A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

FFLUX: Transferability of polarizable machine‐learned electrostatics in peptide chains

The fully polarizable, multipolar, and atomistic force field protein FFLUX is being built from machine learning (i.e., kriging) models, each of which predicts an atomic property. Each atom of a given protein geometry needs to be assigned such a kriging model. Such a knowledgeable atom needs to be informed about a sufficiently large environment around it. The resulting complexity can be tackled by collecting the 20 natural amino acids into a few groups. Using substituted deca‐alanines, we present the proof‐of‐concept that a given atom's charge can be modeled by a few kriging models only. © 2017 Wiley Periodicals, Inc.     

Explicit uniform bounds on integrals of Bessel functions and trace theorems for Fourier transforms

Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L² restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived.     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

Carbon nanospheres with well‐controlled nano‐morphologies as support for palladium‐catalyzed Suzuki coupling reaction

Uniform carbon nanospheres (UCS) with well‐controlled nano‐morphologies were fabricated by hydrothermal carbonization of sucrose in the presence of kayexalate. Highly dispersed and ultrafine palladium nanoparticles were supported on the UCS through a facile co‐reduction process with NaBH₄ as reducing agent. The obtained Pd@UCS exhibited efficient catalytic activity for the Suzuki coupling reaction. Moreover, the as‐prepared catalyst could be recycled and reused at least five times without significant loss of its catalytic activity.     

几种吊钩中的力学问题探析

对吊装机械中使用的几种吊钩在吊装重物时的受力情况进行分析和比较,说明了各自的特点及其应用.     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].