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This paper systematically investigates the exact solutions to an extended (2+1)-dimensional Boussinesq equation, which arises in several physical applications, including the propagation of shallow-water waves, with the help of the Lie symmetry analysis method. We acquired the vector fields, commutation relations, optimal systems, two stages of reductions, and exact solutions to the given equation by taking advantage of the Lie group method. The method plays a crucial role to reduce the number of independent variables by one in each stage and finally forms an ODE which is solved by taking relevant suppositions and choosing the arbitrary constants that appear therein. Furthermore, Lie symmetry analysis (LSA) is implemented for perceiving the symmetries of the Boussinesq equation and then culminating the solitary wave solutions. The behavior of the obtained results for multiple cases of symmetries is obtained in the present framework and demonstrated through three-and two-dimensional dynamical wave profiles. These solutions show single soliton, multiple solitons, elastic behavior of combo soliton profiles, and stationary waves, as can be seen from the graphics. The outcomes of the present investigation manifest that the considered scheme is systematic and significant to solve nonlinear evolution equations.

Thermoacoustics is about conversion between thermal and acoustical energies to provide alternative green technology for power cycle and cooling system. The oscillatory flow across porous structure inside the system is playing the role of energy conversion between the acoustic wave and the surface of the porous structure. Better understanding of fluid dynamics of oscillatory flow inside thermoacoustic system is therefore important for the thermoacoustic based energy conversion system. This paper presents the ‘entrance’ and ‘exit’ effects of the oscillatory flow within a parallel-plate structure that is placed inside a standing-wave thermoacoustic environment. Two-dimensional SST k-ω CFD models which were validated using experimental data and theoretical predictions were used for this investigation. Two different operating frequencies of 14.2 Hz and 23.6 Hz were studied for flow with five different amplitudes that were represented using drive ratios of 0.3%, 0.83%, 1.5%, 2.1% and 3%. These correspond to cases with Reynolds numbers between 5936 and 62926. Due to the cyclic nature of the flow, a region defined as an ‘exit’ region was observed in addition to the usual ‘entrance’ region and the fully developed region for flow inside a channel. The change of shape of velocity profiles from the ‘m’ shape profile, to the ‘slug-like’ profile and ‘parabolic-like’ profile was discussed in relation to the ‘entrance’ and ‘exit’ effects on flow inside the channel. The ‘entrance’ and ‘exit’ effects become bigger as drive ratio increases. The effect of ‘entrance’ and ‘exit’ are slightly reducing as frequency increases from 14.2 Hz to 23.6 Hz. This may be related to the shorter travel distance of fluid as the frequency increases. The results shown in this paper suggest that the flow within a 200 mm parallel-plate structure should be treated as developing flow especially for flow with low resonance frequency at drive ratio higher than 1%.

In this study, the dynamic response and instability of a low-permeability deformable caisson-type quay wall (CQW) with backfill soil exposed to standing waves is evaluated. The focus is on the dynamic response and instantaneous liquefaction of seabed and backfill around the CQW. This study aims at closing the knowledge gap about the wave-induced CQW–seabed response without the presence of a breakwater, as the bulk of the prior research has been done on CQWs considering earthquakes as the primary loading source. Finite elements are used, and numerical results are obtained in terms of displacements, pore-pressure and shear stress variations in temporal and spatial domains. Wave-induced instantaneous liquefaction is analysed, and analyses are performed to determine the effect of soil/wave properties on dynamic response and liquefaction. Results indicate that there is considerable liquefaction potential in both seabed and backfill that may play a key role in the stability of the CQW. While such a response is dependent upon the induced wave energy and the CQW motion, seabed parameters alter the instantaneous liquefaction occurrence as well. A slight decrease in the seabed degree of saturation causes a contraction behaviour under the wave-induced motion of the CQW, which, in turn, affects the mechanism of response and the initiation of instability in the seabed.

Optical tunneling is an effect extremely sensitive to wavelength changes. In this article, we use this effect to design a new type of biosensor. The tunneling effect is excited by long range surface plasmon resonance, the energy is concentrated in the sensing medium in the form of standing waves, which lead a very high wavelength sensitivity and quality factor. By using COMSOL for finite element analysis, for the sensor structure of BK7/Cytop /Al2O3/Ag/Al2O3/sensing media/air, a quality factor of 10296 RIU-1 is achieved under angle modulation, a sensitivity of 170,000 nm/ RIU and a quality factor of 11333 RIU-1 are obtained under wavelength modulation. At the same time, the advantage of this structure is that there is no excessive requirement on the refractive index of the material, and a good sensing effect can be achieved even if the material is cheap and easy to prepare. After optimization, this structure is suitable for sensing media with a refractive index of 1.335-1.375, which can be applied to most liquid solutions.

A dual-polarized endfire array is presented in this paper for millimeter application. The substrate integrated mode-composite transmission line is introduced to exciting the dual-polarized radiation. Specially, the horizontal polarization is excited by the TEM-mode, while the vertical polarization is based on the TE10-mode. Two metal blocks sandwich the substrates to form a sandwich structure, and open-ended slot is designed on the block edge to construed complementary sources radiation. Benefiting from the wdieband feature of complementary sources, the proposed dual-polarized endfire array achieved a considerable bandwidth performance of 26.9% (24.8 GHz -32.5 GHz) based on the standard that both the voltage standing wave ratios of the two ports are less than 2. In terms with the key factor of dual-polarized antenna, isolation, measured results shows a high port isolation of over 36 dB and a cross-polarization discrimination rate of over 30 dB. The excellent dual-polarized performance gives the proposed endfire array the potential of application in millimeter wave mobile communications.

Hemispherical Resonator Gyroscope (HRG) is a classical high precision Coriolis Vibration Gyroscope (CVG), which performs attitude estimation of carrier by detecting the precession of standing wave of resonator, thus, the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope, where the quality factor non-uniformity of resonator is one of main error sources. Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation, which makes the gyroscope have more accurate scale factor, larger measurement range and better dynamic characteristics. In this paper, the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle, then the corresponding equivalent mechanical model is established. According to the “average method”, it can be seen that the ideal resonator excited by the ring electrode works in integral mode, and any position in the circumferential direction of resonator can be a working point, which means that the quality factor non-uniformity has a great effect on the drift of standing wave. Therefore, the equations of motion of resonator with quality factor non-uniformity under the ring electrode excitation are deduced by the equivalent mechanical model, and the drift model of standing wave is established by the “average method”, it can be found that both the amplitude of quality factor non-uniformity and angle between the “inherent damping axis” and antinode axis of standing wave can affect the drift rate of standing wave. Moreover, the drift model indicates that if the input angular rate does not reach the threshold, the precession angular rate of standing wave will appear “self-locking” phenomenon, that is, the gyroscope will lose the integral effect.

The main condition for elimination of growth striations is the formation of standing waves in the melt for damping of convection. The formation of standing waves between the crucible bottom and the solid-liquid interface suppresses convection in the melt and eliminates growth striations in single crystals. Growth striations in InSb and GaAs single crystals were eliminated after the ultrasound was switched on at frequencies of 0.65 MHz and 0.15 MHz in their melts with the Rayleigh numbers 0.18×105 and 0.2×105, respectively. The ultrasound intensity was determined from a model experiment with similar conditions to crystal growth using a light cut method. The model experiments demonstrated formation of standing waves above the waveguide with a piezo transducer after switching on the ultrasound that attended appearance of a dome on a liquid surface. The dome dimensions on the liquid surface were used for calculation of the ultrasound intensity. The calculated ultrasound intensity was 0.85 Wcm-2. It was found that the growth striations disappeared a certain time after switching the ultrasound on, which can be explained by the formation time of standing waves and properties of the melt. The time intervals between switching the ultrasound on and the elimination of striations in grown InSb and GaAs single crystals were measured using the experimental images with the striation elimination, and were 10 s and 22 s, respectively. The controlled formation of ultrasonic standing waves in the melt in crystal growth eliminates growth striations, and this technique can be used for the industrial application.

The aim of the work. The problem of numerical simulation of longitudinal, transverse and surface waves on the free surface of an elastic half-plane is considered. Methods. To solve the non-stationary dynamic problem of elasticity theory with initial and boundary conditions, the finite element method in displacements was used. Using the finite element method in displacements, a linear problem with initial and boundary conditions was led to a linear Cauchy problem. A quasiregular approach to solving a system of second-order linear ordinary differential equations in displacements with initial conditions and to approximating the area under study is proposed. The method is based on the schemes: point, line and plane. The study area is divided by spatial variables into triangular and rectangular finite elements of the first order. According to the time variable, the study area is divided into linear end elements with two nodal points. The Fortran-90 algorithmic language was used in the development of the software package. Results. Some information is given about numerical modeling of elastic stress waves in an elastic half-plane with a concentrated wave action in the form of a Delta function. The estimated area under study has 12 008 001 nodal points. A system of equations consisting of 48 032 004 unknowns is solved. The change of elastic contour stress on the free surface of the half-plane at different points is shown. The amplitude of Rayleigh surface waves is significantly greater than the amplitudes of longitudinal, transverse, and other waves with a concentrated vertical action in the form of a triangular pulse on the surface of an elastic half-plane. After surface Rayleigh waves, a dynamic process is observed in the form of standing waves.

An asymmetric coupled three well system has been shown to exhibit PT-symmetry and electromagnetically induced grating (EIG), owing to electromagnetic induced transparency under the application of standing wave control and pump fields. The detuning of the probe and the uniform amplitudes of the standing wave control and pump fields could be used to tune the PT-symmetry. The probe beam is asymmetrically diffracted by the EIG either in positive or negative diffraction angles owing to the PT symmetry. The angle of diffraction can be controlled by the interaction length, probe detuning, and the uniform amplitudes of the standing wave control and pump fields.

International audience; Many-particle time domain methods are rising alternatives to particle-in-cell (PIC) or frequency methods to simulate the wave–beam interactions in traveling wave tubes (TWTs). We focus on two of those: our Hamiltonian discrete model DIMOHA is compared analytically against the pseudospectral method RUBEUS. Although based on two completely different approaches—the Gel’fand transform for DIMOHA and the telegraphist circuit for RUBEUS—we surprisingly find out that they share perfectly parallel sets of equations and variables. However, we conclude that DIMOHA is more flexible than RUBEUS in terms of pitch tapering and absorbing boundary conditions. It also shows excellent stability for steady-state simulation, allowing us to explain some discrepancies of RUBEUS with experimental results. These come from a standing wave pattern which is detectable in the vicinity of the sever. Finally, DIMOHA is tested for the first time with ultra-short pulses and exhibits excellent agreement with RUBEUS.

In this article, we propose a simulation method to investigate the noise mechanism of traveling-wave tube (TWT). Based on the nonlinear theory of Lagrangian description, 1-D noise model is established to analyze the shot noise and the velocity noise of the electron beam in the drift space, which clearly shows that the beam noise propagates along the electron beam with standing wave shape. The shot noise and the velocity noise can be periodically converted into each other along electron beam transmission, which is consistent with the prediction of the classical noise theory developed by Pierce and Danielson (1954). Using the nonlinear beam–wave interaction theory, the evolution process of the shot noise and the velocity noise of the electron beam transforming to the electromagnetic wave in TWT is illustrated. The calculated results show that the input position of the slow wave circuit may affect the noise power spectral density (NPSD) of the device. The proposed method can provide more intuitive and simple images to explain the noise mechanism of TWT.

We consider a microstretch elastic material with thermal and mass diffusion at the macro- and microlevel and study plane harmonic in time wave solutions. We have an undamped in time wave for the displacement, the microrotation and the microdilatation in the uncoupled case. The functions accounting for the thermal and diffusive effects are standing waves with the amplitude decaying exponentially with time. We also illustrate some of these waves. Finally, we discuss a particular case by not taking into consideration the effects of rotation, contraction and dilatation of the material particles when some of the coupling coefficients are not null.

It is recognized that in very-high-frequency capacitively coupled plasma (VHF CCP) reactors, the standing wave effects can be enhanced by the presence of nonlinear higher harmonics self-excited by the plasma series resonance (PSR). In this work, we investigated the influence of the dc bias on the excitation of the nonlinear standing waves in a parallel-plate capacitively coupled dc/VHF (60 MHz) hybrid discharge sustained in argon, with both the dc source and the VHF source applied to the top electrode. A hairpin probe was employed to determine the axial/radial distribution of the electron density, while a high-frequency B-dot probe was used to measure the radial distributions of the harmonic magnetic field and the harmonic current density. With no dc bias applied, the nonlinear standing wave excitation was observed to be predominant; the high-order harmonic current density exhibited a main peak at the electrode center and one or more minor peaks between the electrode center and the edge, leading to a center-high electron density profile. With the addition of the dc source, the harmonic excitations and the corresponding nonlinear standing wave effect tend to be suppressed with the increase of dc bias, resulting in improved plasma uniformities. Underlying mechanisms of the suppression effect of the dc bias on the nonlinear standing wave excitation were analyzed.

Photoacoustic imaging reveals great potential for the study of individual cells due to the rich imaging contrast for both label-free and labeled cells. However, previously reported photoacoustic imaging flow cytometry configuration suffers from inadequate imaging quality and challenge to distinguish multiple cells. In order to solve such issues, we propose a novel acoustic standing wave aided multiparametric photoacoustic imaging flow cytometry (MPAFC) system. The acoustic standing wave is introduced to improve the imaging quality and speed. Multispectral illumination along with cell geometry, photoacoustic amplitude, and acoustic frequency spectrum enables the proposed system to precisely identify multiple types of cells with one scanning. On the basis of the identification, elimination of melanoma cells, and targeted labeled glioma cells have been performed with an elimination efficiency of >95%. Additionally, the MPAFC system is able to image and capture melanoma cells at a lowest concentration of 100 cells mL-1 in pure blood. Current results suggest that the proposed MPAFC may provide a precise and efficient tool for cell detection, manipulation, and elimination in both fundamental and clinical studies.

Waveguide arrays comprise slot radiators cut into hollow, single-mode, standing wave structures. Their impedance bandwidth and compactness are limited by the waveguide cutoff. By using the TEM mode of a coaxial waveguide, a more compact structure with a larger bandwidth is possible at the expense of increased ohmic loss in the waveguide. Using this basis, a new type of slotted coaxial waveguide antenna is presented. A compact waveguide array means that the element and array aspects are not independent, and with no accurate transmission line models for the structure, the design is from a parametric study by simulation. Two basic designs are demonstrated: the first with no constraint on the azimuthal extent of the slots, and the second where some mechanical strength of the waveguide is maintained by constraining the azimuthal extent of the slots to be 90° or less. The parametric studies provide insight for realizing the high bandwidth, and measurements of prototypes confirm the performance. These antennas are useful for integration with cylindrical structures such as masts or bicycle and drone frames.

This study presents a systematic analysis of double-frequency (DF) microseisms recorded on the unconsolidated sediments in the eastern and southeastern coasts of United States. For all recordings, the site effect parameters (predominant frequency (f0), amplification factor and unconsolidated sediment thickness (UST)) are obtained by Nakamura method and the DF spectra are classified into five groups in terms of the DF peak patterns and the recording locations relative to the coastline. The frequencies and energy levels of the DF peaks in horizontal direction and the amplification factors are associated with the UST which is resulted from seismic site effect. By polarization analysis, the primary vibration directions of the DF peaks are identified and presented as great circles passing through the recording stations intersecting mainly along the continental slope. Correlation analyses of time histories of the DF energy and the ocean wave climate observed at buoys show that the low ( 0.2 Hz) frequency DF microseisms are generated in the deep ocean and the continental shelf respectively. It is concluded that the continental slope plays a significant role in the generation of DF microseisms as it causes reflection of waves from the open ocean, initiating standing waves.

In this paper, we study the existence and concentration behaviour of multi-peak standing waves for a singularly perturbed Davey–Stewartson system, which arises in the theory of shallow water waves. For this purpose, we first give a sharp threshold of the existence of ground-state solutions to the related limiting problem. Next, combining the penalization method and the regularity theory of elliptic equations, we construct a family of positive solutions concentrating around any prescribed finite set of local minima, possibly degenerate, of the potential. A feature of this analysis is that we do not need any uniqueness or non-degeneracy conditions for the limiting equation. To the best of our knowledge, this paper is the first study dealing with the study of concentrating solutions for Davey–Stewartson systems. We emphasize that with respect to the classical Schrödinger equation, the presence of a singular integral operator in the Davey–Stewartson system forces the implementation of new ideas to obtain the existence of multi-peak solutions.

The discovery of a simple numerical formula for the projection of all the atomic mass of life-sustaining CONHSP bioatoms leads to the emergence of a set of Nested CODES unifying all the biological, genetic and genomic components by unifying them from bioatoms up to 'to whole genomes. In particular, we demonstrate the existence of a digital meta-code common to the three languages ​​of biology that are RNA, DNA and amino acid sequences. Through this meta-code, genomic and proteomic images appear almost analogous and correlated. The analysis of the textures of these images then reveals a binary code as well as an undulatory code whose analysis on the human genome makes it possible to predict the alternating bands constituting the cariotypes of the chromosomes. The application of these codes to perspectives in astrobiology and the emergence of binary codes and regions of local stability (voting process), whose fractal nature we demonstrate, is illustrated. The fundamental discovery described here will undoubtedly one day constitute a new biomathematic approach to the emergence of living things.

This manuscript describes an experimental and numerical investigation of transcritical thermoacoustic instability in a standing-wave setup using the refrigerant octafluoropropane (R-218) as the working fluid. Thermoacoustic instability is excited by two microtube heat exchangers separated by a vacuum-jacketed microtube stack. R-218 is allowed to flow axially through the microtubes into a closed resonator while heating and cooling fluids flow radially over the microtubes to create a temperature gradient. The fluid achieved pressure amplitudes up to 669 kPa (97 psi) at a temperature difference ΔT=Thot−Tcold of 150 K and a base pressure, P0, of 1.3 times the critical pressure (3.43 MPa). The high pressure amplitudes obtained are attributed to the strong density variations near the critical point of the working fluid. The thermoacoustic response was characterized in a set of parametric studies in which ΔT, base pressure, and resonator length were varied. A modeling approach based on linearized Navier–Stokes equations reproduces the experimental results with fair agreement. This work demonstrates promising application of transcritical working fluids to thermoacoustic engines as devices for energy extraction and waste heat removal.

About 140 years ago, Lord Kelvin derived the equations describing waves that travel along the axis of concentrated vortices such as tornadoes. Although Kelvin’s vortex waves, also known as centrifugal waves, feature prominently in the engineering and fluid dynamics literature, they have not attracted as much attention in the field of atmospheric science. To remedy this circumstance, Kelvin’s elegant derivation is retraced, and slightly generalized, to obtain solutions for a hierarchy of vortex flows that model basic features of tornado-like vortices. This treatment seeks to draw attention to the important work that Lord Kelvin did in this field, and reveal the remarkably rich structure and dynamics of these waves. Kelvin’s solutions help explain the vortex breakdown phenomenon routinely observed in modeled tornadoes, and it is shown that his work is compatible with the widely used criticality condition put forth by Benjamin in 1962. Moreover, it is demonstrated that Kelvin’s treatment, with the slight generalization, includes unstable wave solutions that have been invoked to explain some aspects of the formation of multiple-vortex tornadoes. The analysis of the unstable solutions also forms the basis for determining whether, for example, an axisymmetric or a spiral vortex breakdown occurs. Kelvin’s work thus helps explain some of the visible features of tornado-like vortices.

Dalam saluran transmisi koaksial, ada teori tentang gelombang berdiri (standing wave). Gelombang berdiri terjadi akibat adanya interferensi antara gelombang satu dengan gelombang yang lain. Beberapa institusi atau perguruan tinggi mungkin tidak semua memiliki peralatan untuk mengamati bentuk gelombang yang tepat dari sinyal listrik atau biasa disebut dengan osiloskop. Salah satunya yaitu Politeknik Negeri Malang. Maka dari itu, pada penelitian ini saya ingin memudahkan para mahasiswa, khususnya dalam mata kuliah praktikum saluran transmisi untuk dapat menggambarkan kurva gelombang berdiri pada kabel koaksial. Hasil penerapan sistem dilakukan dengan menggunakan IC LED VU Display sebagai tampilan kurva gelombang berdiri dimana generator fungsi sebagai masukan sinyal yang mana mengatur frekuensi dan tegangan input yang sudah ditentukan. Hasil dari pengujian sistem ini diperoleh gelombang berdiri dalam kondisi mismatch (Rl50?) pada titik 7/10 ? dan 8/10 ? diperoleh dengan diawali kondisi gelombang dalam kondisi match tidak ada gelombang yang dipantulkan.

Optical vortex beams have attracted significant research interest owing to their potential for application in optical communication and imaging. In this study, we demonstrated devices with electric...

The principle of calculation of a plate from a metamaterial with inductive type chiral inclusions is submitted. It is shown that distribution of an electromagnetic wave to such substance can be investigated with the help of introduction of a chiral parameter and on the basis of a detailed method of calculation. By comparison of two methods the dependence of chiral parameter from frequency of electromagnetic radiation falling on a plate is found. With the help of a detailed method the nonlinear differential equation for potential on the chiral plate is found. It is shown that this equation has solutions as traveling solitary and standing waves but not traveling sine waves. The analysis of the received solutions of the nonlinear equation is carried out. Transition from the multiwave solution to the solution as standing waves is graphically shown at reduction ofdistance between the chiral elements.

Calibration methods and facilities have been employed to directly obtain sensitivities of an underwater acoustic vector receiver using two methods based on laser Doppler vibrometry. The vector receiver was first calibrated in a standing wave tube over the frequency range 20 Hz to 2 kHz, where the oscillatory velocity of the water-air interface was measured to determine the sound particle velocity at the position of vector receiver based on waveguide theory. In the frequency range 2.5-10 kHz, the vector receiver was calibrated in an anechoic vessel with dimensions of 1.2 m diameter × 1.8 m length using wideband signals, with a laser Doppler vibrometer used to detect the oscillatory motion of a plastic pellicle, which was sufficiently thin to follow the acoustic particle motion. The uncertainties of the calibration using the optical method were estimated to be 0.7-0.8 dB at 95% confidence interval. The calibration results were compared with those obtained using a reciprocity method in a 50 m × 15 m × 10 m water tank and using a comparison method in a standing wave tube, and the largest deviation did not exceed 1.0 dB over the frequency range 20 Hz to 10 kHz.

We study the following class of pseudo-relativistic Hartree equations − e 2 Δ + m 2 u + V ( x ) u = e μ − N ( | x | − μ ⁎ F ( u ) ) f ( u ) in R N , where the nonlinearity satisfies general hypotheses of Berestycki-Lions type. By using the method of penalization arguments, we prove the existence of a family of localized positive solutions that concentrate at the local minimum points of the indefinite potential V ( x ) , as e → 0 .

The effect of acoustic streaming generated due to a standing wave over a flat plate in the presence of a magnetic field has been discussed. Due to this unsteadiness, the flow is divided into two regions: the boundary layer region and the core flow region. Invoking successive approximation method, we found the velocity expression for the core region confirming that the velocity is independent of viscosity but depends on a magnetic field and is used to demonstrate the Couette flow.

We consider the finite ribbons of graphene with two principal orientations, zigzag and armchair, of their edges to study in detail impurity effects on their edge states. An alternative to the known description of quasiparticle states in terms of transversal standing waves is proposed in the recurrence relations for their spectra vs discrete numbers of atomic chains in the ribbon, permitting to simplify the Green function approach to the disorder effects in these systems. The derived analysis shows the microscopic mechanisms of perturbation by different types of impurities on low energy states and clarifies how the stability of topological states in zigzag systems to disorder is related to the discrete amplitudes of these states across the ribbon. An opposite possibility for Mott localization under local impurity perturbations is found for armchair type nanoribbons but at special values of their width.

Different accelerating structures are analyzed with respect to their maximum current and shunt resistance depending on the efficiency of the structure. It is found that a structure based on a standing wave with series coupling is an optimal structure in regards to microwave power transfer to the beam.

Spillways may require converging sidewalls because of site or economy constraints. The adverse effects of the converging walls on supercritical flows include the formation of standing waves. In this context, numerical simulations were carried out using the Smoothed Particle Hydrodynamics (SPH) method. The numerical results were compared with experimental data acquired on a spillway model composed of a broad crested weir followed by a 1V:2H sloping chute with wall convergence angle of 9.9º or 19.3º, for a range of discharges. The flow depths at the spillway centerline were reasonably well predicted by the numerical simulations, except on the transition from the weir to the chute. Experimental data and numerical results showed that the sidewall flow depth normalized by the centerline flow depth (uninfluenced by the converging wall), tended to increase along the spillway, reaching maximum values of approximately 2 and 5, for wall convergence angles of 9.9° and 19.3°, respectively. Numerical cross-sectional flow depth profiles were also obtained, showing distinct shapes of the standing waves, depending on the wall convergence angle and position along the spillway. Overall, the simulated development of the standing wave width compared well with the experimental counterparts. The experimental velocity profiles obtained at the spillway centerline with wall convergence angle of 9.9º were also compared with those obtained numerically and the results revealed a fairly good prediction, except near the upstream end of the chute and close to the invert.

Mode splitting induced by coherent optical mode interference in coupled resonant cavities is a key phenomenon in photonic resonators that can lead to powerful and versatile filtering functions, in close analogy to electromagnetically-induced-transparency, Autler-Townes splitting, Fano resonances, and dark states. It can not only break the dependence between quality factor, free spectral range, and physical cavity length, but can also lead to group delay response and mode interactions that are useful for enhancing light-material interaction and dispersion engineering in nonlinear optics. In this work, we investigate mode splitting in standing-wave (SW) resonators implemented by cascaded Sagnac loop reflectors (CSLRs) and demonstrate its use for engineering the spectral profile of integrated photonic filters. By changing the reflectivity of the Sagnac loop reflectors (SLRs) and the phase shifts along the connecting waveguides, we tailor mode splitting in the CSLR resonators to achieve a wide range of filter shapes for diverse applications including enhanced light trapping, flat-top filtering, Q factor enhancement, and signal reshaping. We present the theoretical designs and compare the performance of CSLR resonators with three, four, and eight SLRs fabricated in silicon-on-insulator nanowires. We achieve high performance and versatile filter shapes via diverse mode splitting that agree well with theory. The experimental results confirm the effectiveness of our approach towards realizing integrated multi-functional SW filters for flexible spectral engineering., 11pages, 6 figures, 116 references. arXiv admin note: substantial text overlap with arXiv:1805.05405

We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein-Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point argument and the Hille-Yosida theorem. Stability study relies on the linearization approach and recent results for the NLS equation with the $\delta$-interaction on a star graph.

This paper addresses the wave propagation problem within the context of the theory of materials with triple porosity under local thermal non-equilibrium. The time-harmonic wave solution is studied and the dispersion relation is explicitly established as an eighth-degree algebraic equation. It is shown that there are two shear waves undamped in time, that are non-dispersive and unaltered by the presence of the pore system or by thermal effects. Also, there are seven longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave, three longitudinal quasi-pore standing waves and three other longitudinal quasi-thermal standing waves. An illustrative simulation on a material like Berea sandstone shows that the effects of coupling triple porosity with local thermal imbalance and mechanical deformations leads to an increase in the propagation speed of the longitudinal quasi-elastic wave accompanied by an increase in its rate of decrease over time, as well as to a relaxation of the decrease in time for the quasi-pore and quasi-thermal standing waves.

Microstrip antennas generally have deficiency with small bandwidth, so that their utilization is very minimal and rarely used for antenna user applications on electronic devices. To increase antenna performance parameters bandwidth, voltage standing wave ratio, and return loss, need modification of antenna. This research was carried out by modifying of microstrip antenna with the meader line technique by ground plane wich is useful for increasing performance of microstrip antenna parameters. The ground plane on antenna was modified by adding a copper wire to the antenna. With modifications to ground plane antenna, the antenna performance parameters bandwidth, voltage standing wave ratio and return loss have decreased significantly. Antenna bandwidth has 124 MHz before modification, but has increased upto 214 MHz after modification ground plane, voltage standing wave raio has decreased from 1.835 to 1.12 after modifications ground plane antenna, and return loss of antenna before modification has -10.112 dB, after modification it decreased significanty upto -24.69 dB.

Sound waves are very frequent in everyday life, although they are never seen. The particles of the average vibrations are parallel to the direction of propagation of the wave. In this article, the effect of changing the frequency of the sound wave on standing waves was investigated with different hertz frequencies to show technical images that can be visually translated to give fundamental predictions about the origin of the musical combinations, as it was proved that the sound is a pressure wave by giving the vibrations one side while the gas is released the other side. To obtain accurate results, the variables were fixed in the experiment as the type of gas supplied for the same experiments. It is also installed so that the distance between the diaphragm and the amplifier does not differ. The results analyzed after numerous data collection and calculations verify that the generated wavelength and frequency are directly proportional. As the frequency specified in Hz increased, the number of inverse nodes and nodes also increased. Obtaining standing waves helps to understand the nature of sound as a pressure wave, and to give all the details about the experiment and evaluate it. Sources of error and possible solutions to overcome these problems are also mentioned.

This paper is concerned with asymptotic behavior of positive solutions for coupled Schrödinger equations with mixed interactions between components. We construct locally minimal energy solutions that show distinctively different limiting profile for simultaneously large attractive and repulsive couplings. The components of the solutions constructed exhibit partial synchronization and segregation.

In this paper, we make a comprehensive study for the orbital stability of standing waves for the fractional Schrodinger equation with combined power-type nonlinearities (FNLS) i ∂ t ψ − ( − Δ ) s ψ + a | ψ | p 1 ψ + | ψ | p 2 ψ = 0 . We prove that when p 2 = 4 s N and a ( p 1 − 4 s N ) 0 , there exist the standing waves of (FNLS), which are orbitally stable. When a = 0 and 4 s N p 2 4 s N − 2 s , we present a new, simpler method to study the strong instability of standing waves. When a = − 1 , 0 p 1 p 2 and 4 s N ≤ p 2 4 s N − 2 s , or a = 1 and 4 s N ≤ p 1 p 2 4 s N − 2 s , or a = 1 , 0 p 1 4 s N p 2 4 s N − 2 s and ∂ λ 2 S ω ( u ω λ ) | λ = 1 ≤ 0 , we deduce that the ground state standing waves of (FNLS) are strongly unstable by blow-up.

As a novel space propulsion technology, Ultrasonic Electric Propulsions system mainly employs crests of capillary standing waves as emitters to produce charged droplets with higher impulse and thrust density. In this work, the formation mechanism of capillary standing waves is investigated by experimental and numerical methods. Different morphologies of capillary standing waves are captured by an imaging system and their wavelengths at vibration frequencies 120 kHz, 60 kHz and 25 kHz are measured and compared with theoretical corresponding values, respectively, which are in a good consistency. Irregular patterns of capillary standing waves on emission surface are first found in experiments, which are characterized by partial coverage and alterable boundaries. In order to further explore their micro characteristics, capillary standing waves are also simulated with different vibration frequencies and amplitudes. It is found that multiple factors such as amplitude, vibration frequency and thickness of liquid film affect the formation and condition of capillary standing waves, and a higher vibration frequency with great amplitude more easily forms atomization on emission surface, which emits droplets mainly by ultrasonic vibration rather than electrostatic force. A larger thickness of liquid film needs higher vibration intensity to form capillary standing waves.

In this paper, the design of a 77.3 GHz Standing-Wave oscillator (SWO) is presented. The proposed SWO relies on the distribution of varactors along an asymmetrical slow-wave coplanar stripline, which enables the improvement of the quality factor of the tunable resonator, resulting in superior performance in terms of phase noise and DC-to-RF efficiency. The design methodology, based on the use of analytical models and abaci, is presented in detail and applied to a design in a 55-nm CMOS technology. With a core consumption of 15.1 mW, the proposed SWO operates from 76.09 GHz to 78.60 GHz and presents a phase noise of −115.1 dBc/Hz at 10 MHz offset, leading to a Figure of Merit (FOM) of −181 dBc/Hz. The DC-to-RF efficiency obtained is 3.1%.

In this paper, we consider two kinds of nonlinear Schrodinger equations with the fractional Laplacian and Hardy potential ( λ | x | s , 0 λ ⩽ λ ∗ , λ ∗ is a constant of the Hardy-Sobolev inequality), which represent the generalized form of Hartree and Pekar-Choquard type time dependent fractional Hardy-Schrodinger equations. Applying the direct method of moving planes, we obtain the radial symmetry and monotonicity of the standing waves for the given equations.

Several different combinations of face masks and shields are evaluated for their acoustic performance using a head and torso simulator (HATS). The HATS is used as a controlled and repeatable artificial sound source using white noise in a classroom environment. Sound pressure levels at octave band frequencies due to the face coverings are evaluated at a location of 2.0 meters from the HATS which is within the direct field to reduce the room acoustical effects. The problem is modeled as a barrier separating a source and receiver using fundamental noise control principles. Fabric material properties are used such as thickness, density, stiffness, and damping. The results are compared with experimental tests. The face shield with clear plastic barrier produces a resonance in the 1000 Hz octave band. Analytical models of cavity resonances, standing wave resonances, or plate resonances are calculated and compared with the experimental resonance. The speech interference level is used to determine the frequency content that is most likely to cause hearing difficulties and compared with A-weighted differences between the unmasked condition and masked. © INTER-NOISE 2021 .All right reserved.

A semi-phenomenological model of a many-particle system of 4He atoms is proposed, in which a helium atom is considered as a complex consisting of a nucleus and a bound pair of electrons in the singlet state. At zero temperature, there are two Bose-Einstein condensates of particles with opposite charges, namely, a condensate of positively charged nuclei and a condensate of negatively charged electron pairs. It is shown that in such a system there exist two excitation branches: sound and optical. On the basis of this model an interpretation of experiments on the study of the eltctrical activity of superfluid heliun is proposed. The frequency at which the resonant absorption of a microwave radiation is observed is interpreted as a gap in the optical branch. It is shown that the distribution of the electric potential in a standing wave in a resonator is similar to that observed experimentally., Comment: 8 pages, 2 figures

We performed a quantitative study of the field intensity under surface plasmon (SP) using different impinging source changing the beam width for several metallic structures and compare with the case of an infinite metallic planar surface. We quantified the excitation of field in a metallic ridge, step and groove. The field enhancement obtained in the metallic step close to the wall got the high value than the others ( $$211\%$$ ) structures with the wider width beam used in this work. Finally, we answer, what happen if we confined the field of the SP on a metal groove? The field enhancement for apertures of the cavity $$L < L_{SP}$$ , was very small so, for a length greater than the decay length of the SP, $$L > L_{SP}$$ , the intensity of the field converges to the same amplification obtained for a metallic step. We conclude that the confinement of the SP (Grooves) does not increase the amplification of the electromagnetic fields at the interface; the fields under SP need space to get excited.

Among the many scouring-protection works near a rubble mound breakwater, stacking armoring rocks in multiple or single layers are most popular. The rationale of these scouring-protection works is based on the Equilibrium regime or the maximum scouring depth. However, considering natural beaches, which constantly change their shape according to sea waves conditions, the equilibrium regime or the maximum scouring depth mentioned above seems to foot on the fragile physical background. In this study, in order to test the above hypothesis, numerical simulations were carried out on the partial reflection from the slopes of rubble mound breakwater, and its ensuing standing waves formed in the front seas of a breakwater, the change in the bed profiles due to the formation of standing waves, and scouring depth at the base of a rubble mound breakwater. In doing so, numerical simulations were implemented using OlaFoam, an OpenFoam-based toolbox, and SeoulFoam (Cho, 2020), a physics-based morphology model. Numerical results show that the wave length of sand waves is closely linked with the incoming wave period, while amplitudes of sand waves are determined by incoming wave height. Moreover, the seabed profiles underwent significant changes due to the presence of a rubble mound breakwater. It was shown that the size of sand waves increased when compared before the installation, and the shape of sand waves is getting skewed toward the shore direction. It was also shown that as exposure time to standing waves increased, the amplitude of sand waves also increased, and the scouring depth near the base of a breakwater increased. These results are contrary to the Equilibrium regime, and the scouring prevention works based on the stacking of armoring rocks should be re-evaluated.

Numerous laboratories have observed random lasing from optically pumped solutions of plasmonic nanoparticles (NPs) suspended with organic dye molecules. The underlying mechanism is typically attributed to the formation of closed-loop optical cavities enabled by the large local field and scattering enhancements in the vicinity of plasmonic NPs. In this manuscript, we propose an alternative mechanism that does not directly require the plasmon resonance. We used high-speed confocal microspectroscopy to observe the photophysical dynamics of NPs in solution. Laser pulses induce the formation of microbubbles that surround and encapsulate the NPs, then sharp peaks