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Surface irregularities on the earth, such as hills and ridges, can amplify the ground motion caused by earthquakes and cause damage to buildings. Hence, it is crucial to study the ground motion amplification on hills and their environs under the effect of earthquakes. In this research, the seismic response of a triangular rocky hill subject to cylindrical horizontally polarized shear (SH) waves is investigated by means of a boundary integral equation method. A comparison is made to verify the feasibility of the present method. Parametric studies are performed to evaluate the influences of source location and hill shape on the ground accelerations on the hill and its environs under cylindrical SH waves of different frequencies. The results show that the ground accelerations near the hill are strongly relative to the source location. For a near-source scattering problem, the cylindrical wavefront assumption is more appropriate than the plane wave assumption. The thinner hill is more likely to cause multiple reflections of the seismic waves inside it, resulting in a stronger ground motion near the hillcrest. The acceleration response spectrum at the hillcrest is amplified in a wide period range of 0–4 s, and increasing the hill height will strengthen the amplification effect. The presence of the hill also results in the amplification of the acceleration response spectrum in the period range of 0–0.7 s on the flat ground surface.HighlightsThe seismic response of a triangular hill to cylindrical SH waves was investigated.Necessity of cylindrical wavefront assumption for near-source problem was verified.Mechanism of ground motion amplification on a triangular hill was revealed.

Concentric water waves are ubiquitous in nature and, under certain conditions, may exhibit azimuthal instabilities. Whereas transverse instability of their plane counterparts, governed by nearly plane Korteweg–de Vries and nonlinear Schrödinger equations in the shallow and deep water limits, respectively, have been extensively studied as enabled by the existence of localized solitons, in the cylindrical case stability analysis is impeded by the corresponding finite-amplitude waves being non-localized. The equations, governing such waves, emerge from a balance between dispersive and nonlinear effects and, in particular, admit non-localized solutions of self-similar form. It is the goal of the present work to study transverse stability of such solutions, in both the shallow and deep water limits, as a function of surface tension (a Weber We number). Whereas in the shallow water case, a nearly concentric Korteweg–de Vries equation has been previous deduced, a deep water weakly nonlinear model has not been established yet. With a systematic derivation in cylindrical coordinates, we demonstrate that the appropriate envelope equation becomes of the nearly concentric nonlinear Schrödinger type with time-dependent coefficients. Transverse stability analyses of the concentric self-similar solutions to these models indicate crucial differences from the plane configurations revealing the effects of cylindrical geometry, direction of the base-state wave propagation, and its amplitude variation. In particular, the azimuthal perturbations do not admit, in general, a regular periodic structure, except for the short-wavelength perturbations on deep water which are either stretched or compressed with time as τ 1 / 2 depending on whether the base state concentric wave is traveling outward or inward. In the shallow-water case, transient azimuthal growth of outgoing finite-amplitude concentric waves is observed for all We in contrast to the plane solitons case, in which there exists a nonzero critical We ; also, inward-traveling cylindrical waves are unstable for all values of We . In the deep-water case, azimuthal perturbations of outward-traveling cylindrical wave are stable in the long-time limit, but experience transient growth for short times when W e < 1 2 . As for inward-traveling waves, transverse perturbations grow for all We . These observations are at variance with the plane deep water geometry, in which transverse instability is observed for all We .

We study the electromagnetic radiation of a charged particle bunch with small size moving at a constant velo city and having a variable charge. The environment medium is considered to be isotropic and homogeneous, and it may have frequency dispersion, but not spatial dispersion. The general solution of the problem is obtained. The main attention is paid to the case when the bunch charge, starting from a certain moment, decreases exponentially with time. The saddle point metho d is used to obtain the approximate expressions for the field components that are valid in the wave zone. The energy characteristics of the excited spherical wave are studied and compared with the case of a decelerating charge. In the case of excitation of Vavilov–Cherenkov radiation, we obtain the asymptotics which are valid in the entire wave zone, including the region in which the field cannot be divided into the spherical and cylindrical waves.

Previous studies mostly used plane waves as the source input to study the influence of topography effects without considering the source distance. However, the influence of source effect on topography amplification cannot be ignored. This study presents a series solution for the scattering of cylindrical SH waves by a shallow asymmetric V-shaped canyon, and the effect of the location of the source on the topography magnification is investigated. The presented formulations in this paper first divide the asymmetric shallow V-shaped canyon into enclosed and open regions using the region-matching method. The free wavefield of cylindrical SH wave is solved by the image theory, and the wavefield in the enclosed and open regions is obtained based on the separation of variable method. The Graf’s formula is derived to unify the wavefield coordinates of the two regions, and the unknown coefficients of the wavefield are solved by the continuity condition of the boundary. Then, the proposed solution is verified by comparisons with published data for two cases (e.g. those pertaining to the symmetrical V-shaped canyon of cylindrical SH waves and the asymmetric shallow V-shaped canyon of plane SH waves). Finally, the effect of the source position, the width, and the dimensionless frequency of the asymmetric V-shaped canyon on the surface displacement amplification is discussed. It is found that the difference of displacement amplitude between asymmetric canyon and symmetric canyon can reach 270.2% under the cylindrical SH waves, that is, the asymmetric effect of the canyon has a significant influence on the topography amplification. The cylindrical SH waves cannot simply be regarded as plane SH waves unless the source location r 0 exceeds 100 times canyon depth and it is necessary to use cylindrical SH waves to simulate the influence of near-source effects on topography amplification when the source is relatively close. Therefore, the near-source effect should warrant careful engineering attention in the seismic design of large-span structures such as bridges across shallow V-shaped canyons.

In this study, we report the formation of laser-induced periodic surface nanometric concentric ring structures on silicon surfaces through single-spot irradiation with orthogonally polarized femtosecond laser double-pulse sequences (OP pulses). The period of the ring structures is marginally smaller than the irradiated laser’s wavelength, which indicates that the structures are a type of low-spatial-frequency laser-induced periodic surface structures. Regular nanometric concentric ring structures can be formed when the time delay between two subpulses is approximately 1 ps (roughly from 500 fs to 1.5 ps) and the number of laser bursts is approximately 4. The formation mechanism of the concentric ring structures is attributed to the surface wave (i.e., cylindrical wave) stimulated by OP pulses through single-spot irradiation is radially distributed. Large area of concentric ring structures eliminating anisotropy in the generation of structural colors was shown in this paper.

Microstructure requires nanometer-scale surface roughness and micro- or even sub-micron form error accuracy in different applications. Two kinds of modeling theories and methods of micro-feature of rotating body and non-rotating body are studied, and the corresponding tool turning trajectory planning method is put forward. In order to process the designed micro-feature structure successfully and avoid the interference and overcutting between tool and workpiece caused by improper selection of tool parameters, the cutting parameters are analyzed and two error theories are proposed. Then, a precision-driven turning trajectory planning method is obtained, which can optimize the trajectory by adjusting turning parameters according to the setting errors. The experiments are carried out to verify the proposed theories, and the results of measurements are that the surface roughness and surface form accuracy of the cylindrical sine wave groove micro-feature surface are 0.1714 μm and 1.32 μm, respectively. The surface roughness and surface form accuracy of the cylindrical sinusoidal mesh micro-feature surface are 0.1625 μm and 1.8 μm, respectively. The results meet expectations and verify the reliability of the error theory and the trajectory optimization theory.

Recent years have witnessed a rapidly growing interest in exploring the use of spiral sound carrying artificial orbital angular momentum (OAM), toward establishing a spiral-wave-based technology that is significantly more efficient in energy or information delivering than the ordinary plane wave technology. A major bottleneck of advancing this technology is the efficient excitation of far-field spiral waves in free space, which is a must in exploring the use of spiral waves for long-distance information transmission and particle manipulation. Here, we report a low-profile planar acoustic antenna to modulate wavefronts emitted from a near-field point source and achieve far-field spiral airborne sound carrying OAM. Using the holographic interferogram as a 2D modulated artificial acoustic impedance metasurface, we show the efficient conversion from the surface wave into the propagating spiral shape beam both numerically and experimentally. The vortex fields with spiral phases originate from the complex inter-modal interactions between cylindrical surface waves and a spatially-modulated impedance boundary condition. This antenna can open new routes to highly integrated spiral sound emitters that are critical for practical acoustic functional devices. Acoustic waves that carry orbital angular momentum are difficult to create and maintain at significant distances. Here, the authors present a planar metasurface antenna that enables vortex fields at longer distances.

The interaction of a sandwich plate with a damped cylindrical wave in the ground has been investigated. A sandwich plate is considered as a model of a barrier in the ground, described by a system of equations by V. N. Paimushin, placed in the ground dividing it into two parts. The plane problem formulation is considered. The boundary conditions correspond to the hinge attachment of the barrier, and the initial conditions are zero. A cylindrical damped wave is considered as an external influence. To describe the ground movement, the equations of the elasticity theory, the Cauchy relations and the physical principle, or equivalent displacements in potentials and the Lame equations are used. The problem is solved in a related formulation, where the movement of the plate and its surrounding media is considered together. All components of the equations of motion of the plate and media are decomposed into trigonometric series and the Laplace transform is applied to them. As the conditions for the contact of the plate and the ground, the equality of normal displacements at the boundary of the medium and the plate is assumed. It is also assumed that the pressure amplitudes and normal stresses coincide. After determining the constants from the contact conditions, the displacement values and the values of normal and tangential stresses are found, after which their originals are found.

Rotating spiral waves are dominant dynamical structures in thin layers of excitable media. The three-dimensional (3D) versions are known as scroll waves. For human health, they correspond to cardiac arrhythmia and life-threatening fibrillation. The scroll waves and the corresponding pathological conditions stay longer when they are pinned to unexcitable obstacles, e.g., blood vessels or scars in the heart. In this article, we present a simulation study of the dynamics of scroll waves partially pinned to cylindrical obstacles with varying tilted angles. A simple shaped (untwisted) scroll wave with a linear filament aligning in the vertical direction is generated as the initial conditions. An unexcitable volume with on-flux boundaries is defined as the tilted cylindrical obstacle. The obstacle is shorter than the system height, leaving the system above the obstacle unperturbed. At the beginning, only a small part of scroll wave filament located near the system bottom is pinned to the obstacle. In the course of time, the pinned part gradually advances along the obstacle and becomes twisted wave. After a transient time, the pinned scroll wave has a helical structure that wraps the whole obstacle while the freely rotating part of scroll wave above the obstacle remained untwisted. The transient time increases exponentially with the tilted angle.

Under axial and azimuthal magnetic inductions, the similarity solutions for a cylindrical shock wave in a weakly conducting ideal gas are determined using the Lie group invariance method. The axial and azimuthal magnetic inductions and density are presumed to vary in an ambient medium. This study determines the form of expression for axial and azimuthal magnetic inductions in the ambient medium. The ambient density is considered to be varying according to the power law of the shock radius. The weakly conducting medium causes inadequate magnetic freezing. We have numerically solved the system of ordinary differential equations that resulted from applying the Lie group invariance method to the system of partial differential equations. The impact of the variation in the ambient density exponent, the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers on the shock strength and the flow variables behind the shock front is discussed. It is found that the shock strength decreases with an increase in the ratio of specific heats, magnetic Reynolds number, or the inverse square of axial and azimuthal Alfven Mach numbers.