaging the thermal images obtained when exciting ultrasound at several different points was effective in suppressing the unwanted standing wave heat distributions. [ABSTRACT FROM AUTHOR]

Global ultra‐low frequency (ULF) oscillations are believed to play a significant role in the mass, energy, and momentum transport within the Earth's magnetosphere. In this letter, we observe a ∼1.2 mHz radial standing wave in the dusk‐sector magnetosphere accompanied by the field line resonance (FLR) on 16 July 2017. The frequency estimation from the simple box model also confirms the radial standing wave. The essential characteristics of FLR are concurrently identified at the dusk‐sector magnetosphere and the conjugated ground location. Further, the radial standing wave dissipates energy into upper atmosphere to enhance the local aurora by coupling itself to the FLR. The magnetospheric dominant 1.2/1.1 mHz ULF waves plausibly correspond well with the discrete ∼1 mHz magnetosheath ion dynamic pressure/velocity oscillation, suggesting this radial standing wave and FLR in the flank magnetosphere may be triggered by the solar‐wind and/or magnetosheath dynamic pressure/velocity fluctuations. Plain Language Summary: Just like thumping the strings, the Earth's magnetic field line can also be disturbed by the external impulses or internal instability, generating the rich ultra‐low frequency (ULF) oscillations with period of 1–1,000 s. They are believed to play a significant role in the mass, energy, and momentum transport within the Earth's magnetosphere. But the question of how an external driving mechanism can produce field line disturbances deep inside the magnetosphere is a topic of much debate. One classical global mode resonance model suggests that the magnetospheric space sometimes acts as a huge closed or semi‐closed cavity, where the ULF waves form the radial standing wave structure. So far, the observational evidence of radial standing waves with period of above 8 min accompanied by the field line disturbance in the flank magnetosphere is sparse. In this letter, we report a radial standing wave with period of ∼14 min within dusk‐sector magnetosphere accompanied by the field line disturbance phenomenon by multiple‐satellite observations. The radial standing wave energy sinks down to upper atmosphere to light the local aurora by coupling itself to the field line resonance. We conclude the radial standing wave may be caused by the solar‐wind and/or magnetosheath dynamic pressure/velocity fluctuations. Key Points: A radial standing Pc5‐6 ultra‐low frequency wave is identified within the dusk‐sector magnetosphereRadial standing wave dissipates energy into upper atmosphere by coupling itself to the field line resonanceSolar‐wind and/or magnetosheath dynamic pressure/velocity fluctuations possibly trigger this radial standing wave [ABSTRACT FROM AUTHOR]

In this paper, by using linking methods, we obtain the existence of the nontrivial standing wave solutions for the discrete nonlinear Schrödinger equations with resonance and unbounded potentials. In order to prove the existence of standing wave solutions, we give resonant condition to find a bounded critical sequence, and we show that such a sequence guarantees the existence of one nontrivial standing wave solution in l 2 when the nonlinearity is resonant and the potential is unbounded. To the best of the our knowledge, there is no existence results for the discrete nonlinear Schrödinger equations with resonance in the literature. [ABSTRACT FROM AUTHOR]

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We investigate the existence of solutions to a recent model for large-scale equatorial waves, derived recently by an asymptotic method driven by the thin-shell approximation of the Earth's atmosphere in rotating spherical coordinates. [ABSTRACT FROM AUTHOR]

The deep tunnel stormwater system, consisting of dropshafts and underground tunnels, is used to alleviate or prevent urban water problems associated with extreme rainfall events. The stepped dropshaft can transport surface runoff to the tunnels with high energy dissipation, low risk of cavitation and good exhaust performance, which well meets the requirement of the deep tunnel stormwater system. In the present study, the characteristics of the standing wave were investigated by experiments and numerical simulations, including the peak, trough and length of the standing wave. The flow regimes were divided into the nappe flow, the transition flow and the skimming flow with the increase of discharge, in which the standing wave mainly occurs on the external wall under the nappe flow and the transition flow. Influences of inflow discharge and dropshaft geometries were analyzed, including step rotation angle, relative step height and dropshaft curvature. The relations of the characteristics of standing wave with these effect factors were obtained. The maximum discharge capacity of the stepped dropshaft was established by considering that the standing wave just reached the above steps, which could be useful for the design and safe operation of the stepped dropshaft. HIGHLIGHTS The standing wave properties under various flow regimes in stepped dropshaft are demonstrated and compared.; The major factors affecting the standing wave properties are obtained and their influences are concluded.; The maximum discharge capacity of stepped dropshaft is predicted based on the knowledge of standing wave peak.;

We propose an atomic grating based on an electromagnetically induced transparency phenomenon that switches between zeroth-order diffraction to a distinct higher-order diffraction pattern by driving a planar gaseous medium of a four-level tripod ( ⋔) atoms with three laser beams: modulation of standing wave control beam propagating nearly perpendicular to the planar medium, while vortex and weak plane probe beams directed perpendicular to the medium. We numerically investigate the behavior of the amplitude, phase modulations, and probe field diffraction intensities of different orders by the variation of the field detunings and orbital angular momentum number of the composite vortex light beam. Specifically, in the off-resonant case, the interplay between a square lattice of the control and an additional spatial variation of the vortex beam allows the emergence of higher diffraction orders and variable gain due to double transparency windows in this complex optical system. We believe that our proposed scheme might be useful in optical memory devices via the storage of information to diffraction orders of the atomic grating. [ABSTRACT FROM AUTHOR]

In the present work a numerical modeling of excitation of acoustic gas oscillations in a tube with the help of unevenly heated plates, when placing them near the end wall was carried out. The flow analysis and heat transfer calculation were performed by solving linearized unsteady Navier–Stokes equations using the finite element method. The developed mathematical model makes it possible to theoretically determine the influence of the temperature difference and various geometric parameters of the device on the characteristics of the excited oscillations. The obtained results indicate an increase in acoustic pressure and acoustic power as the temperature gradient along the plates increases. [ABSTRACT FROM AUTHOR]

In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with a repulsive inverse-square potential. It is known that there exist "radial" ground states to the stationary problem of the nonlinear Klein-Gordon equation. Here, "radial" ground states are non-trivial solutions having least energy among all non-trivial radial solutions to the stationary equation. We deal with the stability and instability of "radial" ground state standing waves. [ABSTRACT FROM AUTHOR]

Electrostatic curtains can be simple and yet efficient devices to manipulate micronized particles on flat surfaces. This paper aims to investigate the motion of a 60 µm dielectric particle on the surface of a standing-wave conveyor. The study is based on a numerical model that accounts for the many forces that could potentially influence the particle motion. For that purpose, a numerical calculation of electric field and particle movement was carried out. The particle position above the curtain surface is obtained by a resolution of the dynamic equations using the Runge–Kutta method. The electric field distribution in the space above the curtain is obtained by a finite element calculation of the Laplace equation. The simulation results demonstrated a net dependence of the particle trajectory and movement modes on applied voltage frequency. Overall, low frequencies, typically below 50 Hz, allow for higher levitation and better displacement of the particle over long distances. Conversely, higher frequencies significantly reduce levitation and displacement distance. Moreover, at higher frequencies (around 500 Hz), the particle can vibrate between electrodes without any displacement at all. It is then inferred that low frequency is needed to better carry particles using a standing-wave curtain. [ABSTRACT FROM AUTHOR]

Temperature transducers are frequently employed to keep track of process variables with different kinds of industrial controllers. One of the widely used temperature sensors is Pt100. A novel approach of utilizing an electroacoustic transducer in signal conditioning for Pt100 is proposed in this paper. A "signal conditioner" is a resonance tube filled with air, which is operated in a free resonance mode. The Pt100 wires are connected to one of the leads of the speaker in the resonance tube where the temperature changes, which is related to Pt100 resistance. The resistance affects the amplitude of the standing wave that is detected by an electrolyte microphone. An algorithm for measuring the amplitude of the speaker signal is described, as well as the building and functioning of the electroacoustic resonance tube signal conditioner. The microphone signal is acquired as a voltage using LabVIEW software. A virtual instrument (VI) developed under LabVIEW provides a measure of the voltage using standard VIs. The findings of the experiments reveal a link between the measured amplitude of the standing wave within the tube and the change in Pt100 resistance as the ambient temperature changes. Additionally, the suggested method may interface with any computer system when a sound card is added to it without the need for any extra measuring tools. The maximum nonlinearity error at full-scale deflection (FSD) is estimated at roughly 3.77%, and the experimental results and a regression model are used to assess the relative inaccuracy of the developed signal conditioner. When comparing the proposed approach with well-known approaches for Pt100 signal conditioning, the proposed one has several advantages such as its simplicity of connecting Pt100 to a personal computer directly via the sound card of any personal computer. In addition, there is no need for a reference resistance to perform a temperature measurement using such a signal conditioner. [ABSTRACT FROM AUTHOR]

Friction drive and wear control is a tough issue for linear standing-wave ultrasonic motors with intermittent contact and impact friction. For the widely recognized reduction of friction/wear, minimum quantity lubrication was adopted to improve the output performances and services for motors through friction regulation. Given different preload and driving voltages, the mechanical characteristics of motors with minimal quantity lubrication were investigated using a homemade test rig. Results show that output performances and driving efficiency under film lubrication differ from those of dry friction. The optimized driving voltage was reduced by 31.5% and the minimum startup voltage was reduced by 41.67% using film lubrication. Additionally, the output speed increased by 26.29%, and thrust decreased by 41.26% under uniform exciting conditions (e.g., 150 V at 39.14 kHz). The existence of film lubrication broadens the effective frictional contact boundary, and effective friction contribution enhances the driving efficiency (the maximum efficiency of motors increased by 14%). Furthermore, the singularity of the effect of preload is significantly improved after lubrication, and the friction interface of the stator/slider becomes more controllable. Suitable lubrication is critical to the improvement of startup performance and prone to realize low-voltage driving, and the combination of lubrication regulation and wear inhibition is conducive to the durability and reliability of motors. This study provides an additional alternative for performance improvement of linear standing-wave motors apart from frictional materials. [ABSTRACT FROM AUTHOR]

This paper analyzes a population model with time-dependent advection and an autocatalytic-type growth. As opposed to a logistic growth where the rate of growth of the population decreases from the onset, an autocatalytic growth has a point of inflection where the rate of growth switches from an increasing trend to a decreasing trend. Employing the idea of Painlevé property, we show that a variety of exact traveling wave solutions can be obtained for this model depending on the choice of the advection term. In particular, due to situations in resource distribution or environmental variations, if the advection is represented as a decaying function in time or an oscillating function in time, we are able to find exact solutions with interesting behavior. We also carry out a computational study of the model using an exponentially upwinded numerical scheme and illustrate the movement of the solutions and their characteristics pictorially. [ABSTRACT FROM AUTHOR]

• Numerical modeling of thermoacoustic devices can be classified into 1-D linear and 2-D/3-D non-linear models. • Linear thermoacoustic models lose their utility, in the high amplitude and high frequency regime. • CFD modeling has proven to be an effective tool in capturing the nonlinearities associated with standing wave thermoacoustic devices. • Flow dominance in a 2-D plane inside SWTADs has allowed the performance evaluation of these devices utilizing 2-D CFD models. • CFD modeling of standing wave thermoacoustic devices primarily focus on stack and the region around it. Global environmental concerns have brought the challenge of developing renewable energy technologies to cope up with the world energy needs. Thermoacoustic devices present themselves as a viable alternative to replace conventional refrigeration and power systems due to their minimal carbon footprint. These devices involve complex flow physics encompassing transient phenomenon and conversion of acoustic and thermal energies for their efficient performance. With the rapid advancement in computational capabilities, extensive numerical work is carried out to gain detailed understanding of the thermoacoustic devices. In this paper, a detailed review of the numerical modeling techniques that have been applied in the field of Standing Wave Thermoacoustic Devices (SWTAD) is carried out. At first, a brief review of analytical method is presented and the need for numerical modeling is highlighted. Numerical modeling techniques ranging from simplified linear to detailed Computational Fluid Dynamics (CFD) models are reviewed in detail. Model configurations, capabilities and tools developed and utilized so far in the research area are summarized. Challenges associated with SWTAD and applications modeled using CFD are discussed. The paper concludes with some useful recommendations regarding the numerical modeling of thermoacoustic devices. [ABSTRACT FROM AUTHOR]

Temperature transducers are commonly used to monitor process parameters that are controlled by various types of industrial controllers. The purpose of this study is to design and model a simple microcontroller-based acoustic temperature transducer based on the variations of resonance conditions in a cylindrical resonance tube. The transducer's operation is based on the generation of an acoustic standing wave in the free resonance mode of generation within a cylindrical resonance tube which is converted into a train of pulses using Schmitt trigger circuit. The frequency of the generated standing wave (i.e., the train of pulses) is measured by the Arduino Uno microcontroller, where a digital pin is used to acquire pulses that are counted using a build-in software function in an Arduino IDE environment. Experimental results are performed for three sizes of diameters to investigate the effect of the diameter of resonance tube on the obtained results. The maximum nonlinearity error according to Full-Scale Deflection (FSD) is about 2.3 percent, and the relative error of the transducer is evaluated using experimental findings and the regression model. The circuit simplicity and design of the suggested transducer, as well as the linearity of its measurements, are notable. [ABSTRACT FROM AUTHOR]

The review summarizes the theoretical and numerical results of analysis of the dispersion equation of standing waves on the surface of a viscous liquid published by L.N. Sretensky in 1941. A mechanism for the viscous regularization of wave motion is proposed, according to which the effects observed in the experiment are associated with the presence of a short-wavelength cutoff region, where viscous dissipation becomes the predominant factor and short-wavelength perturbations responsible for the breaking of a standing wave are suppressed. [ABSTRACT FROM AUTHOR]

Standing waves (seiches) in a rectangular channel with varying depth are considered in the case when the channel depth steadily changes starting from zero. The modified accelerated-convergence method is used to solve the problem. The dependences of the form of the seiches on the channel width are obtained for different bottom profiles. The behavior of natural frequencies for channel depth profiles is analyzed. [ABSTRACT FROM AUTHOR]

Accurate knowledge of the natural frequencies and shapes of corresponding standing waves are essential for gaining deeper insight into the nature of response of coils to impulse excitations. Most of the previous analytical studies on coils assumed shape of standing waves as sinusoidal but numerical circuit analysis and measurements suggest otherwise. Hence, this paper revisits the classical standing wave phenomenon in coils to ascertain reasons for this discrepancy and thereafter extends it by analytically deriving the exact mode shape of standing waves for both neutral open/short conditions. For this, the coil is modeled as a distributed network of elemental inductances and capacitances while spatial variation of mutual inductance between turns is described by an exponential function. Initially, an elegant derivation of the governing partial differential equation for surge distribution is presented which is then analytically solved, perhaps for the first time, by the variable-separable method to find the complete solution (sum of time and spatial terms). Hyperbolic terms in spatial part of solution have always been neglected but are included here, thus, yielding the exact mode shapes. Voltage standing waves gotten from analytical solution are plotted and compared with simulation results on a 100-section ladder network. The same is measured on a large-sized single layer coil. So, it emerges that, even in single layer coils, shape of standing waves deviates considerably from being sinusoidal and this deviation depends on spatial variation of mutual inductance, capacitive coupling, and order of standing waves. [ABSTRACT FROM AUTHOR]

We study the existence and orbital stability of standing waves of nonlinear fractional Schrödinger equations with a general nonlinear term. The existence and non-existence of global minimizers with respect to Eα are established for all possible values of α: Under some general assumptions on the nonlinear term f(u), there exists a constant α0 > 0 such that a global minimizer exists for Eα for all α > α0, and there is no global minimizer with respect to Eα for all 0 < α < α0: By virtue of concentration-compactness argument and the strict subadditivity of Eα, the strong convergence of minimizing sequence is obtained. Moreover, we present some criteria which determine α0 = 0 or α0 > 0, and the existence of global minimizers for Eα0: Besides, we show the orbital stability of the global minimizers set. Finally, we prove that an energy minimizer is a least action solution by Pohozaev identity. [ABSTRACT FROM AUTHOR]

This paper presents a new proximity-coupling mechanism between a rectangular patch and a microstrip line with an open circuit terminal. The patch is located to cover both adjacent maximum-voltage (capacitive coupling) and maximum-current (inductive coupling) points of the standing wave on the feedline, and consequently, two orthogonal resonant modes with 90° phase difference are excited on the patch for generating a circularly polarized (CP) radiation. Based on this feeding mechanism, a dual-band dual-sense CP antenna is designed, which is composed of two linear rectangular patch arrays coupled to an open-ending microstrip line. It is realized on a single-layer substrate and its CP rotating sense in each band is opposite to each other. For verification, the antenna operating at 5.0 and 8.0 GHz are designed, fabricated, and tested. Noting that the design concept can be easily implemented to other frequency bands. The measurements result in an impedance-matching bandwidth of 4.72 – 5.10 GHz and 7.50 – 8.20 GHz. The antenna is left-hand CP for the lower band and right-hand CP for the upper band. In addition, the prototype shows a 3-dB axial ratio bandwidth of 4.93 – 5.02 GHz and 7.40 – 8.10 GHz and peak gains of 11.4 and 12.7 dBic at the lower and upper bands, respectively. [ABSTRACT FROM AUTHOR]

A non-destructive inspection technique using infrared thermography and ultrasound excitation (ultrasound-excited thermography method) was focused on in this study. Although this method is effective in the detection of closed defects, the standing waves are generated in the inspection object, and this causes periodic heat distribution in the non-defective area. Such standing wave heat distribution can lead to the misdetection of defects and result in a reduction in inspection capability. In this study, in order to suppress the influence of standing wave heat distribution, we examined a method to average thermal images obtained under different ultrasonic excitation conditions. The experimental results showed that averaging the thermal images obtained when exciting ultrasound at several different points was effective in suppressing the unwanted standing wave heat distributions.