Inverse Problem for the Wave Equation with a White Noise Source

We consider a smooth Riemannian metric tensor g on \({\mathbb{R}^n}\) and study the stochastic wave equation for the Laplace-Beltrami operator \({\partial_t^2 u - \Delta_g u = F}\) . Here, F = F(t, x, ω) is a random source that has white noise distribution supported on the boundary of some smooth compact domain \({M \subset \mathbb{R}^n}\) . We study the following formally posed inverse problem with only one measurement. Suppose that g is known only outside of a compact subset of M ^int and that a solution \({u(t, x, \omega_0)}\) is produced by a single realization of the source \({F(t, x, \omega_0)}\) . We ask what information regarding g can be recovered by measuring \({u(t, x, \omega_0)}\) on \({\mathbb{R}_+ \times \partial M}\) ? We prove that such measurement together with the realization of the source determine the scattering relation of the Riemannian manifold (M, g) with probability one. That is, for all geodesics passing through M, the travel times together with the entering and exit points and directions are determined. In particular, if (M, g) is a simple Riemannian manifold and g is conformally Euclidian in M, the measurement determines the metric g in M.     

Engaging concert hall acoustics is made up of temporal envelope preserving reflections

Strong, exciting, and engaging sound is perceived in the best concert halls. Here, it is shown that wideband early reflections that preserve the temporal envelope of sound contribute to the clear and open acoustics with strong bass. Such reflections are fused with the direct sound due to the precedence effect. In contrast, reflections that distort the temporal envelope render the sound weak and muddy because they partially break down the precedence. The presented findings are based on the earlier psychoacoustics research, and confirmed by a perceptual evaluation with six simulated concert halls that have same monaural room acoustical parameter values according to ISO3382-1.     

Surface functionalization of nanofibrillated cellulose using click-chemistry approach in aqueous media

In the present work, amino functionalized nanofibrillated cellulose (NFC) was prepared using click-chemistry in aqueous reaction conditions. First, reactive azide groups were introduced on the surface of NFC by the etherification of 1-azido-2,3-epoxypropane in alkaline water/isopropanol-mixture at ambient temperature. Then the azide groups were reacted with propargyl amine utilizing copper catalyzed azide-alkyne cycloaddition (CuAAC), leading to pH-responsive 1,2,3-triazole-4-methanamine decorated NFC. The reaction products were characterized using Fourier transform infrared spectroscopy, elemental analysis and X-ray photoelectron spectroscopy. The presence of the attached azide groups was also confirmed by reacting them with 5-(dimethylamino)-N-(2-propyl)-1-naphthalenesulfonamide by CuAAC, yielding highly fluorescent NFC. In addition, atom force microscopy and rheology studies confirmed that the original NFC nanostructure was maintained during the synthesis.