Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

Topological entropy of continuous self-maps on closed surfaces

The objective of this work is to present sufficient conditions for having positive topological entropy for continuous self-maps defined on a closed surface by using the action of this map on the homological groups of the closed surface.     

Thermally Robust yet Deconstructable and Chemically Recyclable High-Density Polyethylene (HDPE)-Like Materials Based on Si−O Bonds

Polyethylene (PE) is the most widely produced synthetic polymer. By installing chemically cleavable bonds into the backbone of PE, it is possible to produce chemically deconstructable PE derivatives; to date, however, such designs have primarily relied on carbonyl- and olefin-related functional groups. Bifunctional silyl ethers (BSEs; SiR₂(OR′₂)) could expand the functional scope of PE mimics as they possess strong Si−O bonds and facile chemical tunability. Here, we report BSE-containing high-density polyethylene (HDPE)-like materials synthesized through a one-pot catalytic ring-opening metathesis polymerization (ROMP) and hydrogenation sequence. The crystallinity of these materials can be adjusted by varying the BSE concentration or the steric bulk of the Si-substituents, providing handles to control thermomechanical properties. Two methods for chemical recycling of HDPE mimics are introduced, including a circular approach that leverages acid-catalyzed Si−O bond exchange with 1-propanol. Additionally, despite the fact that the starting HDPE mimics were synthesized by chain-growth polymerization (ROMP), we show that it is possible to recover the molar mass and dispersity of recycled HDPE products using step-growth Si−O bond formation or exchange, generating high molecular weight recycled HDPE products with mechanical properties similar to commercial HDPE.     

The PyPES library of high quality semi‐global potential energy surfaces

In this article, we present a Python‐based library of high quality semi‐global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro‐vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib . © 2015 Wiley Periodicals, Inc.     

两类图的(d,1)-全标号

主要讨论了W_n与C_m的笛卡尔积和均衡完全r-部图K_r(n)的(d,1)-全标号,并得出了(d,1)-全数λ_d~T(W_n□C_m)和λ_d~T(K_(r(n)))的确切值.     

On categories associated to a Quasi-Hopf algebra

A quasi-Hopf algebra H can be seen as a commutative algebra A in the center 𝒵(H-Mod) of H-Mod. We show that the category of A-modules in 𝒵(H-Mod) is equivalent (as a monoidal category) to H-Mod. This can be regarded as a generalization of the structure theorem of Hopf bimodules of a Hopf algebra to the quasi-Hopf setting.     

Viscous waves and wave-structure interaction in a tank using adapting quadtree grids

Viscous waves and waves over a submerged cylinder in a stationary tank are simulated using a volume-of-fluid numerical scheme on adaptive hierarchical grids. A high resolution interface-capturing method is used to advect the free surface interface and the Navier–Stokes equations are discretised using finite volumes with collocated primitive variables and solved using a Pressure Implicit with Splitting of Operators (PISO) algorithm. The cylinder is modelled by using the technique of Cartesian cut cells. Results of flow of a single fluid past a cylinder at Reynolds number Re=100 are presented and found to agree well with experimental and other numerical data. Viscous free surface waves in a tank are simulated using uniform and quadtree grids for Reynolds numbers in the range from 2 to 2000, and the results compared against analytical solutions where available. The quadtree-based results are of the same accuracy as those on the equivalent uniform grids, and retain a sharp interface at the free surface while leading to considerable savings in both storage and CPU requirements. The nonlinearity in the wave is investigated for a selection of initial wave amplitudes. A submerged cylinder is positioned in the tank and its influence on the waves as well as the hydrodynamic loading on the cylinder is investigated.