In this paper, we extend and complement previous works about propagation in kinetic reaction–transport equations. The model we study describes particles moving according to a velocity-jump process, and proliferating according to a reaction term of monostable type. We focus on the case of bounded velocities, having dimension higher than one. We extend previous results obtained by the first author with Calvez and Nadin in dimension one. We study the large time/large-scale hyperbolic limit via an Hamilton–Jacobi framework together with the half-relaxed limits method. We deduce spreading results and the existence of travelling wave solutions. A crucial difference with the mono-dimensional case is the resolution of the spectral problem at the edge of the front, that yields potential singular velocity distributions. As a consequence, the minimal speed of propagation may not be determined by a first-order condition.

With the consideration of the flexoelectric effect, the dispersion feature of plane waves propagating in infinite piezoelectric medium and the reflection amplitude ratio at a mechanically traction-free and dielectrically charge-free surface of semi-infinite piezoelectric half-space are studied in this paper. The flexoelectric effect is essentially the microstructure effect of heterogeneous piezoelectric medium. Besides, the strain gradient effect and the micro-inertial effect are also introduced to reflect the influences of the microstructure. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the microstructured piezoelectric medium. The influences of the flexoelectric effect, the strain gradient effect and the micro-inertial effect upon the dispersion feature of the coupled elastic waves and the reflection amplitude ratio are studied numerically. The numerical results are shown graphically and are validated by the energy conservation law. It is found that these microstructure effects have obvious influences upon the dispersion feature of the coupled elastic waves and therefore also affect the reflection energy partition at the mechanically free surface. Especially, the micro-inertial effect has fundamental influences on the dispersion properties of the coupled elastic waves.

This paper presents a shallow water depth estimation methodology using S-band Synthetic Aperture Radar (SAR) data from the HJ-1C satellite. It is based on the shoaling and refraction of long surface gravity waves as they propagate shoreward. A two-scale Bragg scattering model is used to describe the imaging process of long waves by SAR. By computing the Fast Fourier Transformation (FFT) for the selected sub image, wavelength and direction of the long wave can be retrieved from the two-dimensional (2D) spectra with wave tracking technology. Shallow water depths are then obtained from the linear dispersion relation with the calculated angular wave frequency obtained from other sources or first guesses of initial water depths or wave periods. Applicability and effectiveness are tested in the near-shore area of the Fujian province, China. Comparison between the derived results and water depths from an Electronic Navigational Chart (ENC) indicates that HJ-1C SAR is capable of higher resolution underwater topography detection, and the methodology can be used for shallow water depth estimation with good accuracy. The average absolute error and average relative error of the estimated results is 0·86 m and 11·05%, respectively.

Matching boundary conditions (MBC’s) are proposed to treat scalar waves in the body-centered-cubic lattices. By matching the dispersion relation, we construct MBC’s for normal incidence and incidence with an angle α. Multiplication of MBC operators then leads to multi-directional absorbing boundary conditions. The effectiveness are illustrated by the reflection coefficient analysis and wave packet tests. In particular, the designed M1M1 treats the scalar waves in a satisfactory manner.

This study describes the estimation of spherical wave parameters that appears in Synthetic Aperture Radar (SAR) images acquired over the coast of Chukk, Micronesia. The main causes for the interaction of SAR signals with ocean waves can be retrieved through the Bragg scattering mechanism. Dominant wavelengths were retrieved by means of Fast Fourier Transform (FFT) analysis in terms of peak frequency responses. Sea surface slopes were then obtained from the dispersion relation with consideration of different water wave conditions for each subset area, and wave heights were estimated with the use of dominant wavelengths and sea surface slopes. The work presented in this paper may be useful to retrieve the various wave parameters over different regions. The method used is a novel technique to correlate the relationship between SAR image parameters and dispersion relation.

In the tape helix slow-wave system, discontinuous dielectrics have great effects on the dispersion characteristics. In this paper, the tape helix slow-wave system, including an inner and an outer metal shield, tape helix, nylon support, and de-ionized water as filling dielectric, was analyzed. Effects of dielectric discontinuity caused by the support dielectric and filling dielectric on the dispersion characteristics were studied in detail. The dispersion relations, phase velocities, slow-wave coefficients, and electric lengths of the spatial harmonics in the system were calculated. Results showed that, if the permittivity of support dielectric was smaller than that of the filling dielectric, frequencies of the spatial harmonics in the system rose, phase velocities and slow-wave coefficients increased, the slow-wave effect of the system was weakened so that the previous electric length was shortened. The reverse condition corresponded to the reverse results, and the electromagnetic simulation also proved it. By use of the helical pulse forming line of accelerator based on the studied tape helix slow-wave system, the electric lengths of the system were tested as 188.5 ns and 200 ns in experiments where the thicknesses of nylon support were 6 mm and 3 mm, respectively. The theoretical calculation results 198 ns and 211 ns basically corresponded to experimental results, which only had relative errors as 5 and 5.5%, respectively.

In the tape helix slow-wave system, discontinuous dielectrics have great effects on the dispersion characteristics. In this paper, the tape helix slow-wave system, including an inner and an outer metal shield, tape helix, nylon support and de-ionized water as filling dielectric, was analyzed. Effects of dielectric discontinuity caused by the support dielectric and filling dielectric on the dispersion characteristics were studied in detail. The dispersion relations, phase velocities, slow-wave coefficients and electric lengths of the spatial harmonics in the system were calculated. Results showed that, if the permittivity of support dielectric was smaller than that of the filling dielectric, frequencies of the spatial harmonics in the system rose, phase velocities and slow-wave coefficients increased, the slow-wave effect of the system was weakened so that the previous electric length was shortened. The reverse condition corresponded to the reverse results, and the electromagnetic simulation also proved it. By use of the helical pulse forming line of accelerator based on the studied tape helix slow-wave system, the electric lengths of the system were tested as 188.5 ns and 200 ns in experiment when the thicknesses of nylon support were 6 mm and 3 mm, respectively. The theoretical calculation results 198 ns and 211 ns basically corresponded to experimental results, which only had relative errors as 5 and 5.5%, respectively.