Fluid‐structure coupling of linear elastic model with compressible flow models

Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure.     

Revealing and comparing different excited-state intramolecular proton transfer processes for 3-(4-dimethylamino-phenyl)-1-(4-fluoro-2-hydroxy-phenyl)-propenone and 3-(4-dimethylamino-phenyl)-1-(4-fluoro-2-hydroxy-phenyl)-3-hydroxy-propenon

Two novel 2′-hydroxychalcone derivatives (i.e., M1 and M2) are explored in this work. We mainly focus on investigating the effects of photoexcitation on hydrogen bonds and on the excited-state intramolecular proton transfer (ESIPT) process. On the basis of calculations of electrostatic potential surface and intramolecular interactions, we verify the formation of hydrogen bond O1 H2···O3 in both S₀ and S₁ states. Exploring the ultraviolet–visible spectra in the liquid phase, our simulated results reappear in the experimental phenomenon. Analyzing molecular geometry and infrared stretching vibrational spectra, we confirm O1 H2···O3 is strengthened for both M1 and M2 in the S₁ state. We further confirm that charge redistribution facilitates ESIPT tendency. Constructing potential energy curves, we find the ultrafast ESIPT behavior for M1, which is because of the deficiency of side hydroxyl moiety comparing with M2. This work makes a reasonable affiliation of the ESIPT mechanism for M1 and M2. We wish this paper could facilitate understanding these two novel systems and promote their applications.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

Analogue of the degree conjecture over function fields

Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.

     

Carousels,Zindler curves and the floating body problem

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem. We prove, using the work of Auerbach, that any figure that floats in equilibrium in every position is drawn by a carousel. Of special interest are such figures with rational perimetral density of the floating chords, which are then drawn by carousels. In particular, we prove that for some perimetral densities the only such figure is the circle, as the problem suggests.     

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayers

High temperature annealing effect on structural and magnetic properties of Ti/Ni multilayer (ML) up to 600 °C have been studied and reported in this paper. Ti/Ni multilayer samples having constant layer thicknesses of 50 Å each are deposited on float glass and Si(1 1 1) substrates using electron-beam evaporation technique under ultra-high vacuum (UHV) conditions at room temperatures. The micro-structural parameters and their evolution with temperature for as-deposited as well as annealed multilayer samples up to 600 °C in a step of 100 °C for 1 h are determined by using X-ray diffraction (XRD) and grazing incidence X-ray reflectivity techniques. The X-ray diffraction pattern recorded at 300 °C annealed multilayer sample shows interesting structural transformation (from crystalline to amorphous) because of the solid-state reaction (SSR) and subsequent re-crystallization at higher temperatures of annealing, particularly at ≥400 °C due to the formation of TiNi₃ and Ti₂Ni alloy phases. Sample quality and surface morphology are examined by using atomic force microscopy (AFM) technique for both as-deposited as well as annealed multilayer samples. In addition to this, a temperature dependent dc resistivity measurement is also used to study the structural transformation and subsequent alloy phase formation due to annealing treatment. The corresponding magnetization behavior of multilayer samples after each stage of annealing has been investigated by using Magneto-Optical Kerr Effect (MOKE) technique and results are interpreted in terms of observed micro-structural changes.     

Influence of Cd and Cr substitutions on the magnetization and permeability of magnesium ferrites

Magnetization and permeability of polycrystalline ferrites with general formula Cd_xMg_1−xFe_2−yCr_yO₄ (x=0, 0.2, 0.4, 0.6, 0.8, 1.0; y=0, 0.05 and 0.10) were studied. Study of saturation magnetization reveals that the Neel's two-sublattice model exists upto x=0.4, for y=0, 0.05 and 0.1 and a three-sublattice model (YK-model) is predominant for x>0.4 and y=0, 0.05 and 0.10. The saturation magnetization and magnetic moment were found to decrease with the increase in Cr³⁺ contents, which is attributed to the dilution of B–B site interaction. Variation of initial permeability with temperature revealed the long-range ferromagnetic ordering in the compounds with x=0.4. The sample with x?0.4 and y=0, 0.05 and 0.10 showed peaking behavior near Curie temperature, which is attributed to the decrease of anisotropy constant K₁ to zero. Low-frequency dispersion of initial permeability suggests domain wall displacement. Addition of Cd²⁺ resulted in a sharp decrease in Curie temperature. With the addition of Cr³⁺, initial permeability was found to decrease.     

Magnetic configurations of hybrid ferromagnetic dot–superconductor systems

In-plane single domain and vortex magnetization configurations of the magnetic dot in the hybrid superconductor–ferromagnet system are considered. Single domain configuration energy shift due to the presence of superconductor is calculated. The change of the phase curve of the ferromagnetic dot magnetization due to the repulsion of the magnetic field by the superconductor is obtained. Up to the two-fold decrease of the ferromagnetic dot critical radius due to the presence of the superconductor is predicted.     

A graphical approach to computing Selmer groups of congruent number curves

Let E _n:y ²=x ³−n ² x denote the family of congruent number elliptic curves. Feng and Xiong (2004) equate the nontriviality of the Selmer groups associated with E _n to the presence of certain types of partitions of graphs associated with the prime factorization of n. In this paper, we extend the ideas of Feng and Xiong in order to compute the Selmer groups of E _n. 2000 Mathematics Subject Classification Primary—11G05; Secondary—14H52, 14H25, 05C90