Main Propagation Direction Research Articles

On the Asymptotic Behavior of Solutions to the (Generalized) Kadomtsev–Petviashvili–Burgers Equations

We show global existence and sharp results on the asymptotic decay of solutions to the generalized KP equations with a power nonlinearity u p u x and with a Burgers-type dissipation in the main direction of propagation appended. Furthermore, we prove that for p∈ N * the decay rate of the L 2-norm of the solution of these equations is that exhibited by the solution of these same equations linearized around the zero solution and that, for p⩾2, this also holds for the L ∞-norm. This limitation seems due to the presence of a dispersive effect in the transverse direction.

Ｍｏｄ．９Ｃｒ‐１Ｍｏ鋼の高温多軸低サイクル疲労および裂伝ぱ挙動

This paper describes the low cycle fatigue criterion of Mod.9Cr-1Mo steel and the fracture mode under multiaxial stress/strain states. Multiaxial tension-torsion low cycle fatigue tests were carried out using plain Mod.9Cr-1Mo tubular specimens at 823K. Plain, surface notched and through notched specimens were also torsionally fatigued at 823K and room temperature to examine the crack propagation direction. LE strain and the equivalent strain based on crack opening displacement were a suitable strain parameter for correlating the multiaxial low cycle fatigue lives with a small scatter. Mises' stress was a suitable stress parameter for the correlation. Main crack of the smooth, surface notched and through notched specimens propagated in the maximum shear strain direction in torsion tests, so there was no influence of the notches on the crack propagation direction. Surface oxidation has no effect on the main crack propagation direction, but it has an influence on the subcrack propagation direction. Oxide films were brittlely broken in the principal direction.

Accuracy analysis of the split-step Fourier propagator: Implications for seismic modeling and migration

AbstractThe split-step Fourier propagator is a one-way wave propagation method that has been widely used to simulate primary forward and backward (reflected) deterministic/random wave propagation due to its fast computational speed and limited computer memory requirement. The method is useful for rapid modeling of seismic-wave propagation in heterogeneous media where forward scattered waveforms can be considered to be dominant or reverberations can be ignored. The method is based on a solution to the one-way wave equation that requires expanding the square root of an operator and splitting of the resulting noncommutative operators to allow calculation by transferring wave fields between the space and wavenumber domains. Previous analysis of the accuracy of the method has focused on the error related to only a portion of the approximations involved in the propagator. To better understand the accuracy of the propagator, we present a complete formal and numerical accuracy analyses. Our formal analysis indicates that the dominant error of the propagator increases as the first order in the marching interval. We show that nonsymmetrically and symmetrically split-step marching solutions have the same first-order error term. Their second- and third-order error terms are similar. Therefore, the differences between the accuracy of different split-step marching solutions are insignificant. This conclusion is confirmed by our numerical tests. The relation among the phase error of the split-step Fourier propagator, relative velocity perturbation, and propagation angle is numerically studied. The results suggest that the propagator is accurate for up to a 60° propagation angle from the main propagation direction for media with small relative velocity perturbations (10%).

Particle tracking velocimetry beneath water waves. Part I: visualization and tracking algorithms

A novel particle tracking system working with a high particle concentration for the measurement of flow fields beneath water waves is described. It features a 1–4 cm thick light sheet parallel to the main wave propagation direction so that the seeding particles stay long enough in the illuminated area to enable tracking over several wave periods. An area of up to 14.0×10.0 cm2 is observed by a CCD camera with up to 200 fields/s. The polychromatic scattering theory of small particles in a light sheet illumination is investigated, enabling the segmentation of individual particles at high particle concentration.

On the origin of the long-period tremor recorded at Stromboli volcano (Italy)

This investigation deals with the nature of the long-period seismic signals (>1 s) observed at Stromboli and addresses the question whether they are of volcanic origin or produced by sources such as Ocean Microseisms (OMS). We present results from the analysis of seismic broadband data recorded during 1992 by an array of 9 Guralp CMG-3T seismometers. The determination of the Array Response Function (ARF) shows that array techniques like delay-and-sum beamforming cannot be applied for this purpose, as the extension of the array is limited by the geographical constraint of the island of Stromboli volcano, being simply too small. Spectral analysis reveals three main peaks with periods at 4.8 s, 6 s and 10 s which are not stable in time but vary according to the regional meteorological situation. Whereas 4.8 s and 10 s show up in amplitude spectra calculated during rainy and stormy weather, the 6 s period can be observed during a period of good weather. The signals were first narrowly filtered and then cross correlation, particle motion and amplitudes of the main long periods studied in detail. Relative arrival times as well as seismic amplitudes of the filtered traces do not show any systematic feature but vary with time. Particle motion analysis demonstrates that all long-period signals are recorded by the array as plane waves and that the main propagation direction of the 10 s signal is parallel to the wind direction. No correlation with volcanic activity is obvious. We conclude therefore that the three main long periods are not generated by a close volcanic source. We assume a local cyclone to be the seismic source at 4.8 s and 10 s, which represent the Double Frequency (DF-band) and the Primary Frequency (PF-band), respectively. Concerning the 6 s peak, we speculate a cyclone near the British Isles to act as a seismic source.

Classical nonlinear dynamics and chaos of rays in problems of wave propagation in inhomogeneous media

We discuss the geometrical theory of wave propagation in regularly inhomogeneous waveguide media from the point of view of nonlinear Hamiltonian dynamics. We consider ray dynamics in waveguides with periodic longitudinal inhomogeneities, including the phenomenon of spatial nonlinear resonance of rays, which leads to the formation of an effective waveguide channel in the neighborhood of the ray in resonance with the periodic inhomogeneities. We consider different properties of spatially resonant rays: the optical path length and propagation velocity of a signal along rays trapped in a separate nonlinear resonance; the fractal properties of rays, such as the devil's staircase form of the dependence of the spatial oscillation frequency of the ray and the propagation time of a signal along the rays. The trajectory of sound rays in a model of the ocean with transverse flow is considered using the adiabatic invariant method and the transverse drift of a ray with respect to the main propagation direction of sound is described. We consider the conditions for dynamical chaos of rays in a waveguide with longitudinal periodic inhomogeneities. We examine the conditions for internal spatial nonlinear resonance and chaos of rays in waveguides with an irregular cross section and their effect on the propagation velocity of a signal. We study the connection between the structure of the wave front and the dynamics of rays in waveguide channels with regular inhomogeneities. Finally, we discuss the applicability of geometrical optics in waveguides under the conditions of nonlinear resonance and chaos of rays, and the relation between this problem and quantum chaos.

Appropriate starting fields for different PE approximations

The suite of parabolic wave equations available today for solving range-dependent propagation problems in ocean acoustics encompasses forms ranging from the standard narrow-angle PE originally introduced by Tappert to very wide-angle PEs based on Padé series expansions. Each PE form has inherent phase errors that increase with increasing angle away from the main propagation direction (horizontal). These phase errors also affect the angular energy distribution in space so that a given initial field leads to different farfield radiation patterns in different PE's. This is explicitly illustrated by solving the classical Lloyd mirror problem for a point source near the free surface in a homogeneous half-space. The results clearly show the importance of selecting a starting field compatible with the particular PE being solved. Thus it is seen that the use of a wide-angle source with a narrow-angle PE may result in an amplitude over-shoot of 3–4 dB for propagation directions around 30° off the main propagation direction.

Sensor for evaluation of shock wave pulses

A sensor for determining the position of shock wave pulses of a shock wave source comprises a device for holding a metal foil in the region of focus for the shock wave source. The metal foil is held to extend perpendicular to the main propagation direction of the pulses and the incidence of the pulses on the metal foil will cause a bulge-like deformation of the material to be formed at the point of incidence. The deformation in the foil can be optically measured, for example, by evaluation in terms of location, diameter, depth, profile and volume to obtain conclusions about the position of the center of the focussed shock waves and also the power or intensity of the shock waves.

On the soliton solutions of the Davey-Stewartson equation for long waves

The Davey-Stewartson equations describe two-dimensional surface waves on water of finite depth. In the long wave limit, it is shown that these equations belong to the class derivable from operator equations in the manner of Zakharov & Shabat. The basic underlying linear system of equations is obtained and solutions to the original nonlinear system sought from the Gelfand-Levitan equations of Inverse Scattering Theory. Single soliton and multi-soliton solutions are deduced corresponding to the one-dimensional solutions already available. The solitons so obtained are pseudo one dimensional in that they have the same form as onedimensional solitons but move at an angle to the main direction of propagation. The multi-soliton solution describes the interaction of many such solitons each propagating in different directions. For two solitons, it is shown that resonance occurs and a triple soliton structure is produced.

On the Fracture Behavior of High Temperature Fatigue in Nickel-Base Superalloy

Nickel-base high temperature superalloys having three different micro-structures have been tested by a rotating fatigue machine at the rate of 3500r.p.m. at 815°C. The test was carried out on the specimens both without and with a 60° notch. The fatigue life of the cast one with a notch was considerably shorter than those of other specimens, but the notch sensitivity was eliminated by the solution heat treatment followed by aging.Fractographic observations were conducted on fracture surfaces. Large MC type carbides have a marked influence in addition to the notch effect on fatigue life. High temperature fatigue fracture surface showed four distinctive features. The planar region including the origin of fracture was the first pattern appearing along the main fatigue crack propagation direction and was very similar to the Stage 1 fracture surface at room temperature in fatigued single crystal of nickel-base superalloy. The second region was the shear mode pattern. The third was the characteristic region containing both transgranular and intergranular fractures. Well defined striations were observed in the transgranular fracture region except the cast one with a notch which showed dull striations. The flat plane, which may be attributed to crystallographic fracture mode, was also observed. The final was the overloading fracture region.

On the non-linear energy transfer in a gravity-wave spectrum. Part 3. Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.

Ultrasonic Attenuation Caused by Thermoelastic Heat Flow

Expressions for the attenuation of sound waves in a standard linear viscoelastic body have been derived and have been applied to the attenuation due to the thermoelastic effect. The thermoelastic attenuation for sound waves has been computed for single crystals and polycrystalline materials under application of the high-frequency approximation of sound propagation. For single crystals the attenuation in the main propagation directions have been computed explicitly for cubic and hexagonal crystals taking into account the anisotropy of the elastic properties and thermal expansion. Comparison with experiments in the megacycle region shows that the attenuation caused by heat flow between the grains of a polycrystalline specimen is usually overpowered by scattering at the grain structure. Also the computed attenuation caused by heat flow between the regions of compressions and rarefaction of the wave is for many materials much smaller than the measured values. For single crystals of certain metals, however, the computed and the measured values have the same order of magnitude. It can be shown that in these cases the attenuation is composed of a thermoelastic component and of a component resulting from dislocations. In zinc the two components can be separated experimentally and the agreement between the measured and the computed thermoelastic damping is very good.