Hydrogen-Bond Catalysis of Imine Exchange in Dynamic Covalent Systems

The reversibility of imine bonds has been exploited to great effect in the field of dynamic covalent chemistry, with applications such as preparation of functional systems, dynamic materials, molecular machines, and covalent organic frameworks. However, acid catalysis is commonly needed for efficient equilibration of imine mixtures. Herein, it is demonstrated that hydrogen bond donors such as thioureas and squaramides can catalyze the equilibration of dynamic imine systems under unprecedentedly mild conditions. Catalysis occurs in a range of solvents and in the presence of many sensitive additives, showing moderate to good rate accelerations for both imine metathesis and transimination with amines, hydrazines, and hydroxylamines. Furthermore, the catalyst proved simple to immobilize, introducing both reusability and extended control of the equilibration process.     

Surface integral analogy approaches for predicting noise from 3D high-lift low-noise wings

Three surface integral approaches of the acoustic analogies are studied to predict the noise from three concep- tual configurations of three-dimensional high-lift low-noise wings. The approaches refer to the Kirchhoff method, the Ffowcs Williams and Hawkings （FW-H） method of the permeable integral surface and the Curle method that is known as a special case of the FW-H method. The first two approaches are used to compute the noise generated by the core flow region where the energetic structures exist. The last approach is adopted to predict the noise specially from the pressure perturbation on the wall. A new way to con- struct the integral surface that encloses the core region is proposed for the first two methods. Considering the local properties of the flow around the complex object-the actual wing with high-lift devices-the integral surface based on the vorticity is constructed to follow the flow structures. The surface location is discussed for the Kirchhoff method and the FW-H method because a common surface is used for them. The noise from the core flow region is studied on the basis of the dependent integral quantities, which are indicated by the Kirchhoff formulation and by the FW-H formulation. The role of each wall component on noise contribution is analyzed using the Curle formulation. Effects of the volume integral terms of Lighthill＇s stress tensors on the noise pre-diction are then evaluated by comparing the results of the Curle method with the other two methods.     

Complexes with Atomic Gold Ions: Efficient Bis-Ligand Formation

Complexes of atomic gold with a variety of ligands have been formed by passing helium nanodroplets (HNDs) through two pickup cells containing gold vapor and the vapor of another dopant, namely a rare gas, a diatomic molecule (H₂, N₂, O₂, I₂, P₂), or various polyatomic molecules (H₂O, CO₂, SF₆, C₆H₆, adamantane, imidazole, dicyclopentadiene, and fullerene). The doped HNDs were irradiated by electrons; ensuing cations were identified in a high-resolution mass spectrometer. Anions were detected for benzene, dicyclopentadiene, and fullerene. For most ligands L, the abundance distribution of AuL_n⁺ versus size n displays a remarkable enhancement at n = 2. The propensity towards bis-ligand formation is attributed to the formation of covalent bonds in Au⁺L₂ which adopt a dumbbell structure, L-Au⁺-L, as previously found for L = Xe and C₆₀. Another interesting observation is the effect of gold on the degree of ionization-induced intramolecular fragmentation. For most systems gold enhances the fragmentation, i.e., intramolecular fragmentation in AuL_n⁺ is larger than in pure L_n⁺. Hydrogen, on the other hand, behaves differently, as intramolecular fragmentation in Au(H₂)_n⁺ is weaker than in pure (H₂)_n⁺ by an order of magnitude.     

Dynamic Covalent Organocatalysts Discovered from Catalytic Systems through Rapid Deconvolution Screening

The first example of a bifunctional organocatalyst assembled through dynamic covalent chemistry (DCC) is described. The catalyst is based on reversible imine chemistry and can catalyze the Morita–Baylis–Hillman (MBH) reaction of enones with aldehydes or N‐tosyl imines. Furthermore, these dynamic catalysts were shown to be optimizable through a systemic screening approach, in which large mixtures of catalyst structures were generated, and the optimal catalyst could be directly identified by using dynamic deconvolution. This strategy allowed one‐pot synthesis and in situ evaluation of several potential catalysts without the need to separate, characterize, and purify each individual structure. The systems were furthermore shown to catalyze and re‐equilibrate their own formation through a previously unknown thiourea‐catalyzed transimination process.     

PIV measurements of velocities and concentrations of wood fibres in pneumatic transport

A method for simultaneous measurement of the concentration and velocity of wood fibres suspended in air was developed. The velocity of the wood fibres was measured by the use of particle image velocimetry (PIV). The concentration of wood fibres was measured using the raw images from the PIV equipment as input data. An image processing procedure was used to determine the volume fraction of the fibre particles in the images. The method gave good qualitative and quantitative results for low volume fractions of fibres; for higher volume fractions the quantitative results were unsatisfactory.Latin letters C Concentration of fibres [g/m³] - d Diameter of fibre [m] - M_w Water mass [kg] - M_f Fibre mass [kg] - m Calibration mass flow [kg/s] - m₂₅ Calibration mass flow at C=25 g/m³ [kg/s] - n Fan rpm [-] - t Thickness of light sheet [m] - t Time between laser pulses [s] - U_i Velocity component in i-direction [m/s] - v Streamwise velocity [m/s] - v_average Average streamwise velocity [m/s] - x_i Particle displacement in i-direction [m] Greek letters _f Volume fraction of fibres [-] - _average Average volume fraction of fibres [-] - Area fraction of fibres in image [-] - Density of fibre particle [kg/m³]     

Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension

We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge–Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is asymptotically just O(w^{1/ p})\mathcal {O}(\omega^{1/ p}) for a pth order Runge–Kutta method, where ω is the frequency. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method and can be close to the asymptotic rate.     

Connections Between Classical and Generalised Trajectories of a State/Signal System

In our earlier article “Well-posed state/signal systems in continuous time”, we originally defined the notion of a trajectory of a state/signal system by means of a generating subspace. However, it was left as an open problem whether the generating subspace is uniquely determined by a given family of all generalised trajectories of a well-posed state/signal system. In this article we give a positive answer to this question and show how this insight simplifies some formulations in the theory of well-posed state/signal systems. The main contribution of the article is an explicit convolution scheme for constructing classical trajectories approximating an arbitrary generalised trajectory. We apply this scheme by studying relationships between classical and generalised trajectories of continuous-time state/signal systems under very weak assumptions. Among others, we show that there exists a space of classical trajectories that is invariant under differentiation and dense in the space of generalised trajectories. Some of our results generalise known results for strongly continuous semigroups and input/state/output systems, but we make no use of decompositions of the signal space into an input space and an output space, and in particular, none of our results depend on well-posedness.