Homogenization of the stationary periodic Maxwell system in the case of constant permeability

The homogenization problem in the small period limit for the stationary periodic Maxwell system in ℝ³ is considered. It is assumed that the permittivity η^ε(x)=η(ε⁻x), ε > 0, is a rapidly oscillating positive matrix function and the permeability μ₀ is a constant positive matrix. For all four physical fields (the electric and magnetic field intensities, the electric displacement field, and the magnetic flux density), we obtain uniform approximations in the L ₂(ℝ³)-norm with order-sharp remainder estimates. __________ Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 2, pp. 3–23, 2007 Original Russian Text Copyright ? by M. Sh. Birman and T. A. Suslina Dedicated to the memory of the great mathematician Mark Grigor’evich Krein Supported by RFBR grants no. 05-01-01076-a, 05-01-02944-YaF-a.     

Structure and Reactivity of an Isolable Seven‐Membered‐Ring trans‐Alkene

The isolation and characterization of a trans‐oxasilacycloheptene is reported. Single‐crystal X‐ray crystallographic studies indicate a high level of strain and deviation from ideal geometry. Reactions with several electrophiles demonstrated the nucleophilicity of the C?C double bond, affording oxasilacycloheptane and tetrahydrofuran products as single diastereomers.     

Catalytic Ring Expansion of Cyclic Hemiaminals for the Synthesis of Medium‐Ring Lactams

A mild and efficient intermolecular ring‐expansion approach was developed for the synthesis of medium‐ring lactams by using siloxy alkynes. Key to success is the suitable combination of a superior catalyst and an exceptional nitrogen‐protecting group. Control experiments indicated that the reaction is remarkably selective toward the desired lactam formation, even with many possible non‐productive pathways.     

The Synthesis of Structurally Diverse Macrocycles By Successive Ring Expansion

Structurally diverse macrocycles and medium‐sized rings (9–24 membered scaffolds, 22 examples) can be generated through a telescoped acylation/ring‐expansion sequence, leading to the insertion of linear fragments into cyclic β‐ketoesters without performing a discrete macrocyclization step. The key β‐ketoester motif is regenerated in the ring‐expanded product, meaning that the same sequence of steps can then be repeated (in theory indefinitely) with other linear fragments, allowing macrocycles with precise substitution patterns to be “grown” from smaller rings using the successive ring‐expansion (SuRE) method.     

Synthesis of photosensitive polyimide for liquid crystal alignment under non-polarised UV ageing lamp irradiation and a study on the possible mechanism of alignment

ABSTRACT

A new photosensitive polyimide (PI) was successfully synthesised via esterification of PI containing hydroxyl groups with cinnamoyl chloride (CL). The cinnamate (CA) group contents of the PI was up to 90%. The PI films could induce uniform parallel alignment of liquid crystal (LC) molecules after the non-polarised ultraviolet ageing lamp exposure, which reduce the cost significantly compared with polarised ultraviolet light equipment. In addition, the PI exhibited good thermal stability. Meanwhile, the possible mechanism of PI alignment films induced by NPUVL was discussed in some detail.     

A Free-Radical Prompted Barrierless Gas-Phase Synthesis of Pentacene

A representative, low-temperature gas-phase reaction mechanism synthesizing polyacenes via ring annulation exemplified by the formation of pentacene (C₂₂H₁₄) along with its benzo[a]tetracene isomer (C₂₂H₁₄) is unraveled by probing the elementary reaction of the 2-tetracenyl radical (C₁₈H₁₁^.) with vinylacetylene (C₄H₄). The pathway to pentacene—a prototype polyacene and a fundamental molecular building block in graphenes, fullerenes, and carbon nanotubes—is facilitated by a barrierless, vinylacetylene mediated gas-phase process thus disputing conventional hypotheses that synthesis of polycyclic aromatic hydrocarbons (PAHs) solely proceeds at elevated temperatures. This low-temperature pathway can launch isomer-selective routes to aromatic structures through submerged reaction barriers, resonantly stabilized free-radical intermediates, and methodical ring annulation in deep space eventually changing our perception about the chemistry of carbon in our universe.     

改进的核密度模型与轻子-核DIS过程中的核效应

提出了改进的核密度模型, 用唯象的方法找到了束缚核子内价夸克和海夸克的 核效应的参数公式, 其中利用了我们已经建立的核密度与原子核的平均结合能 之间的联系. 利用该模型所得到的束缚核子内部分子分布函数, 对轻子与核 的DIS(深度非弹性散射)过程的核效应给出了满意的解释, 深化了对原子核内夸克分布受核效应影响的认识.     

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.     

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.