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In this paper, we show how the Kronecker product can be useful in simplifying the notation encountered in the analysis of linearly coupled systems where the cells are identical and the coupling is uniform. We give two applications where this is useful. First we use it in the analysis of Turing patterns in reaction-diffusion systems to obtain conditions for the coupling to destabilize the uniform equilibrium point. In the second application we use the Kronecker product to obtain simple sufficient conditions for an array of linearly coupled dynamical systems to synchronize. We discuss briefly extensions to additive nonlinear coupling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
This is the FLUXNET2015 version of the carbon flux data for the site US-Ton Tonzi Ranch.
A poly(aryl ether) dendrimer bearing 22 allyl groups throughout the interior of the molecule has been prepared using a convergent synthetic approach. The internal functionalities of this dendrimer can be used to attach small molecule guests to the interior of the dendrimer using olefin metathesis. A ruthenium-based Grubbs catalyst was used to covalently attach an allylated pyrene and imidazolidinone via cross-metathesis. The extent of coupling was estimated by UV, NMR, and elemental analysis data. The high tolerance of cross-metathesis to a range of functional groups enables the incorporation of a wide range of molecules and provides access to different inner environments in one step from a single source of dendrimer.
It is noted that at near-threshold levels, in addition to the role of plasticity-and oxide-induced crackclosure, fracture surface roughness or morphology may promote significant closure effects in plane strain, as similarly noted by Minakawa and McEvily.This is considered to result from the fact that, where maximum plastic zones sizes are small compared to the grain size, fatigue crack growth proceeds by a single shear decohesion mechanism (Stage I) with associated Mode II+I displacements. The resulting serrated or faceted fracture surfaces (“microstructurally-sensitive growth”) coupled with Mode II crack tip displacements thus induce high closure loads (i.e., K cl/K max ~0.5) by wedging the crack open at discrete contact points. At higher growth rates where the plastic zone encompasses many grains, striation growthvia alternating or simultaneous shear mechanisms (Stage II) produces a more planar fracture surface, with pure Mode I displacements, and a corresponding reduction in closure loads. Such concepts of roughness-induced closure are shown to be consistent with observations of the role of coarse grain sizes in reducing near-threshold crack growth rates at low load ratios and of the absence of this effect at high load ratios.
A user-oriented computer program based on the iterative piecewise-linear method is described, which offers a more general approach for analysing multivalued networks than the more commonly used Newton-Raphson method.
Nitrogen atom transfer from salen-derived nitridomanganese(V) to manganese(III) Schiff-base complexes occurs under aerobic conditions in solution at room temperature. A mechanism involving chloride dissociation followed by the formation and decay of a binuclear μ-nitrido-activated complex accounts satisfactorily for the observed kinetics data.
[(CyPF-t-Bu)PdCl2] has been found to be a highly efficient, air- and moisture-resistant catalyst for the aminative coupling of heteroaryl chlorides, bromides and iodides to a variety of primary amines. The required catalyst loading is extremely low, most reactions give a high yield of product with 0.001-0.05 mol% of catalyst. A wide range of functional groups is tolerated in this amination reaction.