Propagation Of Short Waves Research Articles

Excited solitons, breathers and periodic waves for a short pulse equation with time-dependent coefficients in relaxing media

In this study, the attention is focused on the excitation of Vakhnenko–Parkes (VP) equation with time-dependent coefficients, which can describe the short pulse wave propagation in relaxing media with variable perturbations. Hirota bilinear method is employed to construct three types of analytical solutions, namely, soliton, breather and periodic wave solutions. By utilizing the two free functions involved in the solutions, abundant excited patterns are revealed for the equation. Several examples are taken to demonstrate the novel effects of excited solitons, breathers and periodic waves.

The contributions of Gilbert-damping and inhomogeneous exchange effects on the electromagnetic short waves propagation in saturated ferrite films

Numerical simulations of the non-integrable generalized Kraenkel-Manna-Merle (GKMM) system are performed to study the effects of Gilbert-damping and inhomogeneous exchange on the propagation of short waves in various saturated garnet ferrite films. It is observed that the Gilbert-damping mainly acts on reducing the amplitude and velocity of loop-solitons during propagation and the decay rates are slower than that in the linear theory. It is of interesting that such conclusions are suitable for multi-solitons. For different parameter ranges of the inhomogeneous exchange effect and the frequency of short electromagnetic wave, our simulations reveal four types of inhomogeneous exchange processes that effect on the loop-solitons in different ways. The domains of existence are presented and examples of each case are illustrated. Furthermore, the combined effects are discussed while taking both damping and inhomogeneous exchange into account.

Theoretical Study on an Effect of Liquid Viscosity and Thermal Conductivity on Weakly Nonlinear Propagation of Short Pressure Waves in Bubbly Liquids

This study theoretically clarifies an effect of the liquid viscosity and the thermal conductivity on weakly nonlinear propagation of pressure waves in a liquid containing many spherical microbubbles. As in our preceding paper (Kamei et al., J. JSCE, Ser. A2, 75 (2019), 499) focusing on a long wave, by the use of the method of multiple scales, a nonlinear Schrödinger equation describing the long-range propagation of an envelope wave of short carrier wave is derived from the basic equations incorporating the liquid viscosity and the thermal conductivity. As a result, as in our preceding long wave case, the liquid viscosity and the thermal conductivity affect the dissipation effect, and a nonlinear effect in the adiabatic process decreases in comparison with the previous study (Kanagawa et al., J. Fluid Sci. Technol., 6 (2011), 838). On the other hand, unlike in our preceding long wave case, a dispersion effect in the adiabatic process decreases in comparison with the previous study.

Rogue wave, interaction solutions to the KMM system

In this paper, the consistent tanh expansion (CTE) method and the truncated Painlevé analysis are applied to the Kraenkel-Manna-Merle (KMM) system, which describes propagation of short wave in ferromagnets. Two series of analytic solutions of the original KMM system (free of damping effect) are obtained via the CTE method. The interaction solutions contain an arbitrary function, which provides a wide variety of choices to acquire new propagation structures. Particularly, the breather soliton, periodic oscillation soliton and multipole instanton are obtained. Furthermore, we obtain some exact solutions of the damped-KMM equation at the first time. On the other hand, a coupled equation containing quadri-linear form and tri-linear form for the original KMM system is obtained by the truncated Painlevé analysis, and the rogue wave solution and interaction solutions between rogue wave and multi-soliton for the KMM system are discussed.

Synthesis of highly convergent 2D and 3D finite elements for short acoustic wave simulation

New higher-order finite elements of enhanced convergence properties for acoustic wave simulation are presented in the paper. The element matrices are obtained by combining modal synthesis and optimization techniques in order to achieve minimum errors of higher modes of the computational domain. As a result, simulation models of propagating wave pulses require a smaller number of finite element divisions per wavelength compared to the conventional element model thus significantly reducing computational costs. Though finite element matrices are obtained in optimization, the resulting patterns of the matrices are versatile and further can be used in any wave propagation model. The mass matrices of the elements are diagonal, so explicit time integration schemes are applicable. The usage of new elements is especially efficient in situations where wavelengths of the simulated signal are much shorter than the dimensions of the computational domain. This is referred to as short wave propagation analysis. The results of wave propagation simulation for ultrasonic measurements are presented as application examples. The B-scans and computed dispersion curves are provided for visual interpretation of the results.

Spectral variational multiscale model for transient dynamics of phononic crystals and acoustic metamaterials

In this manuscript, a spectral multiscale model is developed for transient elastic wave propagation in periodic composites. The basis of the multiscale approach is the variational multiscale enrichment method that permits analysis of wave propagation in the scale-inseparable condition, i.e., short wave propagation. A spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. A material-phase-based model basis reduction strategy is devised at the fine scale to achieve computational efficiency. An important feature of the proposed method is that it does not rely on the classical assumption of separation of scales, which permits its application to a broad range of architectured composites including phononic crystals and acoustic metamaterials. Transient elastic wave propagation in two-dimensional periodic structures is investigated. The proposed multiscale approach is verified against direct numerical simulations. The accuracy and computational efficiency of the approach are demonstrated for both phononic crystals and acoustic metamaterials.

Interpreting Experimental Results from Shock Impacts on Single Crystal PETN in the Context of Continuum Models

AbstractIn this paper we interpret previous experimental measurements of impacts on single crystal PETN in the context of a simple continuum model. Hugoniot calculations using the simple model framework under various limiting assumptions envelope measured Hugoniot states reasonably well and suggest that non‐negligible deviatoric elastic strains may exist in the shock compressed state for weak impacts. An accompanying simple kinematic model for lattice deformation was used to estimate the expected shifts in X‐ray diffraction peaks for the (211) plane under impacts normal to (110) planes. The results suggest that negligible relaxation of the deviatoric lattice deformation occurs on the short (10–20 ns) time and wave propagation (40–80 m) scales of laser‐driven shock experiments, and that the corresponding elastic strains may be large. Because of the potentially large deviatoric elastic strains, the specific finite deformation strain measure used within thermomechanical single crystal models is of significant consequence, which is explored numerically by the comparison of isothermal purely elastic responses under uniaxial and simple shear deformations.

Numerical study of cascading dam-break characteristics using SWEs and RANS

AbstractThis paper investigates the cascading dam-break flood propagation on the downstream sloping channel and reservoir using the shallow water equations (SWEs) and the Reynolds-average Navier-Stokes equations (RANS). The calculated surface profiles, stage hydrographs and maximum run-up heights for 24 sets of initial conditions are elaborately compared with the experimental measurements, which show the SWEs reproduce the wave oscillation evolution and the maximum run-up height inaccurately. The maximum run-up heights calculated by the SWEs are all smaller than those by the RANS and the measured results, the maximum errors are within −10% to −25%, which may predict delay of the downstream dam-break. However, the maximum errors calculated by the RANS are within ±10%. So the RANS predict more accurate results than the SWEs. Additionally, the generation of short waves must be below a certain upstream-to-downstream ‘depth ratio’, roughly the ‘depth ratio’ <2/3 in this study. If the ratio is too high, it is difficult to form a wavy push due to air entrainment and turbulence. The SWEs predict more accurate results for shallow initial depths than deep initial depths. Therefore, the advantage of the RANS can be more obvious for deep initial depths.

Inhomogeneous exchange within higher-dimensional ferrites: The singularity structure analysis and pattern formations

Abstract In this work the propagation of nonlinear electromagnetic short waves in a ferromagnetic medium with inhomogeneous exchange is discussed. It is shown that such waves propagate perpendicular to the magnetization density. The evolution of waves under the influence of perturbations in one transverse dimension is considered. As result, we derive a new (2+1)-dimensional evolution system in which painleve analysis reveals its integrability properties. In the wake of such analysis, using the arbitrary functions to enter into the Laurent series of solutions to the above system, we present some typical class of excitations.

Traveling magnetic wave motion in ferrites: Impact of inhomogeneous exchange effects

Abstract In this article, we derive new traveling wave solution to a nonlinear evolution equation, describing propagation of short wave in inhomogeneous ferrites. Applying Jacobi elliptic function, we derive as series of new exact solutions to the system of our interest which are either periodic or localized solutions. We point out the influence of the inhomogeneous exchange effects on the dynamics of traveling waves obtained. It appears that the soliton responsible of localization is deformed by the presence of inhomogeneities in particular its structure. We discuss some physical implications of these results.

Influence of damping effects on the propagation of magnetic waves in ferrites

In this paper, we study in details the propagation of ultra short waves in magnetic insulators. We discuss the Kraenkel–Manna–Merle (KMM) system, derived from the Maxwell’s equations in which damping effects and nonlinearity set in from the first order Landau–Lifshitz–Gilbert equation. We investigate this system analytically, using the well developed inverse scattering transformed method and, as a result the impact of damping effects on the propagation of magnetic waves in ferrites is revealed. We launch our investigations with an integrable system that, under the ultra fast process assumption, approximates the one of our interest which shows that damping acts mostly on the energy of the wave that decrease as time evolves. Such a result is confirmed through some numerical simulations in which analytical and numerical results are matching very goodly. We then conclude on the influence of damping effects on the propagation of waves in magnetic insulators.

Coherence between infragravity waves and ambient water motions over cape-associated shoals

Cross-shelf water motions influence fluxes of nutrients, larvae and sediments, which in turn affect nearshore morphodynamics. Among these motions are infragravity waves, which typically exhibit periodicities from 20 to 200 s, and originate from multiple sources including the superposition of incident wave fields. To examine how infragravity waves co-vary with water motions in an area of complex bathymetry, we analyzed measurements from acoustic Doppler current profilers around cape-associated shoals near Cape Canaveral, on the Florida (USA) Atlantic coast. Observations of water motions and infragravity wave heights at the outer and inner swales of two isolated shoals (Shoal E and Shoal D), located approximately 15 km offshore in ∼ 14 m water depth, were subjected to squared coherency and wavelet coherence analyses. Coherences between infragravity wave heights and flow conditions were unsteady, i.e. variable over time, and exhibited differences between outer and inner swales. Subtidal flows (periods > 0.5 days) were sporadically coherent with the total and bound infragravity wave heights at both inner and outer swales. Tidal flows (∼ 2 cycles/day) were coherent with the total infragravity wave heights only at outer swale locations. These results indicate that tidal motions may modulate the generation of free (directed both oppositely to and in the direction of short-wave propagation) infragravity waves by short-wave groups shoaling and by refractive trapping at shoals. Subtidal flows, on the other hand, may influence triad interactions that generate infragravity motions.

The oscillating solitons for a coupled nonlinear system in nanoscale saturated ferromagnetic materials

Abstract A coupled nonlinear system is investigated, which describes the nonlinear short-wave propagation in nanoscale saturated ferromagnetic materials. A series of analytic solutions is constructed via Riccati equation mapping method. Furthermore, two types of novel periodically oscillating solitons are observed by choosing the arbitrary function in the soliton solution as trigonometric function and Jacobian elliptic function, respectively. The parameters can be used to control the compression, stretch, oscillating amplitude and frequency of the solitons.

Stability and convergence of a conservative finite difference scheme for the modified Hunter–Saxton equation

The modified Hunter–Saxton equation models the propagation of short capillary-gravity waves. As the equation involves a mixed derivative, its initial value problem on the periodic domain is much more complicated than the standard evolutionary equations. Although its local well-posedness has recently been proved, the behavior of its solution is yet to be investigated. In this paper, a conservative finite difference scheme is derived as a reliable numerical method for this problem. Then, the stability of the numerical solution in the sense of the uniform norm, and the uniform convergence of the numerical solutions to sufficiently smooth exact solutions are rigorously proved. Discrete conservation laws are used to overcome the difficulty due to the mixed derivative.

An implicit 2D hydrodynamic numerical model for free surface–subsurface coupled flow problems

SummaryA 2‐dimensional hydrodynamic finite volume model has been proposed for simultaneous simulation of free surface and saturated porous media. The governing equations of the former are 2‐dimensional averaged in a unit width of Navier‐Stokes, whereas that of the latter are Darcy law. An efficient, simple, and stable algorithm has been proposed to track the surface elevation in Cartesian coordinate system by which the water elevation in each computational column has been computed along with the other pressure unknowns simultaneously. The surface position has not been considered to remain in a specific layer so the number of cells in each column have been variably adjusted in accordance with the water surface elevation. Performance of the coupled model has been validated against a range of hydrodynamic problems including propagation of linear short wave, seepage test, tidal oscillation in a lagoon system, gravity current, and saltwater intrusion. Comparison between numerical results, analytical solutions, and experimental data demonstrates that the model represents well the interacting surface water and ground water flow and solute transport processes.

Detecting the spatial chirp signals by fractional Fourier lens with transformation materials

Fractional Fourier transform (FrFT) is the general form of the Fourier transform and is an important tool in signal processing. As one typical application of FrFT, detecting the chirp rate (CR, or known as the rate of frequency change) of a chirp signal is important in many optical measurements. The optical FrFT that based on graded index lens fails to detect the high CR chirp because the short wave propagation distance of the impulse in the lens will weaken the paraxial approximation condition. With the help of transformation optics, the improved FrFT lens is proposed to adjust the high CR as well as the impulse location of the given input chirp signal. The designed transformation materials can implement the effect of space compression, making the input chirp signal is equivalent to have lower CR, therefore the system can satisfy the paraxial approximation better. As a result, this lens can improve the detection precision for the high CR. The numerical simulations verified the design. The proposed device may have both theoretical and practical values, and the design demonstrates the ability and flexibility of TO in spatial signal processing.

Optimized Symmetric Bicompact Scheme of the Sixth Order of Approximation with Low Dispersion for Hyperbolic Equations

A dispersion analysis of semidiscrete schemes from the one-parameter family of symmetric bicompact schemes of the sixth order of accuracy in space is performed. In this family, a scheme is found that has the smallest maximum phase error in the entire range of wavelengths resolvable on an integer-node grid. The maximum phase error of this optimized scheme does not exceed one-hundredth of percent. A numerical example is presented that demonstrates the ability of the bicompact scheme to adequately simulate short wave propagation on coarse grids at long times.

Rich Soliton Structures for the Kraenkel-Manna-Merle (KMM) System in Ferromagnetic Materials

A particular attention is paid to investigate the Kraenkel-Manna-Merle (KMM) system, which can describe the nonlinear short-wave propagation in saturated ferromagnetic materials with zero-conductivity in an external field. A class of exact soliton solutions is constructed via the generalized G ′/G-expansion method. Some novel soliton structures are excited by choosing the arbitrary functions in the solution as certain specific functions. Hump-soliton, cusp-soliton, loop-soliton, and kink-soliton are observed graphically. The results reveal the system theoretically possesses extremely rich soliton structures.

Correlation of velocities of the waves сontrolling the thin-plate α-martensite formation and the modulation of the transformation twin structure

For the case of γ-α martensitic transformation (MT) in iron alloys, the concept of transformation twins is explained. As a rule, crystals of α-martensite having the form of thin plates are characterized by a fine twin structure (TS) with interchanging orthogonal directions of main compression axes. An example is given of the real structures of transformation twins that are not strictly regular. It is shown that in dynamic theory of MT the regular TS initiation is connected with coherent propagation of long (ℓ) and short (s) displacement waves belonging to controlling wave process (СWP). An analytical approximation of the dispersion law of s-waves is carried out. The threshold conditions of deformation and the qualitative picture of the formation of a modulated ТS are discussed. On the example of Fe-30Ni alloy the correlation of velocities of the waves сontrolling the thin plate α-martensite formation is established. It is shown that at the real correlation of wave velocities the modulated structure of the transformation twins is induced. The similar structure contains fragments each of which is connected with the short-wave excited cell. The fragment size is associated with the number of Nbas layers of the main component inside the ТS fragment generated by a single spontaneously activated s-cell. Fragments’ sizes depend on the site of localization of spontaneously appearing s-cell generating the fragment in the area of the СWP front. It is shown that the Nbas value can vary within rather wide limits. Therefore, in contrast to regular TS forming, we should expect repeated s-cells spontaneous excitements for long enough twinned thin-plated crystals. Along with difference of s- and ℓ-waves velocities, consideration of waves (especially s-waves) decay is one more quite determined factor making its contribution into TS modulation. Estimation of this contribution seems to be very actual.

On the barotropic instability using wave ray theory

Based on the spherical Rossby wave ray theory, dynamic characteristics of the barotropic disturbances associated with the westerly jet are discussed, and the barotropic instability conditions are reconsidered. The well-known Rayleigh-Kuo instability criterion indicates that the gradient of potential vorticity must change sign in the unstable area. Kuo uses the method of eigenvalues by assuming disturbances to be simple harmonic waves; however, in this work we assume the atmosphere to be a slowly varying medium, and calculate the amplitude of the Rossby wave by ray tracing. We find a band where the quasi-geostrophic potential vorticity gradient ( β M) is negative, and the amplitude of the northward perturbation grows substantially in this area, making it an unstable region for northward perturbations. In addition the perturbations cannot cross the line of β M=0, and therefore, this is referred to as the “trapped line”. Characteristics of the nonstationary Rossby wave are first analyzed using an ideal zonal mean wind profile u = 30 sin 8 ( 2 φ ) + 0.2 , with the “trapped line” located at 58°N and 70°N, and β M l = 8, but with different zonal wave numbers k . The results suggest that the behavior of the disturbances depends on the initial wave numbers k and l . Northward disturbances with smaller k can propagate further, while disturbances with larger k cannot reach high latitudes and turn back towards the south at turning points β M / ( u M − σ k ) − k 2 = 0. As such, only long Rossby waves with small k values can reach the “trapped line”, while short Rossby waves with larger k values cannot reach it. Long Rossby waves with k = 1, l = 8, first propagate northwest, and then turn eastwards at the “trapped line”. Their energy increases while propagating northward, reaching its maximum in the northern part of the jet stream, and then decays rapidly to zero near the “trapped line”. The energy increases during northward propagation, which means the disturbance obtains energy from the base flow in the southern part of the jet stream, and gives it back to the base flow near the “trapped line”, which completes energy transport from south to north. Further, we also calculated the energy evolution with realistic January and June wind profiles using NCEP data. We conclude that long waves with k <3 are easily trapped by the “trapped line” in both winter and summer, while the propagation of short waves differs substantially between winter and summer. The non-stationary disturbances at low latitudes are easily blocked by easterly winds during winter; however, they can cross easterlies and then propagate to the southern hemisphere in summer, forming a westward wave in the easterlies. It is known that stationary Rossby waves cannot propagate in the easterlies, because only non-stationary waves that meet many conditions can propagate in the easterlies; therefore, this scenario will not be detailed in this paper.