On pulsatile flow of non-Newtonian liquids

Rheologica Acta - We consider the behaviour of non-Newtonian liquids as they are made to flow through straight pipes of circular cross section under the action of a pressure -gradient which...     

Catalytic enantioselective Grignard Nozaki-Hiyama methallylation from the alcohol oxidation level: chloride compensates for π-complex instability

Methallyl chloride serves as an efficient allyl donor in highly enantioselective Grignard Nozaki-Hiyama methallylations from the alcohol or aldehyde oxidation level via iridium catalyzed transfer hydrogenation. Under identical conditions, methallyl acetate does not react efficiently. Double methallylation of 1,3-propanediol provides the C(2)-symmetric adduct as a single enantiomer, as determined by HPLC analysis.     

On the temperature dependence of the F-coloring efficiency in KCl

A simple model is presented to account for the major features of the temperature dependence of the primary F-coloring efficiency in KCl. It assumes that irradiation creates Frenkel pairs in three basic configurations followed by some correlated diffusion, leading either to annihilation of the pair or formation of a “surviving” primary pair. Steady irradiation as well as fast pulse data are analyzed in terms of the model.     

Learning Elliptic Partial Differential Equations with Randomized Linear Algebra

Given input–output pairs of an elliptic partial differential equation (PDE) in three dimensions, we derive the first theoretically rigorous scheme for learning the associated Green’s function G. By exploiting the hierarchical low-rank structure of G, we show that one can construct an approximant to G that converges almost surely and achieves a relative error of \(\mathcal {O}(\varGamma _\epsilon ^{-1/2}\log ^3(1/\epsilon )\epsilon )\) using at most \(\mathcal {O}(\epsilon ^{-6}\log ^4(1/\epsilon ))\) input–output training pairs with high probability, for any \(0<\epsilon <1\). The quantity \(0<\varGamma _\epsilon \le 1\) characterizes the quality of the training dataset. Along the way, we extend the randomized singular value decomposition algorithm for learning matrices to Hilbert–Schmidt operators and characterize the quality of covariance kernels for PDE learning.