Steady-state Wave Research Articles

Steady-state harmonic resonance of periodic interfacial waves with free-surface boundary conditions based on the homotopy analysis method

Abstract

Finite-amplitude steady-state resonant waves in a circular basin

Abstract

Systematic approach to the study of the photoluminescence of MAPbI3

In this work, we perform steady-state continuous wave (cw) photoluminescence (PL) measurements on a MAPbI$_3$ thin film in the temperature range of 10-160 K, using excitation densities spanning over almost seven orders of magnitude, in particular investigating very low densities, rarely used in the published literature. The temperature range used in this study is below or at the edge of the orthorhombic-tetragonal phase transition in MAPbI$_3$. In particular, we show that even in high quality MAPbI$_3$, capable of providing high photovoltaic efficiency, the defect density is high enough to give rise to an energy level band. Furthermore, we show that the intensity ratio between the two PL components related to the two crystalline phases, is a function of temperature and excitation. At high excitation intensities, we show that amplified spontaneous emission is attainable even in cw conditions. Time-resolved PL is also performed to justify some assignments of the PL features. Finally, our systematic approach, typical for the characterization of semiconductors, suggests that it should also be applied to hybrid halide perovskites and that, under suitable conditions, the PL characteristics of MAPbI$_3$ can be reconciled with those of conventional inorganic semiconductors.

Numerical model of energy dissipation and shallow-water sloshing motions in tank under different coupled excitations

Shallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.

Quasicrystals’ Resonant Response with Translational Symmetry

Diffraction in quasicrystals is in logarithmic order and icosahedral point group symmetry. Neither of these features are allowed in Bragg diffraction, so a special theory is required. The present work displays exact agreement between the analytic metric with a numeric description of diffraction in quasicrystals that is based on quasi-structure factors. So far, we treated the hierarchic structure as ideal; now, we detail the theory by including two significant features: firstly, the steady state wave function of the incident radiation demonstrates how harmonics, in metrical space and time, enable coherent interaction between the periodic wave packet and hierarchic quasicrystal; secondly, mapping of the hierarchic structure for any influence of defects will allow estimation of possible error margins in the analysis. The hierarchic structure has the required logarithmic periodicity: superclusters, containing about 103 atoms, convincingly map phase contrast images; while higher orders leave space for subsidiary speculation. The diffraction is completely explained for the first time.

The Quantum Redshift Effect of Photon

By applying the relevant contents of time-dependent perturbation theory in present quantum mechanics, this paper operates the Hamiltonian operator on the existing steady-state wave function of the hydrogen atoms, creates the formula of the average energy loss per collision of a single photon with a neutral hydrogen atom. Then, by operating the Hamiltonian operator on the wave function of a helium atom, the expression of photon energy loss is extended to each bound electron in the neutral atoms of the general element. Applying theoretical derivation, it concludes that the photon’s energy, momentum, and frequency decrease with distance in an exponential attenuation law, or the wavelength increases with distance in an exponential growth law during the propagation in intergalactic space, the photons collide with neutral atoms in the medium. Compared with Hubble redshift law, we discover that these laws conform to the so-called Hubble redshift or cosmological redshift in form and quantity. Therefore, this paper reveals a new physical mechanism—the quantum redshift effect of the photon in astronomy, astrophysics, and cosmology, thus challenging Hubble’s law and the Big Bang theory.

Про демпфовані усталені резонансні коливання рідини в контейнері кругового перерізу для довільних періодичних непараметричних збурень

Nonlinear modal Narimanov-Moiseev—type equations are investigated to study resonant sloshing in a vertical cylindrical tank. The tank moves periodically in the space with the forcing frequency close to the lowest natural sloshing frequency. We show that the considered sloshing problem can to within the higher-order asymptotic terms be reduced to the case of orbital tank motions in the horizontal plane. Analytical solutions of the secular system which couples the dominant amplitudes of the steady-state sloshing are analytically solved. Effect of viscous damping is accounted. The results are compared with experimental measurements conducted by diverse authors for longitudinal and circular orbital tank excitations. A parametric analysis of the amplitude curves is done to clarify how the steady-state wave regimes and their stability change versus the forcing frequency and the semi-axes ratio of the elliptic orbit. The main result consists of confirming the experimental disappearance of the counter-directed swirling wave mode (relative to the elliptic orbit direction) when passaging to the circular orbit.

Scattering of SH-waves by oblique semi-elliptical notches in half space

The scattering of steady-state SH waves in a half-space with oblique semi-elliptical notches is presented analytically. Mathieu function addition theorem and multi-elliptical coordinate systems are developed to solve the complex boundary value problem. The existence of local defects has a great influence on the scattering and diffraction of elastic waves. The wave function expansion method which can reveal the physical process of wave scattering and verify the accuracy of numerical methods is a common method to study the influence of defects. The numerical results of the solution are obtained by truncating the infinite equation. Although the truncation of the infinite equation is inevitable, the accuracy of the numerical results has been carefully checked. The proposed solution is verified by comparing the results obtained when the oblique semi-elliptical notch is degraded into a semi-elliptical notch or even a semi-circular notch with previous results. The numerical results for typical cases show the complex effects of the inclination of the notch, the axial ratio of the ellipse, and the incidence angle on the displacement amplitude and dynamic stress concentration near the notch.

Harmonic balance-boundary element and continuation methods for steady-state wave scattering by interior and surface-breaking cracks with contact acoustic nonlinearity

A numerical method for nonlinear steady-state wave scattering due to a crack with contact acoustic nonlinearity (CAN) is developed in this article. The in-plane scattering problem is addressed here. The two systems studied are composed of an unbounded elastic solid that includes an interior crack and an elastic half plane that includes a surface-breaking crack. A time-harmonic plane wave is incident, and clapping and rubbing motions on the crack faces are induced as nonlinear phenomena. A harmonic balance-boundary element method (HB-BEM) is utilized to solve the nonlinear steady-state problem. The system of equations obtained by the HB-BEM consists of an elastostatic boundary integral equation (BIE) and frequency-domain elastodynamic BIEs of several different frequencies, which are coupled by nonlinear boundary conditions. To solve the system numerically, the nonlinear boundary conditions are regularized. In the regularized boundary conditions, traction is expressed by a smooth single-valued function with respect to crack-opening displacement. The solution of the steady-state system is tracked with a parameter continuation method to investigate bifurcations. The parameters that vary in the continuation method are the incident frequency and static field variables. To determine the stability of the steady-state solutions, a stability analysis method based on Hill’s infinite determinant is proposed.The stable solutions obtained by the proposed method agree with the conventional time-domain solutions after enough time has elapsed. A 1/2-order subharmonic resonance is observed with bifurcations for particular parameters. The interaction between the local resonant properties due to the crack and the CAN causes subharmonic resonance.

Influence of a soluble surfactant on the wave characteristics of a liquid film flow

In this paper we present results of experimental investigation of the influence of soluble surfactant (Triton X-100) on wave characteristics of vertically falling liquid film in the range of film flow Reynolds number 25 < Re < 95. Shadowgraph technique is used to analyze wave patterns on the whole length of the test section (140 cm). Film thickness fields obtained with the help of high-speed Laser Induced Fluorescence (LIF) technique in two areas in the bottom part of test section allow analyzing statistical characteristics of the film flow. Expectedly, adding surfactant suppresses wave motion. For some surfactant concentrations the absence of waves is observed in the whole test section. For other concentrations the wave repetition rate decreases with distance from the liquid inlet. Analysis of spectral characteristics reveals that for water with some concentrations of surfactant, as for pure liquids, the steady-state three-dimensional wave regimes are observed. The characteristics in such flow regimes differ from the characteristics of pure water flow.

Rotating Detonation Rocket Engine Operability Under Varied Pressure Drop Injection

Rotating detonation rocket engine (RDRE) experiments have so far been limited to injectors with high pressure drop to limit injector–plenum coupling. However, this corresponds to a reduction in the potential performance benefits of RDREs. To investigate this phenomenon, two injection configurations with different total injection areas are compared with respect to overall engine operability, global performance, and steady-state wave propagation. Notably, the increased area corresponds with a three to four times decrease in pressure drop, with negligible effects on operability and performance. The RDRE is found to operate in a detonative mode for both injectors across equivalence ratios between 0.6 and 2.5, and total mass flows between 0.09 and . The steady-state wave propagation varies significantly between the two injectors, with low pressure drop injection sustaining fewer waves traveling at higher velocities at the maximum performance conditions, but in all other conditions promoted lower wave speeds and counter-propagating behavior, denoting a breakdown in the steady wave propagation. This breakdown is likely due to increased injector–plenum coupling. These results provide insight into the effects of reduced pressure drop on the operation of an RDRE, and indicate challenges that must be overcome in the design of real systems that include RDREs.

Steady-state multiple near resonances of periodic interfacial waves with rigid boundary

Steady-state resonant interfacial waves in a two-layer fluid within a frictionless duct are investigated theoretically. A combination of the homotopy analysis method (HAM) and Galerkin’s method is used to search for accurate steady-state resonant solutions with multiple near resonances. In the HAM, a piecewise parameter in the auxiliary linear operators is introduced to remove the small divisors caused by nearly resonant components. Convergent series solutions are then provided to the Galerkin iterations to accelerate the convergence rate. It is found that weakly nonlinear steady-state resonant waves form a continuum in the parameter space. As nonlinearity (wave steepness) increases, energy appears to be progressively shifted to sideband frequency components, effectively broadening the spectrum. The corresponding interfacial wave profile exhibits an almost fixed spatial pattern of repeated relatively high frequency, high-amplitude bursts followed by low-amplitude, longer waves. On examining the influence of density ratio, though changing slightly, the upper layer enlarges the amplitude of components near primary ones, which reduces the amplitude of higher frequency components, enlarges the wave steepness, and reduces the horizontal velocity in the wave field. Our results indicate that steady-state systems with resonant interactions among periodic interfacial wave components could occur naturally in the ocean. All these should enhance our understanding of periodic resonant interfacial waves.

On the theoretical limitations in estimating thickness of a plate-like structure from a full-field single-tone response Lamb wave measurement

A persistent question in wavenumber analysis in the estimation of thickness from a steady-state wave field is identifying the theoretical sensitivity of the system. A well-known trade-off between spatial frequency/wavenumber resolution and thickness resolution exists. The current work presents a calculation of the Cramer-Rao Lower bound (CRLB), specifically as applied to thickness estimates, for a 2-dimensional multi-mode waveform in Gaussian noise. Cases of near-field and far-field excitation are considered, and transducer position with respect to the scan area is also varied. Additionally, we consider the CRLB in a plate with multiple sources, simulated as sources placed on the boundary of the plate. We conclude by presenting the CRLB values in terms of frequency for various thicknesses, and by presenting optimal excitation frequencies for a nominal thickness, based on the CRLB.

Numerical simulations of collinear finite amplitude steady-state resonant waves in deep water

In this work, numerical simulations of steady-state resonant wave system have been conducted by high-order spectral method (HOS) to study its evolution mechanism in deep water. Convergent high-order series solutions of steady-state resonant waves are first obtained by homotopy analysis method (HAM). Theoretical solutions together with disturbances of different orders of magnitude are then served as the initial solutions in HOS. It is found that as more accurate wave components are generated at the initial stage of the numerical simulation, the time that amplitude of the two largest wave components keeps unchanged increases. Steady-state resonant waves with time-independent spectra can be obtained if sufficient number of wave components are generated at the initial stage. At the end of simulation, additional new wave components that have not been considered at the initial stage appear in the spectra due to four-wave resonant interactions. For steady-state resonant waves with random disturbances, the numerical simulations confirm again the existence of steady-state resonant waves. Besides, energy transfer among different components is more remarkable for steady-state resonant waves with small disturbances before the wave breaking.

Ejecta production from metal Sn into inert gases

Ejecta is produced from the shock-loaded perturbed surface of metals and subsequently breaks into small particles that are an important source of micro-particles/gas mixing during ejecta's transport and conversion. In engineering applications, the surrounding gas is often neglected during ejecta's formation, and many source models have been established based on the vacuum condition. However, the formation of the spike is always accompanied by gas, which has an important effect on the ejecta's mass/velocity distribution and the transformation time for a steady-state shock wave. To study the interaction between ejecta and ambient gases, we explore the ejecta production at the sinusoidal interface in the presence of argon gas. Six values of gas pressure and five interfaces were chosen to study the formation of the spike/micro-jet by using multi-component elastic–plastic hydro-dynamic codes. The results show that gas perturbed by the spike generated a precursory bow-shaped shock and gradually transformed into a plane wave. The transformation time was related to the velocity of the spike tip and the transmitted wave. The total mass of ejecta in gas had no distinct difference with that in vacuum, while it was significantly increased at the jet tip, which indicates that gas resistance reduced the spike velocity but did not influence the bubble. The initial velocity of the spike was insensitive to gas pressure but its decaying rate was positively correlated with gas pressure. As kh0 increased, the initial velocity of the spike tip and its decaying range increased, making it difficult to attain a steady state.

Experimental investigation on special modes with narrow amplification diagrams in harbor oscillations

In studies on harbor oscillations, modes with extremely narrow amplification diagrams are common. The numerical simulation results obtained by Bellotti (2007) and Ma et al. (2020) for these modes (termed as extreme modes) based on regular waves are first validated by physical experiments in this study. Moreover, we investigate whether the extreme mode can be induced by irregular waves and solitary waves. Results show that considering an external force of steady-state waves, extreme modes cannot be triggered in the laboratory as they require an enormous amount of time (such as hundreds of wave periods) to reach full development. This phenomenon is consistent with the research of Bellotti (2007) and Ma et al. (2020). For an external force of solitary waves, extreme modes can be excited. The solitary wave enters and leaves the harbor within a brief period. Some energy is then trapped within the harbor and distributes over various wave components within a very short time, while a majority of the energy concentrates near the natural (resonant) modes of the harbor (i.e., resonant modes are triggered without experiencing the same development process as in the cases induced by steady-state waves). The phenomenon where extreme modes can be triggered by solitary waves is observed and explained in this work for the first time. Once extreme modes are triggered, they decay very slowly. Tsunamis are usually studied through solitary waves and are the main contributor to destructive harbor oscillations, though they are uncommon relative to irregular oceanic waves. Hence, the negative effect of extreme modes on vessels and mooring systems needs to be further studied.

Resonant three-dimensional nonlinear sloshing in a square base basin. Part 5. Three-dimensional non-parametric tank forcing

Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a small-amplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural sloshing frequency, a nine-dimensional Narimanov–Moiseev-type (modal) system of ordinary differential equations with respect to the hydrodynamic generalised coordinates was derived in the Part 1 (Faltinsen et al., J. Fluid Mech., vol. 487, 2003, pp. 1–42). Constructing and analysing asymptotic periodic solutions of the system made it possible to classify steady-state resonant sloshing and its stability for the harmonic reciprocating (longitudinal, diagonal and oblique) forcing. The results were supported by experimental observations and measurements. The present paper finalises the case studies by considering the three-dimensional non-parametric (combined sway, pitch, surge, roll and yaw, but no heave) cyclic tank motions. It becomes possible after establishing an asymptotic equivalence of the associated periodic solutions of the modal system to those for a suitable horizontal translatory elliptic forcing so that, as a consequence, resonant steady-state waves and their stability can be considered versus angular position, semi-axis ratio and direction (counter- or clockwise) of the equivalent orbits. The circular orbit causes stable swirling waves (co-directed with the orbit) but may also excite stable nearly standing waves. The orbit direction does not affect the response curves for wall-symmetric (canonic) and diagonal orbit positions. This is not true for the oblique-type elliptic forcing. When the semi-axis ratio changes from 0 to 1, the response curves exhibit astonishing metamorphoses significantly influencing the frequency ranges of stable nearly standing/swirling waves and ‘irregular’ sloshing. For the experimental input data by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), the counter-directed swirling disappears as but the frequency range of irregular waves vanishes for .

A study on nonlinear steady-state waves at resonance in water of finite depth by the amplitude-based homotopy analysis method

Nonlinear steady-state waves are obtained by the amplitude-based homotopy analysis method (AHAM) when resonances among surface gravity waves are considered in water of finite depth. AHAM, newly proposed in this paper within the context of homotopy analysis method (HAM) and well validated in various ways, is able to deal with nonlinear wave interactions. In waves with small propagation angles, it is confirmed that more components share the wave energy if the wave field has a greater steepness. However, in waves with larger propagation angles, it is newly found that wave energy may also concentrate in some specific components. In such wave fields, off-resonance detuning is also considered. Bifurcation and symmetrical properties are discovered in some wave fields. Our results may provide a deeper understanding on nonlinear wave interactions at resonance in water of finite depth.

Tracing shock type with chemical diagnostics

Aims.The physical structure of a shock wave may take a form unique to its shock type, implying that the chemistry of each shock type is unique as well. We aim to investigate the different chemistries of J-type and C-type shocks in order to identify unique molecular tracers of both shock types. We apply these diagnostics to the protostellar outflow L1157 to establish whether the B2 clump could host shocks exhibiting type-specific behaviour. Of particular interest is the L1157-B2 clump, which has been shown to exhibit bright emission in S-bearing species and HNCO.Methods.We simulate, using a parameterised approach, a planar, steady-state J-type shock wave using UCLCHEM. We compute a grid of models using both C-type and J-type shock models to determine the chemical abundance of shock-tracing species as a function of distance through the shock and apply it to the L1157 outflow. We focus on known shock-tracing molecules such as H2O, HCN, and CH3OH.Results.We find that a range of molecules including H2O and HCN have unique behaviour specific to a J-type shock, but that such differences in behaviour are only evident at lowvsand lownH. We find that CH3OH is enhanced by shocks and is a reliable probe of the pre-shock gas density. However, we find no difference between its gas-phase abundance in C-type and J-type shocks. Finally, from our application to L1157, we find that the fractional abundances within the B2 region are consistent with both C-type and J-type shock emission.

Direct electron transfer-type bioelectrocatalysis of FAD-dependent glucose dehydrogenase using porous gold electrodes and enzymatically implanted platinum nanoclusters

The direct electron transfer (DET)-type bioelectrocatalysis of flavin adenine dinucleotide (FAD)-dependent glucose dehydrogenase (GDH) from Aspergillus terreus (AtGDH) was carried out using porous gold (Au) electrodes and enzymatically implanted platinum nanoclusters (PtNCs). The porous Au electrodes were prepared by anodization of planar Au electrodes in a phosphate buffer containing glucose as a reductant. Moreover, PtNCs were generated into AtGDH by an enzymatic reduction of hexachloroplatinate (IV) ion. The modification was confirmed by native polyacrylamide gel electrophoresis and sodium dodecyl sulfate polyacrylamide gel electrophoresis analyses. The AtGDH-adsorbed porous Au electrode showed a DET-type bioelectrocatalytic wave both in the presence and absence of PtNCs; however, the current density with PtNCs (~1 mA cm−2 at 0 V vs. Ag|AgCl|sat. KCl) was considerably higher than that without PtNCs. The kinetic and thermodynamic analysis of the steady-state catalytic wave indicated that inner PtNCs shortened the distance between the catalytic center of AtGDH (=FAD) and the conductive material, and improved the heterogeneous electron transfer kinetics between them.