Search

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.

We report the results of a study of a multimode semiconductor laser gyroscope (MSLG) with a long fibre-optic ring cavity (RC) and alternating frequency dithering formed by a lithium niobate phase modulator, and discuss the factors that determine the device operation. The fundamental limitations in MSLG operation are phase fluctuations and the multimode nature of radiation. Phase fluctuations caused by spontaneous emission of photons in a semiconductor optical amplifier (SOA) result in a slow drop in the beat amplitude. However, its complete decay does not occur due to the periodic and short-term lock-in phenomenon, which leads to the equalisation of the fluctuation levels in pairs of counterpropagating waves (PCPWs) that form the RC modes, and, thereby, to the restoration of the beat amplitude. The limitations associated with the multimode lasing regime are overcome due to the fact that the emission spectrum consists of a small number of narrow lines, and the positions of the antinodes and nodes of standing waves in the SOA field distribution coincide or are close. Both factors lead to the mode locking in spectral lines and, as a consequence, to synchronisation of PCPW beats at the device output. The mechanism of the formation of these factors is not yet clear.

In this paper, we are interested in standing waves of the nonlinear Schrodinger equation coupled with the Maxwell equation. Our aim is to formulate the orbital stability of standing waves in the full gauge invariant form. For this purpose, we study a new constraint minimization problem.

In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coefficient. This partial differential equation is of mixed type and possesses both elliptic and hyperbolic regions. After establishing a weighted inequality for the Baouendi-Grushin operator and a related compactness property, we establish the existence of stationary waves under arbitrary perturbations of the reaction.

We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational theory, dynamical systems on a phase plane, and the Dirichlet-to-Neumann mappings., 48 pages; 19 figures

The normal incidence x-ray standing wave (NIXSW) technique is the primary source of quantitative experimental information on the adsorption height of many near-planar molecules on metal surfaces, of relevance to organic electronics. The technique yields two structural parameters, the coherent position and the coherent fraction. For high values of the coherent fraction the coherent position can be related directly to the adsorption height, but because the coherent fraction is effectively an order parameter, low values of this parameter are often attributed to partial disorder. It is certainly true that in depositing these large molecules on a surface it is very challenging to produce a perfectly ordered surface. However, is the type of disorder that is likely to occur able to account for no other effect on measured NIXSW data than a lowering of the coherent fraction? Here we show, by considering a wide range of possible types of ‘disorder’, that in almost all such situations it is improbable that the coherent positions associated with very low coherent fractions actually provide a reliable measure of the adsorption height of the ordered component, as is often assumed to be the case. As such, presentations of NIXSW data that only consider coherent position values are likely to be extremely misleading, and provide an unreliable benchmark for detailed understanding of these interfaces.

We study the stability in a partial linearisation framework of a particular travelling wave of the quasilinear Benney system, where is a standing wave with a shock profile for the viscous conservation law.

It is recognized that in large-area, very-high-frequency capacitively coupled plasma (VHF CCP) reactors, the higher harmonics generated by nonlinear sheath motion can lead to enhanced standing wave excitation. In this work, a self-consistent electromagnetic model, which couples a one-dimensional, radial nonlinear transmission line model with a bulk plasma fluid model, is employed to investigate the nonlinear standing wave excitation in a VHF driven, geometrically asymmetric capacitive argon discharge operated at low pressure. By considering a radially non-uniform plasma density profile (case I) calculated self-consistently by the nonlinear electromagnetic model and the corresponding radially-averaged, uniform plasma density profile (case II), we first examine the effect of the plasma density non-uniformity on the propagation of electromagnetic surface waves in a 3 Pa argon discharge driven at 100 MHz and 90 W. Compared to case II, the higher plasma density at the radial center in case I determines a higher plasma series resonance frequency, yielding stronger high-order harmonic excitations and more significant central peak in the harmonic current density J z,n and the harmonic electron power absorption p n profiles. Therefore, under the assumption of the radially uniform plasma density in a CCP discharge, the self-excitation of higher harmonics at the radial center should be underestimated. Second, using the self-consistent electromagnetic model, the effect of the rf power on the excitation of nonlinear standing waves is investigated in a 3 Pa argon discharge driven at 100 MHz. At a low power of 30 W, the discharge is dominated by the first two harmonics. The higher harmonic excitations and the nonlinear standing waves are observed to be enhanced with increasing the rf power, resulting in a more pronounced central peak in the radial profiles of the total electron power absorption density p e, the electron temperature T e, and the electron density n e. For all rf powers, the calculated radial profiles of n e show good agreement with the experimental data obtained by a floating double probe.

In this paper, a new rotating standing wave ultrasonic motor with multiple driving teeth is proposed. Using the method of adding additional teeth, the correction of the B06 surface of the ultrasonic motor vibrator is expected, the design of the optimum position of the drive tooth is realized. At the same time, a method of reducing the stiffness of the rotor is proposed, and the flexibility is met, the integrated design of the rotor and the pressure device can be realized by removing the disc spring. The accuracy of the finite element analysis is verified by the vibration test of the prototype oscillator. The finite element analysis of the main structure parameters of the influence oscillator mode and natural frequency is carried out. It provides theoretical basis for the design and machining of vibration.

The experimental studies of the second sound waves propagation in a resonator with a deuterium-helium gel were carried out. The latest experimental results, combined with those obtained in earlier experiments, have shown that the propagation of the second sound waves in gels leads to their significant attenuation and a decrease in the propagation velocity. This behavior differs from the case of the propagation of the sound waves of a two-component system with a strongly slow normal component and may indicate changes in the properties of superfluidity under confined geometry conditions.

In this work, shielding coatings based on graphene-like carbon films have been investigated. To design the shielding, the Costas massif theory is applied. For microwave studies, the method of recording standing waves with a microwave interferometer was used. The resulting coatings are safe, durable, ecological and have an electromagnetic radiation reflection coefficient of 10-20 dB.

We consider image recording and reproduction using a reversed stimulated echo hologram, with a recording medium exposed to pulses of nonresonant electromagnetic standing waves. It is shown that the spatial intensity distribution in a stimulated echo hologram response depends on the electric field strength of nonresonant standing waves, which makes it possible to control reconstructed images.

Multi-stage pumps used for boiler water supply of thermal power plants have large capacity and pressure. Fluctuations may cause vibration and noise in pumps, piping systems, and surrounding structures. Lots of studies have been conducted on the pressure fluctuation phenomenon of turbopump piping systems. Some of the factors are the rotor-stator interaction, a resonance between the fluid in the pipe and, excitation source and resonance between structure and pump operation. Besides, studies on mitigation method for pressure fluctuations have been conducted. Inserting orifice to add damping, adjusting the length of pipe to change resonance frequency and, installing resonator to mitigate a specific frequency. However, these studies have not quantified the solution to the pressure fluctuations, so further research is needed to elucidate the causes and establish countermeasures quantitatively. In this study, pressure fluctuations due to acoustic resonance are generated by using a speaker. An orifice, a bent tube, and a branch pipe are installed at the node and antinode of the secondary pressure standing wave in the pipe, and the effects on the standing wave are observed. Moreover, the mitigation method for the pressure standing wave is established by performing a sweep test. Numerical analysis is conducted by AMESim to validate the results of experiment. It is clarified that by inserting the orifice at the appropriate position of a standing wave, pressure fluctuations are mitigated. In the case of branch pipe, pressure fluctuations are effectively mitigated by inserting it having appropriate pipe length and boundary condition.

Recently, there has been research into drying by applying an ultrasonic vibrator directly to wet clothes. However, this method may damage the fabric and decorations of clothing because the ultrasonic vibrator is in direct contact with the wet clothing. Therefore, we would like to dry wet clothes without contact using an aerial intense ultrasonic wave. In this paper, an intense standing wave sound field was formed in the air using two sets of transverse vibrating plate type ultrasonic sound sources, and a cloth larger than the wavelength of the sound wave in the ultrasound field was dried. We compared the moisture content on dry basis, drying rate, and drying time of the drying samples, and determined the differences in drying effect depending on differences in the installation position of the drying samples in the ultrasound field.

A thermoacoustic refrigerator is a capable device to produce temperature differences with acoustic work (sound waves) as the source. The advantage of these machines is that the working gas medium used is air, so it doesn’t produce much pollution and of course, it is environmentally friendly. This paper describes the measurement of stack length variations ranging from 4 cm to 7 cm on the performance of the standing wave thermoacoustic refrigerator. This study aimed to find the optimum stack length in a thermoacoustic machine with a resonator pipe length of 80 cm. Operation time is carried out for 30 minutes. The main components of a thermoacoustic device consist of a regenerator, resonator pipe, and a loudspeaker. The regenerator has a big role, namely as a place for energy conversion to occur. The results obtained are a temperature decrease, a temperature increase, and a temperature difference. The results showed that the temperature decrease and the temperature difference on the stack length of 7 cm were the decrease in temperature and the maximum temperature difference with the results of 4.6°C and 9.3°C, respectively. Therefore a standing wave thermoacoustic refrigerator with various lengths of the stack has been experimentally studied.

This study aimed to develop and investigate the efficiency of the DIY Standing Wave apparatus for STEM demonstration and laboratory in Grade 7 for the topic transverse waves under the K-12 curriculum. The efficiency of the apparatus was determined through successive experiments and the percentage error was compared to the Mechanical Wave Vibrator of the College of Science and Mathematics, MSU-IIT. The assessment on the DIY Standing Wave apparatus manual was the basis for the modification of the DIY Standing Wave apparatus and revision of the manual. Results revealed that there was no significant difference in the percentage error between the DIY Standing Wave apparatus and Mechanical Wave Vibrator. The DIY Standing Wave apparatus and the Mechanical Wave Vibrator had an average percentage error of less than ten percent, so the DIY Standing Wave apparatus was also efficient. The manual for the DIY Standing Wave Apparatus can guide teachers on what materials are needed and how to fabricate the apparatus. The manual was appropriate for the DIY Standing Wave apparatus and was intended for the in-service Physics teachers. The apparatus can be a tool for an effective STEM learning.

In this paper, Maxwell equations are coupled with a radially localized global model and an analytical sheath model to investigate the electromagnetic effects under various frequencies and electron powers in large-area very high frequency symmetric capacitive argon discharges. Simulation results indicate that both the vacuum wavelength and the sheath width decrease with frequency, leading to the reduced surface wavelength. As a result, the standing wave effect becomes pronounced, causing the fact that the radial profiles of the electron density, radio frequency voltage, and sheath width shift from uniform over center-high to multiple-node. When the frequency is close to or higher than the series resonance frequency, the surface waves cannot propagate to the radial center because of the significant radial damping. Due to the lack of power deposition near the radial center, the electron density is nearly zero there, i.e. the stop band effect. As power increases, the higher electron density leads to the decrease of the skin depth. Therefore, the importance of the skin effect gradually exceeds that of the standing wave effect, giving rise to the transition from the center-high to edge-high electron density profiles. The method proposed in this work could help to predict the plasma distribution under different discharge conditions in a few minutes, which is of significant importance in optimizing the plasma processing.

Having a continuous mode of transportation, in the manufacturing and pharmaceutical industries, is desirable and this facilitated by the usage of dual transducer-type ultrasonic levitation-based transportation systems. It is well known that the structural and electrical parameters determine what can be transported continuously, but the relationships between these important parameters are still not clear. In this study, the vibrating plate length and the phase shift between the two transducers were investigated as both of these are key parameters for the transportation system, and affect the standing wave ratios (SWRs), the acoustic radiation forces, and consequently the way the transportation system operates. Through numerical analysis and experimental verification, it can be seen that when the sum or difference of the spatial phase difference (determined by the vibrating plate length) and the phase shift is equal to 180° × (1 + 2n) (where n is an integer), except for the spatial phase difference of 180°·m (where m is also an integer) and the SWRs approaches unity, all this implying that traveling waves (TWs) are dominantly excited on the vibrating plate. As a consequence, the TW-induced acoustic radiation force, which greatly exceeds the standing wave-induced force, causes the continuous transportation of the particle being moved in the sound field. This paper not only clarifies the requirements for generating this continuous transportation, but also provides valuable information on the practical design of such a transportation system.

We theoretically and experimentally explore the emergence of a dynamical density wave order in a driven dissipative atom-cavity system. A Bose-Einstein condensate is placed inside a high finesse optical resonator and pumped sideways by an optical standing wave. The pump strength is chosen to induce a stationary superradiant checkerboard density wave order of the atoms stabilized by a strong intracavity light field. We show theoretically that, when the pump is modulated with sufficient strength at a frequency $\omega_{d}$ close to a systemic resonance frequency $\omega_{>}$, a dynamical density wave order emerges, which oscillates at the two frequencies $\omega_{>}$ and $\omega_{}$. This order is associated with a characteristic momentum spectrum, also found in experiments in addition to remnants of the oscillatory dynamics presumably damped by on-site interaction and heating, not included in the calculations. The oscillating density grating, associated with this order, suppresses pump-induced light scattering into the cavity. Similar mechanisms might be conceivable in light-driven electronic matter., Comment: 8 pages, 9 figures

Standing wave thermoacoustic engine (SWTE) is a device for converting heat to propagate acoustic wave within straight and tubular of the resonator. The advantages of this engine include being able to use the waste heat as a source of heating, no moving parts and environmentally friendly. The utilization of this acoustic wave is to rotate air turbine because its movement that goes back and forth. The type of air turbine that appropriates to this character one of these is Wells bi-directional turbine, which is always rotated in the same direction regardless of the moving air direction. This study aims to investigate the performance of Wells turbine when paired with SWTE in the variation on geometry shape of blade and hub to tip ratio. The Wells turbine was embedded inside resonator of this engine has a diameter of 50 mm in the manner of the hub to tip ratio 0.6. The geometry shape of blade varied with airfoil type of NACA 0015, NACA 0018 and NACA 0024. SWTE was generating 4,67 kPa acoustic pressure and 138 Hz frequency within 52 mm inside diameter, 390 mm length of the resonator. The result was the Wells turbine NACA 0018 has rotational motion 2449 rpm, higher than the others types. Wells turbine NACA 0018 then tested with variations of the hub to tip ratio. Results showed that are generated rotational motion at 2614 rpm, 2449 rpm and 1555 rpm for 0.5, 0.6, 0.7 hub to tip ratio, respectively.. It can be concluded that the Well turbine NACA 0018 with hub to tip ratio 0,5 has best performance compare to the others.

The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder, insonified by acoustic standing waves having an arbitrary angle of incidence in the polar (transverse) plane. The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous. Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder, the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials. The method to derive the acoustical scattering, and radiation force and torque components conjointly uses modal matching with the addition theorem, which adequately account for the multiple wave interaction effects between the layer and core fluid materials. The results demonstrate that longitudinal and lateral radiation force components arise. Moreover, an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder, arising from geometrical asymmetry considerations as the eccentricity increases. The computational results reveal the emergence of neutral, positive, and negative radiation force and torque depending on the size parameter of the cylinder, the eccentricity, and the angle of incidence of the insonifying field. Moreover, based on the law of energy conservation applied to scattering, numerical verification is accomplished by computing the extinction/scattering energy efficiency. The results may find some related applications in fluid dynamics, particle trapping, mixing and manipulation using acoustical standing waves.

A Sagnac polarized standing wave interferometer (SPSWI) is extensively developed. It exploits two polarized standing wave signals formed in two orthogonal planes of oscillation to measure the displacement. However, two equal amplitude signals, which are complicated control, are sensitively required for displacement data analysis. Thus, the simple calibration process is necessary to accomplish this situation. In this paper, we present a methodology for calibrating signals from SPSWI by using Python programming to remove the constant signals, normalize oscillating signals and eliminate non-orthogonal error based on technique proposed by Fan. The relative displacement is derived from these calibrated signals.

We investigated the possibility of controlled levitation of particles in the air under the influence of wideband ultrasonic waves. We examined the interference field formed by the radiation of counterpropagating emitters of signals with linear frequency modulation. It is proposed to use two counter-directed emitter arrays focused at the center. The focusing of the emitter arrays is achieved due to the fact that the elements of the arrays are placed on the surface of the sphere in a certain sector. Then the focus point is the center of the sphere at any radiation frequency. When a common-mode wideband signal is applied to all elements of the array, focusing of the wideband signal is achieved in the center of the sphere. When a monochromatic signal is applied, a levitation region elongated along the axis of the system is formed. We consider the case when the distance between the radiating gratings is several times larger than the size of the aperture of the gratings. For wideband signals particles are grouped into a single stable pressure node of standing waves in the center of the system. This provides a single local minimum potential for the selective control of an individual particle. Moreover, a force arises that draws particles into the central region.

The electrical asymmetry effect (EAE) enables separate control of the ion flux and the mean ion energy in capacitively coupled plasmas (CCP). While a variety of plasma processing applications benefit from this, large-area, very-high-frequency CCPs still suffer from lateral nonuniformities caused by electromagnetic standing wave effects (SWE). Many of such plasma sources are geometrically asymmetric and are operated at low pressure so that high frequency nonlinear plasma series resonance (PSR) oscillations of the RF current are self-excited. These PSR oscillations lead to the presence of short wavelength electromagnetic waves and a more pronounced SWE. In this work, we investigate the influence of the EAE on the nonlinear standing wave excitation in a geometrically asymmetric, low pressure capacitively coupled argon plasma driven by two consecutive harmonics (30 MHz and 60 MHz) with an adjustable phase shift, θ. We use a hairpin probe to determine the radial distribution of the electron density in combination with a high-frequency B-dot probe to measure the radial distribution of the harmonic magnetic field, which in turn is used to calculate the harmonic current density based on Ampere’s law. Our experimental results show that the asymmetry of the discharge can be reduced electrically via the EAE. In this way the self-excitation of high frequency PSR oscillations can be attenuated. By tuning θ, it is, therefore, possible to switch on and off the nonlinear standing wave excitation caused by the PSR and, accordingly, the plasma uniformity can be optimized.

In this paper, we consider the standing waves and the global existence for two-dimensional nonlocal nonlinear Schrodinger equations. It is a coupled system which describes the spontaneous generation of a magnetic field in a cold plasma under the static limit. The main difficulty in the proofs lies in exploring the inner structure of the equations due to the fact that the nonlocal terms violate the inner scaling invariance, which may cause the non-zero energy for the ground state. For this reason, we first make a proper use of the inner structure of the equations to establish the existence of standing waves, and then we apply an energy scaling to obtain the instability of standing waves. Finally we show a sharp threshold for the global existence of solutions to the nonlocal nonlinear Schrodinger equations by a variational method, which depends again on the inner structure of the equations under consideration.

We construct multiple families of solitary standing waves of the discrete cubically nonlinear Schrodinger equation (DNLS) in dimensions d = 1, 2 and 3. These states are obtained via a bifurcation analysis about the continuum (NLS) limit. One family consists of onsite symmetric (vertex-centered) states; these are spatially localized solitary standing waves which are symmetric about any fixed lattice site. The other spatially localized states are offsite symmetric. Depending on the spatial dimension, these may be bond-centered, cell-centered or face-centered. Finally, we show that the energy difference among distinct states of the same frequency is exponentially small with respect to a natural parameter. This provides a rigorous bound for the so-called Peierls–Nabarro energy barrier.

We have observed the interference of a long chain of Bose condensates prepared at the initial time moment in antinodes of a standing electromagnetic wave. The initial distribution of the condensate density in the system under consideration is periodic while the condensate phases can be different. Then the standing wave is quickly turned off, and the condensates start to expand and interfere. A spatial order of the interference fringes is observed with a period being substantially different from the period arising in the case of the Talbot effect.

The dielectric tensor of four level atomic medium coupled with dielectric function of silver silica nano-composites material to modify dispersion relation of surface plasmon polaritons (SPPs). The rapid damping of SPPs is used to localized atomic particles in two dimension inverse position space. Directions, phases and intensity of the control field play important roles in the localization of atoms in a unit wavelength domain. Ten, six, four and two localization peaks are investigated by SPPs damping in different quadrants. A single broad localized peak symmetric about origin are also investigated. The theoretical work of this article may be useful for quantum information in Plasmonster technology.

We present an efficient two-dimensional atomic localization in a tripod-type four-level atomic medium using standing-wave fields. The localization behavior is significantly improved, and the maximum localization probability can be achieved under suitable conditions within the one-wavelength domain. Multiple sharp localized peaks are observed in the one-wavelength domain through examination of the absorption of the weak probe field, and theoretically, high-resolution and high-precision atomic localization can be achieved within a region smaller than λ/12 × λ/12, via the exploitation of quantum-coherence effects in laser–matter interactions. The spatial resolution of the atomic localization is extensively improved, compared to the cases with or without microwave fields studied previously. We believe that the results revealed here might have potential applications for atomic nanolithography, neutral-atom laser cooling and trapping, Bose–Einstein condensation and the center-of-mass wave-function measurements.

The efficiency of radio-frequency (RF) power absorption, RF magnetic field structure and plasma parameters were measured in cylindrical inductive RF plasma sources 20 cm in diameter and 22, 32, 53 cm in length with a low value external magnetic field. The experiments were carried out in argon at pressures of 13–140 mPa. The RF power supply changed from 200 W to 800 W. The spiral antenna was used for sustaining the discharge. It was shown that efficiency of RF power absorption depended nonlinearly on the external magnetic field values. At maximal values of the RF power absorption efficiency, the axial distributions of longitudinal Bz and azimuthal B components of RF magnetic field manifested the formation of the partially standing wave with a half wavelength close to 8 cm. At the same conditions, the axial dependence of the radial RF magnetic field component Br differed drastically. It was concluded that the Bz and B amplitudes were largely determined by the RF field of Trivelpiece-Gould wave, while Br amplitude represented the radial RF field of the helicon wave.

In this paper, the question of the separation of particles in a standing wave in closed resonator at first resonance frequency is considered. The threshold values of the frequency of the standing wave, as well as the densities and radii of the particle, which allow to separate the particles depending on their radius and density are studied.

For complex scalar waves, a convenient measure of the local oscillations and (‘faster than Fourier’) superoscillations is the phase gradient vector: the local wavevector, or weak value of the momentum operator. This vanishes for standing waves, described by real functions ψ( r ); for such waves, an alternative descriptor of oscillations is the local weak value of the square of one of the momentum components, i.e. K 2 r = − ∂ 2 ψ r / ∂ x 2 / ψ r , here called the ‘weak curvature’. Superoscillations correspond to places where K 2 lies outside the interval 0 ⩽ K 2 ⩽ 1. Two illustrations are given. First is an explicit family of real waves in dimension d = 2, with arbitrarily strong superoscillations; this could represent Neumann standing modes in a strip waveguide. Second is an exact calculation of the probability distribution of K 2 for Gaussian random real waves in d dimensions. This decays as 1 / K 2 2 , as a consequence of the codimension 1 of nodes (e.g. nodal lines for d = 2). The superoscillation probability varies from 0.3918 (d = 2) to 0.3041 (d = ∞).

The technique to control the resonance mode necessary for enhancing the energy conversion efficiency of thermoacoustic system is discussed. A standing-wave type thermoacoustic system is set in the condition that the self-excited vibration with 3/2 wavelength of the total tube length takes place by adjusting the position of the stack. The sound wave of the fundamental mode is then externally superposed on the sound wave excited in the system. As a result, the resonance of the system is shifted to the fundamental mode from the higher mode. Furthermore, the resonance control is supposed to be realized by the reason that thickness of the viscous boundary layer is reduced and that the self-excited vibration is enabled at the lower entropy generation comparing with the higher-mode resonance. These results suggest that the technique to use the superposing sound wave is valid for enhancing the energy conversion efficiency by the resonance control.

In nuclear power plants (NPPs), the dynamic interactions of the coolant with the structures are among the main factors determining the dynamic loads on the equipments, its service life and reliability. The most hazardous is the resonant interaction of vibrations of the equipment with acoustic standing waves (ASW) that arise in accidental conditions. It is pointed out that the study of accident conditions on a full-scale object model is not possible and, accordingly, the development of adequate computer models to simulate the conditions is of prime importance. The analysis of acoustic systems with single-phase and two-phase fluid media is based on the theory of elastic wave propagation in liquids and gases. The analysis is based on the equations of fluid state, equations of motion, continuity equation and the equation expressing the law of conservation of energy. It is shown that in view of the unity of the differential equations of acoustic and electrical systems, the study of the propagation of the volume flow rate of one-dimensional pulsating flow of a compressible single-phase or two-phase fluid in the acoustic system can be replaced by the study of the propagation of electric current in the lines of electrical circuits. The paper presents an acoustic scheme of the NPP coolant circuit formed by acoustic elements considering their inherent thermal-hydraulic and geometric parameters. It is shown that the results of calculations of the frequencies of the ASW are confirmed by the measurements carried out at the NPP.

This paper is concerned with the study of the propagation of bending and longitudinal waves in homogeneous rods interacting with a nonlinear elastic medium. The dynamic behaviour of the rods is determined by refined theories as follows: for a rod fixed on a nonlinear elastic foundation and executing bending vibrations we select the Tymoshenko model while for a rod immersed in a nonlinear elastic medium and performing longitudinal vibrations we choose the Mindlin-Hermann model. It is demonstrated that evolutionary equations are generalizations of the well-known Ostrovsky equation: the modified Ostrovsky equation with a cubic non-linear term and the Ostrovsky equation with an additional quadratic non-linear term. Both generalized equations have exact soliton solutions of the stationary wave class.

Hydraulic excitation oriented from the turbine is one of the main sources of vibration for hydropower plants. Under different operation conditions, the amplitude, frequency and phase of pressure pulsation are different. The pressure pulsation of spiral case belongs to non-stationary waves, including traveling waves and standing waves. In this paper the pressure pulsation distribution characteristics of the spiral case were discussed and two kinds of distributions were assumed. The dynamic response of the powerhouse structure was simulated with FEM model through harmonic response analysis and transient dynamic analysis and the sensitivity of the pressure behaviour on the structure’s response were presented. The time history responses were also calculated under different turbine loads with different amplitude and frequency. The conclusion is that the structure dynamic responses under the traveling or standing waves are all greater than that with uniform assumption. So the distribution characteristics of pressure pulsation should be reasonably simulated to the dynamic analysis of the concrete structure.

We develop a detailed analysis of edge bifurcations of standing waves in the nonlinear Schrö dinger (NLS) equation on a tadpole graph (a ring attached to a semi-infinite line subject to the Kirchhoff boundary conditions at the junction). It is shown in the recent work [7] by using explicit Jacobi elliptic functions that the cubic NLS equation on a tadpole graph admits a rich structure of standing waves. Among these, there are different branches of localized waves bifurcating from the edge of the essential spectrum of an associated Schrö dinger operator. We show by using a modified Lyapunov-Schmidt reduction method that the bifurcation of localized standing waves occurs for every positive power nonlinearity. We distinguish a primary branch of never vanishing standing waves bifurcating from the trivial solution and an infinite sequence of higher branches with oscillating behavior in the ring. The higher branches bifurcate from the branches of degenerate standing waves with vanishing tail outside the ring. Moreover, we analyze stability of bifurcating standing waves. Namely, we show that the primary branch is composed by orbitally stable standing waves for subcritical power nonlinearities, while all nontrivial higher branches are linearly unstable near the bifurcation point. The stability character of the degenerate branches remains inconclusive at the analytical level, whereas heuristic arguments based on analysis of embedded eigenvalues of negative Krein signatures support the conjecture of their linear instability at least near the bifurcation point. Numerical results for the cubic NLS equation show that this conjecture is valid and that the degenerate branches become spectrally stable far away from the bifurcation point.

We investigate one-dimensional position microscopy of a three-level atom moving through a stationary wave region under the condition of electromagnetically induced transparency. The precise position information of an atom is observed on the resonance absorption and dispersion distribution spectrum of a weak probe field. Single and multiple localization peaks are observed in specific directions of the corresponding wave numbers and phase of the standing wave fields. The strength of space-independent Rabi frequency reduces the position uncertainty in the localized peaks without disturbing the probability of the atom. In a hot atomic medium the localized probability of an atom is reduced which depends upon the temperature of that medium. Our results provide useful applications in the development of laser cooling, atom nanolithography and Bose–Einstein condensation.

Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantum-state manipulation and will contribute to the design and exploration of novel quantum devices. Here we consider a quasi-two-dimensional spin-orbit coupled Bose–Einstein condensate confined in an external harmonic potential, with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system. For the cases with spin-orbit coupling solely in x- or y-axis direction, the ground-state structure can develop to the well-known standing wave phase, in which the two components always form an alternative density arrangement. For a two-dimensional anisotropic spin-orbit coupling, the separated lumps first become bend, then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction. Furthermore, the distance between these two rows of stripe structure is also investigated in detail.

Via a Lyapunov-Schmidt reduction, we obtain multiple semiclassical solutions to a class of fractional nonlinear Schr\"odinger equations. Precisely, we consider \begin{equation*} \varepsilon^{2s}(-\Delta)^{s}u+u+V(x)u=|u|^{p-1}u,\quad u\in H^s(\mathbf R^n), \end{equation*} where $04-4s$, $12s$) and $1, Comment: Some error corrected, several references added

We propose a new modification of a subwavelength, standing-wave optical trap based on photonic jets formed in the 'reflection' regime. The results of the numerical calculations of the electromagnetic field intensity of the generated photonic jet modulated by antinodes of the standing wave are presented. In contrast to known schemes, in the subwavelength optical trap in question, the minimum size of the focusing spot is determined by the width of the generated photonic jet rather than by the focusing lens parameters. A decrease in the diameter of the photonic jet waist compared with the size of the waist in the focus of the lens leads to an increase in the energy density in the focal region.

We observe intensity oscillations along coronal fan loops associated with the active region AR 11428. The intensity oscillations were triggered by blast waves which were generated due to X-class flares in the distant active region AR 11429. To characterise the nature of oscillations, we created time-distance maps along the fan loops and noted that the intensity oscillations at two ends of the loops were out of phase. As we move along the fan loop, the amplitude of the oscillations first decreased and then increased. The out-of-phase nature together with the amplitude variation along the loop implies that these oscillations are very likely to be standing waves. The period of the oscillations are estimated to be $\sim$27 min, damping time to be $\sim$45 min and phase velocity projected in the plane of sky $\sim$ 65-83 km s$^{-1}$. The projected phase speeds were in the range of acoustic speed of coronal plasma at about 0.6 MK which further indicates that these are slow waves. To best of our knowledge, this is the first report on the existence of the standing slow waves in non-flaring fan loops., Comment: 12 pages, 4 figures. Accepted for publication in ApJL