A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

光学特异材料的设计

In this contribution we review our latest achievements of combined experimental and theoretical studies to tailor the properties of optical metamaterials（MMs） at will. We give three examples of metamaterial designs that have been realized by means of electron-beam lithography and whose spectroscopic characteristics have been comprehensively investigated. In every case, our experiments are complemented by rigorous numer ical simulations. Particular emphasis is put on the significance of such tailored effective properties of optical MMs     

The equivalence theorem for the heavy-Higgs Standard Model and the gauged nonlinear σ-model

The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons. The validity of this theorem within the standard model with a heavy Higgs boson and within the gauged nonlinear -model (in which the Higgs boson is absent) is shown. Furthermore it is examined to what extent also internal lines other than scalar lines can be neglected. A simple power-counting method is developed which determines the leading diagrams for a given process at an arbitrary loop order. This method is also applied to effective Lagrangians with additional nonstandard interaction terms of higher dimension (chiral Lagrangians).     

Investigating generation mechanisms of tyre/road noise by speed exponent analysis

The purpose of this study is to clarify the influence of air-pumping related noise sources on typical tyre/road noise. The aim is to increase the understanding of noise generation mechanisms and catalyse the development of existing tyre/road noise simulation tools. The speed dependency of measured and simulated tyre/road noise is analysed and the results show that a large part of the noise can be explained by a high speed exponent traditionally connected with air-pumping mechanisms. Surprisingly, this is also the case for rough road surfaces which are expected to mainly generate noise by tyre vibrations. It is also found that vehicle wind noise may have a strong influence on the pass-by noise and care must be taken when analysing measurement data of quiet tyre/road combinations. Even simulated tyre/road noise shows higher speed exponents than what is anticipated without the inclusion of any type of air-pumping mechanism in the model. It is concluded that it is unfeasible to separate noise created by tyre vibrations from noise created by air-pumping with a speed exponent analysis due to the overlap in the speed exponents connected with the different generation mechanisms.     

All-fiber mode-locked fiber laser

An environmentally stable mode-locked fiber laser based on nonlinear polarization rotation is experimentally demonstrated. The laser is based on a novel laser configuration that has negligible low-power steady-state reflectivity from one side and, consequently, no CW gain. The laser is self starting and the configuration is implementable as an all-fiber laser with standard polarization-maintaining fiber-pigtailed components. A pulse duration of 5.6 ps is obtained at a repetition rate of 5.96 MHz and at an average power of 8 mW. As an application of the proposed laser configuration, 213 mW of supercontinuum (600-1750 nm) was demonstrated from a fiber laser system with no sections of free-space optics.     

Sensing and compensation of femtosecond waveform distortion induced by all-order polarization mode dispersion at selected polarization states

We demonstrate full characterization of femtosecond pulse distortion induced by all-order polarization mode dispersion (PMD) at selected polarization states via second-harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements at an average power of under 28 nW. By applying the inverse of the measured spectral phase via a programmable pulse shaper, we compress the distorted pulses from more than 3 ps to nearly bandwidth-limited durations of less than 500 fs. Our results show that SHG FROG measurements performed by using fiber-pigtailed aperiodically poled lithium niobate waveguides can serve as a robust and sensitive tool for characterization of PMD-induced spectral phase.     

Bosonic enhancement of spontaneous emission near an interface

We show how the spontaneous emission rate of an excited two-level atom placed in a trapped Bose-Einstein condensate of ground-state atoms is enhanced by bosonic stimulation. This stimulation depends on the overlap of the excited matter-wave packet with the macroscopically occupied condensate wave function, and provides a probe of the spatial coherence of the Bose gas. The effect can be used to amplify the distance-dependent decay rate of an excited atom near an interface.     

Breather Solutions in Periodic Media

For nonlinear wave equations existence proofs for breathers are very rare. In the spatially homogeneous case up to rescaling the sine-Gordon equation \({\partial^2_t u = \partial^2_x u - \sin (u)}\) is the only nonlinear wave equation which is known to possess breather solutions. For nonlinear wave equations in periodic media no examples of breather solutions have been known so far. Using spatial dynamics, center manifold theory and bifurcation theory for periodic systems we construct for the first time such time periodic solutions of finite energy for a nonlinear wave equation

$ s(x) \partial^2_t u(x,t) = \partial^2_x u(x,t) - q(x) u(x,t)+ r(x)u(x,t)^3, $

with spatially periodic coefficients s, q, and r on the real axis. Such breather solutions play an important role in theoretical scenarios where photonic crystals are used as optical storage.