An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.     

New Perspectives for Old Clusters: Anderson–Evans Anions as Building Blocks of Large Polyoxometalate Frameworks in a Series of Heterometallic 3 d–4 f Species

A series of nine [Sb₇W₃₆O₁₃₃Ln₃M₂(OAc)(H₂O)₈]^17? heterometallic anions ( Ln₃M₂ ; Ln=La–Gd, M=Co; Ln=Ce, M=Ni and Zn) have been obtained by reacting 3 d metal disubstituted Krebs‐type tungstoantimonates(III) with early lanthanides. Their unique tetrameric structure contains a novel {MW₉O₃₃} capping unit formed by a planar {MW₆O₂₄} fragment to which three {WO₂} groups are condensed to form a tungstate skeleton identical to that of a hypothetical trilacunary derivative of the ?‐Keggin cluster. It is shown, for the first time, that classical Anderson–Evans {MW₆O₂₄} anions can act as building blocks to construct purely inorganic large frameworks. Unprecedented reactivity in the outer ring of these disk‐shaped species is also revealed. The Ln₃M₂ anions possess chirality owing to a {Sb₄O₄} cluster being encapsulated in left‐ or right‐handed orientations. Their ability to self‐associate in blackberry‐type vesicles in solution has been assessed for the Ce₃Co₂ derivative.     

In Situ Generation of ArCu from CuF2 Makes Coupling of Bulky Aryl Silanes Feasible and Highly Efficient

A bimetallic system of Pd/CuF₂, catalytic in Pd and stoichiometric in Cu, is very efficient and selective for the coupling of fairly hindered aryl silanes with aryl, anisyl, phenylaldehyde, p‐cyanophenyl, p‐nitrophenyl, or pyridyl iodides of conventional size. The reaction involves the activation of the silane by Cu^II, followed by disproportionation and transmetalation from the Cu^I(aryl) to Pd^II, upon which coupling takes place. Cu^III formed during disproportionation is reduced to Cu^I(aryl) by excess aryl silane, so that the CuF₂ system is fully converted into Cu^I(aryl) and used in the coupling. Moreover, no extra source of fluoride is needed. Interesting size selectivity towards coupling is found in competitive reactions of hindered aryl silanes. Easily accessible [PdCl₂(IDM)(AsPh₃)] (IDM = 1,3‐dimethylimidazol‐2‐ylidene) is by far the best catalyst, and the isolated products are essentially free from As or Pd (<1 ppm). The mechanistic aspects of the process have been experimentally examined and discussed.     

Dimension reduction for semidefinite programs via Jordan algebras

Mathematical Programming - We propose a new method for simplifying semidefinite programs (SDP) inspired by symmetry reduction. Specifically, we show if an orthogonal projection map satisfies...