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.     

Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

X-ray absorption signatures of hydrogen-bond structure in water–alcohol solutions

Despite fundamental importance, the experimental characterization of the hydrogen bond network, particularly in multicomponent protic solutions, remains a challenge. Although recent work has experimentally validated that the oxygen K-edge X-ray absorption spectra is sensitive to local hydrogen bond patterns in pure water and aqueous alcohol solutions, the generality of this observation is unknown—as is the sensitivity to the electronic structure of the alcohol cosolvent. In this work, we investigate the electronic structure of water solvated alcohol model geometries using energy specific time-dependent density functional theory to calculate oxygen K-edge X-ray excitations. We find that the geometry of dangling hydrogen bonds in pure water is the main contributor to the pre-edge feature seen in the X-ray absorption spectra, agreeing with previous experimental and theoretical work. We then extend this result to solvated alcohol systems and observe a similar phenomenon, yet importantly, the increase of electron donation from alkyl chains to the alcohol OH group directly correlates to the strength of the core excitation on the dangling hydrogen bond model geometry. This trend arises from a stronger transition dipole moment due to electron localization on the OH group.     

Synthesis,self-assembly,and photomechanical actuator performance of a sequence-defined polyviologen crosslinker

ABSTRACT

Although it is well known that viologen radical cations can self-assemble into stacks or complexes on account of radical-radical pairing interactions, it has only recently been demonstrated that reduction of main-chain polyviologens integrated into hydrogel networks can trigger actuation. In these earlier examples, hydrogels comprising oligoethylene glycol-based polyviologens and poly(ethylene glycol) were functionalized with terminal azide groups to prepare ‘click’-based gels. Here, we report a new structural design for the functional polyviologen that consists of main-chain viologen subunits separated by hexamethylene groups instead of glycols and is capped at each end with styrene groups. Activation of this viologen-based macrocrosslinker was achieved using chemical- and photoreduction methods and its ability to undergo intramolecular chain-folding was monitored by absorption spectroscopy. Acrylate-based organogels and hydrogels were also prepared and a comparison was carried out to assess the actuator performance in each gel in terms of the rate of contraction and changes in stiffness.     

Graphene oxide: a surfactant or particle?

Graphene oxide is a two-dimensional carbon nanomaterial that has risen to prominence over the last decade as graphenes water-dispersible counterpart. This key feature offers tremendous potential in the formation of waterborne hybrid materials, coatings, membranes and adsorbents that make use of its diverse surface chemistry and extraordinary surface area. However, the fundamental colloidal properties of graphene oxide remain incompletely understood, with conflicting reports on how the material's amphiphilic nature and adsorption at interfaces render it surfactant-like or particle-like in nature. In the present work, recent developments in understanding the bulk and interfacial colloidal properties of graphene oxide are explored in the context of its chemistry and system thermodynamics, giving insight into the fundamental question of whether its aqueous behaviour is most accurately described as particle-like, surfactant-like or indeed something entirely different.     

Resonance Energy Transfer in a Genetically Engineered Polypeptide Results in Unanticipated Fluorescence Intensity

The fluorescence intensity of a C-terminal acceptor chromophore, N-(7-dimethylamino-4-methyl coumarin (DACM), increased proportionally with 280 nm irradiation of an increasing number of donor tryptophan residues located on a β-sheet forming polypeptide. The fluorescence intensity of the acceptor chromophore increased even as the length of the β-sheet edge approached 256 Å, well beyond the Förster radius for the tryptophan–acceptor chromophore pair. The folding of the peptides under investigation was verified by circular dichroism (CD) and deep UV resonance Raman experiments. Control experiments showed that the enhancement of DACM fluorescence occurred concomitantly with peptide folding. In other control experiments, the DACM fluorescence intensity of the solutions of tryptophan and DACM did not show any enhancement of DACM fluorescence with increasing tryptophan concentrations. Formation of fibrillar aggregates of the substrate peptides prepared for the fluorescence studies was undetectable by thioflavin T (ThT) fluorescence.