非线性玻尔兹曼方程的傅里叶谱方法

玻尔兹曼方程作为空气动理学中最基本的方程之一,是连接微观牛顿力学和宏观连续介质力学的重要桥梁.该方程描述了一个由大量粒子组成的复杂系统的非平衡态时间演化:除了基本的输运项,其最重要的特性是粒子间的相互碰撞由一个高维,非局部且非线性的积分算子来描述,从而给玻尔兹曼方程的数值求解带来非常大的挑战.在过去的二十年间,基于傅里叶级数的谱方法成为了数值求解玻尔兹曼方程的一种很受欢迎且有效的确定性算法.这主要归功于谱方法的高精度及它可以被快速傅里叶变换加速的特质.本文将回顾玻尔兹曼方程的傅里叶谱方法,具体包括方法的导出,稳定性和收敛性分析,快速算法,以及在一大类基于碰撞的空气动理学方程中的推广.     

Conservative and Semismooth Derivatives are Equivalent for Semialgebraic Maps

Set-Valued and Variational Analysis - Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties: conservativity for the...     

Upcycling of Polybutadiene Facilitated by Selenium-Mediated Allylic Amination

Accumulation of end-of-life plastics presents ongoing environmental concerns. One strategy to solve this grand challenge is to invent new techniques that modify post-consumer waste and impart new functionality. While promising approaches for the chemical upcycling of commodity polyolefins and polyaromatics exist, analogous approaches to repurpose unsaturated polymers (e.g., polybutadiene) are scarce. In this work, we propose a method to upcycle polybutadiene, one of the most widely used commercial rubbers, via a mild, metal-free allylic amination reaction. The resulting materials have tunable thermal and surface wetting properties as a function of both sulfonamide identity and grafting density. Importantly, this approach maintains the parent alkene microstructure without evidence of olefin reduction, olefin transposition, and/or chain scission. Based on these findings, we anticipate future applications in the remediation of complex elastomers and vulcanized rubbers.     

Protonation and Proton‐Coupled Electron Transfer at S‐Ligated [4Fe‐4S] Clusters

Biological [Fe‐S] clusters are increasingly recognized to undergo proton‐coupled electron transfer (PCET), but the site of protonation, mechanism, and role for PCET remains largely unknown. Here we explore this reactivity with synthetic model clusters. Protonation of the arylthiolate‐ligated [4Fe‐4S] cluster [Fe₄S₄(SAr)₄]^2? ( 1 , SAr=S‐2,4‐6‐(iPr)₃C₆H₂) leads to thiol dissociation, reversibly forming [Fe₄S₄(SAr)₃L]^1? ( 2 ) and ArSH (L=solvent, and/or conjugate base). Solutions of 2 +ArSH react with the nitroxyl radical TEMPO to give [Fe₄S₄(SAr)₄]^1? ( 1_ox ) and TEMPOH. This reaction involves PCET coupled to thiolate association and may proceed via the unobserved protonated cluster [Fe₄S₄(SAr)₃(HSAr)]^1? ( 1‐H ). Similar reactions with this and related clusters proceed comparably. An understanding of the PCET thermochemistry of this cluster system has been developed, encompassing three different redox levels and two protonation states.     

Optofluidic microsystem with quasi-3 dimensional gold plasmonic nanostructure arrays for online sensitive and reproducible SERS detection

Practical applications of chemical and biological detections through surface-enhanced Raman scattering (SERS) require high reproducibility, sensitivity, and efficiency, along with low-cost, straightforward fabrication. In this work, we integrated a poly-(dimethylsiloxane) (PDMS) chip with quasi-3D gold plasmonic nanostructure arrays (Q3D-PNAs), which serve as SERS-active substrates, into an optofluidic microsystem for online sensitive and reproducible SERS detections. The Q3D-PNA PDMS chip was fabricated through soft lithography to ensure both precision and low-cost fabrication. The optimal dimension of the Q3D-PNA in PDMS was designed using finite-difference time-domain (FDTD) electromagnetic simulations with a simulated enhancement factor (EF) of 1.6 × 10⁶. The real-time monitoring capability of the SERS-based optofluidic microsystem was investigated by kinetic on/off experiments through alternatively flowing Rhodamine 6G (R6G) and ethanol in the microfluidic channel. A switch-off time of ∼2 min at a flow rate of 0.3 mL min⁻¹ was demonstrated. When applied to the detection of low concentration malathion, the SERS-based optofluidic microsystem with Q3D-PNAs showed high reproducibility, significantly improved efficiency and higher detection sensitivity via increasing the flow rate. The optofluidic microsystem presented in this paper offers a simple and low-cost approach for online, label-free chemical and biological analysis and sensing with high sensitivity, reproducibility, efficiency, and molecular specificity.     

Fe-N/C catalysts for oxygen reduction based on silicon carbide derived carbon

Two different Fe-N/C(SiC) catalysts (Fe + Bipyr/C(SiC) and Fe + Phen/C(SiC)) for oxygen reduction based on silicon carbide derived carbon were synthesized and investigated in 0.1 M KOH aqueous solution by rotating disc electrode method. It was found that the electrocatalytic activity and stability are significantly influenced by the change of the nitrogen ligand in the catalyst. Comparable current density values obtained for 20%Pt-Vulcan electrode could be achieved for Fe + Bipyr/C(SiC) and Fe + Phen/C(SiC) catalysts in alkaline media. The durability tests (~ 150 h) showed that the decrease of the activity for Fe + Bipyr/C(SiC) and Fe + Phen/C(SiC) is only 0.5 mV h^− 1 and 0.17 mV h^− 1, respectively. The Fe + Bipyr/C(SiC) catalyst demonstrated higher activity in the RDE measurements, but during the long-term test the Fe + Phen/C(SiC) catalyst prove to be more stable than Fe + Bipyr/C(SiC).     

Approximate solutions for the shear center of plates of variable thickness

Summary In a plate-theoretical formulation of the shear center problem, the relevant boundary-value problem is for a cantilevered rectangular plate of variable thickness with two free opposite edges and with the edge opposite to the clamped end subject to a rigid vertical displacement and free of bending moment. For plates with Poisson's ratiov equal to zero, there is an exact elementary solution for this boundary-value problem from which the exact location of the shear center can be calculated. When Poisson's ratio is not zero, an approximate elementary solution may be obtained within the framework of a Saint-Venant flexure solution for plates by satisfying the displacement boundary conditions at the clamped edge approximately. Different forms of this approximation are discussed in [7], some with rather marked Poisson's ratio effects. Among these, the minimum complementary energy approach of [6] gives a shear center location identical to the exact solution forv=O.A generalized beam theory developed in [6] is implemented here to delineate the effect ofv without altering the edge conditions by ad hoc approximations. The results show that the Poisson's ratio effect is rather moderate and the shear center location is nearly the same as that for zero Poisson's ratio. A finite element solution for the plate theory boundary-value problem confirms this finding.The generalized beam equations are also used to study the effect of the aspect ratio of the plate and orthotropy on the location of the shear center.

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Näherungslösungen für den Schubmittelpunkt von Platten veränderlicher Dicke

Übersicht In der plattentheoretischen Formulierung des Schubmittelpunktproblems [6] betrifft die relevante Randwertaufgabe eine rechteckige Kragplatte mit veränderlicher Dicke in Querrichtung, mit einer Lastverteilung, welche eine gleichförmige Durchbiegung am belasteten Rand erzeugt.Die vorliegende Arbeit implementiert eine Näherungslösung dieses Problems in der Form einer verallgemeinerten Balkentheorie zwölfter Ordnung, welche Verwölbung sowie auch anticlastische Krümmung berücksichtigt [6]. Das Ziel ist, den quantitativen Einfluß der Poissonschen Zahl und auch den der Orthotropie zu bestimmen.Die Resultate zeigen, daß der Einfluß der Poissonschen Zahl, welcher in der bekannten näherungsweisen Bestimmung mit Hilfe des Variationsprinzips für Spannungen vollkommen verschwindet, in der Tat sehr gering ist, insbesondere im Vergleich mit den Folgen einer Anwendung der St.-Venantschen Biegetheorire zusammen mit einer klassischen Stipulierung bezüglich des Verschiebungsfeldes am Schwerpunkt der Querschnittsfläche. Darüber hinausgehend wird gezeigt, daß die numerischen Werte nur unwesentlich von Unterschieden zwischen Isotropie und Orthotropie beeinflußt sind.Die obigen Resultate werden durch die Ableitung und Anwendung einer Balkentheorie sechzehnter Ordnung und durch Rechnungen mit Hilfe von Finiten Elementen bestätigt.