An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable coefcients.In the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are employed.Theoretically,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable coefcients.Moreover,a Toeplitz preconditioner is proposed for linear systems arising from the proposed scheme.The condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges linearly.Numerical results are reported to show the convergence rate and the efciency of the proposed scheme.

Investigations of the dynamical behaviors of a millimeter-scale cavitation bubble near the rigid wall

The collapse of the cavitation bubble near the rigid wall emits shock waves and creates micro-jet,causing cavitation damage and operation instability of the hydraulic machinery.In this paper,the millimeter-scale bubble near the rigid wall was investigated experimentally and numerically with the help of a laser photogrammetry system with nanosecond-micron space-time resolution and the open source package OpenFOAM-2212.The morphological characteristics of the bubble during its growth phase,collapse phase and rebound phase were observed by experiment and numerical simulation,and characteristics of the accompanying phenomena including the shock wave propagation and micro-jet evolution were well elucidated.The numerical results agree well with the experimental data.The bubble starts from a tiny small size with high internal pressure and expands into a sphere with a radius of 1.07 mm forγ=d/R_(max)=1.78.The bubble collapses into a heart shape and moves towards to the rigid wall during its collapse phase,resulting in a higher pressure load for the rigid wall in the second collapse.The maximum pressure of the shock wave of the first bubble collapse phase reaches 5.4 MPa,and the velocity of the micro-jet reaches approximately 100 m/s.This study enriches the existing experimental and numerical results of the dynamics of the near-wall cavitation bubble.

Atomically Precise Imprinting π-Magnetism in Nanographenes via Probe Chemistry

The precise generation and harnessing of carbon magnetism at the single-molecule level have been captivating areas of research in chemistry and nanotechnology.However,the realization of magnetic nanographenes,also known as single-moleculeπ-magnets,through solution-based synthesis has proven challenging because of their high reactivity and insolubility tendency.Recent advancements in on-surface chemistry and scanning probe techniques have significantly propelled the fabrication of carbon-based magnetic nanostructures to offer a rich platform to probe quantumπ-magnetism at the single-molecule level.Atomic manipulation,also referred to as probe chemistry,stands as an exciting and essential approach in the toolbox of on-surface chemistry.This approach enables site-selective chemical reactions,thereby allowing for the atomically precise imprinting and tailoringπ-magnetism in a variety of nanographenes.This review highlights the recent achievements in the precise synthesis of single-moleculeπ-magnets using atomic manipulation.Furthermore,we also provide an outlook on the future of probe chemistry in the fabrication of this intriguing class of magnetic nanographenes,featuring designer quantum magnetism.

分级结构碳纳米笼高效催化苄胺氧化偶联制N-苄烯丁胺

苄胺氧化偶联制N-苄烯丁胺通常需使用贵金属催化剂,开发廉价催化剂具有重要研究价值.本工作以具有大比表面积和丰富表面缺陷的分级结构碳纳米笼(hCNCs)作为无金属催化剂,在无溶剂、100℃和常压O2条件下即可实现苄胺到N-苄烯丁胺的高效转化,反应8 h的苄胺转化率和N-苄烯丁胺选择性均可达98%,远优于碳纳米管、还原氧化石墨烯、活性炭等典型碳材料.hCNC700样品循环使用6次后催化性能基本无衰减,且具有优秀的底物拓展性.hCNC700的优异催化性能源于其超高的比表面积可提供大量的缺陷活性位点,而独特的分级孔结构十分有利于反应过程中的传质,使丰富的表面活性位点(缺陷)得以充分利用.