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Experimental observations are presented of a single surface-piercing column subject to a wide range of surface gravity waves. With the column diameter, D, chosen such that the flow lies within the drag-inertia regime, two types of high-frequency wave scattering are identified. The first is driven by the run-up and wash-down on the surface of the column in the vicinity of the upstream and downstream stagnation points. The second concerns the circulation of fluid around the column, leading to the scattering of a pair of non-concentric wavefronts. The phasing of the wave cycle at which this second mode evolves is dependent upon the time taken for fluid to move around the column. This introduces an additional time-scale, explaining why existing diffraction solutions, based upon a harmonic analysis of the incident waves, cannot describe this scattered component. The interaction between the scattered waves and the next (steep) incident wave can produce a large amplification of the scattered waves, particularly the second type. Evidence is provided to show that these interactions can produce highly localized free-surface effects, including vertical jetting, with important implications for the setting of deck elevations, the occurrence of wave slamming and the development of large run-up velocities.

The precipitation of tens to hundreds of keV electrons from Earth's magnetosphere plays a crucial role in magnetosphere‐ionosphere coupling, primarily driven by chorus wave scattering. Most existing simulations of electron precipitation rely on test particle models that neglect particle feedback on waves. However, both theoretical and observational studies indicate that the feedback from energetic electrons significantly influences chorus wave excitation and evolution. In this study, we quantify electron precipitation driven by chorus waves using self‐consistent simulations at L = 6 with typical magnetospheric plasma parameters. Electrons in the ∼10–200 keV range are precipitated, exhibiting energy‐dispersive characteristics. The precipitation intensity reaches ∼108–109 ${10}^{8}\\!\\mathit{\\mbox{--}}\\!{10}^{9}$ keV/s/sr/cm2/MeV $\\mathrm{k}\\mathrm{e}\\mathrm{V}/\\mathrm{s}/\\mathrm{s}\\mathrm{r}/{\\mathrm{c}\\mathrm{m}}^{2}/\\mathrm{M}\\mathrm{e}\\mathrm{V}$, consistent with the typical values in observations. As a comparison, test particle simulations underestimate the precipitation intensity by nearly an order of magnitude. These results highlight the importance of self‐consistent simulations in quantifying electron precipitation and investigating wave‐particle interactions that modulate magnetospheric dynamics.

The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.

Thermal noise from optical coatings is a growing area of concern and overcoming limits to the sensitivity of high precision measurements by thermal noise is one of the greatest challenges faced by experimental physicists. In this timely book, internationally renowned scientists and engineers examine our current theoretical and experimental understanding. Beginning with the theory of thermal noise in mirrors and substrates, subsequent chapters discuss the technology of depositing coatings and state-of-the-art dielectric coating techniques used in precision measurement. Applications and remedies for noise reduction are also covered. Individual chapters are dedicated to specific fields where coating thermal noise is a particular concern, including the areas of quantum optics/optomechanics, gravitational wave detection, precision timing, high-precision laser stabilisation via optical cavities and cavity quantum electrodynamics. While providing full mathematical detail, the text avoids field-specific jargon, making it a valuable resource for readers with varied backgrounds in modern optics.

In this paper, we study the 3D elastic scattering problem of plane dyadic waves for a rigid body and a cavity in linear elasticity. Initially, for each case, we formulate the direct scattering problem in a dyadic form, and we give the corresponding longitudinal and transverse far-field scattering amplitudes. Due to dyadic formulation of the problems, the main outcome of this paper is to establish the necessary energy considerations as well as to present functionals and formulas for the differential and the scattering cross-section in order to measure the disturbance created by the scatterer to the propagation of the plane dyadic incident field. Further, we assume that our incident field is scattered by a “small” rigid body or cavity and relative results for low-frequency scattering are obtained. Finally, we prove similar corresponding expressions for energy functionals in the far-field region, along with expressions for the differential and the total scattering cross-section, which are recovered as special cases.

Resonant filament-assisted mode conversion (FAMC) scattering of high harmonic fast waves (HHFW) by cylindrical field-aligned density inhomogeneities can efficiently redirect a fraction of the launched HHFW power flux into the parallel direction. Within a simplified analytic approach, this contribution compares the parallel propagation, reflection and dissipation of nearly resonant FAMC modes for three magnetic field line geometries in the scrape-off layer, in the presence of radio-frequency (RF) sheaths at field line extremities and phenomenological wave damping in the plasma volume. When a FAMC mode, excited at the HHFW antenna parallel location and guided along the open magnetic field lines, impinges onto a boundary at normal incidence, we show that it can excite sheath RF oscillations, even toroidally far away from the HHFW launcher. The RF sheaths then dissipate part of the power flux carried by the incident mode, while another part reflects into the FAMC mode with the opposite wave vector parallel to the magnetic field. The reflected FAMC mode in turn propagates and can possibly interact with the sheath at the opposite field line boundary. The two counter-propagating modes then form in the bounded magnetic flux tube a lossy cavity excited by the HHFW scattering. We investigate how the presence of field line boundaries affects the total HHFW power redirected into the filament, and its splitting between sheath and volume losses, as a function of relevant parameters in the model.

This paper deals with a high-order H ( curl ) -conforming Bernstein–Bézier finite element method (BBFEM) to accurately solve time-harmonic Maxwell short wave problems on unstructured triangular mesh grids. We suggest enhanced basis functions, defined on the reference triangle and tetrahedron, aiming to reduce the condition number of the resulting global matrix. Moreover, element-level static condensation of the interior degrees of freedom is performed in order to reduce memory requirements. The performance of BBFEM is assessed using several benchmark tests. A preliminary analysis is first conducted to highlight the advantage of the suggested basis functions in improving the conditioning. Numerical results dealing with the electromagnetic scattering from a perfect electric conductor demonstrate the effectiveness of BBFEM in mitigating the pollution effect and its efficiency in capturing high-order evanescent wave modes. Electromagnetic wave scattering by a circular dielectric, with high wave speed contrast, is also investigated. The interior curved interface between layers is accurately described based on a linear blending map to avoid numerical errors due to geometry description. The achieved results support our expectations for highly accurate and efficient BBFEM for time harmonic wave problems.

The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient and high-precision numerical algorithm for the time harmonic elastic wave scattering problems from cornered domains via the boundary integral equations in two dimensions. The approach is based on the combination of Nyström discretization, analytical singular integrals and kernel-splitting method, which results in a high-order solver for smooth boundaries. It is then combined with the recursively compressed inverse preconditioning (RCIP) method to solve elastic scattering problems from cornered domains. Numerical experiments demonstrate that the proposed approach achieves high accuracy, with stabilized errors close to machine precision in various geometric configurations. The algorithm is further applied to investigate the asymptotic behavior of density functions associated with boundary integral operators near corners, and the numerical results are highly consistent with the theoretical formulas.

The scattering problem of elastic waves impinging on periodic single and double arrays of parallel cylindrical defects is considered for isotropic materials. An analytic expression for the scattering matrix is obtained by means of the Lippmann–Schwinger formalism and analyzed in the long-wavelength approximation. It is proved that, for a specific curve in the space of physical and geometrical parameters, the scattering is dominated by resonances. The shear mode polarized parallel to the cylinders is decoupled from the other two polarization modes due to the translational symmetry along the cylinders. It is found that a relative mass density and relative Lamé coefficients of the scatterers give opposite contributions to the width of resonances in this mode. A relation between the Bloch phase and material parameters is found to obtain a global minimum of the width. The minimal width is shown to vanish in the leading order of the long wavelength limit for the single array. This new effect is not present in similar acoustic and photonic systems. The shear and compression modes in a plane perpendicular to the cylinders are coupled due to the normal traction boundary condition and have different group velocities. For the double array, it is proved that, under certain conditions on physical and geometrical parameters, there exist resonances with the vanishing width, known as Bound States in the Continuum (BSC). Necessary and sufficient conditions for the existence of BSC are found for any number of open diffraction channels. Analytic BSC solutions are obtained. Spectral parameters of BSC are given in terms of the Bloch phase and group velocities of the shear and compression modes.

Topological laws of the Rayleigh wave scattering on a statistical inhomogeneity of an isotropic solid are obtained theoretically in the Rayleigh limit of scattering. They are defined completely by the structure of the inhomogeneity and include the Rayleigh law of scattering as a particular case. Violation by them of the Rayleigh law in cases of a more general topology of inhomogeneity, than the Rayleigh one, enables first to construct theoretically arbitrary form of scattering spectrum up to its oscillations and strong angular anisotropy in the Rayleigh limit of scattering.