Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

基于Matlab GUI的微观化学反应过程可视化设计

Based on the quasi-classical trajectory (QCT) method and Matlab GUI technology, we developed a program code for visualizing the collision process of the elementary chemical reactions of the a + bc type. The general methodology of QCT, abstraction of dynamical properties of molecular collisions and the making of Graphical User Interface are introduced. The running results of an application to the reaction F + HCl→HF + Cl is also presented. The results showed that this program could vividly demonstrate the behavior and final state of the atom-diatom collision process in animated form. Students can interact with internal MATLAB code through graphical user interface, observe the reactive behavior and final results in real-time from multiple angles, which helps students to understand the complex reaction mechanism and deepen their perceptual impression of the chemical process at a microscopic atomic/molecular level.     

Excited-State Dynamics of Non-Luminescent and Luminescent π-Radicals

Recently, the potential use of organic π-radicals and related spin systems has been expanded to modern technological applications. The unique excited-state dynamics of organic π-radicals can be useful to improve the stability of photochemically unstable organic compounds, make the polarization transfer applicable to information technology, and achieve effective up-conversion of interest for luminescence bioimaging, among others. Furthermore, highly luminescent stable π-radicals have been recently reported, which are especially interesting for application in organic light-emitting devices owing to their potential to provide an internal quantum efficiency of 100 %. Thus, the excited-state nature of stable π-radicals as well as the control of their excited-state spin dynamics are emerging topics both in terms of fundamental science and related technological applications. In this minireview, we focus on the excited-state dynamics of both photostable non(weakly)-luminescent and luminescent π-radicals, which are opposites of each other. In particular, we cover the following topics: 1) effective generation of high-spin photoexcited states and control of the excited-state dynamics by using non-luminescent π-radicals, 2) unique excited-state dynamics of luminescent π-radicals and radical excimers, and 3) applications utilizing excited-state dynamics of π-radicals.     

Enhanced Sensitivity to Local Dynamics in Peptides by Use of Temperature-Jump IR Spectroscopy and Isotope Labeling

Site-specific isotopic labeling of molecules is a widely used approach in IR spectroscopy to resolve local contributions to vibrational modes. The induced frequency shift of the corresponding IR band depends on the substituted masses, as well as on hydrogen bonding and vibrational coupling. The impact of these different factors was analyzed with a designed three-stranded β-sheet peptide and by use of selected ¹³C isotope substitutions at multiple positions in the peptide backbone. Single-strand labels give rise to isotopically shifted bands at different frequencies, depending on the specific sites; this demonstrates sensitivity to the local environment. Cross-strand double- and triple-labeled peptides exhibited two resolved bands that could be uniquely assigned to specific residues, the equilibrium IR spectra of which indicated only weak local-mode coupling. Temperature-jump IR laser spectroscopy was applied to monitor structural dynamics and revealed an impressive enhancement of the isotope sensitivity to both local positions and coupling between them, relative to that of equilibrium FTIR spectroscopy. Site-specific relaxation rates were altered upon the introduction of additional cross-strand isotopes. Likewise, the rates for the global β-sheet dynamics were affected in a manner dependent on the distinct relaxation behavior of the labeled oscillator. This study reveals that isotope labels provide not only local structural probes, but rather sense the dynamic complexity of the molecular environment.     

Degeneracy of the Antithrombin Binding Sequence in Heparin: 2-O-Sulfated Iduronic Acid Can Replace the Critical Glucuronic Acid

Heparin binds to and activates antithrombin (AT) through a specific pentasaccharide sequence, in which a trisaccharide subsite, containing glucuronic acid (GlcA), has been considered as the initiator in the recognition of the polysaccharide by the protein. Recently it was suggested that sulfated iduronic acid (IdoA2S) could replace this “canonical” GlcA. Indeed, a heparin octasaccharidic sequence obtained by chemoenzymatic synthesis, in which GlcA is replaced with IdoA2S, has been found to similarly bind to and activate antithrombin. By using saturation-transfer-difference (STD) NMR, NOEs, transferred NOEs (tr-NOEs) NMR and molecular dynamics, we show that, upon binding to AT, this IdoA2S unit develops comparable interactions with AT as GlcA. Interestingly, two IdoA2S units, both present in a ¹C₄-²S₀ equilibrium in the unbound saccharide, shift to full ²S₀ and full ¹C₄ upon binding to antithrombin, providing the best illustration of the critical role of iduronic acid conformational flexibility in biological systems.     

Directed Gas Phase Formation of Silene (H2SiCH2)

The silene molecule (H₂SiCH₂; X¹A₁) has been synthesized under single collision conditions via the bimolecular gas phase reaction of ground state methylidyne radicals (CH) with silane (SiH₄). Exploiting crossed molecular beams experiments augmented by high-level electronic structure calculations, the elementary reaction commenced on the doublet surface through a barrierless insertion of the methylidyne radical into a silicon-hydrogen bond forming the silylmethyl (CH₂SiH₃; X²A′) complex followed by hydrogen migration to the methylsilyl radical (SiH₂CH₃; X²A′). Both silylmethyl and methylsilyl intermediates undergo unimolecular hydrogen loss to silene (H₂SiCH₂; X¹A₁). The exploration of the elementary reaction of methylidyne with silane delivers a unique view at the widely uncharted reaction dynamics and isomerization processes of the carbon–silicon system in the gas phase, which are noticeably different from those of the isovalent carbon system thus contributing to our knowledge on carbon silicon bond couplings at the molecular level.     

Amorphous polymerization of nitrogen in compressed cupric azide

Metal azides have attracted increasing attention as precursors for synthesizing polymeric nitrogen. In this article, we report the amorphous polymerization of nitrogen by compressing cupric azide. The ab initio molecular dynamics simulations show that crystalline cupric azide transforms into a disordered network composed of singly bonded nitrogen at a hydrostatic pressure of 40 GPa and room temperature. The transformation manifests the formation of a π delocalization along the disordered Cu-N network, thus resulting in a semiconductor–metal transition. The estimated heat of formation of the amorphous polymeric nitrogen system is comparable to conventional high-energy-density materials. The amorphization provides an alternative route to the polymerization of nitrogen under moderate conditions.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

Modeling the dynamics of firms' technological impact

Recent studies in complexity science have uncovered temporal regularities in the dynamics of impact along scientific and other creative careers, but they did not extend the obtained insights to firms. In this paper, we show that firms' technological impact patterns cannot be captured by the state-of-the-art dynamical models for the evolution of scientists' research impact, such as the Q model. Therefore, we propose a time-varying returns model which integrates the empirically-observed relation between patent order and technological impact into the Q model. The proposed model can reproduce the timing pattern of firms' highest-impact patents accurately. Our results shed light on modeling the differences behind the impact dynamics of researchers and firms.     

具有复合幂函数和共存吸引子的新混沌系统的动力学分析与电路仿真

构造一个具有复合幂函数的三维连续自治混沌系统。系统的状态方程仅有5项，其中一项是指数小于1的复合幂函数。该系统具有结构简单、非双曲平衡点、吸引子共存的性质，展现出了复杂的动力学行为。首先，对系统的动力学行为进行分析，包括李雅普诺夫（Lyapunov）指数谱、分岔图以及庞加莱映射等，结果表明此系统具有混沌特性。然后进行混沌系统的电路设计，电路仿真结果验证了理论分析的正确性。