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.     

Synthesis of chirped apodized fiber Bragg grating parameters using Direct Tabu Search algorithm: Application to the determination of thermo-optic and thermal expansion coefficients

In this paper, Direct Tabu Search (DTS) is proposed to synthesize the physical parameters of a fiber Bragg grating (FBG) numerically from its reflection response. A reflected spectrum is being calculated by using the Transfer Matrix Method (TMM). Direct search based strategies are used to direct a tabu search. These strategies are based on a new pattern search procedure called Adaptive Pattern Search (APS). In addition, the well-known Nelder-Mead (NME) algorithm is used as a local search method at the final stage of the optimization process. Direct Tabu Search (DTS) is applied for reconstruction of a raised cosine chirped fiber Bragg grating (CFBG) and a Gaussian multi channel fiber grating. The method is then used to synthesize a CFBG from its reflectivity taken at different temperatures. It gives a good estimate of the thermal expansion coefficient and the thermo-optic coefficient of the fiber.     

Oxonitriles: a grignard addition-acylation route to enamides

[reaction: see text] Sequential addition of three different Grignard reagents and pivaloyl chloride to 3-oxo-1-cyclohexene-1-carbonitrile installs four new bonds to generate a diverse array of cyclic enamides. Remarkably, formation of the C-magnesiated nitrile intermediate is followed by preferential acylation by pivaloyl chloride rather than consumption by an in situ Grignard reagent. Rapid N-acylation of the C-magnesiated nitrile generates an acyl ketenimine that reacts readily with Grignard reagents or a trialkylzincate, effectively assembling highly substituted, cyclic enamides.     

Reversible interconversion between a supramolecular polymer and a discrete octameric species from a guanosine derivative by dynamic cation binding and release

[reaction: see text] The tunable interconversion between two highly ordered supramolecular motifs (G-quartet K(+)-templated column and G-ribbon) of a lipophilic guanosine derivative fueled by cation complexation and release in a cryptand [2.2.2] containing guanosine solution is reported. The process is controlled by the sequential addition of acid and base.     

Cyclicity in the Dirichlet space

Let be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We give a new sufficient condition, not far from the known necessary condition, for a function f∈ to be cyclic, i.e. for {pf: p is a polynomial} to be dense in . The proof is based on the notion of Bergman–Smirnov exceptional set introduced by Hedenmalm and Shields. Our methods yield the first known examples of such sets that are uncountable. One of the principal ingredients of the proof is a new converse to the strong-type inequality for capacity.     

Heat-kernel estimates for random walk among random conductances with heavy tail

We study models of discrete-time, symmetric, Z^d${\mathbb{Z}}^d$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances _ωxy∈[0,1]${\omega }_{xy}\in [0,1]$, with polynomial tail near 0 with exponent γ>0$\gamma >0$. We first prove for all d≥5$d\ge 5$ that the return probability shows an anomalous decay (non-Gaussian) that approaches (up to sub-polynomial terms) a random constant times n⁻²$n^{-2}$ when we push the power γ$\gamma$ to zero. In contrast, we prove that the heat-kernel decay is as close as we want, in a logarithmic sense, to the standard decay n^−d/2$n^{-d/2}$ for large values of the parameter γ$\gamma$.